%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV569-1.050 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:40 AM UTC 2025
% Result : Unsatisfiable 14.01s 14.19s
% Output : Proof 14.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 1473
% Syntax : Number of formulae : 4924 (3486 unt; 0 typ; 0 def)
% Number of atoms : 8592 (8558 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 5202 (1567 ~;2817 |; 0 &)
% ( 818 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 35 ( 3 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 461 ( 461 usr; 458 con; 0-3 aty)
% Number of variables : 4193 (4160 !; 0 ?;4193 :)
% Comments :
%------------------------------------------------------------------------------
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(head_type,type,
head: $i ).
tff(q50_type,type,
q50: $i ).
tff(s_type,type,
s: $i > $i ).
tff(queue_298_type,type,
queue_298: $i ).
tff(index_299_type,type,
index_299: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(index_297_type,type,
index_297: $i ).
tff(tail_type,type,
tail: $i ).
tff(queue_296_type,type,
queue_296: $i ).
tff(index_300_type,type,
index_300: $i ).
tff(seq_type,type,
seq: $i ).
tff(q49_type,type,
q49: $i ).
tff(earray_304_type,type,
earray_304: $i ).
tff(q48_type,type,
q48: $i ).
tff(e48_type,type,
e48: $i ).
tff(index_303_type,type,
index_303: $i ).
tff(earray_302_type,type,
earray_302: $i ).
tff(queue_301_type,type,
queue_301: $i ).
tff(queue_307_type,type,
queue_307: $i ).
tff(index_306_type,type,
index_306: $i ).
tff(queue_305_type,type,
queue_305: $i ).
tff(earray_316_type,type,
earray_316: $i ).
tff(e49_type,type,
e49: $i ).
tff(index_315_type,type,
index_315: $i ).
tff(earray_314_type,type,
earray_314: $i ).
tff(queue_319_type,type,
queue_319: $i ).
tff(index_318_type,type,
index_318: $i ).
tff(queue_317_type,type,
queue_317: $i ).
tff(q17_type,type,
q17: $i ).
tff(e17_type,type,
e17: $i ).
tff(e16_type,type,
e16: $i ).
tff(elem_352_type,type,
elem_352: $i ).
tff(q16_type,type,
q16: $i ).
tff(index_51_type,type,
index_51: $i ).
tff(earray_52_type,type,
earray_52: $i ).
tff(q15_type,type,
q15: $i ).
tff(index_54_type,type,
index_54: $i ).
tff(queue_53_type,type,
queue_53: $i ).
tff(queue_55_type,type,
queue_55: $i ).
tff(q14_type,type,
q14: $i ).
tff(index_42_type,type,
index_42: $i ).
tff(earray_43_type,type,
earray_43: $i ).
tff(index_45_type,type,
index_45: $i ).
tff(queue_44_type,type,
queue_44: $i ).
tff(index_47_type,type,
index_47: $i ).
tff(index_48_type,type,
index_48: $i ).
tff(queue_46_type,type,
queue_46: $i ).
tff(queue_49_type,type,
queue_49: $i ).
tff(index_294_type,type,
index_294: $i ).
tff(earray_295_type,type,
earray_295: $i ).
tff(q47_type,type,
q47: $i ).
tff(index_291_type,type,
index_291: $i ).
tff(queue_290_type,type,
queue_290: $i ).
tff(e47_type,type,
e47: $i ).
tff(earray_293_type,type,
earray_293: $i ).
tff(queue_292_type,type,
queue_292: $i ).
tff(index_288_type,type,
index_288: $i ).
tff(earray_289_type,type,
earray_289: $i ).
tff(q46_type,type,
q46: $i ).
tff(index_285_type,type,
index_285: $i ).
tff(queue_284_type,type,
queue_284: $i ).
tff(e46_type,type,
e46: $i ).
tff(earray_287_type,type,
earray_287: $i ).
tff(queue_286_type,type,
queue_286: $i ).
tff(index_282_type,type,
index_282: $i ).
tff(earray_283_type,type,
earray_283: $i ).
tff(q45_type,type,
q45: $i ).
tff(index_279_type,type,
index_279: $i ).
tff(queue_277_type,type,
queue_277: $i ).
tff(e45_type,type,
e45: $i ).
tff(earray_281_type,type,
earray_281: $i ).
tff(queue_280_type,type,
queue_280: $i ).
tff(index_278_type,type,
index_278: $i ).
tff(index_276_type,type,
index_276: $i ).
tff(queue_275_type,type,
queue_275: $i ).
tff(q13_type,type,
q13: $i ).
tff(index_273_type,type,
index_273: $i ).
tff(earray_274_type,type,
earray_274: $i ).
tff(q44_type,type,
q44: $i ).
tff(index_270_type,type,
index_270: $i ).
tff(queue_269_type,type,
queue_269: $i ).
tff(e44_type,type,
e44: $i ).
tff(earray_272_type,type,
earray_272: $i ).
tff(queue_271_type,type,
queue_271: $i ).
tff(index_267_type,type,
index_267: $i ).
tff(earray_268_type,type,
earray_268: $i ).
tff(q43_type,type,
q43: $i ).
tff(index_264_type,type,
index_264: $i ).
tff(queue_263_type,type,
queue_263: $i ).
tff(e43_type,type,
e43: $i ).
tff(earray_266_type,type,
earray_266: $i ).
tff(queue_265_type,type,
queue_265: $i ).
tff(index_261_type,type,
index_261: $i ).
tff(earray_262_type,type,
earray_262: $i ).
tff(q42_type,type,
q42: $i ).
tff(index_258_type,type,
index_258: $i ).
tff(queue_256_type,type,
queue_256: $i ).
tff(e42_type,type,
e42: $i ).
tff(earray_260_type,type,
earray_260: $i ).
tff(queue_259_type,type,
queue_259: $i ).
tff(index_257_type,type,
index_257: $i ).
tff(index_255_type,type,
index_255: $i ).
tff(queue_254_type,type,
queue_254: $i ).
tff(q12_type,type,
q12: $i ).
tff(index_252_type,type,
index_252: $i ).
tff(earray_253_type,type,
earray_253: $i ).
tff(q41_type,type,
q41: $i ).
tff(index_249_type,type,
index_249: $i ).
tff(queue_248_type,type,
queue_248: $i ).
tff(e41_type,type,
e41: $i ).
tff(earray_251_type,type,
earray_251: $i ).
tff(queue_250_type,type,
queue_250: $i ).
tff(index_246_type,type,
index_246: $i ).
tff(earray_247_type,type,
earray_247: $i ).
tff(q40_type,type,
q40: $i ).
tff(index_243_type,type,
index_243: $i ).
tff(queue_242_type,type,
queue_242: $i ).
tff(e40_type,type,
e40: $i ).
tff(earray_245_type,type,
earray_245: $i ).
tff(queue_244_type,type,
queue_244: $i ).
tff(index_240_type,type,
index_240: $i ).
tff(earray_241_type,type,
earray_241: $i ).
tff(q39_type,type,
q39: $i ).
tff(index_231_type,type,
index_231: $i ).
tff(queue_229_type,type,
queue_229: $i ).
tff(e39_type,type,
e39: $i ).
tff(earray_239_type,type,
earray_239: $i ).
tff(queue_232_type,type,
queue_232: $i ).
tff(index_230_type,type,
index_230: $i ).
tff(index_228_type,type,
index_228: $i ).
tff(queue_227_type,type,
queue_227: $i ).
tff(q11_type,type,
q11: $i ).
tff(index_225_type,type,
index_225: $i ).
tff(earray_226_type,type,
earray_226: $i ).
tff(q38_type,type,
q38: $i ).
tff(index_222_type,type,
index_222: $i ).
tff(queue_221_type,type,
queue_221: $i ).
tff(e38_type,type,
e38: $i ).
tff(earray_224_type,type,
earray_224: $i ).
tff(queue_223_type,type,
queue_223: $i ).
tff(index_219_type,type,
index_219: $i ).
tff(earray_220_type,type,
earray_220: $i ).
tff(q37_type,type,
q37: $i ).
tff(index_216_type,type,
index_216: $i ).
tff(queue_215_type,type,
queue_215: $i ).
tff(e37_type,type,
e37: $i ).
tff(earray_218_type,type,
earray_218: $i ).
tff(queue_217_type,type,
queue_217: $i ).
tff(index_213_type,type,
index_213: $i ).
tff(earray_214_type,type,
earray_214: $i ).
tff(q36_type,type,
q36: $i ).
tff(index_210_type,type,
index_210: $i ).
tff(queue_208_type,type,
queue_208: $i ).
tff(e36_type,type,
e36: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(queue_211_type,type,
queue_211: $i ).
tff(index_209_type,type,
index_209: $i ).
tff(index_207_type,type,
index_207: $i ).
tff(queue_206_type,type,
queue_206: $i ).
tff(q10_type,type,
q10: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(earray_205_type,type,
earray_205: $i ).
tff(q35_type,type,
q35: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(queue_200_type,type,
queue_200: $i ).
tff(e35_type,type,
e35: $i ).
tff(earray_203_type,type,
earray_203: $i ).
tff(queue_202_type,type,
queue_202: $i ).
tff(index_198_type,type,
index_198: $i ).
tff(earray_199_type,type,
earray_199: $i ).
tff(q34_type,type,
q34: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(queue_194_type,type,
queue_194: $i ).
tff(e34_type,type,
e34: $i ).
tff(earray_197_type,type,
earray_197: $i ).
tff(queue_196_type,type,
queue_196: $i ).
tff(index_192_type,type,
index_192: $i ).
tff(earray_193_type,type,
earray_193: $i ).
tff(q33_type,type,
q33: $i ).
tff(index_189_type,type,
index_189: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(e33_type,type,
e33: $i ).
tff(earray_191_type,type,
earray_191: $i ).
tff(queue_190_type,type,
queue_190: $i ).
tff(index_188_type,type,
index_188: $i ).
tff(index_186_type,type,
index_186: $i ).
tff(queue_185_type,type,
queue_185: $i ).
tff(q9_type,type,
q9: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(q32_type,type,
q32: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $i ).
tff(e32_type,type,
e32: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(queue_181_type,type,
queue_181: $i ).
tff(index_177_type,type,
index_177: $i ).
tff(earray_178_type,type,
earray_178: $i ).
tff(q31_type,type,
q31: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $i ).
tff(e31_type,type,
e31: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(queue_175_type,type,
queue_175: $i ).
tff(index_171_type,type,
index_171: $i ).
tff(earray_172_type,type,
earray_172: $i ).
tff(q30_type,type,
q30: $i ).
tff(index_168_type,type,
index_168: $i ).
tff(queue_166_type,type,
queue_166: $i ).
tff(e30_type,type,
e30: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(queue_169_type,type,
queue_169: $i ).
tff(index_167_type,type,
index_167: $i ).
tff(index_165_type,type,
index_165: $i ).
tff(queue_164_type,type,
queue_164: $i ).
tff(q8_type,type,
q8: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(earray_163_type,type,
earray_163: $i ).
tff(q29_type,type,
q29: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $i ).
tff(e29_type,type,
e29: $i ).
tff(earray_161_type,type,
earray_161: $i ).
tff(queue_151_type,type,
queue_151: $i ).
tff(index_147_type,type,
index_147: $i ).
tff(earray_148_type,type,
earray_148: $i ).
tff(q28_type,type,
q28: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $i ).
tff(e28_type,type,
e28: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(queue_145_type,type,
queue_145: $i ).
tff(index_141_type,type,
index_141: $i ).
tff(earray_142_type,type,
earray_142: $i ).
tff(q27_type,type,
q27: $i ).
tff(index_138_type,type,
index_138: $i ).
tff(queue_136_type,type,
queue_136: $i ).
tff(e27_type,type,
e27: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(queue_139_type,type,
queue_139: $i ).
tff(index_137_type,type,
index_137: $i ).
tff(index_135_type,type,
index_135: $i ).
tff(queue_134_type,type,
queue_134: $i ).
tff(q7_type,type,
q7: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(earray_133_type,type,
earray_133: $i ).
tff(q26_type,type,
q26: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(queue_128_type,type,
queue_128: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_131_type,type,
earray_131: $i ).
tff(queue_130_type,type,
queue_130: $i ).
tff(index_126_type,type,
index_126: $i ).
tff(earray_127_type,type,
earray_127: $i ).
tff(q25_type,type,
q25: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(queue_122_type,type,
queue_122: $i ).
tff(e25_type,type,
e25: $i ).
tff(earray_125_type,type,
earray_125: $i ).
tff(queue_124_type,type,
queue_124: $i ).
tff(index_120_type,type,
index_120: $i ).
tff(earray_121_type,type,
earray_121: $i ).
tff(q24_type,type,
q24: $i ).
tff(index_117_type,type,
index_117: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(e24_type,type,
e24: $i ).
tff(earray_119_type,type,
earray_119: $i ).
tff(queue_118_type,type,
queue_118: $i ).
tff(index_116_type,type,
index_116: $i ).
tff(index_114_type,type,
index_114: $i ).
tff(queue_113_type,type,
queue_113: $i ).
tff(q6_type,type,
q6: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(q23_type,type,
q23: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(queue_109_type,type,
queue_109: $i ).
tff(index_105_type,type,
index_105: $i ).
tff(earray_106_type,type,
earray_106: $i ).
tff(q22_type,type,
q22: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $i ).
tff(e22_type,type,
e22: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(queue_103_type,type,
queue_103: $i ).
tff(index_99_type,type,
index_99: $i ).
tff(earray_100_type,type,
earray_100: $i ).
tff(q21_type,type,
q21: $i ).
tff(index_96_type,type,
index_96: $i ).
tff(queue_94_type,type,
queue_94: $i ).
tff(e21_type,type,
e21: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(queue_97_type,type,
queue_97: $i ).
tff(index_95_type,type,
index_95: $i ).
tff(index_93_type,type,
index_93: $i ).
tff(queue_92_type,type,
queue_92: $i ).
tff(q5_type,type,
q5: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(earray_91_type,type,
earray_91: $i ).
tff(q20_type,type,
q20: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(queue_86_type,type,
queue_86: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_89_type,type,
earray_89: $i ).
tff(queue_88_type,type,
queue_88: $i ).
tff(index_84_type,type,
index_84: $i ).
tff(earray_85_type,type,
earray_85: $i ).
tff(q19_type,type,
q19: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(queue_74_type,type,
queue_74: $i ).
tff(e19_type,type,
e19: $i ).
tff(earray_83_type,type,
earray_83: $i ).
tff(queue_76_type,type,
queue_76: $i ).
tff(index_72_type,type,
index_72: $i ).
tff(earray_73_type,type,
earray_73: $i ).
tff(q18_type,type,
q18: $i ).
tff(index_69_type,type,
index_69: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(e18_type,type,
e18: $i ).
tff(earray_71_type,type,
earray_71: $i ).
tff(queue_70_type,type,
queue_70: $i ).
tff(index_68_type,type,
index_68: $i ).
tff(index_66_type,type,
index_66: $i ).
tff(queue_65_type,type,
queue_65: $i ).
tff(q4_type,type,
q4: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(queue_61_type,type,
queue_61: $i ).
tff(index_57_type,type,
index_57: $i ).
tff(earray_58_type,type,
earray_58: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_50_type,type,
earray_50: $i ).
tff(q3_type,type,
q3: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(queue_38_type,type,
queue_38: $i ).
tff(e14_type,type,
e14: $i ).
tff(earray_41_type,type,
earray_41: $i ).
tff(queue_40_type,type,
queue_40: $i ).
tff(index_36_type,type,
index_36: $i ).
tff(earray_37_type,type,
earray_37: $i ).
tff(index_33_type,type,
index_33: $i ).
tff(queue_32_type,type,
queue_32: $i ).
tff(e13_type,type,
e13: $i ).
tff(earray_35_type,type,
earray_35: $i ).
tff(queue_34_type,type,
queue_34: $i ).
tff(index_30_type,type,
index_30: $i ).
tff(earray_31_type,type,
earray_31: $i ).
tff(index_27_type,type,
index_27: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_29_type,type,
earray_29: $i ).
tff(queue_28_type,type,
queue_28: $i ).
tff(index_26_type,type,
index_26: $i ).
tff(index_24_type,type,
index_24: $i ).
tff(queue_23_type,type,
queue_23: $i ).
tff(q2_type,type,
q2: $i ).
tff(index_21_type,type,
index_21: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(e11_type,type,
e11: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(index_15_type,type,
index_15: $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(index_9_type,type,
index_9: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(index_348_type,type,
index_348: $i ).
tff(queue_346_type,type,
queue_346: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(queue_349_type,type,
queue_349: $i ).
tff(index_347_type,type,
index_347: $i ).
tff(index_345_type,type,
index_345: $i ).
tff(queue_344_type,type,
queue_344: $i ).
tff(q1_type,type,
q1: $i ).
tff(index_342_type,type,
index_342: $i ).
tff(earray_343_type,type,
earray_343: $i ).
tff(index_339_type,type,
index_339: $i ).
tff(queue_338_type,type,
queue_338: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_341_type,type,
earray_341: $i ).
tff(queue_340_type,type,
queue_340: $i ).
tff(index_336_type,type,
index_336: $i ).
tff(earray_337_type,type,
earray_337: $i ).
tff(index_333_type,type,
index_333: $i ).
tff(queue_332_type,type,
queue_332: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_335_type,type,
earray_335: $i ).
tff(queue_334_type,type,
queue_334: $i ).
tff(index_330_type,type,
index_330: $i ).
tff(earray_331_type,type,
earray_331: $i ).
tff(index_327_type,type,
index_327: $i ).
tff(queue_325_type,type,
queue_325: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_329_type,type,
earray_329: $i ).
tff(queue_328_type,type,
queue_328: $i ).
tff(index_326_type,type,
index_326: $i ).
tff(index_324_type,type,
index_324: $i ).
tff(queue_323_type,type,
queue_323: $i ).
tff(q0_type,type,
q0: $i ).
tff(index_321_type,type,
index_321: $i ).
tff(earray_322_type,type,
earray_322: $i ).
tff(index_312_type,type,
index_312: $i ).
tff(queue_311_type,type,
queue_311: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_320_type,type,
earray_320: $i ).
tff(queue_313_type,type,
queue_313: $i ).
tff(index_309_type,type,
index_309: $i ).
tff(earray_310_type,type,
earray_310: $i ).
tff(index_237_type,type,
index_237: $i ).
tff(queue_236_type,type,
queue_236: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_308_type,type,
earray_308: $i ).
tff(queue_238_type,type,
queue_238: $i ).
tff(index_234_type,type,
index_234: $i ).
tff(earray_235_type,type,
earray_235: $i ).
tff(index_159_type,type,
index_159: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_233_type,type,
earray_233: $i ).
tff(queue_160_type,type,
queue_160: $i ).
tff(index_158_type,type,
index_158: $i ).
tff(index_156_type,type,
index_156: $i ).
tff(queue_155_type,type,
queue_155: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(index_153_type,type,
index_153: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(queue_80_type,type,
queue_80: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(queue_82_type,type,
queue_82: $i ).
tff(index_78_type,type,
index_78: $i ).
tff(earray_79_type,type,
earray_79: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_77_type,type,
earray_77: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(q_type,type,
q: $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(index_351_type,type,
index_351: $i ).
tff(earray_350_type,type,
earray_350: $i ).
tff(1,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(4,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),head) = s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(8,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),head) = s(index_299),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ( index_300 = s(index_299) )
<=> ( index_300 = s(index_299) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
index_300 = s(index_299),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(11,plain,
index_300 = s(index_299),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
s(index_299) = index_300,
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ( queue_298 = store(queue_296,tail,index_297) )
<=> ( queue_298 = store(queue_296,tail,index_297) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
queue_298 = store(queue_296,tail,index_297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp310) ).
tff(15,plain,
queue_298 = store(queue_296,tail,index_297),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
store(queue_296,tail,index_297) = queue_298,
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
store(store(queue_296,tail,index_297),head,s(index_299)) = store(queue_298,head,index_300),
inference(monotonicity,[status(thm)],[16,12]) ).
tff(18,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),head) = select(store(queue_298,head,index_300),head),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
select(store(queue_298,head,index_300),head) = select(store(store(queue_296,tail,index_297),head,s(index_299)),head),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( seq = head )
<=> ( head = seq ) ),
inference(commutativity,[status(thm)],[]) ).
tff(21,plain,
( ( head = seq )
<=> ( seq = head ) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ( head != seq )
<=> ( seq != head ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( head != seq )
<=> ( head != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
head != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_seq) ).
tff(25,plain,
head != seq,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
seq != head,
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
( ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
<=> ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
<=> ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
tff(30,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(queue_298,head,index_300),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(queue_298,head,index_300),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(queue_298,head,index_300),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(queue_298,head,index_300),head) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(queue_298,head,index_300),head),
inference(unit_resolution,[status(thm)],[35,32,26]) ).
tff(37,plain,
( ( earray_304 = store(earray_302,index_303,e48) )
<=> ( earray_304 = store(earray_302,index_303,e48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
earray_304 = store(earray_302,index_303,e48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(39,plain,
earray_304 = store(earray_302,index_303,e48),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
store(earray_302,index_303,e48) = earray_304,
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)),seq) = store(earray_302,index_303,e48) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
select(store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)),seq) = store(earray_302,index_303,e48),
inference(unit_resolution,[status(thm)],[41,6]) ).
tff(43,plain,
( ( q48 = queue_301 )
<=> ( q48 = queue_301 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
q48 = queue_301,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp396) ).
tff(45,plain,
q48 = queue_301,
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
queue_301 = q48,
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ( queue_301 = store(queue_298,head,index_300) )
<=> ( queue_301 = store(queue_298,head,index_300) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
queue_301 = store(queue_298,head,index_300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp311) ).
tff(49,plain,
queue_301 = store(queue_298,head,index_300),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
store(queue_298,head,index_300) = queue_301,
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
store(queue_298,head,index_300) = q48,
inference(transitivity,[status(thm)],[50,46]) ).
tff(52,plain,
store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)) = store(q48,seq,earray_304),
inference(monotonicity,[status(thm)],[51,40]) ).
tff(53,plain,
select(store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)),seq) = select(store(q48,seq,earray_304),seq),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
select(store(q48,seq,earray_304),seq) = select(store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)),seq),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
( ( tail != seq )
<=> ( tail != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
tail != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_distinct_from_seq) ).
tff(57,plain,
tail != seq,
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(store(q48,seq,earray_304),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(store(q48,seq,earray_304),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(store(q48,seq,earray_304),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(store(q48,seq,earray_304),seq) ) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(store(q48,seq,earray_304),seq),
inference(unit_resolution,[status(thm)],[60,32,57]) ).
tff(62,plain,
( ( q49 = queue_307 )
<=> ( q49 = queue_307 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
q49 = queue_307,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp397) ).
tff(64,plain,
q49 = queue_307,
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
queue_307 = q49,
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ( queue_307 = store(queue_305,tail,index_306) )
<=> ( queue_307 = store(queue_305,tail,index_306) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
queue_307 = store(queue_305,tail,index_306),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp313) ).
tff(68,plain,
queue_307 = store(queue_305,tail,index_306),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
store(queue_305,tail,index_306) = queue_307,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( index_306 = s(index_303) )
<=> ( index_306 = s(index_303) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
index_306 = s(index_303),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(72,plain,
index_306 = s(index_303),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
s(index_303) = index_306,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( queue_305 = store(q48,seq,earray_304) )
<=> ( queue_305 = store(q48,seq,earray_304) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
queue_305 = store(q48,seq,earray_304),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp312) ).
tff(76,plain,
queue_305 = store(q48,seq,earray_304),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
store(q48,seq,earray_304) = queue_305,
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
store(store(q48,seq,earray_304),tail,s(index_303)) = store(queue_305,tail,index_306),
inference(monotonicity,[status(thm)],[77,73]) ).
tff(79,plain,
store(store(q48,seq,earray_304),tail,s(index_303)) = q49,
inference(transitivity,[status(thm)],[78,69,65]) ).
tff(80,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),seq) = select(q49,seq),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
select(q49,seq) = select(store(store(q48,seq,earray_304),tail,s(index_303)),seq),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
select(q49,seq) = earray_304,
inference(transitivity,[status(thm)],[81,61,54,42,40]) ).
tff(83,plain,
store(store(queue_298,head,index_300),seq,select(q49,seq)) = store(q48,seq,earray_304),
inference(monotonicity,[status(thm)],[51,82]) ).
tff(84,plain,
select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head) = select(store(q48,seq,earray_304),head),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
select(store(q48,seq,earray_304),head) = select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ( tail = head )
<=> ( head = tail ) ),
inference(commutativity,[status(thm)],[]) ).
tff(87,plain,
( ( head = tail )
<=> ( tail = head ) ),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ( head != tail )
<=> ( tail != head ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( head != tail )
<=> ( head != tail ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
head != tail,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_tail) ).
tff(91,plain,
head != tail,
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
tail != head,
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(q48,seq,earray_304),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(q48,seq,earray_304),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(q48,seq,earray_304),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(q48,seq,earray_304),head) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(q48,seq,earray_304),head),
inference(unit_resolution,[status(thm)],[95,32,92]) ).
tff(97,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),head) = select(store(queue_305,tail,index_306),head),
inference(monotonicity,[status(thm)],[78]) ).
tff(98,plain,
select(store(queue_305,tail,index_306),head) = select(store(store(q48,seq,earray_304),tail,s(index_303)),head),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ( seq = head )
| ( select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head) ) ),
inference(unit_resolution,[status(thm)],[101,32]) ).
tff(103,plain,
select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(queue_305,tail,index_306),head),
inference(unit_resolution,[status(thm)],[102,26]) ).
tff(104,plain,
( ( earray_316 = store(earray_314,index_315,e49) )
<=> ( earray_316 = store(earray_314,index_315,e49) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
earray_316 = store(earray_314,index_315,e49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(106,plain,
earray_316 = store(earray_314,index_315,e49),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
store(earray_314,index_315,e49) = earray_316,
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)),seq) = store(earray_314,index_315,e49) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
select(store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)),seq) = store(earray_314,index_315,e49),
inference(unit_resolution,[status(thm)],[108,6]) ).
tff(110,plain,
store(queue_305,tail,index_306) = q49,
inference(transitivity,[status(thm)],[69,65]) ).
tff(111,plain,
store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)) = store(q49,seq,earray_316),
inference(monotonicity,[status(thm)],[110,107]) ).
tff(112,plain,
select(store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)),seq) = select(store(q49,seq,earray_316),seq),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
select(store(q49,seq,earray_316),seq) = select(store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)),seq),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(store(q49,seq,earray_316),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(store(q49,seq,earray_316),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(store(q49,seq,earray_316),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(store(q49,seq,earray_316),seq) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(store(q49,seq,earray_316),seq),
inference(unit_resolution,[status(thm)],[116,32,57]) ).
tff(118,plain,
( ( q50 = queue_319 )
<=> ( q50 = queue_319 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
q50 = queue_319,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp399) ).
tff(120,plain,
q50 = queue_319,
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
queue_319 = q50,
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ( queue_319 = store(queue_317,tail,index_318) )
<=> ( queue_319 = store(queue_317,tail,index_318) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
queue_319 = store(queue_317,tail,index_318),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp317) ).
tff(124,plain,
queue_319 = store(queue_317,tail,index_318),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
store(queue_317,tail,index_318) = queue_319,
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ( index_318 = s(index_315) )
<=> ( index_318 = s(index_315) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,axiom,
index_318 = s(index_315),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(128,plain,
index_318 = s(index_315),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
s(index_315) = index_318,
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ( queue_317 = store(q49,seq,earray_316) )
<=> ( queue_317 = store(q49,seq,earray_316) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
queue_317 = store(q49,seq,earray_316),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp316) ).
tff(132,plain,
queue_317 = store(q49,seq,earray_316),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
store(q49,seq,earray_316) = queue_317,
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
store(store(q49,seq,earray_316),tail,s(index_315)) = store(queue_317,tail,index_318),
inference(monotonicity,[status(thm)],[133,129]) ).
tff(135,plain,
store(store(q49,seq,earray_316),tail,s(index_315)) = q50,
inference(transitivity,[status(thm)],[134,125,121]) ).
tff(136,plain,
select(store(store(q49,seq,earray_316),tail,s(index_315)),seq) = select(q50,seq),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
select(q50,seq) = select(store(store(q49,seq,earray_316),tail,s(index_315)),seq),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
select(q50,seq) = earray_316,
inference(transitivity,[status(thm)],[137,117,113,109,107]) ).
tff(139,plain,
store(store(queue_305,tail,index_306),seq,select(q50,seq)) = store(q49,seq,earray_316),
inference(monotonicity,[status(thm)],[110,138]) ).
tff(140,plain,
select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head) = select(store(q49,seq,earray_316),head),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
select(store(q49,seq,earray_316),head) = select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
( ( tail = head )
| ( select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head) ) ),
inference(unit_resolution,[status(thm)],[144,32]) ).
tff(146,plain,
select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(store(q49,seq,earray_316),head),
inference(unit_resolution,[status(thm)],[145,92]) ).
tff(147,plain,
select(store(store(q49,seq,earray_316),tail,s(index_315)),head) = select(q50,head),
inference(monotonicity,[status(thm)],[135]) ).
tff(148,plain,
select(q50,head) = select(store(store(q49,seq,earray_316),tail,s(index_315)),head),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
select(q50,head) = s(index_299),
inference(transitivity,[status(thm)],[148,146,141,103,98,96,85,36,19,8]) ).
tff(150,plain,
( ( index_299 = select(queue_298,head) )
<=> ( index_299 = select(queue_298,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,axiom,
index_299 = select(queue_298,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(152,plain,
index_299 = select(queue_298,head),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
select(queue_298,head) = index_299,
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
s(select(queue_298,head)) = s(index_299),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
s(index_299) = s(select(queue_298,head)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
s(s(index_299)) = s(s(select(queue_298,head))),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
s(s(select(queue_298,head))) = s(s(index_299)),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ( s(s(select(queue_298,head))) = select(q50,head) )
<=> ( s(s(index_299)) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[157,149]) ).
tff(159,plain,
( ( s(s(index_299)) = s(index_299) )
<=> ( s(s(select(queue_298,head))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ( s(s(index_299)) != s(index_299) )
<=> ( s(s(select(queue_298,head))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
^ [X: $i] :
refl(( ( s(X) != X )
<=> ( s(X) != X ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,axiom,
! [X: $i] : ( s(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as1) ).
tff(165,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [X: $i] : ( s(X) != X ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,plain,
( ~ ! [X: $i] : ( s(X) != X )
| ( s(s(index_299)) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
s(s(index_299)) != s(index_299),
inference(unit_resolution,[status(thm)],[168,167]) ).
tff(170,plain,
s(s(select(queue_298,head))) != select(q50,head),
inference(modus_ponens,[status(thm)],[169,160]) ).
tff(171,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(select(q16,seq),select(q16,tail),e16),select(q16,tail)) = e16 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
select(store(select(q16,seq),select(q16,tail),e16),select(q16,tail)) = e16,
inference(unit_resolution,[status(thm)],[171,6]) ).
tff(173,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(175,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ( queue_53 = store(q15,seq,earray_52) )
<=> ( queue_53 = store(q15,seq,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
queue_53 = store(q15,seq,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp336) ).
tff(179,plain,
queue_53 = store(q15,seq,earray_52),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
store(q15,seq,earray_52) = queue_53,
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
store(store(q15,seq,earray_52),tail,s(index_51)) = store(queue_53,tail,index_54),
inference(monotonicity,[status(thm)],[180,176]) ).
tff(182,plain,
store(queue_53,tail,index_54) = store(store(q15,seq,earray_52),tail,s(index_51)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ( queue_55 = store(queue_53,tail,index_54) )
<=> ( queue_55 = store(queue_53,tail,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
queue_55 = store(queue_53,tail,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp337) ).
tff(185,plain,
queue_55 = store(queue_53,tail,index_54),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
( ( q16 = queue_55 )
<=> ( q16 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
q16 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp361) ).
tff(188,plain,
q16 = queue_55,
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
q16 = store(store(q15,seq,earray_52),tail,s(index_51)),
inference(transitivity,[status(thm)],[188,185,182]) ).
tff(190,plain,
select(q16,tail) = select(store(store(q15,seq,earray_52),tail,s(index_51)),tail),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = select(q16,tail),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = s(index_51),
inference(unit_resolution,[status(thm)],[192,6]) ).
tff(194,plain,
s(index_51) = select(store(store(q15,seq,earray_52),tail,s(index_51)),tail),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ( index_42 = select(q14,tail) )
<=> ( index_42 = select(q14,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
index_42 = select(q14,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(197,plain,
index_42 = select(q14,tail),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
select(q14,tail) = index_42,
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
s(select(q14,tail)) = s(index_42),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
s(index_42) = s(select(q14,tail)),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),tail) = s(index_42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),tail) = s(index_42),
inference(unit_resolution,[status(thm)],[201,6]) ).
tff(203,plain,
( ( index_45 = s(index_42) )
<=> ( index_45 = s(index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(204,axiom,
index_45 = s(index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(205,plain,
index_45 = s(index_42),
inference(modus_ponens,[status(thm)],[204,203]) ).
tff(206,plain,
s(index_42) = index_45,
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ( queue_44 = store(q14,seq,earray_43) )
<=> ( queue_44 = store(q14,seq,earray_43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,axiom,
queue_44 = store(q14,seq,earray_43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp332) ).
tff(209,plain,
queue_44 = store(q14,seq,earray_43),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
store(q14,seq,earray_43) = queue_44,
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
store(store(q14,seq,earray_43),tail,s(index_42)) = store(queue_44,tail,index_45),
inference(monotonicity,[status(thm)],[210,206]) ).
tff(212,plain,
store(queue_44,tail,index_45) = store(store(q14,seq,earray_43),tail,s(index_42)),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
select(store(queue_44,tail,index_45),tail) = select(store(store(q14,seq,earray_43),tail,s(index_42)),tail),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail),
inference(unit_resolution,[status(thm)],[216,32,91]) ).
tff(218,plain,
( ( index_48 = s(index_47) )
<=> ( index_48 = s(index_47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,axiom,
index_48 = s(index_47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(220,plain,
index_48 = s(index_47),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
s(index_47) = index_48,
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ( queue_46 = store(queue_44,tail,index_45) )
<=> ( queue_46 = store(queue_44,tail,index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,axiom,
queue_46 = store(queue_44,tail,index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp333) ).
tff(224,plain,
queue_46 = store(queue_44,tail,index_45),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
store(queue_44,tail,index_45) = queue_46,
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
store(store(queue_44,tail,index_45),head,s(index_47)) = store(queue_46,head,index_48),
inference(monotonicity,[status(thm)],[225,221]) ).
tff(227,plain,
store(queue_46,head,index_48) = store(store(queue_44,tail,index_45),head,s(index_47)),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
( ( queue_49 = store(queue_46,head,index_48) )
<=> ( queue_49 = store(queue_46,head,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(229,axiom,
queue_49 = store(queue_46,head,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp334) ).
tff(230,plain,
queue_49 = store(queue_46,head,index_48),
inference(modus_ponens,[status(thm)],[229,228]) ).
tff(231,plain,
( ( q15 = queue_49 )
<=> ( q15 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,axiom,
q15 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp360) ).
tff(233,plain,
q15 = queue_49,
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
q15 = store(store(queue_44,tail,index_45),head,s(index_47)),
inference(transitivity,[status(thm)],[233,230,227]) ).
tff(235,plain,
select(q15,tail) = select(store(store(queue_44,tail,index_45),head,s(index_47)),tail),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( index_51 = select(q15,tail) )
<=> ( index_51 = select(q15,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,axiom,
index_51 = select(q15,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(238,plain,
index_51 = select(q15,tail),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
index_51 = s(select(q14,tail)),
inference(transitivity,[status(thm)],[238,235,217,213,202,200]) ).
tff(240,plain,
s(index_51) = s(s(select(q14,tail))),
inference(monotonicity,[status(thm)],[239]) ).
tff(241,plain,
s(s(select(q14,tail))) = s(index_51),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
( ( index_297 = s(index_294) )
<=> ( index_297 = s(index_294) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,axiom,
index_297 = s(index_294),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(244,plain,
index_297 = s(index_294),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
s(index_294) = index_297,
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
( ( queue_296 = store(q47,seq,earray_295) )
<=> ( queue_296 = store(q47,seq,earray_295) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(247,axiom,
queue_296 = store(q47,seq,earray_295),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp309) ).
tff(248,plain,
queue_296 = store(q47,seq,earray_295),
inference(modus_ponens,[status(thm)],[247,246]) ).
tff(249,plain,
store(q47,seq,earray_295) = queue_296,
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
store(store(q47,seq,earray_295),tail,s(index_294)) = store(queue_296,tail,index_297),
inference(monotonicity,[status(thm)],[249,245]) ).
tff(251,plain,
store(store(q47,seq,earray_295),tail,s(index_294)) = queue_298,
inference(transitivity,[status(thm)],[250,16]) ).
tff(252,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(queue_298,head),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head) ) ),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
( ( tail = head )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head) ) ),
inference(unit_resolution,[status(thm)],[255,32]) ).
tff(257,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),head) = select(store(q47,seq,earray_295),head),
inference(unit_resolution,[status(thm)],[256,92]) ).
tff(258,plain,
select(store(q47,seq,earray_295),head) = select(store(store(q47,seq,earray_295),tail,s(index_294)),head),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ( earray_295 = store(earray_293,index_294,e47) )
<=> ( earray_295 = store(earray_293,index_294,e47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
earray_295 = store(earray_293,index_294,e47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(261,plain,
earray_295 = store(earray_293,index_294,e47),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
store(earray_293,index_294,e47) = earray_295,
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)),seq) = store(earray_293,index_294,e47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
select(store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)),seq) = store(earray_293,index_294,e47),
inference(unit_resolution,[status(thm)],[263,6]) ).
tff(265,plain,
( ( q47 = queue_292 )
<=> ( q47 = queue_292 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,axiom,
q47 = queue_292,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp395) ).
tff(267,plain,
q47 = queue_292,
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
queue_292 = q47,
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ( queue_292 = store(queue_290,tail,index_291) )
<=> ( queue_292 = store(queue_290,tail,index_291) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,axiom,
queue_292 = store(queue_290,tail,index_291),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp308) ).
tff(271,plain,
queue_292 = store(queue_290,tail,index_291),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
store(queue_290,tail,index_291) = queue_292,
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
store(queue_290,tail,index_291) = q47,
inference(transitivity,[status(thm)],[272,268]) ).
tff(274,plain,
store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)) = store(q47,seq,earray_295),
inference(monotonicity,[status(thm)],[273,262]) ).
tff(275,plain,
select(store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)),seq) = select(store(q47,seq,earray_295),seq),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
select(store(q47,seq,earray_295),seq) = select(store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)),seq),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(q47,seq,earray_295),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(q47,seq,earray_295),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(q47,seq,earray_295),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(279,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(q47,seq,earray_295),seq) ) ),
inference(modus_ponens,[status(thm)],[278,277]) ).
tff(280,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(q47,seq,earray_295),seq),
inference(unit_resolution,[status(thm)],[279,32,57]) ).
tff(281,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),seq) = select(store(queue_296,tail,index_297),seq),
inference(monotonicity,[status(thm)],[250]) ).
tff(282,plain,
select(store(queue_296,tail,index_297),seq) = select(store(store(q47,seq,earray_295),tail,s(index_294)),seq),
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(store(queue_296,tail,index_297),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(store(queue_296,tail,index_297),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(284,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(store(queue_296,tail,index_297),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(285,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(store(queue_296,tail,index_297),seq) ) ),
inference(modus_ponens,[status(thm)],[284,283]) ).
tff(286,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(store(queue_296,tail,index_297),seq),
inference(unit_resolution,[status(thm)],[285,32,25]) ).
tff(287,plain,
store(store(queue_296,tail,index_297),head,s(index_299)) = q48,
inference(transitivity,[status(thm)],[17,50,46]) ).
tff(288,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),seq) = select(q48,seq),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
select(q48,seq) = select(store(store(queue_296,tail,index_297),head,s(index_299)),seq),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
select(q48,seq) = earray_295,
inference(transitivity,[status(thm)],[289,286,282,280,276,264,262]) ).
tff(291,plain,
store(store(queue_290,tail,index_291),seq,select(q48,seq)) = store(q47,seq,earray_295),
inference(monotonicity,[status(thm)],[273,290]) ).
tff(292,plain,
select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(q47,seq,earray_295),head),
inference(monotonicity,[status(thm)],[291]) ).
tff(293,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(294,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head) ) ),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
( ( seq = head )
| ( select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head) ) ),
inference(unit_resolution,[status(thm)],[295,32]) ).
tff(297,plain,
select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head) = select(store(queue_290,tail,index_291),head),
inference(unit_resolution,[status(thm)],[296,26]) ).
tff(298,plain,
select(store(queue_290,tail,index_291),head) = select(store(store(queue_290,tail,index_291),seq,select(q48,seq)),head),
inference(symmetry,[status(thm)],[297]) ).
tff(299,plain,
( ( index_291 = s(index_288) )
<=> ( index_291 = s(index_288) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(300,axiom,
index_291 = s(index_288),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(301,plain,
index_291 = s(index_288),
inference(modus_ponens,[status(thm)],[300,299]) ).
tff(302,plain,
s(index_288) = index_291,
inference(symmetry,[status(thm)],[301]) ).
tff(303,plain,
( ( queue_290 = store(q46,seq,earray_289) )
<=> ( queue_290 = store(q46,seq,earray_289) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(304,axiom,
queue_290 = store(q46,seq,earray_289),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp307) ).
tff(305,plain,
queue_290 = store(q46,seq,earray_289),
inference(modus_ponens,[status(thm)],[304,303]) ).
tff(306,plain,
store(q46,seq,earray_289) = queue_290,
inference(symmetry,[status(thm)],[305]) ).
tff(307,plain,
store(store(q46,seq,earray_289),tail,s(index_288)) = store(queue_290,tail,index_291),
inference(monotonicity,[status(thm)],[306,302]) ).
tff(308,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(queue_290,tail,index_291),head),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(q46,seq,earray_289),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(q46,seq,earray_289),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(q46,seq,earray_289),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(311,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(q46,seq,earray_289),head) ) ),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),head) = select(store(q46,seq,earray_289),head),
inference(unit_resolution,[status(thm)],[311,32,92]) ).
tff(313,plain,
select(store(q46,seq,earray_289),head) = select(store(store(q46,seq,earray_289),tail,s(index_288)),head),
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
( ( earray_289 = store(earray_287,index_288,e46) )
<=> ( earray_289 = store(earray_287,index_288,e46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,axiom,
earray_289 = store(earray_287,index_288,e46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(316,plain,
earray_289 = store(earray_287,index_288,e46),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
store(earray_287,index_288,e46) = earray_289,
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)),seq) = store(earray_287,index_288,e46) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(319,plain,
select(store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)),seq) = store(earray_287,index_288,e46),
inference(unit_resolution,[status(thm)],[318,6]) ).
tff(320,plain,
( ( q46 = queue_286 )
<=> ( q46 = queue_286 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(321,axiom,
q46 = queue_286,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp394) ).
tff(322,plain,
q46 = queue_286,
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
queue_286 = q46,
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
( ( queue_286 = store(queue_284,tail,index_285) )
<=> ( queue_286 = store(queue_284,tail,index_285) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(325,axiom,
queue_286 = store(queue_284,tail,index_285),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp306) ).
tff(326,plain,
queue_286 = store(queue_284,tail,index_285),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
store(queue_284,tail,index_285) = queue_286,
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
store(queue_284,tail,index_285) = q46,
inference(transitivity,[status(thm)],[327,323]) ).
tff(329,plain,
store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)) = store(q46,seq,earray_289),
inference(monotonicity,[status(thm)],[328,317]) ).
tff(330,plain,
select(store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)),seq) = select(store(q46,seq,earray_289),seq),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
select(store(q46,seq,earray_289),seq) = select(store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)),seq),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(store(q46,seq,earray_289),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(store(q46,seq,earray_289),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(store(q46,seq,earray_289),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(334,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(store(q46,seq,earray_289),seq) ) ),
inference(modus_ponens,[status(thm)],[333,332]) ).
tff(335,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(store(q46,seq,earray_289),seq),
inference(unit_resolution,[status(thm)],[334,32,57]) ).
tff(336,plain,
store(store(q46,seq,earray_289),tail,s(index_288)) = q47,
inference(transitivity,[status(thm)],[307,272,268]) ).
tff(337,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),seq) = select(q47,seq),
inference(monotonicity,[status(thm)],[336]) ).
tff(338,plain,
select(q47,seq) = select(store(store(q46,seq,earray_289),tail,s(index_288)),seq),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
select(q47,seq) = earray_289,
inference(transitivity,[status(thm)],[338,335,331,319,317]) ).
tff(340,plain,
store(store(queue_284,tail,index_285),seq,select(q47,seq)) = store(q46,seq,earray_289),
inference(monotonicity,[status(thm)],[328,339]) ).
tff(341,plain,
select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(q46,seq,earray_289),head),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(queue_284,tail,index_285),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(queue_284,tail,index_285),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(343,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(queue_284,tail,index_285),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(344,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(queue_284,tail,index_285),head) ) ),
inference(modus_ponens,[status(thm)],[343,342]) ).
tff(345,plain,
select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head) = select(store(queue_284,tail,index_285),head),
inference(unit_resolution,[status(thm)],[344,32,26]) ).
tff(346,plain,
select(store(queue_284,tail,index_285),head) = select(store(store(queue_284,tail,index_285),seq,select(q47,seq)),head),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
( ( index_285 = s(index_282) )
<=> ( index_285 = s(index_282) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(348,axiom,
index_285 = s(index_282),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(349,plain,
index_285 = s(index_282),
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
s(index_282) = index_285,
inference(symmetry,[status(thm)],[349]) ).
tff(351,plain,
( ( queue_284 = store(q45,seq,earray_283) )
<=> ( queue_284 = store(q45,seq,earray_283) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(352,axiom,
queue_284 = store(q45,seq,earray_283),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp305) ).
tff(353,plain,
queue_284 = store(q45,seq,earray_283),
inference(modus_ponens,[status(thm)],[352,351]) ).
tff(354,plain,
store(q45,seq,earray_283) = queue_284,
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
store(store(q45,seq,earray_283),tail,s(index_282)) = store(queue_284,tail,index_285),
inference(monotonicity,[status(thm)],[354,350]) ).
tff(356,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(queue_284,tail,index_285),head),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(q45,seq,earray_283),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(q45,seq,earray_283),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(358,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(q45,seq,earray_283),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(q45,seq,earray_283),head) ) ),
inference(modus_ponens,[status(thm)],[358,357]) ).
tff(360,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),head) = select(store(q45,seq,earray_283),head),
inference(unit_resolution,[status(thm)],[359,32,92]) ).
tff(361,plain,
select(store(q45,seq,earray_283),head) = select(store(store(q45,seq,earray_283),tail,s(index_282)),head),
inference(symmetry,[status(thm)],[360]) ).
tff(362,plain,
( ( earray_283 = store(earray_281,index_282,e45) )
<=> ( earray_283 = store(earray_281,index_282,e45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(363,axiom,
earray_283 = store(earray_281,index_282,e45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp58) ).
tff(364,plain,
earray_283 = store(earray_281,index_282,e45),
inference(modus_ponens,[status(thm)],[363,362]) ).
tff(365,plain,
store(earray_281,index_282,e45) = earray_283,
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)),seq) = store(earray_281,index_282,e45) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(367,plain,
select(store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)),seq) = store(earray_281,index_282,e45),
inference(unit_resolution,[status(thm)],[366,6]) ).
tff(368,plain,
( ( q45 = queue_280 )
<=> ( q45 = queue_280 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(369,axiom,
q45 = queue_280,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp393) ).
tff(370,plain,
q45 = queue_280,
inference(modus_ponens,[status(thm)],[369,368]) ).
tff(371,plain,
queue_280 = q45,
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
( ( queue_280 = store(queue_277,head,index_279) )
<=> ( queue_280 = store(queue_277,head,index_279) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(373,axiom,
queue_280 = store(queue_277,head,index_279),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp304) ).
tff(374,plain,
queue_280 = store(queue_277,head,index_279),
inference(modus_ponens,[status(thm)],[373,372]) ).
tff(375,plain,
store(queue_277,head,index_279) = queue_280,
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
store(queue_277,head,index_279) = q45,
inference(transitivity,[status(thm)],[375,371]) ).
tff(377,plain,
store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)) = store(q45,seq,earray_283),
inference(monotonicity,[status(thm)],[376,365]) ).
tff(378,plain,
select(store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)),seq) = select(store(q45,seq,earray_283),seq),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
select(store(q45,seq,earray_283),seq) = select(store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)),seq),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(store(q45,seq,earray_283),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(store(q45,seq,earray_283),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(381,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(store(q45,seq,earray_283),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(382,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(store(q45,seq,earray_283),seq) ) ),
inference(modus_ponens,[status(thm)],[381,380]) ).
tff(383,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(store(q45,seq,earray_283),seq),
inference(unit_resolution,[status(thm)],[382,32,57]) ).
tff(384,plain,
store(store(q45,seq,earray_283),tail,s(index_282)) = q46,
inference(transitivity,[status(thm)],[355,327,323]) ).
tff(385,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),seq) = select(q46,seq),
inference(monotonicity,[status(thm)],[384]) ).
tff(386,plain,
select(q46,seq) = select(store(store(q45,seq,earray_283),tail,s(index_282)),seq),
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
select(q46,seq) = earray_283,
inference(transitivity,[status(thm)],[386,383,379,367,365]) ).
tff(388,plain,
store(store(queue_277,head,index_279),seq,select(q46,seq)) = store(q45,seq,earray_283),
inference(monotonicity,[status(thm)],[376,387]) ).
tff(389,plain,
select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(q45,seq,earray_283),head),
inference(monotonicity,[status(thm)],[388]) ).
tff(390,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(queue_277,head,index_279),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(queue_277,head,index_279),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(391,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(queue_277,head,index_279),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(392,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(queue_277,head,index_279),head) ) ),
inference(modus_ponens,[status(thm)],[391,390]) ).
tff(393,plain,
select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head) = select(store(queue_277,head,index_279),head),
inference(unit_resolution,[status(thm)],[392,32,26]) ).
tff(394,plain,
select(store(queue_277,head,index_279),head) = select(store(store(queue_277,head,index_279),seq,select(q46,seq)),head),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
( ( index_279 = s(index_278) )
<=> ( index_279 = s(index_278) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(396,axiom,
index_279 = s(index_278),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(397,plain,
index_279 = s(index_278),
inference(modus_ponens,[status(thm)],[396,395]) ).
tff(398,plain,
s(index_278) = index_279,
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ( queue_277 = store(queue_275,tail,index_276) )
<=> ( queue_277 = store(queue_275,tail,index_276) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(400,axiom,
queue_277 = store(queue_275,tail,index_276),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp302) ).
tff(401,plain,
queue_277 = store(queue_275,tail,index_276),
inference(modus_ponens,[status(thm)],[400,399]) ).
tff(402,plain,
store(queue_275,tail,index_276) = queue_277,
inference(symmetry,[status(thm)],[401]) ).
tff(403,plain,
store(store(queue_275,tail,index_276),head,s(index_278)) = store(queue_277,head,index_279),
inference(monotonicity,[status(thm)],[402,398]) ).
tff(404,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = select(store(queue_277,head,index_279),head),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = s(index_278) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(406,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = s(index_278),
inference(unit_resolution,[status(thm)],[405,6]) ).
tff(407,plain,
s(index_278) = select(store(store(queue_275,tail,index_276),head,s(index_278)),head),
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
( ( index_278 = select(queue_277,head) )
<=> ( index_278 = select(queue_277,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(409,axiom,
index_278 = select(queue_277,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(410,plain,
index_278 = select(queue_277,head),
inference(modus_ponens,[status(thm)],[409,408]) ).
tff(411,plain,
select(queue_277,head) = index_278,
inference(symmetry,[status(thm)],[410]) ).
tff(412,plain,
( ( index_276 = s(index_273) )
<=> ( index_276 = s(index_273) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(413,axiom,
index_276 = s(index_273),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(414,plain,
index_276 = s(index_273),
inference(modus_ponens,[status(thm)],[413,412]) ).
tff(415,plain,
s(index_273) = index_276,
inference(symmetry,[status(thm)],[414]) ).
tff(416,plain,
( ( queue_275 = store(q44,seq,earray_274) )
<=> ( queue_275 = store(q44,seq,earray_274) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(417,axiom,
queue_275 = store(q44,seq,earray_274),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp301) ).
tff(418,plain,
queue_275 = store(q44,seq,earray_274),
inference(modus_ponens,[status(thm)],[417,416]) ).
tff(419,plain,
store(q44,seq,earray_274) = queue_275,
inference(symmetry,[status(thm)],[418]) ).
tff(420,plain,
store(store(q44,seq,earray_274),tail,s(index_273)) = store(queue_275,tail,index_276),
inference(monotonicity,[status(thm)],[419,415]) ).
tff(421,plain,
store(store(q44,seq,earray_274),tail,s(index_273)) = queue_277,
inference(transitivity,[status(thm)],[420,402]) ).
tff(422,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(queue_277,head),
inference(monotonicity,[status(thm)],[421]) ).
tff(423,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(424,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head) ) ),
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
( ( tail = head )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head) ) ),
inference(unit_resolution,[status(thm)],[425,32]) ).
tff(427,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),head) = select(store(q44,seq,earray_274),head),
inference(unit_resolution,[status(thm)],[426,92]) ).
tff(428,plain,
select(store(q44,seq,earray_274),head) = select(store(store(q44,seq,earray_274),tail,s(index_273)),head),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
( ( earray_274 = store(earray_272,index_273,e44) )
<=> ( earray_274 = store(earray_272,index_273,e44) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(430,axiom,
earray_274 = store(earray_272,index_273,e44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(431,plain,
earray_274 = store(earray_272,index_273,e44),
inference(modus_ponens,[status(thm)],[430,429]) ).
tff(432,plain,
store(earray_272,index_273,e44) = earray_274,
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)),seq) = store(earray_272,index_273,e44) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(434,plain,
select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)),seq) = store(earray_272,index_273,e44),
inference(unit_resolution,[status(thm)],[433,6]) ).
tff(435,plain,
( ( q44 = queue_271 )
<=> ( q44 = queue_271 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(436,axiom,
q44 = queue_271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp392) ).
tff(437,plain,
q44 = queue_271,
inference(modus_ponens,[status(thm)],[436,435]) ).
tff(438,plain,
queue_271 = q44,
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
( ( queue_271 = store(queue_269,tail,index_270) )
<=> ( queue_271 = store(queue_269,tail,index_270) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(440,axiom,
queue_271 = store(queue_269,tail,index_270),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp300) ).
tff(441,plain,
queue_271 = store(queue_269,tail,index_270),
inference(modus_ponens,[status(thm)],[440,439]) ).
tff(442,plain,
store(queue_269,tail,index_270) = queue_271,
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
store(queue_269,tail,index_270) = q44,
inference(transitivity,[status(thm)],[442,438]) ).
tff(444,plain,
store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)) = store(q44,seq,earray_274),
inference(monotonicity,[status(thm)],[443,432]) ).
tff(445,plain,
select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)),seq) = select(store(q44,seq,earray_274),seq),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
select(store(q44,seq,earray_274),seq) = select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)),seq),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(q44,seq,earray_274),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(q44,seq,earray_274),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(448,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(q44,seq,earray_274),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(449,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(q44,seq,earray_274),seq) ) ),
inference(modus_ponens,[status(thm)],[448,447]) ).
tff(450,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(q44,seq,earray_274),seq),
inference(unit_resolution,[status(thm)],[449,32,57]) ).
tff(451,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),seq) = select(store(queue_275,tail,index_276),seq),
inference(monotonicity,[status(thm)],[420]) ).
tff(452,plain,
select(store(queue_275,tail,index_276),seq) = select(store(store(q44,seq,earray_274),tail,s(index_273)),seq),
inference(symmetry,[status(thm)],[451]) ).
tff(453,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(454,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(455,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ),
inference(modus_ponens,[status(thm)],[454,453]) ).
tff(456,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq),
inference(unit_resolution,[status(thm)],[455,32,25]) ).
tff(457,plain,
store(store(queue_275,tail,index_276),head,s(index_278)) = q45,
inference(transitivity,[status(thm)],[403,375,371]) ).
tff(458,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(q45,seq),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
select(q45,seq) = select(store(store(queue_275,tail,index_276),head,s(index_278)),seq),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
select(q45,seq) = earray_274,
inference(transitivity,[status(thm)],[459,456,452,450,446,434,432]) ).
tff(461,plain,
store(store(queue_269,tail,index_270),seq,select(q45,seq)) = store(q44,seq,earray_274),
inference(monotonicity,[status(thm)],[443,460]) ).
tff(462,plain,
select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(q44,seq,earray_274),head),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(464,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(modus_ponens,[status(thm)],[464,463]) ).
tff(466,plain,
( ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(unit_resolution,[status(thm)],[465,32]) ).
tff(467,plain,
select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head) = select(store(queue_269,tail,index_270),head),
inference(unit_resolution,[status(thm)],[466,26]) ).
tff(468,plain,
select(store(queue_269,tail,index_270),head) = select(store(store(queue_269,tail,index_270),seq,select(q45,seq)),head),
inference(symmetry,[status(thm)],[467]) ).
tff(469,plain,
( ( index_270 = s(index_267) )
<=> ( index_270 = s(index_267) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(470,axiom,
index_270 = s(index_267),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(471,plain,
index_270 = s(index_267),
inference(modus_ponens,[status(thm)],[470,469]) ).
tff(472,plain,
s(index_267) = index_270,
inference(symmetry,[status(thm)],[471]) ).
tff(473,plain,
( ( queue_269 = store(q43,seq,earray_268) )
<=> ( queue_269 = store(q43,seq,earray_268) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(474,axiom,
queue_269 = store(q43,seq,earray_268),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp299) ).
tff(475,plain,
queue_269 = store(q43,seq,earray_268),
inference(modus_ponens,[status(thm)],[474,473]) ).
tff(476,plain,
store(q43,seq,earray_268) = queue_269,
inference(symmetry,[status(thm)],[475]) ).
tff(477,plain,
store(store(q43,seq,earray_268),tail,s(index_267)) = store(queue_269,tail,index_270),
inference(monotonicity,[status(thm)],[476,472]) ).
tff(478,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(queue_269,tail,index_270),head),
inference(monotonicity,[status(thm)],[477]) ).
tff(479,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(q43,seq,earray_268),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(q43,seq,earray_268),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(480,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(q43,seq,earray_268),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(481,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(q43,seq,earray_268),head) ) ),
inference(modus_ponens,[status(thm)],[480,479]) ).
tff(482,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),head) = select(store(q43,seq,earray_268),head),
inference(unit_resolution,[status(thm)],[481,32,92]) ).
tff(483,plain,
select(store(q43,seq,earray_268),head) = select(store(store(q43,seq,earray_268),tail,s(index_267)),head),
inference(symmetry,[status(thm)],[482]) ).
tff(484,plain,
( ( earray_268 = store(earray_266,index_267,e43) )
<=> ( earray_268 = store(earray_266,index_267,e43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(485,axiom,
earray_268 = store(earray_266,index_267,e43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(486,plain,
earray_268 = store(earray_266,index_267,e43),
inference(modus_ponens,[status(thm)],[485,484]) ).
tff(487,plain,
store(earray_266,index_267,e43) = earray_268,
inference(symmetry,[status(thm)],[486]) ).
tff(488,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)),seq) = store(earray_266,index_267,e43) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(489,plain,
select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)),seq) = store(earray_266,index_267,e43),
inference(unit_resolution,[status(thm)],[488,6]) ).
tff(490,plain,
( ( q43 = queue_265 )
<=> ( q43 = queue_265 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(491,axiom,
q43 = queue_265,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp391) ).
tff(492,plain,
q43 = queue_265,
inference(modus_ponens,[status(thm)],[491,490]) ).
tff(493,plain,
queue_265 = q43,
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ( queue_265 = store(queue_263,tail,index_264) )
<=> ( queue_265 = store(queue_263,tail,index_264) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(495,axiom,
queue_265 = store(queue_263,tail,index_264),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp298) ).
tff(496,plain,
queue_265 = store(queue_263,tail,index_264),
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
store(queue_263,tail,index_264) = queue_265,
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
store(queue_263,tail,index_264) = q43,
inference(transitivity,[status(thm)],[497,493]) ).
tff(499,plain,
store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)) = store(q43,seq,earray_268),
inference(monotonicity,[status(thm)],[498,487]) ).
tff(500,plain,
select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)),seq) = select(store(q43,seq,earray_268),seq),
inference(monotonicity,[status(thm)],[499]) ).
tff(501,plain,
select(store(q43,seq,earray_268),seq) = select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)),seq),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(store(q43,seq,earray_268),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(store(q43,seq,earray_268),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(503,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(store(q43,seq,earray_268),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(store(q43,seq,earray_268),seq) ) ),
inference(modus_ponens,[status(thm)],[503,502]) ).
tff(505,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(store(q43,seq,earray_268),seq),
inference(unit_resolution,[status(thm)],[504,32,57]) ).
tff(506,plain,
store(store(q43,seq,earray_268),tail,s(index_267)) = q44,
inference(transitivity,[status(thm)],[477,442,438]) ).
tff(507,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),seq) = select(q44,seq),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
select(q44,seq) = select(store(store(q43,seq,earray_268),tail,s(index_267)),seq),
inference(symmetry,[status(thm)],[507]) ).
tff(509,plain,
select(q44,seq) = earray_268,
inference(transitivity,[status(thm)],[508,505,501,489,487]) ).
tff(510,plain,
store(store(queue_263,tail,index_264),seq,select(q44,seq)) = store(q43,seq,earray_268),
inference(monotonicity,[status(thm)],[498,509]) ).
tff(511,plain,
select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(q43,seq,earray_268),head),
inference(monotonicity,[status(thm)],[510]) ).
tff(512,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(queue_263,tail,index_264),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(queue_263,tail,index_264),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(513,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(queue_263,tail,index_264),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(514,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(queue_263,tail,index_264),head) ) ),
inference(modus_ponens,[status(thm)],[513,512]) ).
tff(515,plain,
select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head) = select(store(queue_263,tail,index_264),head),
inference(unit_resolution,[status(thm)],[514,32,26]) ).
tff(516,plain,
select(store(queue_263,tail,index_264),head) = select(store(store(queue_263,tail,index_264),seq,select(q44,seq)),head),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
( ( index_264 = s(index_261) )
<=> ( index_264 = s(index_261) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(518,axiom,
index_264 = s(index_261),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(519,plain,
index_264 = s(index_261),
inference(modus_ponens,[status(thm)],[518,517]) ).
tff(520,plain,
s(index_261) = index_264,
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
( ( queue_263 = store(q42,seq,earray_262) )
<=> ( queue_263 = store(q42,seq,earray_262) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(522,axiom,
queue_263 = store(q42,seq,earray_262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp297) ).
tff(523,plain,
queue_263 = store(q42,seq,earray_262),
inference(modus_ponens,[status(thm)],[522,521]) ).
tff(524,plain,
store(q42,seq,earray_262) = queue_263,
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
store(store(q42,seq,earray_262),tail,s(index_261)) = store(queue_263,tail,index_264),
inference(monotonicity,[status(thm)],[524,520]) ).
tff(526,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(queue_263,tail,index_264),head),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(q42,seq,earray_262),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(q42,seq,earray_262),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(528,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(q42,seq,earray_262),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(529,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(q42,seq,earray_262),head) ) ),
inference(modus_ponens,[status(thm)],[528,527]) ).
tff(530,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),head) = select(store(q42,seq,earray_262),head),
inference(unit_resolution,[status(thm)],[529,32,92]) ).
tff(531,plain,
select(store(q42,seq,earray_262),head) = select(store(store(q42,seq,earray_262),tail,s(index_261)),head),
inference(symmetry,[status(thm)],[530]) ).
tff(532,plain,
( ( earray_262 = store(earray_260,index_261,e42) )
<=> ( earray_262 = store(earray_260,index_261,e42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(533,axiom,
earray_262 = store(earray_260,index_261,e42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(534,plain,
earray_262 = store(earray_260,index_261,e42),
inference(modus_ponens,[status(thm)],[533,532]) ).
tff(535,plain,
store(earray_260,index_261,e42) = earray_262,
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)),seq) = store(earray_260,index_261,e42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)),seq) = store(earray_260,index_261,e42),
inference(unit_resolution,[status(thm)],[536,6]) ).
tff(538,plain,
( ( q42 = queue_259 )
<=> ( q42 = queue_259 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(539,axiom,
q42 = queue_259,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp390) ).
tff(540,plain,
q42 = queue_259,
inference(modus_ponens,[status(thm)],[539,538]) ).
tff(541,plain,
queue_259 = q42,
inference(symmetry,[status(thm)],[540]) ).
tff(542,plain,
( ( queue_259 = store(queue_256,head,index_258) )
<=> ( queue_259 = store(queue_256,head,index_258) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(543,axiom,
queue_259 = store(queue_256,head,index_258),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp296) ).
tff(544,plain,
queue_259 = store(queue_256,head,index_258),
inference(modus_ponens,[status(thm)],[543,542]) ).
tff(545,plain,
store(queue_256,head,index_258) = queue_259,
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
store(queue_256,head,index_258) = q42,
inference(transitivity,[status(thm)],[545,541]) ).
tff(547,plain,
store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)) = store(q42,seq,earray_262),
inference(monotonicity,[status(thm)],[546,535]) ).
tff(548,plain,
select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)),seq) = select(store(q42,seq,earray_262),seq),
inference(monotonicity,[status(thm)],[547]) ).
tff(549,plain,
select(store(q42,seq,earray_262),seq) = select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)),seq),
inference(symmetry,[status(thm)],[548]) ).
tff(550,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(store(q42,seq,earray_262),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(store(q42,seq,earray_262),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(551,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(store(q42,seq,earray_262),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(552,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(store(q42,seq,earray_262),seq) ) ),
inference(modus_ponens,[status(thm)],[551,550]) ).
tff(553,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(store(q42,seq,earray_262),seq),
inference(unit_resolution,[status(thm)],[552,32,57]) ).
tff(554,plain,
store(store(q42,seq,earray_262),tail,s(index_261)) = q43,
inference(transitivity,[status(thm)],[525,497,493]) ).
tff(555,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),seq) = select(q43,seq),
inference(monotonicity,[status(thm)],[554]) ).
tff(556,plain,
select(q43,seq) = select(store(store(q42,seq,earray_262),tail,s(index_261)),seq),
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
select(q43,seq) = earray_262,
inference(transitivity,[status(thm)],[556,553,549,537,535]) ).
tff(558,plain,
store(store(queue_256,head,index_258),seq,select(q43,seq)) = store(q42,seq,earray_262),
inference(monotonicity,[status(thm)],[546,557]) ).
tff(559,plain,
select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(q42,seq,earray_262),head),
inference(monotonicity,[status(thm)],[558]) ).
tff(560,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(queue_256,head,index_258),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(queue_256,head,index_258),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(561,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(queue_256,head,index_258),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(562,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(queue_256,head,index_258),head) ) ),
inference(modus_ponens,[status(thm)],[561,560]) ).
tff(563,plain,
select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head) = select(store(queue_256,head,index_258),head),
inference(unit_resolution,[status(thm)],[562,32,26]) ).
tff(564,plain,
select(store(queue_256,head,index_258),head) = select(store(store(queue_256,head,index_258),seq,select(q43,seq)),head),
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
( ( index_258 = s(index_257) )
<=> ( index_258 = s(index_257) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(566,axiom,
index_258 = s(index_257),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(567,plain,
index_258 = s(index_257),
inference(modus_ponens,[status(thm)],[566,565]) ).
tff(568,plain,
s(index_257) = index_258,
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
( ( queue_256 = store(queue_254,tail,index_255) )
<=> ( queue_256 = store(queue_254,tail,index_255) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(570,axiom,
queue_256 = store(queue_254,tail,index_255),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp295) ).
tff(571,plain,
queue_256 = store(queue_254,tail,index_255),
inference(modus_ponens,[status(thm)],[570,569]) ).
tff(572,plain,
store(queue_254,tail,index_255) = queue_256,
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
store(store(queue_254,tail,index_255),head,s(index_257)) = store(queue_256,head,index_258),
inference(monotonicity,[status(thm)],[572,568]) ).
tff(574,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = select(store(queue_256,head,index_258),head),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = s(index_257) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(576,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = s(index_257),
inference(unit_resolution,[status(thm)],[575,6]) ).
tff(577,plain,
s(index_257) = select(store(store(queue_254,tail,index_255),head,s(index_257)),head),
inference(symmetry,[status(thm)],[576]) ).
tff(578,plain,
( ( index_257 = select(queue_256,head) )
<=> ( index_257 = select(queue_256,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(579,axiom,
index_257 = select(queue_256,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(580,plain,
index_257 = select(queue_256,head),
inference(modus_ponens,[status(thm)],[579,578]) ).
tff(581,plain,
select(queue_256,head) = index_257,
inference(symmetry,[status(thm)],[580]) ).
tff(582,plain,
( ( index_255 = s(index_252) )
<=> ( index_255 = s(index_252) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(583,axiom,
index_255 = s(index_252),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(584,plain,
index_255 = s(index_252),
inference(modus_ponens,[status(thm)],[583,582]) ).
tff(585,plain,
s(index_252) = index_255,
inference(symmetry,[status(thm)],[584]) ).
tff(586,plain,
( ( queue_254 = store(q41,seq,earray_253) )
<=> ( queue_254 = store(q41,seq,earray_253) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(587,axiom,
queue_254 = store(q41,seq,earray_253),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp294) ).
tff(588,plain,
queue_254 = store(q41,seq,earray_253),
inference(modus_ponens,[status(thm)],[587,586]) ).
tff(589,plain,
store(q41,seq,earray_253) = queue_254,
inference(symmetry,[status(thm)],[588]) ).
tff(590,plain,
store(store(q41,seq,earray_253),tail,s(index_252)) = store(queue_254,tail,index_255),
inference(monotonicity,[status(thm)],[589,585]) ).
tff(591,plain,
store(store(q41,seq,earray_253),tail,s(index_252)) = queue_256,
inference(transitivity,[status(thm)],[590,572]) ).
tff(592,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(queue_256,head),
inference(monotonicity,[status(thm)],[591]) ).
tff(593,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(594,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(595,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head) ) ),
inference(modus_ponens,[status(thm)],[594,593]) ).
tff(596,plain,
( ( tail = head )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head) ) ),
inference(unit_resolution,[status(thm)],[595,32]) ).
tff(597,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),head) = select(store(q41,seq,earray_253),head),
inference(unit_resolution,[status(thm)],[596,92]) ).
tff(598,plain,
select(store(q41,seq,earray_253),head) = select(store(store(q41,seq,earray_253),tail,s(index_252)),head),
inference(symmetry,[status(thm)],[597]) ).
tff(599,plain,
( ( earray_253 = store(earray_251,index_252,e41) )
<=> ( earray_253 = store(earray_251,index_252,e41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(600,axiom,
earray_253 = store(earray_251,index_252,e41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(601,plain,
earray_253 = store(earray_251,index_252,e41),
inference(modus_ponens,[status(thm)],[600,599]) ).
tff(602,plain,
store(earray_251,index_252,e41) = earray_253,
inference(symmetry,[status(thm)],[601]) ).
tff(603,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)),seq) = store(earray_251,index_252,e41) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(604,plain,
select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)),seq) = store(earray_251,index_252,e41),
inference(unit_resolution,[status(thm)],[603,6]) ).
tff(605,plain,
( ( q41 = queue_250 )
<=> ( q41 = queue_250 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(606,axiom,
q41 = queue_250,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp389) ).
tff(607,plain,
q41 = queue_250,
inference(modus_ponens,[status(thm)],[606,605]) ).
tff(608,plain,
queue_250 = q41,
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
( ( queue_250 = store(queue_248,tail,index_249) )
<=> ( queue_250 = store(queue_248,tail,index_249) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(610,axiom,
queue_250 = store(queue_248,tail,index_249),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp293) ).
tff(611,plain,
queue_250 = store(queue_248,tail,index_249),
inference(modus_ponens,[status(thm)],[610,609]) ).
tff(612,plain,
store(queue_248,tail,index_249) = queue_250,
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
store(queue_248,tail,index_249) = q41,
inference(transitivity,[status(thm)],[612,608]) ).
tff(614,plain,
store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)) = store(q41,seq,earray_253),
inference(monotonicity,[status(thm)],[613,602]) ).
tff(615,plain,
select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)),seq) = select(store(q41,seq,earray_253),seq),
inference(monotonicity,[status(thm)],[614]) ).
tff(616,plain,
select(store(q41,seq,earray_253),seq) = select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)),seq),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(q41,seq,earray_253),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(q41,seq,earray_253),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(618,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(q41,seq,earray_253),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(619,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(q41,seq,earray_253),seq) ) ),
inference(modus_ponens,[status(thm)],[618,617]) ).
tff(620,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(q41,seq,earray_253),seq),
inference(unit_resolution,[status(thm)],[619,32,57]) ).
tff(621,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),seq) = select(store(queue_254,tail,index_255),seq),
inference(monotonicity,[status(thm)],[590]) ).
tff(622,plain,
select(store(queue_254,tail,index_255),seq) = select(store(store(q41,seq,earray_253),tail,s(index_252)),seq),
inference(symmetry,[status(thm)],[621]) ).
tff(623,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(624,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(625,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ),
inference(modus_ponens,[status(thm)],[624,623]) ).
tff(626,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq),
inference(unit_resolution,[status(thm)],[625,32,25]) ).
tff(627,plain,
store(store(queue_254,tail,index_255),head,s(index_257)) = q42,
inference(transitivity,[status(thm)],[573,545,541]) ).
tff(628,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(q42,seq),
inference(monotonicity,[status(thm)],[627]) ).
tff(629,plain,
select(q42,seq) = select(store(store(queue_254,tail,index_255),head,s(index_257)),seq),
inference(symmetry,[status(thm)],[628]) ).
tff(630,plain,
select(q42,seq) = earray_253,
inference(transitivity,[status(thm)],[629,626,622,620,616,604,602]) ).
tff(631,plain,
store(store(queue_248,tail,index_249),seq,select(q42,seq)) = store(q41,seq,earray_253),
inference(monotonicity,[status(thm)],[613,630]) ).
tff(632,plain,
select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(q41,seq,earray_253),head),
inference(monotonicity,[status(thm)],[631]) ).
tff(633,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(634,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(635,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(modus_ponens,[status(thm)],[634,633]) ).
tff(636,plain,
( ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(unit_resolution,[status(thm)],[635,32]) ).
tff(637,plain,
select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head) = select(store(queue_248,tail,index_249),head),
inference(unit_resolution,[status(thm)],[636,26]) ).
tff(638,plain,
select(store(queue_248,tail,index_249),head) = select(store(store(queue_248,tail,index_249),seq,select(q42,seq)),head),
inference(symmetry,[status(thm)],[637]) ).
tff(639,plain,
( ( index_249 = s(index_246) )
<=> ( index_249 = s(index_246) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(640,axiom,
index_249 = s(index_246),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(641,plain,
index_249 = s(index_246),
inference(modus_ponens,[status(thm)],[640,639]) ).
tff(642,plain,
s(index_246) = index_249,
inference(symmetry,[status(thm)],[641]) ).
tff(643,plain,
( ( queue_248 = store(q40,seq,earray_247) )
<=> ( queue_248 = store(q40,seq,earray_247) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(644,axiom,
queue_248 = store(q40,seq,earray_247),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp291) ).
tff(645,plain,
queue_248 = store(q40,seq,earray_247),
inference(modus_ponens,[status(thm)],[644,643]) ).
tff(646,plain,
store(q40,seq,earray_247) = queue_248,
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
store(store(q40,seq,earray_247),tail,s(index_246)) = store(queue_248,tail,index_249),
inference(monotonicity,[status(thm)],[646,642]) ).
tff(648,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(queue_248,tail,index_249),head),
inference(monotonicity,[status(thm)],[647]) ).
tff(649,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(q40,seq,earray_247),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(q40,seq,earray_247),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(650,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(q40,seq,earray_247),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(651,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(q40,seq,earray_247),head) ) ),
inference(modus_ponens,[status(thm)],[650,649]) ).
tff(652,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),head) = select(store(q40,seq,earray_247),head),
inference(unit_resolution,[status(thm)],[651,32,92]) ).
tff(653,plain,
select(store(q40,seq,earray_247),head) = select(store(store(q40,seq,earray_247),tail,s(index_246)),head),
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ( earray_247 = store(earray_245,index_246,e40) )
<=> ( earray_247 = store(earray_245,index_246,e40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(655,axiom,
earray_247 = store(earray_245,index_246,e40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(656,plain,
earray_247 = store(earray_245,index_246,e40),
inference(modus_ponens,[status(thm)],[655,654]) ).
tff(657,plain,
store(earray_245,index_246,e40) = earray_247,
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)),seq) = store(earray_245,index_246,e40) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(659,plain,
select(store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)),seq) = store(earray_245,index_246,e40),
inference(unit_resolution,[status(thm)],[658,6]) ).
tff(660,plain,
( ( q40 = queue_244 )
<=> ( q40 = queue_244 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(661,axiom,
q40 = queue_244,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp388) ).
tff(662,plain,
q40 = queue_244,
inference(modus_ponens,[status(thm)],[661,660]) ).
tff(663,plain,
queue_244 = q40,
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
( ( queue_244 = store(queue_242,tail,index_243) )
<=> ( queue_244 = store(queue_242,tail,index_243) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(665,axiom,
queue_244 = store(queue_242,tail,index_243),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp290) ).
tff(666,plain,
queue_244 = store(queue_242,tail,index_243),
inference(modus_ponens,[status(thm)],[665,664]) ).
tff(667,plain,
store(queue_242,tail,index_243) = queue_244,
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
store(queue_242,tail,index_243) = q40,
inference(transitivity,[status(thm)],[667,663]) ).
tff(669,plain,
store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)) = store(q40,seq,earray_247),
inference(monotonicity,[status(thm)],[668,657]) ).
tff(670,plain,
select(store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)),seq) = select(store(q40,seq,earray_247),seq),
inference(monotonicity,[status(thm)],[669]) ).
tff(671,plain,
select(store(q40,seq,earray_247),seq) = select(store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)),seq),
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(store(q40,seq,earray_247),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(store(q40,seq,earray_247),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(673,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(store(q40,seq,earray_247),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(674,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(store(q40,seq,earray_247),seq) ) ),
inference(modus_ponens,[status(thm)],[673,672]) ).
tff(675,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(store(q40,seq,earray_247),seq),
inference(unit_resolution,[status(thm)],[674,32,57]) ).
tff(676,plain,
store(store(q40,seq,earray_247),tail,s(index_246)) = q41,
inference(transitivity,[status(thm)],[647,612,608]) ).
tff(677,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),seq) = select(q41,seq),
inference(monotonicity,[status(thm)],[676]) ).
tff(678,plain,
select(q41,seq) = select(store(store(q40,seq,earray_247),tail,s(index_246)),seq),
inference(symmetry,[status(thm)],[677]) ).
tff(679,plain,
select(q41,seq) = earray_247,
inference(transitivity,[status(thm)],[678,675,671,659,657]) ).
tff(680,plain,
store(store(queue_242,tail,index_243),seq,select(q41,seq)) = store(q40,seq,earray_247),
inference(monotonicity,[status(thm)],[668,679]) ).
tff(681,plain,
select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(q40,seq,earray_247),head),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(queue_242,tail,index_243),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(queue_242,tail,index_243),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(683,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(queue_242,tail,index_243),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(684,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(queue_242,tail,index_243),head) ) ),
inference(modus_ponens,[status(thm)],[683,682]) ).
tff(685,plain,
select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head) = select(store(queue_242,tail,index_243),head),
inference(unit_resolution,[status(thm)],[684,32,26]) ).
tff(686,plain,
select(store(queue_242,tail,index_243),head) = select(store(store(queue_242,tail,index_243),seq,select(q41,seq)),head),
inference(symmetry,[status(thm)],[685]) ).
tff(687,plain,
( ( index_243 = s(index_240) )
<=> ( index_243 = s(index_240) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(688,axiom,
index_243 = s(index_240),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(689,plain,
index_243 = s(index_240),
inference(modus_ponens,[status(thm)],[688,687]) ).
tff(690,plain,
s(index_240) = index_243,
inference(symmetry,[status(thm)],[689]) ).
tff(691,plain,
( ( queue_242 = store(q39,seq,earray_241) )
<=> ( queue_242 = store(q39,seq,earray_241) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(692,axiom,
queue_242 = store(q39,seq,earray_241),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp289) ).
tff(693,plain,
queue_242 = store(q39,seq,earray_241),
inference(modus_ponens,[status(thm)],[692,691]) ).
tff(694,plain,
store(q39,seq,earray_241) = queue_242,
inference(symmetry,[status(thm)],[693]) ).
tff(695,plain,
store(store(q39,seq,earray_241),tail,s(index_240)) = store(queue_242,tail,index_243),
inference(monotonicity,[status(thm)],[694,690]) ).
tff(696,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(queue_242,tail,index_243),head),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(698,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(699,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ),
inference(modus_ponens,[status(thm)],[698,697]) ).
tff(700,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head),
inference(unit_resolution,[status(thm)],[699,32,92]) ).
tff(701,plain,
select(store(q39,seq,earray_241),head) = select(store(store(q39,seq,earray_241),tail,s(index_240)),head),
inference(symmetry,[status(thm)],[700]) ).
tff(702,plain,
( ( earray_241 = store(earray_239,index_240,e39) )
<=> ( earray_241 = store(earray_239,index_240,e39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(703,axiom,
earray_241 = store(earray_239,index_240,e39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(704,plain,
earray_241 = store(earray_239,index_240,e39),
inference(modus_ponens,[status(thm)],[703,702]) ).
tff(705,plain,
store(earray_239,index_240,e39) = earray_241,
inference(symmetry,[status(thm)],[704]) ).
tff(706,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = store(earray_239,index_240,e39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(707,plain,
select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = store(earray_239,index_240,e39),
inference(unit_resolution,[status(thm)],[706,6]) ).
tff(708,plain,
( ( q39 = queue_232 )
<=> ( q39 = queue_232 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(709,axiom,
q39 = queue_232,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp386) ).
tff(710,plain,
q39 = queue_232,
inference(modus_ponens,[status(thm)],[709,708]) ).
tff(711,plain,
queue_232 = q39,
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
( ( queue_232 = store(queue_229,head,index_231) )
<=> ( queue_232 = store(queue_229,head,index_231) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(713,axiom,
queue_232 = store(queue_229,head,index_231),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp286) ).
tff(714,plain,
queue_232 = store(queue_229,head,index_231),
inference(modus_ponens,[status(thm)],[713,712]) ).
tff(715,plain,
store(queue_229,head,index_231) = queue_232,
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
store(queue_229,head,index_231) = q39,
inference(transitivity,[status(thm)],[715,711]) ).
tff(717,plain,
store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)) = store(q39,seq,earray_241),
inference(monotonicity,[status(thm)],[716,705]) ).
tff(718,plain,
select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = select(store(q39,seq,earray_241),seq),
inference(monotonicity,[status(thm)],[717]) ).
tff(719,plain,
select(store(q39,seq,earray_241),seq) = select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(721,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(722,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ),
inference(modus_ponens,[status(thm)],[721,720]) ).
tff(723,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq),
inference(unit_resolution,[status(thm)],[722,32,57]) ).
tff(724,plain,
store(store(q39,seq,earray_241),tail,s(index_240)) = q40,
inference(transitivity,[status(thm)],[695,667,663]) ).
tff(725,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(q40,seq),
inference(monotonicity,[status(thm)],[724]) ).
tff(726,plain,
select(q40,seq) = select(store(store(q39,seq,earray_241),tail,s(index_240)),seq),
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
select(q40,seq) = earray_241,
inference(transitivity,[status(thm)],[726,723,719,707,705]) ).
tff(728,plain,
store(store(queue_229,head,index_231),seq,select(q40,seq)) = store(q39,seq,earray_241),
inference(monotonicity,[status(thm)],[716,727]) ).
tff(729,plain,
select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(q39,seq,earray_241),head),
inference(monotonicity,[status(thm)],[728]) ).
tff(730,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(731,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(732,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ),
inference(modus_ponens,[status(thm)],[731,730]) ).
tff(733,plain,
select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head),
inference(unit_resolution,[status(thm)],[732,32,26]) ).
tff(734,plain,
select(store(queue_229,head,index_231),head) = select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head),
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
( ( index_231 = s(index_230) )
<=> ( index_231 = s(index_230) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(736,axiom,
index_231 = s(index_230),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(737,plain,
index_231 = s(index_230),
inference(modus_ponens,[status(thm)],[736,735]) ).
tff(738,plain,
s(index_230) = index_231,
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
( ( queue_229 = store(queue_227,tail,index_228) )
<=> ( queue_229 = store(queue_227,tail,index_228) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(740,axiom,
queue_229 = store(queue_227,tail,index_228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp284) ).
tff(741,plain,
queue_229 = store(queue_227,tail,index_228),
inference(modus_ponens,[status(thm)],[740,739]) ).
tff(742,plain,
store(queue_227,tail,index_228) = queue_229,
inference(symmetry,[status(thm)],[741]) ).
tff(743,plain,
store(store(queue_227,tail,index_228),head,s(index_230)) = store(queue_229,head,index_231),
inference(monotonicity,[status(thm)],[742,738]) ).
tff(744,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = select(store(queue_229,head,index_231),head),
inference(monotonicity,[status(thm)],[743]) ).
tff(745,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(746,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = s(index_230),
inference(unit_resolution,[status(thm)],[745,6]) ).
tff(747,plain,
s(index_230) = select(store(store(queue_227,tail,index_228),head,s(index_230)),head),
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
( ( index_230 = select(queue_229,head) )
<=> ( index_230 = select(queue_229,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(749,axiom,
index_230 = select(queue_229,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(750,plain,
index_230 = select(queue_229,head),
inference(modus_ponens,[status(thm)],[749,748]) ).
tff(751,plain,
select(queue_229,head) = index_230,
inference(symmetry,[status(thm)],[750]) ).
tff(752,plain,
( ( index_228 = s(index_225) )
<=> ( index_228 = s(index_225) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(753,axiom,
index_228 = s(index_225),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(754,plain,
index_228 = s(index_225),
inference(modus_ponens,[status(thm)],[753,752]) ).
tff(755,plain,
s(index_225) = index_228,
inference(symmetry,[status(thm)],[754]) ).
tff(756,plain,
( ( queue_227 = store(q38,seq,earray_226) )
<=> ( queue_227 = store(q38,seq,earray_226) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(757,axiom,
queue_227 = store(q38,seq,earray_226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp283) ).
tff(758,plain,
queue_227 = store(q38,seq,earray_226),
inference(modus_ponens,[status(thm)],[757,756]) ).
tff(759,plain,
store(q38,seq,earray_226) = queue_227,
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
store(store(q38,seq,earray_226),tail,s(index_225)) = store(queue_227,tail,index_228),
inference(monotonicity,[status(thm)],[759,755]) ).
tff(761,plain,
store(store(q38,seq,earray_226),tail,s(index_225)) = queue_229,
inference(transitivity,[status(thm)],[760,742]) ).
tff(762,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(queue_229,head),
inference(monotonicity,[status(thm)],[761]) ).
tff(763,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(764,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(765,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(modus_ponens,[status(thm)],[764,763]) ).
tff(766,plain,
( ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(unit_resolution,[status(thm)],[765,32]) ).
tff(767,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head),
inference(unit_resolution,[status(thm)],[766,92]) ).
tff(768,plain,
select(store(q38,seq,earray_226),head) = select(store(store(q38,seq,earray_226),tail,s(index_225)),head),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
( ( earray_226 = store(earray_224,index_225,e38) )
<=> ( earray_226 = store(earray_224,index_225,e38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(770,axiom,
earray_226 = store(earray_224,index_225,e38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp42) ).
tff(771,plain,
earray_226 = store(earray_224,index_225,e38),
inference(modus_ponens,[status(thm)],[770,769]) ).
tff(772,plain,
store(earray_224,index_225,e38) = earray_226,
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = store(earray_224,index_225,e38) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(774,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = store(earray_224,index_225,e38),
inference(unit_resolution,[status(thm)],[773,6]) ).
tff(775,plain,
( ( q38 = queue_223 )
<=> ( q38 = queue_223 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(776,axiom,
q38 = queue_223,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp385) ).
tff(777,plain,
q38 = queue_223,
inference(modus_ponens,[status(thm)],[776,775]) ).
tff(778,plain,
queue_223 = q38,
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
( ( queue_223 = store(queue_221,tail,index_222) )
<=> ( queue_223 = store(queue_221,tail,index_222) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(780,axiom,
queue_223 = store(queue_221,tail,index_222),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp282) ).
tff(781,plain,
queue_223 = store(queue_221,tail,index_222),
inference(modus_ponens,[status(thm)],[780,779]) ).
tff(782,plain,
store(queue_221,tail,index_222) = queue_223,
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
store(queue_221,tail,index_222) = q38,
inference(transitivity,[status(thm)],[782,778]) ).
tff(784,plain,
store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)) = store(q38,seq,earray_226),
inference(monotonicity,[status(thm)],[783,772]) ).
tff(785,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = select(store(q38,seq,earray_226),seq),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
select(store(q38,seq,earray_226),seq) = select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq),
inference(symmetry,[status(thm)],[785]) ).
tff(787,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(788,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(789,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ),
inference(modus_ponens,[status(thm)],[788,787]) ).
tff(790,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq),
inference(unit_resolution,[status(thm)],[789,32,57]) ).
tff(791,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(queue_227,tail,index_228),seq),
inference(monotonicity,[status(thm)],[760]) ).
tff(792,plain,
select(store(queue_227,tail,index_228),seq) = select(store(store(q38,seq,earray_226),tail,s(index_225)),seq),
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(794,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(795,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ),
inference(modus_ponens,[status(thm)],[794,793]) ).
tff(796,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq),
inference(unit_resolution,[status(thm)],[795,32,25]) ).
tff(797,plain,
store(store(queue_227,tail,index_228),head,s(index_230)) = q39,
inference(transitivity,[status(thm)],[743,715,711]) ).
tff(798,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(q39,seq),
inference(monotonicity,[status(thm)],[797]) ).
tff(799,plain,
select(q39,seq) = select(store(store(queue_227,tail,index_228),head,s(index_230)),seq),
inference(symmetry,[status(thm)],[798]) ).
tff(800,plain,
select(q39,seq) = earray_226,
inference(transitivity,[status(thm)],[799,796,792,790,786,774,772]) ).
tff(801,plain,
store(store(queue_221,tail,index_222),seq,select(q39,seq)) = store(q38,seq,earray_226),
inference(monotonicity,[status(thm)],[783,800]) ).
tff(802,plain,
select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(q38,seq,earray_226),head),
inference(monotonicity,[status(thm)],[801]) ).
tff(803,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(804,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(805,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(modus_ponens,[status(thm)],[804,803]) ).
tff(806,plain,
( ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(unit_resolution,[status(thm)],[805,32]) ).
tff(807,plain,
select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head),
inference(unit_resolution,[status(thm)],[806,26]) ).
tff(808,plain,
select(store(queue_221,tail,index_222),head) = select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
( ( index_222 = s(index_219) )
<=> ( index_222 = s(index_219) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(810,axiom,
index_222 = s(index_219),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(811,plain,
index_222 = s(index_219),
inference(modus_ponens,[status(thm)],[810,809]) ).
tff(812,plain,
s(index_219) = index_222,
inference(symmetry,[status(thm)],[811]) ).
tff(813,plain,
( ( queue_221 = store(q37,seq,earray_220) )
<=> ( queue_221 = store(q37,seq,earray_220) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(814,axiom,
queue_221 = store(q37,seq,earray_220),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp281) ).
tff(815,plain,
queue_221 = store(q37,seq,earray_220),
inference(modus_ponens,[status(thm)],[814,813]) ).
tff(816,plain,
store(q37,seq,earray_220) = queue_221,
inference(symmetry,[status(thm)],[815]) ).
tff(817,plain,
store(store(q37,seq,earray_220),tail,s(index_219)) = store(queue_221,tail,index_222),
inference(monotonicity,[status(thm)],[816,812]) ).
tff(818,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(queue_221,tail,index_222),head),
inference(monotonicity,[status(thm)],[817]) ).
tff(819,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(820,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(821,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ),
inference(modus_ponens,[status(thm)],[820,819]) ).
tff(822,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head),
inference(unit_resolution,[status(thm)],[821,32,92]) ).
tff(823,plain,
select(store(q37,seq,earray_220),head) = select(store(store(q37,seq,earray_220),tail,s(index_219)),head),
inference(symmetry,[status(thm)],[822]) ).
tff(824,plain,
( ( earray_220 = store(earray_218,index_219,e37) )
<=> ( earray_220 = store(earray_218,index_219,e37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(825,axiom,
earray_220 = store(earray_218,index_219,e37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp40) ).
tff(826,plain,
earray_220 = store(earray_218,index_219,e37),
inference(modus_ponens,[status(thm)],[825,824]) ).
tff(827,plain,
store(earray_218,index_219,e37) = earray_220,
inference(symmetry,[status(thm)],[826]) ).
tff(828,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = store(earray_218,index_219,e37) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(829,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = store(earray_218,index_219,e37),
inference(unit_resolution,[status(thm)],[828,6]) ).
tff(830,plain,
( ( q37 = queue_217 )
<=> ( q37 = queue_217 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(831,axiom,
q37 = queue_217,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp384) ).
tff(832,plain,
q37 = queue_217,
inference(modus_ponens,[status(thm)],[831,830]) ).
tff(833,plain,
queue_217 = q37,
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
( ( queue_217 = store(queue_215,tail,index_216) )
<=> ( queue_217 = store(queue_215,tail,index_216) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(835,axiom,
queue_217 = store(queue_215,tail,index_216),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp280) ).
tff(836,plain,
queue_217 = store(queue_215,tail,index_216),
inference(modus_ponens,[status(thm)],[835,834]) ).
tff(837,plain,
store(queue_215,tail,index_216) = queue_217,
inference(symmetry,[status(thm)],[836]) ).
tff(838,plain,
store(queue_215,tail,index_216) = q37,
inference(transitivity,[status(thm)],[837,833]) ).
tff(839,plain,
store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)) = store(q37,seq,earray_220),
inference(monotonicity,[status(thm)],[838,827]) ).
tff(840,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = select(store(q37,seq,earray_220),seq),
inference(monotonicity,[status(thm)],[839]) ).
tff(841,plain,
select(store(q37,seq,earray_220),seq) = select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq),
inference(symmetry,[status(thm)],[840]) ).
tff(842,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(843,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(844,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ),
inference(modus_ponens,[status(thm)],[843,842]) ).
tff(845,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq),
inference(unit_resolution,[status(thm)],[844,32,57]) ).
tff(846,plain,
store(store(q37,seq,earray_220),tail,s(index_219)) = q38,
inference(transitivity,[status(thm)],[817,782,778]) ).
tff(847,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(q38,seq),
inference(monotonicity,[status(thm)],[846]) ).
tff(848,plain,
select(q38,seq) = select(store(store(q37,seq,earray_220),tail,s(index_219)),seq),
inference(symmetry,[status(thm)],[847]) ).
tff(849,plain,
select(q38,seq) = earray_220,
inference(transitivity,[status(thm)],[848,845,841,829,827]) ).
tff(850,plain,
store(store(queue_215,tail,index_216),seq,select(q38,seq)) = store(q37,seq,earray_220),
inference(monotonicity,[status(thm)],[838,849]) ).
tff(851,plain,
select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(q37,seq,earray_220),head),
inference(monotonicity,[status(thm)],[850]) ).
tff(852,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(853,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(854,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(modus_ponens,[status(thm)],[853,852]) ).
tff(855,plain,
select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head),
inference(unit_resolution,[status(thm)],[854,32,26]) ).
tff(856,plain,
select(store(queue_215,tail,index_216),head) = select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head),
inference(symmetry,[status(thm)],[855]) ).
tff(857,plain,
( ( index_216 = s(index_213) )
<=> ( index_216 = s(index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(858,axiom,
index_216 = s(index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(859,plain,
index_216 = s(index_213),
inference(modus_ponens,[status(thm)],[858,857]) ).
tff(860,plain,
s(index_213) = index_216,
inference(symmetry,[status(thm)],[859]) ).
tff(861,plain,
( ( queue_215 = store(q36,seq,earray_214) )
<=> ( queue_215 = store(q36,seq,earray_214) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(862,axiom,
queue_215 = store(q36,seq,earray_214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp279) ).
tff(863,plain,
queue_215 = store(q36,seq,earray_214),
inference(modus_ponens,[status(thm)],[862,861]) ).
tff(864,plain,
store(q36,seq,earray_214) = queue_215,
inference(symmetry,[status(thm)],[863]) ).
tff(865,plain,
store(store(q36,seq,earray_214),tail,s(index_213)) = store(queue_215,tail,index_216),
inference(monotonicity,[status(thm)],[864,860]) ).
tff(866,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(queue_215,tail,index_216),head),
inference(monotonicity,[status(thm)],[865]) ).
tff(867,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(868,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(869,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ),
inference(modus_ponens,[status(thm)],[868,867]) ).
tff(870,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head),
inference(unit_resolution,[status(thm)],[869,32,92]) ).
tff(871,plain,
select(store(q36,seq,earray_214),head) = select(store(store(q36,seq,earray_214),tail,s(index_213)),head),
inference(symmetry,[status(thm)],[870]) ).
tff(872,plain,
( ( earray_214 = store(earray_212,index_213,e36) )
<=> ( earray_214 = store(earray_212,index_213,e36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(873,axiom,
earray_214 = store(earray_212,index_213,e36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp37) ).
tff(874,plain,
earray_214 = store(earray_212,index_213,e36),
inference(modus_ponens,[status(thm)],[873,872]) ).
tff(875,plain,
store(earray_212,index_213,e36) = earray_214,
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = store(earray_212,index_213,e36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(877,plain,
select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = store(earray_212,index_213,e36),
inference(unit_resolution,[status(thm)],[876,6]) ).
tff(878,plain,
( ( q36 = queue_211 )
<=> ( q36 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(879,axiom,
q36 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp383) ).
tff(880,plain,
q36 = queue_211,
inference(modus_ponens,[status(thm)],[879,878]) ).
tff(881,plain,
queue_211 = q36,
inference(symmetry,[status(thm)],[880]) ).
tff(882,plain,
( ( queue_211 = store(queue_208,head,index_210) )
<=> ( queue_211 = store(queue_208,head,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(883,axiom,
queue_211 = store(queue_208,head,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp278) ).
tff(884,plain,
queue_211 = store(queue_208,head,index_210),
inference(modus_ponens,[status(thm)],[883,882]) ).
tff(885,plain,
store(queue_208,head,index_210) = queue_211,
inference(symmetry,[status(thm)],[884]) ).
tff(886,plain,
store(queue_208,head,index_210) = q36,
inference(transitivity,[status(thm)],[885,881]) ).
tff(887,plain,
store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)) = store(q36,seq,earray_214),
inference(monotonicity,[status(thm)],[886,875]) ).
tff(888,plain,
select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = select(store(q36,seq,earray_214),seq),
inference(monotonicity,[status(thm)],[887]) ).
tff(889,plain,
select(store(q36,seq,earray_214),seq) = select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq),
inference(symmetry,[status(thm)],[888]) ).
tff(890,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(891,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(892,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ),
inference(modus_ponens,[status(thm)],[891,890]) ).
tff(893,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq),
inference(unit_resolution,[status(thm)],[892,32,57]) ).
tff(894,plain,
store(store(q36,seq,earray_214),tail,s(index_213)) = q37,
inference(transitivity,[status(thm)],[865,837,833]) ).
tff(895,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(q37,seq),
inference(monotonicity,[status(thm)],[894]) ).
tff(896,plain,
select(q37,seq) = select(store(store(q36,seq,earray_214),tail,s(index_213)),seq),
inference(symmetry,[status(thm)],[895]) ).
tff(897,plain,
select(q37,seq) = earray_214,
inference(transitivity,[status(thm)],[896,893,889,877,875]) ).
tff(898,plain,
store(store(queue_208,head,index_210),seq,select(q37,seq)) = store(q36,seq,earray_214),
inference(monotonicity,[status(thm)],[886,897]) ).
tff(899,plain,
select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(q36,seq,earray_214),head),
inference(monotonicity,[status(thm)],[898]) ).
tff(900,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(901,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(902,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ),
inference(modus_ponens,[status(thm)],[901,900]) ).
tff(903,plain,
select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head),
inference(unit_resolution,[status(thm)],[902,32,26]) ).
tff(904,plain,
select(store(queue_208,head,index_210),head) = select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head),
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
( ( index_210 = s(index_209) )
<=> ( index_210 = s(index_209) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(906,axiom,
index_210 = s(index_209),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(907,plain,
index_210 = s(index_209),
inference(modus_ponens,[status(thm)],[906,905]) ).
tff(908,plain,
s(index_209) = index_210,
inference(symmetry,[status(thm)],[907]) ).
tff(909,plain,
( ( queue_208 = store(queue_206,tail,index_207) )
<=> ( queue_208 = store(queue_206,tail,index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(910,axiom,
queue_208 = store(queue_206,tail,index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp277) ).
tff(911,plain,
queue_208 = store(queue_206,tail,index_207),
inference(modus_ponens,[status(thm)],[910,909]) ).
tff(912,plain,
store(queue_206,tail,index_207) = queue_208,
inference(symmetry,[status(thm)],[911]) ).
tff(913,plain,
store(store(queue_206,tail,index_207),head,s(index_209)) = store(queue_208,head,index_210),
inference(monotonicity,[status(thm)],[912,908]) ).
tff(914,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = select(store(queue_208,head,index_210),head),
inference(monotonicity,[status(thm)],[913]) ).
tff(915,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = s(index_209) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(916,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = s(index_209),
inference(unit_resolution,[status(thm)],[915,6]) ).
tff(917,plain,
s(index_209) = select(store(store(queue_206,tail,index_207),head,s(index_209)),head),
inference(symmetry,[status(thm)],[916]) ).
tff(918,plain,
( ( index_209 = select(queue_208,head) )
<=> ( index_209 = select(queue_208,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(919,axiom,
index_209 = select(queue_208,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(920,plain,
index_209 = select(queue_208,head),
inference(modus_ponens,[status(thm)],[919,918]) ).
tff(921,plain,
select(queue_208,head) = index_209,
inference(symmetry,[status(thm)],[920]) ).
tff(922,plain,
( ( index_207 = s(index_204) )
<=> ( index_207 = s(index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(923,axiom,
index_207 = s(index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(924,plain,
index_207 = s(index_204),
inference(modus_ponens,[status(thm)],[923,922]) ).
tff(925,plain,
s(index_204) = index_207,
inference(symmetry,[status(thm)],[924]) ).
tff(926,plain,
( ( queue_206 = store(q35,seq,earray_205) )
<=> ( queue_206 = store(q35,seq,earray_205) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(927,axiom,
queue_206 = store(q35,seq,earray_205),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp276) ).
tff(928,plain,
queue_206 = store(q35,seq,earray_205),
inference(modus_ponens,[status(thm)],[927,926]) ).
tff(929,plain,
store(q35,seq,earray_205) = queue_206,
inference(symmetry,[status(thm)],[928]) ).
tff(930,plain,
store(store(q35,seq,earray_205),tail,s(index_204)) = store(queue_206,tail,index_207),
inference(monotonicity,[status(thm)],[929,925]) ).
tff(931,plain,
store(store(q35,seq,earray_205),tail,s(index_204)) = queue_208,
inference(transitivity,[status(thm)],[930,912]) ).
tff(932,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(queue_208,head),
inference(monotonicity,[status(thm)],[931]) ).
tff(933,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(934,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(935,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(modus_ponens,[status(thm)],[934,933]) ).
tff(936,plain,
( ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(unit_resolution,[status(thm)],[935,32]) ).
tff(937,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head),
inference(unit_resolution,[status(thm)],[936,92]) ).
tff(938,plain,
select(store(q35,seq,earray_205),head) = select(store(store(q35,seq,earray_205),tail,s(index_204)),head),
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
( ( earray_205 = store(earray_203,index_204,e35) )
<=> ( earray_205 = store(earray_203,index_204,e35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(940,axiom,
earray_205 = store(earray_203,index_204,e35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(941,plain,
earray_205 = store(earray_203,index_204,e35),
inference(modus_ponens,[status(thm)],[940,939]) ).
tff(942,plain,
store(earray_203,index_204,e35) = earray_205,
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = store(earray_203,index_204,e35) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(944,plain,
select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = store(earray_203,index_204,e35),
inference(unit_resolution,[status(thm)],[943,6]) ).
tff(945,plain,
( ( q35 = queue_202 )
<=> ( q35 = queue_202 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(946,axiom,
q35 = queue_202,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp382) ).
tff(947,plain,
q35 = queue_202,
inference(modus_ponens,[status(thm)],[946,945]) ).
tff(948,plain,
queue_202 = q35,
inference(symmetry,[status(thm)],[947]) ).
tff(949,plain,
( ( queue_202 = store(queue_200,tail,index_201) )
<=> ( queue_202 = store(queue_200,tail,index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(950,axiom,
queue_202 = store(queue_200,tail,index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp275) ).
tff(951,plain,
queue_202 = store(queue_200,tail,index_201),
inference(modus_ponens,[status(thm)],[950,949]) ).
tff(952,plain,
store(queue_200,tail,index_201) = queue_202,
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
store(queue_200,tail,index_201) = q35,
inference(transitivity,[status(thm)],[952,948]) ).
tff(954,plain,
store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)) = store(q35,seq,earray_205),
inference(monotonicity,[status(thm)],[953,942]) ).
tff(955,plain,
select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = select(store(q35,seq,earray_205),seq),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
select(store(q35,seq,earray_205),seq) = select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(958,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(959,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ),
inference(modus_ponens,[status(thm)],[958,957]) ).
tff(960,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq),
inference(unit_resolution,[status(thm)],[959,32,57]) ).
tff(961,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(queue_206,tail,index_207),seq),
inference(monotonicity,[status(thm)],[930]) ).
tff(962,plain,
select(store(queue_206,tail,index_207),seq) = select(store(store(q35,seq,earray_205),tail,s(index_204)),seq),
inference(symmetry,[status(thm)],[961]) ).
tff(963,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(964,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(965,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ),
inference(modus_ponens,[status(thm)],[964,963]) ).
tff(966,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq),
inference(unit_resolution,[status(thm)],[965,32,25]) ).
tff(967,plain,
store(store(queue_206,tail,index_207),head,s(index_209)) = q36,
inference(transitivity,[status(thm)],[913,885,881]) ).
tff(968,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(q36,seq),
inference(monotonicity,[status(thm)],[967]) ).
tff(969,plain,
select(q36,seq) = select(store(store(queue_206,tail,index_207),head,s(index_209)),seq),
inference(symmetry,[status(thm)],[968]) ).
tff(970,plain,
select(q36,seq) = earray_205,
inference(transitivity,[status(thm)],[969,966,962,960,956,944,942]) ).
tff(971,plain,
store(store(queue_200,tail,index_201),seq,select(q36,seq)) = store(q35,seq,earray_205),
inference(monotonicity,[status(thm)],[953,970]) ).
tff(972,plain,
select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(q35,seq,earray_205),head),
inference(monotonicity,[status(thm)],[971]) ).
tff(973,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(974,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(975,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(modus_ponens,[status(thm)],[974,973]) ).
tff(976,plain,
( ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(unit_resolution,[status(thm)],[975,32]) ).
tff(977,plain,
select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head),
inference(unit_resolution,[status(thm)],[976,26]) ).
tff(978,plain,
select(store(queue_200,tail,index_201),head) = select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head),
inference(symmetry,[status(thm)],[977]) ).
tff(979,plain,
( ( index_201 = s(index_198) )
<=> ( index_201 = s(index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(980,axiom,
index_201 = s(index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(981,plain,
index_201 = s(index_198),
inference(modus_ponens,[status(thm)],[980,979]) ).
tff(982,plain,
s(index_198) = index_201,
inference(symmetry,[status(thm)],[981]) ).
tff(983,plain,
( ( queue_200 = store(q34,seq,earray_199) )
<=> ( queue_200 = store(q34,seq,earray_199) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(984,axiom,
queue_200 = store(q34,seq,earray_199),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp274) ).
tff(985,plain,
queue_200 = store(q34,seq,earray_199),
inference(modus_ponens,[status(thm)],[984,983]) ).
tff(986,plain,
store(q34,seq,earray_199) = queue_200,
inference(symmetry,[status(thm)],[985]) ).
tff(987,plain,
store(store(q34,seq,earray_199),tail,s(index_198)) = store(queue_200,tail,index_201),
inference(monotonicity,[status(thm)],[986,982]) ).
tff(988,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(queue_200,tail,index_201),head),
inference(monotonicity,[status(thm)],[987]) ).
tff(989,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(990,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(991,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ),
inference(modus_ponens,[status(thm)],[990,989]) ).
tff(992,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head),
inference(unit_resolution,[status(thm)],[991,32,92]) ).
tff(993,plain,
select(store(q34,seq,earray_199),head) = select(store(store(q34,seq,earray_199),tail,s(index_198)),head),
inference(symmetry,[status(thm)],[992]) ).
tff(994,plain,
( ( earray_199 = store(earray_197,index_198,e34) )
<=> ( earray_199 = store(earray_197,index_198,e34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(995,axiom,
earray_199 = store(earray_197,index_198,e34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(996,plain,
earray_199 = store(earray_197,index_198,e34),
inference(modus_ponens,[status(thm)],[995,994]) ).
tff(997,plain,
store(earray_197,index_198,e34) = earray_199,
inference(symmetry,[status(thm)],[996]) ).
tff(998,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = store(earray_197,index_198,e34) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(999,plain,
select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = store(earray_197,index_198,e34),
inference(unit_resolution,[status(thm)],[998,6]) ).
tff(1000,plain,
( ( q34 = queue_196 )
<=> ( q34 = queue_196 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1001,axiom,
q34 = queue_196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp381) ).
tff(1002,plain,
q34 = queue_196,
inference(modus_ponens,[status(thm)],[1001,1000]) ).
tff(1003,plain,
queue_196 = q34,
inference(symmetry,[status(thm)],[1002]) ).
tff(1004,plain,
( ( queue_196 = store(queue_194,tail,index_195) )
<=> ( queue_196 = store(queue_194,tail,index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1005,axiom,
queue_196 = store(queue_194,tail,index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp273) ).
tff(1006,plain,
queue_196 = store(queue_194,tail,index_195),
inference(modus_ponens,[status(thm)],[1005,1004]) ).
tff(1007,plain,
store(queue_194,tail,index_195) = queue_196,
inference(symmetry,[status(thm)],[1006]) ).
tff(1008,plain,
store(queue_194,tail,index_195) = q34,
inference(transitivity,[status(thm)],[1007,1003]) ).
tff(1009,plain,
store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)) = store(q34,seq,earray_199),
inference(monotonicity,[status(thm)],[1008,997]) ).
tff(1010,plain,
select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = select(store(q34,seq,earray_199),seq),
inference(monotonicity,[status(thm)],[1009]) ).
tff(1011,plain,
select(store(q34,seq,earray_199),seq) = select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq),
inference(symmetry,[status(thm)],[1010]) ).
tff(1012,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1013,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1014,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ),
inference(modus_ponens,[status(thm)],[1013,1012]) ).
tff(1015,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq),
inference(unit_resolution,[status(thm)],[1014,32,57]) ).
tff(1016,plain,
store(store(q34,seq,earray_199),tail,s(index_198)) = q35,
inference(transitivity,[status(thm)],[987,952,948]) ).
tff(1017,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(q35,seq),
inference(monotonicity,[status(thm)],[1016]) ).
tff(1018,plain,
select(q35,seq) = select(store(store(q34,seq,earray_199),tail,s(index_198)),seq),
inference(symmetry,[status(thm)],[1017]) ).
tff(1019,plain,
select(q35,seq) = earray_199,
inference(transitivity,[status(thm)],[1018,1015,1011,999,997]) ).
tff(1020,plain,
store(store(queue_194,tail,index_195),seq,select(q35,seq)) = store(q34,seq,earray_199),
inference(monotonicity,[status(thm)],[1008,1019]) ).
tff(1021,plain,
select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(q34,seq,earray_199),head),
inference(monotonicity,[status(thm)],[1020]) ).
tff(1022,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1023,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1024,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ),
inference(modus_ponens,[status(thm)],[1023,1022]) ).
tff(1025,plain,
select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head),
inference(unit_resolution,[status(thm)],[1024,32,26]) ).
tff(1026,plain,
select(store(queue_194,tail,index_195),head) = select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head),
inference(symmetry,[status(thm)],[1025]) ).
tff(1027,plain,
( ( index_195 = s(index_192) )
<=> ( index_195 = s(index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1028,axiom,
index_195 = s(index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(1029,plain,
index_195 = s(index_192),
inference(modus_ponens,[status(thm)],[1028,1027]) ).
tff(1030,plain,
s(index_192) = index_195,
inference(symmetry,[status(thm)],[1029]) ).
tff(1031,plain,
( ( queue_194 = store(q33,seq,earray_193) )
<=> ( queue_194 = store(q33,seq,earray_193) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1032,axiom,
queue_194 = store(q33,seq,earray_193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp272) ).
tff(1033,plain,
queue_194 = store(q33,seq,earray_193),
inference(modus_ponens,[status(thm)],[1032,1031]) ).
tff(1034,plain,
store(q33,seq,earray_193) = queue_194,
inference(symmetry,[status(thm)],[1033]) ).
tff(1035,plain,
store(store(q33,seq,earray_193),tail,s(index_192)) = store(queue_194,tail,index_195),
inference(monotonicity,[status(thm)],[1034,1030]) ).
tff(1036,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(queue_194,tail,index_195),head),
inference(monotonicity,[status(thm)],[1035]) ).
tff(1037,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1038,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1039,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ),
inference(modus_ponens,[status(thm)],[1038,1037]) ).
tff(1040,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head),
inference(unit_resolution,[status(thm)],[1039,32,92]) ).
tff(1041,plain,
select(store(q33,seq,earray_193),head) = select(store(store(q33,seq,earray_193),tail,s(index_192)),head),
inference(symmetry,[status(thm)],[1040]) ).
tff(1042,plain,
( ( earray_193 = store(earray_191,index_192,e33) )
<=> ( earray_193 = store(earray_191,index_192,e33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1043,axiom,
earray_193 = store(earray_191,index_192,e33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(1044,plain,
earray_193 = store(earray_191,index_192,e33),
inference(modus_ponens,[status(thm)],[1043,1042]) ).
tff(1045,plain,
store(earray_191,index_192,e33) = earray_193,
inference(symmetry,[status(thm)],[1044]) ).
tff(1046,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = store(earray_191,index_192,e33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1047,plain,
select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = store(earray_191,index_192,e33),
inference(unit_resolution,[status(thm)],[1046,6]) ).
tff(1048,plain,
( ( q33 = queue_190 )
<=> ( q33 = queue_190 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1049,axiom,
q33 = queue_190,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp380) ).
tff(1050,plain,
q33 = queue_190,
inference(modus_ponens,[status(thm)],[1049,1048]) ).
tff(1051,plain,
queue_190 = q33,
inference(symmetry,[status(thm)],[1050]) ).
tff(1052,plain,
( ( queue_190 = store(queue_187,head,index_189) )
<=> ( queue_190 = store(queue_187,head,index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1053,axiom,
queue_190 = store(queue_187,head,index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp271) ).
tff(1054,plain,
queue_190 = store(queue_187,head,index_189),
inference(modus_ponens,[status(thm)],[1053,1052]) ).
tff(1055,plain,
store(queue_187,head,index_189) = queue_190,
inference(symmetry,[status(thm)],[1054]) ).
tff(1056,plain,
store(queue_187,head,index_189) = q33,
inference(transitivity,[status(thm)],[1055,1051]) ).
tff(1057,plain,
store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)) = store(q33,seq,earray_193),
inference(monotonicity,[status(thm)],[1056,1045]) ).
tff(1058,plain,
select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = select(store(q33,seq,earray_193),seq),
inference(monotonicity,[status(thm)],[1057]) ).
tff(1059,plain,
select(store(q33,seq,earray_193),seq) = select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq),
inference(symmetry,[status(thm)],[1058]) ).
tff(1060,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1062,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ),
inference(modus_ponens,[status(thm)],[1061,1060]) ).
tff(1063,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq),
inference(unit_resolution,[status(thm)],[1062,32,57]) ).
tff(1064,plain,
store(store(q33,seq,earray_193),tail,s(index_192)) = q34,
inference(transitivity,[status(thm)],[1035,1007,1003]) ).
tff(1065,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(q34,seq),
inference(monotonicity,[status(thm)],[1064]) ).
tff(1066,plain,
select(q34,seq) = select(store(store(q33,seq,earray_193),tail,s(index_192)),seq),
inference(symmetry,[status(thm)],[1065]) ).
tff(1067,plain,
select(q34,seq) = earray_193,
inference(transitivity,[status(thm)],[1066,1063,1059,1047,1045]) ).
tff(1068,plain,
store(store(queue_187,head,index_189),seq,select(q34,seq)) = store(q33,seq,earray_193),
inference(monotonicity,[status(thm)],[1056,1067]) ).
tff(1069,plain,
select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(q33,seq,earray_193),head),
inference(monotonicity,[status(thm)],[1068]) ).
tff(1070,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1071,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1072,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ),
inference(modus_ponens,[status(thm)],[1071,1070]) ).
tff(1073,plain,
select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head),
inference(unit_resolution,[status(thm)],[1072,32,26]) ).
tff(1074,plain,
select(store(queue_187,head,index_189),head) = select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head),
inference(symmetry,[status(thm)],[1073]) ).
tff(1075,plain,
( ( index_189 = s(index_188) )
<=> ( index_189 = s(index_188) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1076,axiom,
index_189 = s(index_188),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(1077,plain,
index_189 = s(index_188),
inference(modus_ponens,[status(thm)],[1076,1075]) ).
tff(1078,plain,
s(index_188) = index_189,
inference(symmetry,[status(thm)],[1077]) ).
tff(1079,plain,
( ( queue_187 = store(queue_185,tail,index_186) )
<=> ( queue_187 = store(queue_185,tail,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1080,axiom,
queue_187 = store(queue_185,tail,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp269) ).
tff(1081,plain,
queue_187 = store(queue_185,tail,index_186),
inference(modus_ponens,[status(thm)],[1080,1079]) ).
tff(1082,plain,
store(queue_185,tail,index_186) = queue_187,
inference(symmetry,[status(thm)],[1081]) ).
tff(1083,plain,
store(store(queue_185,tail,index_186),head,s(index_188)) = store(queue_187,head,index_189),
inference(monotonicity,[status(thm)],[1082,1078]) ).
tff(1084,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = select(store(queue_187,head,index_189),head),
inference(monotonicity,[status(thm)],[1083]) ).
tff(1085,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = s(index_188) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1086,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = s(index_188),
inference(unit_resolution,[status(thm)],[1085,6]) ).
tff(1087,plain,
s(index_188) = select(store(store(queue_185,tail,index_186),head,s(index_188)),head),
inference(symmetry,[status(thm)],[1086]) ).
tff(1088,plain,
( ( index_188 = select(queue_187,head) )
<=> ( index_188 = select(queue_187,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1089,axiom,
index_188 = select(queue_187,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(1090,plain,
index_188 = select(queue_187,head),
inference(modus_ponens,[status(thm)],[1089,1088]) ).
tff(1091,plain,
select(queue_187,head) = index_188,
inference(symmetry,[status(thm)],[1090]) ).
tff(1092,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1093,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(1094,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[1093,1092]) ).
tff(1095,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[1094]) ).
tff(1096,plain,
( ( queue_185 = store(q32,seq,earray_184) )
<=> ( queue_185 = store(q32,seq,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1097,axiom,
queue_185 = store(q32,seq,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp268) ).
tff(1098,plain,
queue_185 = store(q32,seq,earray_184),
inference(modus_ponens,[status(thm)],[1097,1096]) ).
tff(1099,plain,
store(q32,seq,earray_184) = queue_185,
inference(symmetry,[status(thm)],[1098]) ).
tff(1100,plain,
store(store(q32,seq,earray_184),tail,s(index_183)) = store(queue_185,tail,index_186),
inference(monotonicity,[status(thm)],[1099,1095]) ).
tff(1101,plain,
store(store(q32,seq,earray_184),tail,s(index_183)) = queue_187,
inference(transitivity,[status(thm)],[1100,1082]) ).
tff(1102,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(queue_187,head),
inference(monotonicity,[status(thm)],[1101]) ).
tff(1103,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1104,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1105,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(modus_ponens,[status(thm)],[1104,1103]) ).
tff(1106,plain,
( ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(unit_resolution,[status(thm)],[1105,32]) ).
tff(1107,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head),
inference(unit_resolution,[status(thm)],[1106,92]) ).
tff(1108,plain,
select(store(q32,seq,earray_184),head) = select(store(store(q32,seq,earray_184),tail,s(index_183)),head),
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
( ( earray_184 = store(earray_182,index_183,e32) )
<=> ( earray_184 = store(earray_182,index_183,e32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1110,axiom,
earray_184 = store(earray_182,index_183,e32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(1111,plain,
earray_184 = store(earray_182,index_183,e32),
inference(modus_ponens,[status(thm)],[1110,1109]) ).
tff(1112,plain,
store(earray_182,index_183,e32) = earray_184,
inference(symmetry,[status(thm)],[1111]) ).
tff(1113,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = store(earray_182,index_183,e32) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1114,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = store(earray_182,index_183,e32),
inference(unit_resolution,[status(thm)],[1113,6]) ).
tff(1115,plain,
( ( q32 = queue_181 )
<=> ( q32 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1116,axiom,
q32 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp379) ).
tff(1117,plain,
q32 = queue_181,
inference(modus_ponens,[status(thm)],[1116,1115]) ).
tff(1118,plain,
queue_181 = q32,
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ( queue_181 = store(queue_179,tail,index_180) )
<=> ( queue_181 = store(queue_179,tail,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1120,axiom,
queue_181 = store(queue_179,tail,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp267) ).
tff(1121,plain,
queue_181 = store(queue_179,tail,index_180),
inference(modus_ponens,[status(thm)],[1120,1119]) ).
tff(1122,plain,
store(queue_179,tail,index_180) = queue_181,
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
store(queue_179,tail,index_180) = q32,
inference(transitivity,[status(thm)],[1122,1118]) ).
tff(1124,plain,
store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)) = store(q32,seq,earray_184),
inference(monotonicity,[status(thm)],[1123,1112]) ).
tff(1125,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = select(store(q32,seq,earray_184),seq),
inference(monotonicity,[status(thm)],[1124]) ).
tff(1126,plain,
select(store(q32,seq,earray_184),seq) = select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq),
inference(symmetry,[status(thm)],[1125]) ).
tff(1127,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1128,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1129,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ),
inference(modus_ponens,[status(thm)],[1128,1127]) ).
tff(1130,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq),
inference(unit_resolution,[status(thm)],[1129,32,57]) ).
tff(1131,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(queue_185,tail,index_186),seq),
inference(monotonicity,[status(thm)],[1100]) ).
tff(1132,plain,
select(store(queue_185,tail,index_186),seq) = select(store(store(q32,seq,earray_184),tail,s(index_183)),seq),
inference(symmetry,[status(thm)],[1131]) ).
tff(1133,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1134,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1135,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ),
inference(modus_ponens,[status(thm)],[1134,1133]) ).
tff(1136,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq),
inference(unit_resolution,[status(thm)],[1135,32,25]) ).
tff(1137,plain,
store(store(queue_185,tail,index_186),head,s(index_188)) = q33,
inference(transitivity,[status(thm)],[1083,1055,1051]) ).
tff(1138,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(q33,seq),
inference(monotonicity,[status(thm)],[1137]) ).
tff(1139,plain,
select(q33,seq) = select(store(store(queue_185,tail,index_186),head,s(index_188)),seq),
inference(symmetry,[status(thm)],[1138]) ).
tff(1140,plain,
select(q33,seq) = earray_184,
inference(transitivity,[status(thm)],[1139,1136,1132,1130,1126,1114,1112]) ).
tff(1141,plain,
store(store(queue_179,tail,index_180),seq,select(q33,seq)) = store(q32,seq,earray_184),
inference(monotonicity,[status(thm)],[1123,1140]) ).
tff(1142,plain,
select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(q32,seq,earray_184),head),
inference(monotonicity,[status(thm)],[1141]) ).
tff(1143,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1144,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1145,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(modus_ponens,[status(thm)],[1144,1143]) ).
tff(1146,plain,
( ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(unit_resolution,[status(thm)],[1145,32]) ).
tff(1147,plain,
select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head),
inference(unit_resolution,[status(thm)],[1146,26]) ).
tff(1148,plain,
select(store(queue_179,tail,index_180),head) = select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head),
inference(symmetry,[status(thm)],[1147]) ).
tff(1149,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1150,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(1151,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[1150,1149]) ).
tff(1152,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[1151]) ).
tff(1153,plain,
( ( queue_179 = store(q31,seq,earray_178) )
<=> ( queue_179 = store(q31,seq,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1154,axiom,
queue_179 = store(q31,seq,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp266) ).
tff(1155,plain,
queue_179 = store(q31,seq,earray_178),
inference(modus_ponens,[status(thm)],[1154,1153]) ).
tff(1156,plain,
store(q31,seq,earray_178) = queue_179,
inference(symmetry,[status(thm)],[1155]) ).
tff(1157,plain,
store(store(q31,seq,earray_178),tail,s(index_177)) = store(queue_179,tail,index_180),
inference(monotonicity,[status(thm)],[1156,1152]) ).
tff(1158,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(queue_179,tail,index_180),head),
inference(monotonicity,[status(thm)],[1157]) ).
tff(1159,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1160,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1161,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ),
inference(modus_ponens,[status(thm)],[1160,1159]) ).
tff(1162,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head),
inference(unit_resolution,[status(thm)],[1161,32,92]) ).
tff(1163,plain,
select(store(q31,seq,earray_178),head) = select(store(store(q31,seq,earray_178),tail,s(index_177)),head),
inference(symmetry,[status(thm)],[1162]) ).
tff(1164,plain,
( ( earray_178 = store(earray_176,index_177,e31) )
<=> ( earray_178 = store(earray_176,index_177,e31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1165,axiom,
earray_178 = store(earray_176,index_177,e31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(1166,plain,
earray_178 = store(earray_176,index_177,e31),
inference(modus_ponens,[status(thm)],[1165,1164]) ).
tff(1167,plain,
store(earray_176,index_177,e31) = earray_178,
inference(symmetry,[status(thm)],[1166]) ).
tff(1168,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = store(earray_176,index_177,e31) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1169,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = store(earray_176,index_177,e31),
inference(unit_resolution,[status(thm)],[1168,6]) ).
tff(1170,plain,
( ( q31 = queue_175 )
<=> ( q31 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1171,axiom,
q31 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp378) ).
tff(1172,plain,
q31 = queue_175,
inference(modus_ponens,[status(thm)],[1171,1170]) ).
tff(1173,plain,
queue_175 = q31,
inference(symmetry,[status(thm)],[1172]) ).
tff(1174,plain,
( ( queue_175 = store(queue_173,tail,index_174) )
<=> ( queue_175 = store(queue_173,tail,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1175,axiom,
queue_175 = store(queue_173,tail,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp265) ).
tff(1176,plain,
queue_175 = store(queue_173,tail,index_174),
inference(modus_ponens,[status(thm)],[1175,1174]) ).
tff(1177,plain,
store(queue_173,tail,index_174) = queue_175,
inference(symmetry,[status(thm)],[1176]) ).
tff(1178,plain,
store(queue_173,tail,index_174) = q31,
inference(transitivity,[status(thm)],[1177,1173]) ).
tff(1179,plain,
store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)) = store(q31,seq,earray_178),
inference(monotonicity,[status(thm)],[1178,1167]) ).
tff(1180,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = select(store(q31,seq,earray_178),seq),
inference(monotonicity,[status(thm)],[1179]) ).
tff(1181,plain,
select(store(q31,seq,earray_178),seq) = select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq),
inference(symmetry,[status(thm)],[1180]) ).
tff(1182,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1183,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1184,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ),
inference(modus_ponens,[status(thm)],[1183,1182]) ).
tff(1185,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq),
inference(unit_resolution,[status(thm)],[1184,32,57]) ).
tff(1186,plain,
store(store(q31,seq,earray_178),tail,s(index_177)) = q32,
inference(transitivity,[status(thm)],[1157,1122,1118]) ).
tff(1187,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(q32,seq),
inference(monotonicity,[status(thm)],[1186]) ).
tff(1188,plain,
select(q32,seq) = select(store(store(q31,seq,earray_178),tail,s(index_177)),seq),
inference(symmetry,[status(thm)],[1187]) ).
tff(1189,plain,
select(q32,seq) = earray_178,
inference(transitivity,[status(thm)],[1188,1185,1181,1169,1167]) ).
tff(1190,plain,
store(store(queue_173,tail,index_174),seq,select(q32,seq)) = store(q31,seq,earray_178),
inference(monotonicity,[status(thm)],[1178,1189]) ).
tff(1191,plain,
select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(q31,seq,earray_178),head),
inference(monotonicity,[status(thm)],[1190]) ).
tff(1192,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1193,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1194,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(modus_ponens,[status(thm)],[1193,1192]) ).
tff(1195,plain,
select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head),
inference(unit_resolution,[status(thm)],[1194,32,26]) ).
tff(1196,plain,
select(store(queue_173,tail,index_174),head) = select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head),
inference(symmetry,[status(thm)],[1195]) ).
tff(1197,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1198,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(1199,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[1198,1197]) ).
tff(1200,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[1199]) ).
tff(1201,plain,
( ( queue_173 = store(q30,seq,earray_172) )
<=> ( queue_173 = store(q30,seq,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1202,axiom,
queue_173 = store(q30,seq,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp264) ).
tff(1203,plain,
queue_173 = store(q30,seq,earray_172),
inference(modus_ponens,[status(thm)],[1202,1201]) ).
tff(1204,plain,
store(q30,seq,earray_172) = queue_173,
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
store(store(q30,seq,earray_172),tail,s(index_171)) = store(queue_173,tail,index_174),
inference(monotonicity,[status(thm)],[1204,1200]) ).
tff(1206,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(queue_173,tail,index_174),head),
inference(monotonicity,[status(thm)],[1205]) ).
tff(1207,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1208,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1209,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ),
inference(modus_ponens,[status(thm)],[1208,1207]) ).
tff(1210,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head),
inference(unit_resolution,[status(thm)],[1209,32,92]) ).
tff(1211,plain,
select(store(q30,seq,earray_172),head) = select(store(store(q30,seq,earray_172),tail,s(index_171)),head),
inference(symmetry,[status(thm)],[1210]) ).
tff(1212,plain,
( ( earray_172 = store(earray_170,index_171,e30) )
<=> ( earray_172 = store(earray_170,index_171,e30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1213,axiom,
earray_172 = store(earray_170,index_171,e30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(1214,plain,
earray_172 = store(earray_170,index_171,e30),
inference(modus_ponens,[status(thm)],[1213,1212]) ).
tff(1215,plain,
store(earray_170,index_171,e30) = earray_172,
inference(symmetry,[status(thm)],[1214]) ).
tff(1216,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = store(earray_170,index_171,e30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1217,plain,
select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = store(earray_170,index_171,e30),
inference(unit_resolution,[status(thm)],[1216,6]) ).
tff(1218,plain,
( ( q30 = queue_169 )
<=> ( q30 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1219,axiom,
q30 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp377) ).
tff(1220,plain,
q30 = queue_169,
inference(modus_ponens,[status(thm)],[1219,1218]) ).
tff(1221,plain,
queue_169 = q30,
inference(symmetry,[status(thm)],[1220]) ).
tff(1222,plain,
( ( queue_169 = store(queue_166,head,index_168) )
<=> ( queue_169 = store(queue_166,head,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1223,axiom,
queue_169 = store(queue_166,head,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp262) ).
tff(1224,plain,
queue_169 = store(queue_166,head,index_168),
inference(modus_ponens,[status(thm)],[1223,1222]) ).
tff(1225,plain,
store(queue_166,head,index_168) = queue_169,
inference(symmetry,[status(thm)],[1224]) ).
tff(1226,plain,
store(queue_166,head,index_168) = q30,
inference(transitivity,[status(thm)],[1225,1221]) ).
tff(1227,plain,
store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)) = store(q30,seq,earray_172),
inference(monotonicity,[status(thm)],[1226,1215]) ).
tff(1228,plain,
select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = select(store(q30,seq,earray_172),seq),
inference(monotonicity,[status(thm)],[1227]) ).
tff(1229,plain,
select(store(q30,seq,earray_172),seq) = select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq),
inference(symmetry,[status(thm)],[1228]) ).
tff(1230,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1231,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1232,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ),
inference(modus_ponens,[status(thm)],[1231,1230]) ).
tff(1233,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq),
inference(unit_resolution,[status(thm)],[1232,32,57]) ).
tff(1234,plain,
store(store(q30,seq,earray_172),tail,s(index_171)) = q31,
inference(transitivity,[status(thm)],[1205,1177,1173]) ).
tff(1235,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(q31,seq),
inference(monotonicity,[status(thm)],[1234]) ).
tff(1236,plain,
select(q31,seq) = select(store(store(q30,seq,earray_172),tail,s(index_171)),seq),
inference(symmetry,[status(thm)],[1235]) ).
tff(1237,plain,
select(q31,seq) = earray_172,
inference(transitivity,[status(thm)],[1236,1233,1229,1217,1215]) ).
tff(1238,plain,
store(store(queue_166,head,index_168),seq,select(q31,seq)) = store(q30,seq,earray_172),
inference(monotonicity,[status(thm)],[1226,1237]) ).
tff(1239,plain,
select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(q30,seq,earray_172),head),
inference(monotonicity,[status(thm)],[1238]) ).
tff(1240,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1241,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1242,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ),
inference(modus_ponens,[status(thm)],[1241,1240]) ).
tff(1243,plain,
select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head),
inference(unit_resolution,[status(thm)],[1242,32,26]) ).
tff(1244,plain,
select(store(queue_166,head,index_168),head) = select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head),
inference(symmetry,[status(thm)],[1243]) ).
tff(1245,plain,
( ( index_168 = s(index_167) )
<=> ( index_168 = s(index_167) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1246,axiom,
index_168 = s(index_167),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(1247,plain,
index_168 = s(index_167),
inference(modus_ponens,[status(thm)],[1246,1245]) ).
tff(1248,plain,
s(index_167) = index_168,
inference(symmetry,[status(thm)],[1247]) ).
tff(1249,plain,
( ( queue_166 = store(queue_164,tail,index_165) )
<=> ( queue_166 = store(queue_164,tail,index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1250,axiom,
queue_166 = store(queue_164,tail,index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp261) ).
tff(1251,plain,
queue_166 = store(queue_164,tail,index_165),
inference(modus_ponens,[status(thm)],[1250,1249]) ).
tff(1252,plain,
store(queue_164,tail,index_165) = queue_166,
inference(symmetry,[status(thm)],[1251]) ).
tff(1253,plain,
store(store(queue_164,tail,index_165),head,s(index_167)) = store(queue_166,head,index_168),
inference(monotonicity,[status(thm)],[1252,1248]) ).
tff(1254,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = select(store(queue_166,head,index_168),head),
inference(monotonicity,[status(thm)],[1253]) ).
tff(1255,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = s(index_167) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1256,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = s(index_167),
inference(unit_resolution,[status(thm)],[1255,6]) ).
tff(1257,plain,
s(index_167) = select(store(store(queue_164,tail,index_165),head,s(index_167)),head),
inference(symmetry,[status(thm)],[1256]) ).
tff(1258,plain,
( ( index_167 = select(queue_166,head) )
<=> ( index_167 = select(queue_166,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1259,axiom,
index_167 = select(queue_166,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(1260,plain,
index_167 = select(queue_166,head),
inference(modus_ponens,[status(thm)],[1259,1258]) ).
tff(1261,plain,
select(queue_166,head) = index_167,
inference(symmetry,[status(thm)],[1260]) ).
tff(1262,plain,
( ( index_165 = s(index_162) )
<=> ( index_165 = s(index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1263,axiom,
index_165 = s(index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(1264,plain,
index_165 = s(index_162),
inference(modus_ponens,[status(thm)],[1263,1262]) ).
tff(1265,plain,
s(index_162) = index_165,
inference(symmetry,[status(thm)],[1264]) ).
tff(1266,plain,
( ( queue_164 = store(q29,seq,earray_163) )
<=> ( queue_164 = store(q29,seq,earray_163) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1267,axiom,
queue_164 = store(q29,seq,earray_163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp260) ).
tff(1268,plain,
queue_164 = store(q29,seq,earray_163),
inference(modus_ponens,[status(thm)],[1267,1266]) ).
tff(1269,plain,
store(q29,seq,earray_163) = queue_164,
inference(symmetry,[status(thm)],[1268]) ).
tff(1270,plain,
store(store(q29,seq,earray_163),tail,s(index_162)) = store(queue_164,tail,index_165),
inference(monotonicity,[status(thm)],[1269,1265]) ).
tff(1271,plain,
store(store(q29,seq,earray_163),tail,s(index_162)) = queue_166,
inference(transitivity,[status(thm)],[1270,1252]) ).
tff(1272,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(queue_166,head),
inference(monotonicity,[status(thm)],[1271]) ).
tff(1273,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1274,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1275,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(modus_ponens,[status(thm)],[1274,1273]) ).
tff(1276,plain,
( ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(unit_resolution,[status(thm)],[1275,32]) ).
tff(1277,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head),
inference(unit_resolution,[status(thm)],[1276,92]) ).
tff(1278,plain,
select(store(q29,seq,earray_163),head) = select(store(store(q29,seq,earray_163),tail,s(index_162)),head),
inference(symmetry,[status(thm)],[1277]) ).
tff(1279,plain,
( ( earray_163 = store(earray_161,index_162,e29) )
<=> ( earray_163 = store(earray_161,index_162,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1280,axiom,
earray_163 = store(earray_161,index_162,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp21) ).
tff(1281,plain,
earray_163 = store(earray_161,index_162,e29),
inference(modus_ponens,[status(thm)],[1280,1279]) ).
tff(1282,plain,
store(earray_161,index_162,e29) = earray_163,
inference(symmetry,[status(thm)],[1281]) ).
tff(1283,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = store(earray_161,index_162,e29) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1284,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = store(earray_161,index_162,e29),
inference(unit_resolution,[status(thm)],[1283,6]) ).
tff(1285,plain,
( ( q29 = queue_151 )
<=> ( q29 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1286,axiom,
q29 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp375) ).
tff(1287,plain,
q29 = queue_151,
inference(modus_ponens,[status(thm)],[1286,1285]) ).
tff(1288,plain,
queue_151 = q29,
inference(symmetry,[status(thm)],[1287]) ).
tff(1289,plain,
( ( queue_151 = store(queue_149,tail,index_150) )
<=> ( queue_151 = store(queue_149,tail,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1290,axiom,
queue_151 = store(queue_149,tail,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp256) ).
tff(1291,plain,
queue_151 = store(queue_149,tail,index_150),
inference(modus_ponens,[status(thm)],[1290,1289]) ).
tff(1292,plain,
store(queue_149,tail,index_150) = queue_151,
inference(symmetry,[status(thm)],[1291]) ).
tff(1293,plain,
store(queue_149,tail,index_150) = q29,
inference(transitivity,[status(thm)],[1292,1288]) ).
tff(1294,plain,
store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)) = store(q29,seq,earray_163),
inference(monotonicity,[status(thm)],[1293,1282]) ).
tff(1295,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = select(store(q29,seq,earray_163),seq),
inference(monotonicity,[status(thm)],[1294]) ).
tff(1296,plain,
select(store(q29,seq,earray_163),seq) = select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq),
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1298,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1299,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ),
inference(modus_ponens,[status(thm)],[1298,1297]) ).
tff(1300,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq),
inference(unit_resolution,[status(thm)],[1299,32,57]) ).
tff(1301,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(queue_164,tail,index_165),seq),
inference(monotonicity,[status(thm)],[1270]) ).
tff(1302,plain,
select(store(queue_164,tail,index_165),seq) = select(store(store(q29,seq,earray_163),tail,s(index_162)),seq),
inference(symmetry,[status(thm)],[1301]) ).
tff(1303,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1304,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1305,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ),
inference(modus_ponens,[status(thm)],[1304,1303]) ).
tff(1306,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq),
inference(unit_resolution,[status(thm)],[1305,32,25]) ).
tff(1307,plain,
store(store(queue_164,tail,index_165),head,s(index_167)) = q30,
inference(transitivity,[status(thm)],[1253,1225,1221]) ).
tff(1308,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(q30,seq),
inference(monotonicity,[status(thm)],[1307]) ).
tff(1309,plain,
select(q30,seq) = select(store(store(queue_164,tail,index_165),head,s(index_167)),seq),
inference(symmetry,[status(thm)],[1308]) ).
tff(1310,plain,
select(q30,seq) = earray_163,
inference(transitivity,[status(thm)],[1309,1306,1302,1300,1296,1284,1282]) ).
tff(1311,plain,
store(store(queue_149,tail,index_150),seq,select(q30,seq)) = store(q29,seq,earray_163),
inference(monotonicity,[status(thm)],[1293,1310]) ).
tff(1312,plain,
select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(q29,seq,earray_163),head),
inference(monotonicity,[status(thm)],[1311]) ).
tff(1313,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1314,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1315,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(modus_ponens,[status(thm)],[1314,1313]) ).
tff(1316,plain,
( ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(unit_resolution,[status(thm)],[1315,32]) ).
tff(1317,plain,
select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head),
inference(unit_resolution,[status(thm)],[1316,26]) ).
tff(1318,plain,
select(store(queue_149,tail,index_150),head) = select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head),
inference(symmetry,[status(thm)],[1317]) ).
tff(1319,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1320,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(1321,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[1320,1319]) ).
tff(1322,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[1321]) ).
tff(1323,plain,
( ( queue_149 = store(q28,seq,earray_148) )
<=> ( queue_149 = store(q28,seq,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1324,axiom,
queue_149 = store(q28,seq,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp255) ).
tff(1325,plain,
queue_149 = store(q28,seq,earray_148),
inference(modus_ponens,[status(thm)],[1324,1323]) ).
tff(1326,plain,
store(q28,seq,earray_148) = queue_149,
inference(symmetry,[status(thm)],[1325]) ).
tff(1327,plain,
store(store(q28,seq,earray_148),tail,s(index_147)) = store(queue_149,tail,index_150),
inference(monotonicity,[status(thm)],[1326,1322]) ).
tff(1328,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(queue_149,tail,index_150),head),
inference(monotonicity,[status(thm)],[1327]) ).
tff(1329,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1330,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1331,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ),
inference(modus_ponens,[status(thm)],[1330,1329]) ).
tff(1332,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head),
inference(unit_resolution,[status(thm)],[1331,32,92]) ).
tff(1333,plain,
select(store(q28,seq,earray_148),head) = select(store(store(q28,seq,earray_148),tail,s(index_147)),head),
inference(symmetry,[status(thm)],[1332]) ).
tff(1334,plain,
( ( earray_148 = store(earray_146,index_147,e28) )
<=> ( earray_148 = store(earray_146,index_147,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1335,axiom,
earray_148 = store(earray_146,index_147,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(1336,plain,
earray_148 = store(earray_146,index_147,e28),
inference(modus_ponens,[status(thm)],[1335,1334]) ).
tff(1337,plain,
store(earray_146,index_147,e28) = earray_148,
inference(symmetry,[status(thm)],[1336]) ).
tff(1338,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = store(earray_146,index_147,e28) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1339,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = store(earray_146,index_147,e28),
inference(unit_resolution,[status(thm)],[1338,6]) ).
tff(1340,plain,
( ( q28 = queue_145 )
<=> ( q28 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1341,axiom,
q28 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp374) ).
tff(1342,plain,
q28 = queue_145,
inference(modus_ponens,[status(thm)],[1341,1340]) ).
tff(1343,plain,
queue_145 = q28,
inference(symmetry,[status(thm)],[1342]) ).
tff(1344,plain,
( ( queue_145 = store(queue_143,tail,index_144) )
<=> ( queue_145 = store(queue_143,tail,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1345,axiom,
queue_145 = store(queue_143,tail,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp254) ).
tff(1346,plain,
queue_145 = store(queue_143,tail,index_144),
inference(modus_ponens,[status(thm)],[1345,1344]) ).
tff(1347,plain,
store(queue_143,tail,index_144) = queue_145,
inference(symmetry,[status(thm)],[1346]) ).
tff(1348,plain,
store(queue_143,tail,index_144) = q28,
inference(transitivity,[status(thm)],[1347,1343]) ).
tff(1349,plain,
store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)) = store(q28,seq,earray_148),
inference(monotonicity,[status(thm)],[1348,1337]) ).
tff(1350,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = select(store(q28,seq,earray_148),seq),
inference(monotonicity,[status(thm)],[1349]) ).
tff(1351,plain,
select(store(q28,seq,earray_148),seq) = select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq),
inference(symmetry,[status(thm)],[1350]) ).
tff(1352,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1353,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1354,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ),
inference(modus_ponens,[status(thm)],[1353,1352]) ).
tff(1355,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq),
inference(unit_resolution,[status(thm)],[1354,32,57]) ).
tff(1356,plain,
store(store(q28,seq,earray_148),tail,s(index_147)) = q29,
inference(transitivity,[status(thm)],[1327,1292,1288]) ).
tff(1357,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(q29,seq),
inference(monotonicity,[status(thm)],[1356]) ).
tff(1358,plain,
select(q29,seq) = select(store(store(q28,seq,earray_148),tail,s(index_147)),seq),
inference(symmetry,[status(thm)],[1357]) ).
tff(1359,plain,
select(q29,seq) = earray_148,
inference(transitivity,[status(thm)],[1358,1355,1351,1339,1337]) ).
tff(1360,plain,
store(store(queue_143,tail,index_144),seq,select(q29,seq)) = store(q28,seq,earray_148),
inference(monotonicity,[status(thm)],[1348,1359]) ).
tff(1361,plain,
select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(q28,seq,earray_148),head),
inference(monotonicity,[status(thm)],[1360]) ).
tff(1362,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1363,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1364,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(modus_ponens,[status(thm)],[1363,1362]) ).
tff(1365,plain,
select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head),
inference(unit_resolution,[status(thm)],[1364,32,26]) ).
tff(1366,plain,
select(store(queue_143,tail,index_144),head) = select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head),
inference(symmetry,[status(thm)],[1365]) ).
tff(1367,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1368,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(1369,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[1368,1367]) ).
tff(1370,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[1369]) ).
tff(1371,plain,
( ( queue_143 = store(q27,seq,earray_142) )
<=> ( queue_143 = store(q27,seq,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1372,axiom,
queue_143 = store(q27,seq,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp253) ).
tff(1373,plain,
queue_143 = store(q27,seq,earray_142),
inference(modus_ponens,[status(thm)],[1372,1371]) ).
tff(1374,plain,
store(q27,seq,earray_142) = queue_143,
inference(symmetry,[status(thm)],[1373]) ).
tff(1375,plain,
store(store(q27,seq,earray_142),tail,s(index_141)) = store(queue_143,tail,index_144),
inference(monotonicity,[status(thm)],[1374,1370]) ).
tff(1376,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(queue_143,tail,index_144),head),
inference(monotonicity,[status(thm)],[1375]) ).
tff(1377,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1378,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1379,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ),
inference(modus_ponens,[status(thm)],[1378,1377]) ).
tff(1380,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head),
inference(unit_resolution,[status(thm)],[1379,32,92]) ).
tff(1381,plain,
select(store(q27,seq,earray_142),head) = select(store(store(q27,seq,earray_142),tail,s(index_141)),head),
inference(symmetry,[status(thm)],[1380]) ).
tff(1382,plain,
( ( earray_142 = store(earray_140,index_141,e27) )
<=> ( earray_142 = store(earray_140,index_141,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1383,axiom,
earray_142 = store(earray_140,index_141,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp14) ).
tff(1384,plain,
earray_142 = store(earray_140,index_141,e27),
inference(modus_ponens,[status(thm)],[1383,1382]) ).
tff(1385,plain,
store(earray_140,index_141,e27) = earray_142,
inference(symmetry,[status(thm)],[1384]) ).
tff(1386,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = store(earray_140,index_141,e27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1387,plain,
select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = store(earray_140,index_141,e27),
inference(unit_resolution,[status(thm)],[1386,6]) ).
tff(1388,plain,
( ( q27 = queue_139 )
<=> ( q27 = queue_139 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1389,axiom,
q27 = queue_139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp373) ).
tff(1390,plain,
q27 = queue_139,
inference(modus_ponens,[status(thm)],[1389,1388]) ).
tff(1391,plain,
queue_139 = q27,
inference(symmetry,[status(thm)],[1390]) ).
tff(1392,plain,
( ( queue_139 = store(queue_136,head,index_138) )
<=> ( queue_139 = store(queue_136,head,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1393,axiom,
queue_139 = store(queue_136,head,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp252) ).
tff(1394,plain,
queue_139 = store(queue_136,head,index_138),
inference(modus_ponens,[status(thm)],[1393,1392]) ).
tff(1395,plain,
store(queue_136,head,index_138) = queue_139,
inference(symmetry,[status(thm)],[1394]) ).
tff(1396,plain,
store(queue_136,head,index_138) = q27,
inference(transitivity,[status(thm)],[1395,1391]) ).
tff(1397,plain,
store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)) = store(q27,seq,earray_142),
inference(monotonicity,[status(thm)],[1396,1385]) ).
tff(1398,plain,
select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = select(store(q27,seq,earray_142),seq),
inference(monotonicity,[status(thm)],[1397]) ).
tff(1399,plain,
select(store(q27,seq,earray_142),seq) = select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq),
inference(symmetry,[status(thm)],[1398]) ).
tff(1400,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1401,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1402,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ),
inference(modus_ponens,[status(thm)],[1401,1400]) ).
tff(1403,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq),
inference(unit_resolution,[status(thm)],[1402,32,57]) ).
tff(1404,plain,
store(store(q27,seq,earray_142),tail,s(index_141)) = q28,
inference(transitivity,[status(thm)],[1375,1347,1343]) ).
tff(1405,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(q28,seq),
inference(monotonicity,[status(thm)],[1404]) ).
tff(1406,plain,
select(q28,seq) = select(store(store(q27,seq,earray_142),tail,s(index_141)),seq),
inference(symmetry,[status(thm)],[1405]) ).
tff(1407,plain,
select(q28,seq) = earray_142,
inference(transitivity,[status(thm)],[1406,1403,1399,1387,1385]) ).
tff(1408,plain,
store(store(queue_136,head,index_138),seq,select(q28,seq)) = store(q27,seq,earray_142),
inference(monotonicity,[status(thm)],[1396,1407]) ).
tff(1409,plain,
select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(q27,seq,earray_142),head),
inference(monotonicity,[status(thm)],[1408]) ).
tff(1410,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1411,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1412,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ),
inference(modus_ponens,[status(thm)],[1411,1410]) ).
tff(1413,plain,
select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head),
inference(unit_resolution,[status(thm)],[1412,32,26]) ).
tff(1414,plain,
select(store(queue_136,head,index_138),head) = select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head),
inference(symmetry,[status(thm)],[1413]) ).
tff(1415,plain,
( ( index_138 = s(index_137) )
<=> ( index_138 = s(index_137) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1416,axiom,
index_138 = s(index_137),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(1417,plain,
index_138 = s(index_137),
inference(modus_ponens,[status(thm)],[1416,1415]) ).
tff(1418,plain,
s(index_137) = index_138,
inference(symmetry,[status(thm)],[1417]) ).
tff(1419,plain,
( ( queue_136 = store(queue_134,tail,index_135) )
<=> ( queue_136 = store(queue_134,tail,index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1420,axiom,
queue_136 = store(queue_134,tail,index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp251) ).
tff(1421,plain,
queue_136 = store(queue_134,tail,index_135),
inference(modus_ponens,[status(thm)],[1420,1419]) ).
tff(1422,plain,
store(queue_134,tail,index_135) = queue_136,
inference(symmetry,[status(thm)],[1421]) ).
tff(1423,plain,
store(store(queue_134,tail,index_135),head,s(index_137)) = store(queue_136,head,index_138),
inference(monotonicity,[status(thm)],[1422,1418]) ).
tff(1424,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = select(store(queue_136,head,index_138),head),
inference(monotonicity,[status(thm)],[1423]) ).
tff(1425,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = s(index_137) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1426,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = s(index_137),
inference(unit_resolution,[status(thm)],[1425,6]) ).
tff(1427,plain,
s(index_137) = select(store(store(queue_134,tail,index_135),head,s(index_137)),head),
inference(symmetry,[status(thm)],[1426]) ).
tff(1428,plain,
( ( index_137 = select(queue_136,head) )
<=> ( index_137 = select(queue_136,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1429,axiom,
index_137 = select(queue_136,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(1430,plain,
index_137 = select(queue_136,head),
inference(modus_ponens,[status(thm)],[1429,1428]) ).
tff(1431,plain,
select(queue_136,head) = index_137,
inference(symmetry,[status(thm)],[1430]) ).
tff(1432,plain,
( ( index_135 = s(index_132) )
<=> ( index_135 = s(index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1433,axiom,
index_135 = s(index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(1434,plain,
index_135 = s(index_132),
inference(modus_ponens,[status(thm)],[1433,1432]) ).
tff(1435,plain,
s(index_132) = index_135,
inference(symmetry,[status(thm)],[1434]) ).
tff(1436,plain,
( ( queue_134 = store(q26,seq,earray_133) )
<=> ( queue_134 = store(q26,seq,earray_133) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1437,axiom,
queue_134 = store(q26,seq,earray_133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp250) ).
tff(1438,plain,
queue_134 = store(q26,seq,earray_133),
inference(modus_ponens,[status(thm)],[1437,1436]) ).
tff(1439,plain,
store(q26,seq,earray_133) = queue_134,
inference(symmetry,[status(thm)],[1438]) ).
tff(1440,plain,
store(store(q26,seq,earray_133),tail,s(index_132)) = store(queue_134,tail,index_135),
inference(monotonicity,[status(thm)],[1439,1435]) ).
tff(1441,plain,
store(store(q26,seq,earray_133),tail,s(index_132)) = queue_136,
inference(transitivity,[status(thm)],[1440,1422]) ).
tff(1442,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(queue_136,head),
inference(monotonicity,[status(thm)],[1441]) ).
tff(1443,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1444,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1445,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(modus_ponens,[status(thm)],[1444,1443]) ).
tff(1446,plain,
( ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(unit_resolution,[status(thm)],[1445,32]) ).
tff(1447,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head),
inference(unit_resolution,[status(thm)],[1446,92]) ).
tff(1448,plain,
select(store(q26,seq,earray_133),head) = select(store(store(q26,seq,earray_133),tail,s(index_132)),head),
inference(symmetry,[status(thm)],[1447]) ).
tff(1449,plain,
( ( earray_133 = store(earray_131,index_132,e26) )
<=> ( earray_133 = store(earray_131,index_132,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1450,axiom,
earray_133 = store(earray_131,index_132,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(1451,plain,
earray_133 = store(earray_131,index_132,e26),
inference(modus_ponens,[status(thm)],[1450,1449]) ).
tff(1452,plain,
store(earray_131,index_132,e26) = earray_133,
inference(symmetry,[status(thm)],[1451]) ).
tff(1453,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = store(earray_131,index_132,e26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1454,plain,
select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = store(earray_131,index_132,e26),
inference(unit_resolution,[status(thm)],[1453,6]) ).
tff(1455,plain,
( ( q26 = queue_130 )
<=> ( q26 = queue_130 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1456,axiom,
q26 = queue_130,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp372) ).
tff(1457,plain,
q26 = queue_130,
inference(modus_ponens,[status(thm)],[1456,1455]) ).
tff(1458,plain,
queue_130 = q26,
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
( ( queue_130 = store(queue_128,tail,index_129) )
<=> ( queue_130 = store(queue_128,tail,index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1460,axiom,
queue_130 = store(queue_128,tail,index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp249) ).
tff(1461,plain,
queue_130 = store(queue_128,tail,index_129),
inference(modus_ponens,[status(thm)],[1460,1459]) ).
tff(1462,plain,
store(queue_128,tail,index_129) = queue_130,
inference(symmetry,[status(thm)],[1461]) ).
tff(1463,plain,
store(queue_128,tail,index_129) = q26,
inference(transitivity,[status(thm)],[1462,1458]) ).
tff(1464,plain,
store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)) = store(q26,seq,earray_133),
inference(monotonicity,[status(thm)],[1463,1452]) ).
tff(1465,plain,
select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = select(store(q26,seq,earray_133),seq),
inference(monotonicity,[status(thm)],[1464]) ).
tff(1466,plain,
select(store(q26,seq,earray_133),seq) = select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq),
inference(symmetry,[status(thm)],[1465]) ).
tff(1467,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1468,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1469,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ),
inference(modus_ponens,[status(thm)],[1468,1467]) ).
tff(1470,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq),
inference(unit_resolution,[status(thm)],[1469,32,57]) ).
tff(1471,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(queue_134,tail,index_135),seq),
inference(monotonicity,[status(thm)],[1440]) ).
tff(1472,plain,
select(store(queue_134,tail,index_135),seq) = select(store(store(q26,seq,earray_133),tail,s(index_132)),seq),
inference(symmetry,[status(thm)],[1471]) ).
tff(1473,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1474,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1475,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ),
inference(modus_ponens,[status(thm)],[1474,1473]) ).
tff(1476,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq),
inference(unit_resolution,[status(thm)],[1475,32,25]) ).
tff(1477,plain,
store(store(queue_134,tail,index_135),head,s(index_137)) = q27,
inference(transitivity,[status(thm)],[1423,1395,1391]) ).
tff(1478,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(q27,seq),
inference(monotonicity,[status(thm)],[1477]) ).
tff(1479,plain,
select(q27,seq) = select(store(store(queue_134,tail,index_135),head,s(index_137)),seq),
inference(symmetry,[status(thm)],[1478]) ).
tff(1480,plain,
select(q27,seq) = earray_133,
inference(transitivity,[status(thm)],[1479,1476,1472,1470,1466,1454,1452]) ).
tff(1481,plain,
store(store(queue_128,tail,index_129),seq,select(q27,seq)) = store(q26,seq,earray_133),
inference(monotonicity,[status(thm)],[1463,1480]) ).
tff(1482,plain,
select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(q26,seq,earray_133),head),
inference(monotonicity,[status(thm)],[1481]) ).
tff(1483,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1484,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1485,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(modus_ponens,[status(thm)],[1484,1483]) ).
tff(1486,plain,
( ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(unit_resolution,[status(thm)],[1485,32]) ).
tff(1487,plain,
select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head),
inference(unit_resolution,[status(thm)],[1486,26]) ).
tff(1488,plain,
select(store(queue_128,tail,index_129),head) = select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head),
inference(symmetry,[status(thm)],[1487]) ).
tff(1489,plain,
( ( index_129 = s(index_126) )
<=> ( index_129 = s(index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1490,axiom,
index_129 = s(index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(1491,plain,
index_129 = s(index_126),
inference(modus_ponens,[status(thm)],[1490,1489]) ).
tff(1492,plain,
s(index_126) = index_129,
inference(symmetry,[status(thm)],[1491]) ).
tff(1493,plain,
( ( queue_128 = store(q25,seq,earray_127) )
<=> ( queue_128 = store(q25,seq,earray_127) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1494,axiom,
queue_128 = store(q25,seq,earray_127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp247) ).
tff(1495,plain,
queue_128 = store(q25,seq,earray_127),
inference(modus_ponens,[status(thm)],[1494,1493]) ).
tff(1496,plain,
store(q25,seq,earray_127) = queue_128,
inference(symmetry,[status(thm)],[1495]) ).
tff(1497,plain,
store(store(q25,seq,earray_127),tail,s(index_126)) = store(queue_128,tail,index_129),
inference(monotonicity,[status(thm)],[1496,1492]) ).
tff(1498,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(queue_128,tail,index_129),head),
inference(monotonicity,[status(thm)],[1497]) ).
tff(1499,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1500,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1501,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ),
inference(modus_ponens,[status(thm)],[1500,1499]) ).
tff(1502,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head),
inference(unit_resolution,[status(thm)],[1501,32,92]) ).
tff(1503,plain,
select(store(q25,seq,earray_127),head) = select(store(store(q25,seq,earray_127),tail,s(index_126)),head),
inference(symmetry,[status(thm)],[1502]) ).
tff(1504,plain,
( ( earray_127 = store(earray_125,index_126,e25) )
<=> ( earray_127 = store(earray_125,index_126,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1505,axiom,
earray_127 = store(earray_125,index_126,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(1506,plain,
earray_127 = store(earray_125,index_126,e25),
inference(modus_ponens,[status(thm)],[1505,1504]) ).
tff(1507,plain,
store(earray_125,index_126,e25) = earray_127,
inference(symmetry,[status(thm)],[1506]) ).
tff(1508,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = store(earray_125,index_126,e25) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1509,plain,
select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = store(earray_125,index_126,e25),
inference(unit_resolution,[status(thm)],[1508,6]) ).
tff(1510,plain,
( ( q25 = queue_124 )
<=> ( q25 = queue_124 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1511,axiom,
q25 = queue_124,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp371) ).
tff(1512,plain,
q25 = queue_124,
inference(modus_ponens,[status(thm)],[1511,1510]) ).
tff(1513,plain,
queue_124 = q25,
inference(symmetry,[status(thm)],[1512]) ).
tff(1514,plain,
( ( queue_124 = store(queue_122,tail,index_123) )
<=> ( queue_124 = store(queue_122,tail,index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1515,axiom,
queue_124 = store(queue_122,tail,index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp246) ).
tff(1516,plain,
queue_124 = store(queue_122,tail,index_123),
inference(modus_ponens,[status(thm)],[1515,1514]) ).
tff(1517,plain,
store(queue_122,tail,index_123) = queue_124,
inference(symmetry,[status(thm)],[1516]) ).
tff(1518,plain,
store(queue_122,tail,index_123) = q25,
inference(transitivity,[status(thm)],[1517,1513]) ).
tff(1519,plain,
store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)) = store(q25,seq,earray_127),
inference(monotonicity,[status(thm)],[1518,1507]) ).
tff(1520,plain,
select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = select(store(q25,seq,earray_127),seq),
inference(monotonicity,[status(thm)],[1519]) ).
tff(1521,plain,
select(store(q25,seq,earray_127),seq) = select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq),
inference(symmetry,[status(thm)],[1520]) ).
tff(1522,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1523,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1524,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ),
inference(modus_ponens,[status(thm)],[1523,1522]) ).
tff(1525,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq),
inference(unit_resolution,[status(thm)],[1524,32,57]) ).
tff(1526,plain,
store(store(q25,seq,earray_127),tail,s(index_126)) = q26,
inference(transitivity,[status(thm)],[1497,1462,1458]) ).
tff(1527,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(q26,seq),
inference(monotonicity,[status(thm)],[1526]) ).
tff(1528,plain,
select(q26,seq) = select(store(store(q25,seq,earray_127),tail,s(index_126)),seq),
inference(symmetry,[status(thm)],[1527]) ).
tff(1529,plain,
select(q26,seq) = earray_127,
inference(transitivity,[status(thm)],[1528,1525,1521,1509,1507]) ).
tff(1530,plain,
store(store(queue_122,tail,index_123),seq,select(q26,seq)) = store(q25,seq,earray_127),
inference(monotonicity,[status(thm)],[1518,1529]) ).
tff(1531,plain,
select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(q25,seq,earray_127),head),
inference(monotonicity,[status(thm)],[1530]) ).
tff(1532,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1533,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1534,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ),
inference(modus_ponens,[status(thm)],[1533,1532]) ).
tff(1535,plain,
select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head),
inference(unit_resolution,[status(thm)],[1534,32,26]) ).
tff(1536,plain,
select(store(queue_122,tail,index_123),head) = select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head),
inference(symmetry,[status(thm)],[1535]) ).
tff(1537,plain,
( ( index_123 = s(index_120) )
<=> ( index_123 = s(index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1538,axiom,
index_123 = s(index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(1539,plain,
index_123 = s(index_120),
inference(modus_ponens,[status(thm)],[1538,1537]) ).
tff(1540,plain,
s(index_120) = index_123,
inference(symmetry,[status(thm)],[1539]) ).
tff(1541,plain,
( ( queue_122 = store(q24,seq,earray_121) )
<=> ( queue_122 = store(q24,seq,earray_121) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1542,axiom,
queue_122 = store(q24,seq,earray_121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(1543,plain,
queue_122 = store(q24,seq,earray_121),
inference(modus_ponens,[status(thm)],[1542,1541]) ).
tff(1544,plain,
store(q24,seq,earray_121) = queue_122,
inference(symmetry,[status(thm)],[1543]) ).
tff(1545,plain,
store(store(q24,seq,earray_121),tail,s(index_120)) = store(queue_122,tail,index_123),
inference(monotonicity,[status(thm)],[1544,1540]) ).
tff(1546,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(queue_122,tail,index_123),head),
inference(monotonicity,[status(thm)],[1545]) ).
tff(1547,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1548,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1549,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ),
inference(modus_ponens,[status(thm)],[1548,1547]) ).
tff(1550,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head),
inference(unit_resolution,[status(thm)],[1549,32,92]) ).
tff(1551,plain,
select(store(q24,seq,earray_121),head) = select(store(store(q24,seq,earray_121),tail,s(index_120)),head),
inference(symmetry,[status(thm)],[1550]) ).
tff(1552,plain,
( ( earray_121 = store(earray_119,index_120,e24) )
<=> ( earray_121 = store(earray_119,index_120,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1553,axiom,
earray_121 = store(earray_119,index_120,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(1554,plain,
earray_121 = store(earray_119,index_120,e24),
inference(modus_ponens,[status(thm)],[1553,1552]) ).
tff(1555,plain,
store(earray_119,index_120,e24) = earray_121,
inference(symmetry,[status(thm)],[1554]) ).
tff(1556,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = store(earray_119,index_120,e24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1557,plain,
select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = store(earray_119,index_120,e24),
inference(unit_resolution,[status(thm)],[1556,6]) ).
tff(1558,plain,
( ( q24 = queue_118 )
<=> ( q24 = queue_118 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1559,axiom,
q24 = queue_118,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp370) ).
tff(1560,plain,
q24 = queue_118,
inference(modus_ponens,[status(thm)],[1559,1558]) ).
tff(1561,plain,
queue_118 = q24,
inference(symmetry,[status(thm)],[1560]) ).
tff(1562,plain,
( ( queue_118 = store(queue_115,head,index_117) )
<=> ( queue_118 = store(queue_115,head,index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1563,axiom,
queue_118 = store(queue_115,head,index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(1564,plain,
queue_118 = store(queue_115,head,index_117),
inference(modus_ponens,[status(thm)],[1563,1562]) ).
tff(1565,plain,
store(queue_115,head,index_117) = queue_118,
inference(symmetry,[status(thm)],[1564]) ).
tff(1566,plain,
store(queue_115,head,index_117) = q24,
inference(transitivity,[status(thm)],[1565,1561]) ).
tff(1567,plain,
store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)) = store(q24,seq,earray_121),
inference(monotonicity,[status(thm)],[1566,1555]) ).
tff(1568,plain,
select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = select(store(q24,seq,earray_121),seq),
inference(monotonicity,[status(thm)],[1567]) ).
tff(1569,plain,
select(store(q24,seq,earray_121),seq) = select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq),
inference(symmetry,[status(thm)],[1568]) ).
tff(1570,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1571,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1572,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ),
inference(modus_ponens,[status(thm)],[1571,1570]) ).
tff(1573,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq),
inference(unit_resolution,[status(thm)],[1572,32,57]) ).
tff(1574,plain,
store(store(q24,seq,earray_121),tail,s(index_120)) = q25,
inference(transitivity,[status(thm)],[1545,1517,1513]) ).
tff(1575,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(q25,seq),
inference(monotonicity,[status(thm)],[1574]) ).
tff(1576,plain,
select(q25,seq) = select(store(store(q24,seq,earray_121),tail,s(index_120)),seq),
inference(symmetry,[status(thm)],[1575]) ).
tff(1577,plain,
select(q25,seq) = earray_121,
inference(transitivity,[status(thm)],[1576,1573,1569,1557,1555]) ).
tff(1578,plain,
store(store(queue_115,head,index_117),seq,select(q25,seq)) = store(q24,seq,earray_121),
inference(monotonicity,[status(thm)],[1566,1577]) ).
tff(1579,plain,
select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(q24,seq,earray_121),head),
inference(monotonicity,[status(thm)],[1578]) ).
tff(1580,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1581,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1582,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ),
inference(modus_ponens,[status(thm)],[1581,1580]) ).
tff(1583,plain,
select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head),
inference(unit_resolution,[status(thm)],[1582,32,26]) ).
tff(1584,plain,
select(store(queue_115,head,index_117),head) = select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head),
inference(symmetry,[status(thm)],[1583]) ).
tff(1585,plain,
( ( index_117 = s(index_116) )
<=> ( index_117 = s(index_116) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1586,axiom,
index_117 = s(index_116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(1587,plain,
index_117 = s(index_116),
inference(modus_ponens,[status(thm)],[1586,1585]) ).
tff(1588,plain,
s(index_116) = index_117,
inference(symmetry,[status(thm)],[1587]) ).
tff(1589,plain,
( ( queue_115 = store(queue_113,tail,index_114) )
<=> ( queue_115 = store(queue_113,tail,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1590,axiom,
queue_115 = store(queue_113,tail,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(1591,plain,
queue_115 = store(queue_113,tail,index_114),
inference(modus_ponens,[status(thm)],[1590,1589]) ).
tff(1592,plain,
store(queue_113,tail,index_114) = queue_115,
inference(symmetry,[status(thm)],[1591]) ).
tff(1593,plain,
store(store(queue_113,tail,index_114),head,s(index_116)) = store(queue_115,head,index_117),
inference(monotonicity,[status(thm)],[1592,1588]) ).
tff(1594,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = select(store(queue_115,head,index_117),head),
inference(monotonicity,[status(thm)],[1593]) ).
tff(1595,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = s(index_116) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1596,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = s(index_116),
inference(unit_resolution,[status(thm)],[1595,6]) ).
tff(1597,plain,
s(index_116) = select(store(store(queue_113,tail,index_114),head,s(index_116)),head),
inference(symmetry,[status(thm)],[1596]) ).
tff(1598,plain,
( ( index_116 = select(queue_115,head) )
<=> ( index_116 = select(queue_115,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1599,axiom,
index_116 = select(queue_115,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(1600,plain,
index_116 = select(queue_115,head),
inference(modus_ponens,[status(thm)],[1599,1598]) ).
tff(1601,plain,
select(queue_115,head) = index_116,
inference(symmetry,[status(thm)],[1600]) ).
tff(1602,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1603,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(1604,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[1603,1602]) ).
tff(1605,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[1604]) ).
tff(1606,plain,
( ( queue_113 = store(q23,seq,earray_112) )
<=> ( queue_113 = store(q23,seq,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1607,axiom,
queue_113 = store(q23,seq,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(1608,plain,
queue_113 = store(q23,seq,earray_112),
inference(modus_ponens,[status(thm)],[1607,1606]) ).
tff(1609,plain,
store(q23,seq,earray_112) = queue_113,
inference(symmetry,[status(thm)],[1608]) ).
tff(1610,plain,
store(store(q23,seq,earray_112),tail,s(index_111)) = store(queue_113,tail,index_114),
inference(monotonicity,[status(thm)],[1609,1605]) ).
tff(1611,plain,
store(store(q23,seq,earray_112),tail,s(index_111)) = queue_115,
inference(transitivity,[status(thm)],[1610,1592]) ).
tff(1612,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(queue_115,head),
inference(monotonicity,[status(thm)],[1611]) ).
tff(1613,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1614,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1615,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(modus_ponens,[status(thm)],[1614,1613]) ).
tff(1616,plain,
( ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(unit_resolution,[status(thm)],[1615,32]) ).
tff(1617,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head),
inference(unit_resolution,[status(thm)],[1616,92]) ).
tff(1618,plain,
select(store(q23,seq,earray_112),head) = select(store(store(q23,seq,earray_112),tail,s(index_111)),head),
inference(symmetry,[status(thm)],[1617]) ).
tff(1619,plain,
( ( earray_112 = store(earray_110,index_111,e23) )
<=> ( earray_112 = store(earray_110,index_111,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1620,axiom,
earray_112 = store(earray_110,index_111,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(1621,plain,
earray_112 = store(earray_110,index_111,e23),
inference(modus_ponens,[status(thm)],[1620,1619]) ).
tff(1622,plain,
store(earray_110,index_111,e23) = earray_112,
inference(symmetry,[status(thm)],[1621]) ).
tff(1623,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = store(earray_110,index_111,e23) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1624,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = store(earray_110,index_111,e23),
inference(unit_resolution,[status(thm)],[1623,6]) ).
tff(1625,plain,
( ( q23 = queue_109 )
<=> ( q23 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1626,axiom,
q23 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp369) ).
tff(1627,plain,
q23 = queue_109,
inference(modus_ponens,[status(thm)],[1626,1625]) ).
tff(1628,plain,
queue_109 = q23,
inference(symmetry,[status(thm)],[1627]) ).
tff(1629,plain,
( ( queue_109 = store(queue_107,tail,index_108) )
<=> ( queue_109 = store(queue_107,tail,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1630,axiom,
queue_109 = store(queue_107,tail,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(1631,plain,
queue_109 = store(queue_107,tail,index_108),
inference(modus_ponens,[status(thm)],[1630,1629]) ).
tff(1632,plain,
store(queue_107,tail,index_108) = queue_109,
inference(symmetry,[status(thm)],[1631]) ).
tff(1633,plain,
store(queue_107,tail,index_108) = q23,
inference(transitivity,[status(thm)],[1632,1628]) ).
tff(1634,plain,
store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)) = store(q23,seq,earray_112),
inference(monotonicity,[status(thm)],[1633,1622]) ).
tff(1635,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = select(store(q23,seq,earray_112),seq),
inference(monotonicity,[status(thm)],[1634]) ).
tff(1636,plain,
select(store(q23,seq,earray_112),seq) = select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq),
inference(symmetry,[status(thm)],[1635]) ).
tff(1637,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1638,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1639,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ),
inference(modus_ponens,[status(thm)],[1638,1637]) ).
tff(1640,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq),
inference(unit_resolution,[status(thm)],[1639,32,57]) ).
tff(1641,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(queue_113,tail,index_114),seq),
inference(monotonicity,[status(thm)],[1610]) ).
tff(1642,plain,
select(store(queue_113,tail,index_114),seq) = select(store(store(q23,seq,earray_112),tail,s(index_111)),seq),
inference(symmetry,[status(thm)],[1641]) ).
tff(1643,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1644,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1645,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ),
inference(modus_ponens,[status(thm)],[1644,1643]) ).
tff(1646,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq),
inference(unit_resolution,[status(thm)],[1645,32,25]) ).
tff(1647,plain,
store(store(queue_113,tail,index_114),head,s(index_116)) = q24,
inference(transitivity,[status(thm)],[1593,1565,1561]) ).
tff(1648,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(q24,seq),
inference(monotonicity,[status(thm)],[1647]) ).
tff(1649,plain,
select(q24,seq) = select(store(store(queue_113,tail,index_114),head,s(index_116)),seq),
inference(symmetry,[status(thm)],[1648]) ).
tff(1650,plain,
select(q24,seq) = earray_112,
inference(transitivity,[status(thm)],[1649,1646,1642,1640,1636,1624,1622]) ).
tff(1651,plain,
store(store(queue_107,tail,index_108),seq,select(q24,seq)) = store(q23,seq,earray_112),
inference(monotonicity,[status(thm)],[1633,1650]) ).
tff(1652,plain,
select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(q23,seq,earray_112),head),
inference(monotonicity,[status(thm)],[1651]) ).
tff(1653,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1654,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1655,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(modus_ponens,[status(thm)],[1654,1653]) ).
tff(1656,plain,
( ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(unit_resolution,[status(thm)],[1655,32]) ).
tff(1657,plain,
select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head),
inference(unit_resolution,[status(thm)],[1656,26]) ).
tff(1658,plain,
select(store(queue_107,tail,index_108),head) = select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head),
inference(symmetry,[status(thm)],[1657]) ).
tff(1659,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1660,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(1661,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[1660,1659]) ).
tff(1662,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[1661]) ).
tff(1663,plain,
( ( queue_107 = store(q22,seq,earray_106) )
<=> ( queue_107 = store(q22,seq,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1664,axiom,
queue_107 = store(q22,seq,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(1665,plain,
queue_107 = store(q22,seq,earray_106),
inference(modus_ponens,[status(thm)],[1664,1663]) ).
tff(1666,plain,
store(q22,seq,earray_106) = queue_107,
inference(symmetry,[status(thm)],[1665]) ).
tff(1667,plain,
store(store(q22,seq,earray_106),tail,s(index_105)) = store(queue_107,tail,index_108),
inference(monotonicity,[status(thm)],[1666,1662]) ).
tff(1668,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(queue_107,tail,index_108),head),
inference(monotonicity,[status(thm)],[1667]) ).
tff(1669,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1670,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1671,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ),
inference(modus_ponens,[status(thm)],[1670,1669]) ).
tff(1672,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head),
inference(unit_resolution,[status(thm)],[1671,32,92]) ).
tff(1673,plain,
select(store(q22,seq,earray_106),head) = select(store(store(q22,seq,earray_106),tail,s(index_105)),head),
inference(symmetry,[status(thm)],[1672]) ).
tff(1674,plain,
( ( earray_106 = store(earray_104,index_105,e22) )
<=> ( earray_106 = store(earray_104,index_105,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1675,axiom,
earray_106 = store(earray_104,index_105,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(1676,plain,
earray_106 = store(earray_104,index_105,e22),
inference(modus_ponens,[status(thm)],[1675,1674]) ).
tff(1677,plain,
store(earray_104,index_105,e22) = earray_106,
inference(symmetry,[status(thm)],[1676]) ).
tff(1678,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = store(earray_104,index_105,e22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1679,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = store(earray_104,index_105,e22),
inference(unit_resolution,[status(thm)],[1678,6]) ).
tff(1680,plain,
( ( q22 = queue_103 )
<=> ( q22 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1681,axiom,
q22 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp368) ).
tff(1682,plain,
q22 = queue_103,
inference(modus_ponens,[status(thm)],[1681,1680]) ).
tff(1683,plain,
queue_103 = q22,
inference(symmetry,[status(thm)],[1682]) ).
tff(1684,plain,
( ( queue_103 = store(queue_101,tail,index_102) )
<=> ( queue_103 = store(queue_101,tail,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1685,axiom,
queue_103 = store(queue_101,tail,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(1686,plain,
queue_103 = store(queue_101,tail,index_102),
inference(modus_ponens,[status(thm)],[1685,1684]) ).
tff(1687,plain,
store(queue_101,tail,index_102) = queue_103,
inference(symmetry,[status(thm)],[1686]) ).
tff(1688,plain,
store(queue_101,tail,index_102) = q22,
inference(transitivity,[status(thm)],[1687,1683]) ).
tff(1689,plain,
store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)) = store(q22,seq,earray_106),
inference(monotonicity,[status(thm)],[1688,1677]) ).
tff(1690,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = select(store(q22,seq,earray_106),seq),
inference(monotonicity,[status(thm)],[1689]) ).
tff(1691,plain,
select(store(q22,seq,earray_106),seq) = select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq),
inference(symmetry,[status(thm)],[1690]) ).
tff(1692,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1693,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1694,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ),
inference(modus_ponens,[status(thm)],[1693,1692]) ).
tff(1695,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq),
inference(unit_resolution,[status(thm)],[1694,32,57]) ).
tff(1696,plain,
store(store(q22,seq,earray_106),tail,s(index_105)) = q23,
inference(transitivity,[status(thm)],[1667,1632,1628]) ).
tff(1697,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(q23,seq),
inference(monotonicity,[status(thm)],[1696]) ).
tff(1698,plain,
select(q23,seq) = select(store(store(q22,seq,earray_106),tail,s(index_105)),seq),
inference(symmetry,[status(thm)],[1697]) ).
tff(1699,plain,
select(q23,seq) = earray_106,
inference(transitivity,[status(thm)],[1698,1695,1691,1679,1677]) ).
tff(1700,plain,
store(store(queue_101,tail,index_102),seq,select(q23,seq)) = store(q22,seq,earray_106),
inference(monotonicity,[status(thm)],[1688,1699]) ).
tff(1701,plain,
select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(q22,seq,earray_106),head),
inference(monotonicity,[status(thm)],[1700]) ).
tff(1702,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1703,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1704,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(modus_ponens,[status(thm)],[1703,1702]) ).
tff(1705,plain,
select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head),
inference(unit_resolution,[status(thm)],[1704,32,26]) ).
tff(1706,plain,
select(store(queue_101,tail,index_102),head) = select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head),
inference(symmetry,[status(thm)],[1705]) ).
tff(1707,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1708,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(1709,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[1708,1707]) ).
tff(1710,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[1709]) ).
tff(1711,plain,
( ( queue_101 = store(q21,seq,earray_100) )
<=> ( queue_101 = store(q21,seq,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1712,axiom,
queue_101 = store(q21,seq,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(1713,plain,
queue_101 = store(q21,seq,earray_100),
inference(modus_ponens,[status(thm)],[1712,1711]) ).
tff(1714,plain,
store(q21,seq,earray_100) = queue_101,
inference(symmetry,[status(thm)],[1713]) ).
tff(1715,plain,
store(store(q21,seq,earray_100),tail,s(index_99)) = store(queue_101,tail,index_102),
inference(monotonicity,[status(thm)],[1714,1710]) ).
tff(1716,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(queue_101,tail,index_102),head),
inference(monotonicity,[status(thm)],[1715]) ).
tff(1717,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1718,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1719,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ),
inference(modus_ponens,[status(thm)],[1718,1717]) ).
tff(1720,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head),
inference(unit_resolution,[status(thm)],[1719,32,92]) ).
tff(1721,plain,
select(store(q21,seq,earray_100),head) = select(store(store(q21,seq,earray_100),tail,s(index_99)),head),
inference(symmetry,[status(thm)],[1720]) ).
tff(1722,plain,
( ( earray_100 = store(earray_98,index_99,e21) )
<=> ( earray_100 = store(earray_98,index_99,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1723,axiom,
earray_100 = store(earray_98,index_99,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(1724,plain,
earray_100 = store(earray_98,index_99,e21),
inference(modus_ponens,[status(thm)],[1723,1722]) ).
tff(1725,plain,
store(earray_98,index_99,e21) = earray_100,
inference(symmetry,[status(thm)],[1724]) ).
tff(1726,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = store(earray_98,index_99,e21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1727,plain,
select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = store(earray_98,index_99,e21),
inference(unit_resolution,[status(thm)],[1726,6]) ).
tff(1728,plain,
( ( q21 = queue_97 )
<=> ( q21 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1729,axiom,
q21 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp367) ).
tff(1730,plain,
q21 = queue_97,
inference(modus_ponens,[status(thm)],[1729,1728]) ).
tff(1731,plain,
queue_97 = q21,
inference(symmetry,[status(thm)],[1730]) ).
tff(1732,plain,
( ( queue_97 = store(queue_94,head,index_96) )
<=> ( queue_97 = store(queue_94,head,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1733,axiom,
queue_97 = store(queue_94,head,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp352) ).
tff(1734,plain,
queue_97 = store(queue_94,head,index_96),
inference(modus_ponens,[status(thm)],[1733,1732]) ).
tff(1735,plain,
store(queue_94,head,index_96) = queue_97,
inference(symmetry,[status(thm)],[1734]) ).
tff(1736,plain,
store(queue_94,head,index_96) = q21,
inference(transitivity,[status(thm)],[1735,1731]) ).
tff(1737,plain,
store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)) = store(q21,seq,earray_100),
inference(monotonicity,[status(thm)],[1736,1725]) ).
tff(1738,plain,
select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = select(store(q21,seq,earray_100),seq),
inference(monotonicity,[status(thm)],[1737]) ).
tff(1739,plain,
select(store(q21,seq,earray_100),seq) = select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq),
inference(symmetry,[status(thm)],[1738]) ).
tff(1740,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1741,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1742,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ),
inference(modus_ponens,[status(thm)],[1741,1740]) ).
tff(1743,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq),
inference(unit_resolution,[status(thm)],[1742,32,57]) ).
tff(1744,plain,
store(store(q21,seq,earray_100),tail,s(index_99)) = q22,
inference(transitivity,[status(thm)],[1715,1687,1683]) ).
tff(1745,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(q22,seq),
inference(monotonicity,[status(thm)],[1744]) ).
tff(1746,plain,
select(q22,seq) = select(store(store(q21,seq,earray_100),tail,s(index_99)),seq),
inference(symmetry,[status(thm)],[1745]) ).
tff(1747,plain,
select(q22,seq) = earray_100,
inference(transitivity,[status(thm)],[1746,1743,1739,1727,1725]) ).
tff(1748,plain,
store(store(queue_94,head,index_96),seq,select(q22,seq)) = store(q21,seq,earray_100),
inference(monotonicity,[status(thm)],[1736,1747]) ).
tff(1749,plain,
select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(q21,seq,earray_100),head),
inference(monotonicity,[status(thm)],[1748]) ).
tff(1750,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1751,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1752,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ),
inference(modus_ponens,[status(thm)],[1751,1750]) ).
tff(1753,plain,
select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head),
inference(unit_resolution,[status(thm)],[1752,32,26]) ).
tff(1754,plain,
select(store(queue_94,head,index_96),head) = select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head),
inference(symmetry,[status(thm)],[1753]) ).
tff(1755,plain,
( ( index_96 = s(index_95) )
<=> ( index_96 = s(index_95) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1756,axiom,
index_96 = s(index_95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(1757,plain,
index_96 = s(index_95),
inference(modus_ponens,[status(thm)],[1756,1755]) ).
tff(1758,plain,
s(index_95) = index_96,
inference(symmetry,[status(thm)],[1757]) ).
tff(1759,plain,
( ( queue_94 = store(queue_92,tail,index_93) )
<=> ( queue_94 = store(queue_92,tail,index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1760,axiom,
queue_94 = store(queue_92,tail,index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp351) ).
tff(1761,plain,
queue_94 = store(queue_92,tail,index_93),
inference(modus_ponens,[status(thm)],[1760,1759]) ).
tff(1762,plain,
store(queue_92,tail,index_93) = queue_94,
inference(symmetry,[status(thm)],[1761]) ).
tff(1763,plain,
store(store(queue_92,tail,index_93),head,s(index_95)) = store(queue_94,head,index_96),
inference(monotonicity,[status(thm)],[1762,1758]) ).
tff(1764,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = select(store(queue_94,head,index_96),head),
inference(monotonicity,[status(thm)],[1763]) ).
tff(1765,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = s(index_95) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1766,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = s(index_95),
inference(unit_resolution,[status(thm)],[1765,6]) ).
tff(1767,plain,
s(index_95) = select(store(store(queue_92,tail,index_93),head,s(index_95)),head),
inference(symmetry,[status(thm)],[1766]) ).
tff(1768,plain,
( ( index_95 = select(queue_94,head) )
<=> ( index_95 = select(queue_94,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1769,axiom,
index_95 = select(queue_94,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(1770,plain,
index_95 = select(queue_94,head),
inference(modus_ponens,[status(thm)],[1769,1768]) ).
tff(1771,plain,
select(queue_94,head) = index_95,
inference(symmetry,[status(thm)],[1770]) ).
tff(1772,plain,
( ( index_93 = s(index_90) )
<=> ( index_93 = s(index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1773,axiom,
index_93 = s(index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(1774,plain,
index_93 = s(index_90),
inference(modus_ponens,[status(thm)],[1773,1772]) ).
tff(1775,plain,
s(index_90) = index_93,
inference(symmetry,[status(thm)],[1774]) ).
tff(1776,plain,
( ( queue_92 = store(q20,seq,earray_91) )
<=> ( queue_92 = store(q20,seq,earray_91) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1777,axiom,
queue_92 = store(q20,seq,earray_91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp350) ).
tff(1778,plain,
queue_92 = store(q20,seq,earray_91),
inference(modus_ponens,[status(thm)],[1777,1776]) ).
tff(1779,plain,
store(q20,seq,earray_91) = queue_92,
inference(symmetry,[status(thm)],[1778]) ).
tff(1780,plain,
store(store(q20,seq,earray_91),tail,s(index_90)) = store(queue_92,tail,index_93),
inference(monotonicity,[status(thm)],[1779,1775]) ).
tff(1781,plain,
store(store(q20,seq,earray_91),tail,s(index_90)) = queue_94,
inference(transitivity,[status(thm)],[1780,1762]) ).
tff(1782,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(queue_94,head),
inference(monotonicity,[status(thm)],[1781]) ).
tff(1783,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1784,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1785,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(modus_ponens,[status(thm)],[1784,1783]) ).
tff(1786,plain,
( ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(unit_resolution,[status(thm)],[1785,32]) ).
tff(1787,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head),
inference(unit_resolution,[status(thm)],[1786,92]) ).
tff(1788,plain,
select(store(q20,seq,earray_91),head) = select(store(store(q20,seq,earray_91),tail,s(index_90)),head),
inference(symmetry,[status(thm)],[1787]) ).
tff(1789,plain,
( ( earray_91 = store(earray_89,index_90,e20) )
<=> ( earray_91 = store(earray_89,index_90,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1790,axiom,
earray_91 = store(earray_89,index_90,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(1791,plain,
earray_91 = store(earray_89,index_90,e20),
inference(modus_ponens,[status(thm)],[1790,1789]) ).
tff(1792,plain,
store(earray_89,index_90,e20) = earray_91,
inference(symmetry,[status(thm)],[1791]) ).
tff(1793,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = store(earray_89,index_90,e20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1794,plain,
select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = store(earray_89,index_90,e20),
inference(unit_resolution,[status(thm)],[1793,6]) ).
tff(1795,plain,
( ( q20 = queue_88 )
<=> ( q20 = queue_88 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1796,axiom,
q20 = queue_88,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp366) ).
tff(1797,plain,
q20 = queue_88,
inference(modus_ponens,[status(thm)],[1796,1795]) ).
tff(1798,plain,
queue_88 = q20,
inference(symmetry,[status(thm)],[1797]) ).
tff(1799,plain,
( ( queue_88 = store(queue_86,tail,index_87) )
<=> ( queue_88 = store(queue_86,tail,index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1800,axiom,
queue_88 = store(queue_86,tail,index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp349) ).
tff(1801,plain,
queue_88 = store(queue_86,tail,index_87),
inference(modus_ponens,[status(thm)],[1800,1799]) ).
tff(1802,plain,
store(queue_86,tail,index_87) = queue_88,
inference(symmetry,[status(thm)],[1801]) ).
tff(1803,plain,
store(queue_86,tail,index_87) = q20,
inference(transitivity,[status(thm)],[1802,1798]) ).
tff(1804,plain,
store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)) = store(q20,seq,earray_91),
inference(monotonicity,[status(thm)],[1803,1792]) ).
tff(1805,plain,
select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = select(store(q20,seq,earray_91),seq),
inference(monotonicity,[status(thm)],[1804]) ).
tff(1806,plain,
select(store(q20,seq,earray_91),seq) = select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq),
inference(symmetry,[status(thm)],[1805]) ).
tff(1807,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1808,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1809,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ),
inference(modus_ponens,[status(thm)],[1808,1807]) ).
tff(1810,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq),
inference(unit_resolution,[status(thm)],[1809,32,57]) ).
tff(1811,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(queue_92,tail,index_93),seq),
inference(monotonicity,[status(thm)],[1780]) ).
tff(1812,plain,
select(store(queue_92,tail,index_93),seq) = select(store(store(q20,seq,earray_91),tail,s(index_90)),seq),
inference(symmetry,[status(thm)],[1811]) ).
tff(1813,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1814,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1815,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ),
inference(modus_ponens,[status(thm)],[1814,1813]) ).
tff(1816,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq),
inference(unit_resolution,[status(thm)],[1815,32,25]) ).
tff(1817,plain,
store(store(queue_92,tail,index_93),head,s(index_95)) = q21,
inference(transitivity,[status(thm)],[1763,1735,1731]) ).
tff(1818,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(q21,seq),
inference(monotonicity,[status(thm)],[1817]) ).
tff(1819,plain,
select(q21,seq) = select(store(store(queue_92,tail,index_93),head,s(index_95)),seq),
inference(symmetry,[status(thm)],[1818]) ).
tff(1820,plain,
select(q21,seq) = earray_91,
inference(transitivity,[status(thm)],[1819,1816,1812,1810,1806,1794,1792]) ).
tff(1821,plain,
store(store(queue_86,tail,index_87),seq,select(q21,seq)) = store(q20,seq,earray_91),
inference(monotonicity,[status(thm)],[1803,1820]) ).
tff(1822,plain,
select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(q20,seq,earray_91),head),
inference(monotonicity,[status(thm)],[1821]) ).
tff(1823,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1824,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1825,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(modus_ponens,[status(thm)],[1824,1823]) ).
tff(1826,plain,
( ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(unit_resolution,[status(thm)],[1825,32]) ).
tff(1827,plain,
select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head),
inference(unit_resolution,[status(thm)],[1826,26]) ).
tff(1828,plain,
select(store(queue_86,tail,index_87),head) = select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head),
inference(symmetry,[status(thm)],[1827]) ).
tff(1829,plain,
( ( index_87 = s(index_84) )
<=> ( index_87 = s(index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1830,axiom,
index_87 = s(index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(1831,plain,
index_87 = s(index_84),
inference(modus_ponens,[status(thm)],[1830,1829]) ).
tff(1832,plain,
s(index_84) = index_87,
inference(symmetry,[status(thm)],[1831]) ).
tff(1833,plain,
( ( queue_86 = store(q19,seq,earray_85) )
<=> ( queue_86 = store(q19,seq,earray_85) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1834,axiom,
queue_86 = store(q19,seq,earray_85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp348) ).
tff(1835,plain,
queue_86 = store(q19,seq,earray_85),
inference(modus_ponens,[status(thm)],[1834,1833]) ).
tff(1836,plain,
store(q19,seq,earray_85) = queue_86,
inference(symmetry,[status(thm)],[1835]) ).
tff(1837,plain,
store(store(q19,seq,earray_85),tail,s(index_84)) = store(queue_86,tail,index_87),
inference(monotonicity,[status(thm)],[1836,1832]) ).
tff(1838,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(queue_86,tail,index_87),head),
inference(monotonicity,[status(thm)],[1837]) ).
tff(1839,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1840,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1841,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ),
inference(modus_ponens,[status(thm)],[1840,1839]) ).
tff(1842,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head),
inference(unit_resolution,[status(thm)],[1841,32,92]) ).
tff(1843,plain,
select(store(q19,seq,earray_85),head) = select(store(store(q19,seq,earray_85),tail,s(index_84)),head),
inference(symmetry,[status(thm)],[1842]) ).
tff(1844,plain,
( ( earray_85 = store(earray_83,index_84,e19) )
<=> ( earray_85 = store(earray_83,index_84,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1845,axiom,
earray_85 = store(earray_83,index_84,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(1846,plain,
earray_85 = store(earray_83,index_84,e19),
inference(modus_ponens,[status(thm)],[1845,1844]) ).
tff(1847,plain,
store(earray_83,index_84,e19) = earray_85,
inference(symmetry,[status(thm)],[1846]) ).
tff(1848,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = store(earray_83,index_84,e19) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1849,plain,
select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = store(earray_83,index_84,e19),
inference(unit_resolution,[status(thm)],[1848,6]) ).
tff(1850,plain,
( ( q19 = queue_76 )
<=> ( q19 = queue_76 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1851,axiom,
q19 = queue_76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp364) ).
tff(1852,plain,
q19 = queue_76,
inference(modus_ponens,[status(thm)],[1851,1850]) ).
tff(1853,plain,
queue_76 = q19,
inference(symmetry,[status(thm)],[1852]) ).
tff(1854,plain,
( ( queue_76 = store(queue_74,tail,index_75) )
<=> ( queue_76 = store(queue_74,tail,index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1855,axiom,
queue_76 = store(queue_74,tail,index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp345) ).
tff(1856,plain,
queue_76 = store(queue_74,tail,index_75),
inference(modus_ponens,[status(thm)],[1855,1854]) ).
tff(1857,plain,
store(queue_74,tail,index_75) = queue_76,
inference(symmetry,[status(thm)],[1856]) ).
tff(1858,plain,
store(queue_74,tail,index_75) = q19,
inference(transitivity,[status(thm)],[1857,1853]) ).
tff(1859,plain,
store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)) = store(q19,seq,earray_85),
inference(monotonicity,[status(thm)],[1858,1847]) ).
tff(1860,plain,
select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = select(store(q19,seq,earray_85),seq),
inference(monotonicity,[status(thm)],[1859]) ).
tff(1861,plain,
select(store(q19,seq,earray_85),seq) = select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq),
inference(symmetry,[status(thm)],[1860]) ).
tff(1862,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1863,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1864,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ),
inference(modus_ponens,[status(thm)],[1863,1862]) ).
tff(1865,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq),
inference(unit_resolution,[status(thm)],[1864,32,57]) ).
tff(1866,plain,
store(store(q19,seq,earray_85),tail,s(index_84)) = q20,
inference(transitivity,[status(thm)],[1837,1802,1798]) ).
tff(1867,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(q20,seq),
inference(monotonicity,[status(thm)],[1866]) ).
tff(1868,plain,
select(q20,seq) = select(store(store(q19,seq,earray_85),tail,s(index_84)),seq),
inference(symmetry,[status(thm)],[1867]) ).
tff(1869,plain,
select(q20,seq) = earray_85,
inference(transitivity,[status(thm)],[1868,1865,1861,1849,1847]) ).
tff(1870,plain,
store(store(queue_74,tail,index_75),seq,select(q20,seq)) = store(q19,seq,earray_85),
inference(monotonicity,[status(thm)],[1858,1869]) ).
tff(1871,plain,
select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(q19,seq,earray_85),head),
inference(monotonicity,[status(thm)],[1870]) ).
tff(1872,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1873,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1874,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ),
inference(modus_ponens,[status(thm)],[1873,1872]) ).
tff(1875,plain,
select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head),
inference(unit_resolution,[status(thm)],[1874,32,26]) ).
tff(1876,plain,
select(store(queue_74,tail,index_75),head) = select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head),
inference(symmetry,[status(thm)],[1875]) ).
tff(1877,plain,
( ( index_75 = s(index_72) )
<=> ( index_75 = s(index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1878,axiom,
index_75 = s(index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(1879,plain,
index_75 = s(index_72),
inference(modus_ponens,[status(thm)],[1878,1877]) ).
tff(1880,plain,
s(index_72) = index_75,
inference(symmetry,[status(thm)],[1879]) ).
tff(1881,plain,
( ( queue_74 = store(q18,seq,earray_73) )
<=> ( queue_74 = store(q18,seq,earray_73) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1882,axiom,
queue_74 = store(q18,seq,earray_73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp344) ).
tff(1883,plain,
queue_74 = store(q18,seq,earray_73),
inference(modus_ponens,[status(thm)],[1882,1881]) ).
tff(1884,plain,
store(q18,seq,earray_73) = queue_74,
inference(symmetry,[status(thm)],[1883]) ).
tff(1885,plain,
store(store(q18,seq,earray_73),tail,s(index_72)) = store(queue_74,tail,index_75),
inference(monotonicity,[status(thm)],[1884,1880]) ).
tff(1886,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(queue_74,tail,index_75),head),
inference(monotonicity,[status(thm)],[1885]) ).
tff(1887,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1888,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1889,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ),
inference(modus_ponens,[status(thm)],[1888,1887]) ).
tff(1890,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head),
inference(unit_resolution,[status(thm)],[1889,32,92]) ).
tff(1891,plain,
select(store(q18,seq,earray_73),head) = select(store(store(q18,seq,earray_73),tail,s(index_72)),head),
inference(symmetry,[status(thm)],[1890]) ).
tff(1892,plain,
( ( earray_73 = store(earray_71,index_72,e18) )
<=> ( earray_73 = store(earray_71,index_72,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1893,axiom,
earray_73 = store(earray_71,index_72,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(1894,plain,
earray_73 = store(earray_71,index_72,e18),
inference(modus_ponens,[status(thm)],[1893,1892]) ).
tff(1895,plain,
store(earray_71,index_72,e18) = earray_73,
inference(symmetry,[status(thm)],[1894]) ).
tff(1896,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = store(earray_71,index_72,e18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1897,plain,
select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = store(earray_71,index_72,e18),
inference(unit_resolution,[status(thm)],[1896,6]) ).
tff(1898,plain,
( ( q18 = queue_70 )
<=> ( q18 = queue_70 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1899,axiom,
q18 = queue_70,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp363) ).
tff(1900,plain,
q18 = queue_70,
inference(modus_ponens,[status(thm)],[1899,1898]) ).
tff(1901,plain,
queue_70 = q18,
inference(symmetry,[status(thm)],[1900]) ).
tff(1902,plain,
( ( queue_70 = store(queue_67,head,index_69) )
<=> ( queue_70 = store(queue_67,head,index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1903,axiom,
queue_70 = store(queue_67,head,index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp343) ).
tff(1904,plain,
queue_70 = store(queue_67,head,index_69),
inference(modus_ponens,[status(thm)],[1903,1902]) ).
tff(1905,plain,
store(queue_67,head,index_69) = queue_70,
inference(symmetry,[status(thm)],[1904]) ).
tff(1906,plain,
store(queue_67,head,index_69) = q18,
inference(transitivity,[status(thm)],[1905,1901]) ).
tff(1907,plain,
store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)) = store(q18,seq,earray_73),
inference(monotonicity,[status(thm)],[1906,1895]) ).
tff(1908,plain,
select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = select(store(q18,seq,earray_73),seq),
inference(monotonicity,[status(thm)],[1907]) ).
tff(1909,plain,
select(store(q18,seq,earray_73),seq) = select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq),
inference(symmetry,[status(thm)],[1908]) ).
tff(1910,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1911,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1912,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ),
inference(modus_ponens,[status(thm)],[1911,1910]) ).
tff(1913,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq),
inference(unit_resolution,[status(thm)],[1912,32,57]) ).
tff(1914,plain,
store(store(q18,seq,earray_73),tail,s(index_72)) = q19,
inference(transitivity,[status(thm)],[1885,1857,1853]) ).
tff(1915,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(q19,seq),
inference(monotonicity,[status(thm)],[1914]) ).
tff(1916,plain,
select(q19,seq) = select(store(store(q18,seq,earray_73),tail,s(index_72)),seq),
inference(symmetry,[status(thm)],[1915]) ).
tff(1917,plain,
select(q19,seq) = earray_73,
inference(transitivity,[status(thm)],[1916,1913,1909,1897,1895]) ).
tff(1918,plain,
store(store(queue_67,head,index_69),seq,select(q19,seq)) = store(q18,seq,earray_73),
inference(monotonicity,[status(thm)],[1906,1917]) ).
tff(1919,plain,
select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(q18,seq,earray_73),head),
inference(monotonicity,[status(thm)],[1918]) ).
tff(1920,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1921,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1922,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ),
inference(modus_ponens,[status(thm)],[1921,1920]) ).
tff(1923,plain,
select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head),
inference(unit_resolution,[status(thm)],[1922,32,26]) ).
tff(1924,plain,
select(store(queue_67,head,index_69),head) = select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head),
inference(symmetry,[status(thm)],[1923]) ).
tff(1925,plain,
( ( index_69 = s(index_68) )
<=> ( index_69 = s(index_68) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1926,axiom,
index_69 = s(index_68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(1927,plain,
index_69 = s(index_68),
inference(modus_ponens,[status(thm)],[1926,1925]) ).
tff(1928,plain,
s(index_68) = index_69,
inference(symmetry,[status(thm)],[1927]) ).
tff(1929,plain,
( ( queue_67 = store(queue_65,tail,index_66) )
<=> ( queue_67 = store(queue_65,tail,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1930,axiom,
queue_67 = store(queue_65,tail,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp341) ).
tff(1931,plain,
queue_67 = store(queue_65,tail,index_66),
inference(modus_ponens,[status(thm)],[1930,1929]) ).
tff(1932,plain,
store(queue_65,tail,index_66) = queue_67,
inference(symmetry,[status(thm)],[1931]) ).
tff(1933,plain,
store(store(queue_65,tail,index_66),head,s(index_68)) = store(queue_67,head,index_69),
inference(monotonicity,[status(thm)],[1932,1928]) ).
tff(1934,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = select(store(queue_67,head,index_69),head),
inference(monotonicity,[status(thm)],[1933]) ).
tff(1935,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = s(index_68) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1936,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = s(index_68),
inference(unit_resolution,[status(thm)],[1935,6]) ).
tff(1937,plain,
s(index_68) = select(store(store(queue_65,tail,index_66),head,s(index_68)),head),
inference(symmetry,[status(thm)],[1936]) ).
tff(1938,plain,
( ( index_68 = select(queue_67,head) )
<=> ( index_68 = select(queue_67,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1939,axiom,
index_68 = select(queue_67,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(1940,plain,
index_68 = select(queue_67,head),
inference(modus_ponens,[status(thm)],[1939,1938]) ).
tff(1941,plain,
select(queue_67,head) = index_68,
inference(symmetry,[status(thm)],[1940]) ).
tff(1942,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1943,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(1944,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[1943,1942]) ).
tff(1945,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[1944]) ).
tff(1946,plain,
( ( queue_65 = store(q17,seq,earray_64) )
<=> ( queue_65 = store(q17,seq,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1947,axiom,
queue_65 = store(q17,seq,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp340) ).
tff(1948,plain,
queue_65 = store(q17,seq,earray_64),
inference(modus_ponens,[status(thm)],[1947,1946]) ).
tff(1949,plain,
store(q17,seq,earray_64) = queue_65,
inference(symmetry,[status(thm)],[1948]) ).
tff(1950,plain,
store(store(q17,seq,earray_64),tail,s(index_63)) = store(queue_65,tail,index_66),
inference(monotonicity,[status(thm)],[1949,1945]) ).
tff(1951,plain,
store(store(q17,seq,earray_64),tail,s(index_63)) = queue_67,
inference(transitivity,[status(thm)],[1950,1932]) ).
tff(1952,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(queue_67,head),
inference(monotonicity,[status(thm)],[1951]) ).
tff(1953,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1954,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1955,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(modus_ponens,[status(thm)],[1954,1953]) ).
tff(1956,plain,
( ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(unit_resolution,[status(thm)],[1955,32]) ).
tff(1957,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head),
inference(unit_resolution,[status(thm)],[1956,92]) ).
tff(1958,plain,
select(store(q17,seq,earray_64),head) = select(store(store(q17,seq,earray_64),tail,s(index_63)),head),
inference(symmetry,[status(thm)],[1957]) ).
tff(1959,plain,
( ( earray_64 = store(earray_62,index_63,e17) )
<=> ( earray_64 = store(earray_62,index_63,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1960,axiom,
earray_64 = store(earray_62,index_63,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(1961,plain,
earray_64 = store(earray_62,index_63,e17),
inference(modus_ponens,[status(thm)],[1960,1959]) ).
tff(1962,plain,
store(earray_62,index_63,e17) = earray_64,
inference(symmetry,[status(thm)],[1961]) ).
tff(1963,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = store(earray_62,index_63,e17) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1964,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = store(earray_62,index_63,e17),
inference(unit_resolution,[status(thm)],[1963,6]) ).
tff(1965,plain,
( ( q17 = queue_61 )
<=> ( q17 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1966,axiom,
q17 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp362) ).
tff(1967,plain,
q17 = queue_61,
inference(modus_ponens,[status(thm)],[1966,1965]) ).
tff(1968,plain,
queue_61 = q17,
inference(symmetry,[status(thm)],[1967]) ).
tff(1969,plain,
( ( queue_61 = store(queue_59,tail,index_60) )
<=> ( queue_61 = store(queue_59,tail,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1970,axiom,
queue_61 = store(queue_59,tail,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp339) ).
tff(1971,plain,
queue_61 = store(queue_59,tail,index_60),
inference(modus_ponens,[status(thm)],[1970,1969]) ).
tff(1972,plain,
store(queue_59,tail,index_60) = queue_61,
inference(symmetry,[status(thm)],[1971]) ).
tff(1973,plain,
store(queue_59,tail,index_60) = q17,
inference(transitivity,[status(thm)],[1972,1968]) ).
tff(1974,plain,
store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)) = store(q17,seq,earray_64),
inference(monotonicity,[status(thm)],[1973,1962]) ).
tff(1975,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = select(store(q17,seq,earray_64),seq),
inference(monotonicity,[status(thm)],[1974]) ).
tff(1976,plain,
select(store(q17,seq,earray_64),seq) = select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq),
inference(symmetry,[status(thm)],[1975]) ).
tff(1977,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1978,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1979,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ),
inference(modus_ponens,[status(thm)],[1978,1977]) ).
tff(1980,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq),
inference(unit_resolution,[status(thm)],[1979,32,57]) ).
tff(1981,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(queue_65,tail,index_66),seq),
inference(monotonicity,[status(thm)],[1950]) ).
tff(1982,plain,
select(store(queue_65,tail,index_66),seq) = select(store(store(q17,seq,earray_64),tail,s(index_63)),seq),
inference(symmetry,[status(thm)],[1981]) ).
tff(1983,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1984,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1985,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ),
inference(modus_ponens,[status(thm)],[1984,1983]) ).
tff(1986,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq),
inference(unit_resolution,[status(thm)],[1985,32,25]) ).
tff(1987,plain,
store(store(queue_65,tail,index_66),head,s(index_68)) = q18,
inference(transitivity,[status(thm)],[1933,1905,1901]) ).
tff(1988,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(q18,seq),
inference(monotonicity,[status(thm)],[1987]) ).
tff(1989,plain,
select(q18,seq) = select(store(store(queue_65,tail,index_66),head,s(index_68)),seq),
inference(symmetry,[status(thm)],[1988]) ).
tff(1990,plain,
select(q18,seq) = earray_64,
inference(transitivity,[status(thm)],[1989,1986,1982,1980,1976,1964,1962]) ).
tff(1991,plain,
store(store(queue_59,tail,index_60),seq,select(q18,seq)) = store(q17,seq,earray_64),
inference(monotonicity,[status(thm)],[1973,1990]) ).
tff(1992,plain,
select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(q17,seq,earray_64),head),
inference(monotonicity,[status(thm)],[1991]) ).
tff(1993,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1994,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1995,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(modus_ponens,[status(thm)],[1994,1993]) ).
tff(1996,plain,
( ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(unit_resolution,[status(thm)],[1995,32]) ).
tff(1997,plain,
select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head),
inference(unit_resolution,[status(thm)],[1996,26]) ).
tff(1998,plain,
select(store(queue_59,tail,index_60),head) = select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head),
inference(symmetry,[status(thm)],[1997]) ).
tff(1999,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2000,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(2001,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[2000,1999]) ).
tff(2002,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[2001]) ).
tff(2003,plain,
( ( queue_59 = store(q16,seq,earray_58) )
<=> ( queue_59 = store(q16,seq,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2004,axiom,
queue_59 = store(q16,seq,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp338) ).
tff(2005,plain,
queue_59 = store(q16,seq,earray_58),
inference(modus_ponens,[status(thm)],[2004,2003]) ).
tff(2006,plain,
store(q16,seq,earray_58) = queue_59,
inference(symmetry,[status(thm)],[2005]) ).
tff(2007,plain,
store(store(q16,seq,earray_58),tail,s(index_57)) = store(queue_59,tail,index_60),
inference(monotonicity,[status(thm)],[2006,2002]) ).
tff(2008,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(queue_59,tail,index_60),head),
inference(monotonicity,[status(thm)],[2007]) ).
tff(2009,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2010,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2011,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ),
inference(modus_ponens,[status(thm)],[2010,2009]) ).
tff(2012,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head),
inference(unit_resolution,[status(thm)],[2011,32,92]) ).
tff(2013,plain,
select(store(q16,seq,earray_58),head) = select(store(store(q16,seq,earray_58),tail,s(index_57)),head),
inference(symmetry,[status(thm)],[2012]) ).
tff(2014,plain,
( ( earray_58 = store(earray_56,index_57,e16) )
<=> ( earray_58 = store(earray_56,index_57,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2015,axiom,
earray_58 = store(earray_56,index_57,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(2016,plain,
earray_58 = store(earray_56,index_57,e16),
inference(modus_ponens,[status(thm)],[2015,2014]) ).
tff(2017,plain,
store(earray_56,index_57,e16) = earray_58,
inference(symmetry,[status(thm)],[2016]) ).
tff(2018,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = store(earray_56,index_57,e16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2019,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = store(earray_56,index_57,e16),
inference(unit_resolution,[status(thm)],[2018,6]) ).
tff(2020,plain,
queue_55 = q16,
inference(symmetry,[status(thm)],[188]) ).
tff(2021,plain,
store(queue_53,tail,index_54) = queue_55,
inference(symmetry,[status(thm)],[185]) ).
tff(2022,plain,
store(queue_53,tail,index_54) = q16,
inference(transitivity,[status(thm)],[2021,2020]) ).
tff(2023,plain,
store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)) = store(q16,seq,earray_58),
inference(monotonicity,[status(thm)],[2022,2017]) ).
tff(2024,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = select(store(q16,seq,earray_58),seq),
inference(monotonicity,[status(thm)],[2023]) ).
tff(2025,plain,
select(store(q16,seq,earray_58),seq) = select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq),
inference(symmetry,[status(thm)],[2024]) ).
tff(2026,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2027,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2028,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ),
inference(modus_ponens,[status(thm)],[2027,2026]) ).
tff(2029,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq),
inference(unit_resolution,[status(thm)],[2028,32,57]) ).
tff(2030,plain,
store(store(q16,seq,earray_58),tail,s(index_57)) = q17,
inference(transitivity,[status(thm)],[2007,1972,1968]) ).
tff(2031,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(q17,seq),
inference(monotonicity,[status(thm)],[2030]) ).
tff(2032,plain,
select(q17,seq) = select(store(store(q16,seq,earray_58),tail,s(index_57)),seq),
inference(symmetry,[status(thm)],[2031]) ).
tff(2033,plain,
select(q17,seq) = earray_58,
inference(transitivity,[status(thm)],[2032,2029,2025,2019,2017]) ).
tff(2034,plain,
store(store(queue_53,tail,index_54),seq,select(q17,seq)) = store(q16,seq,earray_58),
inference(monotonicity,[status(thm)],[2022,2033]) ).
tff(2035,plain,
select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(q16,seq,earray_58),head),
inference(monotonicity,[status(thm)],[2034]) ).
tff(2036,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2037,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2038,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(modus_ponens,[status(thm)],[2037,2036]) ).
tff(2039,plain,
select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head),
inference(unit_resolution,[status(thm)],[2038,32,26]) ).
tff(2040,plain,
select(store(queue_53,tail,index_54),head) = select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head),
inference(symmetry,[status(thm)],[2039]) ).
tff(2041,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(queue_53,tail,index_54),head),
inference(monotonicity,[status(thm)],[181]) ).
tff(2042,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2043,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2044,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ),
inference(modus_ponens,[status(thm)],[2043,2042]) ).
tff(2045,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head),
inference(unit_resolution,[status(thm)],[2044,32,92]) ).
tff(2046,plain,
select(store(q15,seq,earray_52),head) = select(store(store(q15,seq,earray_52),tail,s(index_51)),head),
inference(symmetry,[status(thm)],[2045]) ).
tff(2047,plain,
( ( earray_52 = store(earray_50,index_51,e15) )
<=> ( earray_52 = store(earray_50,index_51,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2048,axiom,
earray_52 = store(earray_50,index_51,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp86) ).
tff(2049,plain,
earray_52 = store(earray_50,index_51,e15),
inference(modus_ponens,[status(thm)],[2048,2047]) ).
tff(2050,plain,
store(earray_50,index_51,e15) = earray_52,
inference(symmetry,[status(thm)],[2049]) ).
tff(2051,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = store(earray_50,index_51,e15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2052,plain,
select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = store(earray_50,index_51,e15),
inference(unit_resolution,[status(thm)],[2051,6]) ).
tff(2053,plain,
queue_49 = q15,
inference(symmetry,[status(thm)],[233]) ).
tff(2054,plain,
store(queue_46,head,index_48) = queue_49,
inference(symmetry,[status(thm)],[230]) ).
tff(2055,plain,
store(queue_46,head,index_48) = q15,
inference(transitivity,[status(thm)],[2054,2053]) ).
tff(2056,plain,
store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)) = store(q15,seq,earray_52),
inference(monotonicity,[status(thm)],[2055,2050]) ).
tff(2057,plain,
select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = select(store(q15,seq,earray_52),seq),
inference(monotonicity,[status(thm)],[2056]) ).
tff(2058,plain,
select(store(q15,seq,earray_52),seq) = select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq),
inference(symmetry,[status(thm)],[2057]) ).
tff(2059,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2060,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ),
inference(modus_ponens,[status(thm)],[2060,2059]) ).
tff(2062,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq),
inference(unit_resolution,[status(thm)],[2061,32,57]) ).
tff(2063,plain,
store(store(q15,seq,earray_52),tail,s(index_51)) = q16,
inference(transitivity,[status(thm)],[181,2021,2020]) ).
tff(2064,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(q16,seq),
inference(monotonicity,[status(thm)],[2063]) ).
tff(2065,plain,
select(q16,seq) = select(store(store(q15,seq,earray_52),tail,s(index_51)),seq),
inference(symmetry,[status(thm)],[2064]) ).
tff(2066,plain,
select(q16,seq) = earray_52,
inference(transitivity,[status(thm)],[2065,2062,2058,2052,2050]) ).
tff(2067,plain,
store(store(queue_46,head,index_48),seq,select(q16,seq)) = store(q15,seq,earray_52),
inference(monotonicity,[status(thm)],[2055,2066]) ).
tff(2068,plain,
select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(q15,seq,earray_52),head),
inference(monotonicity,[status(thm)],[2067]) ).
tff(2069,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2070,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2071,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ),
inference(modus_ponens,[status(thm)],[2070,2069]) ).
tff(2072,plain,
select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head),
inference(unit_resolution,[status(thm)],[2071,32,26]) ).
tff(2073,plain,
select(store(queue_46,head,index_48),head) = select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head),
inference(symmetry,[status(thm)],[2072]) ).
tff(2074,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = select(store(queue_46,head,index_48),head),
inference(monotonicity,[status(thm)],[226]) ).
tff(2075,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = s(index_47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2076,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = s(index_47),
inference(unit_resolution,[status(thm)],[2075,6]) ).
tff(2077,plain,
s(index_47) = select(store(store(queue_44,tail,index_45),head,s(index_47)),head),
inference(symmetry,[status(thm)],[2076]) ).
tff(2078,plain,
( ( index_47 = select(queue_46,head) )
<=> ( index_47 = select(queue_46,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2079,axiom,
index_47 = select(queue_46,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(2080,plain,
index_47 = select(queue_46,head),
inference(modus_ponens,[status(thm)],[2079,2078]) ).
tff(2081,plain,
select(queue_46,head) = index_47,
inference(symmetry,[status(thm)],[2080]) ).
tff(2082,plain,
store(store(q14,seq,earray_43),tail,s(index_42)) = queue_46,
inference(transitivity,[status(thm)],[211,225]) ).
tff(2083,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(queue_46,head),
inference(monotonicity,[status(thm)],[2082]) ).
tff(2084,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2085,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2086,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(modus_ponens,[status(thm)],[2085,2084]) ).
tff(2087,plain,
( ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(unit_resolution,[status(thm)],[2086,32]) ).
tff(2088,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head),
inference(unit_resolution,[status(thm)],[2087,92]) ).
tff(2089,plain,
select(store(q14,seq,earray_43),head) = select(store(store(q14,seq,earray_43),tail,s(index_42)),head),
inference(symmetry,[status(thm)],[2088]) ).
tff(2090,plain,
( ( earray_43 = store(earray_41,index_42,e14) )
<=> ( earray_43 = store(earray_41,index_42,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2091,axiom,
earray_43 = store(earray_41,index_42,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp84) ).
tff(2092,plain,
earray_43 = store(earray_41,index_42,e14),
inference(modus_ponens,[status(thm)],[2091,2090]) ).
tff(2093,plain,
store(earray_41,index_42,e14) = earray_43,
inference(symmetry,[status(thm)],[2092]) ).
tff(2094,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = store(earray_41,index_42,e14) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2095,plain,
select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = store(earray_41,index_42,e14),
inference(unit_resolution,[status(thm)],[2094,6]) ).
tff(2096,plain,
( ( q14 = queue_40 )
<=> ( q14 = queue_40 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2097,axiom,
q14 = queue_40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp359) ).
tff(2098,plain,
q14 = queue_40,
inference(modus_ponens,[status(thm)],[2097,2096]) ).
tff(2099,plain,
queue_40 = q14,
inference(symmetry,[status(thm)],[2098]) ).
tff(2100,plain,
( ( queue_40 = store(queue_38,tail,index_39) )
<=> ( queue_40 = store(queue_38,tail,index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2101,axiom,
queue_40 = store(queue_38,tail,index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp331) ).
tff(2102,plain,
queue_40 = store(queue_38,tail,index_39),
inference(modus_ponens,[status(thm)],[2101,2100]) ).
tff(2103,plain,
store(queue_38,tail,index_39) = queue_40,
inference(symmetry,[status(thm)],[2102]) ).
tff(2104,plain,
store(queue_38,tail,index_39) = q14,
inference(transitivity,[status(thm)],[2103,2099]) ).
tff(2105,plain,
store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)) = store(q14,seq,earray_43),
inference(monotonicity,[status(thm)],[2104,2093]) ).
tff(2106,plain,
select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = select(store(q14,seq,earray_43),seq),
inference(monotonicity,[status(thm)],[2105]) ).
tff(2107,plain,
select(store(q14,seq,earray_43),seq) = select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq),
inference(symmetry,[status(thm)],[2106]) ).
tff(2108,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2109,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2110,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ),
inference(modus_ponens,[status(thm)],[2109,2108]) ).
tff(2111,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq),
inference(unit_resolution,[status(thm)],[2110,32,57]) ).
tff(2112,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(queue_44,tail,index_45),seq),
inference(monotonicity,[status(thm)],[211]) ).
tff(2113,plain,
select(store(queue_44,tail,index_45),seq) = select(store(store(q14,seq,earray_43),tail,s(index_42)),seq),
inference(symmetry,[status(thm)],[2112]) ).
tff(2114,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2115,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2116,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ),
inference(modus_ponens,[status(thm)],[2115,2114]) ).
tff(2117,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq),
inference(unit_resolution,[status(thm)],[2116,32,25]) ).
tff(2118,plain,
store(store(queue_44,tail,index_45),head,s(index_47)) = q15,
inference(transitivity,[status(thm)],[226,2054,2053]) ).
tff(2119,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(q15,seq),
inference(monotonicity,[status(thm)],[2118]) ).
tff(2120,plain,
select(q15,seq) = select(store(store(queue_44,tail,index_45),head,s(index_47)),seq),
inference(symmetry,[status(thm)],[2119]) ).
tff(2121,plain,
select(q15,seq) = earray_43,
inference(transitivity,[status(thm)],[2120,2117,2113,2111,2107,2095,2093]) ).
tff(2122,plain,
store(store(queue_38,tail,index_39),seq,select(q15,seq)) = store(q14,seq,earray_43),
inference(monotonicity,[status(thm)],[2104,2121]) ).
tff(2123,plain,
select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(q14,seq,earray_43),head),
inference(monotonicity,[status(thm)],[2122]) ).
tff(2124,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2125,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2126,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(modus_ponens,[status(thm)],[2125,2124]) ).
tff(2127,plain,
( ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(unit_resolution,[status(thm)],[2126,32]) ).
tff(2128,plain,
select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head),
inference(unit_resolution,[status(thm)],[2127,26]) ).
tff(2129,plain,
select(store(queue_38,tail,index_39),head) = select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head),
inference(symmetry,[status(thm)],[2128]) ).
tff(2130,plain,
( ( index_39 = s(index_36) )
<=> ( index_39 = s(index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2131,axiom,
index_39 = s(index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(2132,plain,
index_39 = s(index_36),
inference(modus_ponens,[status(thm)],[2131,2130]) ).
tff(2133,plain,
s(index_36) = index_39,
inference(symmetry,[status(thm)],[2132]) ).
tff(2134,plain,
( ( queue_38 = store(q13,seq,earray_37) )
<=> ( queue_38 = store(q13,seq,earray_37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2135,axiom,
queue_38 = store(q13,seq,earray_37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp330) ).
tff(2136,plain,
queue_38 = store(q13,seq,earray_37),
inference(modus_ponens,[status(thm)],[2135,2134]) ).
tff(2137,plain,
store(q13,seq,earray_37) = queue_38,
inference(symmetry,[status(thm)],[2136]) ).
tff(2138,plain,
store(store(q13,seq,earray_37),tail,s(index_36)) = store(queue_38,tail,index_39),
inference(monotonicity,[status(thm)],[2137,2133]) ).
tff(2139,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(queue_38,tail,index_39),head),
inference(monotonicity,[status(thm)],[2138]) ).
tff(2140,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2141,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2142,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ),
inference(modus_ponens,[status(thm)],[2141,2140]) ).
tff(2143,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head),
inference(unit_resolution,[status(thm)],[2142,32,92]) ).
tff(2144,plain,
select(store(q13,seq,earray_37),head) = select(store(store(q13,seq,earray_37),tail,s(index_36)),head),
inference(symmetry,[status(thm)],[2143]) ).
tff(2145,plain,
( ( earray_37 = store(earray_35,index_36,e13) )
<=> ( earray_37 = store(earray_35,index_36,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2146,axiom,
earray_37 = store(earray_35,index_36,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(2147,plain,
earray_37 = store(earray_35,index_36,e13),
inference(modus_ponens,[status(thm)],[2146,2145]) ).
tff(2148,plain,
store(earray_35,index_36,e13) = earray_37,
inference(symmetry,[status(thm)],[2147]) ).
tff(2149,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = store(earray_35,index_36,e13) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2150,plain,
select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = store(earray_35,index_36,e13),
inference(unit_resolution,[status(thm)],[2149,6]) ).
tff(2151,plain,
( ( q13 = queue_34 )
<=> ( q13 = queue_34 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2152,axiom,
q13 = queue_34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp358) ).
tff(2153,plain,
q13 = queue_34,
inference(modus_ponens,[status(thm)],[2152,2151]) ).
tff(2154,plain,
queue_34 = q13,
inference(symmetry,[status(thm)],[2153]) ).
tff(2155,plain,
( ( queue_34 = store(queue_32,tail,index_33) )
<=> ( queue_34 = store(queue_32,tail,index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2156,axiom,
queue_34 = store(queue_32,tail,index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp325) ).
tff(2157,plain,
queue_34 = store(queue_32,tail,index_33),
inference(modus_ponens,[status(thm)],[2156,2155]) ).
tff(2158,plain,
store(queue_32,tail,index_33) = queue_34,
inference(symmetry,[status(thm)],[2157]) ).
tff(2159,plain,
store(queue_32,tail,index_33) = q13,
inference(transitivity,[status(thm)],[2158,2154]) ).
tff(2160,plain,
store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)) = store(q13,seq,earray_37),
inference(monotonicity,[status(thm)],[2159,2148]) ).
tff(2161,plain,
select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = select(store(q13,seq,earray_37),seq),
inference(monotonicity,[status(thm)],[2160]) ).
tff(2162,plain,
select(store(q13,seq,earray_37),seq) = select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq),
inference(symmetry,[status(thm)],[2161]) ).
tff(2163,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2164,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2165,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ),
inference(modus_ponens,[status(thm)],[2164,2163]) ).
tff(2166,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq),
inference(unit_resolution,[status(thm)],[2165,32,57]) ).
tff(2167,plain,
store(store(q13,seq,earray_37),tail,s(index_36)) = q14,
inference(transitivity,[status(thm)],[2138,2103,2099]) ).
tff(2168,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(q14,seq),
inference(monotonicity,[status(thm)],[2167]) ).
tff(2169,plain,
select(q14,seq) = select(store(store(q13,seq,earray_37),tail,s(index_36)),seq),
inference(symmetry,[status(thm)],[2168]) ).
tff(2170,plain,
select(q14,seq) = earray_37,
inference(transitivity,[status(thm)],[2169,2166,2162,2150,2148]) ).
tff(2171,plain,
store(store(queue_32,tail,index_33),seq,select(q14,seq)) = store(q13,seq,earray_37),
inference(monotonicity,[status(thm)],[2159,2170]) ).
tff(2172,plain,
select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(q13,seq,earray_37),head),
inference(monotonicity,[status(thm)],[2171]) ).
tff(2173,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2174,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2175,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ),
inference(modus_ponens,[status(thm)],[2174,2173]) ).
tff(2176,plain,
select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head),
inference(unit_resolution,[status(thm)],[2175,32,26]) ).
tff(2177,plain,
select(store(queue_32,tail,index_33),head) = select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head),
inference(symmetry,[status(thm)],[2176]) ).
tff(2178,plain,
( ( index_33 = s(index_30) )
<=> ( index_33 = s(index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2179,axiom,
index_33 = s(index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(2180,plain,
index_33 = s(index_30),
inference(modus_ponens,[status(thm)],[2179,2178]) ).
tff(2181,plain,
s(index_30) = index_33,
inference(symmetry,[status(thm)],[2180]) ).
tff(2182,plain,
( ( queue_32 = store(q12,seq,earray_31) )
<=> ( queue_32 = store(q12,seq,earray_31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2183,axiom,
queue_32 = store(q12,seq,earray_31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp318) ).
tff(2184,plain,
queue_32 = store(q12,seq,earray_31),
inference(modus_ponens,[status(thm)],[2183,2182]) ).
tff(2185,plain,
store(q12,seq,earray_31) = queue_32,
inference(symmetry,[status(thm)],[2184]) ).
tff(2186,plain,
store(store(q12,seq,earray_31),tail,s(index_30)) = store(queue_32,tail,index_33),
inference(monotonicity,[status(thm)],[2185,2181]) ).
tff(2187,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(queue_32,tail,index_33),head),
inference(monotonicity,[status(thm)],[2186]) ).
tff(2188,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2189,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2190,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ),
inference(modus_ponens,[status(thm)],[2189,2188]) ).
tff(2191,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head),
inference(unit_resolution,[status(thm)],[2190,32,92]) ).
tff(2192,plain,
select(store(q12,seq,earray_31),head) = select(store(store(q12,seq,earray_31),tail,s(index_30)),head),
inference(symmetry,[status(thm)],[2191]) ).
tff(2193,plain,
( ( earray_31 = store(earray_29,index_30,e12) )
<=> ( earray_31 = store(earray_29,index_30,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2194,axiom,
earray_31 = store(earray_29,index_30,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp67) ).
tff(2195,plain,
earray_31 = store(earray_29,index_30,e12),
inference(modus_ponens,[status(thm)],[2194,2193]) ).
tff(2196,plain,
store(earray_29,index_30,e12) = earray_31,
inference(symmetry,[status(thm)],[2195]) ).
tff(2197,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = store(earray_29,index_30,e12) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2198,plain,
select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = store(earray_29,index_30,e12),
inference(unit_resolution,[status(thm)],[2197,6]) ).
tff(2199,plain,
( ( q12 = queue_28 )
<=> ( q12 = queue_28 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2200,axiom,
q12 = queue_28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp357) ).
tff(2201,plain,
q12 = queue_28,
inference(modus_ponens,[status(thm)],[2200,2199]) ).
tff(2202,plain,
queue_28 = q12,
inference(symmetry,[status(thm)],[2201]) ).
tff(2203,plain,
( ( queue_28 = store(queue_25,head,index_27) )
<=> ( queue_28 = store(queue_25,head,index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2204,axiom,
queue_28 = store(queue_25,head,index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp303) ).
tff(2205,plain,
queue_28 = store(queue_25,head,index_27),
inference(modus_ponens,[status(thm)],[2204,2203]) ).
tff(2206,plain,
store(queue_25,head,index_27) = queue_28,
inference(symmetry,[status(thm)],[2205]) ).
tff(2207,plain,
store(queue_25,head,index_27) = q12,
inference(transitivity,[status(thm)],[2206,2202]) ).
tff(2208,plain,
store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)) = store(q12,seq,earray_31),
inference(monotonicity,[status(thm)],[2207,2196]) ).
tff(2209,plain,
select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = select(store(q12,seq,earray_31),seq),
inference(monotonicity,[status(thm)],[2208]) ).
tff(2210,plain,
select(store(q12,seq,earray_31),seq) = select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq),
inference(symmetry,[status(thm)],[2209]) ).
tff(2211,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2212,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2213,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ),
inference(modus_ponens,[status(thm)],[2212,2211]) ).
tff(2214,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq),
inference(unit_resolution,[status(thm)],[2213,32,57]) ).
tff(2215,plain,
store(store(q12,seq,earray_31),tail,s(index_30)) = q13,
inference(transitivity,[status(thm)],[2186,2158,2154]) ).
tff(2216,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(q13,seq),
inference(monotonicity,[status(thm)],[2215]) ).
tff(2217,plain,
select(q13,seq) = select(store(store(q12,seq,earray_31),tail,s(index_30)),seq),
inference(symmetry,[status(thm)],[2216]) ).
tff(2218,plain,
select(q13,seq) = earray_31,
inference(transitivity,[status(thm)],[2217,2214,2210,2198,2196]) ).
tff(2219,plain,
store(store(queue_25,head,index_27),seq,select(q13,seq)) = store(q12,seq,earray_31),
inference(monotonicity,[status(thm)],[2207,2218]) ).
tff(2220,plain,
select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(q12,seq,earray_31),head),
inference(monotonicity,[status(thm)],[2219]) ).
tff(2221,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2222,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2223,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ),
inference(modus_ponens,[status(thm)],[2222,2221]) ).
tff(2224,plain,
select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head),
inference(unit_resolution,[status(thm)],[2223,32,26]) ).
tff(2225,plain,
select(store(queue_25,head,index_27),head) = select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head),
inference(symmetry,[status(thm)],[2224]) ).
tff(2226,plain,
( ( index_27 = s(index_26) )
<=> ( index_27 = s(index_26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2227,axiom,
index_27 = s(index_26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(2228,plain,
index_27 = s(index_26),
inference(modus_ponens,[status(thm)],[2227,2226]) ).
tff(2229,plain,
s(index_26) = index_27,
inference(symmetry,[status(thm)],[2228]) ).
tff(2230,plain,
( ( queue_25 = store(queue_23,tail,index_24) )
<=> ( queue_25 = store(queue_23,tail,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2231,axiom,
queue_25 = store(queue_23,tail,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp292) ).
tff(2232,plain,
queue_25 = store(queue_23,tail,index_24),
inference(modus_ponens,[status(thm)],[2231,2230]) ).
tff(2233,plain,
store(queue_23,tail,index_24) = queue_25,
inference(symmetry,[status(thm)],[2232]) ).
tff(2234,plain,
store(store(queue_23,tail,index_24),head,s(index_26)) = store(queue_25,head,index_27),
inference(monotonicity,[status(thm)],[2233,2229]) ).
tff(2235,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = select(store(queue_25,head,index_27),head),
inference(monotonicity,[status(thm)],[2234]) ).
tff(2236,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = s(index_26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2237,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = s(index_26),
inference(unit_resolution,[status(thm)],[2236,6]) ).
tff(2238,plain,
s(index_26) = select(store(store(queue_23,tail,index_24),head,s(index_26)),head),
inference(symmetry,[status(thm)],[2237]) ).
tff(2239,plain,
( ( index_26 = select(queue_25,head) )
<=> ( index_26 = select(queue_25,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2240,axiom,
index_26 = select(queue_25,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(2241,plain,
index_26 = select(queue_25,head),
inference(modus_ponens,[status(thm)],[2240,2239]) ).
tff(2242,plain,
select(queue_25,head) = index_26,
inference(symmetry,[status(thm)],[2241]) ).
tff(2243,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2244,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(2245,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[2244,2243]) ).
tff(2246,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[2245]) ).
tff(2247,plain,
( ( queue_23 = store(q11,seq,earray_22) )
<=> ( queue_23 = store(q11,seq,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2248,axiom,
queue_23 = store(q11,seq,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp285) ).
tff(2249,plain,
queue_23 = store(q11,seq,earray_22),
inference(modus_ponens,[status(thm)],[2248,2247]) ).
tff(2250,plain,
store(q11,seq,earray_22) = queue_23,
inference(symmetry,[status(thm)],[2249]) ).
tff(2251,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = store(queue_23,tail,index_24),
inference(monotonicity,[status(thm)],[2250,2246]) ).
tff(2252,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = queue_25,
inference(transitivity,[status(thm)],[2251,2233]) ).
tff(2253,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(queue_25,head),
inference(monotonicity,[status(thm)],[2252]) ).
tff(2254,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2255,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2256,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(modus_ponens,[status(thm)],[2255,2254]) ).
tff(2257,plain,
( ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(unit_resolution,[status(thm)],[2256,32]) ).
tff(2258,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head),
inference(unit_resolution,[status(thm)],[2257,92]) ).
tff(2259,plain,
select(store(q11,seq,earray_22),head) = select(store(store(q11,seq,earray_22),tail,s(index_21)),head),
inference(symmetry,[status(thm)],[2258]) ).
tff(2260,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2261,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(2262,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[2261,2260]) ).
tff(2263,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[2262]) ).
tff(2264,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = store(earray_20,index_21,e11) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2265,plain,
select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = store(earray_20,index_21,e11),
inference(unit_resolution,[status(thm)],[2264,6]) ).
tff(2266,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2267,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp356) ).
tff(2268,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[2267,2266]) ).
tff(2269,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[2268]) ).
tff(2270,plain,
( ( queue_19 = store(queue_17,tail,index_18) )
<=> ( queue_19 = store(queue_17,tail,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2271,axiom,
queue_19 = store(queue_17,tail,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp270) ).
tff(2272,plain,
queue_19 = store(queue_17,tail,index_18),
inference(modus_ponens,[status(thm)],[2271,2270]) ).
tff(2273,plain,
store(queue_17,tail,index_18) = queue_19,
inference(symmetry,[status(thm)],[2272]) ).
tff(2274,plain,
store(queue_17,tail,index_18) = q11,
inference(transitivity,[status(thm)],[2273,2269]) ).
tff(2275,plain,
store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[2274,2263]) ).
tff(2276,plain,
select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = select(store(q11,seq,earray_22),seq),
inference(monotonicity,[status(thm)],[2275]) ).
tff(2277,plain,
select(store(q11,seq,earray_22),seq) = select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq),
inference(symmetry,[status(thm)],[2276]) ).
tff(2278,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2279,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2280,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ),
inference(modus_ponens,[status(thm)],[2279,2278]) ).
tff(2281,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq),
inference(unit_resolution,[status(thm)],[2280,32,57]) ).
tff(2282,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(queue_23,tail,index_24),seq),
inference(monotonicity,[status(thm)],[2251]) ).
tff(2283,plain,
select(store(queue_23,tail,index_24),seq) = select(store(store(q11,seq,earray_22),tail,s(index_21)),seq),
inference(symmetry,[status(thm)],[2282]) ).
tff(2284,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2285,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2286,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ),
inference(modus_ponens,[status(thm)],[2285,2284]) ).
tff(2287,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq),
inference(unit_resolution,[status(thm)],[2286,32,25]) ).
tff(2288,plain,
store(store(queue_23,tail,index_24),head,s(index_26)) = q12,
inference(transitivity,[status(thm)],[2234,2206,2202]) ).
tff(2289,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(q12,seq),
inference(monotonicity,[status(thm)],[2288]) ).
tff(2290,plain,
select(q12,seq) = select(store(store(queue_23,tail,index_24),head,s(index_26)),seq),
inference(symmetry,[status(thm)],[2289]) ).
tff(2291,plain,
select(q12,seq) = earray_22,
inference(transitivity,[status(thm)],[2290,2287,2283,2281,2277,2265,2263]) ).
tff(2292,plain,
store(store(queue_17,tail,index_18),seq,select(q12,seq)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[2274,2291]) ).
tff(2293,plain,
select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(q11,seq,earray_22),head),
inference(monotonicity,[status(thm)],[2292]) ).
tff(2294,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2295,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2296,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(modus_ponens,[status(thm)],[2295,2294]) ).
tff(2297,plain,
( ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(unit_resolution,[status(thm)],[2296,32]) ).
tff(2298,plain,
select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head),
inference(unit_resolution,[status(thm)],[2297,26]) ).
tff(2299,plain,
select(store(queue_17,tail,index_18),head) = select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head),
inference(symmetry,[status(thm)],[2298]) ).
tff(2300,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2301,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(2302,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[2301,2300]) ).
tff(2303,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[2302]) ).
tff(2304,plain,
( ( queue_17 = store(q10,seq,earray_16) )
<=> ( queue_17 = store(q10,seq,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2305,axiom,
queue_17 = store(q10,seq,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp263) ).
tff(2306,plain,
queue_17 = store(q10,seq,earray_16),
inference(modus_ponens,[status(thm)],[2305,2304]) ).
tff(2307,plain,
store(q10,seq,earray_16) = queue_17,
inference(symmetry,[status(thm)],[2306]) ).
tff(2308,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = store(queue_17,tail,index_18),
inference(monotonicity,[status(thm)],[2307,2303]) ).
tff(2309,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(queue_17,tail,index_18),head),
inference(monotonicity,[status(thm)],[2308]) ).
tff(2310,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2311,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2312,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(modus_ponens,[status(thm)],[2311,2310]) ).
tff(2313,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head),
inference(unit_resolution,[status(thm)],[2312,32,92]) ).
tff(2314,plain,
select(store(q10,seq,earray_16),head) = select(store(store(q10,seq,earray_16),tail,s(index_15)),head),
inference(symmetry,[status(thm)],[2313]) ).
tff(2315,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2316,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp19) ).
tff(2317,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[2316,2315]) ).
tff(2318,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[2317]) ).
tff(2319,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = store(earray_14,index_15,e10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2320,plain,
select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = store(earray_14,index_15,e10),
inference(unit_resolution,[status(thm)],[2319,6]) ).
tff(2321,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2322,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp355) ).
tff(2323,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[2322,2321]) ).
tff(2324,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[2323]) ).
tff(2325,plain,
( ( queue_13 = store(queue_11,tail,index_12) )
<=> ( queue_13 = store(queue_11,tail,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2326,axiom,
queue_13 = store(queue_11,tail,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp248) ).
tff(2327,plain,
queue_13 = store(queue_11,tail,index_12),
inference(modus_ponens,[status(thm)],[2326,2325]) ).
tff(2328,plain,
store(queue_11,tail,index_12) = queue_13,
inference(symmetry,[status(thm)],[2327]) ).
tff(2329,plain,
store(queue_11,tail,index_12) = q10,
inference(transitivity,[status(thm)],[2328,2324]) ).
tff(2330,plain,
store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[2329,2318]) ).
tff(2331,plain,
select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = select(store(q10,seq,earray_16),seq),
inference(monotonicity,[status(thm)],[2330]) ).
tff(2332,plain,
select(store(q10,seq,earray_16),seq) = select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq),
inference(symmetry,[status(thm)],[2331]) ).
tff(2333,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2334,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2335,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ),
inference(modus_ponens,[status(thm)],[2334,2333]) ).
tff(2336,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq),
inference(unit_resolution,[status(thm)],[2335,32,57]) ).
tff(2337,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = q11,
inference(transitivity,[status(thm)],[2308,2273,2269]) ).
tff(2338,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(q11,seq),
inference(monotonicity,[status(thm)],[2337]) ).
tff(2339,plain,
select(q11,seq) = select(store(store(q10,seq,earray_16),tail,s(index_15)),seq),
inference(symmetry,[status(thm)],[2338]) ).
tff(2340,plain,
select(q11,seq) = earray_16,
inference(transitivity,[status(thm)],[2339,2336,2332,2320,2318]) ).
tff(2341,plain,
store(store(queue_11,tail,index_12),seq,select(q11,seq)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[2329,2340]) ).
tff(2342,plain,
select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(q10,seq,earray_16),head),
inference(monotonicity,[status(thm)],[2341]) ).
tff(2343,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2344,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2345,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ),
inference(modus_ponens,[status(thm)],[2344,2343]) ).
tff(2346,plain,
select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head),
inference(unit_resolution,[status(thm)],[2345,32,26]) ).
tff(2347,plain,
select(store(queue_11,tail,index_12),head) = select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head),
inference(symmetry,[status(thm)],[2346]) ).
tff(2348,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2349,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(2350,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[2349,2348]) ).
tff(2351,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[2350]) ).
tff(2352,plain,
( ( queue_11 = store(q9,seq,earray_10) )
<=> ( queue_11 = store(q9,seq,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2353,axiom,
queue_11 = store(q9,seq,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(2354,plain,
queue_11 = store(q9,seq,earray_10),
inference(modus_ponens,[status(thm)],[2353,2352]) ).
tff(2355,plain,
store(q9,seq,earray_10) = queue_11,
inference(symmetry,[status(thm)],[2354]) ).
tff(2356,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = store(queue_11,tail,index_12),
inference(monotonicity,[status(thm)],[2355,2351]) ).
tff(2357,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(queue_11,tail,index_12),head),
inference(monotonicity,[status(thm)],[2356]) ).
tff(2358,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2359,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2360,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(modus_ponens,[status(thm)],[2359,2358]) ).
tff(2361,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head),
inference(unit_resolution,[status(thm)],[2360,32,92]) ).
tff(2362,plain,
select(store(q9,seq,earray_10),head) = select(store(store(q9,seq,earray_10),tail,s(index_9)),head),
inference(symmetry,[status(thm)],[2361]) ).
tff(2363,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2364,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(2365,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[2364,2363]) ).
tff(2366,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[2365]) ).
tff(2367,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_346,head,index_348),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2368,plain,
select(store(store(queue_346,head,index_348),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9),
inference(unit_resolution,[status(thm)],[2367,6]) ).
tff(2369,plain,
( ( q9 = queue_349 )
<=> ( q9 = queue_349 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2370,axiom,
q9 = queue_349,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp403) ).
tff(2371,plain,
q9 = queue_349,
inference(modus_ponens,[status(thm)],[2370,2369]) ).
tff(2372,plain,
queue_349 = q9,
inference(symmetry,[status(thm)],[2371]) ).
tff(2373,plain,
( ( queue_349 = store(queue_346,head,index_348) )
<=> ( queue_349 = store(queue_346,head,index_348) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2374,axiom,
queue_349 = store(queue_346,head,index_348),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp329) ).
tff(2375,plain,
queue_349 = store(queue_346,head,index_348),
inference(modus_ponens,[status(thm)],[2374,2373]) ).
tff(2376,plain,
store(queue_346,head,index_348) = queue_349,
inference(symmetry,[status(thm)],[2375]) ).
tff(2377,plain,
store(queue_346,head,index_348) = q9,
inference(transitivity,[status(thm)],[2376,2372]) ).
tff(2378,plain,
store(store(queue_346,head,index_348),seq,store(earray_8,index_9,e9)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[2377,2366]) ).
tff(2379,plain,
select(store(store(queue_346,head,index_348),seq,store(earray_8,index_9,e9)),seq) = select(store(q9,seq,earray_10),seq),
inference(monotonicity,[status(thm)],[2378]) ).
tff(2380,plain,
select(store(q9,seq,earray_10),seq) = select(store(store(queue_346,head,index_348),seq,store(earray_8,index_9,e9)),seq),
inference(symmetry,[status(thm)],[2379]) ).
tff(2381,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2382,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2383,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ),
inference(modus_ponens,[status(thm)],[2382,2381]) ).
tff(2384,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq),
inference(unit_resolution,[status(thm)],[2383,32,57]) ).
tff(2385,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = q10,
inference(transitivity,[status(thm)],[2356,2328,2324]) ).
tff(2386,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(q10,seq),
inference(monotonicity,[status(thm)],[2385]) ).
tff(2387,plain,
select(q10,seq) = select(store(store(q9,seq,earray_10),tail,s(index_9)),seq),
inference(symmetry,[status(thm)],[2386]) ).
tff(2388,plain,
select(q10,seq) = earray_10,
inference(transitivity,[status(thm)],[2387,2384,2380,2368,2366]) ).
tff(2389,plain,
store(store(queue_346,head,index_348),seq,select(q10,seq)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[2377,2388]) ).
tff(2390,plain,
select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(q9,seq,earray_10),head),
inference(monotonicity,[status(thm)],[2389]) ).
tff(2391,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(queue_346,head,index_348),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(queue_346,head,index_348),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2392,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(queue_346,head,index_348),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2393,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(queue_346,head,index_348),head) ) ),
inference(modus_ponens,[status(thm)],[2392,2391]) ).
tff(2394,plain,
select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head) = select(store(queue_346,head,index_348),head),
inference(unit_resolution,[status(thm)],[2393,32,26]) ).
tff(2395,plain,
select(store(queue_346,head,index_348),head) = select(store(store(queue_346,head,index_348),seq,select(q10,seq)),head),
inference(symmetry,[status(thm)],[2394]) ).
tff(2396,plain,
( ( index_348 = s(index_347) )
<=> ( index_348 = s(index_347) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2397,axiom,
index_348 = s(index_347),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(2398,plain,
index_348 = s(index_347),
inference(modus_ponens,[status(thm)],[2397,2396]) ).
tff(2399,plain,
s(index_347) = index_348,
inference(symmetry,[status(thm)],[2398]) ).
tff(2400,plain,
( ( queue_346 = store(queue_344,tail,index_345) )
<=> ( queue_346 = store(queue_344,tail,index_345) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2401,axiom,
queue_346 = store(queue_344,tail,index_345),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp328) ).
tff(2402,plain,
queue_346 = store(queue_344,tail,index_345),
inference(modus_ponens,[status(thm)],[2401,2400]) ).
tff(2403,plain,
store(queue_344,tail,index_345) = queue_346,
inference(symmetry,[status(thm)],[2402]) ).
tff(2404,plain,
store(store(queue_344,tail,index_345),head,s(index_347)) = store(queue_346,head,index_348),
inference(monotonicity,[status(thm)],[2403,2399]) ).
tff(2405,plain,
select(store(store(queue_344,tail,index_345),head,s(index_347)),head) = select(store(queue_346,head,index_348),head),
inference(monotonicity,[status(thm)],[2404]) ).
tff(2406,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),head) = s(index_347) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2407,plain,
select(store(store(queue_344,tail,index_345),head,s(index_347)),head) = s(index_347),
inference(unit_resolution,[status(thm)],[2406,6]) ).
tff(2408,plain,
s(index_347) = select(store(store(queue_344,tail,index_345),head,s(index_347)),head),
inference(symmetry,[status(thm)],[2407]) ).
tff(2409,plain,
( ( index_347 = select(queue_346,head) )
<=> ( index_347 = select(queue_346,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2410,axiom,
index_347 = select(queue_346,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(2411,plain,
index_347 = select(queue_346,head),
inference(modus_ponens,[status(thm)],[2410,2409]) ).
tff(2412,plain,
select(queue_346,head) = index_347,
inference(symmetry,[status(thm)],[2411]) ).
tff(2413,plain,
( ( index_345 = s(index_342) )
<=> ( index_345 = s(index_342) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2414,axiom,
index_345 = s(index_342),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(2415,plain,
index_345 = s(index_342),
inference(modus_ponens,[status(thm)],[2414,2413]) ).
tff(2416,plain,
s(index_342) = index_345,
inference(symmetry,[status(thm)],[2415]) ).
tff(2417,plain,
( ( queue_344 = store(q8,seq,earray_343) )
<=> ( queue_344 = store(q8,seq,earray_343) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2418,axiom,
queue_344 = store(q8,seq,earray_343),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp327) ).
tff(2419,plain,
queue_344 = store(q8,seq,earray_343),
inference(modus_ponens,[status(thm)],[2418,2417]) ).
tff(2420,plain,
store(q8,seq,earray_343) = queue_344,
inference(symmetry,[status(thm)],[2419]) ).
tff(2421,plain,
store(store(q8,seq,earray_343),tail,s(index_342)) = store(queue_344,tail,index_345),
inference(monotonicity,[status(thm)],[2420,2416]) ).
tff(2422,plain,
store(store(q8,seq,earray_343),tail,s(index_342)) = queue_346,
inference(transitivity,[status(thm)],[2421,2403]) ).
tff(2423,plain,
select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(queue_346,head),
inference(monotonicity,[status(thm)],[2422]) ).
tff(2424,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2425,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2426,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head) ) ),
inference(modus_ponens,[status(thm)],[2425,2424]) ).
tff(2427,plain,
( ( tail = head )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head) ) ),
inference(unit_resolution,[status(thm)],[2426,32]) ).
tff(2428,plain,
select(store(store(q8,seq,earray_343),tail,s(index_342)),head) = select(store(q8,seq,earray_343),head),
inference(unit_resolution,[status(thm)],[2427,92]) ).
tff(2429,plain,
select(store(q8,seq,earray_343),head) = select(store(store(q8,seq,earray_343),tail,s(index_342)),head),
inference(symmetry,[status(thm)],[2428]) ).
tff(2430,plain,
( ( earray_343 = store(earray_341,index_342,e8) )
<=> ( earray_343 = store(earray_341,index_342,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2431,axiom,
earray_343 = store(earray_341,index_342,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(2432,plain,
earray_343 = store(earray_341,index_342,e8),
inference(modus_ponens,[status(thm)],[2431,2430]) ).
tff(2433,plain,
store(earray_341,index_342,e8) = earray_343,
inference(symmetry,[status(thm)],[2432]) ).
tff(2434,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_338,tail,index_339),seq,store(earray_341,index_342,e8)),seq) = store(earray_341,index_342,e8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2435,plain,
select(store(store(queue_338,tail,index_339),seq,store(earray_341,index_342,e8)),seq) = store(earray_341,index_342,e8),
inference(unit_resolution,[status(thm)],[2434,6]) ).
tff(2436,plain,
( ( q8 = queue_340 )
<=> ( q8 = queue_340 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2437,axiom,
q8 = queue_340,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp402) ).
tff(2438,plain,
q8 = queue_340,
inference(modus_ponens,[status(thm)],[2437,2436]) ).
tff(2439,plain,
queue_340 = q8,
inference(symmetry,[status(thm)],[2438]) ).
tff(2440,plain,
( ( queue_340 = store(queue_338,tail,index_339) )
<=> ( queue_340 = store(queue_338,tail,index_339) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2441,axiom,
queue_340 = store(queue_338,tail,index_339),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp326) ).
tff(2442,plain,
queue_340 = store(queue_338,tail,index_339),
inference(modus_ponens,[status(thm)],[2441,2440]) ).
tff(2443,plain,
store(queue_338,tail,index_339) = queue_340,
inference(symmetry,[status(thm)],[2442]) ).
tff(2444,plain,
store(queue_338,tail,index_339) = q8,
inference(transitivity,[status(thm)],[2443,2439]) ).
tff(2445,plain,
store(store(queue_338,tail,index_339),seq,store(earray_341,index_342,e8)) = store(q8,seq,earray_343),
inference(monotonicity,[status(thm)],[2444,2433]) ).
tff(2446,plain,
select(store(store(queue_338,tail,index_339),seq,store(earray_341,index_342,e8)),seq) = select(store(q8,seq,earray_343),seq),
inference(monotonicity,[status(thm)],[2445]) ).
tff(2447,plain,
select(store(q8,seq,earray_343),seq) = select(store(store(queue_338,tail,index_339),seq,store(earray_341,index_342,e8)),seq),
inference(symmetry,[status(thm)],[2446]) ).
tff(2448,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(q8,seq,earray_343),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(q8,seq,earray_343),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2449,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(q8,seq,earray_343),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2450,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(q8,seq,earray_343),seq) ) ),
inference(modus_ponens,[status(thm)],[2449,2448]) ).
tff(2451,plain,
select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(q8,seq,earray_343),seq),
inference(unit_resolution,[status(thm)],[2450,32,57]) ).
tff(2452,plain,
select(store(store(q8,seq,earray_343),tail,s(index_342)),seq) = select(store(queue_344,tail,index_345),seq),
inference(monotonicity,[status(thm)],[2421]) ).
tff(2453,plain,
select(store(queue_344,tail,index_345),seq) = select(store(store(q8,seq,earray_343),tail,s(index_342)),seq),
inference(symmetry,[status(thm)],[2452]) ).
tff(2454,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(store(queue_344,tail,index_345),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(store(queue_344,tail,index_345),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2455,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(store(queue_344,tail,index_345),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2456,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(store(queue_344,tail,index_345),seq) ) ),
inference(modus_ponens,[status(thm)],[2455,2454]) ).
tff(2457,plain,
select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(store(queue_344,tail,index_345),seq),
inference(unit_resolution,[status(thm)],[2456,32,25]) ).
tff(2458,plain,
store(store(queue_344,tail,index_345),head,s(index_347)) = q9,
inference(transitivity,[status(thm)],[2404,2376,2372]) ).
tff(2459,plain,
select(store(store(queue_344,tail,index_345),head,s(index_347)),seq) = select(q9,seq),
inference(monotonicity,[status(thm)],[2458]) ).
tff(2460,plain,
select(q9,seq) = select(store(store(queue_344,tail,index_345),head,s(index_347)),seq),
inference(symmetry,[status(thm)],[2459]) ).
tff(2461,plain,
select(q9,seq) = earray_343,
inference(transitivity,[status(thm)],[2460,2457,2453,2451,2447,2435,2433]) ).
tff(2462,plain,
store(store(queue_338,tail,index_339),seq,select(q9,seq)) = store(q8,seq,earray_343),
inference(monotonicity,[status(thm)],[2444,2461]) ).
tff(2463,plain,
select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(q8,seq,earray_343),head),
inference(monotonicity,[status(thm)],[2462]) ).
tff(2464,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2465,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2466,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head) ) ),
inference(modus_ponens,[status(thm)],[2465,2464]) ).
tff(2467,plain,
( ( seq = head )
| ( select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head) ) ),
inference(unit_resolution,[status(thm)],[2466,32]) ).
tff(2468,plain,
select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head) = select(store(queue_338,tail,index_339),head),
inference(unit_resolution,[status(thm)],[2467,26]) ).
tff(2469,plain,
select(store(queue_338,tail,index_339),head) = select(store(store(queue_338,tail,index_339),seq,select(q9,seq)),head),
inference(symmetry,[status(thm)],[2468]) ).
tff(2470,plain,
( ( index_339 = s(index_336) )
<=> ( index_339 = s(index_336) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2471,axiom,
index_339 = s(index_336),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(2472,plain,
index_339 = s(index_336),
inference(modus_ponens,[status(thm)],[2471,2470]) ).
tff(2473,plain,
s(index_336) = index_339,
inference(symmetry,[status(thm)],[2472]) ).
tff(2474,plain,
( ( queue_338 = store(q7,seq,earray_337) )
<=> ( queue_338 = store(q7,seq,earray_337) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2475,axiom,
queue_338 = store(q7,seq,earray_337),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp324) ).
tff(2476,plain,
queue_338 = store(q7,seq,earray_337),
inference(modus_ponens,[status(thm)],[2475,2474]) ).
tff(2477,plain,
store(q7,seq,earray_337) = queue_338,
inference(symmetry,[status(thm)],[2476]) ).
tff(2478,plain,
store(store(q7,seq,earray_337),tail,s(index_336)) = store(queue_338,tail,index_339),
inference(monotonicity,[status(thm)],[2477,2473]) ).
tff(2479,plain,
select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(queue_338,tail,index_339),head),
inference(monotonicity,[status(thm)],[2478]) ).
tff(2480,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(q7,seq,earray_337),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(q7,seq,earray_337),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2481,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(q7,seq,earray_337),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2482,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(q7,seq,earray_337),head) ) ),
inference(modus_ponens,[status(thm)],[2481,2480]) ).
tff(2483,plain,
select(store(store(q7,seq,earray_337),tail,s(index_336)),head) = select(store(q7,seq,earray_337),head),
inference(unit_resolution,[status(thm)],[2482,32,92]) ).
tff(2484,plain,
select(store(q7,seq,earray_337),head) = select(store(store(q7,seq,earray_337),tail,s(index_336)),head),
inference(symmetry,[status(thm)],[2483]) ).
tff(2485,plain,
( ( earray_337 = store(earray_335,index_336,e7) )
<=> ( earray_337 = store(earray_335,index_336,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2486,axiom,
earray_337 = store(earray_335,index_336,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(2487,plain,
earray_337 = store(earray_335,index_336,e7),
inference(modus_ponens,[status(thm)],[2486,2485]) ).
tff(2488,plain,
store(earray_335,index_336,e7) = earray_337,
inference(symmetry,[status(thm)],[2487]) ).
tff(2489,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_332,tail,index_333),seq,store(earray_335,index_336,e7)),seq) = store(earray_335,index_336,e7) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2490,plain,
select(store(store(queue_332,tail,index_333),seq,store(earray_335,index_336,e7)),seq) = store(earray_335,index_336,e7),
inference(unit_resolution,[status(thm)],[2489,6]) ).
tff(2491,plain,
( ( q7 = queue_334 )
<=> ( q7 = queue_334 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2492,axiom,
q7 = queue_334,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp401) ).
tff(2493,plain,
q7 = queue_334,
inference(modus_ponens,[status(thm)],[2492,2491]) ).
tff(2494,plain,
queue_334 = q7,
inference(symmetry,[status(thm)],[2493]) ).
tff(2495,plain,
( ( queue_334 = store(queue_332,tail,index_333) )
<=> ( queue_334 = store(queue_332,tail,index_333) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2496,axiom,
queue_334 = store(queue_332,tail,index_333),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp323) ).
tff(2497,plain,
queue_334 = store(queue_332,tail,index_333),
inference(modus_ponens,[status(thm)],[2496,2495]) ).
tff(2498,plain,
store(queue_332,tail,index_333) = queue_334,
inference(symmetry,[status(thm)],[2497]) ).
tff(2499,plain,
store(queue_332,tail,index_333) = q7,
inference(transitivity,[status(thm)],[2498,2494]) ).
tff(2500,plain,
store(store(queue_332,tail,index_333),seq,store(earray_335,index_336,e7)) = store(q7,seq,earray_337),
inference(monotonicity,[status(thm)],[2499,2488]) ).
tff(2501,plain,
select(store(store(queue_332,tail,index_333),seq,store(earray_335,index_336,e7)),seq) = select(store(q7,seq,earray_337),seq),
inference(monotonicity,[status(thm)],[2500]) ).
tff(2502,plain,
select(store(q7,seq,earray_337),seq) = select(store(store(queue_332,tail,index_333),seq,store(earray_335,index_336,e7)),seq),
inference(symmetry,[status(thm)],[2501]) ).
tff(2503,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(store(q7,seq,earray_337),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(store(q7,seq,earray_337),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2504,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(store(q7,seq,earray_337),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2505,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(store(q7,seq,earray_337),seq) ) ),
inference(modus_ponens,[status(thm)],[2504,2503]) ).
tff(2506,plain,
select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(store(q7,seq,earray_337),seq),
inference(unit_resolution,[status(thm)],[2505,32,57]) ).
tff(2507,plain,
store(store(q7,seq,earray_337),tail,s(index_336)) = q8,
inference(transitivity,[status(thm)],[2478,2443,2439]) ).
tff(2508,plain,
select(store(store(q7,seq,earray_337),tail,s(index_336)),seq) = select(q8,seq),
inference(monotonicity,[status(thm)],[2507]) ).
tff(2509,plain,
select(q8,seq) = select(store(store(q7,seq,earray_337),tail,s(index_336)),seq),
inference(symmetry,[status(thm)],[2508]) ).
tff(2510,plain,
select(q8,seq) = earray_337,
inference(transitivity,[status(thm)],[2509,2506,2502,2490,2488]) ).
tff(2511,plain,
store(store(queue_332,tail,index_333),seq,select(q8,seq)) = store(q7,seq,earray_337),
inference(monotonicity,[status(thm)],[2499,2510]) ).
tff(2512,plain,
select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(q7,seq,earray_337),head),
inference(monotonicity,[status(thm)],[2511]) ).
tff(2513,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(queue_332,tail,index_333),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(queue_332,tail,index_333),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2514,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(queue_332,tail,index_333),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2515,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(queue_332,tail,index_333),head) ) ),
inference(modus_ponens,[status(thm)],[2514,2513]) ).
tff(2516,plain,
select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head) = select(store(queue_332,tail,index_333),head),
inference(unit_resolution,[status(thm)],[2515,32,26]) ).
tff(2517,plain,
select(store(queue_332,tail,index_333),head) = select(store(store(queue_332,tail,index_333),seq,select(q8,seq)),head),
inference(symmetry,[status(thm)],[2516]) ).
tff(2518,plain,
( ( index_333 = s(index_330) )
<=> ( index_333 = s(index_330) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2519,axiom,
index_333 = s(index_330),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(2520,plain,
index_333 = s(index_330),
inference(modus_ponens,[status(thm)],[2519,2518]) ).
tff(2521,plain,
s(index_330) = index_333,
inference(symmetry,[status(thm)],[2520]) ).
tff(2522,plain,
( ( queue_332 = store(q6,seq,earray_331) )
<=> ( queue_332 = store(q6,seq,earray_331) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2523,axiom,
queue_332 = store(q6,seq,earray_331),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp322) ).
tff(2524,plain,
queue_332 = store(q6,seq,earray_331),
inference(modus_ponens,[status(thm)],[2523,2522]) ).
tff(2525,plain,
store(q6,seq,earray_331) = queue_332,
inference(symmetry,[status(thm)],[2524]) ).
tff(2526,plain,
store(store(q6,seq,earray_331),tail,s(index_330)) = store(queue_332,tail,index_333),
inference(monotonicity,[status(thm)],[2525,2521]) ).
tff(2527,plain,
select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(queue_332,tail,index_333),head),
inference(monotonicity,[status(thm)],[2526]) ).
tff(2528,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(q6,seq,earray_331),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(q6,seq,earray_331),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2529,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(q6,seq,earray_331),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2530,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(q6,seq,earray_331),head) ) ),
inference(modus_ponens,[status(thm)],[2529,2528]) ).
tff(2531,plain,
select(store(store(q6,seq,earray_331),tail,s(index_330)),head) = select(store(q6,seq,earray_331),head),
inference(unit_resolution,[status(thm)],[2530,32,92]) ).
tff(2532,plain,
select(store(q6,seq,earray_331),head) = select(store(store(q6,seq,earray_331),tail,s(index_330)),head),
inference(symmetry,[status(thm)],[2531]) ).
tff(2533,plain,
( ( earray_331 = store(earray_329,index_330,e6) )
<=> ( earray_331 = store(earray_329,index_330,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2534,axiom,
earray_331 = store(earray_329,index_330,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(2535,plain,
earray_331 = store(earray_329,index_330,e6),
inference(modus_ponens,[status(thm)],[2534,2533]) ).
tff(2536,plain,
store(earray_329,index_330,e6) = earray_331,
inference(symmetry,[status(thm)],[2535]) ).
tff(2537,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_325,head,index_327),seq,store(earray_329,index_330,e6)),seq) = store(earray_329,index_330,e6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2538,plain,
select(store(store(queue_325,head,index_327),seq,store(earray_329,index_330,e6)),seq) = store(earray_329,index_330,e6),
inference(unit_resolution,[status(thm)],[2537,6]) ).
tff(2539,plain,
( ( q6 = queue_328 )
<=> ( q6 = queue_328 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2540,axiom,
q6 = queue_328,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp400) ).
tff(2541,plain,
q6 = queue_328,
inference(modus_ponens,[status(thm)],[2540,2539]) ).
tff(2542,plain,
queue_328 = q6,
inference(symmetry,[status(thm)],[2541]) ).
tff(2543,plain,
( ( queue_328 = store(queue_325,head,index_327) )
<=> ( queue_328 = store(queue_325,head,index_327) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2544,axiom,
queue_328 = store(queue_325,head,index_327),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp321) ).
tff(2545,plain,
queue_328 = store(queue_325,head,index_327),
inference(modus_ponens,[status(thm)],[2544,2543]) ).
tff(2546,plain,
store(queue_325,head,index_327) = queue_328,
inference(symmetry,[status(thm)],[2545]) ).
tff(2547,plain,
store(queue_325,head,index_327) = q6,
inference(transitivity,[status(thm)],[2546,2542]) ).
tff(2548,plain,
store(store(queue_325,head,index_327),seq,store(earray_329,index_330,e6)) = store(q6,seq,earray_331),
inference(monotonicity,[status(thm)],[2547,2536]) ).
tff(2549,plain,
select(store(store(queue_325,head,index_327),seq,store(earray_329,index_330,e6)),seq) = select(store(q6,seq,earray_331),seq),
inference(monotonicity,[status(thm)],[2548]) ).
tff(2550,plain,
select(store(q6,seq,earray_331),seq) = select(store(store(queue_325,head,index_327),seq,store(earray_329,index_330,e6)),seq),
inference(symmetry,[status(thm)],[2549]) ).
tff(2551,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(store(q6,seq,earray_331),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(store(q6,seq,earray_331),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2552,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(store(q6,seq,earray_331),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2553,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(store(q6,seq,earray_331),seq) ) ),
inference(modus_ponens,[status(thm)],[2552,2551]) ).
tff(2554,plain,
select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(store(q6,seq,earray_331),seq),
inference(unit_resolution,[status(thm)],[2553,32,57]) ).
tff(2555,plain,
store(store(q6,seq,earray_331),tail,s(index_330)) = q7,
inference(transitivity,[status(thm)],[2526,2498,2494]) ).
tff(2556,plain,
select(store(store(q6,seq,earray_331),tail,s(index_330)),seq) = select(q7,seq),
inference(monotonicity,[status(thm)],[2555]) ).
tff(2557,plain,
select(q7,seq) = select(store(store(q6,seq,earray_331),tail,s(index_330)),seq),
inference(symmetry,[status(thm)],[2556]) ).
tff(2558,plain,
select(q7,seq) = earray_331,
inference(transitivity,[status(thm)],[2557,2554,2550,2538,2536]) ).
tff(2559,plain,
store(store(queue_325,head,index_327),seq,select(q7,seq)) = store(q6,seq,earray_331),
inference(monotonicity,[status(thm)],[2547,2558]) ).
tff(2560,plain,
select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(q6,seq,earray_331),head),
inference(monotonicity,[status(thm)],[2559]) ).
tff(2561,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(queue_325,head,index_327),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(queue_325,head,index_327),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2562,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(queue_325,head,index_327),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2563,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(queue_325,head,index_327),head) ) ),
inference(modus_ponens,[status(thm)],[2562,2561]) ).
tff(2564,plain,
select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head) = select(store(queue_325,head,index_327),head),
inference(unit_resolution,[status(thm)],[2563,32,26]) ).
tff(2565,plain,
select(store(queue_325,head,index_327),head) = select(store(store(queue_325,head,index_327),seq,select(q7,seq)),head),
inference(symmetry,[status(thm)],[2564]) ).
tff(2566,plain,
( ( index_327 = s(index_326) )
<=> ( index_327 = s(index_326) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2567,axiom,
index_327 = s(index_326),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(2568,plain,
index_327 = s(index_326),
inference(modus_ponens,[status(thm)],[2567,2566]) ).
tff(2569,plain,
s(index_326) = index_327,
inference(symmetry,[status(thm)],[2568]) ).
tff(2570,plain,
( ( queue_325 = store(queue_323,tail,index_324) )
<=> ( queue_325 = store(queue_323,tail,index_324) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2571,axiom,
queue_325 = store(queue_323,tail,index_324),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp320) ).
tff(2572,plain,
queue_325 = store(queue_323,tail,index_324),
inference(modus_ponens,[status(thm)],[2571,2570]) ).
tff(2573,plain,
store(queue_323,tail,index_324) = queue_325,
inference(symmetry,[status(thm)],[2572]) ).
tff(2574,plain,
store(store(queue_323,tail,index_324),head,s(index_326)) = store(queue_325,head,index_327),
inference(monotonicity,[status(thm)],[2573,2569]) ).
tff(2575,plain,
select(store(store(queue_323,tail,index_324),head,s(index_326)),head) = select(store(queue_325,head,index_327),head),
inference(monotonicity,[status(thm)],[2574]) ).
tff(2576,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),head) = s(index_326) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2577,plain,
select(store(store(queue_323,tail,index_324),head,s(index_326)),head) = s(index_326),
inference(unit_resolution,[status(thm)],[2576,6]) ).
tff(2578,plain,
s(index_326) = select(store(store(queue_323,tail,index_324),head,s(index_326)),head),
inference(symmetry,[status(thm)],[2577]) ).
tff(2579,plain,
( ( index_326 = select(queue_325,head) )
<=> ( index_326 = select(queue_325,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2580,axiom,
index_326 = select(queue_325,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(2581,plain,
index_326 = select(queue_325,head),
inference(modus_ponens,[status(thm)],[2580,2579]) ).
tff(2582,plain,
select(queue_325,head) = index_326,
inference(symmetry,[status(thm)],[2581]) ).
tff(2583,plain,
( ( index_324 = s(index_321) )
<=> ( index_324 = s(index_321) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2584,axiom,
index_324 = s(index_321),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(2585,plain,
index_324 = s(index_321),
inference(modus_ponens,[status(thm)],[2584,2583]) ).
tff(2586,plain,
s(index_321) = index_324,
inference(symmetry,[status(thm)],[2585]) ).
tff(2587,plain,
( ( queue_323 = store(q5,seq,earray_322) )
<=> ( queue_323 = store(q5,seq,earray_322) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2588,axiom,
queue_323 = store(q5,seq,earray_322),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp319) ).
tff(2589,plain,
queue_323 = store(q5,seq,earray_322),
inference(modus_ponens,[status(thm)],[2588,2587]) ).
tff(2590,plain,
store(q5,seq,earray_322) = queue_323,
inference(symmetry,[status(thm)],[2589]) ).
tff(2591,plain,
store(store(q5,seq,earray_322),tail,s(index_321)) = store(queue_323,tail,index_324),
inference(monotonicity,[status(thm)],[2590,2586]) ).
tff(2592,plain,
store(store(q5,seq,earray_322),tail,s(index_321)) = queue_325,
inference(transitivity,[status(thm)],[2591,2573]) ).
tff(2593,plain,
select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(queue_325,head),
inference(monotonicity,[status(thm)],[2592]) ).
tff(2594,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2595,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2596,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head) ) ),
inference(modus_ponens,[status(thm)],[2595,2594]) ).
tff(2597,plain,
( ( tail = head )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head) ) ),
inference(unit_resolution,[status(thm)],[2596,32]) ).
tff(2598,plain,
select(store(store(q5,seq,earray_322),tail,s(index_321)),head) = select(store(q5,seq,earray_322),head),
inference(unit_resolution,[status(thm)],[2597,92]) ).
tff(2599,plain,
select(store(q5,seq,earray_322),head) = select(store(store(q5,seq,earray_322),tail,s(index_321)),head),
inference(symmetry,[status(thm)],[2598]) ).
tff(2600,plain,
( ( earray_322 = store(earray_320,index_321,e5) )
<=> ( earray_322 = store(earray_320,index_321,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2601,axiom,
earray_322 = store(earray_320,index_321,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(2602,plain,
earray_322 = store(earray_320,index_321,e5),
inference(modus_ponens,[status(thm)],[2601,2600]) ).
tff(2603,plain,
store(earray_320,index_321,e5) = earray_322,
inference(symmetry,[status(thm)],[2602]) ).
tff(2604,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_311,tail,index_312),seq,store(earray_320,index_321,e5)),seq) = store(earray_320,index_321,e5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2605,plain,
select(store(store(queue_311,tail,index_312),seq,store(earray_320,index_321,e5)),seq) = store(earray_320,index_321,e5),
inference(unit_resolution,[status(thm)],[2604,6]) ).
tff(2606,plain,
( ( q5 = queue_313 )
<=> ( q5 = queue_313 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2607,axiom,
q5 = queue_313,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp398) ).
tff(2608,plain,
q5 = queue_313,
inference(modus_ponens,[status(thm)],[2607,2606]) ).
tff(2609,plain,
queue_313 = q5,
inference(symmetry,[status(thm)],[2608]) ).
tff(2610,plain,
( ( queue_313 = store(queue_311,tail,index_312) )
<=> ( queue_313 = store(queue_311,tail,index_312) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2611,axiom,
queue_313 = store(queue_311,tail,index_312),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp315) ).
tff(2612,plain,
queue_313 = store(queue_311,tail,index_312),
inference(modus_ponens,[status(thm)],[2611,2610]) ).
tff(2613,plain,
store(queue_311,tail,index_312) = queue_313,
inference(symmetry,[status(thm)],[2612]) ).
tff(2614,plain,
store(queue_311,tail,index_312) = q5,
inference(transitivity,[status(thm)],[2613,2609]) ).
tff(2615,plain,
store(store(queue_311,tail,index_312),seq,store(earray_320,index_321,e5)) = store(q5,seq,earray_322),
inference(monotonicity,[status(thm)],[2614,2603]) ).
tff(2616,plain,
select(store(store(queue_311,tail,index_312),seq,store(earray_320,index_321,e5)),seq) = select(store(q5,seq,earray_322),seq),
inference(monotonicity,[status(thm)],[2615]) ).
tff(2617,plain,
select(store(q5,seq,earray_322),seq) = select(store(store(queue_311,tail,index_312),seq,store(earray_320,index_321,e5)),seq),
inference(symmetry,[status(thm)],[2616]) ).
tff(2618,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(q5,seq,earray_322),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(q5,seq,earray_322),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2619,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(q5,seq,earray_322),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2620,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(q5,seq,earray_322),seq) ) ),
inference(modus_ponens,[status(thm)],[2619,2618]) ).
tff(2621,plain,
select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(q5,seq,earray_322),seq),
inference(unit_resolution,[status(thm)],[2620,32,57]) ).
tff(2622,plain,
select(store(store(q5,seq,earray_322),tail,s(index_321)),seq) = select(store(queue_323,tail,index_324),seq),
inference(monotonicity,[status(thm)],[2591]) ).
tff(2623,plain,
select(store(queue_323,tail,index_324),seq) = select(store(store(q5,seq,earray_322),tail,s(index_321)),seq),
inference(symmetry,[status(thm)],[2622]) ).
tff(2624,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(store(queue_323,tail,index_324),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(store(queue_323,tail,index_324),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2625,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(store(queue_323,tail,index_324),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2626,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(store(queue_323,tail,index_324),seq) ) ),
inference(modus_ponens,[status(thm)],[2625,2624]) ).
tff(2627,plain,
select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(store(queue_323,tail,index_324),seq),
inference(unit_resolution,[status(thm)],[2626,32,25]) ).
tff(2628,plain,
store(store(queue_323,tail,index_324),head,s(index_326)) = q6,
inference(transitivity,[status(thm)],[2574,2546,2542]) ).
tff(2629,plain,
select(store(store(queue_323,tail,index_324),head,s(index_326)),seq) = select(q6,seq),
inference(monotonicity,[status(thm)],[2628]) ).
tff(2630,plain,
select(q6,seq) = select(store(store(queue_323,tail,index_324),head,s(index_326)),seq),
inference(symmetry,[status(thm)],[2629]) ).
tff(2631,plain,
select(q6,seq) = earray_322,
inference(transitivity,[status(thm)],[2630,2627,2623,2621,2617,2605,2603]) ).
tff(2632,plain,
store(store(queue_311,tail,index_312),seq,select(q6,seq)) = store(q5,seq,earray_322),
inference(monotonicity,[status(thm)],[2614,2631]) ).
tff(2633,plain,
select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(q5,seq,earray_322),head),
inference(monotonicity,[status(thm)],[2632]) ).
tff(2634,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2635,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2636,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head) ) ),
inference(modus_ponens,[status(thm)],[2635,2634]) ).
tff(2637,plain,
( ( seq = head )
| ( select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head) ) ),
inference(unit_resolution,[status(thm)],[2636,32]) ).
tff(2638,plain,
select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head) = select(store(queue_311,tail,index_312),head),
inference(unit_resolution,[status(thm)],[2637,26]) ).
tff(2639,plain,
select(store(queue_311,tail,index_312),head) = select(store(store(queue_311,tail,index_312),seq,select(q6,seq)),head),
inference(symmetry,[status(thm)],[2638]) ).
tff(2640,plain,
( ( index_312 = s(index_309) )
<=> ( index_312 = s(index_309) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2641,axiom,
index_312 = s(index_309),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(2642,plain,
index_312 = s(index_309),
inference(modus_ponens,[status(thm)],[2641,2640]) ).
tff(2643,plain,
s(index_309) = index_312,
inference(symmetry,[status(thm)],[2642]) ).
tff(2644,plain,
( ( queue_311 = store(q4,seq,earray_310) )
<=> ( queue_311 = store(q4,seq,earray_310) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2645,axiom,
queue_311 = store(q4,seq,earray_310),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp314) ).
tff(2646,plain,
queue_311 = store(q4,seq,earray_310),
inference(modus_ponens,[status(thm)],[2645,2644]) ).
tff(2647,plain,
store(q4,seq,earray_310) = queue_311,
inference(symmetry,[status(thm)],[2646]) ).
tff(2648,plain,
store(store(q4,seq,earray_310),tail,s(index_309)) = store(queue_311,tail,index_312),
inference(monotonicity,[status(thm)],[2647,2643]) ).
tff(2649,plain,
select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(queue_311,tail,index_312),head),
inference(monotonicity,[status(thm)],[2648]) ).
tff(2650,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(q4,seq,earray_310),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(q4,seq,earray_310),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2651,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(q4,seq,earray_310),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2652,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(q4,seq,earray_310),head) ) ),
inference(modus_ponens,[status(thm)],[2651,2650]) ).
tff(2653,plain,
select(store(store(q4,seq,earray_310),tail,s(index_309)),head) = select(store(q4,seq,earray_310),head),
inference(unit_resolution,[status(thm)],[2652,32,92]) ).
tff(2654,plain,
select(store(q4,seq,earray_310),head) = select(store(store(q4,seq,earray_310),tail,s(index_309)),head),
inference(symmetry,[status(thm)],[2653]) ).
tff(2655,plain,
( ( earray_310 = store(earray_308,index_309,e4) )
<=> ( earray_310 = store(earray_308,index_309,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2656,axiom,
earray_310 = store(earray_308,index_309,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(2657,plain,
earray_310 = store(earray_308,index_309,e4),
inference(modus_ponens,[status(thm)],[2656,2655]) ).
tff(2658,plain,
store(earray_308,index_309,e4) = earray_310,
inference(symmetry,[status(thm)],[2657]) ).
tff(2659,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_236,tail,index_237),seq,store(earray_308,index_309,e4)),seq) = store(earray_308,index_309,e4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2660,plain,
select(store(store(queue_236,tail,index_237),seq,store(earray_308,index_309,e4)),seq) = store(earray_308,index_309,e4),
inference(unit_resolution,[status(thm)],[2659,6]) ).
tff(2661,plain,
( ( q4 = queue_238 )
<=> ( q4 = queue_238 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2662,axiom,
q4 = queue_238,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp387) ).
tff(2663,plain,
q4 = queue_238,
inference(modus_ponens,[status(thm)],[2662,2661]) ).
tff(2664,plain,
queue_238 = q4,
inference(symmetry,[status(thm)],[2663]) ).
tff(2665,plain,
( ( queue_238 = store(queue_236,tail,index_237) )
<=> ( queue_238 = store(queue_236,tail,index_237) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2666,axiom,
queue_238 = store(queue_236,tail,index_237),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp288) ).
tff(2667,plain,
queue_238 = store(queue_236,tail,index_237),
inference(modus_ponens,[status(thm)],[2666,2665]) ).
tff(2668,plain,
store(queue_236,tail,index_237) = queue_238,
inference(symmetry,[status(thm)],[2667]) ).
tff(2669,plain,
store(queue_236,tail,index_237) = q4,
inference(transitivity,[status(thm)],[2668,2664]) ).
tff(2670,plain,
store(store(queue_236,tail,index_237),seq,store(earray_308,index_309,e4)) = store(q4,seq,earray_310),
inference(monotonicity,[status(thm)],[2669,2658]) ).
tff(2671,plain,
select(store(store(queue_236,tail,index_237),seq,store(earray_308,index_309,e4)),seq) = select(store(q4,seq,earray_310),seq),
inference(monotonicity,[status(thm)],[2670]) ).
tff(2672,plain,
select(store(q4,seq,earray_310),seq) = select(store(store(queue_236,tail,index_237),seq,store(earray_308,index_309,e4)),seq),
inference(symmetry,[status(thm)],[2671]) ).
tff(2673,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(store(q4,seq,earray_310),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(store(q4,seq,earray_310),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2674,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(store(q4,seq,earray_310),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2675,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(store(q4,seq,earray_310),seq) ) ),
inference(modus_ponens,[status(thm)],[2674,2673]) ).
tff(2676,plain,
select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(store(q4,seq,earray_310),seq),
inference(unit_resolution,[status(thm)],[2675,32,57]) ).
tff(2677,plain,
store(store(q4,seq,earray_310),tail,s(index_309)) = q5,
inference(transitivity,[status(thm)],[2648,2613,2609]) ).
tff(2678,plain,
select(store(store(q4,seq,earray_310),tail,s(index_309)),seq) = select(q5,seq),
inference(monotonicity,[status(thm)],[2677]) ).
tff(2679,plain,
select(q5,seq) = select(store(store(q4,seq,earray_310),tail,s(index_309)),seq),
inference(symmetry,[status(thm)],[2678]) ).
tff(2680,plain,
select(q5,seq) = earray_310,
inference(transitivity,[status(thm)],[2679,2676,2672,2660,2658]) ).
tff(2681,plain,
store(store(queue_236,tail,index_237),seq,select(q5,seq)) = store(q4,seq,earray_310),
inference(monotonicity,[status(thm)],[2669,2680]) ).
tff(2682,plain,
select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(q4,seq,earray_310),head),
inference(monotonicity,[status(thm)],[2681]) ).
tff(2683,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2684,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2685,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ),
inference(modus_ponens,[status(thm)],[2684,2683]) ).
tff(2686,plain,
select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head),
inference(unit_resolution,[status(thm)],[2685,32,26]) ).
tff(2687,plain,
select(store(queue_236,tail,index_237),head) = select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head),
inference(symmetry,[status(thm)],[2686]) ).
tff(2688,plain,
( ( index_237 = s(index_234) )
<=> ( index_237 = s(index_234) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2689,axiom,
index_237 = s(index_234),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(2690,plain,
index_237 = s(index_234),
inference(modus_ponens,[status(thm)],[2689,2688]) ).
tff(2691,plain,
s(index_234) = index_237,
inference(symmetry,[status(thm)],[2690]) ).
tff(2692,plain,
( ( queue_236 = store(q3,seq,earray_235) )
<=> ( queue_236 = store(q3,seq,earray_235) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2693,axiom,
queue_236 = store(q3,seq,earray_235),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp287) ).
tff(2694,plain,
queue_236 = store(q3,seq,earray_235),
inference(modus_ponens,[status(thm)],[2693,2692]) ).
tff(2695,plain,
store(q3,seq,earray_235) = queue_236,
inference(symmetry,[status(thm)],[2694]) ).
tff(2696,plain,
store(store(q3,seq,earray_235),tail,s(index_234)) = store(queue_236,tail,index_237),
inference(monotonicity,[status(thm)],[2695,2691]) ).
tff(2697,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(queue_236,tail,index_237),head),
inference(monotonicity,[status(thm)],[2696]) ).
tff(2698,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2699,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2700,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ),
inference(modus_ponens,[status(thm)],[2699,2698]) ).
tff(2701,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head),
inference(unit_resolution,[status(thm)],[2700,32,92]) ).
tff(2702,plain,
select(store(q3,seq,earray_235),head) = select(store(store(q3,seq,earray_235),tail,s(index_234)),head),
inference(symmetry,[status(thm)],[2701]) ).
tff(2703,plain,
( ( earray_235 = store(earray_233,index_234,e3) )
<=> ( earray_235 = store(earray_233,index_234,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2704,axiom,
earray_235 = store(earray_233,index_234,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp44) ).
tff(2705,plain,
earray_235 = store(earray_233,index_234,e3),
inference(modus_ponens,[status(thm)],[2704,2703]) ).
tff(2706,plain,
store(earray_233,index_234,e3) = earray_235,
inference(symmetry,[status(thm)],[2705]) ).
tff(2707,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = store(earray_233,index_234,e3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2708,plain,
select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = store(earray_233,index_234,e3),
inference(unit_resolution,[status(thm)],[2707,6]) ).
tff(2709,plain,
( ( q3 = queue_160 )
<=> ( q3 = queue_160 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2710,axiom,
q3 = queue_160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp376) ).
tff(2711,plain,
q3 = queue_160,
inference(modus_ponens,[status(thm)],[2710,2709]) ).
tff(2712,plain,
queue_160 = q3,
inference(symmetry,[status(thm)],[2711]) ).
tff(2713,plain,
( ( queue_160 = store(queue_157,head,index_159) )
<=> ( queue_160 = store(queue_157,head,index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2714,axiom,
queue_160 = store(queue_157,head,index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp259) ).
tff(2715,plain,
queue_160 = store(queue_157,head,index_159),
inference(modus_ponens,[status(thm)],[2714,2713]) ).
tff(2716,plain,
store(queue_157,head,index_159) = queue_160,
inference(symmetry,[status(thm)],[2715]) ).
tff(2717,plain,
store(queue_157,head,index_159) = q3,
inference(transitivity,[status(thm)],[2716,2712]) ).
tff(2718,plain,
store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)) = store(q3,seq,earray_235),
inference(monotonicity,[status(thm)],[2717,2706]) ).
tff(2719,plain,
select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = select(store(q3,seq,earray_235),seq),
inference(monotonicity,[status(thm)],[2718]) ).
tff(2720,plain,
select(store(q3,seq,earray_235),seq) = select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq),
inference(symmetry,[status(thm)],[2719]) ).
tff(2721,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2722,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2723,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ),
inference(modus_ponens,[status(thm)],[2722,2721]) ).
tff(2724,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq),
inference(unit_resolution,[status(thm)],[2723,32,57]) ).
tff(2725,plain,
store(store(q3,seq,earray_235),tail,s(index_234)) = q4,
inference(transitivity,[status(thm)],[2696,2668,2664]) ).
tff(2726,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(q4,seq),
inference(monotonicity,[status(thm)],[2725]) ).
tff(2727,plain,
select(q4,seq) = select(store(store(q3,seq,earray_235),tail,s(index_234)),seq),
inference(symmetry,[status(thm)],[2726]) ).
tff(2728,plain,
select(q4,seq) = earray_235,
inference(transitivity,[status(thm)],[2727,2724,2720,2708,2706]) ).
tff(2729,plain,
store(store(queue_157,head,index_159),seq,select(q4,seq)) = store(q3,seq,earray_235),
inference(monotonicity,[status(thm)],[2717,2728]) ).
tff(2730,plain,
select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(q3,seq,earray_235),head),
inference(monotonicity,[status(thm)],[2729]) ).
tff(2731,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2732,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2733,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ),
inference(modus_ponens,[status(thm)],[2732,2731]) ).
tff(2734,plain,
select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head),
inference(unit_resolution,[status(thm)],[2733,32,26]) ).
tff(2735,plain,
select(store(queue_157,head,index_159),head) = select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head),
inference(symmetry,[status(thm)],[2734]) ).
tff(2736,plain,
( ( index_159 = s(index_158) )
<=> ( index_159 = s(index_158) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2737,axiom,
index_159 = s(index_158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(2738,plain,
index_159 = s(index_158),
inference(modus_ponens,[status(thm)],[2737,2736]) ).
tff(2739,plain,
s(index_158) = index_159,
inference(symmetry,[status(thm)],[2738]) ).
tff(2740,plain,
( ( queue_157 = store(queue_155,tail,index_156) )
<=> ( queue_157 = store(queue_155,tail,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2741,axiom,
queue_157 = store(queue_155,tail,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp258) ).
tff(2742,plain,
queue_157 = store(queue_155,tail,index_156),
inference(modus_ponens,[status(thm)],[2741,2740]) ).
tff(2743,plain,
store(queue_155,tail,index_156) = queue_157,
inference(symmetry,[status(thm)],[2742]) ).
tff(2744,plain,
store(store(queue_155,tail,index_156),head,s(index_158)) = store(queue_157,head,index_159),
inference(monotonicity,[status(thm)],[2743,2739]) ).
tff(2745,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = select(store(queue_157,head,index_159),head),
inference(monotonicity,[status(thm)],[2744]) ).
tff(2746,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = s(index_158) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2747,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = s(index_158),
inference(unit_resolution,[status(thm)],[2746,6]) ).
tff(2748,plain,
s(index_158) = select(store(store(queue_155,tail,index_156),head,s(index_158)),head),
inference(symmetry,[status(thm)],[2747]) ).
tff(2749,plain,
( ( index_158 = select(queue_157,head) )
<=> ( index_158 = select(queue_157,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2750,axiom,
index_158 = select(queue_157,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(2751,plain,
index_158 = select(queue_157,head),
inference(modus_ponens,[status(thm)],[2750,2749]) ).
tff(2752,plain,
select(queue_157,head) = index_158,
inference(symmetry,[status(thm)],[2751]) ).
tff(2753,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2754,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(2755,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[2754,2753]) ).
tff(2756,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[2755]) ).
tff(2757,plain,
( ( queue_155 = store(q2,seq,earray_154) )
<=> ( queue_155 = store(q2,seq,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2758,axiom,
queue_155 = store(q2,seq,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp257) ).
tff(2759,plain,
queue_155 = store(q2,seq,earray_154),
inference(modus_ponens,[status(thm)],[2758,2757]) ).
tff(2760,plain,
store(q2,seq,earray_154) = queue_155,
inference(symmetry,[status(thm)],[2759]) ).
tff(2761,plain,
store(store(q2,seq,earray_154),tail,s(index_153)) = store(queue_155,tail,index_156),
inference(monotonicity,[status(thm)],[2760,2756]) ).
tff(2762,plain,
store(store(q2,seq,earray_154),tail,s(index_153)) = queue_157,
inference(transitivity,[status(thm)],[2761,2743]) ).
tff(2763,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(queue_157,head),
inference(monotonicity,[status(thm)],[2762]) ).
tff(2764,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2765,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2766,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(modus_ponens,[status(thm)],[2765,2764]) ).
tff(2767,plain,
( ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(unit_resolution,[status(thm)],[2766,32]) ).
tff(2768,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head),
inference(unit_resolution,[status(thm)],[2767,92]) ).
tff(2769,plain,
select(store(q2,seq,earray_154),head) = select(store(store(q2,seq,earray_154),tail,s(index_153)),head),
inference(symmetry,[status(thm)],[2768]) ).
tff(2770,plain,
( ( earray_154 = store(earray_152,index_153,e2) )
<=> ( earray_154 = store(earray_152,index_153,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2771,axiom,
earray_154 = store(earray_152,index_153,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(2772,plain,
earray_154 = store(earray_152,index_153,e2),
inference(modus_ponens,[status(thm)],[2771,2770]) ).
tff(2773,plain,
store(earray_152,index_153,e2) = earray_154,
inference(symmetry,[status(thm)],[2772]) ).
tff(2774,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = store(earray_152,index_153,e2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2775,plain,
select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = store(earray_152,index_153,e2),
inference(unit_resolution,[status(thm)],[2774,6]) ).
tff(2776,plain,
( ( q2 = queue_82 )
<=> ( q2 = queue_82 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2777,axiom,
q2 = queue_82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp365) ).
tff(2778,plain,
q2 = queue_82,
inference(modus_ponens,[status(thm)],[2777,2776]) ).
tff(2779,plain,
queue_82 = q2,
inference(symmetry,[status(thm)],[2778]) ).
tff(2780,plain,
( ( queue_82 = store(queue_80,tail,index_81) )
<=> ( queue_82 = store(queue_80,tail,index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2781,axiom,
queue_82 = store(queue_80,tail,index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp347) ).
tff(2782,plain,
queue_82 = store(queue_80,tail,index_81),
inference(modus_ponens,[status(thm)],[2781,2780]) ).
tff(2783,plain,
store(queue_80,tail,index_81) = queue_82,
inference(symmetry,[status(thm)],[2782]) ).
tff(2784,plain,
store(queue_80,tail,index_81) = q2,
inference(transitivity,[status(thm)],[2783,2779]) ).
tff(2785,plain,
store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)) = store(q2,seq,earray_154),
inference(monotonicity,[status(thm)],[2784,2773]) ).
tff(2786,plain,
select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = select(store(q2,seq,earray_154),seq),
inference(monotonicity,[status(thm)],[2785]) ).
tff(2787,plain,
select(store(q2,seq,earray_154),seq) = select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq),
inference(symmetry,[status(thm)],[2786]) ).
tff(2788,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2789,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2790,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ),
inference(modus_ponens,[status(thm)],[2789,2788]) ).
tff(2791,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq),
inference(unit_resolution,[status(thm)],[2790,32,57]) ).
tff(2792,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(queue_155,tail,index_156),seq),
inference(monotonicity,[status(thm)],[2761]) ).
tff(2793,plain,
select(store(queue_155,tail,index_156),seq) = select(store(store(q2,seq,earray_154),tail,s(index_153)),seq),
inference(symmetry,[status(thm)],[2792]) ).
tff(2794,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2795,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2796,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ),
inference(modus_ponens,[status(thm)],[2795,2794]) ).
tff(2797,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq),
inference(unit_resolution,[status(thm)],[2796,32,25]) ).
tff(2798,plain,
store(store(queue_155,tail,index_156),head,s(index_158)) = q3,
inference(transitivity,[status(thm)],[2744,2716,2712]) ).
tff(2799,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(q3,seq),
inference(monotonicity,[status(thm)],[2798]) ).
tff(2800,plain,
select(q3,seq) = select(store(store(queue_155,tail,index_156),head,s(index_158)),seq),
inference(symmetry,[status(thm)],[2799]) ).
tff(2801,plain,
select(q3,seq) = earray_154,
inference(transitivity,[status(thm)],[2800,2797,2793,2791,2787,2775,2773]) ).
tff(2802,plain,
store(store(queue_80,tail,index_81),seq,select(q3,seq)) = store(q2,seq,earray_154),
inference(monotonicity,[status(thm)],[2784,2801]) ).
tff(2803,plain,
select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(q2,seq,earray_154),head),
inference(monotonicity,[status(thm)],[2802]) ).
tff(2804,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2805,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2806,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(modus_ponens,[status(thm)],[2805,2804]) ).
tff(2807,plain,
( ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(unit_resolution,[status(thm)],[2806,32]) ).
tff(2808,plain,
select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head),
inference(unit_resolution,[status(thm)],[2807,26]) ).
tff(2809,plain,
select(store(queue_80,tail,index_81),head) = select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head),
inference(symmetry,[status(thm)],[2808]) ).
tff(2810,plain,
( ( index_81 = s(index_78) )
<=> ( index_81 = s(index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2811,axiom,
index_81 = s(index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(2812,plain,
index_81 = s(index_78),
inference(modus_ponens,[status(thm)],[2811,2810]) ).
tff(2813,plain,
s(index_78) = index_81,
inference(symmetry,[status(thm)],[2812]) ).
tff(2814,plain,
( ( queue_80 = store(q1,seq,earray_79) )
<=> ( queue_80 = store(q1,seq,earray_79) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2815,axiom,
queue_80 = store(q1,seq,earray_79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp346) ).
tff(2816,plain,
queue_80 = store(q1,seq,earray_79),
inference(modus_ponens,[status(thm)],[2815,2814]) ).
tff(2817,plain,
store(q1,seq,earray_79) = queue_80,
inference(symmetry,[status(thm)],[2816]) ).
tff(2818,plain,
store(store(q1,seq,earray_79),tail,s(index_78)) = store(queue_80,tail,index_81),
inference(monotonicity,[status(thm)],[2817,2813]) ).
tff(2819,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(queue_80,tail,index_81),head),
inference(monotonicity,[status(thm)],[2818]) ).
tff(2820,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2821,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2822,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ),
inference(modus_ponens,[status(thm)],[2821,2820]) ).
tff(2823,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head),
inference(unit_resolution,[status(thm)],[2822,32,92]) ).
tff(2824,plain,
select(store(q1,seq,earray_79),head) = select(store(store(q1,seq,earray_79),tail,s(index_78)),head),
inference(symmetry,[status(thm)],[2823]) ).
tff(2825,plain,
( ( earray_79 = store(earray_77,index_78,e1) )
<=> ( earray_79 = store(earray_77,index_78,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2826,axiom,
earray_79 = store(earray_77,index_78,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(2827,plain,
earray_79 = store(earray_77,index_78,e1),
inference(modus_ponens,[status(thm)],[2826,2825]) ).
tff(2828,plain,
store(earray_77,index_78,e1) = earray_79,
inference(symmetry,[status(thm)],[2827]) ).
tff(2829,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = store(earray_77,index_78,e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2830,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = store(earray_77,index_78,e1),
inference(unit_resolution,[status(thm)],[2829,6]) ).
tff(2831,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2832,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp354) ).
tff(2833,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[2832,2831]) ).
tff(2834,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[2833]) ).
tff(2835,plain,
( ( queue_7 = store(queue_5,tail,index_6) )
<=> ( queue_7 = store(queue_5,tail,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2836,axiom,
queue_7 = store(queue_5,tail,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp342) ).
tff(2837,plain,
queue_7 = store(queue_5,tail,index_6),
inference(modus_ponens,[status(thm)],[2836,2835]) ).
tff(2838,plain,
store(queue_5,tail,index_6) = queue_7,
inference(symmetry,[status(thm)],[2837]) ).
tff(2839,plain,
store(queue_5,tail,index_6) = q1,
inference(transitivity,[status(thm)],[2838,2834]) ).
tff(2840,plain,
store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)) = store(q1,seq,earray_79),
inference(monotonicity,[status(thm)],[2839,2828]) ).
tff(2841,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = select(store(q1,seq,earray_79),seq),
inference(monotonicity,[status(thm)],[2840]) ).
tff(2842,plain,
select(store(q1,seq,earray_79),seq) = select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq),
inference(symmetry,[status(thm)],[2841]) ).
tff(2843,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2844,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2845,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ),
inference(modus_ponens,[status(thm)],[2844,2843]) ).
tff(2846,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq),
inference(unit_resolution,[status(thm)],[2845,32,57]) ).
tff(2847,plain,
store(store(q1,seq,earray_79),tail,s(index_78)) = q2,
inference(transitivity,[status(thm)],[2818,2783,2779]) ).
tff(2848,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(q2,seq),
inference(monotonicity,[status(thm)],[2847]) ).
tff(2849,plain,
select(q2,seq) = select(store(store(q1,seq,earray_79),tail,s(index_78)),seq),
inference(symmetry,[status(thm)],[2848]) ).
tff(2850,plain,
select(q2,seq) = earray_79,
inference(transitivity,[status(thm)],[2849,2846,2842,2830,2828]) ).
tff(2851,plain,
store(store(queue_5,tail,index_6),seq,select(q2,seq)) = store(q1,seq,earray_79),
inference(monotonicity,[status(thm)],[2839,2850]) ).
tff(2852,plain,
select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(q1,seq,earray_79),head),
inference(monotonicity,[status(thm)],[2851]) ).
tff(2853,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2854,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2855,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ),
inference(modus_ponens,[status(thm)],[2854,2853]) ).
tff(2856,plain,
select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head),
inference(unit_resolution,[status(thm)],[2855,32,26]) ).
tff(2857,plain,
select(store(queue_5,tail,index_6),head) = select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head),
inference(symmetry,[status(thm)],[2856]) ).
tff(2858,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2859,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(2860,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[2859,2858]) ).
tff(2861,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[2860]) ).
tff(2862,plain,
( ( queue_5 = store(q0,seq,earray_4) )
<=> ( queue_5 = store(q0,seq,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2863,axiom,
queue_5 = store(q0,seq,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp335) ).
tff(2864,plain,
queue_5 = store(q0,seq,earray_4),
inference(modus_ponens,[status(thm)],[2863,2862]) ).
tff(2865,plain,
store(q0,seq,earray_4) = queue_5,
inference(symmetry,[status(thm)],[2864]) ).
tff(2866,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = store(queue_5,tail,index_6),
inference(monotonicity,[status(thm)],[2865,2861]) ).
tff(2867,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(queue_5,tail,index_6),head),
inference(monotonicity,[status(thm)],[2866]) ).
tff(2868,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2869,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2870,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ),
inference(modus_ponens,[status(thm)],[2869,2868]) ).
tff(2871,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head),
inference(unit_resolution,[status(thm)],[2870,32,92]) ).
tff(2872,plain,
select(store(q0,seq,earray_4),head) = select(store(store(q0,seq,earray_4),tail,s(index_3)),head),
inference(symmetry,[status(thm)],[2871]) ).
tff(2873,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2874,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp82) ).
tff(2875,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[2874,2873]) ).
tff(2876,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[2875]) ).
tff(2877,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = store(earray_2,index_3,e0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2878,plain,
select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = store(earray_2,index_3,e0),
inference(unit_resolution,[status(thm)],[2877,6]) ).
tff(2879,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2880,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp353) ).
tff(2881,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[2880,2879]) ).
tff(2882,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[2881]) ).
tff(2883,plain,
( ( queue_1 = store(q,head,index_0) )
<=> ( queue_1 = store(q,head,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2884,axiom,
queue_1 = store(q,head,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(2885,plain,
queue_1 = store(q,head,index_0),
inference(modus_ponens,[status(thm)],[2884,2883]) ).
tff(2886,plain,
store(q,head,index_0) = queue_1,
inference(symmetry,[status(thm)],[2885]) ).
tff(2887,plain,
store(q,head,index_0) = q0,
inference(transitivity,[status(thm)],[2886,2882]) ).
tff(2888,plain,
store(store(q,head,index_0),seq,store(earray_2,index_3,e0)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[2887,2876]) ).
tff(2889,plain,
select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = select(store(q0,seq,earray_4),seq),
inference(monotonicity,[status(thm)],[2888]) ).
tff(2890,plain,
select(store(q0,seq,earray_4),seq) = select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq),
inference(symmetry,[status(thm)],[2889]) ).
tff(2891,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2892,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2893,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ),
inference(modus_ponens,[status(thm)],[2892,2891]) ).
tff(2894,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq),
inference(unit_resolution,[status(thm)],[2893,32,57]) ).
tff(2895,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = q1,
inference(transitivity,[status(thm)],[2866,2838,2834]) ).
tff(2896,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(q1,seq),
inference(monotonicity,[status(thm)],[2895]) ).
tff(2897,plain,
select(q1,seq) = select(store(store(q0,seq,earray_4),tail,s(index_3)),seq),
inference(symmetry,[status(thm)],[2896]) ).
tff(2898,plain,
select(q1,seq) = earray_4,
inference(transitivity,[status(thm)],[2897,2894,2890,2878,2876]) ).
tff(2899,plain,
store(store(q,head,index_0),seq,select(q1,seq)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[2887,2898]) ).
tff(2900,plain,
select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q0,seq,earray_4),head),
inference(monotonicity,[status(thm)],[2899]) ).
tff(2901,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2902,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2903,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ),
inference(modus_ponens,[status(thm)],[2902,2901]) ).
tff(2904,plain,
select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head),
inference(unit_resolution,[status(thm)],[2903,32,26]) ).
tff(2905,plain,
select(store(q,head,index_0),head) = select(store(store(q,head,index_0),seq,select(q1,seq)),head),
inference(symmetry,[status(thm)],[2904]) ).
tff(2906,plain,
( ( index_0 = select(q,tail) )
<=> ( index_0 = select(q,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2907,axiom,
index_0 = select(q,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(2908,plain,
index_0 = select(q,tail),
inference(modus_ponens,[status(thm)],[2907,2906]) ).
tff(2909,plain,
select(q,tail) = index_0,
inference(symmetry,[status(thm)],[2908]) ).
tff(2910,plain,
store(q,head,select(q,tail)) = store(q,head,index_0),
inference(monotonicity,[status(thm)],[2909]) ).
tff(2911,plain,
select(store(q,head,select(q,tail)),head) = select(store(q,head,index_0),head),
inference(monotonicity,[status(thm)],[2910]) ).
tff(2912,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(q,head,select(q,tail)),head) = select(q,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2913,plain,
select(store(q,head,select(q,tail)),head) = select(q,tail),
inference(unit_resolution,[status(thm)],[2912,6]) ).
tff(2914,plain,
select(q,tail) = select(store(q,head,select(q,tail)),head),
inference(symmetry,[status(thm)],[2913]) ).
tff(2915,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2916,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2917,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ),
inference(modus_ponens,[status(thm)],[2916,2915]) ).
tff(2918,plain,
select(store(q,head,select(q,tail)),tail) = select(q,tail),
inference(unit_resolution,[status(thm)],[2917,32,91]) ).
tff(2919,plain,
store(q,head,index_0) = store(q,head,select(q,tail)),
inference(symmetry,[status(thm)],[2910]) ).
tff(2920,plain,
q0 = store(q,head,select(q,tail)),
inference(transitivity,[status(thm)],[2881,2885,2919]) ).
tff(2921,plain,
select(q0,tail) = select(store(q,head,select(q,tail)),tail),
inference(monotonicity,[status(thm)],[2920]) ).
tff(2922,plain,
( ( index_3 = select(q0,tail) )
<=> ( index_3 = select(q0,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2923,axiom,
index_3 = select(q0,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(2924,plain,
index_3 = select(q0,tail),
inference(modus_ponens,[status(thm)],[2923,2922]) ).
tff(2925,plain,
index_3 = index_158,
inference(transitivity,[status(thm)],[2924,2921,2918,2914,2911,2905,2900,2872,2867,2857,2852,2824,2819,2809,2803,2769,2763,2752]) ).
tff(2926,plain,
s(index_3) = s(index_158),
inference(monotonicity,[status(thm)],[2925]) ).
tff(2927,plain,
select(q0,tail) = index_3,
inference(symmetry,[status(thm)],[2924]) ).
tff(2928,plain,
s(select(q0,tail)) = s(index_3),
inference(monotonicity,[status(thm)],[2927]) ).
tff(2929,plain,
s(select(q0,tail)) = index_326,
inference(transitivity,[status(thm)],[2928,2926,2748,2745,2735,2730,2702,2697,2687,2682,2654,2649,2639,2633,2599,2593,2582]) ).
tff(2930,plain,
s(s(select(q0,tail))) = s(index_326),
inference(monotonicity,[status(thm)],[2929]) ).
tff(2931,plain,
s(index_3) = s(select(q0,tail)),
inference(symmetry,[status(thm)],[2928]) ).
tff(2932,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = s(index_3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2933,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = s(index_3),
inference(unit_resolution,[status(thm)],[2932,6]) ).
tff(2934,plain,
store(queue_5,tail,index_6) = store(store(q0,seq,earray_4),tail,s(index_3)),
inference(symmetry,[status(thm)],[2866]) ).
tff(2935,plain,
q1 = store(store(q0,seq,earray_4),tail,s(index_3)),
inference(transitivity,[status(thm)],[2833,2837,2934]) ).
tff(2936,plain,
select(q1,tail) = select(store(store(q0,seq,earray_4),tail,s(index_3)),tail),
inference(monotonicity,[status(thm)],[2935]) ).
tff(2937,plain,
( ( index_78 = select(q1,tail) )
<=> ( index_78 = select(q1,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2938,axiom,
index_78 = select(q1,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(2939,plain,
index_78 = select(q1,tail),
inference(modus_ponens,[status(thm)],[2938,2937]) ).
tff(2940,plain,
index_78 = s(select(q0,tail)),
inference(transitivity,[status(thm)],[2939,2936,2933,2931]) ).
tff(2941,plain,
s(index_78) = s(s(select(q0,tail))),
inference(monotonicity,[status(thm)],[2940]) ).
tff(2942,plain,
select(q1,tail) = index_78,
inference(symmetry,[status(thm)],[2939]) ).
tff(2943,plain,
s(select(q1,tail)) = s(index_78),
inference(monotonicity,[status(thm)],[2942]) ).
tff(2944,plain,
s(select(q1,tail)) = index_347,
inference(transitivity,[status(thm)],[2943,2941,2930,2578,2575,2565,2560,2532,2527,2517,2512,2484,2479,2469,2463,2429,2423,2412]) ).
tff(2945,plain,
s(s(select(q1,tail))) = s(index_347),
inference(monotonicity,[status(thm)],[2944]) ).
tff(2946,plain,
s(index_78) = s(select(q1,tail)),
inference(symmetry,[status(thm)],[2943]) ).
tff(2947,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),tail) = s(index_78) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2948,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),tail) = s(index_78),
inference(unit_resolution,[status(thm)],[2947,6]) ).
tff(2949,plain,
store(queue_80,tail,index_81) = store(store(q1,seq,earray_79),tail,s(index_78)),
inference(symmetry,[status(thm)],[2818]) ).
tff(2950,plain,
q2 = store(store(q1,seq,earray_79),tail,s(index_78)),
inference(transitivity,[status(thm)],[2778,2782,2949]) ).
tff(2951,plain,
select(q2,tail) = select(store(store(q1,seq,earray_79),tail,s(index_78)),tail),
inference(monotonicity,[status(thm)],[2950]) ).
tff(2952,plain,
( ( index_153 = select(q2,tail) )
<=> ( index_153 = select(q2,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2953,axiom,
index_153 = select(q2,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(2954,plain,
index_153 = select(q2,tail),
inference(modus_ponens,[status(thm)],[2953,2952]) ).
tff(2955,plain,
index_153 = s(select(q1,tail)),
inference(transitivity,[status(thm)],[2954,2951,2948,2946]) ).
tff(2956,plain,
s(index_153) = s(s(select(q1,tail))),
inference(monotonicity,[status(thm)],[2955]) ).
tff(2957,plain,
select(q2,tail) = index_153,
inference(symmetry,[status(thm)],[2954]) ).
tff(2958,plain,
s(select(q2,tail)) = s(index_153),
inference(monotonicity,[status(thm)],[2957]) ).
tff(2959,plain,
s(select(q2,tail)) = index_26,
inference(transitivity,[status(thm)],[2958,2956,2945,2408,2405,2395,2390,2362,2357,2347,2342,2314,2309,2299,2293,2259,2253,2242]) ).
tff(2960,plain,
s(s(select(q2,tail))) = s(index_26),
inference(monotonicity,[status(thm)],[2959]) ).
tff(2961,plain,
s(index_153) = s(select(q2,tail)),
inference(symmetry,[status(thm)],[2958]) ).
tff(2962,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),tail) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2963,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),tail) = s(index_153),
inference(unit_resolution,[status(thm)],[2962,6]) ).
tff(2964,plain,
store(queue_155,tail,index_156) = store(store(q2,seq,earray_154),tail,s(index_153)),
inference(symmetry,[status(thm)],[2761]) ).
tff(2965,plain,
select(store(queue_155,tail,index_156),tail) = select(store(store(q2,seq,earray_154),tail,s(index_153)),tail),
inference(monotonicity,[status(thm)],[2964]) ).
tff(2966,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2967,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2968,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ),
inference(modus_ponens,[status(thm)],[2967,2966]) ).
tff(2969,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail),
inference(unit_resolution,[status(thm)],[2968,32,91]) ).
tff(2970,plain,
store(queue_157,head,index_159) = store(store(queue_155,tail,index_156),head,s(index_158)),
inference(symmetry,[status(thm)],[2744]) ).
tff(2971,plain,
q3 = store(store(queue_155,tail,index_156),head,s(index_158)),
inference(transitivity,[status(thm)],[2711,2715,2970]) ).
tff(2972,plain,
select(q3,tail) = select(store(store(queue_155,tail,index_156),head,s(index_158)),tail),
inference(monotonicity,[status(thm)],[2971]) ).
tff(2973,plain,
( ( index_234 = select(q3,tail) )
<=> ( index_234 = select(q3,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2974,axiom,
index_234 = select(q3,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(2975,plain,
index_234 = select(q3,tail),
inference(modus_ponens,[status(thm)],[2974,2973]) ).
tff(2976,plain,
index_234 = s(select(q2,tail)),
inference(transitivity,[status(thm)],[2975,2972,2969,2965,2963,2961]) ).
tff(2977,plain,
s(index_234) = s(s(select(q2,tail))),
inference(monotonicity,[status(thm)],[2976]) ).
tff(2978,plain,
select(q3,tail) = index_234,
inference(symmetry,[status(thm)],[2975]) ).
tff(2979,plain,
s(select(q3,tail)) = s(index_234),
inference(monotonicity,[status(thm)],[2978]) ).
tff(2980,plain,
s(select(q3,tail)) = index_47,
inference(transitivity,[status(thm)],[2979,2977,2960,2238,2235,2225,2220,2192,2187,2177,2172,2144,2139,2129,2123,2089,2083,2081]) ).
tff(2981,plain,
s(s(select(q3,tail))) = s(index_47),
inference(monotonicity,[status(thm)],[2980]) ).
tff(2982,plain,
s(index_234) = s(select(q3,tail)),
inference(symmetry,[status(thm)],[2979]) ).
tff(2983,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),tail) = s(index_234) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2984,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),tail) = s(index_234),
inference(unit_resolution,[status(thm)],[2983,6]) ).
tff(2985,plain,
store(queue_236,tail,index_237) = store(store(q3,seq,earray_235),tail,s(index_234)),
inference(symmetry,[status(thm)],[2696]) ).
tff(2986,plain,
q4 = store(store(q3,seq,earray_235),tail,s(index_234)),
inference(transitivity,[status(thm)],[2663,2667,2985]) ).
tff(2987,plain,
select(q4,tail) = select(store(store(q3,seq,earray_235),tail,s(index_234)),tail),
inference(monotonicity,[status(thm)],[2986]) ).
tff(2988,plain,
( ( index_309 = select(q4,tail) )
<=> ( index_309 = select(q4,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2989,axiom,
index_309 = select(q4,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(2990,plain,
index_309 = select(q4,tail),
inference(modus_ponens,[status(thm)],[2989,2988]) ).
tff(2991,plain,
index_309 = s(select(q3,tail)),
inference(transitivity,[status(thm)],[2990,2987,2984,2982]) ).
tff(2992,plain,
s(index_309) = s(s(select(q3,tail))),
inference(monotonicity,[status(thm)],[2991]) ).
tff(2993,plain,
select(q4,tail) = index_309,
inference(symmetry,[status(thm)],[2990]) ).
tff(2994,plain,
s(select(q4,tail)) = s(index_309),
inference(monotonicity,[status(thm)],[2993]) ).
tff(2995,plain,
s(select(q4,tail)) = index_68,
inference(transitivity,[status(thm)],[2994,2992,2981,2077,2074,2073,2068,2046,2041,2040,2035,2013,2008,1998,1992,1958,1952,1941]) ).
tff(2996,plain,
s(s(select(q4,tail))) = s(index_68),
inference(monotonicity,[status(thm)],[2995]) ).
tff(2997,plain,
s(index_309) = s(select(q4,tail)),
inference(symmetry,[status(thm)],[2994]) ).
tff(2998,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q4,seq,earray_310),tail,s(index_309)),tail) = s(index_309) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2999,plain,
select(store(store(q4,seq,earray_310),tail,s(index_309)),tail) = s(index_309),
inference(unit_resolution,[status(thm)],[2998,6]) ).
tff(3000,plain,
store(queue_311,tail,index_312) = store(store(q4,seq,earray_310),tail,s(index_309)),
inference(symmetry,[status(thm)],[2648]) ).
tff(3001,plain,
q5 = store(store(q4,seq,earray_310),tail,s(index_309)),
inference(transitivity,[status(thm)],[2608,2612,3000]) ).
tff(3002,plain,
select(q5,tail) = select(store(store(q4,seq,earray_310),tail,s(index_309)),tail),
inference(monotonicity,[status(thm)],[3001]) ).
tff(3003,plain,
( ( index_321 = select(q5,tail) )
<=> ( index_321 = select(q5,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3004,axiom,
index_321 = select(q5,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(3005,plain,
index_321 = select(q5,tail),
inference(modus_ponens,[status(thm)],[3004,3003]) ).
tff(3006,plain,
index_321 = s(select(q4,tail)),
inference(transitivity,[status(thm)],[3005,3002,2999,2997]) ).
tff(3007,plain,
s(index_321) = s(s(select(q4,tail))),
inference(monotonicity,[status(thm)],[3006]) ).
tff(3008,plain,
select(q5,tail) = index_321,
inference(symmetry,[status(thm)],[3005]) ).
tff(3009,plain,
s(select(q5,tail)) = s(index_321),
inference(monotonicity,[status(thm)],[3008]) ).
tff(3010,plain,
s(select(q5,tail)) = index_95,
inference(transitivity,[status(thm)],[3009,3007,2996,1937,1934,1924,1919,1891,1886,1876,1871,1843,1838,1828,1822,1788,1782,1771]) ).
tff(3011,plain,
s(s(select(q5,tail))) = s(index_95),
inference(monotonicity,[status(thm)],[3010]) ).
tff(3012,plain,
s(index_321) = s(select(q5,tail)),
inference(symmetry,[status(thm)],[3009]) ).
tff(3013,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q5,seq,earray_322),tail,s(index_321)),tail) = s(index_321) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3014,plain,
select(store(store(q5,seq,earray_322),tail,s(index_321)),tail) = s(index_321),
inference(unit_resolution,[status(thm)],[3013,6]) ).
tff(3015,plain,
store(queue_323,tail,index_324) = store(store(q5,seq,earray_322),tail,s(index_321)),
inference(symmetry,[status(thm)],[2591]) ).
tff(3016,plain,
select(store(queue_323,tail,index_324),tail) = select(store(store(q5,seq,earray_322),tail,s(index_321)),tail),
inference(monotonicity,[status(thm)],[3015]) ).
tff(3017,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),tail) = select(store(queue_323,tail,index_324),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),tail) = select(store(queue_323,tail,index_324),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3018,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),tail) = select(store(queue_323,tail,index_324),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3019,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_323,tail,index_324),head,s(index_326)),tail) = select(store(queue_323,tail,index_324),tail) ) ),
inference(modus_ponens,[status(thm)],[3018,3017]) ).
tff(3020,plain,
select(store(store(queue_323,tail,index_324),head,s(index_326)),tail) = select(store(queue_323,tail,index_324),tail),
inference(unit_resolution,[status(thm)],[3019,32,91]) ).
tff(3021,plain,
store(queue_325,head,index_327) = store(store(queue_323,tail,index_324),head,s(index_326)),
inference(symmetry,[status(thm)],[2574]) ).
tff(3022,plain,
q6 = store(store(queue_323,tail,index_324),head,s(index_326)),
inference(transitivity,[status(thm)],[2541,2545,3021]) ).
tff(3023,plain,
select(q6,tail) = select(store(store(queue_323,tail,index_324),head,s(index_326)),tail),
inference(monotonicity,[status(thm)],[3022]) ).
tff(3024,plain,
( ( index_330 = select(q6,tail) )
<=> ( index_330 = select(q6,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3025,axiom,
index_330 = select(q6,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(3026,plain,
index_330 = select(q6,tail),
inference(modus_ponens,[status(thm)],[3025,3024]) ).
tff(3027,plain,
index_330 = s(select(q5,tail)),
inference(transitivity,[status(thm)],[3026,3023,3020,3016,3014,3012]) ).
tff(3028,plain,
s(index_330) = s(s(select(q5,tail))),
inference(monotonicity,[status(thm)],[3027]) ).
tff(3029,plain,
select(q6,tail) = index_330,
inference(symmetry,[status(thm)],[3026]) ).
tff(3030,plain,
s(select(q6,tail)) = s(index_330),
inference(monotonicity,[status(thm)],[3029]) ).
tff(3031,plain,
s(select(q6,tail)) = index_116,
inference(transitivity,[status(thm)],[3030,3028,3011,1767,1764,1754,1749,1721,1716,1706,1701,1673,1668,1658,1652,1618,1612,1601]) ).
tff(3032,plain,
s(s(select(q6,tail))) = s(index_116),
inference(monotonicity,[status(thm)],[3031]) ).
tff(3033,plain,
s(index_330) = s(select(q6,tail)),
inference(symmetry,[status(thm)],[3030]) ).
tff(3034,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q6,seq,earray_331),tail,s(index_330)),tail) = s(index_330) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3035,plain,
select(store(store(q6,seq,earray_331),tail,s(index_330)),tail) = s(index_330),
inference(unit_resolution,[status(thm)],[3034,6]) ).
tff(3036,plain,
store(queue_332,tail,index_333) = store(store(q6,seq,earray_331),tail,s(index_330)),
inference(symmetry,[status(thm)],[2526]) ).
tff(3037,plain,
q7 = store(store(q6,seq,earray_331),tail,s(index_330)),
inference(transitivity,[status(thm)],[2493,2497,3036]) ).
tff(3038,plain,
select(q7,tail) = select(store(store(q6,seq,earray_331),tail,s(index_330)),tail),
inference(monotonicity,[status(thm)],[3037]) ).
tff(3039,plain,
( ( index_336 = select(q7,tail) )
<=> ( index_336 = select(q7,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3040,axiom,
index_336 = select(q7,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(3041,plain,
index_336 = select(q7,tail),
inference(modus_ponens,[status(thm)],[3040,3039]) ).
tff(3042,plain,
index_336 = s(select(q6,tail)),
inference(transitivity,[status(thm)],[3041,3038,3035,3033]) ).
tff(3043,plain,
s(index_336) = s(s(select(q6,tail))),
inference(monotonicity,[status(thm)],[3042]) ).
tff(3044,plain,
select(q7,tail) = index_336,
inference(symmetry,[status(thm)],[3041]) ).
tff(3045,plain,
s(select(q7,tail)) = s(index_336),
inference(monotonicity,[status(thm)],[3044]) ).
tff(3046,plain,
s(select(q7,tail)) = index_137,
inference(transitivity,[status(thm)],[3045,3043,3032,1597,1594,1584,1579,1551,1546,1536,1531,1503,1498,1488,1482,1448,1442,1431]) ).
tff(3047,plain,
s(s(select(q7,tail))) = s(index_137),
inference(monotonicity,[status(thm)],[3046]) ).
tff(3048,plain,
s(index_336) = s(select(q7,tail)),
inference(symmetry,[status(thm)],[3045]) ).
tff(3049,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q7,seq,earray_337),tail,s(index_336)),tail) = s(index_336) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3050,plain,
select(store(store(q7,seq,earray_337),tail,s(index_336)),tail) = s(index_336),
inference(unit_resolution,[status(thm)],[3049,6]) ).
tff(3051,plain,
store(queue_338,tail,index_339) = store(store(q7,seq,earray_337),tail,s(index_336)),
inference(symmetry,[status(thm)],[2478]) ).
tff(3052,plain,
q8 = store(store(q7,seq,earray_337),tail,s(index_336)),
inference(transitivity,[status(thm)],[2438,2442,3051]) ).
tff(3053,plain,
select(q8,tail) = select(store(store(q7,seq,earray_337),tail,s(index_336)),tail),
inference(monotonicity,[status(thm)],[3052]) ).
tff(3054,plain,
( ( index_342 = select(q8,tail) )
<=> ( index_342 = select(q8,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3055,axiom,
index_342 = select(q8,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(3056,plain,
index_342 = select(q8,tail),
inference(modus_ponens,[status(thm)],[3055,3054]) ).
tff(3057,plain,
index_342 = s(select(q7,tail)),
inference(transitivity,[status(thm)],[3056,3053,3050,3048]) ).
tff(3058,plain,
s(index_342) = s(s(select(q7,tail))),
inference(monotonicity,[status(thm)],[3057]) ).
tff(3059,plain,
select(q8,tail) = index_342,
inference(symmetry,[status(thm)],[3056]) ).
tff(3060,plain,
s(select(q8,tail)) = s(index_342),
inference(monotonicity,[status(thm)],[3059]) ).
tff(3061,plain,
s(select(q8,tail)) = index_167,
inference(transitivity,[status(thm)],[3060,3058,3047,1427,1424,1414,1409,1381,1376,1366,1361,1333,1328,1318,1312,1278,1272,1261]) ).
tff(3062,plain,
s(s(select(q8,tail))) = s(index_167),
inference(monotonicity,[status(thm)],[3061]) ).
tff(3063,plain,
s(index_342) = s(select(q8,tail)),
inference(symmetry,[status(thm)],[3060]) ).
tff(3064,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q8,seq,earray_343),tail,s(index_342)),tail) = s(index_342) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3065,plain,
select(store(store(q8,seq,earray_343),tail,s(index_342)),tail) = s(index_342),
inference(unit_resolution,[status(thm)],[3064,6]) ).
tff(3066,plain,
store(queue_344,tail,index_345) = store(store(q8,seq,earray_343),tail,s(index_342)),
inference(symmetry,[status(thm)],[2421]) ).
tff(3067,plain,
select(store(queue_344,tail,index_345),tail) = select(store(store(q8,seq,earray_343),tail,s(index_342)),tail),
inference(monotonicity,[status(thm)],[3066]) ).
tff(3068,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),tail) = select(store(queue_344,tail,index_345),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),tail) = select(store(queue_344,tail,index_345),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3069,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),tail) = select(store(queue_344,tail,index_345),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3070,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_344,tail,index_345),head,s(index_347)),tail) = select(store(queue_344,tail,index_345),tail) ) ),
inference(modus_ponens,[status(thm)],[3069,3068]) ).
tff(3071,plain,
select(store(store(queue_344,tail,index_345),head,s(index_347)),tail) = select(store(queue_344,tail,index_345),tail),
inference(unit_resolution,[status(thm)],[3070,32,91]) ).
tff(3072,plain,
store(queue_346,head,index_348) = store(store(queue_344,tail,index_345),head,s(index_347)),
inference(symmetry,[status(thm)],[2404]) ).
tff(3073,plain,
q9 = store(store(queue_344,tail,index_345),head,s(index_347)),
inference(transitivity,[status(thm)],[2371,2375,3072]) ).
tff(3074,plain,
select(q9,tail) = select(store(store(queue_344,tail,index_345),head,s(index_347)),tail),
inference(monotonicity,[status(thm)],[3073]) ).
tff(3075,plain,
( ( index_9 = select(q9,tail) )
<=> ( index_9 = select(q9,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3076,axiom,
index_9 = select(q9,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(3077,plain,
index_9 = select(q9,tail),
inference(modus_ponens,[status(thm)],[3076,3075]) ).
tff(3078,plain,
index_9 = s(select(q8,tail)),
inference(transitivity,[status(thm)],[3077,3074,3071,3067,3065,3063]) ).
tff(3079,plain,
s(index_9) = s(s(select(q8,tail))),
inference(monotonicity,[status(thm)],[3078]) ).
tff(3080,plain,
select(q9,tail) = index_9,
inference(symmetry,[status(thm)],[3077]) ).
tff(3081,plain,
s(select(q9,tail)) = s(index_9),
inference(monotonicity,[status(thm)],[3080]) ).
tff(3082,plain,
s(select(q9,tail)) = index_188,
inference(transitivity,[status(thm)],[3081,3079,3062,1257,1254,1244,1239,1211,1206,1196,1191,1163,1158,1148,1142,1108,1102,1091]) ).
tff(3083,plain,
s(s(select(q9,tail))) = s(index_188),
inference(monotonicity,[status(thm)],[3082]) ).
tff(3084,plain,
s(index_9) = s(select(q9,tail)),
inference(symmetry,[status(thm)],[3081]) ).
tff(3085,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = s(index_9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3086,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = s(index_9),
inference(unit_resolution,[status(thm)],[3085,6]) ).
tff(3087,plain,
store(queue_11,tail,index_12) = store(store(q9,seq,earray_10),tail,s(index_9)),
inference(symmetry,[status(thm)],[2356]) ).
tff(3088,plain,
q10 = store(store(q9,seq,earray_10),tail,s(index_9)),
inference(transitivity,[status(thm)],[2323,2327,3087]) ).
tff(3089,plain,
select(q10,tail) = select(store(store(q9,seq,earray_10),tail,s(index_9)),tail),
inference(monotonicity,[status(thm)],[3088]) ).
tff(3090,plain,
( ( index_15 = select(q10,tail) )
<=> ( index_15 = select(q10,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3091,axiom,
index_15 = select(q10,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(3092,plain,
index_15 = select(q10,tail),
inference(modus_ponens,[status(thm)],[3091,3090]) ).
tff(3093,plain,
index_15 = s(select(q9,tail)),
inference(transitivity,[status(thm)],[3092,3089,3086,3084]) ).
tff(3094,plain,
s(index_15) = s(s(select(q9,tail))),
inference(monotonicity,[status(thm)],[3093]) ).
tff(3095,plain,
select(q10,tail) = index_15,
inference(symmetry,[status(thm)],[3092]) ).
tff(3096,plain,
s(select(q10,tail)) = s(index_15),
inference(monotonicity,[status(thm)],[3095]) ).
tff(3097,plain,
s(select(q10,tail)) = index_209,
inference(transitivity,[status(thm)],[3096,3094,3083,1087,1084,1074,1069,1041,1036,1026,1021,993,988,978,972,938,932,921]) ).
tff(3098,plain,
s(s(select(q10,tail))) = s(index_209),
inference(monotonicity,[status(thm)],[3097]) ).
tff(3099,plain,
s(index_15) = s(select(q10,tail)),
inference(symmetry,[status(thm)],[3096]) ).
tff(3100,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = s(index_15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3101,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = s(index_15),
inference(unit_resolution,[status(thm)],[3100,6]) ).
tff(3102,plain,
store(queue_17,tail,index_18) = store(store(q10,seq,earray_16),tail,s(index_15)),
inference(symmetry,[status(thm)],[2308]) ).
tff(3103,plain,
q11 = store(store(q10,seq,earray_16),tail,s(index_15)),
inference(transitivity,[status(thm)],[2268,2272,3102]) ).
tff(3104,plain,
select(q11,tail) = select(store(store(q10,seq,earray_16),tail,s(index_15)),tail),
inference(monotonicity,[status(thm)],[3103]) ).
tff(3105,plain,
( ( index_21 = select(q11,tail) )
<=> ( index_21 = select(q11,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3106,axiom,
index_21 = select(q11,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(3107,plain,
index_21 = select(q11,tail),
inference(modus_ponens,[status(thm)],[3106,3105]) ).
tff(3108,plain,
index_21 = s(select(q10,tail)),
inference(transitivity,[status(thm)],[3107,3104,3101,3099]) ).
tff(3109,plain,
s(index_21) = s(s(select(q10,tail))),
inference(monotonicity,[status(thm)],[3108]) ).
tff(3110,plain,
select(q11,tail) = index_21,
inference(symmetry,[status(thm)],[3107]) ).
tff(3111,plain,
s(select(q11,tail)) = s(index_21),
inference(monotonicity,[status(thm)],[3110]) ).
tff(3112,plain,
s(select(q11,tail)) = index_230,
inference(transitivity,[status(thm)],[3111,3109,3098,917,914,904,899,871,866,856,851,823,818,808,802,768,762,751]) ).
tff(3113,plain,
s(s(select(q11,tail))) = s(index_230),
inference(monotonicity,[status(thm)],[3112]) ).
tff(3114,plain,
s(index_21) = s(select(q11,tail)),
inference(symmetry,[status(thm)],[3111]) ).
tff(3115,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = s(index_21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3116,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = s(index_21),
inference(unit_resolution,[status(thm)],[3115,6]) ).
tff(3117,plain,
store(queue_23,tail,index_24) = store(store(q11,seq,earray_22),tail,s(index_21)),
inference(symmetry,[status(thm)],[2251]) ).
tff(3118,plain,
select(store(queue_23,tail,index_24),tail) = select(store(store(q11,seq,earray_22),tail,s(index_21)),tail),
inference(monotonicity,[status(thm)],[3117]) ).
tff(3119,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3120,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3121,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ),
inference(modus_ponens,[status(thm)],[3120,3119]) ).
tff(3122,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail),
inference(unit_resolution,[status(thm)],[3121,32,91]) ).
tff(3123,plain,
store(queue_25,head,index_27) = store(store(queue_23,tail,index_24),head,s(index_26)),
inference(symmetry,[status(thm)],[2234]) ).
tff(3124,plain,
q12 = store(store(queue_23,tail,index_24),head,s(index_26)),
inference(transitivity,[status(thm)],[2201,2205,3123]) ).
tff(3125,plain,
select(q12,tail) = select(store(store(queue_23,tail,index_24),head,s(index_26)),tail),
inference(monotonicity,[status(thm)],[3124]) ).
tff(3126,plain,
( ( index_30 = select(q12,tail) )
<=> ( index_30 = select(q12,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3127,axiom,
index_30 = select(q12,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(3128,plain,
index_30 = select(q12,tail),
inference(modus_ponens,[status(thm)],[3127,3126]) ).
tff(3129,plain,
index_30 = s(select(q11,tail)),
inference(transitivity,[status(thm)],[3128,3125,3122,3118,3116,3114]) ).
tff(3130,plain,
s(index_30) = s(s(select(q11,tail))),
inference(monotonicity,[status(thm)],[3129]) ).
tff(3131,plain,
select(q12,tail) = index_30,
inference(symmetry,[status(thm)],[3128]) ).
tff(3132,plain,
s(select(q12,tail)) = s(index_30),
inference(monotonicity,[status(thm)],[3131]) ).
tff(3133,plain,
s(select(q12,tail)) = index_257,
inference(transitivity,[status(thm)],[3132,3130,3113,747,744,734,729,701,696,686,681,653,648,638,632,598,592,581]) ).
tff(3134,plain,
s(s(select(q12,tail))) = s(index_257),
inference(monotonicity,[status(thm)],[3133]) ).
tff(3135,plain,
s(index_30) = s(select(q12,tail)),
inference(symmetry,[status(thm)],[3132]) ).
tff(3136,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),tail) = s(index_30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3137,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),tail) = s(index_30),
inference(unit_resolution,[status(thm)],[3136,6]) ).
tff(3138,plain,
store(queue_32,tail,index_33) = store(store(q12,seq,earray_31),tail,s(index_30)),
inference(symmetry,[status(thm)],[2186]) ).
tff(3139,plain,
q13 = store(store(q12,seq,earray_31),tail,s(index_30)),
inference(transitivity,[status(thm)],[2153,2157,3138]) ).
tff(3140,plain,
select(q13,tail) = select(store(store(q12,seq,earray_31),tail,s(index_30)),tail),
inference(monotonicity,[status(thm)],[3139]) ).
tff(3141,plain,
( ( index_36 = select(q13,tail) )
<=> ( index_36 = select(q13,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3142,axiom,
index_36 = select(q13,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(3143,plain,
index_36 = select(q13,tail),
inference(modus_ponens,[status(thm)],[3142,3141]) ).
tff(3144,plain,
index_36 = s(select(q12,tail)),
inference(transitivity,[status(thm)],[3143,3140,3137,3135]) ).
tff(3145,plain,
s(index_36) = s(s(select(q12,tail))),
inference(monotonicity,[status(thm)],[3144]) ).
tff(3146,plain,
select(q13,tail) = index_36,
inference(symmetry,[status(thm)],[3143]) ).
tff(3147,plain,
s(select(q13,tail)) = s(index_36),
inference(monotonicity,[status(thm)],[3146]) ).
tff(3148,plain,
s(select(q13,tail)) = index_278,
inference(transitivity,[status(thm)],[3147,3145,3134,577,574,564,559,531,526,516,511,483,478,468,462,428,422,411]) ).
tff(3149,plain,
s(s(select(q13,tail))) = s(index_278),
inference(monotonicity,[status(thm)],[3148]) ).
tff(3150,plain,
s(index_36) = s(select(q13,tail)),
inference(symmetry,[status(thm)],[3147]) ).
tff(3151,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),tail) = s(index_36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3152,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),tail) = s(index_36),
inference(unit_resolution,[status(thm)],[3151,6]) ).
tff(3153,plain,
store(queue_38,tail,index_39) = store(store(q13,seq,earray_37),tail,s(index_36)),
inference(symmetry,[status(thm)],[2138]) ).
tff(3154,plain,
q14 = store(store(q13,seq,earray_37),tail,s(index_36)),
inference(transitivity,[status(thm)],[2098,2102,3153]) ).
tff(3155,plain,
select(q14,tail) = select(store(store(q13,seq,earray_37),tail,s(index_36)),tail),
inference(monotonicity,[status(thm)],[3154]) ).
tff(3156,plain,
index_42 = s(select(q13,tail)),
inference(transitivity,[status(thm)],[197,3155,3152,3150]) ).
tff(3157,plain,
s(index_42) = s(s(select(q13,tail))),
inference(monotonicity,[status(thm)],[3156]) ).
tff(3158,plain,
s(select(q14,tail)) = index_299,
inference(transitivity,[status(thm)],[199,3157,3149,407,404,394,389,361,356,346,341,313,308,298,292,258,252,153]) ).
tff(3159,plain,
s(s(select(q14,tail))) = s(index_299),
inference(monotonicity,[status(thm)],[3158]) ).
tff(3160,plain,
s(index_299) = s(s(select(q14,tail))),
inference(symmetry,[status(thm)],[3159]) ).
tff(3161,plain,
select(q50,head) = select(q16,tail),
inference(transitivity,[status(thm)],[148,146,141,103,98,96,85,36,19,8,3160,241,194,191]) ).
tff(3162,plain,
( ( index_57 = select(q16,tail) )
<=> ( index_57 = select(q16,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3163,axiom,
index_57 = select(q16,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(3164,plain,
index_57 = select(q16,tail),
inference(modus_ponens,[status(thm)],[3163,3162]) ).
tff(3165,plain,
select(q16,tail) = index_57,
inference(symmetry,[status(thm)],[3164]) ).
tff(3166,plain,
( ( earray_56 = select(q16,seq) )
<=> ( earray_56 = select(q16,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3167,axiom,
earray_56 = select(q16,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(3168,plain,
earray_56 = select(q16,seq),
inference(modus_ponens,[status(thm)],[3167,3166]) ).
tff(3169,plain,
select(q16,seq) = earray_56,
inference(symmetry,[status(thm)],[3168]) ).
tff(3170,plain,
store(select(q16,seq),select(q16,tail),e16) = store(earray_56,index_57,e16),
inference(monotonicity,[status(thm)],[3169,3165]) ).
tff(3171,plain,
store(earray_56,index_57,e16) = store(select(q16,seq),select(q16,tail),e16),
inference(symmetry,[status(thm)],[3170]) ).
tff(3172,plain,
select(q17,seq) = store(select(q16,seq),select(q16,tail),e16),
inference(transitivity,[status(thm)],[2032,2029,2025,2019,3171]) ).
tff(3173,plain,
select(select(q17,seq),select(q50,head)) = select(store(select(q16,seq),select(q16,tail),e16),select(q16,tail)),
inference(monotonicity,[status(thm)],[3172,3161]) ).
tff(3174,plain,
select(select(q17,seq),select(q50,head)) = e16,
inference(transitivity,[status(thm)],[3173,172]) ).
tff(3175,plain,
( ( elem_352 = select(earray_350,index_351) )
<=> ( elem_352 = select(earray_350,index_351) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3176,axiom,
elem_352 = select(earray_350,index_351),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(3177,plain,
elem_352 = select(earray_350,index_351),
inference(modus_ponens,[status(thm)],[3176,3175]) ).
tff(3178,plain,
select(earray_350,index_351) = elem_352,
inference(symmetry,[status(thm)],[3177]) ).
tff(3179,plain,
( ( index_351 = select(q50,head) )
<=> ( index_351 = select(q50,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3180,axiom,
index_351 = select(q50,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(3181,plain,
index_351 = select(q50,head),
inference(modus_ponens,[status(thm)],[3180,3179]) ).
tff(3182,plain,
select(q50,head) = index_351,
inference(symmetry,[status(thm)],[3181]) ).
tff(3183,plain,
( ( earray_350 = select(q50,seq) )
<=> ( earray_350 = select(q50,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3184,axiom,
earray_350 = select(q50,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp80) ).
tff(3185,plain,
earray_350 = select(q50,seq),
inference(modus_ponens,[status(thm)],[3184,3183]) ).
tff(3186,plain,
select(q50,seq) = earray_350,
inference(symmetry,[status(thm)],[3185]) ).
tff(3187,plain,
select(store(q49,seq,earray_316),seq) = select(store(store(q49,seq,earray_316),tail,s(index_315)),seq),
inference(symmetry,[status(thm)],[117]) ).
tff(3188,plain,
store(earray_314,index_315,e49) = select(store(store(queue_305,tail,index_306),seq,store(earray_314,index_315,e49)),seq),
inference(symmetry,[status(thm)],[109]) ).
tff(3189,plain,
( ( index_315 = select(q49,tail) )
<=> ( index_315 = select(q49,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3190,axiom,
index_315 = select(q49,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(3191,plain,
index_315 = select(q49,tail),
inference(modus_ponens,[status(thm)],[3190,3189]) ).
tff(3192,plain,
select(q49,tail) = index_315,
inference(symmetry,[status(thm)],[3191]) ).
tff(3193,plain,
store(queue_305,tail,index_306) = store(store(q48,seq,earray_304),tail,s(index_303)),
inference(symmetry,[status(thm)],[78]) ).
tff(3194,plain,
q49 = store(store(q48,seq,earray_304),tail,s(index_303)),
inference(transitivity,[status(thm)],[64,68,3193]) ).
tff(3195,plain,
select(q49,tail) = select(store(store(q48,seq,earray_304),tail,s(index_303)),tail),
inference(monotonicity,[status(thm)],[3194]) ).
tff(3196,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),tail) = select(q49,tail),
inference(symmetry,[status(thm)],[3195]) ).
tff(3197,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q48,seq,earray_304),tail,s(index_303)),tail) = s(index_303) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3198,plain,
select(store(store(q48,seq,earray_304),tail,s(index_303)),tail) = s(index_303),
inference(unit_resolution,[status(thm)],[3197,6]) ).
tff(3199,plain,
s(index_303) = select(store(store(q48,seq,earray_304),tail,s(index_303)),tail),
inference(symmetry,[status(thm)],[3198]) ).
tff(3200,plain,
s(index_303) = index_315,
inference(transitivity,[status(thm)],[3199,3196,3192]) ).
tff(3201,plain,
( ( earray_314 = select(q49,seq) )
<=> ( earray_314 = select(q49,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3202,axiom,
earray_314 = select(q49,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp69) ).
tff(3203,plain,
earray_314 = select(q49,seq),
inference(modus_ponens,[status(thm)],[3202,3201]) ).
tff(3204,plain,
select(q49,seq) = earray_314,
inference(symmetry,[status(thm)],[3203]) ).
tff(3205,plain,
store(select(q49,seq),s(index_303),e49) = store(earray_314,index_315,e49),
inference(monotonicity,[status(thm)],[3204,3200]) ).
tff(3206,plain,
store(select(q49,seq),s(index_303),e49) = earray_350,
inference(transitivity,[status(thm)],[3205,3188,112,3187,136,3186]) ).
tff(3207,plain,
select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(earray_350,index_351),
inference(monotonicity,[status(thm)],[3206,3182]) ).
tff(3208,plain,
select(store(q49,seq,earray_316),head) = select(store(store(q49,seq,earray_316),tail,s(index_315)),head),
inference(symmetry,[status(thm)],[146]) ).
tff(3209,plain,
select(store(queue_305,tail,index_306),head) = select(store(store(queue_305,tail,index_306),seq,select(q50,seq)),head),
inference(symmetry,[status(thm)],[103]) ).
tff(3210,plain,
select(store(q48,seq,earray_304),head) = select(store(store(q48,seq,earray_304),tail,s(index_303)),head),
inference(symmetry,[status(thm)],[96]) ).
tff(3211,plain,
select(store(queue_298,head,index_300),head) = select(store(store(queue_298,head,index_300),seq,select(q49,seq)),head),
inference(symmetry,[status(thm)],[36]) ).
tff(3212,plain,
s(index_299) = select(store(store(queue_296,tail,index_297),head,s(index_299)),head),
inference(symmetry,[status(thm)],[8]) ).
tff(3213,plain,
select(q16,tail) = select(q50,head),
inference(transitivity,[status(thm)],[190,193,240,3159,3212,18,3211,84,3210,97,3209,140,3208,147]) ).
tff(3214,plain,
( ( index_303 = select(q48,tail) )
<=> ( index_303 = select(q48,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3215,axiom,
index_303 = select(q48,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(3216,plain,
index_303 = select(q48,tail),
inference(modus_ponens,[status(thm)],[3215,3214]) ).
tff(3217,plain,
select(q48,tail) = index_303,
inference(symmetry,[status(thm)],[3216]) ).
tff(3218,plain,
store(queue_298,head,index_300) = store(store(queue_296,tail,index_297),head,s(index_299)),
inference(symmetry,[status(thm)],[17]) ).
tff(3219,plain,
q48 = store(store(queue_296,tail,index_297),head,s(index_299)),
inference(transitivity,[status(thm)],[45,49,3218]) ).
tff(3220,plain,
select(q48,tail) = select(store(store(queue_296,tail,index_297),head,s(index_299)),tail),
inference(monotonicity,[status(thm)],[3219]) ).
tff(3221,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(q48,tail),
inference(symmetry,[status(thm)],[3220]) ).
tff(3222,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(store(queue_296,tail,index_297),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(store(queue_296,tail,index_297),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3223,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(store(queue_296,tail,index_297),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3224,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(store(queue_296,tail,index_297),tail) ) ),
inference(modus_ponens,[status(thm)],[3223,3222]) ).
tff(3225,plain,
select(store(store(queue_296,tail,index_297),head,s(index_299)),tail) = select(store(queue_296,tail,index_297),tail),
inference(unit_resolution,[status(thm)],[3224,32,91]) ).
tff(3226,plain,
select(store(queue_296,tail,index_297),tail) = select(store(store(queue_296,tail,index_297),head,s(index_299)),tail),
inference(symmetry,[status(thm)],[3225]) ).
tff(3227,plain,
store(queue_296,tail,index_297) = store(store(q47,seq,earray_295),tail,s(index_294)),
inference(symmetry,[status(thm)],[250]) ).
tff(3228,plain,
select(store(queue_296,tail,index_297),tail) = select(store(store(q47,seq,earray_295),tail,s(index_294)),tail),
inference(monotonicity,[status(thm)],[3227]) ).
tff(3229,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),tail) = select(store(queue_296,tail,index_297),tail),
inference(symmetry,[status(thm)],[3228]) ).
tff(3230,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q47,seq,earray_295),tail,s(index_294)),tail) = s(index_294) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3231,plain,
select(store(store(q47,seq,earray_295),tail,s(index_294)),tail) = s(index_294),
inference(unit_resolution,[status(thm)],[3230,6]) ).
tff(3232,plain,
s(index_294) = select(store(store(q47,seq,earray_295),tail,s(index_294)),tail),
inference(symmetry,[status(thm)],[3231]) ).
tff(3233,plain,
( ( index_294 = select(q47,tail) )
<=> ( index_294 = select(q47,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3234,axiom,
index_294 = select(q47,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(3235,plain,
index_294 = select(q47,tail),
inference(modus_ponens,[status(thm)],[3234,3233]) ).
tff(3236,plain,
select(q47,tail) = index_294,
inference(symmetry,[status(thm)],[3235]) ).
tff(3237,plain,
s(select(q47,tail)) = s(index_294),
inference(monotonicity,[status(thm)],[3236]) ).
tff(3238,plain,
s(select(q47,tail)) = index_303,
inference(transitivity,[status(thm)],[3237,3232,3229,3226,3221,3217]) ).
tff(3239,plain,
s(s(select(q47,tail))) = s(index_303),
inference(monotonicity,[status(thm)],[3238]) ).
tff(3240,plain,
s(index_294) = s(select(q47,tail)),
inference(symmetry,[status(thm)],[3237]) ).
tff(3241,plain,
store(queue_290,tail,index_291) = store(store(q46,seq,earray_289),tail,s(index_288)),
inference(symmetry,[status(thm)],[307]) ).
tff(3242,plain,
q47 = store(store(q46,seq,earray_289),tail,s(index_288)),
inference(transitivity,[status(thm)],[267,271,3241]) ).
tff(3243,plain,
select(q47,tail) = select(store(store(q46,seq,earray_289),tail,s(index_288)),tail),
inference(monotonicity,[status(thm)],[3242]) ).
tff(3244,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),tail) = select(q47,tail),
inference(symmetry,[status(thm)],[3243]) ).
tff(3245,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q46,seq,earray_289),tail,s(index_288)),tail) = s(index_288) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3246,plain,
select(store(store(q46,seq,earray_289),tail,s(index_288)),tail) = s(index_288),
inference(unit_resolution,[status(thm)],[3245,6]) ).
tff(3247,plain,
s(index_288) = select(store(store(q46,seq,earray_289),tail,s(index_288)),tail),
inference(symmetry,[status(thm)],[3246]) ).
tff(3248,plain,
( ( index_288 = select(q46,tail) )
<=> ( index_288 = select(q46,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3249,axiom,
index_288 = select(q46,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(3250,plain,
index_288 = select(q46,tail),
inference(modus_ponens,[status(thm)],[3249,3248]) ).
tff(3251,plain,
select(q46,tail) = index_288,
inference(symmetry,[status(thm)],[3250]) ).
tff(3252,plain,
s(select(q46,tail)) = s(index_288),
inference(monotonicity,[status(thm)],[3251]) ).
tff(3253,plain,
s(select(q46,tail)) = index_294,
inference(transitivity,[status(thm)],[3252,3247,3244,3236]) ).
tff(3254,plain,
s(s(select(q46,tail))) = s(index_294),
inference(monotonicity,[status(thm)],[3253]) ).
tff(3255,plain,
s(index_288) = s(select(q46,tail)),
inference(symmetry,[status(thm)],[3252]) ).
tff(3256,plain,
store(queue_284,tail,index_285) = store(store(q45,seq,earray_283),tail,s(index_282)),
inference(symmetry,[status(thm)],[355]) ).
tff(3257,plain,
q46 = store(store(q45,seq,earray_283),tail,s(index_282)),
inference(transitivity,[status(thm)],[322,326,3256]) ).
tff(3258,plain,
select(q46,tail) = select(store(store(q45,seq,earray_283),tail,s(index_282)),tail),
inference(monotonicity,[status(thm)],[3257]) ).
tff(3259,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),tail) = select(q46,tail),
inference(symmetry,[status(thm)],[3258]) ).
tff(3260,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q45,seq,earray_283),tail,s(index_282)),tail) = s(index_282) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3261,plain,
select(store(store(q45,seq,earray_283),tail,s(index_282)),tail) = s(index_282),
inference(unit_resolution,[status(thm)],[3260,6]) ).
tff(3262,plain,
s(index_282) = select(store(store(q45,seq,earray_283),tail,s(index_282)),tail),
inference(symmetry,[status(thm)],[3261]) ).
tff(3263,plain,
( ( index_282 = select(q45,tail) )
<=> ( index_282 = select(q45,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3264,axiom,
index_282 = select(q45,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(3265,plain,
index_282 = select(q45,tail),
inference(modus_ponens,[status(thm)],[3264,3263]) ).
tff(3266,plain,
select(q45,tail) = index_282,
inference(symmetry,[status(thm)],[3265]) ).
tff(3267,plain,
s(select(q45,tail)) = s(index_282),
inference(monotonicity,[status(thm)],[3266]) ).
tff(3268,plain,
s(select(q45,tail)) = index_288,
inference(transitivity,[status(thm)],[3267,3262,3259,3251]) ).
tff(3269,plain,
s(s(select(q45,tail))) = s(index_288),
inference(monotonicity,[status(thm)],[3268]) ).
tff(3270,plain,
s(index_282) = s(select(q45,tail)),
inference(symmetry,[status(thm)],[3267]) ).
tff(3271,plain,
store(queue_277,head,index_279) = store(store(queue_275,tail,index_276),head,s(index_278)),
inference(symmetry,[status(thm)],[403]) ).
tff(3272,plain,
q45 = store(store(queue_275,tail,index_276),head,s(index_278)),
inference(transitivity,[status(thm)],[370,374,3271]) ).
tff(3273,plain,
select(q45,tail) = select(store(store(queue_275,tail,index_276),head,s(index_278)),tail),
inference(monotonicity,[status(thm)],[3272]) ).
tff(3274,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(q45,tail),
inference(symmetry,[status(thm)],[3273]) ).
tff(3275,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3276,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3277,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ),
inference(modus_ponens,[status(thm)],[3276,3275]) ).
tff(3278,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail),
inference(unit_resolution,[status(thm)],[3277,32,91]) ).
tff(3279,plain,
select(store(queue_275,tail,index_276),tail) = select(store(store(queue_275,tail,index_276),head,s(index_278)),tail),
inference(symmetry,[status(thm)],[3278]) ).
tff(3280,plain,
store(queue_275,tail,index_276) = store(store(q44,seq,earray_274),tail,s(index_273)),
inference(symmetry,[status(thm)],[420]) ).
tff(3281,plain,
select(store(queue_275,tail,index_276),tail) = select(store(store(q44,seq,earray_274),tail,s(index_273)),tail),
inference(monotonicity,[status(thm)],[3280]) ).
tff(3282,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),tail) = select(store(queue_275,tail,index_276),tail),
inference(symmetry,[status(thm)],[3281]) ).
tff(3283,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q44,seq,earray_274),tail,s(index_273)),tail) = s(index_273) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3284,plain,
select(store(store(q44,seq,earray_274),tail,s(index_273)),tail) = s(index_273),
inference(unit_resolution,[status(thm)],[3283,6]) ).
tff(3285,plain,
s(index_273) = select(store(store(q44,seq,earray_274),tail,s(index_273)),tail),
inference(symmetry,[status(thm)],[3284]) ).
tff(3286,plain,
( ( index_273 = select(q44,tail) )
<=> ( index_273 = select(q44,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3287,axiom,
index_273 = select(q44,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(3288,plain,
index_273 = select(q44,tail),
inference(modus_ponens,[status(thm)],[3287,3286]) ).
tff(3289,plain,
select(q44,tail) = index_273,
inference(symmetry,[status(thm)],[3288]) ).
tff(3290,plain,
s(select(q44,tail)) = s(index_273),
inference(monotonicity,[status(thm)],[3289]) ).
tff(3291,plain,
s(select(q44,tail)) = index_282,
inference(transitivity,[status(thm)],[3290,3285,3282,3279,3274,3266]) ).
tff(3292,plain,
s(s(select(q44,tail))) = s(index_282),
inference(monotonicity,[status(thm)],[3291]) ).
tff(3293,plain,
s(index_273) = s(select(q44,tail)),
inference(symmetry,[status(thm)],[3290]) ).
tff(3294,plain,
store(queue_269,tail,index_270) = store(store(q43,seq,earray_268),tail,s(index_267)),
inference(symmetry,[status(thm)],[477]) ).
tff(3295,plain,
q44 = store(store(q43,seq,earray_268),tail,s(index_267)),
inference(transitivity,[status(thm)],[437,441,3294]) ).
tff(3296,plain,
select(q44,tail) = select(store(store(q43,seq,earray_268),tail,s(index_267)),tail),
inference(monotonicity,[status(thm)],[3295]) ).
tff(3297,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),tail) = select(q44,tail),
inference(symmetry,[status(thm)],[3296]) ).
tff(3298,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q43,seq,earray_268),tail,s(index_267)),tail) = s(index_267) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3299,plain,
select(store(store(q43,seq,earray_268),tail,s(index_267)),tail) = s(index_267),
inference(unit_resolution,[status(thm)],[3298,6]) ).
tff(3300,plain,
s(index_267) = select(store(store(q43,seq,earray_268),tail,s(index_267)),tail),
inference(symmetry,[status(thm)],[3299]) ).
tff(3301,plain,
( ( index_267 = select(q43,tail) )
<=> ( index_267 = select(q43,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3302,axiom,
index_267 = select(q43,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(3303,plain,
index_267 = select(q43,tail),
inference(modus_ponens,[status(thm)],[3302,3301]) ).
tff(3304,plain,
select(q43,tail) = index_267,
inference(symmetry,[status(thm)],[3303]) ).
tff(3305,plain,
s(select(q43,tail)) = s(index_267),
inference(monotonicity,[status(thm)],[3304]) ).
tff(3306,plain,
s(select(q43,tail)) = index_273,
inference(transitivity,[status(thm)],[3305,3300,3297,3289]) ).
tff(3307,plain,
s(s(select(q43,tail))) = s(index_273),
inference(monotonicity,[status(thm)],[3306]) ).
tff(3308,plain,
s(index_267) = s(select(q43,tail)),
inference(symmetry,[status(thm)],[3305]) ).
tff(3309,plain,
store(queue_263,tail,index_264) = store(store(q42,seq,earray_262),tail,s(index_261)),
inference(symmetry,[status(thm)],[525]) ).
tff(3310,plain,
q43 = store(store(q42,seq,earray_262),tail,s(index_261)),
inference(transitivity,[status(thm)],[492,496,3309]) ).
tff(3311,plain,
select(q43,tail) = select(store(store(q42,seq,earray_262),tail,s(index_261)),tail),
inference(monotonicity,[status(thm)],[3310]) ).
tff(3312,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),tail) = select(q43,tail),
inference(symmetry,[status(thm)],[3311]) ).
tff(3313,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q42,seq,earray_262),tail,s(index_261)),tail) = s(index_261) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3314,plain,
select(store(store(q42,seq,earray_262),tail,s(index_261)),tail) = s(index_261),
inference(unit_resolution,[status(thm)],[3313,6]) ).
tff(3315,plain,
s(index_261) = select(store(store(q42,seq,earray_262),tail,s(index_261)),tail),
inference(symmetry,[status(thm)],[3314]) ).
tff(3316,plain,
( ( index_261 = select(q42,tail) )
<=> ( index_261 = select(q42,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3317,axiom,
index_261 = select(q42,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(3318,plain,
index_261 = select(q42,tail),
inference(modus_ponens,[status(thm)],[3317,3316]) ).
tff(3319,plain,
select(q42,tail) = index_261,
inference(symmetry,[status(thm)],[3318]) ).
tff(3320,plain,
s(select(q42,tail)) = s(index_261),
inference(monotonicity,[status(thm)],[3319]) ).
tff(3321,plain,
s(select(q42,tail)) = index_267,
inference(transitivity,[status(thm)],[3320,3315,3312,3304]) ).
tff(3322,plain,
s(s(select(q42,tail))) = s(index_267),
inference(monotonicity,[status(thm)],[3321]) ).
tff(3323,plain,
s(index_261) = s(select(q42,tail)),
inference(symmetry,[status(thm)],[3320]) ).
tff(3324,plain,
store(queue_256,head,index_258) = store(store(queue_254,tail,index_255),head,s(index_257)),
inference(symmetry,[status(thm)],[573]) ).
tff(3325,plain,
q42 = store(store(queue_254,tail,index_255),head,s(index_257)),
inference(transitivity,[status(thm)],[540,544,3324]) ).
tff(3326,plain,
select(q42,tail) = select(store(store(queue_254,tail,index_255),head,s(index_257)),tail),
inference(monotonicity,[status(thm)],[3325]) ).
tff(3327,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(q42,tail),
inference(symmetry,[status(thm)],[3326]) ).
tff(3328,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3329,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3330,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ),
inference(modus_ponens,[status(thm)],[3329,3328]) ).
tff(3331,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail),
inference(unit_resolution,[status(thm)],[3330,32,91]) ).
tff(3332,plain,
select(store(queue_254,tail,index_255),tail) = select(store(store(queue_254,tail,index_255),head,s(index_257)),tail),
inference(symmetry,[status(thm)],[3331]) ).
tff(3333,plain,
store(queue_254,tail,index_255) = store(store(q41,seq,earray_253),tail,s(index_252)),
inference(symmetry,[status(thm)],[590]) ).
tff(3334,plain,
select(store(queue_254,tail,index_255),tail) = select(store(store(q41,seq,earray_253),tail,s(index_252)),tail),
inference(monotonicity,[status(thm)],[3333]) ).
tff(3335,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),tail) = select(store(queue_254,tail,index_255),tail),
inference(symmetry,[status(thm)],[3334]) ).
tff(3336,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q41,seq,earray_253),tail,s(index_252)),tail) = s(index_252) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3337,plain,
select(store(store(q41,seq,earray_253),tail,s(index_252)),tail) = s(index_252),
inference(unit_resolution,[status(thm)],[3336,6]) ).
tff(3338,plain,
s(index_252) = select(store(store(q41,seq,earray_253),tail,s(index_252)),tail),
inference(symmetry,[status(thm)],[3337]) ).
tff(3339,plain,
( ( index_252 = select(q41,tail) )
<=> ( index_252 = select(q41,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3340,axiom,
index_252 = select(q41,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(3341,plain,
index_252 = select(q41,tail),
inference(modus_ponens,[status(thm)],[3340,3339]) ).
tff(3342,plain,
select(q41,tail) = index_252,
inference(symmetry,[status(thm)],[3341]) ).
tff(3343,plain,
s(select(q41,tail)) = s(index_252),
inference(monotonicity,[status(thm)],[3342]) ).
tff(3344,plain,
s(select(q41,tail)) = index_261,
inference(transitivity,[status(thm)],[3343,3338,3335,3332,3327,3319]) ).
tff(3345,plain,
s(s(select(q41,tail))) = s(index_261),
inference(monotonicity,[status(thm)],[3344]) ).
tff(3346,plain,
s(index_252) = s(select(q41,tail)),
inference(symmetry,[status(thm)],[3343]) ).
tff(3347,plain,
store(queue_248,tail,index_249) = store(store(q40,seq,earray_247),tail,s(index_246)),
inference(symmetry,[status(thm)],[647]) ).
tff(3348,plain,
q41 = store(store(q40,seq,earray_247),tail,s(index_246)),
inference(transitivity,[status(thm)],[607,611,3347]) ).
tff(3349,plain,
select(q41,tail) = select(store(store(q40,seq,earray_247),tail,s(index_246)),tail),
inference(monotonicity,[status(thm)],[3348]) ).
tff(3350,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),tail) = select(q41,tail),
inference(symmetry,[status(thm)],[3349]) ).
tff(3351,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q40,seq,earray_247),tail,s(index_246)),tail) = s(index_246) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3352,plain,
select(store(store(q40,seq,earray_247),tail,s(index_246)),tail) = s(index_246),
inference(unit_resolution,[status(thm)],[3351,6]) ).
tff(3353,plain,
s(index_246) = select(store(store(q40,seq,earray_247),tail,s(index_246)),tail),
inference(symmetry,[status(thm)],[3352]) ).
tff(3354,plain,
( ( index_246 = select(q40,tail) )
<=> ( index_246 = select(q40,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3355,axiom,
index_246 = select(q40,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(3356,plain,
index_246 = select(q40,tail),
inference(modus_ponens,[status(thm)],[3355,3354]) ).
tff(3357,plain,
select(q40,tail) = index_246,
inference(symmetry,[status(thm)],[3356]) ).
tff(3358,plain,
s(select(q40,tail)) = s(index_246),
inference(monotonicity,[status(thm)],[3357]) ).
tff(3359,plain,
s(select(q40,tail)) = index_252,
inference(transitivity,[status(thm)],[3358,3353,3350,3342]) ).
tff(3360,plain,
s(s(select(q40,tail))) = s(index_252),
inference(monotonicity,[status(thm)],[3359]) ).
tff(3361,plain,
s(index_246) = s(select(q40,tail)),
inference(symmetry,[status(thm)],[3358]) ).
tff(3362,plain,
store(queue_242,tail,index_243) = store(store(q39,seq,earray_241),tail,s(index_240)),
inference(symmetry,[status(thm)],[695]) ).
tff(3363,plain,
q40 = store(store(q39,seq,earray_241),tail,s(index_240)),
inference(transitivity,[status(thm)],[662,666,3362]) ).
tff(3364,plain,
select(q40,tail) = select(store(store(q39,seq,earray_241),tail,s(index_240)),tail),
inference(monotonicity,[status(thm)],[3363]) ).
tff(3365,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),tail) = select(q40,tail),
inference(symmetry,[status(thm)],[3364]) ).
tff(3366,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),tail) = s(index_240) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3367,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),tail) = s(index_240),
inference(unit_resolution,[status(thm)],[3366,6]) ).
tff(3368,plain,
s(index_240) = select(store(store(q39,seq,earray_241),tail,s(index_240)),tail),
inference(symmetry,[status(thm)],[3367]) ).
tff(3369,plain,
( ( index_240 = select(q39,tail) )
<=> ( index_240 = select(q39,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3370,axiom,
index_240 = select(q39,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(3371,plain,
index_240 = select(q39,tail),
inference(modus_ponens,[status(thm)],[3370,3369]) ).
tff(3372,plain,
select(q39,tail) = index_240,
inference(symmetry,[status(thm)],[3371]) ).
tff(3373,plain,
s(select(q39,tail)) = s(index_240),
inference(monotonicity,[status(thm)],[3372]) ).
tff(3374,plain,
s(select(q39,tail)) = index_246,
inference(transitivity,[status(thm)],[3373,3368,3365,3357]) ).
tff(3375,plain,
s(s(select(q39,tail))) = s(index_246),
inference(monotonicity,[status(thm)],[3374]) ).
tff(3376,plain,
s(index_240) = s(select(q39,tail)),
inference(symmetry,[status(thm)],[3373]) ).
tff(3377,plain,
store(queue_229,head,index_231) = store(store(queue_227,tail,index_228),head,s(index_230)),
inference(symmetry,[status(thm)],[743]) ).
tff(3378,plain,
q39 = store(store(queue_227,tail,index_228),head,s(index_230)),
inference(transitivity,[status(thm)],[710,714,3377]) ).
tff(3379,plain,
select(q39,tail) = select(store(store(queue_227,tail,index_228),head,s(index_230)),tail),
inference(monotonicity,[status(thm)],[3378]) ).
tff(3380,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(q39,tail),
inference(symmetry,[status(thm)],[3379]) ).
tff(3381,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3382,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3383,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ),
inference(modus_ponens,[status(thm)],[3382,3381]) ).
tff(3384,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail),
inference(unit_resolution,[status(thm)],[3383,32,91]) ).
tff(3385,plain,
select(store(queue_227,tail,index_228),tail) = select(store(store(queue_227,tail,index_228),head,s(index_230)),tail),
inference(symmetry,[status(thm)],[3384]) ).
tff(3386,plain,
store(queue_227,tail,index_228) = store(store(q38,seq,earray_226),tail,s(index_225)),
inference(symmetry,[status(thm)],[760]) ).
tff(3387,plain,
select(store(queue_227,tail,index_228),tail) = select(store(store(q38,seq,earray_226),tail,s(index_225)),tail),
inference(monotonicity,[status(thm)],[3386]) ).
tff(3388,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = select(store(queue_227,tail,index_228),tail),
inference(symmetry,[status(thm)],[3387]) ).
tff(3389,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = s(index_225) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3390,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = s(index_225),
inference(unit_resolution,[status(thm)],[3389,6]) ).
tff(3391,plain,
s(index_225) = select(store(store(q38,seq,earray_226),tail,s(index_225)),tail),
inference(symmetry,[status(thm)],[3390]) ).
tff(3392,plain,
( ( index_225 = select(q38,tail) )
<=> ( index_225 = select(q38,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3393,axiom,
index_225 = select(q38,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(3394,plain,
index_225 = select(q38,tail),
inference(modus_ponens,[status(thm)],[3393,3392]) ).
tff(3395,plain,
select(q38,tail) = index_225,
inference(symmetry,[status(thm)],[3394]) ).
tff(3396,plain,
s(select(q38,tail)) = s(index_225),
inference(monotonicity,[status(thm)],[3395]) ).
tff(3397,plain,
s(select(q38,tail)) = index_240,
inference(transitivity,[status(thm)],[3396,3391,3388,3385,3380,3372]) ).
tff(3398,plain,
s(s(select(q38,tail))) = s(index_240),
inference(monotonicity,[status(thm)],[3397]) ).
tff(3399,plain,
s(index_225) = s(select(q38,tail)),
inference(symmetry,[status(thm)],[3396]) ).
tff(3400,plain,
store(queue_221,tail,index_222) = store(store(q37,seq,earray_220),tail,s(index_219)),
inference(symmetry,[status(thm)],[817]) ).
tff(3401,plain,
q38 = store(store(q37,seq,earray_220),tail,s(index_219)),
inference(transitivity,[status(thm)],[777,781,3400]) ).
tff(3402,plain,
select(q38,tail) = select(store(store(q37,seq,earray_220),tail,s(index_219)),tail),
inference(monotonicity,[status(thm)],[3401]) ).
tff(3403,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = select(q38,tail),
inference(symmetry,[status(thm)],[3402]) ).
tff(3404,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = s(index_219) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3405,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = s(index_219),
inference(unit_resolution,[status(thm)],[3404,6]) ).
tff(3406,plain,
s(index_219) = select(store(store(q37,seq,earray_220),tail,s(index_219)),tail),
inference(symmetry,[status(thm)],[3405]) ).
tff(3407,plain,
( ( index_219 = select(q37,tail) )
<=> ( index_219 = select(q37,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3408,axiom,
index_219 = select(q37,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(3409,plain,
index_219 = select(q37,tail),
inference(modus_ponens,[status(thm)],[3408,3407]) ).
tff(3410,plain,
select(q37,tail) = index_219,
inference(symmetry,[status(thm)],[3409]) ).
tff(3411,plain,
s(select(q37,tail)) = s(index_219),
inference(monotonicity,[status(thm)],[3410]) ).
tff(3412,plain,
s(select(q37,tail)) = index_225,
inference(transitivity,[status(thm)],[3411,3406,3403,3395]) ).
tff(3413,plain,
s(s(select(q37,tail))) = s(index_225),
inference(monotonicity,[status(thm)],[3412]) ).
tff(3414,plain,
s(index_219) = s(select(q37,tail)),
inference(symmetry,[status(thm)],[3411]) ).
tff(3415,plain,
store(queue_215,tail,index_216) = store(store(q36,seq,earray_214),tail,s(index_213)),
inference(symmetry,[status(thm)],[865]) ).
tff(3416,plain,
q37 = store(store(q36,seq,earray_214),tail,s(index_213)),
inference(transitivity,[status(thm)],[832,836,3415]) ).
tff(3417,plain,
select(q37,tail) = select(store(store(q36,seq,earray_214),tail,s(index_213)),tail),
inference(monotonicity,[status(thm)],[3416]) ).
tff(3418,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = select(q37,tail),
inference(symmetry,[status(thm)],[3417]) ).
tff(3419,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = s(index_213) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3420,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = s(index_213),
inference(unit_resolution,[status(thm)],[3419,6]) ).
tff(3421,plain,
s(index_213) = select(store(store(q36,seq,earray_214),tail,s(index_213)),tail),
inference(symmetry,[status(thm)],[3420]) ).
tff(3422,plain,
( ( index_213 = select(q36,tail) )
<=> ( index_213 = select(q36,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3423,axiom,
index_213 = select(q36,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(3424,plain,
index_213 = select(q36,tail),
inference(modus_ponens,[status(thm)],[3423,3422]) ).
tff(3425,plain,
select(q36,tail) = index_213,
inference(symmetry,[status(thm)],[3424]) ).
tff(3426,plain,
s(select(q36,tail)) = s(index_213),
inference(monotonicity,[status(thm)],[3425]) ).
tff(3427,plain,
s(select(q36,tail)) = index_219,
inference(transitivity,[status(thm)],[3426,3421,3418,3410]) ).
tff(3428,plain,
s(s(select(q36,tail))) = s(index_219),
inference(monotonicity,[status(thm)],[3427]) ).
tff(3429,plain,
s(index_213) = s(select(q36,tail)),
inference(symmetry,[status(thm)],[3426]) ).
tff(3430,plain,
store(queue_208,head,index_210) = store(store(queue_206,tail,index_207),head,s(index_209)),
inference(symmetry,[status(thm)],[913]) ).
tff(3431,plain,
q36 = store(store(queue_206,tail,index_207),head,s(index_209)),
inference(transitivity,[status(thm)],[880,884,3430]) ).
tff(3432,plain,
select(q36,tail) = select(store(store(queue_206,tail,index_207),head,s(index_209)),tail),
inference(monotonicity,[status(thm)],[3431]) ).
tff(3433,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(q36,tail),
inference(symmetry,[status(thm)],[3432]) ).
tff(3434,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3435,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3436,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ),
inference(modus_ponens,[status(thm)],[3435,3434]) ).
tff(3437,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail),
inference(unit_resolution,[status(thm)],[3436,32,91]) ).
tff(3438,plain,
select(store(queue_206,tail,index_207),tail) = select(store(store(queue_206,tail,index_207),head,s(index_209)),tail),
inference(symmetry,[status(thm)],[3437]) ).
tff(3439,plain,
store(queue_206,tail,index_207) = store(store(q35,seq,earray_205),tail,s(index_204)),
inference(symmetry,[status(thm)],[930]) ).
tff(3440,plain,
select(store(queue_206,tail,index_207),tail) = select(store(store(q35,seq,earray_205),tail,s(index_204)),tail),
inference(monotonicity,[status(thm)],[3439]) ).
tff(3441,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = select(store(queue_206,tail,index_207),tail),
inference(symmetry,[status(thm)],[3440]) ).
tff(3442,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = s(index_204) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3443,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = s(index_204),
inference(unit_resolution,[status(thm)],[3442,6]) ).
tff(3444,plain,
s(index_204) = select(store(store(q35,seq,earray_205),tail,s(index_204)),tail),
inference(symmetry,[status(thm)],[3443]) ).
tff(3445,plain,
( ( index_204 = select(q35,tail) )
<=> ( index_204 = select(q35,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3446,axiom,
index_204 = select(q35,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(3447,plain,
index_204 = select(q35,tail),
inference(modus_ponens,[status(thm)],[3446,3445]) ).
tff(3448,plain,
select(q35,tail) = index_204,
inference(symmetry,[status(thm)],[3447]) ).
tff(3449,plain,
s(select(q35,tail)) = s(index_204),
inference(monotonicity,[status(thm)],[3448]) ).
tff(3450,plain,
s(select(q35,tail)) = index_213,
inference(transitivity,[status(thm)],[3449,3444,3441,3438,3433,3425]) ).
tff(3451,plain,
s(s(select(q35,tail))) = s(index_213),
inference(monotonicity,[status(thm)],[3450]) ).
tff(3452,plain,
s(index_204) = s(select(q35,tail)),
inference(symmetry,[status(thm)],[3449]) ).
tff(3453,plain,
store(queue_200,tail,index_201) = store(store(q34,seq,earray_199),tail,s(index_198)),
inference(symmetry,[status(thm)],[987]) ).
tff(3454,plain,
q35 = store(store(q34,seq,earray_199),tail,s(index_198)),
inference(transitivity,[status(thm)],[947,951,3453]) ).
tff(3455,plain,
select(q35,tail) = select(store(store(q34,seq,earray_199),tail,s(index_198)),tail),
inference(monotonicity,[status(thm)],[3454]) ).
tff(3456,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = select(q35,tail),
inference(symmetry,[status(thm)],[3455]) ).
tff(3457,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = s(index_198) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3458,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = s(index_198),
inference(unit_resolution,[status(thm)],[3457,6]) ).
tff(3459,plain,
s(index_198) = select(store(store(q34,seq,earray_199),tail,s(index_198)),tail),
inference(symmetry,[status(thm)],[3458]) ).
tff(3460,plain,
( ( index_198 = select(q34,tail) )
<=> ( index_198 = select(q34,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3461,axiom,
index_198 = select(q34,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(3462,plain,
index_198 = select(q34,tail),
inference(modus_ponens,[status(thm)],[3461,3460]) ).
tff(3463,plain,
select(q34,tail) = index_198,
inference(symmetry,[status(thm)],[3462]) ).
tff(3464,plain,
s(select(q34,tail)) = s(index_198),
inference(monotonicity,[status(thm)],[3463]) ).
tff(3465,plain,
s(select(q34,tail)) = index_204,
inference(transitivity,[status(thm)],[3464,3459,3456,3448]) ).
tff(3466,plain,
s(s(select(q34,tail))) = s(index_204),
inference(monotonicity,[status(thm)],[3465]) ).
tff(3467,plain,
s(index_198) = s(select(q34,tail)),
inference(symmetry,[status(thm)],[3464]) ).
tff(3468,plain,
store(queue_194,tail,index_195) = store(store(q33,seq,earray_193),tail,s(index_192)),
inference(symmetry,[status(thm)],[1035]) ).
tff(3469,plain,
q34 = store(store(q33,seq,earray_193),tail,s(index_192)),
inference(transitivity,[status(thm)],[1002,1006,3468]) ).
tff(3470,plain,
select(q34,tail) = select(store(store(q33,seq,earray_193),tail,s(index_192)),tail),
inference(monotonicity,[status(thm)],[3469]) ).
tff(3471,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = select(q34,tail),
inference(symmetry,[status(thm)],[3470]) ).
tff(3472,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = s(index_192) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3473,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = s(index_192),
inference(unit_resolution,[status(thm)],[3472,6]) ).
tff(3474,plain,
s(index_192) = select(store(store(q33,seq,earray_193),tail,s(index_192)),tail),
inference(symmetry,[status(thm)],[3473]) ).
tff(3475,plain,
( ( index_192 = select(q33,tail) )
<=> ( index_192 = select(q33,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3476,axiom,
index_192 = select(q33,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(3477,plain,
index_192 = select(q33,tail),
inference(modus_ponens,[status(thm)],[3476,3475]) ).
tff(3478,plain,
select(q33,tail) = index_192,
inference(symmetry,[status(thm)],[3477]) ).
tff(3479,plain,
s(select(q33,tail)) = s(index_192),
inference(monotonicity,[status(thm)],[3478]) ).
tff(3480,plain,
s(select(q33,tail)) = index_198,
inference(transitivity,[status(thm)],[3479,3474,3471,3463]) ).
tff(3481,plain,
s(s(select(q33,tail))) = s(index_198),
inference(monotonicity,[status(thm)],[3480]) ).
tff(3482,plain,
s(index_192) = s(select(q33,tail)),
inference(symmetry,[status(thm)],[3479]) ).
tff(3483,plain,
store(queue_187,head,index_189) = store(store(queue_185,tail,index_186),head,s(index_188)),
inference(symmetry,[status(thm)],[1083]) ).
tff(3484,plain,
q33 = store(store(queue_185,tail,index_186),head,s(index_188)),
inference(transitivity,[status(thm)],[1050,1054,3483]) ).
tff(3485,plain,
select(q33,tail) = select(store(store(queue_185,tail,index_186),head,s(index_188)),tail),
inference(monotonicity,[status(thm)],[3484]) ).
tff(3486,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(q33,tail),
inference(symmetry,[status(thm)],[3485]) ).
tff(3487,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3488,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3489,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ),
inference(modus_ponens,[status(thm)],[3488,3487]) ).
tff(3490,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail),
inference(unit_resolution,[status(thm)],[3489,32,91]) ).
tff(3491,plain,
select(store(queue_185,tail,index_186),tail) = select(store(store(queue_185,tail,index_186),head,s(index_188)),tail),
inference(symmetry,[status(thm)],[3490]) ).
tff(3492,plain,
store(queue_185,tail,index_186) = store(store(q32,seq,earray_184),tail,s(index_183)),
inference(symmetry,[status(thm)],[1100]) ).
tff(3493,plain,
select(store(queue_185,tail,index_186),tail) = select(store(store(q32,seq,earray_184),tail,s(index_183)),tail),
inference(monotonicity,[status(thm)],[3492]) ).
tff(3494,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = select(store(queue_185,tail,index_186),tail),
inference(symmetry,[status(thm)],[3493]) ).
tff(3495,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3496,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = s(index_183),
inference(unit_resolution,[status(thm)],[3495,6]) ).
tff(3497,plain,
s(index_183) = select(store(store(q32,seq,earray_184),tail,s(index_183)),tail),
inference(symmetry,[status(thm)],[3496]) ).
tff(3498,plain,
( ( index_183 = select(q32,tail) )
<=> ( index_183 = select(q32,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3499,axiom,
index_183 = select(q32,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(3500,plain,
index_183 = select(q32,tail),
inference(modus_ponens,[status(thm)],[3499,3498]) ).
tff(3501,plain,
select(q32,tail) = index_183,
inference(symmetry,[status(thm)],[3500]) ).
tff(3502,plain,
s(select(q32,tail)) = s(index_183),
inference(monotonicity,[status(thm)],[3501]) ).
tff(3503,plain,
s(select(q32,tail)) = index_192,
inference(transitivity,[status(thm)],[3502,3497,3494,3491,3486,3478]) ).
tff(3504,plain,
s(s(select(q32,tail))) = s(index_192),
inference(monotonicity,[status(thm)],[3503]) ).
tff(3505,plain,
s(index_183) = s(select(q32,tail)),
inference(symmetry,[status(thm)],[3502]) ).
tff(3506,plain,
store(queue_179,tail,index_180) = store(store(q31,seq,earray_178),tail,s(index_177)),
inference(symmetry,[status(thm)],[1157]) ).
tff(3507,plain,
q32 = store(store(q31,seq,earray_178),tail,s(index_177)),
inference(transitivity,[status(thm)],[1117,1121,3506]) ).
tff(3508,plain,
select(q32,tail) = select(store(store(q31,seq,earray_178),tail,s(index_177)),tail),
inference(monotonicity,[status(thm)],[3507]) ).
tff(3509,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = select(q32,tail),
inference(symmetry,[status(thm)],[3508]) ).
tff(3510,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3511,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = s(index_177),
inference(unit_resolution,[status(thm)],[3510,6]) ).
tff(3512,plain,
s(index_177) = select(store(store(q31,seq,earray_178),tail,s(index_177)),tail),
inference(symmetry,[status(thm)],[3511]) ).
tff(3513,plain,
( ( index_177 = select(q31,tail) )
<=> ( index_177 = select(q31,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3514,axiom,
index_177 = select(q31,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(3515,plain,
index_177 = select(q31,tail),
inference(modus_ponens,[status(thm)],[3514,3513]) ).
tff(3516,plain,
select(q31,tail) = index_177,
inference(symmetry,[status(thm)],[3515]) ).
tff(3517,plain,
s(select(q31,tail)) = s(index_177),
inference(monotonicity,[status(thm)],[3516]) ).
tff(3518,plain,
s(select(q31,tail)) = index_183,
inference(transitivity,[status(thm)],[3517,3512,3509,3501]) ).
tff(3519,plain,
s(s(select(q31,tail))) = s(index_183),
inference(monotonicity,[status(thm)],[3518]) ).
tff(3520,plain,
s(index_177) = s(select(q31,tail)),
inference(symmetry,[status(thm)],[3517]) ).
tff(3521,plain,
store(queue_173,tail,index_174) = store(store(q30,seq,earray_172),tail,s(index_171)),
inference(symmetry,[status(thm)],[1205]) ).
tff(3522,plain,
q31 = store(store(q30,seq,earray_172),tail,s(index_171)),
inference(transitivity,[status(thm)],[1172,1176,3521]) ).
tff(3523,plain,
select(q31,tail) = select(store(store(q30,seq,earray_172),tail,s(index_171)),tail),
inference(monotonicity,[status(thm)],[3522]) ).
tff(3524,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = select(q31,tail),
inference(symmetry,[status(thm)],[3523]) ).
tff(3525,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3526,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = s(index_171),
inference(unit_resolution,[status(thm)],[3525,6]) ).
tff(3527,plain,
s(index_171) = select(store(store(q30,seq,earray_172),tail,s(index_171)),tail),
inference(symmetry,[status(thm)],[3526]) ).
tff(3528,plain,
( ( index_171 = select(q30,tail) )
<=> ( index_171 = select(q30,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3529,axiom,
index_171 = select(q30,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(3530,plain,
index_171 = select(q30,tail),
inference(modus_ponens,[status(thm)],[3529,3528]) ).
tff(3531,plain,
select(q30,tail) = index_171,
inference(symmetry,[status(thm)],[3530]) ).
tff(3532,plain,
s(select(q30,tail)) = s(index_171),
inference(monotonicity,[status(thm)],[3531]) ).
tff(3533,plain,
s(select(q30,tail)) = index_177,
inference(transitivity,[status(thm)],[3532,3527,3524,3516]) ).
tff(3534,plain,
s(s(select(q30,tail))) = s(index_177),
inference(monotonicity,[status(thm)],[3533]) ).
tff(3535,plain,
s(index_171) = s(select(q30,tail)),
inference(symmetry,[status(thm)],[3532]) ).
tff(3536,plain,
store(queue_166,head,index_168) = store(store(queue_164,tail,index_165),head,s(index_167)),
inference(symmetry,[status(thm)],[1253]) ).
tff(3537,plain,
q30 = store(store(queue_164,tail,index_165),head,s(index_167)),
inference(transitivity,[status(thm)],[1220,1224,3536]) ).
tff(3538,plain,
select(q30,tail) = select(store(store(queue_164,tail,index_165),head,s(index_167)),tail),
inference(monotonicity,[status(thm)],[3537]) ).
tff(3539,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(q30,tail),
inference(symmetry,[status(thm)],[3538]) ).
tff(3540,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3541,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3542,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ),
inference(modus_ponens,[status(thm)],[3541,3540]) ).
tff(3543,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail),
inference(unit_resolution,[status(thm)],[3542,32,91]) ).
tff(3544,plain,
select(store(queue_164,tail,index_165),tail) = select(store(store(queue_164,tail,index_165),head,s(index_167)),tail),
inference(symmetry,[status(thm)],[3543]) ).
tff(3545,plain,
store(queue_164,tail,index_165) = store(store(q29,seq,earray_163),tail,s(index_162)),
inference(symmetry,[status(thm)],[1270]) ).
tff(3546,plain,
select(store(queue_164,tail,index_165),tail) = select(store(store(q29,seq,earray_163),tail,s(index_162)),tail),
inference(monotonicity,[status(thm)],[3545]) ).
tff(3547,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = select(store(queue_164,tail,index_165),tail),
inference(symmetry,[status(thm)],[3546]) ).
tff(3548,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = s(index_162) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3549,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = s(index_162),
inference(unit_resolution,[status(thm)],[3548,6]) ).
tff(3550,plain,
s(index_162) = select(store(store(q29,seq,earray_163),tail,s(index_162)),tail),
inference(symmetry,[status(thm)],[3549]) ).
tff(3551,plain,
( ( index_162 = select(q29,tail) )
<=> ( index_162 = select(q29,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3552,axiom,
index_162 = select(q29,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(3553,plain,
index_162 = select(q29,tail),
inference(modus_ponens,[status(thm)],[3552,3551]) ).
tff(3554,plain,
select(q29,tail) = index_162,
inference(symmetry,[status(thm)],[3553]) ).
tff(3555,plain,
s(select(q29,tail)) = s(index_162),
inference(monotonicity,[status(thm)],[3554]) ).
tff(3556,plain,
s(select(q29,tail)) = index_171,
inference(transitivity,[status(thm)],[3555,3550,3547,3544,3539,3531]) ).
tff(3557,plain,
s(s(select(q29,tail))) = s(index_171),
inference(monotonicity,[status(thm)],[3556]) ).
tff(3558,plain,
s(index_162) = s(select(q29,tail)),
inference(symmetry,[status(thm)],[3555]) ).
tff(3559,plain,
store(queue_149,tail,index_150) = store(store(q28,seq,earray_148),tail,s(index_147)),
inference(symmetry,[status(thm)],[1327]) ).
tff(3560,plain,
q29 = store(store(q28,seq,earray_148),tail,s(index_147)),
inference(transitivity,[status(thm)],[1287,1291,3559]) ).
tff(3561,plain,
select(q29,tail) = select(store(store(q28,seq,earray_148),tail,s(index_147)),tail),
inference(monotonicity,[status(thm)],[3560]) ).
tff(3562,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = select(q29,tail),
inference(symmetry,[status(thm)],[3561]) ).
tff(3563,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3564,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = s(index_147),
inference(unit_resolution,[status(thm)],[3563,6]) ).
tff(3565,plain,
s(index_147) = select(store(store(q28,seq,earray_148),tail,s(index_147)),tail),
inference(symmetry,[status(thm)],[3564]) ).
tff(3566,plain,
( ( index_147 = select(q28,tail) )
<=> ( index_147 = select(q28,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3567,axiom,
index_147 = select(q28,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(3568,plain,
index_147 = select(q28,tail),
inference(modus_ponens,[status(thm)],[3567,3566]) ).
tff(3569,plain,
select(q28,tail) = index_147,
inference(symmetry,[status(thm)],[3568]) ).
tff(3570,plain,
s(select(q28,tail)) = s(index_147),
inference(monotonicity,[status(thm)],[3569]) ).
tff(3571,plain,
s(select(q28,tail)) = index_162,
inference(transitivity,[status(thm)],[3570,3565,3562,3554]) ).
tff(3572,plain,
s(s(select(q28,tail))) = s(index_162),
inference(monotonicity,[status(thm)],[3571]) ).
tff(3573,plain,
s(index_147) = s(select(q28,tail)),
inference(symmetry,[status(thm)],[3570]) ).
tff(3574,plain,
store(queue_143,tail,index_144) = store(store(q27,seq,earray_142),tail,s(index_141)),
inference(symmetry,[status(thm)],[1375]) ).
tff(3575,plain,
q28 = store(store(q27,seq,earray_142),tail,s(index_141)),
inference(transitivity,[status(thm)],[1342,1346,3574]) ).
tff(3576,plain,
select(q28,tail) = select(store(store(q27,seq,earray_142),tail,s(index_141)),tail),
inference(monotonicity,[status(thm)],[3575]) ).
tff(3577,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = select(q28,tail),
inference(symmetry,[status(thm)],[3576]) ).
tff(3578,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3579,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = s(index_141),
inference(unit_resolution,[status(thm)],[3578,6]) ).
tff(3580,plain,
s(index_141) = select(store(store(q27,seq,earray_142),tail,s(index_141)),tail),
inference(symmetry,[status(thm)],[3579]) ).
tff(3581,plain,
( ( index_141 = select(q27,tail) )
<=> ( index_141 = select(q27,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3582,axiom,
index_141 = select(q27,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(3583,plain,
index_141 = select(q27,tail),
inference(modus_ponens,[status(thm)],[3582,3581]) ).
tff(3584,plain,
select(q27,tail) = index_141,
inference(symmetry,[status(thm)],[3583]) ).
tff(3585,plain,
s(select(q27,tail)) = s(index_141),
inference(monotonicity,[status(thm)],[3584]) ).
tff(3586,plain,
s(select(q27,tail)) = index_147,
inference(transitivity,[status(thm)],[3585,3580,3577,3569]) ).
tff(3587,plain,
s(s(select(q27,tail))) = s(index_147),
inference(monotonicity,[status(thm)],[3586]) ).
tff(3588,plain,
s(index_141) = s(select(q27,tail)),
inference(symmetry,[status(thm)],[3585]) ).
tff(3589,plain,
store(queue_136,head,index_138) = store(store(queue_134,tail,index_135),head,s(index_137)),
inference(symmetry,[status(thm)],[1423]) ).
tff(3590,plain,
q27 = store(store(queue_134,tail,index_135),head,s(index_137)),
inference(transitivity,[status(thm)],[1390,1394,3589]) ).
tff(3591,plain,
select(q27,tail) = select(store(store(queue_134,tail,index_135),head,s(index_137)),tail),
inference(monotonicity,[status(thm)],[3590]) ).
tff(3592,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(q27,tail),
inference(symmetry,[status(thm)],[3591]) ).
tff(3593,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3594,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3595,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ),
inference(modus_ponens,[status(thm)],[3594,3593]) ).
tff(3596,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail),
inference(unit_resolution,[status(thm)],[3595,32,91]) ).
tff(3597,plain,
select(store(queue_134,tail,index_135),tail) = select(store(store(queue_134,tail,index_135),head,s(index_137)),tail),
inference(symmetry,[status(thm)],[3596]) ).
tff(3598,plain,
store(queue_134,tail,index_135) = store(store(q26,seq,earray_133),tail,s(index_132)),
inference(symmetry,[status(thm)],[1440]) ).
tff(3599,plain,
select(store(queue_134,tail,index_135),tail) = select(store(store(q26,seq,earray_133),tail,s(index_132)),tail),
inference(monotonicity,[status(thm)],[3598]) ).
tff(3600,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = select(store(queue_134,tail,index_135),tail),
inference(symmetry,[status(thm)],[3599]) ).
tff(3601,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = s(index_132) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3602,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = s(index_132),
inference(unit_resolution,[status(thm)],[3601,6]) ).
tff(3603,plain,
s(index_132) = select(store(store(q26,seq,earray_133),tail,s(index_132)),tail),
inference(symmetry,[status(thm)],[3602]) ).
tff(3604,plain,
( ( index_132 = select(q26,tail) )
<=> ( index_132 = select(q26,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3605,axiom,
index_132 = select(q26,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(3606,plain,
index_132 = select(q26,tail),
inference(modus_ponens,[status(thm)],[3605,3604]) ).
tff(3607,plain,
select(q26,tail) = index_132,
inference(symmetry,[status(thm)],[3606]) ).
tff(3608,plain,
s(select(q26,tail)) = s(index_132),
inference(monotonicity,[status(thm)],[3607]) ).
tff(3609,plain,
s(select(q26,tail)) = index_141,
inference(transitivity,[status(thm)],[3608,3603,3600,3597,3592,3584]) ).
tff(3610,plain,
s(s(select(q26,tail))) = s(index_141),
inference(monotonicity,[status(thm)],[3609]) ).
tff(3611,plain,
s(index_132) = s(select(q26,tail)),
inference(symmetry,[status(thm)],[3608]) ).
tff(3612,plain,
store(queue_128,tail,index_129) = store(store(q25,seq,earray_127),tail,s(index_126)),
inference(symmetry,[status(thm)],[1497]) ).
tff(3613,plain,
q26 = store(store(q25,seq,earray_127),tail,s(index_126)),
inference(transitivity,[status(thm)],[1457,1461,3612]) ).
tff(3614,plain,
select(q26,tail) = select(store(store(q25,seq,earray_127),tail,s(index_126)),tail),
inference(monotonicity,[status(thm)],[3613]) ).
tff(3615,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = select(q26,tail),
inference(symmetry,[status(thm)],[3614]) ).
tff(3616,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = s(index_126) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3617,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = s(index_126),
inference(unit_resolution,[status(thm)],[3616,6]) ).
tff(3618,plain,
s(index_126) = select(store(store(q25,seq,earray_127),tail,s(index_126)),tail),
inference(symmetry,[status(thm)],[3617]) ).
tff(3619,plain,
( ( index_126 = select(q25,tail) )
<=> ( index_126 = select(q25,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3620,axiom,
index_126 = select(q25,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(3621,plain,
index_126 = select(q25,tail),
inference(modus_ponens,[status(thm)],[3620,3619]) ).
tff(3622,plain,
select(q25,tail) = index_126,
inference(symmetry,[status(thm)],[3621]) ).
tff(3623,plain,
s(select(q25,tail)) = s(index_126),
inference(monotonicity,[status(thm)],[3622]) ).
tff(3624,plain,
s(select(q25,tail)) = index_132,
inference(transitivity,[status(thm)],[3623,3618,3615,3607]) ).
tff(3625,plain,
s(s(select(q25,tail))) = s(index_132),
inference(monotonicity,[status(thm)],[3624]) ).
tff(3626,plain,
s(index_126) = s(select(q25,tail)),
inference(symmetry,[status(thm)],[3623]) ).
tff(3627,plain,
( ( index_120 = select(q24,tail) )
<=> ( index_120 = select(q24,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3628,axiom,
index_120 = select(q24,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(3629,plain,
index_120 = select(q24,tail),
inference(modus_ponens,[status(thm)],[3628,3627]) ).
tff(3630,plain,
select(q24,tail) = index_120,
inference(symmetry,[status(thm)],[3629]) ).
tff(3631,plain,
s(select(q24,tail)) = s(index_120),
inference(monotonicity,[status(thm)],[3630]) ).
tff(3632,plain,
s(index_120) = s(select(q24,tail)),
inference(symmetry,[status(thm)],[3631]) ).
tff(3633,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = s(index_120) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3634,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = s(index_120),
inference(unit_resolution,[status(thm)],[3633,6]) ).
tff(3635,plain,
store(queue_122,tail,index_123) = store(store(q24,seq,earray_121),tail,s(index_120)),
inference(symmetry,[status(thm)],[1545]) ).
tff(3636,plain,
q25 = store(store(q24,seq,earray_121),tail,s(index_120)),
inference(transitivity,[status(thm)],[1512,1516,3635]) ).
tff(3637,plain,
select(q25,tail) = select(store(store(q24,seq,earray_121),tail,s(index_120)),tail),
inference(monotonicity,[status(thm)],[3636]) ).
tff(3638,plain,
index_126 = s(select(q24,tail)),
inference(transitivity,[status(thm)],[3621,3637,3634,3632]) ).
tff(3639,plain,
s(index_126) = s(s(select(q24,tail))),
inference(monotonicity,[status(thm)],[3638]) ).
tff(3640,plain,
s(s(select(q24,tail))) = s(index_126),
inference(symmetry,[status(thm)],[3639]) ).
tff(3641,plain,
( ( index_111 = select(q23,tail) )
<=> ( index_111 = select(q23,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3642,axiom,
index_111 = select(q23,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(3643,plain,
index_111 = select(q23,tail),
inference(modus_ponens,[status(thm)],[3642,3641]) ).
tff(3644,plain,
select(q23,tail) = index_111,
inference(symmetry,[status(thm)],[3643]) ).
tff(3645,plain,
s(select(q23,tail)) = s(index_111),
inference(monotonicity,[status(thm)],[3644]) ).
tff(3646,plain,
s(index_111) = s(select(q23,tail)),
inference(symmetry,[status(thm)],[3645]) ).
tff(3647,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3648,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = s(index_111),
inference(unit_resolution,[status(thm)],[3647,6]) ).
tff(3649,plain,
store(queue_113,tail,index_114) = store(store(q23,seq,earray_112),tail,s(index_111)),
inference(symmetry,[status(thm)],[1610]) ).
tff(3650,plain,
select(store(queue_113,tail,index_114),tail) = select(store(store(q23,seq,earray_112),tail,s(index_111)),tail),
inference(monotonicity,[status(thm)],[3649]) ).
tff(3651,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3652,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3653,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ),
inference(modus_ponens,[status(thm)],[3652,3651]) ).
tff(3654,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail),
inference(unit_resolution,[status(thm)],[3653,32,91]) ).
tff(3655,plain,
store(queue_115,head,index_117) = store(store(queue_113,tail,index_114),head,s(index_116)),
inference(symmetry,[status(thm)],[1593]) ).
tff(3656,plain,
q24 = store(store(queue_113,tail,index_114),head,s(index_116)),
inference(transitivity,[status(thm)],[1560,1564,3655]) ).
tff(3657,plain,
select(q24,tail) = select(store(store(queue_113,tail,index_114),head,s(index_116)),tail),
inference(monotonicity,[status(thm)],[3656]) ).
tff(3658,plain,
index_120 = s(select(q23,tail)),
inference(transitivity,[status(thm)],[3629,3657,3654,3650,3648,3646]) ).
tff(3659,plain,
s(index_120) = s(s(select(q23,tail))),
inference(monotonicity,[status(thm)],[3658]) ).
tff(3660,plain,
s(s(select(q23,tail))) = s(index_120),
inference(symmetry,[status(thm)],[3659]) ).
tff(3661,plain,
( ( index_105 = select(q22,tail) )
<=> ( index_105 = select(q22,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3662,axiom,
index_105 = select(q22,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(3663,plain,
index_105 = select(q22,tail),
inference(modus_ponens,[status(thm)],[3662,3661]) ).
tff(3664,plain,
select(q22,tail) = index_105,
inference(symmetry,[status(thm)],[3663]) ).
tff(3665,plain,
s(select(q22,tail)) = s(index_105),
inference(monotonicity,[status(thm)],[3664]) ).
tff(3666,plain,
s(index_105) = s(select(q22,tail)),
inference(symmetry,[status(thm)],[3665]) ).
tff(3667,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3668,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = s(index_105),
inference(unit_resolution,[status(thm)],[3667,6]) ).
tff(3669,plain,
store(queue_107,tail,index_108) = store(store(q22,seq,earray_106),tail,s(index_105)),
inference(symmetry,[status(thm)],[1667]) ).
tff(3670,plain,
q23 = store(store(q22,seq,earray_106),tail,s(index_105)),
inference(transitivity,[status(thm)],[1627,1631,3669]) ).
tff(3671,plain,
select(q23,tail) = select(store(store(q22,seq,earray_106),tail,s(index_105)),tail),
inference(monotonicity,[status(thm)],[3670]) ).
tff(3672,plain,
index_111 = s(select(q22,tail)),
inference(transitivity,[status(thm)],[3643,3671,3668,3666]) ).
tff(3673,plain,
s(index_111) = s(s(select(q22,tail))),
inference(monotonicity,[status(thm)],[3672]) ).
tff(3674,plain,
s(s(select(q22,tail))) = s(index_111),
inference(symmetry,[status(thm)],[3673]) ).
tff(3675,plain,
( ( index_99 = select(q21,tail) )
<=> ( index_99 = select(q21,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3676,axiom,
index_99 = select(q21,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(3677,plain,
index_99 = select(q21,tail),
inference(modus_ponens,[status(thm)],[3676,3675]) ).
tff(3678,plain,
select(q21,tail) = index_99,
inference(symmetry,[status(thm)],[3677]) ).
tff(3679,plain,
s(select(q21,tail)) = s(index_99),
inference(monotonicity,[status(thm)],[3678]) ).
tff(3680,plain,
s(index_99) = s(select(q21,tail)),
inference(symmetry,[status(thm)],[3679]) ).
tff(3681,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3682,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = s(index_99),
inference(unit_resolution,[status(thm)],[3681,6]) ).
tff(3683,plain,
store(queue_101,tail,index_102) = store(store(q21,seq,earray_100),tail,s(index_99)),
inference(symmetry,[status(thm)],[1715]) ).
tff(3684,plain,
q22 = store(store(q21,seq,earray_100),tail,s(index_99)),
inference(transitivity,[status(thm)],[1682,1686,3683]) ).
tff(3685,plain,
select(q22,tail) = select(store(store(q21,seq,earray_100),tail,s(index_99)),tail),
inference(monotonicity,[status(thm)],[3684]) ).
tff(3686,plain,
index_105 = s(select(q21,tail)),
inference(transitivity,[status(thm)],[3663,3685,3682,3680]) ).
tff(3687,plain,
s(index_105) = s(s(select(q21,tail))),
inference(monotonicity,[status(thm)],[3686]) ).
tff(3688,plain,
s(s(select(q21,tail))) = s(index_105),
inference(symmetry,[status(thm)],[3687]) ).
tff(3689,plain,
( ( index_90 = select(q20,tail) )
<=> ( index_90 = select(q20,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3690,axiom,
index_90 = select(q20,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(3691,plain,
index_90 = select(q20,tail),
inference(modus_ponens,[status(thm)],[3690,3689]) ).
tff(3692,plain,
select(q20,tail) = index_90,
inference(symmetry,[status(thm)],[3691]) ).
tff(3693,plain,
s(select(q20,tail)) = s(index_90),
inference(monotonicity,[status(thm)],[3692]) ).
tff(3694,plain,
s(index_90) = s(select(q20,tail)),
inference(symmetry,[status(thm)],[3693]) ).
tff(3695,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = s(index_90) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3696,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = s(index_90),
inference(unit_resolution,[status(thm)],[3695,6]) ).
tff(3697,plain,
store(queue_92,tail,index_93) = store(store(q20,seq,earray_91),tail,s(index_90)),
inference(symmetry,[status(thm)],[1780]) ).
tff(3698,plain,
select(store(queue_92,tail,index_93),tail) = select(store(store(q20,seq,earray_91),tail,s(index_90)),tail),
inference(monotonicity,[status(thm)],[3697]) ).
tff(3699,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3700,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3701,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ),
inference(modus_ponens,[status(thm)],[3700,3699]) ).
tff(3702,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail),
inference(unit_resolution,[status(thm)],[3701,32,91]) ).
tff(3703,plain,
store(queue_94,head,index_96) = store(store(queue_92,tail,index_93),head,s(index_95)),
inference(symmetry,[status(thm)],[1763]) ).
tff(3704,plain,
q21 = store(store(queue_92,tail,index_93),head,s(index_95)),
inference(transitivity,[status(thm)],[1730,1734,3703]) ).
tff(3705,plain,
select(q21,tail) = select(store(store(queue_92,tail,index_93),head,s(index_95)),tail),
inference(monotonicity,[status(thm)],[3704]) ).
tff(3706,plain,
index_99 = s(select(q20,tail)),
inference(transitivity,[status(thm)],[3677,3705,3702,3698,3696,3694]) ).
tff(3707,plain,
s(index_99) = s(s(select(q20,tail))),
inference(monotonicity,[status(thm)],[3706]) ).
tff(3708,plain,
s(s(select(q20,tail))) = s(index_99),
inference(symmetry,[status(thm)],[3707]) ).
tff(3709,plain,
( ( index_84 = select(q19,tail) )
<=> ( index_84 = select(q19,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3710,axiom,
index_84 = select(q19,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(3711,plain,
index_84 = select(q19,tail),
inference(modus_ponens,[status(thm)],[3710,3709]) ).
tff(3712,plain,
select(q19,tail) = index_84,
inference(symmetry,[status(thm)],[3711]) ).
tff(3713,plain,
s(select(q19,tail)) = s(index_84),
inference(monotonicity,[status(thm)],[3712]) ).
tff(3714,plain,
s(index_84) = s(select(q19,tail)),
inference(symmetry,[status(thm)],[3713]) ).
tff(3715,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = s(index_84) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3716,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = s(index_84),
inference(unit_resolution,[status(thm)],[3715,6]) ).
tff(3717,plain,
store(queue_86,tail,index_87) = store(store(q19,seq,earray_85),tail,s(index_84)),
inference(symmetry,[status(thm)],[1837]) ).
tff(3718,plain,
q20 = store(store(q19,seq,earray_85),tail,s(index_84)),
inference(transitivity,[status(thm)],[1797,1801,3717]) ).
tff(3719,plain,
select(q20,tail) = select(store(store(q19,seq,earray_85),tail,s(index_84)),tail),
inference(monotonicity,[status(thm)],[3718]) ).
tff(3720,plain,
index_90 = s(select(q19,tail)),
inference(transitivity,[status(thm)],[3691,3719,3716,3714]) ).
tff(3721,plain,
s(index_90) = s(s(select(q19,tail))),
inference(monotonicity,[status(thm)],[3720]) ).
tff(3722,plain,
s(s(select(q19,tail))) = s(index_90),
inference(symmetry,[status(thm)],[3721]) ).
tff(3723,plain,
( ( index_72 = select(q18,tail) )
<=> ( index_72 = select(q18,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3724,axiom,
index_72 = select(q18,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(3725,plain,
index_72 = select(q18,tail),
inference(modus_ponens,[status(thm)],[3724,3723]) ).
tff(3726,plain,
select(q18,tail) = index_72,
inference(symmetry,[status(thm)],[3725]) ).
tff(3727,plain,
s(select(q18,tail)) = s(index_72),
inference(monotonicity,[status(thm)],[3726]) ).
tff(3728,plain,
s(index_72) = s(select(q18,tail)),
inference(symmetry,[status(thm)],[3727]) ).
tff(3729,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = s(index_72) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3730,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = s(index_72),
inference(unit_resolution,[status(thm)],[3729,6]) ).
tff(3731,plain,
store(queue_74,tail,index_75) = store(store(q18,seq,earray_73),tail,s(index_72)),
inference(symmetry,[status(thm)],[1885]) ).
tff(3732,plain,
q19 = store(store(q18,seq,earray_73),tail,s(index_72)),
inference(transitivity,[status(thm)],[1852,1856,3731]) ).
tff(3733,plain,
select(q19,tail) = select(store(store(q18,seq,earray_73),tail,s(index_72)),tail),
inference(monotonicity,[status(thm)],[3732]) ).
tff(3734,plain,
index_84 = s(select(q18,tail)),
inference(transitivity,[status(thm)],[3711,3733,3730,3728]) ).
tff(3735,plain,
s(index_84) = s(s(select(q18,tail))),
inference(monotonicity,[status(thm)],[3734]) ).
tff(3736,plain,
s(s(select(q18,tail))) = s(index_84),
inference(symmetry,[status(thm)],[3735]) ).
tff(3737,plain,
( ( index_63 = select(q17,tail) )
<=> ( index_63 = select(q17,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3738,axiom,
index_63 = select(q17,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(3739,plain,
index_63 = select(q17,tail),
inference(modus_ponens,[status(thm)],[3738,3737]) ).
tff(3740,plain,
select(q17,tail) = index_63,
inference(symmetry,[status(thm)],[3739]) ).
tff(3741,plain,
s(select(q17,tail)) = s(index_63),
inference(monotonicity,[status(thm)],[3740]) ).
tff(3742,plain,
s(index_63) = s(select(q17,tail)),
inference(symmetry,[status(thm)],[3741]) ).
tff(3743,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3744,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = s(index_63),
inference(unit_resolution,[status(thm)],[3743,6]) ).
tff(3745,plain,
store(queue_65,tail,index_66) = store(store(q17,seq,earray_64),tail,s(index_63)),
inference(symmetry,[status(thm)],[1950]) ).
tff(3746,plain,
select(store(queue_65,tail,index_66),tail) = select(store(store(q17,seq,earray_64),tail,s(index_63)),tail),
inference(monotonicity,[status(thm)],[3745]) ).
tff(3747,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3748,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3749,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ),
inference(modus_ponens,[status(thm)],[3748,3747]) ).
tff(3750,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail),
inference(unit_resolution,[status(thm)],[3749,32,91]) ).
tff(3751,plain,
store(queue_67,head,index_69) = store(store(queue_65,tail,index_66),head,s(index_68)),
inference(symmetry,[status(thm)],[1933]) ).
tff(3752,plain,
q18 = store(store(queue_65,tail,index_66),head,s(index_68)),
inference(transitivity,[status(thm)],[1900,1904,3751]) ).
tff(3753,plain,
select(q18,tail) = select(store(store(queue_65,tail,index_66),head,s(index_68)),tail),
inference(monotonicity,[status(thm)],[3752]) ).
tff(3754,plain,
index_72 = s(select(q17,tail)),
inference(transitivity,[status(thm)],[3725,3753,3750,3746,3744,3742]) ).
tff(3755,plain,
s(index_72) = s(s(select(q17,tail))),
inference(monotonicity,[status(thm)],[3754]) ).
tff(3756,plain,
s(s(select(q17,tail))) = s(index_72),
inference(symmetry,[status(thm)],[3755]) ).
tff(3757,plain,
s(select(q16,tail)) = s(index_57),
inference(monotonicity,[status(thm)],[3165]) ).
tff(3758,plain,
s(index_57) = s(select(q16,tail)),
inference(symmetry,[status(thm)],[3757]) ).
tff(3759,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3760,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = s(index_57),
inference(unit_resolution,[status(thm)],[3759,6]) ).
tff(3761,plain,
store(queue_59,tail,index_60) = store(store(q16,seq,earray_58),tail,s(index_57)),
inference(symmetry,[status(thm)],[2007]) ).
tff(3762,plain,
q17 = store(store(q16,seq,earray_58),tail,s(index_57)),
inference(transitivity,[status(thm)],[1967,1971,3761]) ).
tff(3763,plain,
select(q17,tail) = select(store(store(q16,seq,earray_58),tail,s(index_57)),tail),
inference(monotonicity,[status(thm)],[3762]) ).
tff(3764,plain,
index_63 = s(select(q16,tail)),
inference(transitivity,[status(thm)],[3739,3763,3760,3758]) ).
tff(3765,plain,
s(index_63) = s(s(select(q16,tail))),
inference(monotonicity,[status(thm)],[3764]) ).
tff(3766,plain,
s(s(select(q16,tail))) = s(index_63),
inference(symmetry,[status(thm)],[3765]) ).
tff(3767,plain,
s(s(select(q16,tail))) = s(select(q17,tail)),
inference(transitivity,[status(thm)],[3766,3742]) ).
tff(3768,plain,
s(s(s(select(q16,tail)))) = s(s(select(q17,tail))),
inference(monotonicity,[status(thm)],[3767]) ).
tff(3769,plain,
s(s(s(select(q16,tail)))) = s(select(q18,tail)),
inference(transitivity,[status(thm)],[3768,3756,3728]) ).
tff(3770,plain,
s(s(s(s(select(q16,tail))))) = s(s(select(q18,tail))),
inference(monotonicity,[status(thm)],[3769]) ).
tff(3771,plain,
s(s(s(s(select(q16,tail))))) = s(select(q19,tail)),
inference(transitivity,[status(thm)],[3770,3736,3714]) ).
tff(3772,plain,
s(s(s(s(s(select(q16,tail)))))) = s(s(select(q19,tail))),
inference(monotonicity,[status(thm)],[3771]) ).
tff(3773,plain,
s(s(s(s(s(select(q16,tail)))))) = s(select(q20,tail)),
inference(transitivity,[status(thm)],[3772,3722,3694]) ).
tff(3774,plain,
s(s(s(s(s(s(select(q16,tail))))))) = s(s(select(q20,tail))),
inference(monotonicity,[status(thm)],[3773]) ).
tff(3775,plain,
s(s(s(s(s(s(select(q16,tail))))))) = s(select(q21,tail)),
inference(transitivity,[status(thm)],[3774,3708,3680]) ).
tff(3776,plain,
s(s(s(s(s(s(s(select(q16,tail)))))))) = s(s(select(q21,tail))),
inference(monotonicity,[status(thm)],[3775]) ).
tff(3777,plain,
s(s(s(s(s(s(s(select(q16,tail)))))))) = s(select(q22,tail)),
inference(transitivity,[status(thm)],[3776,3688,3666]) ).
tff(3778,plain,
s(s(s(s(s(s(s(s(select(q16,tail))))))))) = s(s(select(q22,tail))),
inference(monotonicity,[status(thm)],[3777]) ).
tff(3779,plain,
s(s(s(s(s(s(s(s(select(q16,tail))))))))) = s(select(q23,tail)),
inference(transitivity,[status(thm)],[3778,3674,3646]) ).
tff(3780,plain,
s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))) = s(s(select(q23,tail))),
inference(monotonicity,[status(thm)],[3779]) ).
tff(3781,plain,
s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))) = s(select(q24,tail)),
inference(transitivity,[status(thm)],[3780,3660,3632]) ).
tff(3782,plain,
s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))) = s(s(select(q24,tail))),
inference(monotonicity,[status(thm)],[3781]) ).
tff(3783,plain,
s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))) = s(select(q25,tail)),
inference(transitivity,[status(thm)],[3782,3640,3626]) ).
tff(3784,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) = s(s(select(q25,tail))),
inference(monotonicity,[status(thm)],[3783]) ).
tff(3785,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) = s(select(q26,tail)),
inference(transitivity,[status(thm)],[3784,3625,3611]) ).
tff(3786,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) = s(s(select(q26,tail))),
inference(monotonicity,[status(thm)],[3785]) ).
tff(3787,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) = s(select(q27,tail)),
inference(transitivity,[status(thm)],[3786,3610,3588]) ).
tff(3788,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) = s(s(select(q27,tail))),
inference(monotonicity,[status(thm)],[3787]) ).
tff(3789,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) = s(select(q28,tail)),
inference(transitivity,[status(thm)],[3788,3587,3573]) ).
tff(3790,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) = s(s(select(q28,tail))),
inference(monotonicity,[status(thm)],[3789]) ).
tff(3791,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) = s(select(q29,tail)),
inference(transitivity,[status(thm)],[3790,3572,3558]) ).
tff(3792,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) = s(s(select(q29,tail))),
inference(monotonicity,[status(thm)],[3791]) ).
tff(3793,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) = s(select(q30,tail)),
inference(transitivity,[status(thm)],[3792,3557,3535]) ).
tff(3794,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) = s(s(select(q30,tail))),
inference(monotonicity,[status(thm)],[3793]) ).
tff(3795,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) = s(select(q31,tail)),
inference(transitivity,[status(thm)],[3794,3534,3520]) ).
tff(3796,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) = s(s(select(q31,tail))),
inference(monotonicity,[status(thm)],[3795]) ).
tff(3797,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) = s(select(q32,tail)),
inference(transitivity,[status(thm)],[3796,3519,3505]) ).
tff(3798,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) = s(s(select(q32,tail))),
inference(monotonicity,[status(thm)],[3797]) ).
tff(3799,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) = s(select(q33,tail)),
inference(transitivity,[status(thm)],[3798,3504,3482]) ).
tff(3800,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) = s(s(select(q33,tail))),
inference(monotonicity,[status(thm)],[3799]) ).
tff(3801,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) = s(select(q34,tail)),
inference(transitivity,[status(thm)],[3800,3481,3467]) ).
tff(3802,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) = s(s(select(q34,tail))),
inference(monotonicity,[status(thm)],[3801]) ).
tff(3803,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) = s(select(q35,tail)),
inference(transitivity,[status(thm)],[3802,3466,3452]) ).
tff(3804,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) = s(s(select(q35,tail))),
inference(monotonicity,[status(thm)],[3803]) ).
tff(3805,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) = s(select(q36,tail)),
inference(transitivity,[status(thm)],[3804,3451,3429]) ).
tff(3806,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) = s(s(select(q36,tail))),
inference(monotonicity,[status(thm)],[3805]) ).
tff(3807,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) = s(select(q37,tail)),
inference(transitivity,[status(thm)],[3806,3428,3414]) ).
tff(3808,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) = s(s(select(q37,tail))),
inference(monotonicity,[status(thm)],[3807]) ).
tff(3809,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) = s(select(q38,tail)),
inference(transitivity,[status(thm)],[3808,3413,3399]) ).
tff(3810,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) = s(s(select(q38,tail))),
inference(monotonicity,[status(thm)],[3809]) ).
tff(3811,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) = s(select(q39,tail)),
inference(transitivity,[status(thm)],[3810,3398,3376]) ).
tff(3812,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) = s(s(select(q39,tail))),
inference(monotonicity,[status(thm)],[3811]) ).
tff(3813,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) = s(select(q40,tail)),
inference(transitivity,[status(thm)],[3812,3375,3361]) ).
tff(3814,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) = s(s(select(q40,tail))),
inference(monotonicity,[status(thm)],[3813]) ).
tff(3815,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) = s(select(q41,tail)),
inference(transitivity,[status(thm)],[3814,3360,3346]) ).
tff(3816,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) = s(s(select(q41,tail))),
inference(monotonicity,[status(thm)],[3815]) ).
tff(3817,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) = s(select(q42,tail)),
inference(transitivity,[status(thm)],[3816,3345,3323]) ).
tff(3818,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) = s(s(select(q42,tail))),
inference(monotonicity,[status(thm)],[3817]) ).
tff(3819,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) = s(select(q43,tail)),
inference(transitivity,[status(thm)],[3818,3322,3308]) ).
tff(3820,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) = s(s(select(q43,tail))),
inference(monotonicity,[status(thm)],[3819]) ).
tff(3821,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) = s(select(q44,tail)),
inference(transitivity,[status(thm)],[3820,3307,3293]) ).
tff(3822,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) = s(s(select(q44,tail))),
inference(monotonicity,[status(thm)],[3821]) ).
tff(3823,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) = s(select(q45,tail)),
inference(transitivity,[status(thm)],[3822,3292,3270]) ).
tff(3824,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) = s(s(select(q45,tail))),
inference(monotonicity,[status(thm)],[3823]) ).
tff(3825,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) = s(select(q46,tail)),
inference(transitivity,[status(thm)],[3824,3269,3255]) ).
tff(3826,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) = s(s(select(q46,tail))),
inference(monotonicity,[status(thm)],[3825]) ).
tff(3827,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) = s(select(q47,tail)),
inference(transitivity,[status(thm)],[3826,3254,3240]) ).
tff(3828,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) = s(s(select(q47,tail))),
inference(monotonicity,[status(thm)],[3827]) ).
tff(3829,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) = s(index_303),
inference(transitivity,[status(thm)],[3828,3239]) ).
tff(3830,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_303) = select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3829,3213]) ).
tff(3831,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_303) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3830]) ).
tff(3832,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3833,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3832]) ).
tff(3834,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3835,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as33) ).
tff(3836,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3835,3834]) ).
tff(3837,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3836]) ).
tff(3838,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3837,3833]) ).
tff(3839,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3840,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[3839,3838]) ).
tff(3841,plain,
s(index_303) != select(q50,head),
inference(modus_ponens,[status(thm)],[3840,3831]) ).
tff(3842,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_303) = select(q50,head) )
| ( select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_303) = select(q50,head) )
| ( select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3843,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_303) = select(q50,head) )
| ( select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3844,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_303) = select(q50,head) )
| ( select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[3843,3842]) ).
tff(3845,plain,
( ( s(index_303) = select(q50,head) )
| ( select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[3844,32]) ).
tff(3846,plain,
select(store(select(q49,seq),s(index_303),e49),select(q50,head)) = select(select(q49,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[3845,3841]) ).
tff(3847,plain,
select(select(q49,seq),select(q50,head)) = select(store(select(q49,seq),s(index_303),e49),select(q50,head)),
inference(symmetry,[status(thm)],[3846]) ).
tff(3848,plain,
select(store(q48,seq,earray_304),seq) = select(store(store(q48,seq,earray_304),tail,s(index_303)),seq),
inference(symmetry,[status(thm)],[61]) ).
tff(3849,plain,
store(earray_302,index_303,e48) = select(store(store(queue_298,head,index_300),seq,store(earray_302,index_303,e48)),seq),
inference(symmetry,[status(thm)],[42]) ).
tff(3850,plain,
s(index_294) = index_303,
inference(transitivity,[status(thm)],[3232,3229,3226,3221,3217]) ).
tff(3851,plain,
( ( earray_302 = select(q48,seq) )
<=> ( earray_302 = select(q48,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3852,axiom,
earray_302 = select(q48,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp64) ).
tff(3853,plain,
earray_302 = select(q48,seq),
inference(modus_ponens,[status(thm)],[3852,3851]) ).
tff(3854,plain,
select(q48,seq) = earray_302,
inference(symmetry,[status(thm)],[3853]) ).
tff(3855,plain,
store(select(q48,seq),s(index_294),e48) = store(earray_302,index_303,e48),
inference(monotonicity,[status(thm)],[3854,3850]) ).
tff(3856,plain,
store(select(q48,seq),s(index_294),e48) = select(q49,seq),
inference(transitivity,[status(thm)],[3855,3849,53,3848,80]) ).
tff(3857,plain,
select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q49,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[3856]) ).
tff(3858,plain,
s(s(select(q46,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3826]) ).
tff(3859,plain,
s(index_294) = s(s(select(q46,tail))),
inference(symmetry,[status(thm)],[3254]) ).
tff(3860,plain,
s(index_294) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3859,3858]) ).
tff(3861,plain,
( ( s(index_294) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[3860,3161]) ).
tff(3862,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_294) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[3861]) ).
tff(3863,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_294) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3862]) ).
tff(3864,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3865,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3864]) ).
tff(3866,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3867,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as32) ).
tff(3868,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3867,3866]) ).
tff(3869,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3868]) ).
tff(3870,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3869,3865]) ).
tff(3871,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3872,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[3871,3870]) ).
tff(3873,plain,
s(index_294) != select(q50,head),
inference(modus_ponens,[status(thm)],[3872,3863]) ).
tff(3874,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_294) = select(q50,head) )
| ( select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_294) = select(q50,head) )
| ( select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3875,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_294) = select(q50,head) )
| ( select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3876,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_294) = select(q50,head) )
| ( select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[3875,3874]) ).
tff(3877,plain,
( ( s(index_294) = select(q50,head) )
| ( select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[3876,32]) ).
tff(3878,plain,
select(store(select(q48,seq),s(index_294),e48),select(q50,head)) = select(select(q48,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[3877,3873]) ).
tff(3879,plain,
select(select(q48,seq),select(q50,head)) = select(store(select(q48,seq),s(index_294),e48),select(q50,head)),
inference(symmetry,[status(thm)],[3878]) ).
tff(3880,plain,
select(store(queue_296,tail,index_297),seq) = select(store(store(queue_296,tail,index_297),head,s(index_299)),seq),
inference(symmetry,[status(thm)],[286]) ).
tff(3881,plain,
select(store(q47,seq,earray_295),seq) = select(store(store(q47,seq,earray_295),tail,s(index_294)),seq),
inference(symmetry,[status(thm)],[280]) ).
tff(3882,plain,
store(earray_293,index_294,e47) = select(store(store(queue_290,tail,index_291),seq,store(earray_293,index_294,e47)),seq),
inference(symmetry,[status(thm)],[264]) ).
tff(3883,plain,
s(index_288) = index_294,
inference(transitivity,[status(thm)],[3247,3244,3236]) ).
tff(3884,plain,
( ( earray_293 = select(q47,seq) )
<=> ( earray_293 = select(q47,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3885,axiom,
earray_293 = select(q47,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp62) ).
tff(3886,plain,
earray_293 = select(q47,seq),
inference(modus_ponens,[status(thm)],[3885,3884]) ).
tff(3887,plain,
select(q47,seq) = earray_293,
inference(symmetry,[status(thm)],[3886]) ).
tff(3888,plain,
store(select(q47,seq),s(index_288),e47) = store(earray_293,index_294,e47),
inference(monotonicity,[status(thm)],[3887,3883]) ).
tff(3889,plain,
store(select(q47,seq),s(index_288),e47) = select(q48,seq),
inference(transitivity,[status(thm)],[3888,3882,275,3881,281,3880,288]) ).
tff(3890,plain,
select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q48,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[3889]) ).
tff(3891,plain,
s(s(select(q45,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3824]) ).
tff(3892,plain,
s(index_288) = s(s(select(q45,tail))),
inference(symmetry,[status(thm)],[3269]) ).
tff(3893,plain,
s(index_288) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3892,3891]) ).
tff(3894,plain,
( ( s(index_288) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[3893,3161]) ).
tff(3895,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_288) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[3894]) ).
tff(3896,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_288) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3895]) ).
tff(3897,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3898,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3897]) ).
tff(3899,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3900,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as31) ).
tff(3901,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3900,3899]) ).
tff(3902,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3901]) ).
tff(3903,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3902,3898]) ).
tff(3904,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3905,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[3904,3903]) ).
tff(3906,plain,
s(index_288) != select(q50,head),
inference(modus_ponens,[status(thm)],[3905,3896]) ).
tff(3907,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_288) = select(q50,head) )
| ( select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_288) = select(q50,head) )
| ( select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3908,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_288) = select(q50,head) )
| ( select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3909,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_288) = select(q50,head) )
| ( select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[3908,3907]) ).
tff(3910,plain,
( ( s(index_288) = select(q50,head) )
| ( select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[3909,32]) ).
tff(3911,plain,
select(store(select(q47,seq),s(index_288),e47),select(q50,head)) = select(select(q47,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[3910,3906]) ).
tff(3912,plain,
select(select(q47,seq),select(q50,head)) = select(store(select(q47,seq),s(index_288),e47),select(q50,head)),
inference(symmetry,[status(thm)],[3911]) ).
tff(3913,plain,
select(store(q46,seq,earray_289),seq) = select(store(store(q46,seq,earray_289),tail,s(index_288)),seq),
inference(symmetry,[status(thm)],[335]) ).
tff(3914,plain,
store(earray_287,index_288,e46) = select(store(store(queue_284,tail,index_285),seq,store(earray_287,index_288,e46)),seq),
inference(symmetry,[status(thm)],[319]) ).
tff(3915,plain,
s(index_282) = index_288,
inference(transitivity,[status(thm)],[3262,3259,3251]) ).
tff(3916,plain,
( ( earray_287 = select(q46,seq) )
<=> ( earray_287 = select(q46,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3917,axiom,
earray_287 = select(q46,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp59) ).
tff(3918,plain,
earray_287 = select(q46,seq),
inference(modus_ponens,[status(thm)],[3917,3916]) ).
tff(3919,plain,
select(q46,seq) = earray_287,
inference(symmetry,[status(thm)],[3918]) ).
tff(3920,plain,
store(select(q46,seq),s(index_282),e46) = store(earray_287,index_288,e46),
inference(monotonicity,[status(thm)],[3919,3915]) ).
tff(3921,plain,
store(select(q46,seq),s(index_282),e46) = select(q47,seq),
inference(transitivity,[status(thm)],[3920,3914,330,3913,337]) ).
tff(3922,plain,
select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q47,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[3921]) ).
tff(3923,plain,
s(s(select(q44,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3822]) ).
tff(3924,plain,
s(index_282) = s(s(select(q44,tail))),
inference(symmetry,[status(thm)],[3292]) ).
tff(3925,plain,
s(index_282) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3924,3923]) ).
tff(3926,plain,
( ( s(index_282) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[3925,3161]) ).
tff(3927,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_282) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[3926]) ).
tff(3928,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_282) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3927]) ).
tff(3929,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3930,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3929]) ).
tff(3931,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3932,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as30) ).
tff(3933,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3932,3931]) ).
tff(3934,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3933]) ).
tff(3935,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3934,3930]) ).
tff(3936,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3937,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[3936,3935]) ).
tff(3938,plain,
s(index_282) != select(q50,head),
inference(modus_ponens,[status(thm)],[3937,3928]) ).
tff(3939,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_282) = select(q50,head) )
| ( select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_282) = select(q50,head) )
| ( select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3940,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_282) = select(q50,head) )
| ( select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3941,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_282) = select(q50,head) )
| ( select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[3940,3939]) ).
tff(3942,plain,
( ( s(index_282) = select(q50,head) )
| ( select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[3941,32]) ).
tff(3943,plain,
select(store(select(q46,seq),s(index_282),e46),select(q50,head)) = select(select(q46,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[3942,3938]) ).
tff(3944,plain,
select(select(q46,seq),select(q50,head)) = select(store(select(q46,seq),s(index_282),e46),select(q50,head)),
inference(symmetry,[status(thm)],[3943]) ).
tff(3945,plain,
select(store(q45,seq,earray_283),seq) = select(store(store(q45,seq,earray_283),tail,s(index_282)),seq),
inference(symmetry,[status(thm)],[383]) ).
tff(3946,plain,
store(earray_281,index_282,e45) = select(store(store(queue_277,head,index_279),seq,store(earray_281,index_282,e45)),seq),
inference(symmetry,[status(thm)],[367]) ).
tff(3947,plain,
s(index_273) = index_282,
inference(transitivity,[status(thm)],[3285,3282,3279,3274,3266]) ).
tff(3948,plain,
( ( earray_281 = select(q45,seq) )
<=> ( earray_281 = select(q45,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3949,axiom,
earray_281 = select(q45,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp57) ).
tff(3950,plain,
earray_281 = select(q45,seq),
inference(modus_ponens,[status(thm)],[3949,3948]) ).
tff(3951,plain,
select(q45,seq) = earray_281,
inference(symmetry,[status(thm)],[3950]) ).
tff(3952,plain,
store(select(q45,seq),s(index_273),e45) = store(earray_281,index_282,e45),
inference(monotonicity,[status(thm)],[3951,3947]) ).
tff(3953,plain,
store(select(q45,seq),s(index_273),e45) = select(q46,seq),
inference(transitivity,[status(thm)],[3952,3946,378,3945,385]) ).
tff(3954,plain,
select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q46,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[3953]) ).
tff(3955,plain,
s(s(select(q43,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3820]) ).
tff(3956,plain,
s(index_273) = s(s(select(q43,tail))),
inference(symmetry,[status(thm)],[3307]) ).
tff(3957,plain,
s(index_273) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3956,3955]) ).
tff(3958,plain,
( ( s(index_273) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[3957,3161]) ).
tff(3959,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_273) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[3958]) ).
tff(3960,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_273) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3959]) ).
tff(3961,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3962,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3961]) ).
tff(3963,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3964,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as29) ).
tff(3965,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3964,3963]) ).
tff(3966,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3965]) ).
tff(3967,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3966,3962]) ).
tff(3968,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3969,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[3968,3967]) ).
tff(3970,plain,
s(index_273) != select(q50,head),
inference(modus_ponens,[status(thm)],[3969,3960]) ).
tff(3971,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_273) = select(q50,head) )
| ( select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_273) = select(q50,head) )
| ( select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3972,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_273) = select(q50,head) )
| ( select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3973,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_273) = select(q50,head) )
| ( select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[3972,3971]) ).
tff(3974,plain,
( ( s(index_273) = select(q50,head) )
| ( select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[3973,32]) ).
tff(3975,plain,
select(store(select(q45,seq),s(index_273),e45),select(q50,head)) = select(select(q45,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[3974,3970]) ).
tff(3976,plain,
select(select(q45,seq),select(q50,head)) = select(store(select(q45,seq),s(index_273),e45),select(q50,head)),
inference(symmetry,[status(thm)],[3975]) ).
tff(3977,plain,
select(store(queue_275,tail,index_276),seq) = select(store(store(queue_275,tail,index_276),head,s(index_278)),seq),
inference(symmetry,[status(thm)],[456]) ).
tff(3978,plain,
select(store(q44,seq,earray_274),seq) = select(store(store(q44,seq,earray_274),tail,s(index_273)),seq),
inference(symmetry,[status(thm)],[450]) ).
tff(3979,plain,
store(earray_272,index_273,e44) = select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e44)),seq),
inference(symmetry,[status(thm)],[434]) ).
tff(3980,plain,
s(index_267) = index_273,
inference(transitivity,[status(thm)],[3300,3297,3289]) ).
tff(3981,plain,
( ( earray_272 = select(q44,seq) )
<=> ( earray_272 = select(q44,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3982,axiom,
earray_272 = select(q44,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp55) ).
tff(3983,plain,
earray_272 = select(q44,seq),
inference(modus_ponens,[status(thm)],[3982,3981]) ).
tff(3984,plain,
select(q44,seq) = earray_272,
inference(symmetry,[status(thm)],[3983]) ).
tff(3985,plain,
store(select(q44,seq),s(index_267),e44) = store(earray_272,index_273,e44),
inference(monotonicity,[status(thm)],[3984,3980]) ).
tff(3986,plain,
store(select(q44,seq),s(index_267),e44) = select(q45,seq),
inference(transitivity,[status(thm)],[3985,3979,445,3978,451,3977,458]) ).
tff(3987,plain,
select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q45,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[3986]) ).
tff(3988,plain,
s(s(select(q42,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3818]) ).
tff(3989,plain,
s(index_267) = s(s(select(q42,tail))),
inference(symmetry,[status(thm)],[3322]) ).
tff(3990,plain,
s(index_267) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3989,3988]) ).
tff(3991,plain,
( ( s(index_267) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[3990,3161]) ).
tff(3992,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_267) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[3991]) ).
tff(3993,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_267) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[3992]) ).
tff(3994,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3995,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[3994]) ).
tff(3996,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3997,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as28) ).
tff(3998,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3997,3996]) ).
tff(3999,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3998]) ).
tff(4000,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3999,3995]) ).
tff(4001,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4002,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4001,4000]) ).
tff(4003,plain,
s(index_267) != select(q50,head),
inference(modus_ponens,[status(thm)],[4002,3993]) ).
tff(4004,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_267) = select(q50,head) )
| ( select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_267) = select(q50,head) )
| ( select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4005,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_267) = select(q50,head) )
| ( select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4006,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_267) = select(q50,head) )
| ( select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4005,4004]) ).
tff(4007,plain,
( ( s(index_267) = select(q50,head) )
| ( select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4006,32]) ).
tff(4008,plain,
select(store(select(q44,seq),s(index_267),e44),select(q50,head)) = select(select(q44,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4007,4003]) ).
tff(4009,plain,
select(select(q44,seq),select(q50,head)) = select(store(select(q44,seq),s(index_267),e44),select(q50,head)),
inference(symmetry,[status(thm)],[4008]) ).
tff(4010,plain,
select(store(q43,seq,earray_268),seq) = select(store(store(q43,seq,earray_268),tail,s(index_267)),seq),
inference(symmetry,[status(thm)],[505]) ).
tff(4011,plain,
store(earray_266,index_267,e43) = select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e43)),seq),
inference(symmetry,[status(thm)],[489]) ).
tff(4012,plain,
s(index_261) = index_267,
inference(transitivity,[status(thm)],[3315,3312,3304]) ).
tff(4013,plain,
( ( earray_266 = select(q43,seq) )
<=> ( earray_266 = select(q43,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4014,axiom,
earray_266 = select(q43,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp53) ).
tff(4015,plain,
earray_266 = select(q43,seq),
inference(modus_ponens,[status(thm)],[4014,4013]) ).
tff(4016,plain,
select(q43,seq) = earray_266,
inference(symmetry,[status(thm)],[4015]) ).
tff(4017,plain,
store(select(q43,seq),s(index_261),e43) = store(earray_266,index_267,e43),
inference(monotonicity,[status(thm)],[4016,4012]) ).
tff(4018,plain,
store(select(q43,seq),s(index_261),e43) = select(q44,seq),
inference(transitivity,[status(thm)],[4017,4011,500,4010,507]) ).
tff(4019,plain,
select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q44,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4018]) ).
tff(4020,plain,
s(s(select(q41,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3816]) ).
tff(4021,plain,
s(index_261) = s(s(select(q41,tail))),
inference(symmetry,[status(thm)],[3345]) ).
tff(4022,plain,
s(index_261) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4021,4020]) ).
tff(4023,plain,
( ( s(index_261) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4022,3161]) ).
tff(4024,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_261) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4023]) ).
tff(4025,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_261) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4024]) ).
tff(4026,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4027,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4026]) ).
tff(4028,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4029,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as27) ).
tff(4030,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4029,4028]) ).
tff(4031,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4030]) ).
tff(4032,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4031,4027]) ).
tff(4033,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4034,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4033,4032]) ).
tff(4035,plain,
s(index_261) != select(q50,head),
inference(modus_ponens,[status(thm)],[4034,4025]) ).
tff(4036,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_261) = select(q50,head) )
| ( select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_261) = select(q50,head) )
| ( select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4037,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_261) = select(q50,head) )
| ( select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4038,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_261) = select(q50,head) )
| ( select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4037,4036]) ).
tff(4039,plain,
( ( s(index_261) = select(q50,head) )
| ( select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4038,32]) ).
tff(4040,plain,
select(store(select(q43,seq),s(index_261),e43),select(q50,head)) = select(select(q43,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4039,4035]) ).
tff(4041,plain,
select(select(q43,seq),select(q50,head)) = select(store(select(q43,seq),s(index_261),e43),select(q50,head)),
inference(symmetry,[status(thm)],[4040]) ).
tff(4042,plain,
select(store(q42,seq,earray_262),seq) = select(store(store(q42,seq,earray_262),tail,s(index_261)),seq),
inference(symmetry,[status(thm)],[553]) ).
tff(4043,plain,
store(earray_260,index_261,e42) = select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e42)),seq),
inference(symmetry,[status(thm)],[537]) ).
tff(4044,plain,
s(index_252) = index_261,
inference(transitivity,[status(thm)],[3338,3335,3332,3327,3319]) ).
tff(4045,plain,
( ( earray_260 = select(q42,seq) )
<=> ( earray_260 = select(q42,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4046,axiom,
earray_260 = select(q42,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp51) ).
tff(4047,plain,
earray_260 = select(q42,seq),
inference(modus_ponens,[status(thm)],[4046,4045]) ).
tff(4048,plain,
select(q42,seq) = earray_260,
inference(symmetry,[status(thm)],[4047]) ).
tff(4049,plain,
store(select(q42,seq),s(index_252),e42) = store(earray_260,index_261,e42),
inference(monotonicity,[status(thm)],[4048,4044]) ).
tff(4050,plain,
store(select(q42,seq),s(index_252),e42) = select(q43,seq),
inference(transitivity,[status(thm)],[4049,4043,548,4042,555]) ).
tff(4051,plain,
select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q43,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4050]) ).
tff(4052,plain,
s(s(select(q40,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3814]) ).
tff(4053,plain,
s(index_252) = s(s(select(q40,tail))),
inference(symmetry,[status(thm)],[3360]) ).
tff(4054,plain,
s(index_252) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4053,4052]) ).
tff(4055,plain,
( ( s(index_252) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4054,3161]) ).
tff(4056,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_252) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4055]) ).
tff(4057,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_252) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4056]) ).
tff(4058,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4059,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4058]) ).
tff(4060,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4061,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as26) ).
tff(4062,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4061,4060]) ).
tff(4063,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4062]) ).
tff(4064,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4063,4059]) ).
tff(4065,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4066,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4065,4064]) ).
tff(4067,plain,
s(index_252) != select(q50,head),
inference(modus_ponens,[status(thm)],[4066,4057]) ).
tff(4068,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_252) = select(q50,head) )
| ( select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_252) = select(q50,head) )
| ( select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4069,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_252) = select(q50,head) )
| ( select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4070,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_252) = select(q50,head) )
| ( select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4069,4068]) ).
tff(4071,plain,
( ( s(index_252) = select(q50,head) )
| ( select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4070,32]) ).
tff(4072,plain,
select(store(select(q42,seq),s(index_252),e42),select(q50,head)) = select(select(q42,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4071,4067]) ).
tff(4073,plain,
select(select(q42,seq),select(q50,head)) = select(store(select(q42,seq),s(index_252),e42),select(q50,head)),
inference(symmetry,[status(thm)],[4072]) ).
tff(4074,plain,
select(store(queue_254,tail,index_255),seq) = select(store(store(queue_254,tail,index_255),head,s(index_257)),seq),
inference(symmetry,[status(thm)],[626]) ).
tff(4075,plain,
select(store(q41,seq,earray_253),seq) = select(store(store(q41,seq,earray_253),tail,s(index_252)),seq),
inference(symmetry,[status(thm)],[620]) ).
tff(4076,plain,
store(earray_251,index_252,e41) = select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e41)),seq),
inference(symmetry,[status(thm)],[604]) ).
tff(4077,plain,
s(index_246) = index_252,
inference(transitivity,[status(thm)],[3353,3350,3342]) ).
tff(4078,plain,
( ( earray_251 = select(q41,seq) )
<=> ( earray_251 = select(q41,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4079,axiom,
earray_251 = select(q41,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp49) ).
tff(4080,plain,
earray_251 = select(q41,seq),
inference(modus_ponens,[status(thm)],[4079,4078]) ).
tff(4081,plain,
select(q41,seq) = earray_251,
inference(symmetry,[status(thm)],[4080]) ).
tff(4082,plain,
store(select(q41,seq),s(index_246),e41) = store(earray_251,index_252,e41),
inference(monotonicity,[status(thm)],[4081,4077]) ).
tff(4083,plain,
store(select(q41,seq),s(index_246),e41) = select(q42,seq),
inference(transitivity,[status(thm)],[4082,4076,615,4075,621,4074,628]) ).
tff(4084,plain,
select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q42,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4083]) ).
tff(4085,plain,
s(s(select(q39,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3812]) ).
tff(4086,plain,
s(index_246) = s(s(select(q39,tail))),
inference(symmetry,[status(thm)],[3375]) ).
tff(4087,plain,
s(index_246) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4086,4085]) ).
tff(4088,plain,
( ( s(index_246) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4087,3161]) ).
tff(4089,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_246) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4088]) ).
tff(4090,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_246) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4089]) ).
tff(4091,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4092,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4091]) ).
tff(4093,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4094,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as25) ).
tff(4095,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4094,4093]) ).
tff(4096,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4095]) ).
tff(4097,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4096,4092]) ).
tff(4098,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4099,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4098,4097]) ).
tff(4100,plain,
s(index_246) != select(q50,head),
inference(modus_ponens,[status(thm)],[4099,4090]) ).
tff(4101,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_246) = select(q50,head) )
| ( select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_246) = select(q50,head) )
| ( select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4102,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_246) = select(q50,head) )
| ( select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4103,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_246) = select(q50,head) )
| ( select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4102,4101]) ).
tff(4104,plain,
( ( s(index_246) = select(q50,head) )
| ( select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4103,32]) ).
tff(4105,plain,
select(store(select(q41,seq),s(index_246),e41),select(q50,head)) = select(select(q41,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4104,4100]) ).
tff(4106,plain,
select(select(q41,seq),select(q50,head)) = select(store(select(q41,seq),s(index_246),e41),select(q50,head)),
inference(symmetry,[status(thm)],[4105]) ).
tff(4107,plain,
select(store(q40,seq,earray_247),seq) = select(store(store(q40,seq,earray_247),tail,s(index_246)),seq),
inference(symmetry,[status(thm)],[675]) ).
tff(4108,plain,
store(earray_245,index_246,e40) = select(store(store(queue_242,tail,index_243),seq,store(earray_245,index_246,e40)),seq),
inference(symmetry,[status(thm)],[659]) ).
tff(4109,plain,
s(index_240) = index_246,
inference(transitivity,[status(thm)],[3368,3365,3357]) ).
tff(4110,plain,
( ( earray_245 = select(q40,seq) )
<=> ( earray_245 = select(q40,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4111,axiom,
earray_245 = select(q40,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp47) ).
tff(4112,plain,
earray_245 = select(q40,seq),
inference(modus_ponens,[status(thm)],[4111,4110]) ).
tff(4113,plain,
select(q40,seq) = earray_245,
inference(symmetry,[status(thm)],[4112]) ).
tff(4114,plain,
store(select(q40,seq),s(index_240),e40) = store(earray_245,index_246,e40),
inference(monotonicity,[status(thm)],[4113,4109]) ).
tff(4115,plain,
store(select(q40,seq),s(index_240),e40) = select(q41,seq),
inference(transitivity,[status(thm)],[4114,4108,670,4107,677]) ).
tff(4116,plain,
select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q41,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4115]) ).
tff(4117,plain,
s(s(select(q38,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3810]) ).
tff(4118,plain,
s(index_240) = s(s(select(q38,tail))),
inference(symmetry,[status(thm)],[3398]) ).
tff(4119,plain,
s(index_240) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4118,4117]) ).
tff(4120,plain,
( ( s(index_240) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4119,3161]) ).
tff(4121,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_240) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4120]) ).
tff(4122,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_240) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4121]) ).
tff(4123,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4124,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4123]) ).
tff(4125,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4126,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as24) ).
tff(4127,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4126,4125]) ).
tff(4128,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4127]) ).
tff(4129,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4128,4124]) ).
tff(4130,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4131,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4130,4129]) ).
tff(4132,plain,
s(index_240) != select(q50,head),
inference(modus_ponens,[status(thm)],[4131,4122]) ).
tff(4133,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_240) = select(q50,head) )
| ( select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_240) = select(q50,head) )
| ( select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4134,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_240) = select(q50,head) )
| ( select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4135,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_240) = select(q50,head) )
| ( select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4134,4133]) ).
tff(4136,plain,
( ( s(index_240) = select(q50,head) )
| ( select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4135,32]) ).
tff(4137,plain,
select(store(select(q40,seq),s(index_240),e40),select(q50,head)) = select(select(q40,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4136,4132]) ).
tff(4138,plain,
select(select(q40,seq),select(q50,head)) = select(store(select(q40,seq),s(index_240),e40),select(q50,head)),
inference(symmetry,[status(thm)],[4137]) ).
tff(4139,plain,
select(store(q39,seq,earray_241),seq) = select(store(store(q39,seq,earray_241),tail,s(index_240)),seq),
inference(symmetry,[status(thm)],[723]) ).
tff(4140,plain,
store(earray_239,index_240,e39) = select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq),
inference(symmetry,[status(thm)],[707]) ).
tff(4141,plain,
s(index_225) = index_240,
inference(transitivity,[status(thm)],[3391,3388,3385,3380,3372]) ).
tff(4142,plain,
( ( earray_239 = select(q39,seq) )
<=> ( earray_239 = select(q39,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4143,axiom,
earray_239 = select(q39,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(4144,plain,
earray_239 = select(q39,seq),
inference(modus_ponens,[status(thm)],[4143,4142]) ).
tff(4145,plain,
select(q39,seq) = earray_239,
inference(symmetry,[status(thm)],[4144]) ).
tff(4146,plain,
store(select(q39,seq),s(index_225),e39) = store(earray_239,index_240,e39),
inference(monotonicity,[status(thm)],[4145,4141]) ).
tff(4147,plain,
store(select(q39,seq),s(index_225),e39) = select(q40,seq),
inference(transitivity,[status(thm)],[4146,4140,718,4139,725]) ).
tff(4148,plain,
select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q40,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4147]) ).
tff(4149,plain,
s(s(select(q37,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3808]) ).
tff(4150,plain,
s(index_225) = s(s(select(q37,tail))),
inference(symmetry,[status(thm)],[3413]) ).
tff(4151,plain,
s(index_225) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4150,4149]) ).
tff(4152,plain,
( ( s(index_225) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4151,3161]) ).
tff(4153,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_225) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4152]) ).
tff(4154,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_225) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4153]) ).
tff(4155,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4156,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4155]) ).
tff(4157,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4158,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as23) ).
tff(4159,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4158,4157]) ).
tff(4160,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4159]) ).
tff(4161,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4160,4156]) ).
tff(4162,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4163,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4162,4161]) ).
tff(4164,plain,
s(index_225) != select(q50,head),
inference(modus_ponens,[status(thm)],[4163,4154]) ).
tff(4165,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q50,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q50,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4166,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q50,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4167,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q50,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4166,4165]) ).
tff(4168,plain,
( ( s(index_225) = select(q50,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4167,32]) ).
tff(4169,plain,
select(store(select(q39,seq),s(index_225),e39),select(q50,head)) = select(select(q39,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4168,4164]) ).
tff(4170,plain,
select(select(q39,seq),select(q50,head)) = select(store(select(q39,seq),s(index_225),e39),select(q50,head)),
inference(symmetry,[status(thm)],[4169]) ).
tff(4171,plain,
select(store(queue_227,tail,index_228),seq) = select(store(store(queue_227,tail,index_228),head,s(index_230)),seq),
inference(symmetry,[status(thm)],[796]) ).
tff(4172,plain,
select(store(q38,seq,earray_226),seq) = select(store(store(q38,seq,earray_226),tail,s(index_225)),seq),
inference(symmetry,[status(thm)],[790]) ).
tff(4173,plain,
store(earray_224,index_225,e38) = select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq),
inference(symmetry,[status(thm)],[774]) ).
tff(4174,plain,
s(index_219) = index_225,
inference(transitivity,[status(thm)],[3406,3403,3395]) ).
tff(4175,plain,
( ( earray_224 = select(q38,seq) )
<=> ( earray_224 = select(q38,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4176,axiom,
earray_224 = select(q38,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(4177,plain,
earray_224 = select(q38,seq),
inference(modus_ponens,[status(thm)],[4176,4175]) ).
tff(4178,plain,
select(q38,seq) = earray_224,
inference(symmetry,[status(thm)],[4177]) ).
tff(4179,plain,
store(select(q38,seq),s(index_219),e38) = store(earray_224,index_225,e38),
inference(monotonicity,[status(thm)],[4178,4174]) ).
tff(4180,plain,
store(select(q38,seq),s(index_219),e38) = select(q39,seq),
inference(transitivity,[status(thm)],[4179,4173,785,4172,791,4171,798]) ).
tff(4181,plain,
select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q39,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4180]) ).
tff(4182,plain,
s(s(select(q36,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3806]) ).
tff(4183,plain,
s(index_219) = s(s(select(q36,tail))),
inference(symmetry,[status(thm)],[3428]) ).
tff(4184,plain,
s(index_219) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))),
inference(transitivity,[status(thm)],[4183,4182]) ).
tff(4185,plain,
( ( s(index_219) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4184,3161]) ).
tff(4186,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_219) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4185]) ).
tff(4187,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_219) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4186]) ).
tff(4188,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4189,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4188]) ).
tff(4190,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4191,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as22) ).
tff(4192,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4191,4190]) ).
tff(4193,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4192]) ).
tff(4194,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4193,4189]) ).
tff(4195,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4196,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4195,4194]) ).
tff(4197,plain,
s(index_219) != select(q50,head),
inference(modus_ponens,[status(thm)],[4196,4187]) ).
tff(4198,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = select(q50,head) )
| ( select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = select(q50,head) )
| ( select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4199,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = select(q50,head) )
| ( select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4200,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = select(q50,head) )
| ( select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4199,4198]) ).
tff(4201,plain,
( ( s(index_219) = select(q50,head) )
| ( select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4200,32]) ).
tff(4202,plain,
select(store(select(q38,seq),s(index_219),e38),select(q50,head)) = select(select(q38,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4201,4197]) ).
tff(4203,plain,
select(select(q38,seq),select(q50,head)) = select(store(select(q38,seq),s(index_219),e38),select(q50,head)),
inference(symmetry,[status(thm)],[4202]) ).
tff(4204,plain,
select(store(q37,seq,earray_220),seq) = select(store(store(q37,seq,earray_220),tail,s(index_219)),seq),
inference(symmetry,[status(thm)],[845]) ).
tff(4205,plain,
store(earray_218,index_219,e37) = select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq),
inference(symmetry,[status(thm)],[829]) ).
tff(4206,plain,
s(index_213) = index_219,
inference(transitivity,[status(thm)],[3421,3418,3410]) ).
tff(4207,plain,
( ( earray_218 = select(q37,seq) )
<=> ( earray_218 = select(q37,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4208,axiom,
earray_218 = select(q37,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp38) ).
tff(4209,plain,
earray_218 = select(q37,seq),
inference(modus_ponens,[status(thm)],[4208,4207]) ).
tff(4210,plain,
select(q37,seq) = earray_218,
inference(symmetry,[status(thm)],[4209]) ).
tff(4211,plain,
store(select(q37,seq),s(index_213),e37) = store(earray_218,index_219,e37),
inference(monotonicity,[status(thm)],[4210,4206]) ).
tff(4212,plain,
store(select(q37,seq),s(index_213),e37) = select(q38,seq),
inference(transitivity,[status(thm)],[4211,4205,840,4204,847]) ).
tff(4213,plain,
select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q38,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4212]) ).
tff(4214,plain,
s(s(select(q35,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))),
inference(symmetry,[status(thm)],[3804]) ).
tff(4215,plain,
s(index_213) = s(s(select(q35,tail))),
inference(symmetry,[status(thm)],[3451]) ).
tff(4216,plain,
s(index_213) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))),
inference(transitivity,[status(thm)],[4215,4214]) ).
tff(4217,plain,
( ( s(index_213) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4216,3161]) ).
tff(4218,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_213) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4217]) ).
tff(4219,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_213) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4218]) ).
tff(4220,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4221,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4220]) ).
tff(4222,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4223,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as21) ).
tff(4224,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4223,4222]) ).
tff(4225,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4224]) ).
tff(4226,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4225,4221]) ).
tff(4227,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4228,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4227,4226]) ).
tff(4229,plain,
s(index_213) != select(q50,head),
inference(modus_ponens,[status(thm)],[4228,4219]) ).
tff(4230,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = select(q50,head) )
| ( select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = select(q50,head) )
| ( select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4231,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = select(q50,head) )
| ( select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4232,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = select(q50,head) )
| ( select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4231,4230]) ).
tff(4233,plain,
( ( s(index_213) = select(q50,head) )
| ( select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4232,32]) ).
tff(4234,plain,
select(store(select(q37,seq),s(index_213),e37),select(q50,head)) = select(select(q37,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4233,4229]) ).
tff(4235,plain,
select(select(q37,seq),select(q50,head)) = select(store(select(q37,seq),s(index_213),e37),select(q50,head)),
inference(symmetry,[status(thm)],[4234]) ).
tff(4236,plain,
select(store(q36,seq,earray_214),seq) = select(store(store(q36,seq,earray_214),tail,s(index_213)),seq),
inference(symmetry,[status(thm)],[893]) ).
tff(4237,plain,
store(earray_212,index_213,e36) = select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq),
inference(symmetry,[status(thm)],[877]) ).
tff(4238,plain,
s(index_204) = index_213,
inference(transitivity,[status(thm)],[3444,3441,3438,3433,3425]) ).
tff(4239,plain,
( ( earray_212 = select(q36,seq) )
<=> ( earray_212 = select(q36,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4240,axiom,
earray_212 = select(q36,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp36) ).
tff(4241,plain,
earray_212 = select(q36,seq),
inference(modus_ponens,[status(thm)],[4240,4239]) ).
tff(4242,plain,
select(q36,seq) = earray_212,
inference(symmetry,[status(thm)],[4241]) ).
tff(4243,plain,
store(select(q36,seq),s(index_204),e36) = store(earray_212,index_213,e36),
inference(monotonicity,[status(thm)],[4242,4238]) ).
tff(4244,plain,
store(select(q36,seq),s(index_204),e36) = select(q37,seq),
inference(transitivity,[status(thm)],[4243,4237,888,4236,895]) ).
tff(4245,plain,
select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q37,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4244]) ).
tff(4246,plain,
s(s(select(q34,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))),
inference(symmetry,[status(thm)],[3802]) ).
tff(4247,plain,
s(index_204) = s(s(select(q34,tail))),
inference(symmetry,[status(thm)],[3466]) ).
tff(4248,plain,
s(index_204) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))),
inference(transitivity,[status(thm)],[4247,4246]) ).
tff(4249,plain,
( ( s(index_204) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4248,3161]) ).
tff(4250,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_204) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4249]) ).
tff(4251,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_204) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4250]) ).
tff(4252,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4253,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4252]) ).
tff(4254,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4255,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as20) ).
tff(4256,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4255,4254]) ).
tff(4257,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4256]) ).
tff(4258,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4257,4253]) ).
tff(4259,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4260,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4259,4258]) ).
tff(4261,plain,
s(index_204) != select(q50,head),
inference(modus_ponens,[status(thm)],[4260,4251]) ).
tff(4262,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = select(q50,head) )
| ( select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = select(q50,head) )
| ( select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4263,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = select(q50,head) )
| ( select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4264,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = select(q50,head) )
| ( select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4263,4262]) ).
tff(4265,plain,
( ( s(index_204) = select(q50,head) )
| ( select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4264,32]) ).
tff(4266,plain,
select(store(select(q36,seq),s(index_204),e36),select(q50,head)) = select(select(q36,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4265,4261]) ).
tff(4267,plain,
select(select(q36,seq),select(q50,head)) = select(store(select(q36,seq),s(index_204),e36),select(q50,head)),
inference(symmetry,[status(thm)],[4266]) ).
tff(4268,plain,
select(store(queue_206,tail,index_207),seq) = select(store(store(queue_206,tail,index_207),head,s(index_209)),seq),
inference(symmetry,[status(thm)],[966]) ).
tff(4269,plain,
select(store(q35,seq,earray_205),seq) = select(store(store(q35,seq,earray_205),tail,s(index_204)),seq),
inference(symmetry,[status(thm)],[960]) ).
tff(4270,plain,
store(earray_203,index_204,e35) = select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq),
inference(symmetry,[status(thm)],[944]) ).
tff(4271,plain,
s(index_198) = index_204,
inference(transitivity,[status(thm)],[3459,3456,3448]) ).
tff(4272,plain,
( ( earray_203 = select(q35,seq) )
<=> ( earray_203 = select(q35,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4273,axiom,
earray_203 = select(q35,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp34) ).
tff(4274,plain,
earray_203 = select(q35,seq),
inference(modus_ponens,[status(thm)],[4273,4272]) ).
tff(4275,plain,
select(q35,seq) = earray_203,
inference(symmetry,[status(thm)],[4274]) ).
tff(4276,plain,
store(select(q35,seq),s(index_198),e35) = store(earray_203,index_204,e35),
inference(monotonicity,[status(thm)],[4275,4271]) ).
tff(4277,plain,
store(select(q35,seq),s(index_198),e35) = select(q36,seq),
inference(transitivity,[status(thm)],[4276,4270,955,4269,961,4268,968]) ).
tff(4278,plain,
select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q36,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4277]) ).
tff(4279,plain,
s(s(select(q33,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))),
inference(symmetry,[status(thm)],[3800]) ).
tff(4280,plain,
s(index_198) = s(s(select(q33,tail))),
inference(symmetry,[status(thm)],[3481]) ).
tff(4281,plain,
s(index_198) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))),
inference(transitivity,[status(thm)],[4280,4279]) ).
tff(4282,plain,
( ( s(index_198) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4281,3161]) ).
tff(4283,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_198) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4282]) ).
tff(4284,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_198) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4283]) ).
tff(4285,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4286,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4285]) ).
tff(4287,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4288,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as19) ).
tff(4289,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4288,4287]) ).
tff(4290,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4289]) ).
tff(4291,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4290,4286]) ).
tff(4292,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4293,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4292,4291]) ).
tff(4294,plain,
s(index_198) != select(q50,head),
inference(modus_ponens,[status(thm)],[4293,4284]) ).
tff(4295,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = select(q50,head) )
| ( select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = select(q50,head) )
| ( select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4296,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = select(q50,head) )
| ( select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4297,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = select(q50,head) )
| ( select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4296,4295]) ).
tff(4298,plain,
( ( s(index_198) = select(q50,head) )
| ( select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4297,32]) ).
tff(4299,plain,
select(store(select(q35,seq),s(index_198),e35),select(q50,head)) = select(select(q35,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4298,4294]) ).
tff(4300,plain,
select(select(q35,seq),select(q50,head)) = select(store(select(q35,seq),s(index_198),e35),select(q50,head)),
inference(symmetry,[status(thm)],[4299]) ).
tff(4301,plain,
select(store(q34,seq,earray_199),seq) = select(store(store(q34,seq,earray_199),tail,s(index_198)),seq),
inference(symmetry,[status(thm)],[1015]) ).
tff(4302,plain,
store(earray_197,index_198,e34) = select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq),
inference(symmetry,[status(thm)],[999]) ).
tff(4303,plain,
s(index_192) = index_198,
inference(transitivity,[status(thm)],[3474,3471,3463]) ).
tff(4304,plain,
( ( earray_197 = select(q34,seq) )
<=> ( earray_197 = select(q34,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4305,axiom,
earray_197 = select(q34,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp30) ).
tff(4306,plain,
earray_197 = select(q34,seq),
inference(modus_ponens,[status(thm)],[4305,4304]) ).
tff(4307,plain,
select(q34,seq) = earray_197,
inference(symmetry,[status(thm)],[4306]) ).
tff(4308,plain,
store(select(q34,seq),s(index_192),e34) = store(earray_197,index_198,e34),
inference(monotonicity,[status(thm)],[4307,4303]) ).
tff(4309,plain,
store(select(q34,seq),s(index_192),e34) = select(q35,seq),
inference(transitivity,[status(thm)],[4308,4302,1010,4301,1017]) ).
tff(4310,plain,
select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q35,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4309]) ).
tff(4311,plain,
s(s(select(q32,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))),
inference(symmetry,[status(thm)],[3798]) ).
tff(4312,plain,
s(index_192) = s(s(select(q32,tail))),
inference(symmetry,[status(thm)],[3504]) ).
tff(4313,plain,
s(index_192) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))),
inference(transitivity,[status(thm)],[4312,4311]) ).
tff(4314,plain,
( ( s(index_192) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4313,3161]) ).
tff(4315,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) = select(q16,tail) )
<=> ( s(index_192) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4314]) ).
tff(4316,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) != select(q16,tail) )
<=> ( s(index_192) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4315]) ).
tff(4317,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4318,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4317]) ).
tff(4319,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4320,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as18) ).
tff(4321,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4320,4319]) ).
tff(4322,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4321]) ).
tff(4323,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4322,4318]) ).
tff(4324,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4325,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4324,4323]) ).
tff(4326,plain,
s(index_192) != select(q50,head),
inference(modus_ponens,[status(thm)],[4325,4316]) ).
tff(4327,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = select(q50,head) )
| ( select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = select(q50,head) )
| ( select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4328,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = select(q50,head) )
| ( select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4329,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = select(q50,head) )
| ( select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4328,4327]) ).
tff(4330,plain,
( ( s(index_192) = select(q50,head) )
| ( select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4329,32]) ).
tff(4331,plain,
select(store(select(q34,seq),s(index_192),e34),select(q50,head)) = select(select(q34,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4330,4326]) ).
tff(4332,plain,
select(select(q34,seq),select(q50,head)) = select(store(select(q34,seq),s(index_192),e34),select(q50,head)),
inference(symmetry,[status(thm)],[4331]) ).
tff(4333,plain,
select(store(q33,seq,earray_193),seq) = select(store(store(q33,seq,earray_193),tail,s(index_192)),seq),
inference(symmetry,[status(thm)],[1063]) ).
tff(4334,plain,
store(earray_191,index_192,e33) = select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq),
inference(symmetry,[status(thm)],[1047]) ).
tff(4335,plain,
s(index_183) = index_192,
inference(transitivity,[status(thm)],[3497,3494,3491,3486,3478]) ).
tff(4336,plain,
( ( earray_191 = select(q33,seq) )
<=> ( earray_191 = select(q33,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4337,axiom,
earray_191 = select(q33,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp28) ).
tff(4338,plain,
earray_191 = select(q33,seq),
inference(modus_ponens,[status(thm)],[4337,4336]) ).
tff(4339,plain,
select(q33,seq) = earray_191,
inference(symmetry,[status(thm)],[4338]) ).
tff(4340,plain,
store(select(q33,seq),s(index_183),e33) = store(earray_191,index_192,e33),
inference(monotonicity,[status(thm)],[4339,4335]) ).
tff(4341,plain,
store(select(q33,seq),s(index_183),e33) = select(q34,seq),
inference(transitivity,[status(thm)],[4340,4334,1058,4333,1065]) ).
tff(4342,plain,
select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q34,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4341]) ).
tff(4343,plain,
s(s(select(q31,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))),
inference(symmetry,[status(thm)],[3796]) ).
tff(4344,plain,
s(index_183) = s(s(select(q31,tail))),
inference(symmetry,[status(thm)],[3519]) ).
tff(4345,plain,
s(index_183) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))),
inference(transitivity,[status(thm)],[4344,4343]) ).
tff(4346,plain,
( ( s(index_183) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4345,3161]) ).
tff(4347,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) = select(q16,tail) )
<=> ( s(index_183) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4346]) ).
tff(4348,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) != select(q16,tail) )
<=> ( s(index_183) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4347]) ).
tff(4349,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4350,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4349]) ).
tff(4351,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4352,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as17) ).
tff(4353,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4352,4351]) ).
tff(4354,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4353]) ).
tff(4355,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4354,4350]) ).
tff(4356,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4357,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4356,4355]) ).
tff(4358,plain,
s(index_183) != select(q50,head),
inference(modus_ponens,[status(thm)],[4357,4348]) ).
tff(4359,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = select(q50,head) )
| ( select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = select(q50,head) )
| ( select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4360,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = select(q50,head) )
| ( select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4361,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = select(q50,head) )
| ( select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4360,4359]) ).
tff(4362,plain,
( ( s(index_183) = select(q50,head) )
| ( select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4361,32]) ).
tff(4363,plain,
select(store(select(q33,seq),s(index_183),e33),select(q50,head)) = select(select(q33,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4362,4358]) ).
tff(4364,plain,
select(select(q33,seq),select(q50,head)) = select(store(select(q33,seq),s(index_183),e33),select(q50,head)),
inference(symmetry,[status(thm)],[4363]) ).
tff(4365,plain,
select(store(queue_185,tail,index_186),seq) = select(store(store(queue_185,tail,index_186),head,s(index_188)),seq),
inference(symmetry,[status(thm)],[1136]) ).
tff(4366,plain,
select(store(q32,seq,earray_184),seq) = select(store(store(q32,seq,earray_184),tail,s(index_183)),seq),
inference(symmetry,[status(thm)],[1130]) ).
tff(4367,plain,
store(earray_182,index_183,e32) = select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq),
inference(symmetry,[status(thm)],[1114]) ).
tff(4368,plain,
s(index_177) = index_183,
inference(transitivity,[status(thm)],[3512,3509,3501]) ).
tff(4369,plain,
( ( earray_182 = select(q32,seq) )
<=> ( earray_182 = select(q32,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4370,axiom,
earray_182 = select(q32,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp26) ).
tff(4371,plain,
earray_182 = select(q32,seq),
inference(modus_ponens,[status(thm)],[4370,4369]) ).
tff(4372,plain,
select(q32,seq) = earray_182,
inference(symmetry,[status(thm)],[4371]) ).
tff(4373,plain,
store(select(q32,seq),s(index_177),e32) = store(earray_182,index_183,e32),
inference(monotonicity,[status(thm)],[4372,4368]) ).
tff(4374,plain,
store(select(q32,seq),s(index_177),e32) = select(q33,seq),
inference(transitivity,[status(thm)],[4373,4367,1125,4366,1131,4365,1138]) ).
tff(4375,plain,
select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q33,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4374]) ).
tff(4376,plain,
s(s(select(q30,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))),
inference(symmetry,[status(thm)],[3794]) ).
tff(4377,plain,
s(index_177) = s(s(select(q30,tail))),
inference(symmetry,[status(thm)],[3534]) ).
tff(4378,plain,
s(index_177) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))),
inference(transitivity,[status(thm)],[4377,4376]) ).
tff(4379,plain,
( ( s(index_177) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4378,3161]) ).
tff(4380,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) = select(q16,tail) )
<=> ( s(index_177) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4379]) ).
tff(4381,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) != select(q16,tail) )
<=> ( s(index_177) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4380]) ).
tff(4382,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4383,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4382]) ).
tff(4384,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4385,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as16) ).
tff(4386,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4385,4384]) ).
tff(4387,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4386]) ).
tff(4388,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4387,4383]) ).
tff(4389,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4390,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4389,4388]) ).
tff(4391,plain,
s(index_177) != select(q50,head),
inference(modus_ponens,[status(thm)],[4390,4381]) ).
tff(4392,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = select(q50,head) )
| ( select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = select(q50,head) )
| ( select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4393,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = select(q50,head) )
| ( select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4394,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = select(q50,head) )
| ( select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4393,4392]) ).
tff(4395,plain,
( ( s(index_177) = select(q50,head) )
| ( select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4394,32]) ).
tff(4396,plain,
select(store(select(q32,seq),s(index_177),e32),select(q50,head)) = select(select(q32,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4395,4391]) ).
tff(4397,plain,
select(select(q32,seq),select(q50,head)) = select(store(select(q32,seq),s(index_177),e32),select(q50,head)),
inference(symmetry,[status(thm)],[4396]) ).
tff(4398,plain,
select(store(q31,seq,earray_178),seq) = select(store(store(q31,seq,earray_178),tail,s(index_177)),seq),
inference(symmetry,[status(thm)],[1185]) ).
tff(4399,plain,
store(earray_176,index_177,e31) = select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq),
inference(symmetry,[status(thm)],[1169]) ).
tff(4400,plain,
s(index_171) = index_177,
inference(transitivity,[status(thm)],[3527,3524,3516]) ).
tff(4401,plain,
( ( earray_176 = select(q31,seq) )
<=> ( earray_176 = select(q31,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4402,axiom,
earray_176 = select(q31,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp24) ).
tff(4403,plain,
earray_176 = select(q31,seq),
inference(modus_ponens,[status(thm)],[4402,4401]) ).
tff(4404,plain,
select(q31,seq) = earray_176,
inference(symmetry,[status(thm)],[4403]) ).
tff(4405,plain,
store(select(q31,seq),s(index_171),e31) = store(earray_176,index_177,e31),
inference(monotonicity,[status(thm)],[4404,4400]) ).
tff(4406,plain,
store(select(q31,seq),s(index_171),e31) = select(q32,seq),
inference(transitivity,[status(thm)],[4405,4399,1180,4398,1187]) ).
tff(4407,plain,
select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q32,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4406]) ).
tff(4408,plain,
s(s(select(q29,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))),
inference(symmetry,[status(thm)],[3792]) ).
tff(4409,plain,
s(index_171) = s(s(select(q29,tail))),
inference(symmetry,[status(thm)],[3557]) ).
tff(4410,plain,
s(index_171) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))),
inference(transitivity,[status(thm)],[4409,4408]) ).
tff(4411,plain,
( ( s(index_171) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4410,3161]) ).
tff(4412,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) = select(q16,tail) )
<=> ( s(index_171) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4411]) ).
tff(4413,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) != select(q16,tail) )
<=> ( s(index_171) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4412]) ).
tff(4414,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4415,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4414]) ).
tff(4416,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4417,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as15) ).
tff(4418,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4417,4416]) ).
tff(4419,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(skolemize,[status(sab)],[4418]) ).
tff(4420,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4419,4415]) ).
tff(4421,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4422,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4421,4420]) ).
tff(4423,plain,
s(index_171) != select(q50,head),
inference(modus_ponens,[status(thm)],[4422,4413]) ).
tff(4424,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = select(q50,head) )
| ( select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = select(q50,head) )
| ( select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4425,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = select(q50,head) )
| ( select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4426,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = select(q50,head) )
| ( select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4425,4424]) ).
tff(4427,plain,
( ( s(index_171) = select(q50,head) )
| ( select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4426,32]) ).
tff(4428,plain,
select(store(select(q31,seq),s(index_171),e31),select(q50,head)) = select(select(q31,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4427,4423]) ).
tff(4429,plain,
select(select(q31,seq),select(q50,head)) = select(store(select(q31,seq),s(index_171),e31),select(q50,head)),
inference(symmetry,[status(thm)],[4428]) ).
tff(4430,plain,
select(store(q30,seq,earray_172),seq) = select(store(store(q30,seq,earray_172),tail,s(index_171)),seq),
inference(symmetry,[status(thm)],[1233]) ).
tff(4431,plain,
store(earray_170,index_171,e30) = select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq),
inference(symmetry,[status(thm)],[1217]) ).
tff(4432,plain,
s(index_162) = index_171,
inference(transitivity,[status(thm)],[3550,3547,3544,3539,3531]) ).
tff(4433,plain,
( ( earray_170 = select(q30,seq) )
<=> ( earray_170 = select(q30,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4434,axiom,
earray_170 = select(q30,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(4435,plain,
earray_170 = select(q30,seq),
inference(modus_ponens,[status(thm)],[4434,4433]) ).
tff(4436,plain,
select(q30,seq) = earray_170,
inference(symmetry,[status(thm)],[4435]) ).
tff(4437,plain,
store(select(q30,seq),s(index_162),e30) = store(earray_170,index_171,e30),
inference(monotonicity,[status(thm)],[4436,4432]) ).
tff(4438,plain,
store(select(q30,seq),s(index_162),e30) = select(q31,seq),
inference(transitivity,[status(thm)],[4437,4431,1228,4430,1235]) ).
tff(4439,plain,
select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q31,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4438]) ).
tff(4440,plain,
s(s(select(q28,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))),
inference(symmetry,[status(thm)],[3790]) ).
tff(4441,plain,
s(index_162) = s(s(select(q28,tail))),
inference(symmetry,[status(thm)],[3572]) ).
tff(4442,plain,
s(index_162) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))),
inference(transitivity,[status(thm)],[4441,4440]) ).
tff(4443,plain,
( ( s(index_162) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4442,3161]) ).
tff(4444,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) = select(q16,tail) )
<=> ( s(index_162) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4443]) ).
tff(4445,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) != select(q16,tail) )
<=> ( s(index_162) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4444]) ).
tff(4446,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4447,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4446]) ).
tff(4448,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4449,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as14) ).
tff(4450,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4449,4448]) ).
tff(4451,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(skolemize,[status(sab)],[4450]) ).
tff(4452,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4451,4447]) ).
tff(4453,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4454,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4453,4452]) ).
tff(4455,plain,
s(index_162) != select(q50,head),
inference(modus_ponens,[status(thm)],[4454,4445]) ).
tff(4456,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = select(q50,head) )
| ( select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = select(q50,head) )
| ( select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4457,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = select(q50,head) )
| ( select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4458,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = select(q50,head) )
| ( select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4457,4456]) ).
tff(4459,plain,
( ( s(index_162) = select(q50,head) )
| ( select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4458,32]) ).
tff(4460,plain,
select(store(select(q30,seq),s(index_162),e30),select(q50,head)) = select(select(q30,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4459,4455]) ).
tff(4461,plain,
select(select(q30,seq),select(q50,head)) = select(store(select(q30,seq),s(index_162),e30),select(q50,head)),
inference(symmetry,[status(thm)],[4460]) ).
tff(4462,plain,
select(store(queue_164,tail,index_165),seq) = select(store(store(queue_164,tail,index_165),head,s(index_167)),seq),
inference(symmetry,[status(thm)],[1306]) ).
tff(4463,plain,
select(store(q29,seq,earray_163),seq) = select(store(store(q29,seq,earray_163),tail,s(index_162)),seq),
inference(symmetry,[status(thm)],[1300]) ).
tff(4464,plain,
store(earray_161,index_162,e29) = select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq),
inference(symmetry,[status(thm)],[1284]) ).
tff(4465,plain,
s(index_147) = index_162,
inference(transitivity,[status(thm)],[3565,3562,3554]) ).
tff(4466,plain,
( ( earray_161 = select(q29,seq) )
<=> ( earray_161 = select(q29,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4467,axiom,
earray_161 = select(q29,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(4468,plain,
earray_161 = select(q29,seq),
inference(modus_ponens,[status(thm)],[4467,4466]) ).
tff(4469,plain,
select(q29,seq) = earray_161,
inference(symmetry,[status(thm)],[4468]) ).
tff(4470,plain,
store(select(q29,seq),s(index_147),e29) = store(earray_161,index_162,e29),
inference(monotonicity,[status(thm)],[4469,4465]) ).
tff(4471,plain,
store(select(q29,seq),s(index_147),e29) = select(q30,seq),
inference(transitivity,[status(thm)],[4470,4464,1295,4463,1301,4462,1308]) ).
tff(4472,plain,
select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q30,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4471]) ).
tff(4473,plain,
s(s(select(q27,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))),
inference(symmetry,[status(thm)],[3788]) ).
tff(4474,plain,
s(index_147) = s(s(select(q27,tail))),
inference(symmetry,[status(thm)],[3587]) ).
tff(4475,plain,
s(index_147) = s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))),
inference(transitivity,[status(thm)],[4474,4473]) ).
tff(4476,plain,
( ( s(index_147) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4475,3161]) ).
tff(4477,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) = select(q16,tail) )
<=> ( s(index_147) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4476]) ).
tff(4478,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) != select(q16,tail) )
<=> ( s(index_147) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4477]) ).
tff(4479,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4480,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4479]) ).
tff(4481,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4482,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as13) ).
tff(4483,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4482,4481]) ).
tff(4484,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(skolemize,[status(sab)],[4483]) ).
tff(4485,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4484,4480]) ).
tff(4486,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4487,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4486,4485]) ).
tff(4488,plain,
s(index_147) != select(q50,head),
inference(modus_ponens,[status(thm)],[4487,4478]) ).
tff(4489,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = select(q50,head) )
| ( select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = select(q50,head) )
| ( select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4490,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = select(q50,head) )
| ( select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4491,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = select(q50,head) )
| ( select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4490,4489]) ).
tff(4492,plain,
( ( s(index_147) = select(q50,head) )
| ( select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4491,32]) ).
tff(4493,plain,
select(store(select(q29,seq),s(index_147),e29),select(q50,head)) = select(select(q29,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4492,4488]) ).
tff(4494,plain,
select(select(q29,seq),select(q50,head)) = select(store(select(q29,seq),s(index_147),e29),select(q50,head)),
inference(symmetry,[status(thm)],[4493]) ).
tff(4495,plain,
select(store(q28,seq,earray_148),seq) = select(store(store(q28,seq,earray_148),tail,s(index_147)),seq),
inference(symmetry,[status(thm)],[1355]) ).
tff(4496,plain,
store(earray_146,index_147,e28) = select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq),
inference(symmetry,[status(thm)],[1339]) ).
tff(4497,plain,
s(index_141) = index_147,
inference(transitivity,[status(thm)],[3580,3577,3569]) ).
tff(4498,plain,
( ( earray_146 = select(q28,seq) )
<=> ( earray_146 = select(q28,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4499,axiom,
earray_146 = select(q28,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(4500,plain,
earray_146 = select(q28,seq),
inference(modus_ponens,[status(thm)],[4499,4498]) ).
tff(4501,plain,
select(q28,seq) = earray_146,
inference(symmetry,[status(thm)],[4500]) ).
tff(4502,plain,
store(select(q28,seq),s(index_141),e28) = store(earray_146,index_147,e28),
inference(monotonicity,[status(thm)],[4501,4497]) ).
tff(4503,plain,
store(select(q28,seq),s(index_141),e28) = select(q29,seq),
inference(transitivity,[status(thm)],[4502,4496,1350,4495,1357]) ).
tff(4504,plain,
select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q29,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4503]) ).
tff(4505,plain,
s(s(select(q26,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))),
inference(symmetry,[status(thm)],[3786]) ).
tff(4506,plain,
s(index_141) = s(s(select(q26,tail))),
inference(symmetry,[status(thm)],[3610]) ).
tff(4507,plain,
s(index_141) = s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))),
inference(transitivity,[status(thm)],[4506,4505]) ).
tff(4508,plain,
( ( s(index_141) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4507,3161]) ).
tff(4509,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) = select(q16,tail) )
<=> ( s(index_141) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4508]) ).
tff(4510,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) != select(q16,tail) )
<=> ( s(index_141) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4509]) ).
tff(4511,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4512,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4511]) ).
tff(4513,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4514,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as12) ).
tff(4515,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4514,4513]) ).
tff(4516,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(skolemize,[status(sab)],[4515]) ).
tff(4517,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4516,4512]) ).
tff(4518,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4519,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q16,tail))))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4518,4517]) ).
tff(4520,plain,
s(index_141) != select(q50,head),
inference(modus_ponens,[status(thm)],[4519,4510]) ).
tff(4521,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = select(q50,head) )
| ( select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = select(q50,head) )
| ( select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4522,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = select(q50,head) )
| ( select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4523,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = select(q50,head) )
| ( select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4522,4521]) ).
tff(4524,plain,
( ( s(index_141) = select(q50,head) )
| ( select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4523,32]) ).
tff(4525,plain,
select(store(select(q28,seq),s(index_141),e28),select(q50,head)) = select(select(q28,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4524,4520]) ).
tff(4526,plain,
select(select(q28,seq),select(q50,head)) = select(store(select(q28,seq),s(index_141),e28),select(q50,head)),
inference(symmetry,[status(thm)],[4525]) ).
tff(4527,plain,
select(store(q27,seq,earray_142),seq) = select(store(store(q27,seq,earray_142),tail,s(index_141)),seq),
inference(symmetry,[status(thm)],[1403]) ).
tff(4528,plain,
store(earray_140,index_141,e27) = select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq),
inference(symmetry,[status(thm)],[1387]) ).
tff(4529,plain,
s(index_132) = index_141,
inference(transitivity,[status(thm)],[3603,3600,3597,3592,3584]) ).
tff(4530,plain,
( ( earray_140 = select(q27,seq) )
<=> ( earray_140 = select(q27,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4531,axiom,
earray_140 = select(q27,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(4532,plain,
earray_140 = select(q27,seq),
inference(modus_ponens,[status(thm)],[4531,4530]) ).
tff(4533,plain,
select(q27,seq) = earray_140,
inference(symmetry,[status(thm)],[4532]) ).
tff(4534,plain,
store(select(q27,seq),s(index_132),e27) = store(earray_140,index_141,e27),
inference(monotonicity,[status(thm)],[4533,4529]) ).
tff(4535,plain,
store(select(q27,seq),s(index_132),e27) = select(q28,seq),
inference(transitivity,[status(thm)],[4534,4528,1398,4527,1405]) ).
tff(4536,plain,
select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q28,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4535]) ).
tff(4537,plain,
s(s(select(q25,tail))) = s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))),
inference(symmetry,[status(thm)],[3784]) ).
tff(4538,plain,
s(index_132) = s(s(select(q25,tail))),
inference(symmetry,[status(thm)],[3625]) ).
tff(4539,plain,
s(index_132) = s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))),
inference(transitivity,[status(thm)],[4538,4537]) ).
tff(4540,plain,
( ( s(index_132) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) = select(q16,tail) ) ),
inference(monotonicity,[status(thm)],[4539,3161]) ).
tff(4541,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) = select(q16,tail) )
<=> ( s(index_132) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4540]) ).
tff(4542,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) != select(q16,tail) )
<=> ( s(index_132) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4541]) ).
tff(4543,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4544,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4543]) ).
tff(4545,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4546,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as11) ).
tff(4547,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4546,4545]) ).
tff(4548,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(skolemize,[status(sab)],[4547]) ).
tff(4549,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[4548,4544]) ).
tff(4550,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) != select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4551,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q16,tail)))))))))))) != select(q16,tail),
inference(unit_resolution,[status(thm)],[4550,4549]) ).
tff(4552,plain,
s(index_132) != select(q50,head),
inference(modus_ponens,[status(thm)],[4551,4542]) ).
tff(4553,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = select(q50,head) )
| ( select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = select(q50,head) )
| ( select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4554,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = select(q50,head) )
| ( select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4555,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = select(q50,head) )
| ( select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4554,4553]) ).
tff(4556,plain,
( ( s(index_132) = select(q50,head) )
| ( select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4555,32]) ).
tff(4557,plain,
select(store(select(q27,seq),s(index_132),e27),select(q50,head)) = select(select(q27,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4556,4552]) ).
tff(4558,plain,
select(select(q27,seq),select(q50,head)) = select(store(select(q27,seq),s(index_132),e27),select(q50,head)),
inference(symmetry,[status(thm)],[4557]) ).
tff(4559,plain,
select(store(queue_134,tail,index_135),seq) = select(store(store(queue_134,tail,index_135),head,s(index_137)),seq),
inference(symmetry,[status(thm)],[1476]) ).
tff(4560,plain,
select(store(q26,seq,earray_133),seq) = select(store(store(q26,seq,earray_133),tail,s(index_132)),seq),
inference(symmetry,[status(thm)],[1470]) ).
tff(4561,plain,
store(earray_131,index_132,e26) = select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq),
inference(symmetry,[status(thm)],[1454]) ).
tff(4562,plain,
select(q15,tail) = index_51,
inference(symmetry,[status(thm)],[238]) ).
tff(4563,plain,
s(select(q15,tail)) = s(index_51),
inference(monotonicity,[status(thm)],[4562]) ).
tff(4564,plain,
s(select(q15,tail)) = s(select(queue_298,head)),
inference(transitivity,[status(thm)],[4563,240,3159,155]) ).
tff(4565,plain,
s(s(select(q15,tail))) = s(s(select(queue_298,head))),
inference(monotonicity,[status(thm)],[4564]) ).
tff(4566,plain,
s(index_51) = s(select(q15,tail)),
inference(symmetry,[status(thm)],[4563]) ).
tff(4567,plain,
index_57 = s(select(q15,tail)),
inference(transitivity,[status(thm)],[3164,190,193,4566]) ).
tff(4568,plain,
s(index_57) = s(s(select(q15,tail))),
inference(monotonicity,[status(thm)],[4567]) ).
tff(4569,plain,
s(select(q16,tail)) = s(s(select(queue_298,head))),
inference(transitivity,[status(thm)],[3757,4568,4565]) ).
tff(4570,plain,
s(s(select(q16,tail))) = s(s(s(select(queue_298,head)))),
inference(monotonicity,[status(thm)],[4569]) ).
tff(4571,plain,
s(select(q17,tail)) = s(s(s(select(queue_298,head)))),
inference(transitivity,[status(thm)],[3741,3765,4570]) ).
tff(4572,plain,
s(s(select(q17,tail))) = s(s(s(s(select(queue_298,head))))),
inference(monotonicity,[status(thm)],[4571]) ).
tff(4573,plain,
s(select(q18,tail)) = s(s(s(s(select(queue_298,head))))),
inference(transitivity,[status(thm)],[3727,3755,4572]) ).
tff(4574,plain,
s(s(select(q18,tail))) = s(s(s(s(s(select(queue_298,head)))))),
inference(monotonicity,[status(thm)],[4573]) ).
tff(4575,plain,
s(select(q19,tail)) = s(s(s(s(s(select(queue_298,head)))))),
inference(transitivity,[status(thm)],[3713,3735,4574]) ).
tff(4576,plain,
s(s(select(q19,tail))) = s(s(s(s(s(s(select(queue_298,head))))))),
inference(monotonicity,[status(thm)],[4575]) ).
tff(4577,plain,
s(select(q20,tail)) = s(s(s(s(s(s(select(queue_298,head))))))),
inference(transitivity,[status(thm)],[3693,3721,4576]) ).
tff(4578,plain,
s(s(select(q20,tail))) = s(s(s(s(s(s(s(select(queue_298,head)))))))),
inference(monotonicity,[status(thm)],[4577]) ).
tff(4579,plain,
s(select(q21,tail)) = s(s(s(s(s(s(s(select(queue_298,head)))))))),
inference(transitivity,[status(thm)],[3679,3707,4578]) ).
tff(4580,plain,
s(s(select(q21,tail))) = s(s(s(s(s(s(s(s(select(queue_298,head))))))))),
inference(monotonicity,[status(thm)],[4579]) ).
tff(4581,plain,
s(select(q22,tail)) = s(s(s(s(s(s(s(s(select(queue_298,head))))))))),
inference(transitivity,[status(thm)],[3665,3687,4580]) ).
tff(4582,plain,
s(s(select(q22,tail))) = s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),
inference(monotonicity,[status(thm)],[4581]) ).
tff(4583,plain,
s(select(q23,tail)) = s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),
inference(transitivity,[status(thm)],[3645,3673,4582]) ).
tff(4584,plain,
s(s(select(q23,tail))) = s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),
inference(monotonicity,[status(thm)],[4583]) ).
tff(4585,plain,
s(select(q24,tail)) = s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),
inference(transitivity,[status(thm)],[3631,3659,4584]) ).
tff(4586,plain,
s(s(select(q24,tail))) = s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),
inference(monotonicity,[status(thm)],[4585]) ).
tff(4587,plain,
s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = s(s(select(q24,tail))),
inference(symmetry,[status(thm)],[4586]) ).
tff(4588,plain,
s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = index_132,
inference(transitivity,[status(thm)],[4587,3640,3618,3615,3607]) ).
tff(4589,plain,
( ( earray_131 = select(q26,seq) )
<=> ( earray_131 = select(q26,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4590,axiom,
earray_131 = select(q26,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(4591,plain,
earray_131 = select(q26,seq),
inference(modus_ponens,[status(thm)],[4590,4589]) ).
tff(4592,plain,
select(q26,seq) = earray_131,
inference(symmetry,[status(thm)],[4591]) ).
tff(4593,plain,
store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26) = store(earray_131,index_132,e26),
inference(monotonicity,[status(thm)],[4592,4588]) ).
tff(4594,plain,
store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26) = select(q27,seq),
inference(transitivity,[status(thm)],[4593,4561,1465,4560,1471,4559,1478]) ).
tff(4595,plain,
select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q27,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4594]) ).
tff(4596,plain,
s(s(s(index_299))) = s(s(s(select(queue_298,head)))),
inference(monotonicity,[status(thm)],[156]) ).
tff(4597,plain,
s(s(s(s(index_299)))) = s(s(s(s(select(queue_298,head))))),
inference(monotonicity,[status(thm)],[4596]) ).
tff(4598,plain,
s(s(s(s(s(index_299))))) = s(s(s(s(s(select(queue_298,head)))))),
inference(monotonicity,[status(thm)],[4597]) ).
tff(4599,plain,
s(s(s(s(s(s(index_299)))))) = s(s(s(s(s(s(select(queue_298,head))))))),
inference(monotonicity,[status(thm)],[4598]) ).
tff(4600,plain,
s(s(s(s(s(s(s(index_299))))))) = s(s(s(s(s(s(s(select(queue_298,head)))))))),
inference(monotonicity,[status(thm)],[4599]) ).
tff(4601,plain,
s(s(s(s(s(s(s(s(index_299)))))))) = s(s(s(s(s(s(s(s(select(queue_298,head))))))))),
inference(monotonicity,[status(thm)],[4600]) ).
tff(4602,plain,
s(s(s(s(s(s(s(s(s(index_299))))))))) = s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),
inference(monotonicity,[status(thm)],[4601]) ).
tff(4603,plain,
s(s(s(s(s(s(s(s(s(s(index_299)))))))))) = s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),
inference(monotonicity,[status(thm)],[4602]) ).
tff(4604,plain,
s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) = s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),
inference(monotonicity,[status(thm)],[4603]) ).
tff(4605,plain,
s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))),
inference(symmetry,[status(thm)],[4604]) ).
tff(4606,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4605,149]) ).
tff(4607,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) = s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4606]) ).
tff(4608,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) != s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4607]) ).
tff(4609,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4610,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4609]) ).
tff(4611,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4612,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as10) ).
tff(4613,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[4612,4611]) ).
tff(4614,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(skolemize,[status(sab)],[4613]) ).
tff(4615,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[4614,4610]) ).
tff(4616,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4617,plain,
s(s(s(s(s(s(s(s(s(s(s(index_299))))))))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4616,4615]) ).
tff(4618,plain,
s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4617,4608]) ).
tff(4619,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
| ( select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
| ( select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4620,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
| ( select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4621,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
| ( select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4620,4619]) ).
tff(4622,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))) = select(q50,head) )
| ( select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4621,32]) ).
tff(4623,plain,
select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)) = select(select(q26,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4622,4618]) ).
tff(4624,plain,
select(select(q26,seq),select(q50,head)) = select(store(select(q26,seq),s(s(s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))))),e26),select(q50,head)),
inference(symmetry,[status(thm)],[4623]) ).
tff(4625,plain,
select(store(q25,seq,earray_127),seq) = select(store(store(q25,seq,earray_127),tail,s(index_126)),seq),
inference(symmetry,[status(thm)],[1525]) ).
tff(4626,plain,
store(earray_125,index_126,e25) = select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq),
inference(symmetry,[status(thm)],[1509]) ).
tff(4627,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = select(q25,tail),
inference(symmetry,[status(thm)],[3637]) ).
tff(4628,plain,
s(index_120) = select(store(store(q24,seq,earray_121),tail,s(index_120)),tail),
inference(symmetry,[status(thm)],[3634]) ).
tff(4629,plain,
s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = s(s(select(q23,tail))),
inference(symmetry,[status(thm)],[4584]) ).
tff(4630,plain,
s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = index_126,
inference(transitivity,[status(thm)],[4629,3660,4628,4627,3622]) ).
tff(4631,plain,
( ( earray_125 = select(q25,seq) )
<=> ( earray_125 = select(q25,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4632,axiom,
earray_125 = select(q25,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(4633,plain,
earray_125 = select(q25,seq),
inference(modus_ponens,[status(thm)],[4632,4631]) ).
tff(4634,plain,
select(q25,seq) = earray_125,
inference(symmetry,[status(thm)],[4633]) ).
tff(4635,plain,
store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25) = store(earray_125,index_126,e25),
inference(monotonicity,[status(thm)],[4634,4630]) ).
tff(4636,plain,
store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25) = select(q26,seq),
inference(transitivity,[status(thm)],[4635,4626,1520,4625,1527]) ).
tff(4637,plain,
select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q26,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4636]) ).
tff(4638,plain,
s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = s(s(s(s(s(s(s(s(s(s(index_299)))))))))),
inference(symmetry,[status(thm)],[4603]) ).
tff(4639,plain,
( ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(s(index_299)))))))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4638,149]) ).
tff(4640,plain,
( ( s(s(s(s(s(s(s(s(s(s(index_299)))))))))) = s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4639]) ).
tff(4641,plain,
( ( s(s(s(s(s(s(s(s(s(s(index_299)))))))))) != s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4640]) ).
tff(4642,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4643,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) ),
inference(quant_intro,[status(thm)],[4642]) ).
tff(4644,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4645,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as9) ).
tff(4646,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[4645,4644]) ).
tff(4647,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(skolemize,[status(sab)],[4646]) ).
tff(4648,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[4647,4643]) ).
tff(4649,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(index_299)))))))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4650,plain,
s(s(s(s(s(s(s(s(s(s(index_299)))))))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4649,4648]) ).
tff(4651,plain,
s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4650,4641]) ).
tff(4652,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
| ( select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
| ( select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4653,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
| ( select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4654,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
| ( select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4653,4652]) ).
tff(4655,plain,
( ( s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))) = select(q50,head) )
| ( select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4654,32]) ).
tff(4656,plain,
select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)) = select(select(q25,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4655,4651]) ).
tff(4657,plain,
select(select(q25,seq),select(q50,head)) = select(store(select(q25,seq),s(s(s(s(s(s(s(s(s(s(select(queue_298,head))))))))))),e25),select(q50,head)),
inference(symmetry,[status(thm)],[4656]) ).
tff(4658,plain,
select(store(q24,seq,earray_121),seq) = select(store(store(q24,seq,earray_121),tail,s(index_120)),seq),
inference(symmetry,[status(thm)],[1573]) ).
tff(4659,plain,
store(earray_119,index_120,e24) = select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq),
inference(symmetry,[status(thm)],[1557]) ).
tff(4660,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(q24,tail),
inference(symmetry,[status(thm)],[3657]) ).
tff(4661,plain,
select(store(queue_113,tail,index_114),tail) = select(store(store(queue_113,tail,index_114),head,s(index_116)),tail),
inference(symmetry,[status(thm)],[3654]) ).
tff(4662,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = select(store(queue_113,tail,index_114),tail),
inference(symmetry,[status(thm)],[3650]) ).
tff(4663,plain,
s(index_111) = select(store(store(q23,seq,earray_112),tail,s(index_111)),tail),
inference(symmetry,[status(thm)],[3648]) ).
tff(4664,plain,
s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = s(s(select(q22,tail))),
inference(symmetry,[status(thm)],[4582]) ).
tff(4665,plain,
s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = index_120,
inference(transitivity,[status(thm)],[4664,3674,4663,4662,4661,4660,3630]) ).
tff(4666,plain,
( ( earray_119 = select(q24,seq) )
<=> ( earray_119 = select(q24,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4667,axiom,
earray_119 = select(q24,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(4668,plain,
earray_119 = select(q24,seq),
inference(modus_ponens,[status(thm)],[4667,4666]) ).
tff(4669,plain,
select(q24,seq) = earray_119,
inference(symmetry,[status(thm)],[4668]) ).
tff(4670,plain,
store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24) = store(earray_119,index_120,e24),
inference(monotonicity,[status(thm)],[4669,4665]) ).
tff(4671,plain,
store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24) = select(q25,seq),
inference(transitivity,[status(thm)],[4670,4659,1568,4658,1575]) ).
tff(4672,plain,
select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q25,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4671]) ).
tff(4673,plain,
s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = s(s(s(s(s(s(s(s(s(index_299))))))))),
inference(symmetry,[status(thm)],[4602]) ).
tff(4674,plain,
( ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(s(index_299))))))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4673,149]) ).
tff(4675,plain,
( ( s(s(s(s(s(s(s(s(s(index_299))))))))) = s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4674]) ).
tff(4676,plain,
( ( s(s(s(s(s(s(s(s(s(index_299))))))))) != s(index_299) )
<=> ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4675]) ).
tff(4677,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ( s(s(s(s(s(s(s(s(X)))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4678,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ) ),
inference(quant_intro,[status(thm)],[4677]) ).
tff(4679,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4680,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as8) ).
tff(4681,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[4680,4679]) ).
tff(4682,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(skolemize,[status(sab)],[4681]) ).
tff(4683,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[4682,4678]) ).
tff(4684,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
| ( s(s(s(s(s(s(s(s(s(index_299))))))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4685,plain,
s(s(s(s(s(s(s(s(s(index_299))))))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4684,4683]) ).
tff(4686,plain,
s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4685,4676]) ).
tff(4687,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
| ( select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
| ( select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4688,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
| ( select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4689,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
| ( select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4688,4687]) ).
tff(4690,plain,
( ( s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))) = select(q50,head) )
| ( select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4689,32]) ).
tff(4691,plain,
select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)) = select(select(q24,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4690,4686]) ).
tff(4692,plain,
select(select(q24,seq),select(q50,head)) = select(store(select(q24,seq),s(s(s(s(s(s(s(s(s(select(queue_298,head)))))))))),e24),select(q50,head)),
inference(symmetry,[status(thm)],[4691]) ).
tff(4693,plain,
select(store(queue_113,tail,index_114),seq) = select(store(store(queue_113,tail,index_114),head,s(index_116)),seq),
inference(symmetry,[status(thm)],[1646]) ).
tff(4694,plain,
select(store(q23,seq,earray_112),seq) = select(store(store(q23,seq,earray_112),tail,s(index_111)),seq),
inference(symmetry,[status(thm)],[1640]) ).
tff(4695,plain,
store(earray_110,index_111,e23) = select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq),
inference(symmetry,[status(thm)],[1624]) ).
tff(4696,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = select(q23,tail),
inference(symmetry,[status(thm)],[3671]) ).
tff(4697,plain,
s(index_105) = select(store(store(q22,seq,earray_106),tail,s(index_105)),tail),
inference(symmetry,[status(thm)],[3668]) ).
tff(4698,plain,
s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = s(s(select(q21,tail))),
inference(symmetry,[status(thm)],[4580]) ).
tff(4699,plain,
s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = index_111,
inference(transitivity,[status(thm)],[4698,3688,4697,4696,3644]) ).
tff(4700,plain,
( ( earray_110 = select(q23,seq) )
<=> ( earray_110 = select(q23,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4701,axiom,
earray_110 = select(q23,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(4702,plain,
earray_110 = select(q23,seq),
inference(modus_ponens,[status(thm)],[4701,4700]) ).
tff(4703,plain,
select(q23,seq) = earray_110,
inference(symmetry,[status(thm)],[4702]) ).
tff(4704,plain,
store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23) = store(earray_110,index_111,e23),
inference(monotonicity,[status(thm)],[4703,4699]) ).
tff(4705,plain,
store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23) = select(q24,seq),
inference(transitivity,[status(thm)],[4704,4695,1635,4694,1641,4693,1648]) ).
tff(4706,plain,
select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q24,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4705]) ).
tff(4707,plain,
s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = s(s(s(s(s(s(s(s(index_299)))))))),
inference(symmetry,[status(thm)],[4601]) ).
tff(4708,plain,
( ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(s(index_299)))))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4707,149]) ).
tff(4709,plain,
( ( s(s(s(s(s(s(s(s(index_299)))))))) = s(index_299) )
<=> ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4708]) ).
tff(4710,plain,
( ( s(s(s(s(s(s(s(s(index_299)))))))) != s(index_299) )
<=> ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4709]) ).
tff(4711,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(X))))))) != X )
<=> ( s(s(s(s(s(s(s(X))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4712,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ) ),
inference(quant_intro,[status(thm)],[4711]) ).
tff(4713,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4714,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as7) ).
tff(4715,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[4714,4713]) ).
tff(4716,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(skolemize,[status(sab)],[4715]) ).
tff(4717,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[4716,4712]) ).
tff(4718,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
| ( s(s(s(s(s(s(s(s(index_299)))))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4719,plain,
s(s(s(s(s(s(s(s(index_299)))))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4718,4717]) ).
tff(4720,plain,
s(s(s(s(s(s(s(s(select(queue_298,head))))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4719,4710]) ).
tff(4721,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
| ( select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
| ( select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4722,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
| ( select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4723,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
| ( select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4722,4721]) ).
tff(4724,plain,
( ( s(s(s(s(s(s(s(s(select(queue_298,head))))))))) = select(q50,head) )
| ( select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4723,32]) ).
tff(4725,plain,
select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)) = select(select(q23,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4724,4720]) ).
tff(4726,plain,
select(select(q23,seq),select(q50,head)) = select(store(select(q23,seq),s(s(s(s(s(s(s(s(select(queue_298,head))))))))),e23),select(q50,head)),
inference(symmetry,[status(thm)],[4725]) ).
tff(4727,plain,
select(store(q22,seq,earray_106),seq) = select(store(store(q22,seq,earray_106),tail,s(index_105)),seq),
inference(symmetry,[status(thm)],[1695]) ).
tff(4728,plain,
store(earray_104,index_105,e22) = select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq),
inference(symmetry,[status(thm)],[1679]) ).
tff(4729,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = select(q22,tail),
inference(symmetry,[status(thm)],[3685]) ).
tff(4730,plain,
s(index_99) = select(store(store(q21,seq,earray_100),tail,s(index_99)),tail),
inference(symmetry,[status(thm)],[3682]) ).
tff(4731,plain,
s(s(s(s(s(s(s(select(queue_298,head)))))))) = s(s(select(q20,tail))),
inference(symmetry,[status(thm)],[4578]) ).
tff(4732,plain,
s(s(s(s(s(s(s(select(queue_298,head)))))))) = index_105,
inference(transitivity,[status(thm)],[4731,3708,4730,4729,3664]) ).
tff(4733,plain,
( ( earray_104 = select(q22,seq) )
<=> ( earray_104 = select(q22,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4734,axiom,
earray_104 = select(q22,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(4735,plain,
earray_104 = select(q22,seq),
inference(modus_ponens,[status(thm)],[4734,4733]) ).
tff(4736,plain,
select(q22,seq) = earray_104,
inference(symmetry,[status(thm)],[4735]) ).
tff(4737,plain,
store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22) = store(earray_104,index_105,e22),
inference(monotonicity,[status(thm)],[4736,4732]) ).
tff(4738,plain,
store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22) = select(q23,seq),
inference(transitivity,[status(thm)],[4737,4728,1690,4727,1697]) ).
tff(4739,plain,
select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q23,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4738]) ).
tff(4740,plain,
s(s(s(s(s(s(s(select(queue_298,head)))))))) = s(s(s(s(s(s(s(index_299))))))),
inference(symmetry,[status(thm)],[4600]) ).
tff(4741,plain,
( ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(s(index_299))))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4740,149]) ).
tff(4742,plain,
( ( s(s(s(s(s(s(s(index_299))))))) = s(index_299) )
<=> ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4741]) ).
tff(4743,plain,
( ( s(s(s(s(s(s(s(index_299))))))) != s(index_299) )
<=> ( s(s(s(s(s(s(s(select(queue_298,head)))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4742]) ).
tff(4744,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(X)))))) != X )
<=> ( s(s(s(s(s(s(X)))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4745,plain,
( ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ) ),
inference(quant_intro,[status(thm)],[4744]) ).
tff(4746,plain,
( ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4747,axiom,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as6) ).
tff(4748,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[4747,4746]) ).
tff(4749,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(skolemize,[status(sab)],[4748]) ).
tff(4750,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[4749,4745]) ).
tff(4751,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
| ( s(s(s(s(s(s(s(index_299))))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4752,plain,
s(s(s(s(s(s(s(index_299))))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4751,4750]) ).
tff(4753,plain,
s(s(s(s(s(s(s(select(queue_298,head)))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4752,4743]) ).
tff(4754,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
| ( select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
| ( select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4755,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
| ( select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4756,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
| ( select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4755,4754]) ).
tff(4757,plain,
( ( s(s(s(s(s(s(s(select(queue_298,head)))))))) = select(q50,head) )
| ( select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4756,32]) ).
tff(4758,plain,
select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)) = select(select(q22,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4757,4753]) ).
tff(4759,plain,
select(select(q22,seq),select(q50,head)) = select(store(select(q22,seq),s(s(s(s(s(s(s(select(queue_298,head)))))))),e22),select(q50,head)),
inference(symmetry,[status(thm)],[4758]) ).
tff(4760,plain,
select(store(q21,seq,earray_100),seq) = select(store(store(q21,seq,earray_100),tail,s(index_99)),seq),
inference(symmetry,[status(thm)],[1743]) ).
tff(4761,plain,
store(earray_98,index_99,e21) = select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq),
inference(symmetry,[status(thm)],[1727]) ).
tff(4762,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(q21,tail),
inference(symmetry,[status(thm)],[3705]) ).
tff(4763,plain,
select(store(queue_92,tail,index_93),tail) = select(store(store(queue_92,tail,index_93),head,s(index_95)),tail),
inference(symmetry,[status(thm)],[3702]) ).
tff(4764,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = select(store(queue_92,tail,index_93),tail),
inference(symmetry,[status(thm)],[3698]) ).
tff(4765,plain,
s(index_90) = select(store(store(q20,seq,earray_91),tail,s(index_90)),tail),
inference(symmetry,[status(thm)],[3696]) ).
tff(4766,plain,
s(s(s(s(s(s(select(queue_298,head))))))) = s(s(select(q19,tail))),
inference(symmetry,[status(thm)],[4576]) ).
tff(4767,plain,
s(s(s(s(s(s(select(queue_298,head))))))) = index_99,
inference(transitivity,[status(thm)],[4766,3722,4765,4764,4763,4762,3678]) ).
tff(4768,plain,
( ( earray_98 = select(q21,seq) )
<=> ( earray_98 = select(q21,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4769,axiom,
earray_98 = select(q21,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(4770,plain,
earray_98 = select(q21,seq),
inference(modus_ponens,[status(thm)],[4769,4768]) ).
tff(4771,plain,
select(q21,seq) = earray_98,
inference(symmetry,[status(thm)],[4770]) ).
tff(4772,plain,
store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21) = store(earray_98,index_99,e21),
inference(monotonicity,[status(thm)],[4771,4767]) ).
tff(4773,plain,
store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21) = select(q22,seq),
inference(transitivity,[status(thm)],[4772,4761,1738,4760,1745]) ).
tff(4774,plain,
select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q22,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4773]) ).
tff(4775,plain,
s(s(s(s(s(s(select(queue_298,head))))))) = s(s(s(s(s(s(index_299)))))),
inference(symmetry,[status(thm)],[4599]) ).
tff(4776,plain,
( ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
<=> ( s(s(s(s(s(s(index_299)))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4775,149]) ).
tff(4777,plain,
( ( s(s(s(s(s(s(index_299)))))) = s(index_299) )
<=> ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4776]) ).
tff(4778,plain,
( ( s(s(s(s(s(s(index_299)))))) != s(index_299) )
<=> ( s(s(s(s(s(s(select(queue_298,head))))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4777]) ).
tff(4779,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(X))))) != X )
<=> ( s(s(s(s(s(X))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4780,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(quant_intro,[status(thm)],[4779]) ).
tff(4781,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4782,axiom,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as5) ).
tff(4783,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[4782,4781]) ).
tff(4784,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(skolemize,[status(sab)],[4783]) ).
tff(4785,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[4784,4780]) ).
tff(4786,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(X))))) != X )
| ( s(s(s(s(s(s(index_299)))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4787,plain,
s(s(s(s(s(s(index_299)))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4786,4785]) ).
tff(4788,plain,
s(s(s(s(s(s(select(queue_298,head))))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4787,4778]) ).
tff(4789,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
| ( select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
| ( select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4790,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
| ( select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4791,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
| ( select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4790,4789]) ).
tff(4792,plain,
( ( s(s(s(s(s(s(select(queue_298,head))))))) = select(q50,head) )
| ( select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4791,32]) ).
tff(4793,plain,
select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)) = select(select(q21,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4792,4788]) ).
tff(4794,plain,
select(select(q21,seq),select(q50,head)) = select(store(select(q21,seq),s(s(s(s(s(s(select(queue_298,head))))))),e21),select(q50,head)),
inference(symmetry,[status(thm)],[4793]) ).
tff(4795,plain,
select(store(queue_92,tail,index_93),seq) = select(store(store(queue_92,tail,index_93),head,s(index_95)),seq),
inference(symmetry,[status(thm)],[1816]) ).
tff(4796,plain,
select(store(q20,seq,earray_91),seq) = select(store(store(q20,seq,earray_91),tail,s(index_90)),seq),
inference(symmetry,[status(thm)],[1810]) ).
tff(4797,plain,
store(earray_89,index_90,e20) = select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq),
inference(symmetry,[status(thm)],[1794]) ).
tff(4798,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = select(q20,tail),
inference(symmetry,[status(thm)],[3719]) ).
tff(4799,plain,
s(index_84) = select(store(store(q19,seq,earray_85),tail,s(index_84)),tail),
inference(symmetry,[status(thm)],[3716]) ).
tff(4800,plain,
s(s(s(s(s(select(queue_298,head)))))) = s(s(select(q18,tail))),
inference(symmetry,[status(thm)],[4574]) ).
tff(4801,plain,
s(s(s(s(s(select(queue_298,head)))))) = index_90,
inference(transitivity,[status(thm)],[4800,3736,4799,4798,3692]) ).
tff(4802,plain,
( ( earray_89 = select(q20,seq) )
<=> ( earray_89 = select(q20,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4803,axiom,
earray_89 = select(q20,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(4804,plain,
earray_89 = select(q20,seq),
inference(modus_ponens,[status(thm)],[4803,4802]) ).
tff(4805,plain,
select(q20,seq) = earray_89,
inference(symmetry,[status(thm)],[4804]) ).
tff(4806,plain,
store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20) = store(earray_89,index_90,e20),
inference(monotonicity,[status(thm)],[4805,4801]) ).
tff(4807,plain,
store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20) = select(q21,seq),
inference(transitivity,[status(thm)],[4806,4797,1805,4796,1811,4795,1818]) ).
tff(4808,plain,
select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q21,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4807]) ).
tff(4809,plain,
s(s(s(s(s(select(queue_298,head)))))) = s(s(s(s(s(index_299))))),
inference(symmetry,[status(thm)],[4598]) ).
tff(4810,plain,
( ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
<=> ( s(s(s(s(s(index_299))))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4809,149]) ).
tff(4811,plain,
( ( s(s(s(s(s(index_299))))) = s(index_299) )
<=> ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4810]) ).
tff(4812,plain,
( ( s(s(s(s(s(index_299))))) != s(index_299) )
<=> ( s(s(s(s(s(select(queue_298,head)))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4811]) ).
tff(4813,plain,
^ [X: $i] :
refl(( ( s(s(s(s(X)))) != X )
<=> ( s(s(s(s(X)))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4814,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(quant_intro,[status(thm)],[4813]) ).
tff(4815,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4816,axiom,
! [X: $i] : ( s(s(s(s(X)))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as4) ).
tff(4817,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[4816,4815]) ).
tff(4818,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(skolemize,[status(sab)],[4817]) ).
tff(4819,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[4818,4814]) ).
tff(4820,plain,
( ~ ! [X: $i] : ( s(s(s(s(X)))) != X )
| ( s(s(s(s(s(index_299))))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4821,plain,
s(s(s(s(s(index_299))))) != s(index_299),
inference(unit_resolution,[status(thm)],[4820,4819]) ).
tff(4822,plain,
s(s(s(s(s(select(queue_298,head)))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4821,4812]) ).
tff(4823,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
| ( select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
| ( select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4824,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
| ( select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4825,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
| ( select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4824,4823]) ).
tff(4826,plain,
( ( s(s(s(s(s(select(queue_298,head)))))) = select(q50,head) )
| ( select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4825,32]) ).
tff(4827,plain,
select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)) = select(select(q20,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4826,4822]) ).
tff(4828,plain,
select(select(q20,seq),select(q50,head)) = select(store(select(q20,seq),s(s(s(s(s(select(queue_298,head)))))),e20),select(q50,head)),
inference(symmetry,[status(thm)],[4827]) ).
tff(4829,plain,
select(store(q19,seq,earray_85),seq) = select(store(store(q19,seq,earray_85),tail,s(index_84)),seq),
inference(symmetry,[status(thm)],[1865]) ).
tff(4830,plain,
store(earray_83,index_84,e19) = select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq),
inference(symmetry,[status(thm)],[1849]) ).
tff(4831,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = select(q19,tail),
inference(symmetry,[status(thm)],[3733]) ).
tff(4832,plain,
s(index_72) = select(store(store(q18,seq,earray_73),tail,s(index_72)),tail),
inference(symmetry,[status(thm)],[3730]) ).
tff(4833,plain,
s(s(s(s(select(queue_298,head))))) = s(s(select(q17,tail))),
inference(symmetry,[status(thm)],[4572]) ).
tff(4834,plain,
s(s(s(s(select(queue_298,head))))) = index_84,
inference(transitivity,[status(thm)],[4833,3756,4832,4831,3712]) ).
tff(4835,plain,
( ( earray_83 = select(q19,seq) )
<=> ( earray_83 = select(q19,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4836,axiom,
earray_83 = select(q19,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(4837,plain,
earray_83 = select(q19,seq),
inference(modus_ponens,[status(thm)],[4836,4835]) ).
tff(4838,plain,
select(q19,seq) = earray_83,
inference(symmetry,[status(thm)],[4837]) ).
tff(4839,plain,
store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19) = store(earray_83,index_84,e19),
inference(monotonicity,[status(thm)],[4838,4834]) ).
tff(4840,plain,
store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19) = select(q20,seq),
inference(transitivity,[status(thm)],[4839,4830,1860,4829,1867]) ).
tff(4841,plain,
select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q20,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4840]) ).
tff(4842,plain,
s(s(s(s(select(queue_298,head))))) = s(s(s(s(index_299)))),
inference(symmetry,[status(thm)],[4597]) ).
tff(4843,plain,
( ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
<=> ( s(s(s(s(index_299)))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4842,149]) ).
tff(4844,plain,
( ( s(s(s(s(index_299)))) = s(index_299) )
<=> ( s(s(s(s(select(queue_298,head))))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4843]) ).
tff(4845,plain,
( ( s(s(s(s(index_299)))) != s(index_299) )
<=> ( s(s(s(s(select(queue_298,head))))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4844]) ).
tff(4846,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) != X )
<=> ( s(s(s(X))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4847,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(quant_intro,[status(thm)],[4846]) ).
tff(4848,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4849,axiom,
! [X: $i] : ( s(s(s(X))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as3) ).
tff(4850,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[4849,4848]) ).
tff(4851,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(skolemize,[status(sab)],[4850]) ).
tff(4852,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[4851,4847]) ).
tff(4853,plain,
( ~ ! [X: $i] : ( s(s(s(X))) != X )
| ( s(s(s(s(index_299)))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4854,plain,
s(s(s(s(index_299)))) != s(index_299),
inference(unit_resolution,[status(thm)],[4853,4852]) ).
tff(4855,plain,
s(s(s(s(select(queue_298,head))))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4854,4845]) ).
tff(4856,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
| ( select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
| ( select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4857,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
| ( select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4858,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
| ( select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4857,4856]) ).
tff(4859,plain,
( ( s(s(s(s(select(queue_298,head))))) = select(q50,head) )
| ( select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4858,32]) ).
tff(4860,plain,
select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)) = select(select(q19,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4859,4855]) ).
tff(4861,plain,
select(select(q19,seq),select(q50,head)) = select(store(select(q19,seq),s(s(s(s(select(queue_298,head))))),e19),select(q50,head)),
inference(symmetry,[status(thm)],[4860]) ).
tff(4862,plain,
select(store(q18,seq,earray_73),seq) = select(store(store(q18,seq,earray_73),tail,s(index_72)),seq),
inference(symmetry,[status(thm)],[1913]) ).
tff(4863,plain,
store(earray_71,index_72,e18) = select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq),
inference(symmetry,[status(thm)],[1897]) ).
tff(4864,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(q18,tail),
inference(symmetry,[status(thm)],[3753]) ).
tff(4865,plain,
select(store(queue_65,tail,index_66),tail) = select(store(store(queue_65,tail,index_66),head,s(index_68)),tail),
inference(symmetry,[status(thm)],[3750]) ).
tff(4866,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = select(store(queue_65,tail,index_66),tail),
inference(symmetry,[status(thm)],[3746]) ).
tff(4867,plain,
s(index_63) = select(store(store(q17,seq,earray_64),tail,s(index_63)),tail),
inference(symmetry,[status(thm)],[3744]) ).
tff(4868,plain,
s(s(s(select(queue_298,head)))) = s(s(select(q16,tail))),
inference(symmetry,[status(thm)],[4570]) ).
tff(4869,plain,
s(s(s(select(queue_298,head)))) = index_72,
inference(transitivity,[status(thm)],[4868,3766,4867,4866,4865,4864,3726]) ).
tff(4870,plain,
( ( earray_71 = select(q18,seq) )
<=> ( earray_71 = select(q18,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4871,axiom,
earray_71 = select(q18,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(4872,plain,
earray_71 = select(q18,seq),
inference(modus_ponens,[status(thm)],[4871,4870]) ).
tff(4873,plain,
select(q18,seq) = earray_71,
inference(symmetry,[status(thm)],[4872]) ).
tff(4874,plain,
store(select(q18,seq),s(s(s(select(queue_298,head)))),e18) = store(earray_71,index_72,e18),
inference(monotonicity,[status(thm)],[4873,4869]) ).
tff(4875,plain,
store(select(q18,seq),s(s(s(select(queue_298,head)))),e18) = select(q19,seq),
inference(transitivity,[status(thm)],[4874,4863,1908,4862,1915]) ).
tff(4876,plain,
select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q19,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4875]) ).
tff(4877,plain,
s(s(s(select(queue_298,head)))) = s(s(s(index_299))),
inference(symmetry,[status(thm)],[4596]) ).
tff(4878,plain,
( ( s(s(s(select(queue_298,head)))) = select(q50,head) )
<=> ( s(s(s(index_299))) = s(index_299) ) ),
inference(monotonicity,[status(thm)],[4877,149]) ).
tff(4879,plain,
( ( s(s(s(index_299))) = s(index_299) )
<=> ( s(s(s(select(queue_298,head)))) = select(q50,head) ) ),
inference(symmetry,[status(thm)],[4878]) ).
tff(4880,plain,
( ( s(s(s(index_299))) != s(index_299) )
<=> ( s(s(s(select(queue_298,head)))) != select(q50,head) ) ),
inference(monotonicity,[status(thm)],[4879]) ).
tff(4881,plain,
^ [X: $i] :
refl(( ( s(s(X)) != X )
<=> ( s(s(X)) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4882,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(quant_intro,[status(thm)],[4881]) ).
tff(4883,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4884,axiom,
! [X: $i] : ( s(s(X)) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as2) ).
tff(4885,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[4884,4883]) ).
tff(4886,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(skolemize,[status(sab)],[4885]) ).
tff(4887,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[4886,4882]) ).
tff(4888,plain,
( ~ ! [X: $i] : ( s(s(X)) != X )
| ( s(s(s(index_299))) != s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4889,plain,
s(s(s(index_299))) != s(index_299),
inference(unit_resolution,[status(thm)],[4888,4887]) ).
tff(4890,plain,
s(s(s(select(queue_298,head)))) != select(q50,head),
inference(modus_ponens,[status(thm)],[4889,4880]) ).
tff(4891,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_298,head)))) = select(q50,head) )
| ( select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_298,head)))) = select(q50,head) )
| ( select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4892,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_298,head)))) = select(q50,head) )
| ( select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4893,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_298,head)))) = select(q50,head) )
| ( select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4892,4891]) ).
tff(4894,plain,
( ( s(s(s(select(queue_298,head)))) = select(q50,head) )
| ( select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4893,32]) ).
tff(4895,plain,
select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)) = select(select(q18,seq),select(q50,head)),
inference(unit_resolution,[status(thm)],[4894,4890]) ).
tff(4896,plain,
select(select(q18,seq),select(q50,head)) = select(store(select(q18,seq),s(s(s(select(queue_298,head)))),e18),select(q50,head)),
inference(symmetry,[status(thm)],[4895]) ).
tff(4897,plain,
select(store(queue_65,tail,index_66),seq) = select(store(store(queue_65,tail,index_66),head,s(index_68)),seq),
inference(symmetry,[status(thm)],[1986]) ).
tff(4898,plain,
select(store(q17,seq,earray_64),seq) = select(store(store(q17,seq,earray_64),tail,s(index_63)),seq),
inference(symmetry,[status(thm)],[1980]) ).
tff(4899,plain,
store(earray_62,index_63,e17) = select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq),
inference(symmetry,[status(thm)],[1964]) ).
tff(4900,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = select(q17,tail),
inference(symmetry,[status(thm)],[3763]) ).
tff(4901,plain,
s(index_57) = select(store(store(q16,seq,earray_58),tail,s(index_57)),tail),
inference(symmetry,[status(thm)],[3760]) ).
tff(4902,plain,
s(s(select(q15,tail))) = s(index_57),
inference(symmetry,[status(thm)],[4568]) ).
tff(4903,plain,
s(s(select(queue_298,head))) = s(s(select(q15,tail))),
inference(symmetry,[status(thm)],[4565]) ).
tff(4904,plain,
s(s(select(queue_298,head))) = index_63,
inference(transitivity,[status(thm)],[4903,4902,4901,4900,3740]) ).
tff(4905,plain,
( ( earray_62 = select(q17,seq) )
<=> ( earray_62 = select(q17,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4906,axiom,
earray_62 = select(q17,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(4907,plain,
earray_62 = select(q17,seq),
inference(modus_ponens,[status(thm)],[4906,4905]) ).
tff(4908,plain,
select(q17,seq) = earray_62,
inference(symmetry,[status(thm)],[4907]) ).
tff(4909,plain,
store(select(q17,seq),s(s(select(queue_298,head))),e17) = store(earray_62,index_63,e17),
inference(monotonicity,[status(thm)],[4908,4904]) ).
tff(4910,plain,
store(select(q17,seq),s(s(select(queue_298,head))),e17) = select(q18,seq),
inference(transitivity,[status(thm)],[4909,4899,1975,4898,1981,4897,1988]) ).
tff(4911,plain,
select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q18,seq),select(q50,head)),
inference(monotonicity,[status(thm)],[4910]) ).
tff(4912,plain,
select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = elem_352,
inference(transitivity,[status(thm)],[4911,4896,4876,4861,4841,4828,4808,4794,4774,4759,4739,4726,4706,4692,4672,4657,4637,4624,4595,4558,4536,4526,4504,4494,4472,4461,4439,4429,4407,4397,4375,4364,4342,4332,4310,4300,4278,4267,4245,4235,4213,4203,4181,4170,4148,4138,4116,4106,4084,4073,4051,4041,4019,4009,3987,3976,3954,3944,3922,3912,3890,3879,3857,3847,3207,3178]) ).
tff(4913,plain,
( ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) )
<=> ( elem_352 = e16 ) ),
inference(monotonicity,[status(thm)],[4912,3174]) ).
tff(4914,plain,
( ( elem_352 = e16 )
<=> ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) ),
inference(symmetry,[status(thm)],[4913]) ).
tff(4915,plain,
( ( elem_352 != e16 )
<=> ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) != select(select(q17,seq),select(q50,head)) ) ),
inference(monotonicity,[status(thm)],[4914]) ).
tff(4916,plain,
( ( elem_352 != e16 )
<=> ( elem_352 != e16 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4917,axiom,
elem_352 != e16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(4918,plain,
elem_352 != e16,
inference(modus_ponens,[status(thm)],[4917,4916]) ).
tff(4919,plain,
select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) != select(select(q17,seq),select(q50,head)),
inference(modus_ponens,[status(thm)],[4918,4915]) ).
tff(4920,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_298,head))) = select(q50,head) )
| ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_298,head))) = select(q50,head) )
| ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4921,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_298,head))) = select(q50,head) )
| ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4922,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_298,head))) = select(q50,head) )
| ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) ),
inference(modus_ponens,[status(thm)],[4921,4920]) ).
tff(4923,plain,
( ( s(s(select(queue_298,head))) = select(q50,head) )
| ( select(store(select(q17,seq),s(s(select(queue_298,head))),e17),select(q50,head)) = select(select(q17,seq),select(q50,head)) ) ),
inference(unit_resolution,[status(thm)],[4922,32]) ).
tff(4924,plain,
$false,
inference(unit_resolution,[status(thm)],[4923,4919,170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV569-1.050 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 10:24:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 14.01/14.19 % SZS status Unsatisfiable
% 14.01/14.19 % SZS output start Proof
% See solution above
% 14.40/14.60 % E exiting
%------------------------------------------------------------------------------