%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV568-1.050 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:35:38 AM UTC 2025
% Result : Unsatisfiable 1.31s 1.52s
% Output : Proof 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 83
% Number of leaves : 1269
% Syntax : Number of formulae : 4184 (3175 unt; 0 typ; 0 def)
% Number of atoms : 5609 (5567 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 2347 ( 963 ~; 733 |; 0 &)
% ( 651 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 35 ( 4 avg)
% Number of FOOLs : 41 ( 41 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 : 464 ( 464 usr; 455 con; 0-3 aty)
% Number of variables : 1585 (1536 !; 0 ?;1585 :)
% Comments :
%------------------------------------------------------------------------------
tff(rselect_head_type,type,
rselect_head: $i > $i ).
tff(rstore_seq_type,type,
rstore_seq: ( $i * $i ) > $i ).
tff(earray_304_type,type,
earray_304: $i ).
tff(q48_type,type,
q48: $i ).
tff(rselect_tail_type,type,
rselect_tail: $i > $i ).
tff(q17_type,type,
q17: $i ).
tff(q16_type,type,
q16: $i ).
tff(s_type,type,
s: $i > $i ).
tff(rstore_tail_type,type,
rstore_tail: ( $i * $i ) > $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(queue_277_type,type,
queue_277: $i ).
tff(index_278_type,type,
index_278: $i ).
tff(queue_256_type,type,
queue_256: $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_276_type,type,
index_276: $i ).
tff(queue_275_type,type,
queue_275: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e44_type,type,
e44: $i ).
tff(earray_272_type,type,
earray_272: $i ).
tff(index_270_type,type,
index_270: $i ).
tff(queue_269_type,type,
queue_269: $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(e43_type,type,
e43: $i ).
tff(earray_266_type,type,
earray_266: $i ).
tff(index_264_type,type,
index_264: $i ).
tff(queue_263_type,type,
queue_263: $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(e42_type,type,
e42: $i ).
tff(earray_260_type,type,
earray_260: $i ).
tff(rstore_head_type,type,
rstore_head: ( $i * $i ) > $i ).
tff(index_258_type,type,
index_258: $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(index_42_type,type,
index_42: $i ).
tff(queue_229_type,type,
queue_229: $i ).
tff(index_252_type,type,
index_252: $i ).
tff(earray_253_type,type,
earray_253: $i ).
tff(q41_type,type,
q41: $i ).
tff(e41_type,type,
e41: $i ).
tff(earray_251_type,type,
earray_251: $i ).
tff(index_249_type,type,
index_249: $i ).
tff(queue_248_type,type,
queue_248: $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(e40_type,type,
e40: $i ).
tff(earray_245_type,type,
earray_245: $i ).
tff(index_243_type,type,
index_243: $i ).
tff(queue_242_type,type,
queue_242: $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(e39_type,type,
e39: $i ).
tff(earray_239_type,type,
earray_239: $i ).
tff(index_231_type,type,
index_231: $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(index_36_type,type,
index_36: $i ).
tff(queue_208_type,type,
queue_208: $i ).
tff(index_225_type,type,
index_225: $i ).
tff(earray_226_type,type,
earray_226: $i ).
tff(q38_type,type,
q38: $i ).
tff(e38_type,type,
e38: $i ).
tff(earray_224_type,type,
earray_224: $i ).
tff(index_222_type,type,
index_222: $i ).
tff(queue_221_type,type,
queue_221: $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(e37_type,type,
e37: $i ).
tff(earray_218_type,type,
earray_218: $i ).
tff(index_216_type,type,
index_216: $i ).
tff(queue_215_type,type,
queue_215: $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(e36_type,type,
e36: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(index_210_type,type,
index_210: $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(index_30_type,type,
index_30: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(earray_205_type,type,
earray_205: $i ).
tff(q35_type,type,
q35: $i ).
tff(e35_type,type,
e35: $i ).
tff(earray_203_type,type,
earray_203: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(queue_200_type,type,
queue_200: $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(e34_type,type,
e34: $i ).
tff(earray_197_type,type,
earray_197: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(queue_194_type,type,
queue_194: $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(e33_type,type,
e33: $i ).
tff(earray_191_type,type,
earray_191: $i ).
tff(index_189_type,type,
index_189: $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(index_21_type,type,
index_21: $i ).
tff(queue_166_type,type,
queue_166: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(q32_type,type,
q32: $i ).
tff(e32_type,type,
e32: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $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(e31_type,type,
e31: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $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(e30_type,type,
e30: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(index_168_type,type,
index_168: $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(index_15_type,type,
index_15: $i ).
tff(queue_136_type,type,
queue_136: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(earray_163_type,type,
earray_163: $i ).
tff(q29_type,type,
q29: $i ).
tff(e29_type,type,
e29: $i ).
tff(earray_161_type,type,
earray_161: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $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(e28_type,type,
e28: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $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(e27_type,type,
e27: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(index_138_type,type,
index_138: $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(index_9_type,type,
index_9: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(earray_133_type,type,
earray_133: $i ).
tff(q26_type,type,
q26: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_131_type,type,
earray_131: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(queue_128_type,type,
queue_128: $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(e25_type,type,
e25: $i ).
tff(earray_125_type,type,
earray_125: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(queue_122_type,type,
queue_122: $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(e24_type,type,
e24: $i ).
tff(earray_119_type,type,
earray_119: $i ).
tff(index_117_type,type,
index_117: $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(index_342_type,type,
index_342: $i ).
tff(queue_94_type,type,
queue_94: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(q23_type,type,
q23: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $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(e22_type,type,
e22: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $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(e21_type,type,
e21: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(index_96_type,type,
index_96: $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(index_336_type,type,
index_336: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(earray_91_type,type,
earray_91: $i ).
tff(q20_type,type,
q20: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_89_type,type,
earray_89: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(queue_86_type,type,
queue_86: $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(e19_type,type,
e19: $i ).
tff(earray_83_type,type,
earray_83: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(queue_74_type,type,
queue_74: $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(e18_type,type,
e18: $i ).
tff(earray_71_type,type,
earray_71: $i ).
tff(index_69_type,type,
index_69: $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(index_330_type,type,
index_330: $i ).
tff(queue_46_type,type,
queue_46: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(e17_type,type,
e17: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $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(e16_type,type,
e16: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_50_type,type,
earray_50: $i ).
tff(index_48_type,type,
index_48: $i ).
tff(queue_49_type,type,
queue_49: $i ).
tff(index_47_type,type,
index_47: $i ).
tff(index_45_type,type,
index_45: $i ).
tff(queue_44_type,type,
queue_44: $i ).
tff(index_321_type,type,
index_321: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(earray_43_type,type,
earray_43: $i ).
tff(q14_type,type,
q14: $i ).
tff(e14_type,type,
e14: $i ).
tff(earray_41_type,type,
earray_41: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(queue_38_type,type,
queue_38: $i ).
tff(queue_40_type,type,
queue_40: $i ).
tff(earray_37_type,type,
earray_37: $i ).
tff(q13_type,type,
q13: $i ).
tff(e13_type,type,
e13: $i ).
tff(earray_35_type,type,
earray_35: $i ).
tff(index_33_type,type,
index_33: $i ).
tff(queue_32_type,type,
queue_32: $i ).
tff(queue_34_type,type,
queue_34: $i ).
tff(earray_31_type,type,
earray_31: $i ).
tff(q12_type,type,
q12: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_29_type,type,
earray_29: $i ).
tff(index_27_type,type,
index_27: $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(index_309_type,type,
index_309: $i ).
tff(queue_346_type,type,
queue_346: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(q11_type,type,
q11: $i ).
tff(e11_type,type,
e11: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(q10_type,type,
q10: $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(q9_type,type,
q9: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(index_348_type,type,
index_348: $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(index_234_type,type,
index_234: $i ).
tff(queue_325_type,type,
queue_325: $i ).
tff(earray_343_type,type,
earray_343: $i ).
tff(q8_type,type,
q8: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_341_type,type,
earray_341: $i ).
tff(index_339_type,type,
index_339: $i ).
tff(queue_338_type,type,
queue_338: $i ).
tff(queue_340_type,type,
queue_340: $i ).
tff(earray_337_type,type,
earray_337: $i ).
tff(q7_type,type,
q7: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_335_type,type,
earray_335: $i ).
tff(index_333_type,type,
index_333: $i ).
tff(queue_332_type,type,
queue_332: $i ).
tff(queue_334_type,type,
queue_334: $i ).
tff(earray_331_type,type,
earray_331: $i ).
tff(q6_type,type,
q6: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_329_type,type,
earray_329: $i ).
tff(index_327_type,type,
index_327: $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(index_153_type,type,
index_153: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(earray_322_type,type,
earray_322: $i ).
tff(q5_type,type,
q5: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_320_type,type,
earray_320: $i ).
tff(index_312_type,type,
index_312: $i ).
tff(queue_311_type,type,
queue_311: $i ).
tff(queue_313_type,type,
queue_313: $i ).
tff(earray_310_type,type,
earray_310: $i ).
tff(q4_type,type,
q4: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_308_type,type,
earray_308: $i ).
tff(index_237_type,type,
index_237: $i ).
tff(queue_236_type,type,
queue_236: $i ).
tff(queue_238_type,type,
queue_238: $i ).
tff(earray_235_type,type,
earray_235: $i ).
tff(q3_type,type,
q3: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_233_type,type,
earray_233: $i ).
tff(index_159_type,type,
index_159: $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_78_type,type,
index_78: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(q2_type,type,
q2: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(queue_80_type,type,
queue_80: $i ).
tff(queue_82_type,type,
queue_82: $i ).
tff(earray_79_type,type,
earray_79: $i ).
tff(q1_type,type,
q1: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_77_type,type,
earray_77: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(q0_type,type,
q0: $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(q_type,type,
q: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(index_299_type,type,
index_299: $i ).
tff(queue_298_type,type,
queue_298: $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_297_type,type,
index_297: $i ).
tff(queue_296_type,type,
queue_296: $i ).
tff(e47_type,type,
e47: $i ).
tff(earray_293_type,type,
earray_293: $i ).
tff(index_291_type,type,
index_291: $i ).
tff(queue_290_type,type,
queue_290: $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(e46_type,type,
e46: $i ).
tff(earray_287_type,type,
earray_287: $i ).
tff(index_285_type,type,
index_285: $i ).
tff(queue_284_type,type,
queue_284: $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(e45_type,type,
e45: $i ).
tff(earray_281_type,type,
earray_281: $i ).
tff(index_279_type,type,
index_279: $i ).
tff(queue_280_type,type,
queue_280: $i ).
tff(index_300_type,type,
index_300: $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(select_type,type,
select: ( $i * $i ) > $i ).
tff(elem_352_type,type,
elem_352: $i ).
tff(rselect_seq_type,type,
rselect_seq: $i > $i ).
tff(index_351_type,type,
index_351: $i ).
tff(earray_350_type,type,
earray_350: $i ).
tff(e49_type,type,
e49: $i ).
tff(q49_type,type,
q49: $i ).
tff(q50_type,type,
q50: $i ).
tff(index_315_type,type,
index_315: $i ).
tff(earray_316_type,type,
earray_316: $i ).
tff(index_318_type,type,
index_318: $i ).
tff(queue_317_type,type,
queue_317: $i ).
tff(queue_319_type,type,
queue_319: $i ).
tff(earray_314_type,type,
earray_314: $i ).
tff(index_306_type,type,
index_306: $i ).
tff(queue_305_type,type,
queue_305: $i ).
tff(queue_307_type,type,
queue_307: $i ).
tff(1,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(3,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( queue_53 = rstore_seq(q15,earray_52) )
<=> ( queue_53 = rstore_seq(q15,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
queue_53 = rstore_seq(q15,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp336) ).
tff(7,plain,
queue_53 = rstore_seq(q15,earray_52),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
rstore_seq(q15,earray_52) = queue_53,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
rstore_tail(rstore_seq(q15,earray_52),s(index_51)) = rstore_tail(queue_53,index_54),
inference(monotonicity,[status(thm)],[8,4]) ).
tff(10,plain,
rstore_tail(queue_53,index_54) = rstore_tail(rstore_seq(q15,earray_52),s(index_51)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( queue_55 = rstore_tail(queue_53,index_54) )
<=> ( queue_55 = rstore_tail(queue_53,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
queue_55 = rstore_tail(queue_53,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp337) ).
tff(13,plain,
queue_55 = rstore_tail(queue_53,index_54),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( q16 = queue_55 )
<=> ( q16 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
q16 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp361) ).
tff(16,plain,
q16 = queue_55,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
q16 = rstore_tail(rstore_seq(q15,earray_52),s(index_51)),
inference(transitivity,[status(thm)],[16,13,10]) ).
tff(18,plain,
rselect_tail(q16) = rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_tail(q16),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_tail(A,E)) = E )
<=> ( rselect_tail(rstore_tail(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_tail) ).
tff(24,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = s(index_51),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
s(index_51) = rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ( index_278 = rselect_head(queue_277) )
<=> ( index_278 = rselect_head(queue_277) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
index_278 = rselect_head(queue_277),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(32,plain,
index_278 = rselect_head(queue_277),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
rselect_head(queue_277) = index_278,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
s(rselect_head(queue_277)) = s(index_278),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
s(index_278) = s(rselect_head(queue_277)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( index_276 = s(index_273) )
<=> ( index_276 = s(index_273) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
index_276 = s(index_273),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(38,plain,
index_276 = s(index_273),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
s(index_273) = index_276,
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ( queue_275 = rstore_seq(q44,earray_274) )
<=> ( queue_275 = rstore_seq(q44,earray_274) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
queue_275 = rstore_seq(q44,earray_274),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp301) ).
tff(42,plain,
queue_275 = rstore_seq(q44,earray_274),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
rstore_seq(q44,earray_274) = queue_275,
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
rstore_tail(rstore_seq(q44,earray_274),s(index_273)) = rstore_tail(queue_275,index_276),
inference(monotonicity,[status(thm)],[43,39]) ).
tff(45,plain,
rstore_tail(queue_275,index_276) = rstore_tail(rstore_seq(q44,earray_274),s(index_273)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( ( queue_277 = rstore_tail(queue_275,index_276) )
<=> ( queue_277 = rstore_tail(queue_275,index_276) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
queue_277 = rstore_tail(queue_275,index_276),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp302) ).
tff(48,plain,
queue_277 = rstore_tail(queue_275,index_276),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
queue_277 = rstore_tail(rstore_seq(q44,earray_274),s(index_273)),
inference(transitivity,[status(thm)],[48,45]) ).
tff(50,plain,
rselect_head(queue_277) = rselect_head(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
rselect_head(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_head(queue_277),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_tail) ).
tff(56,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_head(rstore_seq(q44,earray_274)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
rselect_head(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_head(rstore_seq(q44,earray_274)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
rselect_head(rstore_seq(q44,earray_274)) = rselect_head(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ( earray_274 = store(earray_272,index_273,e44) )
<=> ( earray_274 = store(earray_272,index_273,e44) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
earray_274 = store(earray_272,index_273,e44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(64,plain,
earray_274 = store(earray_272,index_273,e44),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
store(earray_272,index_273,e44) = earray_274,
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ( q44 = queue_271 )
<=> ( q44 = queue_271 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
q44 = queue_271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp392) ).
tff(68,plain,
q44 = queue_271,
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
queue_271 = q44,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( queue_271 = rstore_tail(queue_269,index_270) )
<=> ( queue_271 = rstore_tail(queue_269,index_270) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
queue_271 = rstore_tail(queue_269,index_270),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp300) ).
tff(72,plain,
queue_271 = rstore_tail(queue_269,index_270),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
rstore_tail(queue_269,index_270) = queue_271,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
rstore_tail(queue_269,index_270) = q44,
inference(transitivity,[status(thm)],[73,69]) ).
tff(75,plain,
rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44)) = rstore_seq(q44,earray_274),
inference(monotonicity,[status(thm)],[74,65]) ).
tff(76,plain,
rstore_seq(q44,earray_274) = rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
rselect_head(rstore_seq(q44,earray_274)) = rselect_head(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
rselect_head(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = rselect_head(rstore_seq(q44,earray_274)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_seq) ).
tff(83,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = rselect_head(rstore_tail(queue_269,index_270)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
rselect_head(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = rselect_head(rstore_tail(queue_269,index_270)),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
rselect_head(rstore_tail(queue_269,index_270)) = rselect_head(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ( index_270 = s(index_267) )
<=> ( index_270 = s(index_267) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
index_270 = s(index_267),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(91,plain,
index_270 = s(index_267),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
s(index_267) = index_270,
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ( queue_269 = rstore_seq(q43,earray_268) )
<=> ( queue_269 = rstore_seq(q43,earray_268) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
queue_269 = rstore_seq(q43,earray_268),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp299) ).
tff(95,plain,
queue_269 = rstore_seq(q43,earray_268),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
rstore_seq(q43,earray_268) = queue_269,
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
rstore_tail(rstore_seq(q43,earray_268),s(index_267)) = rstore_tail(queue_269,index_270),
inference(monotonicity,[status(thm)],[96,92]) ).
tff(98,plain,
rstore_tail(queue_269,index_270) = rstore_tail(rstore_seq(q43,earray_268),s(index_267)),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
rselect_head(rstore_tail(queue_269,index_270)) = rselect_head(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
rselect_head(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_head(rstore_tail(queue_269,index_270)),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_head(rstore_seq(q43,earray_268)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
rselect_head(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_head(rstore_seq(q43,earray_268)),
inference(unit_resolution,[status(thm)],[101,58]) ).
tff(103,plain,
rselect_head(rstore_seq(q43,earray_268)) = rselect_head(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ( earray_268 = store(earray_266,index_267,e43) )
<=> ( earray_268 = store(earray_266,index_267,e43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,axiom,
earray_268 = store(earray_266,index_267,e43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(106,plain,
earray_268 = store(earray_266,index_267,e43),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
store(earray_266,index_267,e43) = earray_268,
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ( q43 = queue_265 )
<=> ( q43 = queue_265 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
q43 = queue_265,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp391) ).
tff(110,plain,
q43 = queue_265,
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
queue_265 = q43,
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ( queue_265 = rstore_tail(queue_263,index_264) )
<=> ( queue_265 = rstore_tail(queue_263,index_264) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
queue_265 = rstore_tail(queue_263,index_264),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp298) ).
tff(114,plain,
queue_265 = rstore_tail(queue_263,index_264),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
rstore_tail(queue_263,index_264) = queue_265,
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
rstore_tail(queue_263,index_264) = q43,
inference(transitivity,[status(thm)],[115,111]) ).
tff(117,plain,
rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43)) = rstore_seq(q43,earray_268),
inference(monotonicity,[status(thm)],[116,107]) ).
tff(118,plain,
rstore_seq(q43,earray_268) = rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
rselect_head(rstore_seq(q43,earray_268)) = rselect_head(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
rselect_head(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = rselect_head(rstore_seq(q43,earray_268)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = rselect_head(rstore_tail(queue_263,index_264)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
rselect_head(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = rselect_head(rstore_tail(queue_263,index_264)),
inference(unit_resolution,[status(thm)],[121,85]) ).
tff(123,plain,
rselect_head(rstore_tail(queue_263,index_264)) = rselect_head(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ( index_264 = s(index_261) )
<=> ( index_264 = s(index_261) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
index_264 = s(index_261),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(126,plain,
index_264 = s(index_261),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
s(index_261) = index_264,
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
( ( queue_263 = rstore_seq(q42,earray_262) )
<=> ( queue_263 = rstore_seq(q42,earray_262) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
queue_263 = rstore_seq(q42,earray_262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp297) ).
tff(130,plain,
queue_263 = rstore_seq(q42,earray_262),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
rstore_seq(q42,earray_262) = queue_263,
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
rstore_tail(rstore_seq(q42,earray_262),s(index_261)) = rstore_tail(queue_263,index_264),
inference(monotonicity,[status(thm)],[131,127]) ).
tff(133,plain,
rstore_tail(queue_263,index_264) = rstore_tail(rstore_seq(q42,earray_262),s(index_261)),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
rselect_head(rstore_tail(queue_263,index_264)) = rselect_head(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
rselect_head(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_head(rstore_tail(queue_263,index_264)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_head(rstore_seq(q42,earray_262)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
rselect_head(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_head(rstore_seq(q42,earray_262)),
inference(unit_resolution,[status(thm)],[136,58]) ).
tff(138,plain,
rselect_head(rstore_seq(q42,earray_262)) = rselect_head(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ( earray_262 = store(earray_260,index_261,e42) )
<=> ( earray_262 = store(earray_260,index_261,e42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
earray_262 = store(earray_260,index_261,e42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(141,plain,
earray_262 = store(earray_260,index_261,e42),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
store(earray_260,index_261,e42) = earray_262,
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ( q42 = queue_259 )
<=> ( q42 = queue_259 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
q42 = queue_259,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp390) ).
tff(145,plain,
q42 = queue_259,
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
queue_259 = q42,
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ( queue_259 = rstore_head(queue_256,index_258) )
<=> ( queue_259 = rstore_head(queue_256,index_258) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
queue_259 = rstore_head(queue_256,index_258),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp296) ).
tff(149,plain,
queue_259 = rstore_head(queue_256,index_258),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
rstore_head(queue_256,index_258) = queue_259,
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
rstore_head(queue_256,index_258) = q42,
inference(transitivity,[status(thm)],[150,146]) ).
tff(152,plain,
rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42)) = rstore_seq(q42,earray_262),
inference(monotonicity,[status(thm)],[151,142]) ).
tff(153,plain,
rselect_head(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = rselect_head(rstore_seq(q42,earray_262)),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = rselect_head(rstore_head(queue_256,index_258)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
rselect_head(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = rselect_head(rstore_head(queue_256,index_258)),
inference(unit_resolution,[status(thm)],[154,85]) ).
tff(156,plain,
rselect_head(rstore_head(queue_256,index_258)) = rselect_head(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
( ( index_258 = s(index_257) )
<=> ( index_258 = s(index_257) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
index_258 = s(index_257),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(159,plain,
index_258 = s(index_257),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
s(index_257) = index_258,
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ( queue_256 = rstore_tail(queue_254,index_255) )
<=> ( queue_256 = rstore_tail(queue_254,index_255) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
queue_256 = rstore_tail(queue_254,index_255),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp295) ).
tff(163,plain,
queue_256 = rstore_tail(queue_254,index_255),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
rstore_tail(queue_254,index_255) = queue_256,
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
rstore_head(rstore_tail(queue_254,index_255),s(index_257)) = rstore_head(queue_256,index_258),
inference(monotonicity,[status(thm)],[164,160]) ).
tff(166,plain,
rselect_head(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_head(rstore_head(queue_256,index_258)),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_head(A,E)) = E )
<=> ( rselect_head(rstore_head(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(168,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[167]) ).
tff(169,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_head) ).
tff(171,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(skolemize,[status(sab)],[171]) ).
tff(173,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[172,168]) ).
tff(174,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = s(index_257) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
rselect_head(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = s(index_257),
inference(unit_resolution,[status(thm)],[174,173]) ).
tff(176,plain,
s(index_257) = rselect_head(rstore_head(rstore_tail(queue_254,index_255),s(index_257))),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ( index_257 = rselect_head(queue_256) )
<=> ( index_257 = rselect_head(queue_256) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
index_257 = rselect_head(queue_256),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(179,plain,
index_257 = rselect_head(queue_256),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
rselect_head(queue_256) = index_257,
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
s(rselect_head(queue_256)) = s(index_257),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
s(rselect_head(queue_256)) = index_278,
inference(transitivity,[status(thm)],[181,176,166,156,153,138,135,123,120,103,100,88,78,61,51,33]) ).
tff(183,plain,
s(s(rselect_head(queue_256))) = s(index_278),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
s(index_257) = s(rselect_head(queue_256)),
inference(symmetry,[status(thm)],[181]) ).
tff(185,plain,
( ( index_255 = s(index_252) )
<=> ( index_255 = s(index_252) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,axiom,
index_255 = s(index_252),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(187,plain,
index_255 = s(index_252),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
s(index_252) = index_255,
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ( queue_254 = rstore_seq(q41,earray_253) )
<=> ( queue_254 = rstore_seq(q41,earray_253) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,axiom,
queue_254 = rstore_seq(q41,earray_253),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp294) ).
tff(191,plain,
queue_254 = rstore_seq(q41,earray_253),
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
rstore_seq(q41,earray_253) = queue_254,
inference(symmetry,[status(thm)],[191]) ).
tff(193,plain,
rstore_tail(rstore_seq(q41,earray_253),s(index_252)) = rstore_tail(queue_254,index_255),
inference(monotonicity,[status(thm)],[192,188]) ).
tff(194,plain,
rstore_tail(queue_254,index_255) = rstore_tail(rstore_seq(q41,earray_253),s(index_252)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
queue_256 = rstore_tail(rstore_seq(q41,earray_253),s(index_252)),
inference(transitivity,[status(thm)],[163,194]) ).
tff(196,plain,
rselect_head(queue_256) = rselect_head(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
rselect_head(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_head(queue_256),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_head(rstore_seq(q41,earray_253)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
rselect_head(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_head(rstore_seq(q41,earray_253)),
inference(unit_resolution,[status(thm)],[198,58]) ).
tff(200,plain,
rselect_head(rstore_seq(q41,earray_253)) = rselect_head(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ( earray_253 = store(earray_251,index_252,e41) )
<=> ( earray_253 = store(earray_251,index_252,e41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,axiom,
earray_253 = store(earray_251,index_252,e41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(203,plain,
earray_253 = store(earray_251,index_252,e41),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
store(earray_251,index_252,e41) = earray_253,
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
( ( q41 = queue_250 )
<=> ( q41 = queue_250 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,axiom,
q41 = queue_250,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp389) ).
tff(207,plain,
q41 = queue_250,
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
queue_250 = q41,
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
( ( queue_250 = rstore_tail(queue_248,index_249) )
<=> ( queue_250 = rstore_tail(queue_248,index_249) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
queue_250 = rstore_tail(queue_248,index_249),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp293) ).
tff(211,plain,
queue_250 = rstore_tail(queue_248,index_249),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
rstore_tail(queue_248,index_249) = queue_250,
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
rstore_tail(queue_248,index_249) = q41,
inference(transitivity,[status(thm)],[212,208]) ).
tff(214,plain,
rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41)) = rstore_seq(q41,earray_253),
inference(monotonicity,[status(thm)],[213,204]) ).
tff(215,plain,
rstore_seq(q41,earray_253) = rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41)),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
rselect_head(rstore_seq(q41,earray_253)) = rselect_head(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
rselect_head(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = rselect_head(rstore_seq(q41,earray_253)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = rselect_head(rstore_tail(queue_248,index_249)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
rselect_head(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = rselect_head(rstore_tail(queue_248,index_249)),
inference(unit_resolution,[status(thm)],[218,85]) ).
tff(220,plain,
rselect_head(rstore_tail(queue_248,index_249)) = rselect_head(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ( index_249 = s(index_246) )
<=> ( index_249 = s(index_246) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,axiom,
index_249 = s(index_246),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(223,plain,
index_249 = s(index_246),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
s(index_246) = index_249,
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
( ( queue_248 = rstore_seq(q40,earray_247) )
<=> ( queue_248 = rstore_seq(q40,earray_247) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,axiom,
queue_248 = rstore_seq(q40,earray_247),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp291) ).
tff(227,plain,
queue_248 = rstore_seq(q40,earray_247),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
rstore_seq(q40,earray_247) = queue_248,
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
rstore_tail(rstore_seq(q40,earray_247),s(index_246)) = rstore_tail(queue_248,index_249),
inference(monotonicity,[status(thm)],[228,224]) ).
tff(230,plain,
rstore_tail(queue_248,index_249) = rstore_tail(rstore_seq(q40,earray_247),s(index_246)),
inference(symmetry,[status(thm)],[229]) ).
tff(231,plain,
rselect_head(rstore_tail(queue_248,index_249)) = rselect_head(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(monotonicity,[status(thm)],[230]) ).
tff(232,plain,
rselect_head(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_head(rstore_tail(queue_248,index_249)),
inference(symmetry,[status(thm)],[231]) ).
tff(233,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_head(rstore_seq(q40,earray_247)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
rselect_head(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_head(rstore_seq(q40,earray_247)),
inference(unit_resolution,[status(thm)],[233,58]) ).
tff(235,plain,
rselect_head(rstore_seq(q40,earray_247)) = rselect_head(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ( earray_247 = store(earray_245,index_246,e40) )
<=> ( earray_247 = store(earray_245,index_246,e40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,axiom,
earray_247 = store(earray_245,index_246,e40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(238,plain,
earray_247 = store(earray_245,index_246,e40),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
store(earray_245,index_246,e40) = earray_247,
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ( q40 = queue_244 )
<=> ( q40 = queue_244 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,axiom,
q40 = queue_244,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp388) ).
tff(242,plain,
q40 = queue_244,
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
queue_244 = q40,
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ( queue_244 = rstore_tail(queue_242,index_243) )
<=> ( queue_244 = rstore_tail(queue_242,index_243) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
queue_244 = rstore_tail(queue_242,index_243),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp290) ).
tff(246,plain,
queue_244 = rstore_tail(queue_242,index_243),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
rstore_tail(queue_242,index_243) = queue_244,
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
rstore_tail(queue_242,index_243) = q40,
inference(transitivity,[status(thm)],[247,243]) ).
tff(249,plain,
rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40)) = rstore_seq(q40,earray_247),
inference(monotonicity,[status(thm)],[248,239]) ).
tff(250,plain,
rstore_seq(q40,earray_247) = rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40)),
inference(symmetry,[status(thm)],[249]) ).
tff(251,plain,
rselect_head(rstore_seq(q40,earray_247)) = rselect_head(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))),
inference(monotonicity,[status(thm)],[250]) ).
tff(252,plain,
rselect_head(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = rselect_head(rstore_seq(q40,earray_247)),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = rselect_head(rstore_tail(queue_242,index_243)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(254,plain,
rselect_head(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = rselect_head(rstore_tail(queue_242,index_243)),
inference(unit_resolution,[status(thm)],[253,85]) ).
tff(255,plain,
rselect_head(rstore_tail(queue_242,index_243)) = rselect_head(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
( ( index_243 = s(index_240) )
<=> ( index_243 = s(index_240) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(257,axiom,
index_243 = s(index_240),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(258,plain,
index_243 = s(index_240),
inference(modus_ponens,[status(thm)],[257,256]) ).
tff(259,plain,
s(index_240) = index_243,
inference(symmetry,[status(thm)],[258]) ).
tff(260,plain,
( ( queue_242 = rstore_seq(q39,earray_241) )
<=> ( queue_242 = rstore_seq(q39,earray_241) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(261,axiom,
queue_242 = rstore_seq(q39,earray_241),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp289) ).
tff(262,plain,
queue_242 = rstore_seq(q39,earray_241),
inference(modus_ponens,[status(thm)],[261,260]) ).
tff(263,plain,
rstore_seq(q39,earray_241) = queue_242,
inference(symmetry,[status(thm)],[262]) ).
tff(264,plain,
rstore_tail(rstore_seq(q39,earray_241),s(index_240)) = rstore_tail(queue_242,index_243),
inference(monotonicity,[status(thm)],[263,259]) ).
tff(265,plain,
rstore_tail(queue_242,index_243) = rstore_tail(rstore_seq(q39,earray_241),s(index_240)),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
rselect_head(rstore_tail(queue_242,index_243)) = rselect_head(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
rselect_head(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_head(rstore_tail(queue_242,index_243)),
inference(symmetry,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_head(rstore_seq(q39,earray_241)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
rselect_head(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_head(rstore_seq(q39,earray_241)),
inference(unit_resolution,[status(thm)],[268,58]) ).
tff(270,plain,
rselect_head(rstore_seq(q39,earray_241)) = rselect_head(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(symmetry,[status(thm)],[269]) ).
tff(271,plain,
( ( earray_241 = store(earray_239,index_240,e39) )
<=> ( earray_241 = store(earray_239,index_240,e39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(272,axiom,
earray_241 = store(earray_239,index_240,e39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(273,plain,
earray_241 = store(earray_239,index_240,e39),
inference(modus_ponens,[status(thm)],[272,271]) ).
tff(274,plain,
store(earray_239,index_240,e39) = earray_241,
inference(symmetry,[status(thm)],[273]) ).
tff(275,plain,
( ( q39 = queue_232 )
<=> ( q39 = queue_232 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(276,axiom,
q39 = queue_232,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp386) ).
tff(277,plain,
q39 = queue_232,
inference(modus_ponens,[status(thm)],[276,275]) ).
tff(278,plain,
queue_232 = q39,
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
( ( queue_232 = rstore_head(queue_229,index_231) )
<=> ( queue_232 = rstore_head(queue_229,index_231) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(280,axiom,
queue_232 = rstore_head(queue_229,index_231),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp286) ).
tff(281,plain,
queue_232 = rstore_head(queue_229,index_231),
inference(modus_ponens,[status(thm)],[280,279]) ).
tff(282,plain,
rstore_head(queue_229,index_231) = queue_232,
inference(symmetry,[status(thm)],[281]) ).
tff(283,plain,
rstore_head(queue_229,index_231) = q39,
inference(transitivity,[status(thm)],[282,278]) ).
tff(284,plain,
rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39)) = rstore_seq(q39,earray_241),
inference(monotonicity,[status(thm)],[283,274]) ).
tff(285,plain,
rselect_head(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = rselect_head(rstore_seq(q39,earray_241)),
inference(monotonicity,[status(thm)],[284]) ).
tff(286,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = rselect_head(rstore_head(queue_229,index_231)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(287,plain,
rselect_head(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = rselect_head(rstore_head(queue_229,index_231)),
inference(unit_resolution,[status(thm)],[286,85]) ).
tff(288,plain,
rselect_head(rstore_head(queue_229,index_231)) = rselect_head(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))),
inference(symmetry,[status(thm)],[287]) ).
tff(289,plain,
( ( index_231 = s(index_230) )
<=> ( index_231 = s(index_230) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
index_231 = s(index_230),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(291,plain,
index_231 = s(index_230),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
s(index_230) = index_231,
inference(symmetry,[status(thm)],[291]) ).
tff(293,plain,
( ( queue_229 = rstore_tail(queue_227,index_228) )
<=> ( queue_229 = rstore_tail(queue_227,index_228) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(294,axiom,
queue_229 = rstore_tail(queue_227,index_228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp284) ).
tff(295,plain,
queue_229 = rstore_tail(queue_227,index_228),
inference(modus_ponens,[status(thm)],[294,293]) ).
tff(296,plain,
rstore_tail(queue_227,index_228) = queue_229,
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
rstore_head(rstore_tail(queue_227,index_228),s(index_230)) = rstore_head(queue_229,index_231),
inference(monotonicity,[status(thm)],[296,292]) ).
tff(298,plain,
rselect_head(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_head(rstore_head(queue_229,index_231)),
inference(monotonicity,[status(thm)],[297]) ).
tff(299,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(300,plain,
rselect_head(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = s(index_230),
inference(unit_resolution,[status(thm)],[299,173]) ).
tff(301,plain,
s(index_230) = rselect_head(rstore_head(rstore_tail(queue_227,index_228),s(index_230))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ( index_230 = rselect_head(queue_229) )
<=> ( index_230 = rselect_head(queue_229) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(303,axiom,
index_230 = rselect_head(queue_229),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(304,plain,
index_230 = rselect_head(queue_229),
inference(modus_ponens,[status(thm)],[303,302]) ).
tff(305,plain,
rselect_head(queue_229) = index_230,
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
s(rselect_head(queue_229)) = s(index_230),
inference(monotonicity,[status(thm)],[305]) ).
tff(307,plain,
s(rselect_head(queue_229)) = index_257,
inference(transitivity,[status(thm)],[306,301,298,288,285,270,267,255,252,235,232,220,217,200,197,180]) ).
tff(308,plain,
s(s(rselect_head(queue_229))) = s(index_257),
inference(monotonicity,[status(thm)],[307]) ).
tff(309,plain,
s(index_230) = s(rselect_head(queue_229)),
inference(symmetry,[status(thm)],[306]) ).
tff(310,plain,
( ( index_228 = s(index_225) )
<=> ( index_228 = s(index_225) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(311,axiom,
index_228 = s(index_225),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(312,plain,
index_228 = s(index_225),
inference(modus_ponens,[status(thm)],[311,310]) ).
tff(313,plain,
s(index_225) = index_228,
inference(symmetry,[status(thm)],[312]) ).
tff(314,plain,
( ( queue_227 = rstore_seq(q38,earray_226) )
<=> ( queue_227 = rstore_seq(q38,earray_226) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(315,axiom,
queue_227 = rstore_seq(q38,earray_226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp283) ).
tff(316,plain,
queue_227 = rstore_seq(q38,earray_226),
inference(modus_ponens,[status(thm)],[315,314]) ).
tff(317,plain,
rstore_seq(q38,earray_226) = queue_227,
inference(symmetry,[status(thm)],[316]) ).
tff(318,plain,
rstore_tail(rstore_seq(q38,earray_226),s(index_225)) = rstore_tail(queue_227,index_228),
inference(monotonicity,[status(thm)],[317,313]) ).
tff(319,plain,
rstore_tail(queue_227,index_228) = rstore_tail(rstore_seq(q38,earray_226),s(index_225)),
inference(symmetry,[status(thm)],[318]) ).
tff(320,plain,
queue_229 = rstore_tail(rstore_seq(q38,earray_226),s(index_225)),
inference(transitivity,[status(thm)],[295,319]) ).
tff(321,plain,
rselect_head(queue_229) = rselect_head(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(monotonicity,[status(thm)],[320]) ).
tff(322,plain,
rselect_head(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_head(queue_229),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_head(rstore_seq(q38,earray_226)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
rselect_head(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_head(rstore_seq(q38,earray_226)),
inference(unit_resolution,[status(thm)],[323,58]) ).
tff(325,plain,
rselect_head(rstore_seq(q38,earray_226)) = rselect_head(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
( ( earray_226 = store(earray_224,index_225,e38) )
<=> ( earray_226 = store(earray_224,index_225,e38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(327,axiom,
earray_226 = store(earray_224,index_225,e38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp42) ).
tff(328,plain,
earray_226 = store(earray_224,index_225,e38),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
store(earray_224,index_225,e38) = earray_226,
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
( ( q38 = queue_223 )
<=> ( q38 = queue_223 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(331,axiom,
q38 = queue_223,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp385) ).
tff(332,plain,
q38 = queue_223,
inference(modus_ponens,[status(thm)],[331,330]) ).
tff(333,plain,
queue_223 = q38,
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
( ( queue_223 = rstore_tail(queue_221,index_222) )
<=> ( queue_223 = rstore_tail(queue_221,index_222) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,axiom,
queue_223 = rstore_tail(queue_221,index_222),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp282) ).
tff(336,plain,
queue_223 = rstore_tail(queue_221,index_222),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
rstore_tail(queue_221,index_222) = queue_223,
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
rstore_tail(queue_221,index_222) = q38,
inference(transitivity,[status(thm)],[337,333]) ).
tff(339,plain,
rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38)) = rstore_seq(q38,earray_226),
inference(monotonicity,[status(thm)],[338,329]) ).
tff(340,plain,
rstore_seq(q38,earray_226) = rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38)),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
rselect_head(rstore_seq(q38,earray_226)) = rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = rselect_head(rstore_seq(q38,earray_226)),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = rselect_head(rstore_tail(queue_221,index_222)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(344,plain,
rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = rselect_head(rstore_tail(queue_221,index_222)),
inference(unit_resolution,[status(thm)],[343,85]) ).
tff(345,plain,
rselect_head(rstore_tail(queue_221,index_222)) = rselect_head(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))),
inference(symmetry,[status(thm)],[344]) ).
tff(346,plain,
( ( index_222 = s(index_219) )
<=> ( index_222 = s(index_219) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(347,axiom,
index_222 = s(index_219),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(348,plain,
index_222 = s(index_219),
inference(modus_ponens,[status(thm)],[347,346]) ).
tff(349,plain,
s(index_219) = index_222,
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ( queue_221 = rstore_seq(q37,earray_220) )
<=> ( queue_221 = rstore_seq(q37,earray_220) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(351,axiom,
queue_221 = rstore_seq(q37,earray_220),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp281) ).
tff(352,plain,
queue_221 = rstore_seq(q37,earray_220),
inference(modus_ponens,[status(thm)],[351,350]) ).
tff(353,plain,
rstore_seq(q37,earray_220) = queue_221,
inference(symmetry,[status(thm)],[352]) ).
tff(354,plain,
rstore_tail(rstore_seq(q37,earray_220),s(index_219)) = rstore_tail(queue_221,index_222),
inference(monotonicity,[status(thm)],[353,349]) ).
tff(355,plain,
rstore_tail(queue_221,index_222) = rstore_tail(rstore_seq(q37,earray_220),s(index_219)),
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
rselect_head(rstore_tail(queue_221,index_222)) = rselect_head(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
rselect_head(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_head(rstore_tail(queue_221,index_222)),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_head(rstore_seq(q37,earray_220)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
rselect_head(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_head(rstore_seq(q37,earray_220)),
inference(unit_resolution,[status(thm)],[358,58]) ).
tff(360,plain,
rselect_head(rstore_seq(q37,earray_220)) = rselect_head(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
( ( earray_220 = store(earray_218,index_219,e37) )
<=> ( earray_220 = store(earray_218,index_219,e37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(362,axiom,
earray_220 = store(earray_218,index_219,e37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp40) ).
tff(363,plain,
earray_220 = store(earray_218,index_219,e37),
inference(modus_ponens,[status(thm)],[362,361]) ).
tff(364,plain,
store(earray_218,index_219,e37) = earray_220,
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
( ( q37 = queue_217 )
<=> ( q37 = queue_217 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(366,axiom,
q37 = queue_217,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp384) ).
tff(367,plain,
q37 = queue_217,
inference(modus_ponens,[status(thm)],[366,365]) ).
tff(368,plain,
queue_217 = q37,
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
( ( queue_217 = rstore_tail(queue_215,index_216) )
<=> ( queue_217 = rstore_tail(queue_215,index_216) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(370,axiom,
queue_217 = rstore_tail(queue_215,index_216),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp280) ).
tff(371,plain,
queue_217 = rstore_tail(queue_215,index_216),
inference(modus_ponens,[status(thm)],[370,369]) ).
tff(372,plain,
rstore_tail(queue_215,index_216) = queue_217,
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
rstore_tail(queue_215,index_216) = q37,
inference(transitivity,[status(thm)],[372,368]) ).
tff(374,plain,
rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37)) = rstore_seq(q37,earray_220),
inference(monotonicity,[status(thm)],[373,364]) ).
tff(375,plain,
rstore_seq(q37,earray_220) = rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37)),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
rselect_head(rstore_seq(q37,earray_220)) = rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))),
inference(monotonicity,[status(thm)],[375]) ).
tff(377,plain,
rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = rselect_head(rstore_seq(q37,earray_220)),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = rselect_head(rstore_tail(queue_215,index_216)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(379,plain,
rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = rselect_head(rstore_tail(queue_215,index_216)),
inference(unit_resolution,[status(thm)],[378,85]) ).
tff(380,plain,
rselect_head(rstore_tail(queue_215,index_216)) = rselect_head(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
( ( index_216 = s(index_213) )
<=> ( index_216 = s(index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(382,axiom,
index_216 = s(index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(383,plain,
index_216 = s(index_213),
inference(modus_ponens,[status(thm)],[382,381]) ).
tff(384,plain,
s(index_213) = index_216,
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
( ( queue_215 = rstore_seq(q36,earray_214) )
<=> ( queue_215 = rstore_seq(q36,earray_214) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(386,axiom,
queue_215 = rstore_seq(q36,earray_214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp279) ).
tff(387,plain,
queue_215 = rstore_seq(q36,earray_214),
inference(modus_ponens,[status(thm)],[386,385]) ).
tff(388,plain,
rstore_seq(q36,earray_214) = queue_215,
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
rstore_tail(rstore_seq(q36,earray_214),s(index_213)) = rstore_tail(queue_215,index_216),
inference(monotonicity,[status(thm)],[388,384]) ).
tff(390,plain,
rstore_tail(queue_215,index_216) = rstore_tail(rstore_seq(q36,earray_214),s(index_213)),
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
rselect_head(rstore_tail(queue_215,index_216)) = rselect_head(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
rselect_head(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_head(rstore_tail(queue_215,index_216)),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_head(rstore_seq(q36,earray_214)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(394,plain,
rselect_head(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_head(rstore_seq(q36,earray_214)),
inference(unit_resolution,[status(thm)],[393,58]) ).
tff(395,plain,
rselect_head(rstore_seq(q36,earray_214)) = rselect_head(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(symmetry,[status(thm)],[394]) ).
tff(396,plain,
( ( earray_214 = store(earray_212,index_213,e36) )
<=> ( earray_214 = store(earray_212,index_213,e36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(397,axiom,
earray_214 = store(earray_212,index_213,e36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp37) ).
tff(398,plain,
earray_214 = store(earray_212,index_213,e36),
inference(modus_ponens,[status(thm)],[397,396]) ).
tff(399,plain,
store(earray_212,index_213,e36) = earray_214,
inference(symmetry,[status(thm)],[398]) ).
tff(400,plain,
( ( q36 = queue_211 )
<=> ( q36 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(401,axiom,
q36 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp383) ).
tff(402,plain,
q36 = queue_211,
inference(modus_ponens,[status(thm)],[401,400]) ).
tff(403,plain,
queue_211 = q36,
inference(symmetry,[status(thm)],[402]) ).
tff(404,plain,
( ( queue_211 = rstore_head(queue_208,index_210) )
<=> ( queue_211 = rstore_head(queue_208,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(405,axiom,
queue_211 = rstore_head(queue_208,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp278) ).
tff(406,plain,
queue_211 = rstore_head(queue_208,index_210),
inference(modus_ponens,[status(thm)],[405,404]) ).
tff(407,plain,
rstore_head(queue_208,index_210) = queue_211,
inference(symmetry,[status(thm)],[406]) ).
tff(408,plain,
rstore_head(queue_208,index_210) = q36,
inference(transitivity,[status(thm)],[407,403]) ).
tff(409,plain,
rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36)) = rstore_seq(q36,earray_214),
inference(monotonicity,[status(thm)],[408,399]) ).
tff(410,plain,
rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = rselect_head(rstore_seq(q36,earray_214)),
inference(monotonicity,[status(thm)],[409]) ).
tff(411,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = rselect_head(rstore_head(queue_208,index_210)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(412,plain,
rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = rselect_head(rstore_head(queue_208,index_210)),
inference(unit_resolution,[status(thm)],[411,85]) ).
tff(413,plain,
rselect_head(rstore_head(queue_208,index_210)) = rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
( ( index_210 = s(index_209) )
<=> ( index_210 = s(index_209) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(415,axiom,
index_210 = s(index_209),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(416,plain,
index_210 = s(index_209),
inference(modus_ponens,[status(thm)],[415,414]) ).
tff(417,plain,
s(index_209) = index_210,
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ( queue_208 = rstore_tail(queue_206,index_207) )
<=> ( queue_208 = rstore_tail(queue_206,index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(419,axiom,
queue_208 = rstore_tail(queue_206,index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp277) ).
tff(420,plain,
queue_208 = rstore_tail(queue_206,index_207),
inference(modus_ponens,[status(thm)],[419,418]) ).
tff(421,plain,
rstore_tail(queue_206,index_207) = queue_208,
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
rstore_head(rstore_tail(queue_206,index_207),s(index_209)) = rstore_head(queue_208,index_210),
inference(monotonicity,[status(thm)],[421,417]) ).
tff(423,plain,
rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_head(rstore_head(queue_208,index_210)),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = s(index_209) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(425,plain,
rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = s(index_209),
inference(unit_resolution,[status(thm)],[424,173]) ).
tff(426,plain,
s(index_209) = rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
( ( index_209 = rselect_head(queue_208) )
<=> ( index_209 = rselect_head(queue_208) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(428,axiom,
index_209 = rselect_head(queue_208),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(429,plain,
index_209 = rselect_head(queue_208),
inference(modus_ponens,[status(thm)],[428,427]) ).
tff(430,plain,
rselect_head(queue_208) = index_209,
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
s(rselect_head(queue_208)) = s(index_209),
inference(monotonicity,[status(thm)],[430]) ).
tff(432,plain,
s(rselect_head(queue_208)) = index_230,
inference(transitivity,[status(thm)],[431,426,423,413,410,395,392,380,377,360,357,345,342,325,322,305]) ).
tff(433,plain,
s(s(rselect_head(queue_208))) = s(index_230),
inference(monotonicity,[status(thm)],[432]) ).
tff(434,plain,
s(index_209) = s(rselect_head(queue_208)),
inference(symmetry,[status(thm)],[431]) ).
tff(435,plain,
( ( index_207 = s(index_204) )
<=> ( index_207 = s(index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(436,axiom,
index_207 = s(index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(437,plain,
index_207 = s(index_204),
inference(modus_ponens,[status(thm)],[436,435]) ).
tff(438,plain,
s(index_204) = index_207,
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
( ( queue_206 = rstore_seq(q35,earray_205) )
<=> ( queue_206 = rstore_seq(q35,earray_205) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(440,axiom,
queue_206 = rstore_seq(q35,earray_205),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp276) ).
tff(441,plain,
queue_206 = rstore_seq(q35,earray_205),
inference(modus_ponens,[status(thm)],[440,439]) ).
tff(442,plain,
rstore_seq(q35,earray_205) = queue_206,
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
rstore_tail(rstore_seq(q35,earray_205),s(index_204)) = rstore_tail(queue_206,index_207),
inference(monotonicity,[status(thm)],[442,438]) ).
tff(444,plain,
rstore_tail(queue_206,index_207) = rstore_tail(rstore_seq(q35,earray_205),s(index_204)),
inference(symmetry,[status(thm)],[443]) ).
tff(445,plain,
queue_208 = rstore_tail(rstore_seq(q35,earray_205),s(index_204)),
inference(transitivity,[status(thm)],[420,444]) ).
tff(446,plain,
rselect_head(queue_208) = rselect_head(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(monotonicity,[status(thm)],[445]) ).
tff(447,plain,
rselect_head(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_head(queue_208),
inference(symmetry,[status(thm)],[446]) ).
tff(448,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_head(rstore_seq(q35,earray_205)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(449,plain,
rselect_head(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_head(rstore_seq(q35,earray_205)),
inference(unit_resolution,[status(thm)],[448,58]) ).
tff(450,plain,
rselect_head(rstore_seq(q35,earray_205)) = rselect_head(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ( earray_205 = store(earray_203,index_204,e35) )
<=> ( earray_205 = store(earray_203,index_204,e35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(452,axiom,
earray_205 = store(earray_203,index_204,e35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(453,plain,
earray_205 = store(earray_203,index_204,e35),
inference(modus_ponens,[status(thm)],[452,451]) ).
tff(454,plain,
store(earray_203,index_204,e35) = earray_205,
inference(symmetry,[status(thm)],[453]) ).
tff(455,plain,
( ( q35 = queue_202 )
<=> ( q35 = queue_202 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(456,axiom,
q35 = queue_202,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp382) ).
tff(457,plain,
q35 = queue_202,
inference(modus_ponens,[status(thm)],[456,455]) ).
tff(458,plain,
queue_202 = q35,
inference(symmetry,[status(thm)],[457]) ).
tff(459,plain,
( ( queue_202 = rstore_tail(queue_200,index_201) )
<=> ( queue_202 = rstore_tail(queue_200,index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(460,axiom,
queue_202 = rstore_tail(queue_200,index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp275) ).
tff(461,plain,
queue_202 = rstore_tail(queue_200,index_201),
inference(modus_ponens,[status(thm)],[460,459]) ).
tff(462,plain,
rstore_tail(queue_200,index_201) = queue_202,
inference(symmetry,[status(thm)],[461]) ).
tff(463,plain,
rstore_tail(queue_200,index_201) = q35,
inference(transitivity,[status(thm)],[462,458]) ).
tff(464,plain,
rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35)) = rstore_seq(q35,earray_205),
inference(monotonicity,[status(thm)],[463,454]) ).
tff(465,plain,
rstore_seq(q35,earray_205) = rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35)),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
rselect_head(rstore_seq(q35,earray_205)) = rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))),
inference(monotonicity,[status(thm)],[465]) ).
tff(467,plain,
rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = rselect_head(rstore_seq(q35,earray_205)),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = rselect_head(rstore_tail(queue_200,index_201)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(469,plain,
rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = rselect_head(rstore_tail(queue_200,index_201)),
inference(unit_resolution,[status(thm)],[468,85]) ).
tff(470,plain,
rselect_head(rstore_tail(queue_200,index_201)) = rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))),
inference(symmetry,[status(thm)],[469]) ).
tff(471,plain,
( ( index_201 = s(index_198) )
<=> ( index_201 = s(index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(472,axiom,
index_201 = s(index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(473,plain,
index_201 = s(index_198),
inference(modus_ponens,[status(thm)],[472,471]) ).
tff(474,plain,
s(index_198) = index_201,
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ( queue_200 = rstore_seq(q34,earray_199) )
<=> ( queue_200 = rstore_seq(q34,earray_199) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(476,axiom,
queue_200 = rstore_seq(q34,earray_199),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp274) ).
tff(477,plain,
queue_200 = rstore_seq(q34,earray_199),
inference(modus_ponens,[status(thm)],[476,475]) ).
tff(478,plain,
rstore_seq(q34,earray_199) = queue_200,
inference(symmetry,[status(thm)],[477]) ).
tff(479,plain,
rstore_tail(rstore_seq(q34,earray_199),s(index_198)) = rstore_tail(queue_200,index_201),
inference(monotonicity,[status(thm)],[478,474]) ).
tff(480,plain,
rstore_tail(queue_200,index_201) = rstore_tail(rstore_seq(q34,earray_199),s(index_198)),
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
rselect_head(rstore_tail(queue_200,index_201)) = rselect_head(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(monotonicity,[status(thm)],[480]) ).
tff(482,plain,
rselect_head(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_head(rstore_tail(queue_200,index_201)),
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_head(rstore_seq(q34,earray_199)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(484,plain,
rselect_head(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_head(rstore_seq(q34,earray_199)),
inference(unit_resolution,[status(thm)],[483,58]) ).
tff(485,plain,
rselect_head(rstore_seq(q34,earray_199)) = rselect_head(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
( ( earray_199 = store(earray_197,index_198,e34) )
<=> ( earray_199 = store(earray_197,index_198,e34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(487,axiom,
earray_199 = store(earray_197,index_198,e34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(488,plain,
earray_199 = store(earray_197,index_198,e34),
inference(modus_ponens,[status(thm)],[487,486]) ).
tff(489,plain,
store(earray_197,index_198,e34) = earray_199,
inference(symmetry,[status(thm)],[488]) ).
tff(490,plain,
( ( q34 = queue_196 )
<=> ( q34 = queue_196 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(491,axiom,
q34 = queue_196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp381) ).
tff(492,plain,
q34 = queue_196,
inference(modus_ponens,[status(thm)],[491,490]) ).
tff(493,plain,
queue_196 = q34,
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ( queue_196 = rstore_tail(queue_194,index_195) )
<=> ( queue_196 = rstore_tail(queue_194,index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(495,axiom,
queue_196 = rstore_tail(queue_194,index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp273) ).
tff(496,plain,
queue_196 = rstore_tail(queue_194,index_195),
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
rstore_tail(queue_194,index_195) = queue_196,
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
rstore_tail(queue_194,index_195) = q34,
inference(transitivity,[status(thm)],[497,493]) ).
tff(499,plain,
rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34)) = rstore_seq(q34,earray_199),
inference(monotonicity,[status(thm)],[498,489]) ).
tff(500,plain,
rstore_seq(q34,earray_199) = rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34)),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
rselect_head(rstore_seq(q34,earray_199)) = rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))),
inference(monotonicity,[status(thm)],[500]) ).
tff(502,plain,
rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = rselect_head(rstore_seq(q34,earray_199)),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = rselect_head(rstore_tail(queue_194,index_195)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(504,plain,
rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = rselect_head(rstore_tail(queue_194,index_195)),
inference(unit_resolution,[status(thm)],[503,85]) ).
tff(505,plain,
rselect_head(rstore_tail(queue_194,index_195)) = rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))),
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
( ( index_195 = s(index_192) )
<=> ( index_195 = s(index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(507,axiom,
index_195 = s(index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(508,plain,
index_195 = s(index_192),
inference(modus_ponens,[status(thm)],[507,506]) ).
tff(509,plain,
s(index_192) = index_195,
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
( ( queue_194 = rstore_seq(q33,earray_193) )
<=> ( queue_194 = rstore_seq(q33,earray_193) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(511,axiom,
queue_194 = rstore_seq(q33,earray_193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp272) ).
tff(512,plain,
queue_194 = rstore_seq(q33,earray_193),
inference(modus_ponens,[status(thm)],[511,510]) ).
tff(513,plain,
rstore_seq(q33,earray_193) = queue_194,
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
rstore_tail(rstore_seq(q33,earray_193),s(index_192)) = rstore_tail(queue_194,index_195),
inference(monotonicity,[status(thm)],[513,509]) ).
tff(515,plain,
rstore_tail(queue_194,index_195) = rstore_tail(rstore_seq(q33,earray_193),s(index_192)),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
rselect_head(rstore_tail(queue_194,index_195)) = rselect_head(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(monotonicity,[status(thm)],[515]) ).
tff(517,plain,
rselect_head(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_head(rstore_tail(queue_194,index_195)),
inference(symmetry,[status(thm)],[516]) ).
tff(518,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_head(rstore_seq(q33,earray_193)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(519,plain,
rselect_head(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_head(rstore_seq(q33,earray_193)),
inference(unit_resolution,[status(thm)],[518,58]) ).
tff(520,plain,
rselect_head(rstore_seq(q33,earray_193)) = rselect_head(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(symmetry,[status(thm)],[519]) ).
tff(521,plain,
( ( earray_193 = store(earray_191,index_192,e33) )
<=> ( earray_193 = store(earray_191,index_192,e33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(522,axiom,
earray_193 = store(earray_191,index_192,e33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(523,plain,
earray_193 = store(earray_191,index_192,e33),
inference(modus_ponens,[status(thm)],[522,521]) ).
tff(524,plain,
store(earray_191,index_192,e33) = earray_193,
inference(symmetry,[status(thm)],[523]) ).
tff(525,plain,
( ( q33 = queue_190 )
<=> ( q33 = queue_190 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(526,axiom,
q33 = queue_190,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp380) ).
tff(527,plain,
q33 = queue_190,
inference(modus_ponens,[status(thm)],[526,525]) ).
tff(528,plain,
queue_190 = q33,
inference(symmetry,[status(thm)],[527]) ).
tff(529,plain,
( ( queue_190 = rstore_head(queue_187,index_189) )
<=> ( queue_190 = rstore_head(queue_187,index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(530,axiom,
queue_190 = rstore_head(queue_187,index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp271) ).
tff(531,plain,
queue_190 = rstore_head(queue_187,index_189),
inference(modus_ponens,[status(thm)],[530,529]) ).
tff(532,plain,
rstore_head(queue_187,index_189) = queue_190,
inference(symmetry,[status(thm)],[531]) ).
tff(533,plain,
rstore_head(queue_187,index_189) = q33,
inference(transitivity,[status(thm)],[532,528]) ).
tff(534,plain,
rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33)) = rstore_seq(q33,earray_193),
inference(monotonicity,[status(thm)],[533,524]) ).
tff(535,plain,
rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = rselect_head(rstore_seq(q33,earray_193)),
inference(monotonicity,[status(thm)],[534]) ).
tff(536,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = rselect_head(rstore_head(queue_187,index_189)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(537,plain,
rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = rselect_head(rstore_head(queue_187,index_189)),
inference(unit_resolution,[status(thm)],[536,85]) ).
tff(538,plain,
rselect_head(rstore_head(queue_187,index_189)) = rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))),
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
( ( index_189 = s(index_188) )
<=> ( index_189 = s(index_188) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(540,axiom,
index_189 = s(index_188),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(541,plain,
index_189 = s(index_188),
inference(modus_ponens,[status(thm)],[540,539]) ).
tff(542,plain,
s(index_188) = index_189,
inference(symmetry,[status(thm)],[541]) ).
tff(543,plain,
( ( queue_187 = rstore_tail(queue_185,index_186) )
<=> ( queue_187 = rstore_tail(queue_185,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(544,axiom,
queue_187 = rstore_tail(queue_185,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp269) ).
tff(545,plain,
queue_187 = rstore_tail(queue_185,index_186),
inference(modus_ponens,[status(thm)],[544,543]) ).
tff(546,plain,
rstore_tail(queue_185,index_186) = queue_187,
inference(symmetry,[status(thm)],[545]) ).
tff(547,plain,
rstore_head(rstore_tail(queue_185,index_186),s(index_188)) = rstore_head(queue_187,index_189),
inference(monotonicity,[status(thm)],[546,542]) ).
tff(548,plain,
rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_head(rstore_head(queue_187,index_189)),
inference(monotonicity,[status(thm)],[547]) ).
tff(549,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = s(index_188) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(550,plain,
rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = s(index_188),
inference(unit_resolution,[status(thm)],[549,173]) ).
tff(551,plain,
s(index_188) = rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(symmetry,[status(thm)],[550]) ).
tff(552,plain,
( ( index_188 = rselect_head(queue_187) )
<=> ( index_188 = rselect_head(queue_187) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(553,axiom,
index_188 = rselect_head(queue_187),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(554,plain,
index_188 = rselect_head(queue_187),
inference(modus_ponens,[status(thm)],[553,552]) ).
tff(555,plain,
rselect_head(queue_187) = index_188,
inference(symmetry,[status(thm)],[554]) ).
tff(556,plain,
s(rselect_head(queue_187)) = s(index_188),
inference(monotonicity,[status(thm)],[555]) ).
tff(557,plain,
s(rselect_head(queue_187)) = index_209,
inference(transitivity,[status(thm)],[556,551,548,538,535,520,517,505,502,485,482,470,467,450,447,430]) ).
tff(558,plain,
s(s(rselect_head(queue_187))) = s(index_209),
inference(monotonicity,[status(thm)],[557]) ).
tff(559,plain,
s(index_188) = s(rselect_head(queue_187)),
inference(symmetry,[status(thm)],[556]) ).
tff(560,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(561,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(562,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[561,560]) ).
tff(563,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[562]) ).
tff(564,plain,
( ( queue_185 = rstore_seq(q32,earray_184) )
<=> ( queue_185 = rstore_seq(q32,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(565,axiom,
queue_185 = rstore_seq(q32,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp268) ).
tff(566,plain,
queue_185 = rstore_seq(q32,earray_184),
inference(modus_ponens,[status(thm)],[565,564]) ).
tff(567,plain,
rstore_seq(q32,earray_184) = queue_185,
inference(symmetry,[status(thm)],[566]) ).
tff(568,plain,
rstore_tail(rstore_seq(q32,earray_184),s(index_183)) = rstore_tail(queue_185,index_186),
inference(monotonicity,[status(thm)],[567,563]) ).
tff(569,plain,
rstore_tail(queue_185,index_186) = rstore_tail(rstore_seq(q32,earray_184),s(index_183)),
inference(symmetry,[status(thm)],[568]) ).
tff(570,plain,
queue_187 = rstore_tail(rstore_seq(q32,earray_184),s(index_183)),
inference(transitivity,[status(thm)],[545,569]) ).
tff(571,plain,
rselect_head(queue_187) = rselect_head(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[570]) ).
tff(572,plain,
rselect_head(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_head(queue_187),
inference(symmetry,[status(thm)],[571]) ).
tff(573,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_head(rstore_seq(q32,earray_184)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(574,plain,
rselect_head(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_head(rstore_seq(q32,earray_184)),
inference(unit_resolution,[status(thm)],[573,58]) ).
tff(575,plain,
rselect_head(rstore_seq(q32,earray_184)) = rselect_head(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ( earray_184 = store(earray_182,index_183,e32) )
<=> ( earray_184 = store(earray_182,index_183,e32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(577,axiom,
earray_184 = store(earray_182,index_183,e32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(578,plain,
earray_184 = store(earray_182,index_183,e32),
inference(modus_ponens,[status(thm)],[577,576]) ).
tff(579,plain,
store(earray_182,index_183,e32) = earray_184,
inference(symmetry,[status(thm)],[578]) ).
tff(580,plain,
( ( q32 = queue_181 )
<=> ( q32 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(581,axiom,
q32 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp379) ).
tff(582,plain,
q32 = queue_181,
inference(modus_ponens,[status(thm)],[581,580]) ).
tff(583,plain,
queue_181 = q32,
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
( ( queue_181 = rstore_tail(queue_179,index_180) )
<=> ( queue_181 = rstore_tail(queue_179,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(585,axiom,
queue_181 = rstore_tail(queue_179,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp267) ).
tff(586,plain,
queue_181 = rstore_tail(queue_179,index_180),
inference(modus_ponens,[status(thm)],[585,584]) ).
tff(587,plain,
rstore_tail(queue_179,index_180) = queue_181,
inference(symmetry,[status(thm)],[586]) ).
tff(588,plain,
rstore_tail(queue_179,index_180) = q32,
inference(transitivity,[status(thm)],[587,583]) ).
tff(589,plain,
rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32)) = rstore_seq(q32,earray_184),
inference(monotonicity,[status(thm)],[588,579]) ).
tff(590,plain,
rstore_seq(q32,earray_184) = rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32)),
inference(symmetry,[status(thm)],[589]) ).
tff(591,plain,
rselect_head(rstore_seq(q32,earray_184)) = rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))),
inference(monotonicity,[status(thm)],[590]) ).
tff(592,plain,
rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = rselect_head(rstore_seq(q32,earray_184)),
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = rselect_head(rstore_tail(queue_179,index_180)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(594,plain,
rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = rselect_head(rstore_tail(queue_179,index_180)),
inference(unit_resolution,[status(thm)],[593,85]) ).
tff(595,plain,
rselect_head(rstore_tail(queue_179,index_180)) = rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))),
inference(symmetry,[status(thm)],[594]) ).
tff(596,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(597,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(598,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[597,596]) ).
tff(599,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[598]) ).
tff(600,plain,
( ( queue_179 = rstore_seq(q31,earray_178) )
<=> ( queue_179 = rstore_seq(q31,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(601,axiom,
queue_179 = rstore_seq(q31,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp266) ).
tff(602,plain,
queue_179 = rstore_seq(q31,earray_178),
inference(modus_ponens,[status(thm)],[601,600]) ).
tff(603,plain,
rstore_seq(q31,earray_178) = queue_179,
inference(symmetry,[status(thm)],[602]) ).
tff(604,plain,
rstore_tail(rstore_seq(q31,earray_178),s(index_177)) = rstore_tail(queue_179,index_180),
inference(monotonicity,[status(thm)],[603,599]) ).
tff(605,plain,
rstore_tail(queue_179,index_180) = rstore_tail(rstore_seq(q31,earray_178),s(index_177)),
inference(symmetry,[status(thm)],[604]) ).
tff(606,plain,
rselect_head(rstore_tail(queue_179,index_180)) = rselect_head(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,plain,
rselect_head(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_head(rstore_tail(queue_179,index_180)),
inference(symmetry,[status(thm)],[606]) ).
tff(608,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_head(rstore_seq(q31,earray_178)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(609,plain,
rselect_head(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_head(rstore_seq(q31,earray_178)),
inference(unit_resolution,[status(thm)],[608,58]) ).
tff(610,plain,
rselect_head(rstore_seq(q31,earray_178)) = rselect_head(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[609]) ).
tff(611,plain,
( ( earray_178 = store(earray_176,index_177,e31) )
<=> ( earray_178 = store(earray_176,index_177,e31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(612,axiom,
earray_178 = store(earray_176,index_177,e31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(613,plain,
earray_178 = store(earray_176,index_177,e31),
inference(modus_ponens,[status(thm)],[612,611]) ).
tff(614,plain,
store(earray_176,index_177,e31) = earray_178,
inference(symmetry,[status(thm)],[613]) ).
tff(615,plain,
( ( q31 = queue_175 )
<=> ( q31 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(616,axiom,
q31 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp378) ).
tff(617,plain,
q31 = queue_175,
inference(modus_ponens,[status(thm)],[616,615]) ).
tff(618,plain,
queue_175 = q31,
inference(symmetry,[status(thm)],[617]) ).
tff(619,plain,
( ( queue_175 = rstore_tail(queue_173,index_174) )
<=> ( queue_175 = rstore_tail(queue_173,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(620,axiom,
queue_175 = rstore_tail(queue_173,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp265) ).
tff(621,plain,
queue_175 = rstore_tail(queue_173,index_174),
inference(modus_ponens,[status(thm)],[620,619]) ).
tff(622,plain,
rstore_tail(queue_173,index_174) = queue_175,
inference(symmetry,[status(thm)],[621]) ).
tff(623,plain,
rstore_tail(queue_173,index_174) = q31,
inference(transitivity,[status(thm)],[622,618]) ).
tff(624,plain,
rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31)) = rstore_seq(q31,earray_178),
inference(monotonicity,[status(thm)],[623,614]) ).
tff(625,plain,
rstore_seq(q31,earray_178) = rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31)),
inference(symmetry,[status(thm)],[624]) ).
tff(626,plain,
rselect_head(rstore_seq(q31,earray_178)) = rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))),
inference(monotonicity,[status(thm)],[625]) ).
tff(627,plain,
rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = rselect_head(rstore_seq(q31,earray_178)),
inference(symmetry,[status(thm)],[626]) ).
tff(628,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = rselect_head(rstore_tail(queue_173,index_174)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(629,plain,
rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = rselect_head(rstore_tail(queue_173,index_174)),
inference(unit_resolution,[status(thm)],[628,85]) ).
tff(630,plain,
rselect_head(rstore_tail(queue_173,index_174)) = rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))),
inference(symmetry,[status(thm)],[629]) ).
tff(631,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(632,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(633,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[632,631]) ).
tff(634,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[633]) ).
tff(635,plain,
( ( queue_173 = rstore_seq(q30,earray_172) )
<=> ( queue_173 = rstore_seq(q30,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(636,axiom,
queue_173 = rstore_seq(q30,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp264) ).
tff(637,plain,
queue_173 = rstore_seq(q30,earray_172),
inference(modus_ponens,[status(thm)],[636,635]) ).
tff(638,plain,
rstore_seq(q30,earray_172) = queue_173,
inference(symmetry,[status(thm)],[637]) ).
tff(639,plain,
rstore_tail(rstore_seq(q30,earray_172),s(index_171)) = rstore_tail(queue_173,index_174),
inference(monotonicity,[status(thm)],[638,634]) ).
tff(640,plain,
rstore_tail(queue_173,index_174) = rstore_tail(rstore_seq(q30,earray_172),s(index_171)),
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
rselect_head(rstore_tail(queue_173,index_174)) = rselect_head(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
rselect_head(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_head(rstore_tail(queue_173,index_174)),
inference(symmetry,[status(thm)],[641]) ).
tff(643,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_head(rstore_seq(q30,earray_172)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(644,plain,
rselect_head(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_head(rstore_seq(q30,earray_172)),
inference(unit_resolution,[status(thm)],[643,58]) ).
tff(645,plain,
rselect_head(rstore_seq(q30,earray_172)) = rselect_head(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(symmetry,[status(thm)],[644]) ).
tff(646,plain,
( ( earray_172 = store(earray_170,index_171,e30) )
<=> ( earray_172 = store(earray_170,index_171,e30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(647,axiom,
earray_172 = store(earray_170,index_171,e30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(648,plain,
earray_172 = store(earray_170,index_171,e30),
inference(modus_ponens,[status(thm)],[647,646]) ).
tff(649,plain,
store(earray_170,index_171,e30) = earray_172,
inference(symmetry,[status(thm)],[648]) ).
tff(650,plain,
( ( q30 = queue_169 )
<=> ( q30 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(651,axiom,
q30 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp377) ).
tff(652,plain,
q30 = queue_169,
inference(modus_ponens,[status(thm)],[651,650]) ).
tff(653,plain,
queue_169 = q30,
inference(symmetry,[status(thm)],[652]) ).
tff(654,plain,
( ( queue_169 = rstore_head(queue_166,index_168) )
<=> ( queue_169 = rstore_head(queue_166,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(655,axiom,
queue_169 = rstore_head(queue_166,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp262) ).
tff(656,plain,
queue_169 = rstore_head(queue_166,index_168),
inference(modus_ponens,[status(thm)],[655,654]) ).
tff(657,plain,
rstore_head(queue_166,index_168) = queue_169,
inference(symmetry,[status(thm)],[656]) ).
tff(658,plain,
rstore_head(queue_166,index_168) = q30,
inference(transitivity,[status(thm)],[657,653]) ).
tff(659,plain,
rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30)) = rstore_seq(q30,earray_172),
inference(monotonicity,[status(thm)],[658,649]) ).
tff(660,plain,
rselect_head(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = rselect_head(rstore_seq(q30,earray_172)),
inference(monotonicity,[status(thm)],[659]) ).
tff(661,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = rselect_head(rstore_head(queue_166,index_168)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(662,plain,
rselect_head(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = rselect_head(rstore_head(queue_166,index_168)),
inference(unit_resolution,[status(thm)],[661,85]) ).
tff(663,plain,
rselect_head(rstore_head(queue_166,index_168)) = rselect_head(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))),
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
( ( index_168 = s(index_167) )
<=> ( index_168 = s(index_167) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(665,axiom,
index_168 = s(index_167),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(666,plain,
index_168 = s(index_167),
inference(modus_ponens,[status(thm)],[665,664]) ).
tff(667,plain,
s(index_167) = index_168,
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
( ( queue_166 = rstore_tail(queue_164,index_165) )
<=> ( queue_166 = rstore_tail(queue_164,index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(669,axiom,
queue_166 = rstore_tail(queue_164,index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp261) ).
tff(670,plain,
queue_166 = rstore_tail(queue_164,index_165),
inference(modus_ponens,[status(thm)],[669,668]) ).
tff(671,plain,
rstore_tail(queue_164,index_165) = queue_166,
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
rstore_head(rstore_tail(queue_164,index_165),s(index_167)) = rstore_head(queue_166,index_168),
inference(monotonicity,[status(thm)],[671,667]) ).
tff(673,plain,
rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_head(rstore_head(queue_166,index_168)),
inference(monotonicity,[status(thm)],[672]) ).
tff(674,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = s(index_167) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(675,plain,
rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = s(index_167),
inference(unit_resolution,[status(thm)],[674,173]) ).
tff(676,plain,
s(index_167) = rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[675]) ).
tff(677,plain,
( ( index_167 = rselect_head(queue_166) )
<=> ( index_167 = rselect_head(queue_166) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(678,axiom,
index_167 = rselect_head(queue_166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(679,plain,
index_167 = rselect_head(queue_166),
inference(modus_ponens,[status(thm)],[678,677]) ).
tff(680,plain,
rselect_head(queue_166) = index_167,
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
s(rselect_head(queue_166)) = s(index_167),
inference(monotonicity,[status(thm)],[680]) ).
tff(682,plain,
s(rselect_head(queue_166)) = index_188,
inference(transitivity,[status(thm)],[681,676,673,663,660,645,642,630,627,610,607,595,592,575,572,555]) ).
tff(683,plain,
s(s(rselect_head(queue_166))) = s(index_188),
inference(monotonicity,[status(thm)],[682]) ).
tff(684,plain,
s(index_167) = s(rselect_head(queue_166)),
inference(symmetry,[status(thm)],[681]) ).
tff(685,plain,
( ( index_165 = s(index_162) )
<=> ( index_165 = s(index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(686,axiom,
index_165 = s(index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(687,plain,
index_165 = s(index_162),
inference(modus_ponens,[status(thm)],[686,685]) ).
tff(688,plain,
s(index_162) = index_165,
inference(symmetry,[status(thm)],[687]) ).
tff(689,plain,
( ( queue_164 = rstore_seq(q29,earray_163) )
<=> ( queue_164 = rstore_seq(q29,earray_163) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(690,axiom,
queue_164 = rstore_seq(q29,earray_163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp260) ).
tff(691,plain,
queue_164 = rstore_seq(q29,earray_163),
inference(modus_ponens,[status(thm)],[690,689]) ).
tff(692,plain,
rstore_seq(q29,earray_163) = queue_164,
inference(symmetry,[status(thm)],[691]) ).
tff(693,plain,
rstore_tail(rstore_seq(q29,earray_163),s(index_162)) = rstore_tail(queue_164,index_165),
inference(monotonicity,[status(thm)],[692,688]) ).
tff(694,plain,
rstore_tail(queue_164,index_165) = rstore_tail(rstore_seq(q29,earray_163),s(index_162)),
inference(symmetry,[status(thm)],[693]) ).
tff(695,plain,
queue_166 = rstore_tail(rstore_seq(q29,earray_163),s(index_162)),
inference(transitivity,[status(thm)],[670,694]) ).
tff(696,plain,
rselect_head(queue_166) = rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_head(queue_166),
inference(symmetry,[status(thm)],[696]) ).
tff(698,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_head(rstore_seq(q29,earray_163)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(699,plain,
rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_head(rstore_seq(q29,earray_163)),
inference(unit_resolution,[status(thm)],[698,58]) ).
tff(700,plain,
rselect_head(rstore_seq(q29,earray_163)) = rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
( ( earray_163 = store(earray_161,index_162,e29) )
<=> ( earray_163 = store(earray_161,index_162,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(702,axiom,
earray_163 = store(earray_161,index_162,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp21) ).
tff(703,plain,
earray_163 = store(earray_161,index_162,e29),
inference(modus_ponens,[status(thm)],[702,701]) ).
tff(704,plain,
store(earray_161,index_162,e29) = earray_163,
inference(symmetry,[status(thm)],[703]) ).
tff(705,plain,
( ( q29 = queue_151 )
<=> ( q29 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(706,axiom,
q29 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp375) ).
tff(707,plain,
q29 = queue_151,
inference(modus_ponens,[status(thm)],[706,705]) ).
tff(708,plain,
queue_151 = q29,
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
( ( queue_151 = rstore_tail(queue_149,index_150) )
<=> ( queue_151 = rstore_tail(queue_149,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(710,axiom,
queue_151 = rstore_tail(queue_149,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp256) ).
tff(711,plain,
queue_151 = rstore_tail(queue_149,index_150),
inference(modus_ponens,[status(thm)],[710,709]) ).
tff(712,plain,
rstore_tail(queue_149,index_150) = queue_151,
inference(symmetry,[status(thm)],[711]) ).
tff(713,plain,
rstore_tail(queue_149,index_150) = q29,
inference(transitivity,[status(thm)],[712,708]) ).
tff(714,plain,
rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29)) = rstore_seq(q29,earray_163),
inference(monotonicity,[status(thm)],[713,704]) ).
tff(715,plain,
rstore_seq(q29,earray_163) = rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29)),
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
rselect_head(rstore_seq(q29,earray_163)) = rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(monotonicity,[status(thm)],[715]) ).
tff(717,plain,
rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_head(rstore_seq(q29,earray_163)),
inference(symmetry,[status(thm)],[716]) ).
tff(718,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_head(rstore_tail(queue_149,index_150)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(719,plain,
rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_head(rstore_tail(queue_149,index_150)),
inference(unit_resolution,[status(thm)],[718,85]) ).
tff(720,plain,
rselect_head(rstore_tail(queue_149,index_150)) = rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(722,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(723,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[722,721]) ).
tff(724,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[723]) ).
tff(725,plain,
( ( queue_149 = rstore_seq(q28,earray_148) )
<=> ( queue_149 = rstore_seq(q28,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(726,axiom,
queue_149 = rstore_seq(q28,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp255) ).
tff(727,plain,
queue_149 = rstore_seq(q28,earray_148),
inference(modus_ponens,[status(thm)],[726,725]) ).
tff(728,plain,
rstore_seq(q28,earray_148) = queue_149,
inference(symmetry,[status(thm)],[727]) ).
tff(729,plain,
rstore_tail(rstore_seq(q28,earray_148),s(index_147)) = rstore_tail(queue_149,index_150),
inference(monotonicity,[status(thm)],[728,724]) ).
tff(730,plain,
rstore_tail(queue_149,index_150) = rstore_tail(rstore_seq(q28,earray_148),s(index_147)),
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
rselect_head(rstore_tail(queue_149,index_150)) = rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[730]) ).
tff(732,plain,
rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_head(rstore_tail(queue_149,index_150)),
inference(symmetry,[status(thm)],[731]) ).
tff(733,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_head(rstore_seq(q28,earray_148)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(734,plain,
rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_head(rstore_seq(q28,earray_148)),
inference(unit_resolution,[status(thm)],[733,58]) ).
tff(735,plain,
rselect_head(rstore_seq(q28,earray_148)) = rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[734]) ).
tff(736,plain,
( ( earray_148 = store(earray_146,index_147,e28) )
<=> ( earray_148 = store(earray_146,index_147,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(737,axiom,
earray_148 = store(earray_146,index_147,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(738,plain,
earray_148 = store(earray_146,index_147,e28),
inference(modus_ponens,[status(thm)],[737,736]) ).
tff(739,plain,
store(earray_146,index_147,e28) = earray_148,
inference(symmetry,[status(thm)],[738]) ).
tff(740,plain,
( ( q28 = queue_145 )
<=> ( q28 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(741,axiom,
q28 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp374) ).
tff(742,plain,
q28 = queue_145,
inference(modus_ponens,[status(thm)],[741,740]) ).
tff(743,plain,
queue_145 = q28,
inference(symmetry,[status(thm)],[742]) ).
tff(744,plain,
( ( queue_145 = rstore_tail(queue_143,index_144) )
<=> ( queue_145 = rstore_tail(queue_143,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(745,axiom,
queue_145 = rstore_tail(queue_143,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp254) ).
tff(746,plain,
queue_145 = rstore_tail(queue_143,index_144),
inference(modus_ponens,[status(thm)],[745,744]) ).
tff(747,plain,
rstore_tail(queue_143,index_144) = queue_145,
inference(symmetry,[status(thm)],[746]) ).
tff(748,plain,
rstore_tail(queue_143,index_144) = q28,
inference(transitivity,[status(thm)],[747,743]) ).
tff(749,plain,
rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28)) = rstore_seq(q28,earray_148),
inference(monotonicity,[status(thm)],[748,739]) ).
tff(750,plain,
rstore_seq(q28,earray_148) = rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28)),
inference(symmetry,[status(thm)],[749]) ).
tff(751,plain,
rselect_head(rstore_seq(q28,earray_148)) = rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(monotonicity,[status(thm)],[750]) ).
tff(752,plain,
rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_head(rstore_seq(q28,earray_148)),
inference(symmetry,[status(thm)],[751]) ).
tff(753,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_head(rstore_tail(queue_143,index_144)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(754,plain,
rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_head(rstore_tail(queue_143,index_144)),
inference(unit_resolution,[status(thm)],[753,85]) ).
tff(755,plain,
rselect_head(rstore_tail(queue_143,index_144)) = rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(symmetry,[status(thm)],[754]) ).
tff(756,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(757,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(758,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[757,756]) ).
tff(759,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[758]) ).
tff(760,plain,
( ( queue_143 = rstore_seq(q27,earray_142) )
<=> ( queue_143 = rstore_seq(q27,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(761,axiom,
queue_143 = rstore_seq(q27,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp253) ).
tff(762,plain,
queue_143 = rstore_seq(q27,earray_142),
inference(modus_ponens,[status(thm)],[761,760]) ).
tff(763,plain,
rstore_seq(q27,earray_142) = queue_143,
inference(symmetry,[status(thm)],[762]) ).
tff(764,plain,
rstore_tail(rstore_seq(q27,earray_142),s(index_141)) = rstore_tail(queue_143,index_144),
inference(monotonicity,[status(thm)],[763,759]) ).
tff(765,plain,
rstore_tail(queue_143,index_144) = rstore_tail(rstore_seq(q27,earray_142),s(index_141)),
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
rselect_head(rstore_tail(queue_143,index_144)) = rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[765]) ).
tff(767,plain,
rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_head(rstore_tail(queue_143,index_144)),
inference(symmetry,[status(thm)],[766]) ).
tff(768,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_head(rstore_seq(q27,earray_142)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(769,plain,
rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_head(rstore_seq(q27,earray_142)),
inference(unit_resolution,[status(thm)],[768,58]) ).
tff(770,plain,
rselect_head(rstore_seq(q27,earray_142)) = rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[769]) ).
tff(771,plain,
( ( earray_142 = store(earray_140,index_141,e27) )
<=> ( earray_142 = store(earray_140,index_141,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(772,axiom,
earray_142 = store(earray_140,index_141,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp14) ).
tff(773,plain,
earray_142 = store(earray_140,index_141,e27),
inference(modus_ponens,[status(thm)],[772,771]) ).
tff(774,plain,
store(earray_140,index_141,e27) = earray_142,
inference(symmetry,[status(thm)],[773]) ).
tff(775,plain,
( ( q27 = queue_139 )
<=> ( q27 = queue_139 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(776,axiom,
q27 = queue_139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp373) ).
tff(777,plain,
q27 = queue_139,
inference(modus_ponens,[status(thm)],[776,775]) ).
tff(778,plain,
queue_139 = q27,
inference(symmetry,[status(thm)],[777]) ).
tff(779,plain,
( ( queue_139 = rstore_head(queue_136,index_138) )
<=> ( queue_139 = rstore_head(queue_136,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(780,axiom,
queue_139 = rstore_head(queue_136,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp252) ).
tff(781,plain,
queue_139 = rstore_head(queue_136,index_138),
inference(modus_ponens,[status(thm)],[780,779]) ).
tff(782,plain,
rstore_head(queue_136,index_138) = queue_139,
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
rstore_head(queue_136,index_138) = q27,
inference(transitivity,[status(thm)],[782,778]) ).
tff(784,plain,
rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27)) = rstore_seq(q27,earray_142),
inference(monotonicity,[status(thm)],[783,774]) ).
tff(785,plain,
rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_seq(q27,earray_142)),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_head(queue_136,index_138)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(787,plain,
rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_head(queue_136,index_138)),
inference(unit_resolution,[status(thm)],[786,85]) ).
tff(788,plain,
rselect_head(rstore_head(queue_136,index_138)) = rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
( ( index_138 = s(index_137) )
<=> ( index_138 = s(index_137) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(790,axiom,
index_138 = s(index_137),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(791,plain,
index_138 = s(index_137),
inference(modus_ponens,[status(thm)],[790,789]) ).
tff(792,plain,
s(index_137) = index_138,
inference(symmetry,[status(thm)],[791]) ).
tff(793,plain,
( ( queue_136 = rstore_tail(queue_134,index_135) )
<=> ( queue_136 = rstore_tail(queue_134,index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(794,axiom,
queue_136 = rstore_tail(queue_134,index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp251) ).
tff(795,plain,
queue_136 = rstore_tail(queue_134,index_135),
inference(modus_ponens,[status(thm)],[794,793]) ).
tff(796,plain,
rstore_tail(queue_134,index_135) = queue_136,
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
rstore_head(rstore_tail(queue_134,index_135),s(index_137)) = rstore_head(queue_136,index_138),
inference(monotonicity,[status(thm)],[796,792]) ).
tff(798,plain,
rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_head(rstore_head(queue_136,index_138)),
inference(monotonicity,[status(thm)],[797]) ).
tff(799,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = s(index_137) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(800,plain,
rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = s(index_137),
inference(unit_resolution,[status(thm)],[799,173]) ).
tff(801,plain,
s(index_137) = rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
( ( index_137 = rselect_head(queue_136) )
<=> ( index_137 = rselect_head(queue_136) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(803,axiom,
index_137 = rselect_head(queue_136),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(804,plain,
index_137 = rselect_head(queue_136),
inference(modus_ponens,[status(thm)],[803,802]) ).
tff(805,plain,
rselect_head(queue_136) = index_137,
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
s(rselect_head(queue_136)) = s(index_137),
inference(monotonicity,[status(thm)],[805]) ).
tff(807,plain,
s(rselect_head(queue_136)) = index_167,
inference(transitivity,[status(thm)],[806,801,798,788,785,770,767,755,752,735,732,720,717,700,697,680]) ).
tff(808,plain,
s(s(rselect_head(queue_136))) = s(index_167),
inference(monotonicity,[status(thm)],[807]) ).
tff(809,plain,
s(index_137) = s(rselect_head(queue_136)),
inference(symmetry,[status(thm)],[806]) ).
tff(810,plain,
( ( index_135 = s(index_132) )
<=> ( index_135 = s(index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(811,axiom,
index_135 = s(index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(812,plain,
index_135 = s(index_132),
inference(modus_ponens,[status(thm)],[811,810]) ).
tff(813,plain,
s(index_132) = index_135,
inference(symmetry,[status(thm)],[812]) ).
tff(814,plain,
( ( queue_134 = rstore_seq(q26,earray_133) )
<=> ( queue_134 = rstore_seq(q26,earray_133) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(815,axiom,
queue_134 = rstore_seq(q26,earray_133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp250) ).
tff(816,plain,
queue_134 = rstore_seq(q26,earray_133),
inference(modus_ponens,[status(thm)],[815,814]) ).
tff(817,plain,
rstore_seq(q26,earray_133) = queue_134,
inference(symmetry,[status(thm)],[816]) ).
tff(818,plain,
rstore_tail(rstore_seq(q26,earray_133),s(index_132)) = rstore_tail(queue_134,index_135),
inference(monotonicity,[status(thm)],[817,813]) ).
tff(819,plain,
rstore_tail(queue_134,index_135) = rstore_tail(rstore_seq(q26,earray_133),s(index_132)),
inference(symmetry,[status(thm)],[818]) ).
tff(820,plain,
queue_136 = rstore_tail(rstore_seq(q26,earray_133),s(index_132)),
inference(transitivity,[status(thm)],[795,819]) ).
tff(821,plain,
rselect_head(queue_136) = rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(monotonicity,[status(thm)],[820]) ).
tff(822,plain,
rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(queue_136),
inference(symmetry,[status(thm)],[821]) ).
tff(823,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(rstore_seq(q26,earray_133)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(824,plain,
rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(rstore_seq(q26,earray_133)),
inference(unit_resolution,[status(thm)],[823,58]) ).
tff(825,plain,
rselect_head(rstore_seq(q26,earray_133)) = rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[824]) ).
tff(826,plain,
( ( earray_133 = store(earray_131,index_132,e26) )
<=> ( earray_133 = store(earray_131,index_132,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(827,axiom,
earray_133 = store(earray_131,index_132,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(828,plain,
earray_133 = store(earray_131,index_132,e26),
inference(modus_ponens,[status(thm)],[827,826]) ).
tff(829,plain,
store(earray_131,index_132,e26) = earray_133,
inference(symmetry,[status(thm)],[828]) ).
tff(830,plain,
( ( q26 = queue_130 )
<=> ( q26 = queue_130 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(831,axiom,
q26 = queue_130,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp372) ).
tff(832,plain,
q26 = queue_130,
inference(modus_ponens,[status(thm)],[831,830]) ).
tff(833,plain,
queue_130 = q26,
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
( ( queue_130 = rstore_tail(queue_128,index_129) )
<=> ( queue_130 = rstore_tail(queue_128,index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(835,axiom,
queue_130 = rstore_tail(queue_128,index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp249) ).
tff(836,plain,
queue_130 = rstore_tail(queue_128,index_129),
inference(modus_ponens,[status(thm)],[835,834]) ).
tff(837,plain,
rstore_tail(queue_128,index_129) = queue_130,
inference(symmetry,[status(thm)],[836]) ).
tff(838,plain,
rstore_tail(queue_128,index_129) = q26,
inference(transitivity,[status(thm)],[837,833]) ).
tff(839,plain,
rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26)) = rstore_seq(q26,earray_133),
inference(monotonicity,[status(thm)],[838,829]) ).
tff(840,plain,
rstore_seq(q26,earray_133) = rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26)),
inference(symmetry,[status(thm)],[839]) ).
tff(841,plain,
rselect_head(rstore_seq(q26,earray_133)) = rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(monotonicity,[status(thm)],[840]) ).
tff(842,plain,
rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_seq(q26,earray_133)),
inference(symmetry,[status(thm)],[841]) ).
tff(843,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_tail(queue_128,index_129)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(844,plain,
rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_tail(queue_128,index_129)),
inference(unit_resolution,[status(thm)],[843,85]) ).
tff(845,plain,
rselect_head(rstore_tail(queue_128,index_129)) = rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(symmetry,[status(thm)],[844]) ).
tff(846,plain,
( ( index_129 = s(index_126) )
<=> ( index_129 = s(index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(847,axiom,
index_129 = s(index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(848,plain,
index_129 = s(index_126),
inference(modus_ponens,[status(thm)],[847,846]) ).
tff(849,plain,
s(index_126) = index_129,
inference(symmetry,[status(thm)],[848]) ).
tff(850,plain,
( ( queue_128 = rstore_seq(q25,earray_127) )
<=> ( queue_128 = rstore_seq(q25,earray_127) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(851,axiom,
queue_128 = rstore_seq(q25,earray_127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp247) ).
tff(852,plain,
queue_128 = rstore_seq(q25,earray_127),
inference(modus_ponens,[status(thm)],[851,850]) ).
tff(853,plain,
rstore_seq(q25,earray_127) = queue_128,
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
rstore_tail(rstore_seq(q25,earray_127),s(index_126)) = rstore_tail(queue_128,index_129),
inference(monotonicity,[status(thm)],[853,849]) ).
tff(855,plain,
rstore_tail(queue_128,index_129) = rstore_tail(rstore_seq(q25,earray_127),s(index_126)),
inference(symmetry,[status(thm)],[854]) ).
tff(856,plain,
rselect_head(rstore_tail(queue_128,index_129)) = rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(monotonicity,[status(thm)],[855]) ).
tff(857,plain,
rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_tail(queue_128,index_129)),
inference(symmetry,[status(thm)],[856]) ).
tff(858,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_seq(q25,earray_127)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(859,plain,
rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_seq(q25,earray_127)),
inference(unit_resolution,[status(thm)],[858,58]) ).
tff(860,plain,
rselect_head(rstore_seq(q25,earray_127)) = rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[859]) ).
tff(861,plain,
( ( earray_127 = store(earray_125,index_126,e25) )
<=> ( earray_127 = store(earray_125,index_126,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(862,axiom,
earray_127 = store(earray_125,index_126,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(863,plain,
earray_127 = store(earray_125,index_126,e25),
inference(modus_ponens,[status(thm)],[862,861]) ).
tff(864,plain,
store(earray_125,index_126,e25) = earray_127,
inference(symmetry,[status(thm)],[863]) ).
tff(865,plain,
( ( q25 = queue_124 )
<=> ( q25 = queue_124 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(866,axiom,
q25 = queue_124,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp371) ).
tff(867,plain,
q25 = queue_124,
inference(modus_ponens,[status(thm)],[866,865]) ).
tff(868,plain,
queue_124 = q25,
inference(symmetry,[status(thm)],[867]) ).
tff(869,plain,
( ( queue_124 = rstore_tail(queue_122,index_123) )
<=> ( queue_124 = rstore_tail(queue_122,index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(870,axiom,
queue_124 = rstore_tail(queue_122,index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp246) ).
tff(871,plain,
queue_124 = rstore_tail(queue_122,index_123),
inference(modus_ponens,[status(thm)],[870,869]) ).
tff(872,plain,
rstore_tail(queue_122,index_123) = queue_124,
inference(symmetry,[status(thm)],[871]) ).
tff(873,plain,
rstore_tail(queue_122,index_123) = q25,
inference(transitivity,[status(thm)],[872,868]) ).
tff(874,plain,
rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25)) = rstore_seq(q25,earray_127),
inference(monotonicity,[status(thm)],[873,864]) ).
tff(875,plain,
rstore_seq(q25,earray_127) = rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25)),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
rselect_head(rstore_seq(q25,earray_127)) = rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(monotonicity,[status(thm)],[875]) ).
tff(877,plain,
rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_seq(q25,earray_127)),
inference(symmetry,[status(thm)],[876]) ).
tff(878,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_tail(queue_122,index_123)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(879,plain,
rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_tail(queue_122,index_123)),
inference(unit_resolution,[status(thm)],[878,85]) ).
tff(880,plain,
rselect_head(rstore_tail(queue_122,index_123)) = rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(symmetry,[status(thm)],[879]) ).
tff(881,plain,
( ( index_123 = s(index_120) )
<=> ( index_123 = s(index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(882,axiom,
index_123 = s(index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(883,plain,
index_123 = s(index_120),
inference(modus_ponens,[status(thm)],[882,881]) ).
tff(884,plain,
s(index_120) = index_123,
inference(symmetry,[status(thm)],[883]) ).
tff(885,plain,
( ( queue_122 = rstore_seq(q24,earray_121) )
<=> ( queue_122 = rstore_seq(q24,earray_121) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(886,axiom,
queue_122 = rstore_seq(q24,earray_121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(887,plain,
queue_122 = rstore_seq(q24,earray_121),
inference(modus_ponens,[status(thm)],[886,885]) ).
tff(888,plain,
rstore_seq(q24,earray_121) = queue_122,
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
rstore_tail(rstore_seq(q24,earray_121),s(index_120)) = rstore_tail(queue_122,index_123),
inference(monotonicity,[status(thm)],[888,884]) ).
tff(890,plain,
rstore_tail(queue_122,index_123) = rstore_tail(rstore_seq(q24,earray_121),s(index_120)),
inference(symmetry,[status(thm)],[889]) ).
tff(891,plain,
rselect_head(rstore_tail(queue_122,index_123)) = rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(monotonicity,[status(thm)],[890]) ).
tff(892,plain,
rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_tail(queue_122,index_123)),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_seq(q24,earray_121)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(894,plain,
rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_seq(q24,earray_121)),
inference(unit_resolution,[status(thm)],[893,58]) ).
tff(895,plain,
rselect_head(rstore_seq(q24,earray_121)) = rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
( ( earray_121 = store(earray_119,index_120,e24) )
<=> ( earray_121 = store(earray_119,index_120,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(897,axiom,
earray_121 = store(earray_119,index_120,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(898,plain,
earray_121 = store(earray_119,index_120,e24),
inference(modus_ponens,[status(thm)],[897,896]) ).
tff(899,plain,
store(earray_119,index_120,e24) = earray_121,
inference(symmetry,[status(thm)],[898]) ).
tff(900,plain,
( ( q24 = queue_118 )
<=> ( q24 = queue_118 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(901,axiom,
q24 = queue_118,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp370) ).
tff(902,plain,
q24 = queue_118,
inference(modus_ponens,[status(thm)],[901,900]) ).
tff(903,plain,
queue_118 = q24,
inference(symmetry,[status(thm)],[902]) ).
tff(904,plain,
( ( queue_118 = rstore_head(queue_115,index_117) )
<=> ( queue_118 = rstore_head(queue_115,index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(905,axiom,
queue_118 = rstore_head(queue_115,index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(906,plain,
queue_118 = rstore_head(queue_115,index_117),
inference(modus_ponens,[status(thm)],[905,904]) ).
tff(907,plain,
rstore_head(queue_115,index_117) = queue_118,
inference(symmetry,[status(thm)],[906]) ).
tff(908,plain,
rstore_head(queue_115,index_117) = q24,
inference(transitivity,[status(thm)],[907,903]) ).
tff(909,plain,
rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24)) = rstore_seq(q24,earray_121),
inference(monotonicity,[status(thm)],[908,899]) ).
tff(910,plain,
rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_seq(q24,earray_121)),
inference(monotonicity,[status(thm)],[909]) ).
tff(911,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_head(queue_115,index_117)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(912,plain,
rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_head(queue_115,index_117)),
inference(unit_resolution,[status(thm)],[911,85]) ).
tff(913,plain,
rselect_head(rstore_head(queue_115,index_117)) = rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(symmetry,[status(thm)],[912]) ).
tff(914,plain,
( ( index_117 = s(index_116) )
<=> ( index_117 = s(index_116) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(915,axiom,
index_117 = s(index_116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(916,plain,
index_117 = s(index_116),
inference(modus_ponens,[status(thm)],[915,914]) ).
tff(917,plain,
s(index_116) = index_117,
inference(symmetry,[status(thm)],[916]) ).
tff(918,plain,
( ( queue_115 = rstore_tail(queue_113,index_114) )
<=> ( queue_115 = rstore_tail(queue_113,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(919,axiom,
queue_115 = rstore_tail(queue_113,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(920,plain,
queue_115 = rstore_tail(queue_113,index_114),
inference(modus_ponens,[status(thm)],[919,918]) ).
tff(921,plain,
rstore_tail(queue_113,index_114) = queue_115,
inference(symmetry,[status(thm)],[920]) ).
tff(922,plain,
rstore_head(rstore_tail(queue_113,index_114),s(index_116)) = rstore_head(queue_115,index_117),
inference(monotonicity,[status(thm)],[921,917]) ).
tff(923,plain,
rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_head(rstore_head(queue_115,index_117)),
inference(monotonicity,[status(thm)],[922]) ).
tff(924,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = s(index_116) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(925,plain,
rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = s(index_116),
inference(unit_resolution,[status(thm)],[924,173]) ).
tff(926,plain,
s(index_116) = rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
( ( index_116 = rselect_head(queue_115) )
<=> ( index_116 = rselect_head(queue_115) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(928,axiom,
index_116 = rselect_head(queue_115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(929,plain,
index_116 = rselect_head(queue_115),
inference(modus_ponens,[status(thm)],[928,927]) ).
tff(930,plain,
rselect_head(queue_115) = index_116,
inference(symmetry,[status(thm)],[929]) ).
tff(931,plain,
s(rselect_head(queue_115)) = s(index_116),
inference(monotonicity,[status(thm)],[930]) ).
tff(932,plain,
s(rselect_head(queue_115)) = index_137,
inference(transitivity,[status(thm)],[931,926,923,913,910,895,892,880,877,860,857,845,842,825,822,805]) ).
tff(933,plain,
s(s(rselect_head(queue_115))) = s(index_137),
inference(monotonicity,[status(thm)],[932]) ).
tff(934,plain,
s(index_116) = s(rselect_head(queue_115)),
inference(symmetry,[status(thm)],[931]) ).
tff(935,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(936,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(937,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[936,935]) ).
tff(938,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
( ( queue_113 = rstore_seq(q23,earray_112) )
<=> ( queue_113 = rstore_seq(q23,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(940,axiom,
queue_113 = rstore_seq(q23,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(941,plain,
queue_113 = rstore_seq(q23,earray_112),
inference(modus_ponens,[status(thm)],[940,939]) ).
tff(942,plain,
rstore_seq(q23,earray_112) = queue_113,
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
rstore_tail(rstore_seq(q23,earray_112),s(index_111)) = rstore_tail(queue_113,index_114),
inference(monotonicity,[status(thm)],[942,938]) ).
tff(944,plain,
rstore_tail(queue_113,index_114) = rstore_tail(rstore_seq(q23,earray_112),s(index_111)),
inference(symmetry,[status(thm)],[943]) ).
tff(945,plain,
queue_115 = rstore_tail(rstore_seq(q23,earray_112),s(index_111)),
inference(transitivity,[status(thm)],[920,944]) ).
tff(946,plain,
rselect_head(queue_115) = rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(monotonicity,[status(thm)],[945]) ).
tff(947,plain,
rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(queue_115),
inference(symmetry,[status(thm)],[946]) ).
tff(948,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(rstore_seq(q23,earray_112)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(949,plain,
rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(rstore_seq(q23,earray_112)),
inference(unit_resolution,[status(thm)],[948,58]) ).
tff(950,plain,
rselect_head(rstore_seq(q23,earray_112)) = rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[949]) ).
tff(951,plain,
( ( earray_112 = store(earray_110,index_111,e23) )
<=> ( earray_112 = store(earray_110,index_111,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(952,axiom,
earray_112 = store(earray_110,index_111,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(953,plain,
earray_112 = store(earray_110,index_111,e23),
inference(modus_ponens,[status(thm)],[952,951]) ).
tff(954,plain,
store(earray_110,index_111,e23) = earray_112,
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
( ( q23 = queue_109 )
<=> ( q23 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(956,axiom,
q23 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp369) ).
tff(957,plain,
q23 = queue_109,
inference(modus_ponens,[status(thm)],[956,955]) ).
tff(958,plain,
queue_109 = q23,
inference(symmetry,[status(thm)],[957]) ).
tff(959,plain,
( ( queue_109 = rstore_tail(queue_107,index_108) )
<=> ( queue_109 = rstore_tail(queue_107,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(960,axiom,
queue_109 = rstore_tail(queue_107,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(961,plain,
queue_109 = rstore_tail(queue_107,index_108),
inference(modus_ponens,[status(thm)],[960,959]) ).
tff(962,plain,
rstore_tail(queue_107,index_108) = queue_109,
inference(symmetry,[status(thm)],[961]) ).
tff(963,plain,
rstore_tail(queue_107,index_108) = q23,
inference(transitivity,[status(thm)],[962,958]) ).
tff(964,plain,
rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23)) = rstore_seq(q23,earray_112),
inference(monotonicity,[status(thm)],[963,954]) ).
tff(965,plain,
rstore_seq(q23,earray_112) = rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23)),
inference(symmetry,[status(thm)],[964]) ).
tff(966,plain,
rselect_head(rstore_seq(q23,earray_112)) = rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(monotonicity,[status(thm)],[965]) ).
tff(967,plain,
rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_seq(q23,earray_112)),
inference(symmetry,[status(thm)],[966]) ).
tff(968,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_tail(queue_107,index_108)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(969,plain,
rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_tail(queue_107,index_108)),
inference(unit_resolution,[status(thm)],[968,85]) ).
tff(970,plain,
rselect_head(rstore_tail(queue_107,index_108)) = rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(symmetry,[status(thm)],[969]) ).
tff(971,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(972,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(973,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[972,971]) ).
tff(974,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[973]) ).
tff(975,plain,
( ( queue_107 = rstore_seq(q22,earray_106) )
<=> ( queue_107 = rstore_seq(q22,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(976,axiom,
queue_107 = rstore_seq(q22,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(977,plain,
queue_107 = rstore_seq(q22,earray_106),
inference(modus_ponens,[status(thm)],[976,975]) ).
tff(978,plain,
rstore_seq(q22,earray_106) = queue_107,
inference(symmetry,[status(thm)],[977]) ).
tff(979,plain,
rstore_tail(rstore_seq(q22,earray_106),s(index_105)) = rstore_tail(queue_107,index_108),
inference(monotonicity,[status(thm)],[978,974]) ).
tff(980,plain,
rstore_tail(queue_107,index_108) = rstore_tail(rstore_seq(q22,earray_106),s(index_105)),
inference(symmetry,[status(thm)],[979]) ).
tff(981,plain,
rselect_head(rstore_tail(queue_107,index_108)) = rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[980]) ).
tff(982,plain,
rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_tail(queue_107,index_108)),
inference(symmetry,[status(thm)],[981]) ).
tff(983,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_seq(q22,earray_106)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(984,plain,
rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_seq(q22,earray_106)),
inference(unit_resolution,[status(thm)],[983,58]) ).
tff(985,plain,
rselect_head(rstore_seq(q22,earray_106)) = rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[984]) ).
tff(986,plain,
( ( earray_106 = store(earray_104,index_105,e22) )
<=> ( earray_106 = store(earray_104,index_105,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(987,axiom,
earray_106 = store(earray_104,index_105,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(988,plain,
earray_106 = store(earray_104,index_105,e22),
inference(modus_ponens,[status(thm)],[987,986]) ).
tff(989,plain,
store(earray_104,index_105,e22) = earray_106,
inference(symmetry,[status(thm)],[988]) ).
tff(990,plain,
( ( q22 = queue_103 )
<=> ( q22 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(991,axiom,
q22 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp368) ).
tff(992,plain,
q22 = queue_103,
inference(modus_ponens,[status(thm)],[991,990]) ).
tff(993,plain,
queue_103 = q22,
inference(symmetry,[status(thm)],[992]) ).
tff(994,plain,
( ( queue_103 = rstore_tail(queue_101,index_102) )
<=> ( queue_103 = rstore_tail(queue_101,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(995,axiom,
queue_103 = rstore_tail(queue_101,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(996,plain,
queue_103 = rstore_tail(queue_101,index_102),
inference(modus_ponens,[status(thm)],[995,994]) ).
tff(997,plain,
rstore_tail(queue_101,index_102) = queue_103,
inference(symmetry,[status(thm)],[996]) ).
tff(998,plain,
rstore_tail(queue_101,index_102) = q22,
inference(transitivity,[status(thm)],[997,993]) ).
tff(999,plain,
rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22)) = rstore_seq(q22,earray_106),
inference(monotonicity,[status(thm)],[998,989]) ).
tff(1000,plain,
rstore_seq(q22,earray_106) = rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22)),
inference(symmetry,[status(thm)],[999]) ).
tff(1001,plain,
rselect_head(rstore_seq(q22,earray_106)) = rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(monotonicity,[status(thm)],[1000]) ).
tff(1002,plain,
rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_seq(q22,earray_106)),
inference(symmetry,[status(thm)],[1001]) ).
tff(1003,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_tail(queue_101,index_102)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1004,plain,
rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_tail(queue_101,index_102)),
inference(unit_resolution,[status(thm)],[1003,85]) ).
tff(1005,plain,
rselect_head(rstore_tail(queue_101,index_102)) = rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(symmetry,[status(thm)],[1004]) ).
tff(1006,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1007,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(1008,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[1007,1006]) ).
tff(1009,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[1008]) ).
tff(1010,plain,
( ( queue_101 = rstore_seq(q21,earray_100) )
<=> ( queue_101 = rstore_seq(q21,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1011,axiom,
queue_101 = rstore_seq(q21,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(1012,plain,
queue_101 = rstore_seq(q21,earray_100),
inference(modus_ponens,[status(thm)],[1011,1010]) ).
tff(1013,plain,
rstore_seq(q21,earray_100) = queue_101,
inference(symmetry,[status(thm)],[1012]) ).
tff(1014,plain,
rstore_tail(rstore_seq(q21,earray_100),s(index_99)) = rstore_tail(queue_101,index_102),
inference(monotonicity,[status(thm)],[1013,1009]) ).
tff(1015,plain,
rstore_tail(queue_101,index_102) = rstore_tail(rstore_seq(q21,earray_100),s(index_99)),
inference(symmetry,[status(thm)],[1014]) ).
tff(1016,plain,
rselect_head(rstore_tail(queue_101,index_102)) = rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[1015]) ).
tff(1017,plain,
rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_tail(queue_101,index_102)),
inference(symmetry,[status(thm)],[1016]) ).
tff(1018,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_seq(q21,earray_100)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1019,plain,
rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_seq(q21,earray_100)),
inference(unit_resolution,[status(thm)],[1018,58]) ).
tff(1020,plain,
rselect_head(rstore_seq(q21,earray_100)) = rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[1019]) ).
tff(1021,plain,
( ( earray_100 = store(earray_98,index_99,e21) )
<=> ( earray_100 = store(earray_98,index_99,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1022,axiom,
earray_100 = store(earray_98,index_99,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(1023,plain,
earray_100 = store(earray_98,index_99,e21),
inference(modus_ponens,[status(thm)],[1022,1021]) ).
tff(1024,plain,
store(earray_98,index_99,e21) = earray_100,
inference(symmetry,[status(thm)],[1023]) ).
tff(1025,plain,
( ( q21 = queue_97 )
<=> ( q21 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1026,axiom,
q21 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp367) ).
tff(1027,plain,
q21 = queue_97,
inference(modus_ponens,[status(thm)],[1026,1025]) ).
tff(1028,plain,
queue_97 = q21,
inference(symmetry,[status(thm)],[1027]) ).
tff(1029,plain,
( ( queue_97 = rstore_head(queue_94,index_96) )
<=> ( queue_97 = rstore_head(queue_94,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1030,axiom,
queue_97 = rstore_head(queue_94,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp352) ).
tff(1031,plain,
queue_97 = rstore_head(queue_94,index_96),
inference(modus_ponens,[status(thm)],[1030,1029]) ).
tff(1032,plain,
rstore_head(queue_94,index_96) = queue_97,
inference(symmetry,[status(thm)],[1031]) ).
tff(1033,plain,
rstore_head(queue_94,index_96) = q21,
inference(transitivity,[status(thm)],[1032,1028]) ).
tff(1034,plain,
rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21)) = rstore_seq(q21,earray_100),
inference(monotonicity,[status(thm)],[1033,1024]) ).
tff(1035,plain,
rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_seq(q21,earray_100)),
inference(monotonicity,[status(thm)],[1034]) ).
tff(1036,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_head(queue_94,index_96)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1037,plain,
rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_head(queue_94,index_96)),
inference(unit_resolution,[status(thm)],[1036,85]) ).
tff(1038,plain,
rselect_head(rstore_head(queue_94,index_96)) = rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(symmetry,[status(thm)],[1037]) ).
tff(1039,plain,
( ( index_96 = s(index_95) )
<=> ( index_96 = s(index_95) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1040,axiom,
index_96 = s(index_95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(1041,plain,
index_96 = s(index_95),
inference(modus_ponens,[status(thm)],[1040,1039]) ).
tff(1042,plain,
s(index_95) = index_96,
inference(symmetry,[status(thm)],[1041]) ).
tff(1043,plain,
( ( queue_94 = rstore_tail(queue_92,index_93) )
<=> ( queue_94 = rstore_tail(queue_92,index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1044,axiom,
queue_94 = rstore_tail(queue_92,index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp351) ).
tff(1045,plain,
queue_94 = rstore_tail(queue_92,index_93),
inference(modus_ponens,[status(thm)],[1044,1043]) ).
tff(1046,plain,
rstore_tail(queue_92,index_93) = queue_94,
inference(symmetry,[status(thm)],[1045]) ).
tff(1047,plain,
rstore_head(rstore_tail(queue_92,index_93),s(index_95)) = rstore_head(queue_94,index_96),
inference(monotonicity,[status(thm)],[1046,1042]) ).
tff(1048,plain,
rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_head(rstore_head(queue_94,index_96)),
inference(monotonicity,[status(thm)],[1047]) ).
tff(1049,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = s(index_95) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1050,plain,
rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = s(index_95),
inference(unit_resolution,[status(thm)],[1049,173]) ).
tff(1051,plain,
s(index_95) = rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[1050]) ).
tff(1052,plain,
( ( index_95 = rselect_head(queue_94) )
<=> ( index_95 = rselect_head(queue_94) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1053,axiom,
index_95 = rselect_head(queue_94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(1054,plain,
index_95 = rselect_head(queue_94),
inference(modus_ponens,[status(thm)],[1053,1052]) ).
tff(1055,plain,
rselect_head(queue_94) = index_95,
inference(symmetry,[status(thm)],[1054]) ).
tff(1056,plain,
s(rselect_head(queue_94)) = s(index_95),
inference(monotonicity,[status(thm)],[1055]) ).
tff(1057,plain,
s(rselect_head(queue_94)) = index_116,
inference(transitivity,[status(thm)],[1056,1051,1048,1038,1035,1020,1017,1005,1002,985,982,970,967,950,947,930]) ).
tff(1058,plain,
s(s(rselect_head(queue_94))) = s(index_116),
inference(monotonicity,[status(thm)],[1057]) ).
tff(1059,plain,
s(index_95) = s(rselect_head(queue_94)),
inference(symmetry,[status(thm)],[1056]) ).
tff(1060,plain,
( ( index_93 = s(index_90) )
<=> ( index_93 = s(index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1061,axiom,
index_93 = s(index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(1062,plain,
index_93 = s(index_90),
inference(modus_ponens,[status(thm)],[1061,1060]) ).
tff(1063,plain,
s(index_90) = index_93,
inference(symmetry,[status(thm)],[1062]) ).
tff(1064,plain,
( ( queue_92 = rstore_seq(q20,earray_91) )
<=> ( queue_92 = rstore_seq(q20,earray_91) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1065,axiom,
queue_92 = rstore_seq(q20,earray_91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp350) ).
tff(1066,plain,
queue_92 = rstore_seq(q20,earray_91),
inference(modus_ponens,[status(thm)],[1065,1064]) ).
tff(1067,plain,
rstore_seq(q20,earray_91) = queue_92,
inference(symmetry,[status(thm)],[1066]) ).
tff(1068,plain,
rstore_tail(rstore_seq(q20,earray_91),s(index_90)) = rstore_tail(queue_92,index_93),
inference(monotonicity,[status(thm)],[1067,1063]) ).
tff(1069,plain,
rstore_tail(queue_92,index_93) = rstore_tail(rstore_seq(q20,earray_91),s(index_90)),
inference(symmetry,[status(thm)],[1068]) ).
tff(1070,plain,
queue_94 = rstore_tail(rstore_seq(q20,earray_91),s(index_90)),
inference(transitivity,[status(thm)],[1045,1069]) ).
tff(1071,plain,
rselect_head(queue_94) = rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(monotonicity,[status(thm)],[1070]) ).
tff(1072,plain,
rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(queue_94),
inference(symmetry,[status(thm)],[1071]) ).
tff(1073,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(rstore_seq(q20,earray_91)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1074,plain,
rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(rstore_seq(q20,earray_91)),
inference(unit_resolution,[status(thm)],[1073,58]) ).
tff(1075,plain,
rselect_head(rstore_seq(q20,earray_91)) = rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[1074]) ).
tff(1076,plain,
( ( earray_91 = store(earray_89,index_90,e20) )
<=> ( earray_91 = store(earray_89,index_90,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1077,axiom,
earray_91 = store(earray_89,index_90,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(1078,plain,
earray_91 = store(earray_89,index_90,e20),
inference(modus_ponens,[status(thm)],[1077,1076]) ).
tff(1079,plain,
store(earray_89,index_90,e20) = earray_91,
inference(symmetry,[status(thm)],[1078]) ).
tff(1080,plain,
( ( q20 = queue_88 )
<=> ( q20 = queue_88 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1081,axiom,
q20 = queue_88,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp366) ).
tff(1082,plain,
q20 = queue_88,
inference(modus_ponens,[status(thm)],[1081,1080]) ).
tff(1083,plain,
queue_88 = q20,
inference(symmetry,[status(thm)],[1082]) ).
tff(1084,plain,
( ( queue_88 = rstore_tail(queue_86,index_87) )
<=> ( queue_88 = rstore_tail(queue_86,index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1085,axiom,
queue_88 = rstore_tail(queue_86,index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp349) ).
tff(1086,plain,
queue_88 = rstore_tail(queue_86,index_87),
inference(modus_ponens,[status(thm)],[1085,1084]) ).
tff(1087,plain,
rstore_tail(queue_86,index_87) = queue_88,
inference(symmetry,[status(thm)],[1086]) ).
tff(1088,plain,
rstore_tail(queue_86,index_87) = q20,
inference(transitivity,[status(thm)],[1087,1083]) ).
tff(1089,plain,
rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20)) = rstore_seq(q20,earray_91),
inference(monotonicity,[status(thm)],[1088,1079]) ).
tff(1090,plain,
rstore_seq(q20,earray_91) = rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20)),
inference(symmetry,[status(thm)],[1089]) ).
tff(1091,plain,
rselect_head(rstore_seq(q20,earray_91)) = rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(monotonicity,[status(thm)],[1090]) ).
tff(1092,plain,
rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_seq(q20,earray_91)),
inference(symmetry,[status(thm)],[1091]) ).
tff(1093,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_tail(queue_86,index_87)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1094,plain,
rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_tail(queue_86,index_87)),
inference(unit_resolution,[status(thm)],[1093,85]) ).
tff(1095,plain,
rselect_head(rstore_tail(queue_86,index_87)) = rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(symmetry,[status(thm)],[1094]) ).
tff(1096,plain,
( ( index_87 = s(index_84) )
<=> ( index_87 = s(index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1097,axiom,
index_87 = s(index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(1098,plain,
index_87 = s(index_84),
inference(modus_ponens,[status(thm)],[1097,1096]) ).
tff(1099,plain,
s(index_84) = index_87,
inference(symmetry,[status(thm)],[1098]) ).
tff(1100,plain,
( ( queue_86 = rstore_seq(q19,earray_85) )
<=> ( queue_86 = rstore_seq(q19,earray_85) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1101,axiom,
queue_86 = rstore_seq(q19,earray_85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp348) ).
tff(1102,plain,
queue_86 = rstore_seq(q19,earray_85),
inference(modus_ponens,[status(thm)],[1101,1100]) ).
tff(1103,plain,
rstore_seq(q19,earray_85) = queue_86,
inference(symmetry,[status(thm)],[1102]) ).
tff(1104,plain,
rstore_tail(rstore_seq(q19,earray_85),s(index_84)) = rstore_tail(queue_86,index_87),
inference(monotonicity,[status(thm)],[1103,1099]) ).
tff(1105,plain,
rstore_tail(queue_86,index_87) = rstore_tail(rstore_seq(q19,earray_85),s(index_84)),
inference(symmetry,[status(thm)],[1104]) ).
tff(1106,plain,
rselect_head(rstore_tail(queue_86,index_87)) = rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(monotonicity,[status(thm)],[1105]) ).
tff(1107,plain,
rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_tail(queue_86,index_87)),
inference(symmetry,[status(thm)],[1106]) ).
tff(1108,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_seq(q19,earray_85)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1109,plain,
rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_seq(q19,earray_85)),
inference(unit_resolution,[status(thm)],[1108,58]) ).
tff(1110,plain,
rselect_head(rstore_seq(q19,earray_85)) = rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[1109]) ).
tff(1111,plain,
( ( earray_85 = store(earray_83,index_84,e19) )
<=> ( earray_85 = store(earray_83,index_84,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1112,axiom,
earray_85 = store(earray_83,index_84,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(1113,plain,
earray_85 = store(earray_83,index_84,e19),
inference(modus_ponens,[status(thm)],[1112,1111]) ).
tff(1114,plain,
store(earray_83,index_84,e19) = earray_85,
inference(symmetry,[status(thm)],[1113]) ).
tff(1115,plain,
( ( q19 = queue_76 )
<=> ( q19 = queue_76 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1116,axiom,
q19 = queue_76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp364) ).
tff(1117,plain,
q19 = queue_76,
inference(modus_ponens,[status(thm)],[1116,1115]) ).
tff(1118,plain,
queue_76 = q19,
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ( queue_76 = rstore_tail(queue_74,index_75) )
<=> ( queue_76 = rstore_tail(queue_74,index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1120,axiom,
queue_76 = rstore_tail(queue_74,index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp345) ).
tff(1121,plain,
queue_76 = rstore_tail(queue_74,index_75),
inference(modus_ponens,[status(thm)],[1120,1119]) ).
tff(1122,plain,
rstore_tail(queue_74,index_75) = queue_76,
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
rstore_tail(queue_74,index_75) = q19,
inference(transitivity,[status(thm)],[1122,1118]) ).
tff(1124,plain,
rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19)) = rstore_seq(q19,earray_85),
inference(monotonicity,[status(thm)],[1123,1114]) ).
tff(1125,plain,
rstore_seq(q19,earray_85) = rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19)),
inference(symmetry,[status(thm)],[1124]) ).
tff(1126,plain,
rselect_head(rstore_seq(q19,earray_85)) = rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(monotonicity,[status(thm)],[1125]) ).
tff(1127,plain,
rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_seq(q19,earray_85)),
inference(symmetry,[status(thm)],[1126]) ).
tff(1128,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_tail(queue_74,index_75)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1129,plain,
rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_tail(queue_74,index_75)),
inference(unit_resolution,[status(thm)],[1128,85]) ).
tff(1130,plain,
rselect_head(rstore_tail(queue_74,index_75)) = rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(symmetry,[status(thm)],[1129]) ).
tff(1131,plain,
( ( index_75 = s(index_72) )
<=> ( index_75 = s(index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1132,axiom,
index_75 = s(index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(1133,plain,
index_75 = s(index_72),
inference(modus_ponens,[status(thm)],[1132,1131]) ).
tff(1134,plain,
s(index_72) = index_75,
inference(symmetry,[status(thm)],[1133]) ).
tff(1135,plain,
( ( queue_74 = rstore_seq(q18,earray_73) )
<=> ( queue_74 = rstore_seq(q18,earray_73) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1136,axiom,
queue_74 = rstore_seq(q18,earray_73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp344) ).
tff(1137,plain,
queue_74 = rstore_seq(q18,earray_73),
inference(modus_ponens,[status(thm)],[1136,1135]) ).
tff(1138,plain,
rstore_seq(q18,earray_73) = queue_74,
inference(symmetry,[status(thm)],[1137]) ).
tff(1139,plain,
rstore_tail(rstore_seq(q18,earray_73),s(index_72)) = rstore_tail(queue_74,index_75),
inference(monotonicity,[status(thm)],[1138,1134]) ).
tff(1140,plain,
rstore_tail(queue_74,index_75) = rstore_tail(rstore_seq(q18,earray_73),s(index_72)),
inference(symmetry,[status(thm)],[1139]) ).
tff(1141,plain,
rselect_head(rstore_tail(queue_74,index_75)) = rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(monotonicity,[status(thm)],[1140]) ).
tff(1142,plain,
rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_tail(queue_74,index_75)),
inference(symmetry,[status(thm)],[1141]) ).
tff(1143,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_seq(q18,earray_73)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1144,plain,
rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_seq(q18,earray_73)),
inference(unit_resolution,[status(thm)],[1143,58]) ).
tff(1145,plain,
rselect_head(rstore_seq(q18,earray_73)) = rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[1144]) ).
tff(1146,plain,
( ( earray_73 = store(earray_71,index_72,e18) )
<=> ( earray_73 = store(earray_71,index_72,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1147,axiom,
earray_73 = store(earray_71,index_72,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(1148,plain,
earray_73 = store(earray_71,index_72,e18),
inference(modus_ponens,[status(thm)],[1147,1146]) ).
tff(1149,plain,
store(earray_71,index_72,e18) = earray_73,
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
( ( q18 = queue_70 )
<=> ( q18 = queue_70 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1151,axiom,
q18 = queue_70,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp363) ).
tff(1152,plain,
q18 = queue_70,
inference(modus_ponens,[status(thm)],[1151,1150]) ).
tff(1153,plain,
queue_70 = q18,
inference(symmetry,[status(thm)],[1152]) ).
tff(1154,plain,
( ( queue_70 = rstore_head(queue_67,index_69) )
<=> ( queue_70 = rstore_head(queue_67,index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1155,axiom,
queue_70 = rstore_head(queue_67,index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp343) ).
tff(1156,plain,
queue_70 = rstore_head(queue_67,index_69),
inference(modus_ponens,[status(thm)],[1155,1154]) ).
tff(1157,plain,
rstore_head(queue_67,index_69) = queue_70,
inference(symmetry,[status(thm)],[1156]) ).
tff(1158,plain,
rstore_head(queue_67,index_69) = q18,
inference(transitivity,[status(thm)],[1157,1153]) ).
tff(1159,plain,
rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18)) = rstore_seq(q18,earray_73),
inference(monotonicity,[status(thm)],[1158,1149]) ).
tff(1160,plain,
rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_seq(q18,earray_73)),
inference(monotonicity,[status(thm)],[1159]) ).
tff(1161,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_head(queue_67,index_69)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1162,plain,
rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_head(queue_67,index_69)),
inference(unit_resolution,[status(thm)],[1161,85]) ).
tff(1163,plain,
rselect_head(rstore_head(queue_67,index_69)) = rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(symmetry,[status(thm)],[1162]) ).
tff(1164,plain,
( ( index_69 = s(index_68) )
<=> ( index_69 = s(index_68) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1165,axiom,
index_69 = s(index_68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(1166,plain,
index_69 = s(index_68),
inference(modus_ponens,[status(thm)],[1165,1164]) ).
tff(1167,plain,
s(index_68) = index_69,
inference(symmetry,[status(thm)],[1166]) ).
tff(1168,plain,
( ( queue_67 = rstore_tail(queue_65,index_66) )
<=> ( queue_67 = rstore_tail(queue_65,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1169,axiom,
queue_67 = rstore_tail(queue_65,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp341) ).
tff(1170,plain,
queue_67 = rstore_tail(queue_65,index_66),
inference(modus_ponens,[status(thm)],[1169,1168]) ).
tff(1171,plain,
rstore_tail(queue_65,index_66) = queue_67,
inference(symmetry,[status(thm)],[1170]) ).
tff(1172,plain,
rstore_head(rstore_tail(queue_65,index_66),s(index_68)) = rstore_head(queue_67,index_69),
inference(monotonicity,[status(thm)],[1171,1167]) ).
tff(1173,plain,
rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_head(rstore_head(queue_67,index_69)),
inference(monotonicity,[status(thm)],[1172]) ).
tff(1174,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = s(index_68) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1175,plain,
rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = s(index_68),
inference(unit_resolution,[status(thm)],[1174,173]) ).
tff(1176,plain,
s(index_68) = rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[1175]) ).
tff(1177,plain,
( ( index_68 = rselect_head(queue_67) )
<=> ( index_68 = rselect_head(queue_67) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1178,axiom,
index_68 = rselect_head(queue_67),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(1179,plain,
index_68 = rselect_head(queue_67),
inference(modus_ponens,[status(thm)],[1178,1177]) ).
tff(1180,plain,
rselect_head(queue_67) = index_68,
inference(symmetry,[status(thm)],[1179]) ).
tff(1181,plain,
s(rselect_head(queue_67)) = s(index_68),
inference(monotonicity,[status(thm)],[1180]) ).
tff(1182,plain,
s(rselect_head(queue_67)) = index_95,
inference(transitivity,[status(thm)],[1181,1176,1173,1163,1160,1145,1142,1130,1127,1110,1107,1095,1092,1075,1072,1055]) ).
tff(1183,plain,
s(s(rselect_head(queue_67))) = s(index_95),
inference(monotonicity,[status(thm)],[1182]) ).
tff(1184,plain,
s(index_68) = s(rselect_head(queue_67)),
inference(symmetry,[status(thm)],[1181]) ).
tff(1185,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1186,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(1187,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[1186,1185]) ).
tff(1188,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[1187]) ).
tff(1189,plain,
( ( queue_65 = rstore_seq(q17,earray_64) )
<=> ( queue_65 = rstore_seq(q17,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1190,axiom,
queue_65 = rstore_seq(q17,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp340) ).
tff(1191,plain,
queue_65 = rstore_seq(q17,earray_64),
inference(modus_ponens,[status(thm)],[1190,1189]) ).
tff(1192,plain,
rstore_seq(q17,earray_64) = queue_65,
inference(symmetry,[status(thm)],[1191]) ).
tff(1193,plain,
rstore_tail(rstore_seq(q17,earray_64),s(index_63)) = rstore_tail(queue_65,index_66),
inference(monotonicity,[status(thm)],[1192,1188]) ).
tff(1194,plain,
rstore_tail(queue_65,index_66) = rstore_tail(rstore_seq(q17,earray_64),s(index_63)),
inference(symmetry,[status(thm)],[1193]) ).
tff(1195,plain,
queue_67 = rstore_tail(rstore_seq(q17,earray_64),s(index_63)),
inference(transitivity,[status(thm)],[1170,1194]) ).
tff(1196,plain,
rselect_head(queue_67) = rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[1195]) ).
tff(1197,plain,
rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(queue_67),
inference(symmetry,[status(thm)],[1196]) ).
tff(1198,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(rstore_seq(q17,earray_64)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1199,plain,
rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(rstore_seq(q17,earray_64)),
inference(unit_resolution,[status(thm)],[1198,58]) ).
tff(1200,plain,
rselect_head(rstore_seq(q17,earray_64)) = rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[1199]) ).
tff(1201,plain,
( ( earray_64 = store(earray_62,index_63,e17) )
<=> ( earray_64 = store(earray_62,index_63,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1202,axiom,
earray_64 = store(earray_62,index_63,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(1203,plain,
earray_64 = store(earray_62,index_63,e17),
inference(modus_ponens,[status(thm)],[1202,1201]) ).
tff(1204,plain,
store(earray_62,index_63,e17) = earray_64,
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
( ( q17 = queue_61 )
<=> ( q17 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1206,axiom,
q17 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp362) ).
tff(1207,plain,
q17 = queue_61,
inference(modus_ponens,[status(thm)],[1206,1205]) ).
tff(1208,plain,
queue_61 = q17,
inference(symmetry,[status(thm)],[1207]) ).
tff(1209,plain,
( ( queue_61 = rstore_tail(queue_59,index_60) )
<=> ( queue_61 = rstore_tail(queue_59,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1210,axiom,
queue_61 = rstore_tail(queue_59,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp339) ).
tff(1211,plain,
queue_61 = rstore_tail(queue_59,index_60),
inference(modus_ponens,[status(thm)],[1210,1209]) ).
tff(1212,plain,
rstore_tail(queue_59,index_60) = queue_61,
inference(symmetry,[status(thm)],[1211]) ).
tff(1213,plain,
rstore_tail(queue_59,index_60) = q17,
inference(transitivity,[status(thm)],[1212,1208]) ).
tff(1214,plain,
rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17)) = rstore_seq(q17,earray_64),
inference(monotonicity,[status(thm)],[1213,1204]) ).
tff(1215,plain,
rstore_seq(q17,earray_64) = rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17)),
inference(symmetry,[status(thm)],[1214]) ).
tff(1216,plain,
rselect_head(rstore_seq(q17,earray_64)) = rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(monotonicity,[status(thm)],[1215]) ).
tff(1217,plain,
rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_seq(q17,earray_64)),
inference(symmetry,[status(thm)],[1216]) ).
tff(1218,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_tail(queue_59,index_60)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1219,plain,
rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_tail(queue_59,index_60)),
inference(unit_resolution,[status(thm)],[1218,85]) ).
tff(1220,plain,
rselect_head(rstore_tail(queue_59,index_60)) = rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(symmetry,[status(thm)],[1219]) ).
tff(1221,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1222,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(1223,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[1222,1221]) ).
tff(1224,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[1223]) ).
tff(1225,plain,
( ( queue_59 = rstore_seq(q16,earray_58) )
<=> ( queue_59 = rstore_seq(q16,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1226,axiom,
queue_59 = rstore_seq(q16,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp338) ).
tff(1227,plain,
queue_59 = rstore_seq(q16,earray_58),
inference(modus_ponens,[status(thm)],[1226,1225]) ).
tff(1228,plain,
rstore_seq(q16,earray_58) = queue_59,
inference(symmetry,[status(thm)],[1227]) ).
tff(1229,plain,
rstore_tail(rstore_seq(q16,earray_58),s(index_57)) = rstore_tail(queue_59,index_60),
inference(monotonicity,[status(thm)],[1228,1224]) ).
tff(1230,plain,
rstore_tail(queue_59,index_60) = rstore_tail(rstore_seq(q16,earray_58),s(index_57)),
inference(symmetry,[status(thm)],[1229]) ).
tff(1231,plain,
rselect_head(rstore_tail(queue_59,index_60)) = rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[1230]) ).
tff(1232,plain,
rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_tail(queue_59,index_60)),
inference(symmetry,[status(thm)],[1231]) ).
tff(1233,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_seq(q16,earray_58)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1234,plain,
rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_seq(q16,earray_58)),
inference(unit_resolution,[status(thm)],[1233,58]) ).
tff(1235,plain,
rselect_head(rstore_seq(q16,earray_58)) = rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[1234]) ).
tff(1236,plain,
( ( earray_58 = store(earray_56,index_57,e16) )
<=> ( earray_58 = store(earray_56,index_57,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1237,axiom,
earray_58 = store(earray_56,index_57,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(1238,plain,
earray_58 = store(earray_56,index_57,e16),
inference(modus_ponens,[status(thm)],[1237,1236]) ).
tff(1239,plain,
store(earray_56,index_57,e16) = earray_58,
inference(symmetry,[status(thm)],[1238]) ).
tff(1240,plain,
queue_55 = q16,
inference(symmetry,[status(thm)],[16]) ).
tff(1241,plain,
rstore_tail(queue_53,index_54) = queue_55,
inference(symmetry,[status(thm)],[13]) ).
tff(1242,plain,
rstore_tail(queue_53,index_54) = q16,
inference(transitivity,[status(thm)],[1241,1240]) ).
tff(1243,plain,
rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16)) = rstore_seq(q16,earray_58),
inference(monotonicity,[status(thm)],[1242,1239]) ).
tff(1244,plain,
rstore_seq(q16,earray_58) = rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16)),
inference(symmetry,[status(thm)],[1243]) ).
tff(1245,plain,
rselect_head(rstore_seq(q16,earray_58)) = rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(monotonicity,[status(thm)],[1244]) ).
tff(1246,plain,
rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_seq(q16,earray_58)),
inference(symmetry,[status(thm)],[1245]) ).
tff(1247,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_tail(queue_53,index_54)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1248,plain,
rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_tail(queue_53,index_54)),
inference(unit_resolution,[status(thm)],[1247,85]) ).
tff(1249,plain,
rselect_head(rstore_tail(queue_53,index_54)) = rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(symmetry,[status(thm)],[1248]) ).
tff(1250,plain,
rselect_head(rstore_tail(queue_53,index_54)) = rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(monotonicity,[status(thm)],[10]) ).
tff(1251,plain,
rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_tail(queue_53,index_54)),
inference(symmetry,[status(thm)],[1250]) ).
tff(1252,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_seq(q15,earray_52)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1253,plain,
rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_seq(q15,earray_52)),
inference(unit_resolution,[status(thm)],[1252,58]) ).
tff(1254,plain,
rselect_head(rstore_seq(q15,earray_52)) = rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[1253]) ).
tff(1255,plain,
( ( earray_52 = store(earray_50,index_51,e15) )
<=> ( earray_52 = store(earray_50,index_51,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1256,axiom,
earray_52 = store(earray_50,index_51,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp86) ).
tff(1257,plain,
earray_52 = store(earray_50,index_51,e15),
inference(modus_ponens,[status(thm)],[1256,1255]) ).
tff(1258,plain,
store(earray_50,index_51,e15) = earray_52,
inference(symmetry,[status(thm)],[1257]) ).
tff(1259,plain,
( ( q15 = queue_49 )
<=> ( q15 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1260,axiom,
q15 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp360) ).
tff(1261,plain,
q15 = queue_49,
inference(modus_ponens,[status(thm)],[1260,1259]) ).
tff(1262,plain,
queue_49 = q15,
inference(symmetry,[status(thm)],[1261]) ).
tff(1263,plain,
( ( queue_49 = rstore_head(queue_46,index_48) )
<=> ( queue_49 = rstore_head(queue_46,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1264,axiom,
queue_49 = rstore_head(queue_46,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp334) ).
tff(1265,plain,
queue_49 = rstore_head(queue_46,index_48),
inference(modus_ponens,[status(thm)],[1264,1263]) ).
tff(1266,plain,
rstore_head(queue_46,index_48) = queue_49,
inference(symmetry,[status(thm)],[1265]) ).
tff(1267,plain,
rstore_head(queue_46,index_48) = q15,
inference(transitivity,[status(thm)],[1266,1262]) ).
tff(1268,plain,
rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15)) = rstore_seq(q15,earray_52),
inference(monotonicity,[status(thm)],[1267,1258]) ).
tff(1269,plain,
rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_seq(q15,earray_52)),
inference(monotonicity,[status(thm)],[1268]) ).
tff(1270,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_head(queue_46,index_48)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1271,plain,
rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_head(queue_46,index_48)),
inference(unit_resolution,[status(thm)],[1270,85]) ).
tff(1272,plain,
rselect_head(rstore_head(queue_46,index_48)) = rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))),
inference(symmetry,[status(thm)],[1271]) ).
tff(1273,plain,
( ( index_48 = s(index_47) )
<=> ( index_48 = s(index_47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1274,axiom,
index_48 = s(index_47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(1275,plain,
index_48 = s(index_47),
inference(modus_ponens,[status(thm)],[1274,1273]) ).
tff(1276,plain,
s(index_47) = index_48,
inference(symmetry,[status(thm)],[1275]) ).
tff(1277,plain,
( ( queue_46 = rstore_tail(queue_44,index_45) )
<=> ( queue_46 = rstore_tail(queue_44,index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1278,axiom,
queue_46 = rstore_tail(queue_44,index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp333) ).
tff(1279,plain,
queue_46 = rstore_tail(queue_44,index_45),
inference(modus_ponens,[status(thm)],[1278,1277]) ).
tff(1280,plain,
rstore_tail(queue_44,index_45) = queue_46,
inference(symmetry,[status(thm)],[1279]) ).
tff(1281,plain,
rstore_head(rstore_tail(queue_44,index_45),s(index_47)) = rstore_head(queue_46,index_48),
inference(monotonicity,[status(thm)],[1280,1276]) ).
tff(1282,plain,
rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_head(rstore_head(queue_46,index_48)),
inference(monotonicity,[status(thm)],[1281]) ).
tff(1283,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = s(index_47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1284,plain,
rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = s(index_47),
inference(unit_resolution,[status(thm)],[1283,173]) ).
tff(1285,plain,
s(index_47) = rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(symmetry,[status(thm)],[1284]) ).
tff(1286,plain,
( ( index_47 = rselect_head(queue_46) )
<=> ( index_47 = rselect_head(queue_46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1287,axiom,
index_47 = rselect_head(queue_46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(1288,plain,
index_47 = rselect_head(queue_46),
inference(modus_ponens,[status(thm)],[1287,1286]) ).
tff(1289,plain,
rselect_head(queue_46) = index_47,
inference(symmetry,[status(thm)],[1288]) ).
tff(1290,plain,
s(rselect_head(queue_46)) = s(index_47),
inference(monotonicity,[status(thm)],[1289]) ).
tff(1291,plain,
s(rselect_head(queue_46)) = index_68,
inference(transitivity,[status(thm)],[1290,1285,1282,1272,1269,1254,1251,1249,1246,1235,1232,1220,1217,1200,1197,1180]) ).
tff(1292,plain,
s(s(rselect_head(queue_46))) = s(index_68),
inference(monotonicity,[status(thm)],[1291]) ).
tff(1293,plain,
s(index_47) = s(rselect_head(queue_46)),
inference(symmetry,[status(thm)],[1290]) ).
tff(1294,plain,
( ( index_45 = s(index_42) )
<=> ( index_45 = s(index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1295,axiom,
index_45 = s(index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(1296,plain,
index_45 = s(index_42),
inference(modus_ponens,[status(thm)],[1295,1294]) ).
tff(1297,plain,
s(index_42) = index_45,
inference(symmetry,[status(thm)],[1296]) ).
tff(1298,plain,
( ( queue_44 = rstore_seq(q14,earray_43) )
<=> ( queue_44 = rstore_seq(q14,earray_43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1299,axiom,
queue_44 = rstore_seq(q14,earray_43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp332) ).
tff(1300,plain,
queue_44 = rstore_seq(q14,earray_43),
inference(modus_ponens,[status(thm)],[1299,1298]) ).
tff(1301,plain,
rstore_seq(q14,earray_43) = queue_44,
inference(symmetry,[status(thm)],[1300]) ).
tff(1302,plain,
rstore_tail(rstore_seq(q14,earray_43),s(index_42)) = rstore_tail(queue_44,index_45),
inference(monotonicity,[status(thm)],[1301,1297]) ).
tff(1303,plain,
rstore_tail(queue_44,index_45) = rstore_tail(rstore_seq(q14,earray_43),s(index_42)),
inference(symmetry,[status(thm)],[1302]) ).
tff(1304,plain,
queue_46 = rstore_tail(rstore_seq(q14,earray_43),s(index_42)),
inference(transitivity,[status(thm)],[1279,1303]) ).
tff(1305,plain,
rselect_head(queue_46) = rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(monotonicity,[status(thm)],[1304]) ).
tff(1306,plain,
rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(queue_46),
inference(symmetry,[status(thm)],[1305]) ).
tff(1307,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(rstore_seq(q14,earray_43)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1308,plain,
rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(rstore_seq(q14,earray_43)),
inference(unit_resolution,[status(thm)],[1307,58]) ).
tff(1309,plain,
rselect_head(rstore_seq(q14,earray_43)) = rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(symmetry,[status(thm)],[1308]) ).
tff(1310,plain,
( ( earray_43 = store(earray_41,index_42,e14) )
<=> ( earray_43 = store(earray_41,index_42,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1311,axiom,
earray_43 = store(earray_41,index_42,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp84) ).
tff(1312,plain,
earray_43 = store(earray_41,index_42,e14),
inference(modus_ponens,[status(thm)],[1311,1310]) ).
tff(1313,plain,
store(earray_41,index_42,e14) = earray_43,
inference(symmetry,[status(thm)],[1312]) ).
tff(1314,plain,
( ( q14 = queue_40 )
<=> ( q14 = queue_40 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1315,axiom,
q14 = queue_40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp359) ).
tff(1316,plain,
q14 = queue_40,
inference(modus_ponens,[status(thm)],[1315,1314]) ).
tff(1317,plain,
queue_40 = q14,
inference(symmetry,[status(thm)],[1316]) ).
tff(1318,plain,
( ( queue_40 = rstore_tail(queue_38,index_39) )
<=> ( queue_40 = rstore_tail(queue_38,index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1319,axiom,
queue_40 = rstore_tail(queue_38,index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp331) ).
tff(1320,plain,
queue_40 = rstore_tail(queue_38,index_39),
inference(modus_ponens,[status(thm)],[1319,1318]) ).
tff(1321,plain,
rstore_tail(queue_38,index_39) = queue_40,
inference(symmetry,[status(thm)],[1320]) ).
tff(1322,plain,
rstore_tail(queue_38,index_39) = q14,
inference(transitivity,[status(thm)],[1321,1317]) ).
tff(1323,plain,
rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14)) = rstore_seq(q14,earray_43),
inference(monotonicity,[status(thm)],[1322,1313]) ).
tff(1324,plain,
rstore_seq(q14,earray_43) = rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14)),
inference(symmetry,[status(thm)],[1323]) ).
tff(1325,plain,
rselect_head(rstore_seq(q14,earray_43)) = rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(monotonicity,[status(thm)],[1324]) ).
tff(1326,plain,
rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_seq(q14,earray_43)),
inference(symmetry,[status(thm)],[1325]) ).
tff(1327,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_tail(queue_38,index_39)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1328,plain,
rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_tail(queue_38,index_39)),
inference(unit_resolution,[status(thm)],[1327,85]) ).
tff(1329,plain,
rselect_head(rstore_tail(queue_38,index_39)) = rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(symmetry,[status(thm)],[1328]) ).
tff(1330,plain,
( ( index_39 = s(index_36) )
<=> ( index_39 = s(index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1331,axiom,
index_39 = s(index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(1332,plain,
index_39 = s(index_36),
inference(modus_ponens,[status(thm)],[1331,1330]) ).
tff(1333,plain,
s(index_36) = index_39,
inference(symmetry,[status(thm)],[1332]) ).
tff(1334,plain,
( ( queue_38 = rstore_seq(q13,earray_37) )
<=> ( queue_38 = rstore_seq(q13,earray_37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1335,axiom,
queue_38 = rstore_seq(q13,earray_37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp330) ).
tff(1336,plain,
queue_38 = rstore_seq(q13,earray_37),
inference(modus_ponens,[status(thm)],[1335,1334]) ).
tff(1337,plain,
rstore_seq(q13,earray_37) = queue_38,
inference(symmetry,[status(thm)],[1336]) ).
tff(1338,plain,
rstore_tail(rstore_seq(q13,earray_37),s(index_36)) = rstore_tail(queue_38,index_39),
inference(monotonicity,[status(thm)],[1337,1333]) ).
tff(1339,plain,
rstore_tail(queue_38,index_39) = rstore_tail(rstore_seq(q13,earray_37),s(index_36)),
inference(symmetry,[status(thm)],[1338]) ).
tff(1340,plain,
rselect_head(rstore_tail(queue_38,index_39)) = rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(monotonicity,[status(thm)],[1339]) ).
tff(1341,plain,
rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_tail(queue_38,index_39)),
inference(symmetry,[status(thm)],[1340]) ).
tff(1342,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_seq(q13,earray_37)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1343,plain,
rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_seq(q13,earray_37)),
inference(unit_resolution,[status(thm)],[1342,58]) ).
tff(1344,plain,
rselect_head(rstore_seq(q13,earray_37)) = rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(symmetry,[status(thm)],[1343]) ).
tff(1345,plain,
( ( earray_37 = store(earray_35,index_36,e13) )
<=> ( earray_37 = store(earray_35,index_36,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1346,axiom,
earray_37 = store(earray_35,index_36,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(1347,plain,
earray_37 = store(earray_35,index_36,e13),
inference(modus_ponens,[status(thm)],[1346,1345]) ).
tff(1348,plain,
store(earray_35,index_36,e13) = earray_37,
inference(symmetry,[status(thm)],[1347]) ).
tff(1349,plain,
( ( q13 = queue_34 )
<=> ( q13 = queue_34 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1350,axiom,
q13 = queue_34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp358) ).
tff(1351,plain,
q13 = queue_34,
inference(modus_ponens,[status(thm)],[1350,1349]) ).
tff(1352,plain,
queue_34 = q13,
inference(symmetry,[status(thm)],[1351]) ).
tff(1353,plain,
( ( queue_34 = rstore_tail(queue_32,index_33) )
<=> ( queue_34 = rstore_tail(queue_32,index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1354,axiom,
queue_34 = rstore_tail(queue_32,index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp325) ).
tff(1355,plain,
queue_34 = rstore_tail(queue_32,index_33),
inference(modus_ponens,[status(thm)],[1354,1353]) ).
tff(1356,plain,
rstore_tail(queue_32,index_33) = queue_34,
inference(symmetry,[status(thm)],[1355]) ).
tff(1357,plain,
rstore_tail(queue_32,index_33) = q13,
inference(transitivity,[status(thm)],[1356,1352]) ).
tff(1358,plain,
rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13)) = rstore_seq(q13,earray_37),
inference(monotonicity,[status(thm)],[1357,1348]) ).
tff(1359,plain,
rstore_seq(q13,earray_37) = rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13)),
inference(symmetry,[status(thm)],[1358]) ).
tff(1360,plain,
rselect_head(rstore_seq(q13,earray_37)) = rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(monotonicity,[status(thm)],[1359]) ).
tff(1361,plain,
rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_seq(q13,earray_37)),
inference(symmetry,[status(thm)],[1360]) ).
tff(1362,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_tail(queue_32,index_33)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1363,plain,
rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_tail(queue_32,index_33)),
inference(unit_resolution,[status(thm)],[1362,85]) ).
tff(1364,plain,
rselect_head(rstore_tail(queue_32,index_33)) = rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(symmetry,[status(thm)],[1363]) ).
tff(1365,plain,
( ( index_33 = s(index_30) )
<=> ( index_33 = s(index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1366,axiom,
index_33 = s(index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(1367,plain,
index_33 = s(index_30),
inference(modus_ponens,[status(thm)],[1366,1365]) ).
tff(1368,plain,
s(index_30) = index_33,
inference(symmetry,[status(thm)],[1367]) ).
tff(1369,plain,
( ( queue_32 = rstore_seq(q12,earray_31) )
<=> ( queue_32 = rstore_seq(q12,earray_31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1370,axiom,
queue_32 = rstore_seq(q12,earray_31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp318) ).
tff(1371,plain,
queue_32 = rstore_seq(q12,earray_31),
inference(modus_ponens,[status(thm)],[1370,1369]) ).
tff(1372,plain,
rstore_seq(q12,earray_31) = queue_32,
inference(symmetry,[status(thm)],[1371]) ).
tff(1373,plain,
rstore_tail(rstore_seq(q12,earray_31),s(index_30)) = rstore_tail(queue_32,index_33),
inference(monotonicity,[status(thm)],[1372,1368]) ).
tff(1374,plain,
rstore_tail(queue_32,index_33) = rstore_tail(rstore_seq(q12,earray_31),s(index_30)),
inference(symmetry,[status(thm)],[1373]) ).
tff(1375,plain,
rselect_head(rstore_tail(queue_32,index_33)) = rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(monotonicity,[status(thm)],[1374]) ).
tff(1376,plain,
rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_tail(queue_32,index_33)),
inference(symmetry,[status(thm)],[1375]) ).
tff(1377,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_seq(q12,earray_31)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1378,plain,
rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_seq(q12,earray_31)),
inference(unit_resolution,[status(thm)],[1377,58]) ).
tff(1379,plain,
rselect_head(rstore_seq(q12,earray_31)) = rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(symmetry,[status(thm)],[1378]) ).
tff(1380,plain,
( ( earray_31 = store(earray_29,index_30,e12) )
<=> ( earray_31 = store(earray_29,index_30,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1381,axiom,
earray_31 = store(earray_29,index_30,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp67) ).
tff(1382,plain,
earray_31 = store(earray_29,index_30,e12),
inference(modus_ponens,[status(thm)],[1381,1380]) ).
tff(1383,plain,
store(earray_29,index_30,e12) = earray_31,
inference(symmetry,[status(thm)],[1382]) ).
tff(1384,plain,
( ( q12 = queue_28 )
<=> ( q12 = queue_28 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1385,axiom,
q12 = queue_28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp357) ).
tff(1386,plain,
q12 = queue_28,
inference(modus_ponens,[status(thm)],[1385,1384]) ).
tff(1387,plain,
queue_28 = q12,
inference(symmetry,[status(thm)],[1386]) ).
tff(1388,plain,
( ( queue_28 = rstore_head(queue_25,index_27) )
<=> ( queue_28 = rstore_head(queue_25,index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1389,axiom,
queue_28 = rstore_head(queue_25,index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp303) ).
tff(1390,plain,
queue_28 = rstore_head(queue_25,index_27),
inference(modus_ponens,[status(thm)],[1389,1388]) ).
tff(1391,plain,
rstore_head(queue_25,index_27) = queue_28,
inference(symmetry,[status(thm)],[1390]) ).
tff(1392,plain,
rstore_head(queue_25,index_27) = q12,
inference(transitivity,[status(thm)],[1391,1387]) ).
tff(1393,plain,
rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12)) = rstore_seq(q12,earray_31),
inference(monotonicity,[status(thm)],[1392,1383]) ).
tff(1394,plain,
rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_seq(q12,earray_31)),
inference(monotonicity,[status(thm)],[1393]) ).
tff(1395,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_head(queue_25,index_27)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1396,plain,
rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_head(queue_25,index_27)),
inference(unit_resolution,[status(thm)],[1395,85]) ).
tff(1397,plain,
rselect_head(rstore_head(queue_25,index_27)) = rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))),
inference(symmetry,[status(thm)],[1396]) ).
tff(1398,plain,
( ( index_27 = s(index_26) )
<=> ( index_27 = s(index_26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1399,axiom,
index_27 = s(index_26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(1400,plain,
index_27 = s(index_26),
inference(modus_ponens,[status(thm)],[1399,1398]) ).
tff(1401,plain,
s(index_26) = index_27,
inference(symmetry,[status(thm)],[1400]) ).
tff(1402,plain,
( ( queue_25 = rstore_tail(queue_23,index_24) )
<=> ( queue_25 = rstore_tail(queue_23,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1403,axiom,
queue_25 = rstore_tail(queue_23,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp292) ).
tff(1404,plain,
queue_25 = rstore_tail(queue_23,index_24),
inference(modus_ponens,[status(thm)],[1403,1402]) ).
tff(1405,plain,
rstore_tail(queue_23,index_24) = queue_25,
inference(symmetry,[status(thm)],[1404]) ).
tff(1406,plain,
rstore_head(rstore_tail(queue_23,index_24),s(index_26)) = rstore_head(queue_25,index_27),
inference(monotonicity,[status(thm)],[1405,1401]) ).
tff(1407,plain,
rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_head(rstore_head(queue_25,index_27)),
inference(monotonicity,[status(thm)],[1406]) ).
tff(1408,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = s(index_26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1409,plain,
rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = s(index_26),
inference(unit_resolution,[status(thm)],[1408,173]) ).
tff(1410,plain,
s(index_26) = rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(symmetry,[status(thm)],[1409]) ).
tff(1411,plain,
( ( index_26 = rselect_head(queue_25) )
<=> ( index_26 = rselect_head(queue_25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1412,axiom,
index_26 = rselect_head(queue_25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(1413,plain,
index_26 = rselect_head(queue_25),
inference(modus_ponens,[status(thm)],[1412,1411]) ).
tff(1414,plain,
rselect_head(queue_25) = index_26,
inference(symmetry,[status(thm)],[1413]) ).
tff(1415,plain,
s(rselect_head(queue_25)) = s(index_26),
inference(monotonicity,[status(thm)],[1414]) ).
tff(1416,plain,
s(rselect_head(queue_25)) = index_47,
inference(transitivity,[status(thm)],[1415,1410,1407,1397,1394,1379,1376,1364,1361,1344,1341,1329,1326,1309,1306,1289]) ).
tff(1417,plain,
s(s(rselect_head(queue_25))) = s(index_47),
inference(monotonicity,[status(thm)],[1416]) ).
tff(1418,plain,
s(index_26) = s(rselect_head(queue_25)),
inference(symmetry,[status(thm)],[1415]) ).
tff(1419,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1420,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(1421,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[1420,1419]) ).
tff(1422,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[1421]) ).
tff(1423,plain,
( ( queue_23 = rstore_seq(q11,earray_22) )
<=> ( queue_23 = rstore_seq(q11,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1424,axiom,
queue_23 = rstore_seq(q11,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp285) ).
tff(1425,plain,
queue_23 = rstore_seq(q11,earray_22),
inference(modus_ponens,[status(thm)],[1424,1423]) ).
tff(1426,plain,
rstore_seq(q11,earray_22) = queue_23,
inference(symmetry,[status(thm)],[1425]) ).
tff(1427,plain,
rstore_tail(rstore_seq(q11,earray_22),s(index_21)) = rstore_tail(queue_23,index_24),
inference(monotonicity,[status(thm)],[1426,1422]) ).
tff(1428,plain,
rstore_tail(queue_23,index_24) = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(symmetry,[status(thm)],[1427]) ).
tff(1429,plain,
queue_25 = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(transitivity,[status(thm)],[1404,1428]) ).
tff(1430,plain,
rselect_head(queue_25) = rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[1429]) ).
tff(1431,plain,
rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(queue_25),
inference(symmetry,[status(thm)],[1430]) ).
tff(1432,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1433,plain,
rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)),
inference(unit_resolution,[status(thm)],[1432,58]) ).
tff(1434,plain,
rselect_head(rstore_seq(q11,earray_22)) = rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[1433]) ).
tff(1435,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1436,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(1437,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[1436,1435]) ).
tff(1438,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[1437]) ).
tff(1439,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1440,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp356) ).
tff(1441,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[1440,1439]) ).
tff(1442,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[1441]) ).
tff(1443,plain,
( ( queue_19 = rstore_tail(queue_17,index_18) )
<=> ( queue_19 = rstore_tail(queue_17,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1444,axiom,
queue_19 = rstore_tail(queue_17,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp270) ).
tff(1445,plain,
queue_19 = rstore_tail(queue_17,index_18),
inference(modus_ponens,[status(thm)],[1444,1443]) ).
tff(1446,plain,
rstore_tail(queue_17,index_18) = queue_19,
inference(symmetry,[status(thm)],[1445]) ).
tff(1447,plain,
rstore_tail(queue_17,index_18) = q11,
inference(transitivity,[status(thm)],[1446,1442]) ).
tff(1448,plain,
rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)) = rstore_seq(q11,earray_22),
inference(monotonicity,[status(thm)],[1447,1438]) ).
tff(1449,plain,
rstore_seq(q11,earray_22) = rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)),
inference(symmetry,[status(thm)],[1448]) ).
tff(1450,plain,
rselect_head(rstore_seq(q11,earray_22)) = rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(monotonicity,[status(thm)],[1449]) ).
tff(1451,plain,
rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_seq(q11,earray_22)),
inference(symmetry,[status(thm)],[1450]) ).
tff(1452,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1453,plain,
rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)),
inference(unit_resolution,[status(thm)],[1452,85]) ).
tff(1454,plain,
rselect_head(rstore_tail(queue_17,index_18)) = rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(symmetry,[status(thm)],[1453]) ).
tff(1455,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1456,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(1457,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[1456,1455]) ).
tff(1458,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
( ( queue_17 = rstore_seq(q10,earray_16) )
<=> ( queue_17 = rstore_seq(q10,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1460,axiom,
queue_17 = rstore_seq(q10,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp263) ).
tff(1461,plain,
queue_17 = rstore_seq(q10,earray_16),
inference(modus_ponens,[status(thm)],[1460,1459]) ).
tff(1462,plain,
rstore_seq(q10,earray_16) = queue_17,
inference(symmetry,[status(thm)],[1461]) ).
tff(1463,plain,
rstore_tail(rstore_seq(q10,earray_16),s(index_15)) = rstore_tail(queue_17,index_18),
inference(monotonicity,[status(thm)],[1462,1458]) ).
tff(1464,plain,
rstore_tail(queue_17,index_18) = rstore_tail(rstore_seq(q10,earray_16),s(index_15)),
inference(symmetry,[status(thm)],[1463]) ).
tff(1465,plain,
rselect_head(rstore_tail(queue_17,index_18)) = rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(monotonicity,[status(thm)],[1464]) ).
tff(1466,plain,
rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_tail(queue_17,index_18)),
inference(symmetry,[status(thm)],[1465]) ).
tff(1467,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1468,plain,
rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)),
inference(unit_resolution,[status(thm)],[1467,58]) ).
tff(1469,plain,
rselect_head(rstore_seq(q10,earray_16)) = rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[1468]) ).
tff(1470,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1471,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp19) ).
tff(1472,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[1471,1470]) ).
tff(1473,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[1472]) ).
tff(1474,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1475,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp355) ).
tff(1476,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[1475,1474]) ).
tff(1477,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[1476]) ).
tff(1478,plain,
( ( queue_13 = rstore_tail(queue_11,index_12) )
<=> ( queue_13 = rstore_tail(queue_11,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1479,axiom,
queue_13 = rstore_tail(queue_11,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp248) ).
tff(1480,plain,
queue_13 = rstore_tail(queue_11,index_12),
inference(modus_ponens,[status(thm)],[1479,1478]) ).
tff(1481,plain,
rstore_tail(queue_11,index_12) = queue_13,
inference(symmetry,[status(thm)],[1480]) ).
tff(1482,plain,
rstore_tail(queue_11,index_12) = q10,
inference(transitivity,[status(thm)],[1481,1477]) ).
tff(1483,plain,
rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)) = rstore_seq(q10,earray_16),
inference(monotonicity,[status(thm)],[1482,1473]) ).
tff(1484,plain,
rstore_seq(q10,earray_16) = rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)),
inference(symmetry,[status(thm)],[1483]) ).
tff(1485,plain,
rselect_head(rstore_seq(q10,earray_16)) = rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(monotonicity,[status(thm)],[1484]) ).
tff(1486,plain,
rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_seq(q10,earray_16)),
inference(symmetry,[status(thm)],[1485]) ).
tff(1487,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1488,plain,
rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)),
inference(unit_resolution,[status(thm)],[1487,85]) ).
tff(1489,plain,
rselect_head(rstore_tail(queue_11,index_12)) = rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(symmetry,[status(thm)],[1488]) ).
tff(1490,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1491,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(1492,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[1491,1490]) ).
tff(1493,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[1492]) ).
tff(1494,plain,
( ( queue_11 = rstore_seq(q9,earray_10) )
<=> ( queue_11 = rstore_seq(q9,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1495,axiom,
queue_11 = rstore_seq(q9,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(1496,plain,
queue_11 = rstore_seq(q9,earray_10),
inference(modus_ponens,[status(thm)],[1495,1494]) ).
tff(1497,plain,
rstore_seq(q9,earray_10) = queue_11,
inference(symmetry,[status(thm)],[1496]) ).
tff(1498,plain,
rstore_tail(rstore_seq(q9,earray_10),s(index_9)) = rstore_tail(queue_11,index_12),
inference(monotonicity,[status(thm)],[1497,1493]) ).
tff(1499,plain,
rstore_tail(queue_11,index_12) = rstore_tail(rstore_seq(q9,earray_10),s(index_9)),
inference(symmetry,[status(thm)],[1498]) ).
tff(1500,plain,
rselect_head(rstore_tail(queue_11,index_12)) = rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(monotonicity,[status(thm)],[1499]) ).
tff(1501,plain,
rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_tail(queue_11,index_12)),
inference(symmetry,[status(thm)],[1500]) ).
tff(1502,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1503,plain,
rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)),
inference(unit_resolution,[status(thm)],[1502,58]) ).
tff(1504,plain,
rselect_head(rstore_seq(q9,earray_10)) = rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(symmetry,[status(thm)],[1503]) ).
tff(1505,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1506,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(1507,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[1506,1505]) ).
tff(1508,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[1507]) ).
tff(1509,plain,
( ( q9 = queue_349 )
<=> ( q9 = queue_349 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1510,axiom,
q9 = queue_349,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp403) ).
tff(1511,plain,
q9 = queue_349,
inference(modus_ponens,[status(thm)],[1510,1509]) ).
tff(1512,plain,
queue_349 = q9,
inference(symmetry,[status(thm)],[1511]) ).
tff(1513,plain,
( ( queue_349 = rstore_head(queue_346,index_348) )
<=> ( queue_349 = rstore_head(queue_346,index_348) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1514,axiom,
queue_349 = rstore_head(queue_346,index_348),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp329) ).
tff(1515,plain,
queue_349 = rstore_head(queue_346,index_348),
inference(modus_ponens,[status(thm)],[1514,1513]) ).
tff(1516,plain,
rstore_head(queue_346,index_348) = queue_349,
inference(symmetry,[status(thm)],[1515]) ).
tff(1517,plain,
rstore_head(queue_346,index_348) = q9,
inference(transitivity,[status(thm)],[1516,1512]) ).
tff(1518,plain,
rstore_seq(rstore_head(queue_346,index_348),store(earray_8,index_9,e9)) = rstore_seq(q9,earray_10),
inference(monotonicity,[status(thm)],[1517,1508]) ).
tff(1519,plain,
rselect_head(rstore_seq(rstore_head(queue_346,index_348),store(earray_8,index_9,e9))) = rselect_head(rstore_seq(q9,earray_10)),
inference(monotonicity,[status(thm)],[1518]) ).
tff(1520,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_346,index_348),store(earray_8,index_9,e9))) = rselect_head(rstore_head(queue_346,index_348)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1521,plain,
rselect_head(rstore_seq(rstore_head(queue_346,index_348),store(earray_8,index_9,e9))) = rselect_head(rstore_head(queue_346,index_348)),
inference(unit_resolution,[status(thm)],[1520,85]) ).
tff(1522,plain,
rselect_head(rstore_head(queue_346,index_348)) = rselect_head(rstore_seq(rstore_head(queue_346,index_348),store(earray_8,index_9,e9))),
inference(symmetry,[status(thm)],[1521]) ).
tff(1523,plain,
( ( index_348 = s(index_347) )
<=> ( index_348 = s(index_347) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1524,axiom,
index_348 = s(index_347),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(1525,plain,
index_348 = s(index_347),
inference(modus_ponens,[status(thm)],[1524,1523]) ).
tff(1526,plain,
s(index_347) = index_348,
inference(symmetry,[status(thm)],[1525]) ).
tff(1527,plain,
( ( queue_346 = rstore_tail(queue_344,index_345) )
<=> ( queue_346 = rstore_tail(queue_344,index_345) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1528,axiom,
queue_346 = rstore_tail(queue_344,index_345),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp328) ).
tff(1529,plain,
queue_346 = rstore_tail(queue_344,index_345),
inference(modus_ponens,[status(thm)],[1528,1527]) ).
tff(1530,plain,
rstore_tail(queue_344,index_345) = queue_346,
inference(symmetry,[status(thm)],[1529]) ).
tff(1531,plain,
rstore_head(rstore_tail(queue_344,index_345),s(index_347)) = rstore_head(queue_346,index_348),
inference(monotonicity,[status(thm)],[1530,1526]) ).
tff(1532,plain,
rselect_head(rstore_head(rstore_tail(queue_344,index_345),s(index_347))) = rselect_head(rstore_head(queue_346,index_348)),
inference(monotonicity,[status(thm)],[1531]) ).
tff(1533,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_344,index_345),s(index_347))) = s(index_347) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1534,plain,
rselect_head(rstore_head(rstore_tail(queue_344,index_345),s(index_347))) = s(index_347),
inference(unit_resolution,[status(thm)],[1533,173]) ).
tff(1535,plain,
s(index_347) = rselect_head(rstore_head(rstore_tail(queue_344,index_345),s(index_347))),
inference(symmetry,[status(thm)],[1534]) ).
tff(1536,plain,
( ( index_347 = rselect_head(queue_346) )
<=> ( index_347 = rselect_head(queue_346) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1537,axiom,
index_347 = rselect_head(queue_346),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(1538,plain,
index_347 = rselect_head(queue_346),
inference(modus_ponens,[status(thm)],[1537,1536]) ).
tff(1539,plain,
rselect_head(queue_346) = index_347,
inference(symmetry,[status(thm)],[1538]) ).
tff(1540,plain,
s(rselect_head(queue_346)) = s(index_347),
inference(monotonicity,[status(thm)],[1539]) ).
tff(1541,plain,
s(rselect_head(queue_346)) = index_26,
inference(transitivity,[status(thm)],[1540,1535,1532,1522,1519,1504,1501,1489,1486,1469,1466,1454,1451,1434,1431,1414]) ).
tff(1542,plain,
s(s(rselect_head(queue_346))) = s(index_26),
inference(monotonicity,[status(thm)],[1541]) ).
tff(1543,plain,
s(index_347) = s(rselect_head(queue_346)),
inference(symmetry,[status(thm)],[1540]) ).
tff(1544,plain,
( ( index_345 = s(index_342) )
<=> ( index_345 = s(index_342) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1545,axiom,
index_345 = s(index_342),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(1546,plain,
index_345 = s(index_342),
inference(modus_ponens,[status(thm)],[1545,1544]) ).
tff(1547,plain,
s(index_342) = index_345,
inference(symmetry,[status(thm)],[1546]) ).
tff(1548,plain,
( ( queue_344 = rstore_seq(q8,earray_343) )
<=> ( queue_344 = rstore_seq(q8,earray_343) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1549,axiom,
queue_344 = rstore_seq(q8,earray_343),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp327) ).
tff(1550,plain,
queue_344 = rstore_seq(q8,earray_343),
inference(modus_ponens,[status(thm)],[1549,1548]) ).
tff(1551,plain,
rstore_seq(q8,earray_343) = queue_344,
inference(symmetry,[status(thm)],[1550]) ).
tff(1552,plain,
rstore_tail(rstore_seq(q8,earray_343),s(index_342)) = rstore_tail(queue_344,index_345),
inference(monotonicity,[status(thm)],[1551,1547]) ).
tff(1553,plain,
rstore_tail(queue_344,index_345) = rstore_tail(rstore_seq(q8,earray_343),s(index_342)),
inference(symmetry,[status(thm)],[1552]) ).
tff(1554,plain,
queue_346 = rstore_tail(rstore_seq(q8,earray_343),s(index_342)),
inference(transitivity,[status(thm)],[1529,1553]) ).
tff(1555,plain,
rselect_head(queue_346) = rselect_head(rstore_tail(rstore_seq(q8,earray_343),s(index_342))),
inference(monotonicity,[status(thm)],[1554]) ).
tff(1556,plain,
rselect_head(rstore_tail(rstore_seq(q8,earray_343),s(index_342))) = rselect_head(queue_346),
inference(symmetry,[status(thm)],[1555]) ).
tff(1557,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q8,earray_343),s(index_342))) = rselect_head(rstore_seq(q8,earray_343)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1558,plain,
rselect_head(rstore_tail(rstore_seq(q8,earray_343),s(index_342))) = rselect_head(rstore_seq(q8,earray_343)),
inference(unit_resolution,[status(thm)],[1557,58]) ).
tff(1559,plain,
rselect_head(rstore_seq(q8,earray_343)) = rselect_head(rstore_tail(rstore_seq(q8,earray_343),s(index_342))),
inference(symmetry,[status(thm)],[1558]) ).
tff(1560,plain,
( ( earray_343 = store(earray_341,index_342,e8) )
<=> ( earray_343 = store(earray_341,index_342,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1561,axiom,
earray_343 = store(earray_341,index_342,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(1562,plain,
earray_343 = store(earray_341,index_342,e8),
inference(modus_ponens,[status(thm)],[1561,1560]) ).
tff(1563,plain,
store(earray_341,index_342,e8) = earray_343,
inference(symmetry,[status(thm)],[1562]) ).
tff(1564,plain,
( ( q8 = queue_340 )
<=> ( q8 = queue_340 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1565,axiom,
q8 = queue_340,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp402) ).
tff(1566,plain,
q8 = queue_340,
inference(modus_ponens,[status(thm)],[1565,1564]) ).
tff(1567,plain,
queue_340 = q8,
inference(symmetry,[status(thm)],[1566]) ).
tff(1568,plain,
( ( queue_340 = rstore_tail(queue_338,index_339) )
<=> ( queue_340 = rstore_tail(queue_338,index_339) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1569,axiom,
queue_340 = rstore_tail(queue_338,index_339),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp326) ).
tff(1570,plain,
queue_340 = rstore_tail(queue_338,index_339),
inference(modus_ponens,[status(thm)],[1569,1568]) ).
tff(1571,plain,
rstore_tail(queue_338,index_339) = queue_340,
inference(symmetry,[status(thm)],[1570]) ).
tff(1572,plain,
rstore_tail(queue_338,index_339) = q8,
inference(transitivity,[status(thm)],[1571,1567]) ).
tff(1573,plain,
rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8)) = rstore_seq(q8,earray_343),
inference(monotonicity,[status(thm)],[1572,1563]) ).
tff(1574,plain,
rstore_seq(q8,earray_343) = rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8)),
inference(symmetry,[status(thm)],[1573]) ).
tff(1575,plain,
rselect_head(rstore_seq(q8,earray_343)) = rselect_head(rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8))),
inference(monotonicity,[status(thm)],[1574]) ).
tff(1576,plain,
rselect_head(rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8))) = rselect_head(rstore_seq(q8,earray_343)),
inference(symmetry,[status(thm)],[1575]) ).
tff(1577,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8))) = rselect_head(rstore_tail(queue_338,index_339)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1578,plain,
rselect_head(rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8))) = rselect_head(rstore_tail(queue_338,index_339)),
inference(unit_resolution,[status(thm)],[1577,85]) ).
tff(1579,plain,
rselect_head(rstore_tail(queue_338,index_339)) = rselect_head(rstore_seq(rstore_tail(queue_338,index_339),store(earray_341,index_342,e8))),
inference(symmetry,[status(thm)],[1578]) ).
tff(1580,plain,
( ( index_339 = s(index_336) )
<=> ( index_339 = s(index_336) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1581,axiom,
index_339 = s(index_336),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(1582,plain,
index_339 = s(index_336),
inference(modus_ponens,[status(thm)],[1581,1580]) ).
tff(1583,plain,
s(index_336) = index_339,
inference(symmetry,[status(thm)],[1582]) ).
tff(1584,plain,
( ( queue_338 = rstore_seq(q7,earray_337) )
<=> ( queue_338 = rstore_seq(q7,earray_337) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1585,axiom,
queue_338 = rstore_seq(q7,earray_337),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp324) ).
tff(1586,plain,
queue_338 = rstore_seq(q7,earray_337),
inference(modus_ponens,[status(thm)],[1585,1584]) ).
tff(1587,plain,
rstore_seq(q7,earray_337) = queue_338,
inference(symmetry,[status(thm)],[1586]) ).
tff(1588,plain,
rstore_tail(rstore_seq(q7,earray_337),s(index_336)) = rstore_tail(queue_338,index_339),
inference(monotonicity,[status(thm)],[1587,1583]) ).
tff(1589,plain,
rstore_tail(queue_338,index_339) = rstore_tail(rstore_seq(q7,earray_337),s(index_336)),
inference(symmetry,[status(thm)],[1588]) ).
tff(1590,plain,
rselect_head(rstore_tail(queue_338,index_339)) = rselect_head(rstore_tail(rstore_seq(q7,earray_337),s(index_336))),
inference(monotonicity,[status(thm)],[1589]) ).
tff(1591,plain,
rselect_head(rstore_tail(rstore_seq(q7,earray_337),s(index_336))) = rselect_head(rstore_tail(queue_338,index_339)),
inference(symmetry,[status(thm)],[1590]) ).
tff(1592,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q7,earray_337),s(index_336))) = rselect_head(rstore_seq(q7,earray_337)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1593,plain,
rselect_head(rstore_tail(rstore_seq(q7,earray_337),s(index_336))) = rselect_head(rstore_seq(q7,earray_337)),
inference(unit_resolution,[status(thm)],[1592,58]) ).
tff(1594,plain,
rselect_head(rstore_seq(q7,earray_337)) = rselect_head(rstore_tail(rstore_seq(q7,earray_337),s(index_336))),
inference(symmetry,[status(thm)],[1593]) ).
tff(1595,plain,
( ( earray_337 = store(earray_335,index_336,e7) )
<=> ( earray_337 = store(earray_335,index_336,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1596,axiom,
earray_337 = store(earray_335,index_336,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(1597,plain,
earray_337 = store(earray_335,index_336,e7),
inference(modus_ponens,[status(thm)],[1596,1595]) ).
tff(1598,plain,
store(earray_335,index_336,e7) = earray_337,
inference(symmetry,[status(thm)],[1597]) ).
tff(1599,plain,
( ( q7 = queue_334 )
<=> ( q7 = queue_334 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1600,axiom,
q7 = queue_334,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp401) ).
tff(1601,plain,
q7 = queue_334,
inference(modus_ponens,[status(thm)],[1600,1599]) ).
tff(1602,plain,
queue_334 = q7,
inference(symmetry,[status(thm)],[1601]) ).
tff(1603,plain,
( ( queue_334 = rstore_tail(queue_332,index_333) )
<=> ( queue_334 = rstore_tail(queue_332,index_333) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1604,axiom,
queue_334 = rstore_tail(queue_332,index_333),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp323) ).
tff(1605,plain,
queue_334 = rstore_tail(queue_332,index_333),
inference(modus_ponens,[status(thm)],[1604,1603]) ).
tff(1606,plain,
rstore_tail(queue_332,index_333) = queue_334,
inference(symmetry,[status(thm)],[1605]) ).
tff(1607,plain,
rstore_tail(queue_332,index_333) = q7,
inference(transitivity,[status(thm)],[1606,1602]) ).
tff(1608,plain,
rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7)) = rstore_seq(q7,earray_337),
inference(monotonicity,[status(thm)],[1607,1598]) ).
tff(1609,plain,
rstore_seq(q7,earray_337) = rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7)),
inference(symmetry,[status(thm)],[1608]) ).
tff(1610,plain,
rselect_head(rstore_seq(q7,earray_337)) = rselect_head(rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7))),
inference(monotonicity,[status(thm)],[1609]) ).
tff(1611,plain,
rselect_head(rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7))) = rselect_head(rstore_seq(q7,earray_337)),
inference(symmetry,[status(thm)],[1610]) ).
tff(1612,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7))) = rselect_head(rstore_tail(queue_332,index_333)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1613,plain,
rselect_head(rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7))) = rselect_head(rstore_tail(queue_332,index_333)),
inference(unit_resolution,[status(thm)],[1612,85]) ).
tff(1614,plain,
rselect_head(rstore_tail(queue_332,index_333)) = rselect_head(rstore_seq(rstore_tail(queue_332,index_333),store(earray_335,index_336,e7))),
inference(symmetry,[status(thm)],[1613]) ).
tff(1615,plain,
( ( index_333 = s(index_330) )
<=> ( index_333 = s(index_330) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1616,axiom,
index_333 = s(index_330),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(1617,plain,
index_333 = s(index_330),
inference(modus_ponens,[status(thm)],[1616,1615]) ).
tff(1618,plain,
s(index_330) = index_333,
inference(symmetry,[status(thm)],[1617]) ).
tff(1619,plain,
( ( queue_332 = rstore_seq(q6,earray_331) )
<=> ( queue_332 = rstore_seq(q6,earray_331) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1620,axiom,
queue_332 = rstore_seq(q6,earray_331),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp322) ).
tff(1621,plain,
queue_332 = rstore_seq(q6,earray_331),
inference(modus_ponens,[status(thm)],[1620,1619]) ).
tff(1622,plain,
rstore_seq(q6,earray_331) = queue_332,
inference(symmetry,[status(thm)],[1621]) ).
tff(1623,plain,
rstore_tail(rstore_seq(q6,earray_331),s(index_330)) = rstore_tail(queue_332,index_333),
inference(monotonicity,[status(thm)],[1622,1618]) ).
tff(1624,plain,
rstore_tail(queue_332,index_333) = rstore_tail(rstore_seq(q6,earray_331),s(index_330)),
inference(symmetry,[status(thm)],[1623]) ).
tff(1625,plain,
rselect_head(rstore_tail(queue_332,index_333)) = rselect_head(rstore_tail(rstore_seq(q6,earray_331),s(index_330))),
inference(monotonicity,[status(thm)],[1624]) ).
tff(1626,plain,
rselect_head(rstore_tail(rstore_seq(q6,earray_331),s(index_330))) = rselect_head(rstore_tail(queue_332,index_333)),
inference(symmetry,[status(thm)],[1625]) ).
tff(1627,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q6,earray_331),s(index_330))) = rselect_head(rstore_seq(q6,earray_331)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1628,plain,
rselect_head(rstore_tail(rstore_seq(q6,earray_331),s(index_330))) = rselect_head(rstore_seq(q6,earray_331)),
inference(unit_resolution,[status(thm)],[1627,58]) ).
tff(1629,plain,
rselect_head(rstore_seq(q6,earray_331)) = rselect_head(rstore_tail(rstore_seq(q6,earray_331),s(index_330))),
inference(symmetry,[status(thm)],[1628]) ).
tff(1630,plain,
( ( earray_331 = store(earray_329,index_330,e6) )
<=> ( earray_331 = store(earray_329,index_330,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1631,axiom,
earray_331 = store(earray_329,index_330,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(1632,plain,
earray_331 = store(earray_329,index_330,e6),
inference(modus_ponens,[status(thm)],[1631,1630]) ).
tff(1633,plain,
store(earray_329,index_330,e6) = earray_331,
inference(symmetry,[status(thm)],[1632]) ).
tff(1634,plain,
( ( q6 = queue_328 )
<=> ( q6 = queue_328 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1635,axiom,
q6 = queue_328,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp400) ).
tff(1636,plain,
q6 = queue_328,
inference(modus_ponens,[status(thm)],[1635,1634]) ).
tff(1637,plain,
queue_328 = q6,
inference(symmetry,[status(thm)],[1636]) ).
tff(1638,plain,
( ( queue_328 = rstore_head(queue_325,index_327) )
<=> ( queue_328 = rstore_head(queue_325,index_327) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1639,axiom,
queue_328 = rstore_head(queue_325,index_327),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp321) ).
tff(1640,plain,
queue_328 = rstore_head(queue_325,index_327),
inference(modus_ponens,[status(thm)],[1639,1638]) ).
tff(1641,plain,
rstore_head(queue_325,index_327) = queue_328,
inference(symmetry,[status(thm)],[1640]) ).
tff(1642,plain,
rstore_head(queue_325,index_327) = q6,
inference(transitivity,[status(thm)],[1641,1637]) ).
tff(1643,plain,
rstore_seq(rstore_head(queue_325,index_327),store(earray_329,index_330,e6)) = rstore_seq(q6,earray_331),
inference(monotonicity,[status(thm)],[1642,1633]) ).
tff(1644,plain,
rselect_head(rstore_seq(rstore_head(queue_325,index_327),store(earray_329,index_330,e6))) = rselect_head(rstore_seq(q6,earray_331)),
inference(monotonicity,[status(thm)],[1643]) ).
tff(1645,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_325,index_327),store(earray_329,index_330,e6))) = rselect_head(rstore_head(queue_325,index_327)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1646,plain,
rselect_head(rstore_seq(rstore_head(queue_325,index_327),store(earray_329,index_330,e6))) = rselect_head(rstore_head(queue_325,index_327)),
inference(unit_resolution,[status(thm)],[1645,85]) ).
tff(1647,plain,
rselect_head(rstore_head(queue_325,index_327)) = rselect_head(rstore_seq(rstore_head(queue_325,index_327),store(earray_329,index_330,e6))),
inference(symmetry,[status(thm)],[1646]) ).
tff(1648,plain,
( ( index_327 = s(index_326) )
<=> ( index_327 = s(index_326) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1649,axiom,
index_327 = s(index_326),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(1650,plain,
index_327 = s(index_326),
inference(modus_ponens,[status(thm)],[1649,1648]) ).
tff(1651,plain,
s(index_326) = index_327,
inference(symmetry,[status(thm)],[1650]) ).
tff(1652,plain,
( ( queue_325 = rstore_tail(queue_323,index_324) )
<=> ( queue_325 = rstore_tail(queue_323,index_324) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1653,axiom,
queue_325 = rstore_tail(queue_323,index_324),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp320) ).
tff(1654,plain,
queue_325 = rstore_tail(queue_323,index_324),
inference(modus_ponens,[status(thm)],[1653,1652]) ).
tff(1655,plain,
rstore_tail(queue_323,index_324) = queue_325,
inference(symmetry,[status(thm)],[1654]) ).
tff(1656,plain,
rstore_head(rstore_tail(queue_323,index_324),s(index_326)) = rstore_head(queue_325,index_327),
inference(monotonicity,[status(thm)],[1655,1651]) ).
tff(1657,plain,
rselect_head(rstore_head(rstore_tail(queue_323,index_324),s(index_326))) = rselect_head(rstore_head(queue_325,index_327)),
inference(monotonicity,[status(thm)],[1656]) ).
tff(1658,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_323,index_324),s(index_326))) = s(index_326) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1659,plain,
rselect_head(rstore_head(rstore_tail(queue_323,index_324),s(index_326))) = s(index_326),
inference(unit_resolution,[status(thm)],[1658,173]) ).
tff(1660,plain,
s(index_326) = rselect_head(rstore_head(rstore_tail(queue_323,index_324),s(index_326))),
inference(symmetry,[status(thm)],[1659]) ).
tff(1661,plain,
( ( index_326 = rselect_head(queue_325) )
<=> ( index_326 = rselect_head(queue_325) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1662,axiom,
index_326 = rselect_head(queue_325),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(1663,plain,
index_326 = rselect_head(queue_325),
inference(modus_ponens,[status(thm)],[1662,1661]) ).
tff(1664,plain,
rselect_head(queue_325) = index_326,
inference(symmetry,[status(thm)],[1663]) ).
tff(1665,plain,
s(rselect_head(queue_325)) = s(index_326),
inference(monotonicity,[status(thm)],[1664]) ).
tff(1666,plain,
s(rselect_head(queue_325)) = index_347,
inference(transitivity,[status(thm)],[1665,1660,1657,1647,1644,1629,1626,1614,1611,1594,1591,1579,1576,1559,1556,1539]) ).
tff(1667,plain,
s(s(rselect_head(queue_325))) = s(index_347),
inference(monotonicity,[status(thm)],[1666]) ).
tff(1668,plain,
s(index_326) = s(rselect_head(queue_325)),
inference(symmetry,[status(thm)],[1665]) ).
tff(1669,plain,
( ( index_324 = s(index_321) )
<=> ( index_324 = s(index_321) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1670,axiom,
index_324 = s(index_321),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(1671,plain,
index_324 = s(index_321),
inference(modus_ponens,[status(thm)],[1670,1669]) ).
tff(1672,plain,
s(index_321) = index_324,
inference(symmetry,[status(thm)],[1671]) ).
tff(1673,plain,
( ( queue_323 = rstore_seq(q5,earray_322) )
<=> ( queue_323 = rstore_seq(q5,earray_322) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1674,axiom,
queue_323 = rstore_seq(q5,earray_322),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp319) ).
tff(1675,plain,
queue_323 = rstore_seq(q5,earray_322),
inference(modus_ponens,[status(thm)],[1674,1673]) ).
tff(1676,plain,
rstore_seq(q5,earray_322) = queue_323,
inference(symmetry,[status(thm)],[1675]) ).
tff(1677,plain,
rstore_tail(rstore_seq(q5,earray_322),s(index_321)) = rstore_tail(queue_323,index_324),
inference(monotonicity,[status(thm)],[1676,1672]) ).
tff(1678,plain,
rstore_tail(queue_323,index_324) = rstore_tail(rstore_seq(q5,earray_322),s(index_321)),
inference(symmetry,[status(thm)],[1677]) ).
tff(1679,plain,
queue_325 = rstore_tail(rstore_seq(q5,earray_322),s(index_321)),
inference(transitivity,[status(thm)],[1654,1678]) ).
tff(1680,plain,
rselect_head(queue_325) = rselect_head(rstore_tail(rstore_seq(q5,earray_322),s(index_321))),
inference(monotonicity,[status(thm)],[1679]) ).
tff(1681,plain,
rselect_head(rstore_tail(rstore_seq(q5,earray_322),s(index_321))) = rselect_head(queue_325),
inference(symmetry,[status(thm)],[1680]) ).
tff(1682,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q5,earray_322),s(index_321))) = rselect_head(rstore_seq(q5,earray_322)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1683,plain,
rselect_head(rstore_tail(rstore_seq(q5,earray_322),s(index_321))) = rselect_head(rstore_seq(q5,earray_322)),
inference(unit_resolution,[status(thm)],[1682,58]) ).
tff(1684,plain,
rselect_head(rstore_seq(q5,earray_322)) = rselect_head(rstore_tail(rstore_seq(q5,earray_322),s(index_321))),
inference(symmetry,[status(thm)],[1683]) ).
tff(1685,plain,
( ( earray_322 = store(earray_320,index_321,e5) )
<=> ( earray_322 = store(earray_320,index_321,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1686,axiom,
earray_322 = store(earray_320,index_321,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(1687,plain,
earray_322 = store(earray_320,index_321,e5),
inference(modus_ponens,[status(thm)],[1686,1685]) ).
tff(1688,plain,
store(earray_320,index_321,e5) = earray_322,
inference(symmetry,[status(thm)],[1687]) ).
tff(1689,plain,
( ( q5 = queue_313 )
<=> ( q5 = queue_313 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1690,axiom,
q5 = queue_313,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp398) ).
tff(1691,plain,
q5 = queue_313,
inference(modus_ponens,[status(thm)],[1690,1689]) ).
tff(1692,plain,
queue_313 = q5,
inference(symmetry,[status(thm)],[1691]) ).
tff(1693,plain,
( ( queue_313 = rstore_tail(queue_311,index_312) )
<=> ( queue_313 = rstore_tail(queue_311,index_312) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1694,axiom,
queue_313 = rstore_tail(queue_311,index_312),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp315) ).
tff(1695,plain,
queue_313 = rstore_tail(queue_311,index_312),
inference(modus_ponens,[status(thm)],[1694,1693]) ).
tff(1696,plain,
rstore_tail(queue_311,index_312) = queue_313,
inference(symmetry,[status(thm)],[1695]) ).
tff(1697,plain,
rstore_tail(queue_311,index_312) = q5,
inference(transitivity,[status(thm)],[1696,1692]) ).
tff(1698,plain,
rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5)) = rstore_seq(q5,earray_322),
inference(monotonicity,[status(thm)],[1697,1688]) ).
tff(1699,plain,
rstore_seq(q5,earray_322) = rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5)),
inference(symmetry,[status(thm)],[1698]) ).
tff(1700,plain,
rselect_head(rstore_seq(q5,earray_322)) = rselect_head(rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5))),
inference(monotonicity,[status(thm)],[1699]) ).
tff(1701,plain,
rselect_head(rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5))) = rselect_head(rstore_seq(q5,earray_322)),
inference(symmetry,[status(thm)],[1700]) ).
tff(1702,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5))) = rselect_head(rstore_tail(queue_311,index_312)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1703,plain,
rselect_head(rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5))) = rselect_head(rstore_tail(queue_311,index_312)),
inference(unit_resolution,[status(thm)],[1702,85]) ).
tff(1704,plain,
rselect_head(rstore_tail(queue_311,index_312)) = rselect_head(rstore_seq(rstore_tail(queue_311,index_312),store(earray_320,index_321,e5))),
inference(symmetry,[status(thm)],[1703]) ).
tff(1705,plain,
( ( index_312 = s(index_309) )
<=> ( index_312 = s(index_309) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1706,axiom,
index_312 = s(index_309),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(1707,plain,
index_312 = s(index_309),
inference(modus_ponens,[status(thm)],[1706,1705]) ).
tff(1708,plain,
s(index_309) = index_312,
inference(symmetry,[status(thm)],[1707]) ).
tff(1709,plain,
( ( queue_311 = rstore_seq(q4,earray_310) )
<=> ( queue_311 = rstore_seq(q4,earray_310) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1710,axiom,
queue_311 = rstore_seq(q4,earray_310),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp314) ).
tff(1711,plain,
queue_311 = rstore_seq(q4,earray_310),
inference(modus_ponens,[status(thm)],[1710,1709]) ).
tff(1712,plain,
rstore_seq(q4,earray_310) = queue_311,
inference(symmetry,[status(thm)],[1711]) ).
tff(1713,plain,
rstore_tail(rstore_seq(q4,earray_310),s(index_309)) = rstore_tail(queue_311,index_312),
inference(monotonicity,[status(thm)],[1712,1708]) ).
tff(1714,plain,
rstore_tail(queue_311,index_312) = rstore_tail(rstore_seq(q4,earray_310),s(index_309)),
inference(symmetry,[status(thm)],[1713]) ).
tff(1715,plain,
rselect_head(rstore_tail(queue_311,index_312)) = rselect_head(rstore_tail(rstore_seq(q4,earray_310),s(index_309))),
inference(monotonicity,[status(thm)],[1714]) ).
tff(1716,plain,
rselect_head(rstore_tail(rstore_seq(q4,earray_310),s(index_309))) = rselect_head(rstore_tail(queue_311,index_312)),
inference(symmetry,[status(thm)],[1715]) ).
tff(1717,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q4,earray_310),s(index_309))) = rselect_head(rstore_seq(q4,earray_310)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1718,plain,
rselect_head(rstore_tail(rstore_seq(q4,earray_310),s(index_309))) = rselect_head(rstore_seq(q4,earray_310)),
inference(unit_resolution,[status(thm)],[1717,58]) ).
tff(1719,plain,
rselect_head(rstore_seq(q4,earray_310)) = rselect_head(rstore_tail(rstore_seq(q4,earray_310),s(index_309))),
inference(symmetry,[status(thm)],[1718]) ).
tff(1720,plain,
( ( earray_310 = store(earray_308,index_309,e4) )
<=> ( earray_310 = store(earray_308,index_309,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1721,axiom,
earray_310 = store(earray_308,index_309,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(1722,plain,
earray_310 = store(earray_308,index_309,e4),
inference(modus_ponens,[status(thm)],[1721,1720]) ).
tff(1723,plain,
store(earray_308,index_309,e4) = earray_310,
inference(symmetry,[status(thm)],[1722]) ).
tff(1724,plain,
( ( q4 = queue_238 )
<=> ( q4 = queue_238 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1725,axiom,
q4 = queue_238,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp387) ).
tff(1726,plain,
q4 = queue_238,
inference(modus_ponens,[status(thm)],[1725,1724]) ).
tff(1727,plain,
queue_238 = q4,
inference(symmetry,[status(thm)],[1726]) ).
tff(1728,plain,
( ( queue_238 = rstore_tail(queue_236,index_237) )
<=> ( queue_238 = rstore_tail(queue_236,index_237) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1729,axiom,
queue_238 = rstore_tail(queue_236,index_237),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp288) ).
tff(1730,plain,
queue_238 = rstore_tail(queue_236,index_237),
inference(modus_ponens,[status(thm)],[1729,1728]) ).
tff(1731,plain,
rstore_tail(queue_236,index_237) = queue_238,
inference(symmetry,[status(thm)],[1730]) ).
tff(1732,plain,
rstore_tail(queue_236,index_237) = q4,
inference(transitivity,[status(thm)],[1731,1727]) ).
tff(1733,plain,
rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4)) = rstore_seq(q4,earray_310),
inference(monotonicity,[status(thm)],[1732,1723]) ).
tff(1734,plain,
rstore_seq(q4,earray_310) = rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4)),
inference(symmetry,[status(thm)],[1733]) ).
tff(1735,plain,
rselect_head(rstore_seq(q4,earray_310)) = rselect_head(rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4))),
inference(monotonicity,[status(thm)],[1734]) ).
tff(1736,plain,
rselect_head(rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4))) = rselect_head(rstore_seq(q4,earray_310)),
inference(symmetry,[status(thm)],[1735]) ).
tff(1737,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4))) = rselect_head(rstore_tail(queue_236,index_237)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1738,plain,
rselect_head(rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4))) = rselect_head(rstore_tail(queue_236,index_237)),
inference(unit_resolution,[status(thm)],[1737,85]) ).
tff(1739,plain,
rselect_head(rstore_tail(queue_236,index_237)) = rselect_head(rstore_seq(rstore_tail(queue_236,index_237),store(earray_308,index_309,e4))),
inference(symmetry,[status(thm)],[1738]) ).
tff(1740,plain,
( ( index_237 = s(index_234) )
<=> ( index_237 = s(index_234) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1741,axiom,
index_237 = s(index_234),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(1742,plain,
index_237 = s(index_234),
inference(modus_ponens,[status(thm)],[1741,1740]) ).
tff(1743,plain,
s(index_234) = index_237,
inference(symmetry,[status(thm)],[1742]) ).
tff(1744,plain,
( ( queue_236 = rstore_seq(q3,earray_235) )
<=> ( queue_236 = rstore_seq(q3,earray_235) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1745,axiom,
queue_236 = rstore_seq(q3,earray_235),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp287) ).
tff(1746,plain,
queue_236 = rstore_seq(q3,earray_235),
inference(modus_ponens,[status(thm)],[1745,1744]) ).
tff(1747,plain,
rstore_seq(q3,earray_235) = queue_236,
inference(symmetry,[status(thm)],[1746]) ).
tff(1748,plain,
rstore_tail(rstore_seq(q3,earray_235),s(index_234)) = rstore_tail(queue_236,index_237),
inference(monotonicity,[status(thm)],[1747,1743]) ).
tff(1749,plain,
rstore_tail(queue_236,index_237) = rstore_tail(rstore_seq(q3,earray_235),s(index_234)),
inference(symmetry,[status(thm)],[1748]) ).
tff(1750,plain,
rselect_head(rstore_tail(queue_236,index_237)) = rselect_head(rstore_tail(rstore_seq(q3,earray_235),s(index_234))),
inference(monotonicity,[status(thm)],[1749]) ).
tff(1751,plain,
rselect_head(rstore_tail(rstore_seq(q3,earray_235),s(index_234))) = rselect_head(rstore_tail(queue_236,index_237)),
inference(symmetry,[status(thm)],[1750]) ).
tff(1752,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q3,earray_235),s(index_234))) = rselect_head(rstore_seq(q3,earray_235)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1753,plain,
rselect_head(rstore_tail(rstore_seq(q3,earray_235),s(index_234))) = rselect_head(rstore_seq(q3,earray_235)),
inference(unit_resolution,[status(thm)],[1752,58]) ).
tff(1754,plain,
rselect_head(rstore_seq(q3,earray_235)) = rselect_head(rstore_tail(rstore_seq(q3,earray_235),s(index_234))),
inference(symmetry,[status(thm)],[1753]) ).
tff(1755,plain,
( ( earray_235 = store(earray_233,index_234,e3) )
<=> ( earray_235 = store(earray_233,index_234,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1756,axiom,
earray_235 = store(earray_233,index_234,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp44) ).
tff(1757,plain,
earray_235 = store(earray_233,index_234,e3),
inference(modus_ponens,[status(thm)],[1756,1755]) ).
tff(1758,plain,
store(earray_233,index_234,e3) = earray_235,
inference(symmetry,[status(thm)],[1757]) ).
tff(1759,plain,
( ( q3 = queue_160 )
<=> ( q3 = queue_160 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1760,axiom,
q3 = queue_160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp376) ).
tff(1761,plain,
q3 = queue_160,
inference(modus_ponens,[status(thm)],[1760,1759]) ).
tff(1762,plain,
queue_160 = q3,
inference(symmetry,[status(thm)],[1761]) ).
tff(1763,plain,
( ( queue_160 = rstore_head(queue_157,index_159) )
<=> ( queue_160 = rstore_head(queue_157,index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1764,axiom,
queue_160 = rstore_head(queue_157,index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp259) ).
tff(1765,plain,
queue_160 = rstore_head(queue_157,index_159),
inference(modus_ponens,[status(thm)],[1764,1763]) ).
tff(1766,plain,
rstore_head(queue_157,index_159) = queue_160,
inference(symmetry,[status(thm)],[1765]) ).
tff(1767,plain,
rstore_head(queue_157,index_159) = q3,
inference(transitivity,[status(thm)],[1766,1762]) ).
tff(1768,plain,
rstore_seq(rstore_head(queue_157,index_159),store(earray_233,index_234,e3)) = rstore_seq(q3,earray_235),
inference(monotonicity,[status(thm)],[1767,1758]) ).
tff(1769,plain,
rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_233,index_234,e3))) = rselect_head(rstore_seq(q3,earray_235)),
inference(monotonicity,[status(thm)],[1768]) ).
tff(1770,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_233,index_234,e3))) = rselect_head(rstore_head(queue_157,index_159)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1771,plain,
rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_233,index_234,e3))) = rselect_head(rstore_head(queue_157,index_159)),
inference(unit_resolution,[status(thm)],[1770,85]) ).
tff(1772,plain,
rselect_head(rstore_head(queue_157,index_159)) = rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_233,index_234,e3))),
inference(symmetry,[status(thm)],[1771]) ).
tff(1773,plain,
( ( index_159 = s(index_158) )
<=> ( index_159 = s(index_158) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1774,axiom,
index_159 = s(index_158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(1775,plain,
index_159 = s(index_158),
inference(modus_ponens,[status(thm)],[1774,1773]) ).
tff(1776,plain,
s(index_158) = index_159,
inference(symmetry,[status(thm)],[1775]) ).
tff(1777,plain,
( ( queue_157 = rstore_tail(queue_155,index_156) )
<=> ( queue_157 = rstore_tail(queue_155,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1778,axiom,
queue_157 = rstore_tail(queue_155,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp258) ).
tff(1779,plain,
queue_157 = rstore_tail(queue_155,index_156),
inference(modus_ponens,[status(thm)],[1778,1777]) ).
tff(1780,plain,
rstore_tail(queue_155,index_156) = queue_157,
inference(symmetry,[status(thm)],[1779]) ).
tff(1781,plain,
rstore_head(rstore_tail(queue_155,index_156),s(index_158)) = rstore_head(queue_157,index_159),
inference(monotonicity,[status(thm)],[1780,1776]) ).
tff(1782,plain,
rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_head(rstore_head(queue_157,index_159)),
inference(monotonicity,[status(thm)],[1781]) ).
tff(1783,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = s(index_158) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1784,plain,
rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = s(index_158),
inference(unit_resolution,[status(thm)],[1783,173]) ).
tff(1785,plain,
s(index_158) = rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))),
inference(symmetry,[status(thm)],[1784]) ).
tff(1786,plain,
( ( index_158 = rselect_head(queue_157) )
<=> ( index_158 = rselect_head(queue_157) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1787,axiom,
index_158 = rselect_head(queue_157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(1788,plain,
index_158 = rselect_head(queue_157),
inference(modus_ponens,[status(thm)],[1787,1786]) ).
tff(1789,plain,
rselect_head(queue_157) = index_158,
inference(symmetry,[status(thm)],[1788]) ).
tff(1790,plain,
s(rselect_head(queue_157)) = s(index_158),
inference(monotonicity,[status(thm)],[1789]) ).
tff(1791,plain,
s(rselect_head(queue_157)) = index_326,
inference(transitivity,[status(thm)],[1790,1785,1782,1772,1769,1754,1751,1739,1736,1719,1716,1704,1701,1684,1681,1664]) ).
tff(1792,plain,
s(s(rselect_head(queue_157))) = s(index_326),
inference(monotonicity,[status(thm)],[1791]) ).
tff(1793,plain,
s(index_158) = s(rselect_head(queue_157)),
inference(symmetry,[status(thm)],[1790]) ).
tff(1794,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1795,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(1796,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[1795,1794]) ).
tff(1797,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[1796]) ).
tff(1798,plain,
( ( queue_155 = rstore_seq(q2,earray_154) )
<=> ( queue_155 = rstore_seq(q2,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1799,axiom,
queue_155 = rstore_seq(q2,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp257) ).
tff(1800,plain,
queue_155 = rstore_seq(q2,earray_154),
inference(modus_ponens,[status(thm)],[1799,1798]) ).
tff(1801,plain,
rstore_seq(q2,earray_154) = queue_155,
inference(symmetry,[status(thm)],[1800]) ).
tff(1802,plain,
rstore_tail(rstore_seq(q2,earray_154),s(index_153)) = rstore_tail(queue_155,index_156),
inference(monotonicity,[status(thm)],[1801,1797]) ).
tff(1803,plain,
rstore_tail(queue_155,index_156) = rstore_tail(rstore_seq(q2,earray_154),s(index_153)),
inference(symmetry,[status(thm)],[1802]) ).
tff(1804,plain,
queue_157 = rstore_tail(rstore_seq(q2,earray_154),s(index_153)),
inference(transitivity,[status(thm)],[1779,1803]) ).
tff(1805,plain,
rselect_head(queue_157) = rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[1804]) ).
tff(1806,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(queue_157),
inference(symmetry,[status(thm)],[1805]) ).
tff(1807,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(rstore_seq(q2,earray_154)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1808,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(rstore_seq(q2,earray_154)),
inference(unit_resolution,[status(thm)],[1807,58]) ).
tff(1809,plain,
rselect_head(rstore_seq(q2,earray_154)) = rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(symmetry,[status(thm)],[1808]) ).
tff(1810,plain,
( ( earray_154 = store(earray_152,index_153,e2) )
<=> ( earray_154 = store(earray_152,index_153,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1811,axiom,
earray_154 = store(earray_152,index_153,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(1812,plain,
earray_154 = store(earray_152,index_153,e2),
inference(modus_ponens,[status(thm)],[1811,1810]) ).
tff(1813,plain,
store(earray_152,index_153,e2) = earray_154,
inference(symmetry,[status(thm)],[1812]) ).
tff(1814,plain,
( ( q2 = queue_82 )
<=> ( q2 = queue_82 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1815,axiom,
q2 = queue_82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp365) ).
tff(1816,plain,
q2 = queue_82,
inference(modus_ponens,[status(thm)],[1815,1814]) ).
tff(1817,plain,
queue_82 = q2,
inference(symmetry,[status(thm)],[1816]) ).
tff(1818,plain,
( ( queue_82 = rstore_tail(queue_80,index_81) )
<=> ( queue_82 = rstore_tail(queue_80,index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1819,axiom,
queue_82 = rstore_tail(queue_80,index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp347) ).
tff(1820,plain,
queue_82 = rstore_tail(queue_80,index_81),
inference(modus_ponens,[status(thm)],[1819,1818]) ).
tff(1821,plain,
rstore_tail(queue_80,index_81) = queue_82,
inference(symmetry,[status(thm)],[1820]) ).
tff(1822,plain,
rstore_tail(queue_80,index_81) = q2,
inference(transitivity,[status(thm)],[1821,1817]) ).
tff(1823,plain,
rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2)) = rstore_seq(q2,earray_154),
inference(monotonicity,[status(thm)],[1822,1813]) ).
tff(1824,plain,
rstore_seq(q2,earray_154) = rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2)),
inference(symmetry,[status(thm)],[1823]) ).
tff(1825,plain,
rselect_head(rstore_seq(q2,earray_154)) = rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))),
inference(monotonicity,[status(thm)],[1824]) ).
tff(1826,plain,
rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_seq(q2,earray_154)),
inference(symmetry,[status(thm)],[1825]) ).
tff(1827,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_tail(queue_80,index_81)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1828,plain,
rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_tail(queue_80,index_81)),
inference(unit_resolution,[status(thm)],[1827,85]) ).
tff(1829,plain,
rselect_head(rstore_tail(queue_80,index_81)) = rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))),
inference(symmetry,[status(thm)],[1828]) ).
tff(1830,plain,
( ( index_81 = s(index_78) )
<=> ( index_81 = s(index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1831,axiom,
index_81 = s(index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(1832,plain,
index_81 = s(index_78),
inference(modus_ponens,[status(thm)],[1831,1830]) ).
tff(1833,plain,
s(index_78) = index_81,
inference(symmetry,[status(thm)],[1832]) ).
tff(1834,plain,
( ( queue_80 = rstore_seq(q1,earray_79) )
<=> ( queue_80 = rstore_seq(q1,earray_79) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1835,axiom,
queue_80 = rstore_seq(q1,earray_79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp346) ).
tff(1836,plain,
queue_80 = rstore_seq(q1,earray_79),
inference(modus_ponens,[status(thm)],[1835,1834]) ).
tff(1837,plain,
rstore_seq(q1,earray_79) = queue_80,
inference(symmetry,[status(thm)],[1836]) ).
tff(1838,plain,
rstore_tail(rstore_seq(q1,earray_79),s(index_78)) = rstore_tail(queue_80,index_81),
inference(monotonicity,[status(thm)],[1837,1833]) ).
tff(1839,plain,
rstore_tail(queue_80,index_81) = rstore_tail(rstore_seq(q1,earray_79),s(index_78)),
inference(symmetry,[status(thm)],[1838]) ).
tff(1840,plain,
rselect_head(rstore_tail(queue_80,index_81)) = rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(monotonicity,[status(thm)],[1839]) ).
tff(1841,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_tail(queue_80,index_81)),
inference(symmetry,[status(thm)],[1840]) ).
tff(1842,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_seq(q1,earray_79)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1843,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_seq(q1,earray_79)),
inference(unit_resolution,[status(thm)],[1842,58]) ).
tff(1844,plain,
rselect_head(rstore_seq(q1,earray_79)) = rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(symmetry,[status(thm)],[1843]) ).
tff(1845,plain,
( ( earray_79 = store(earray_77,index_78,e1) )
<=> ( earray_79 = store(earray_77,index_78,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1846,axiom,
earray_79 = store(earray_77,index_78,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(1847,plain,
earray_79 = store(earray_77,index_78,e1),
inference(modus_ponens,[status(thm)],[1846,1845]) ).
tff(1848,plain,
store(earray_77,index_78,e1) = earray_79,
inference(symmetry,[status(thm)],[1847]) ).
tff(1849,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1850,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp354) ).
tff(1851,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[1850,1849]) ).
tff(1852,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[1851]) ).
tff(1853,plain,
( ( queue_7 = rstore_tail(queue_5,index_6) )
<=> ( queue_7 = rstore_tail(queue_5,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1854,axiom,
queue_7 = rstore_tail(queue_5,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp342) ).
tff(1855,plain,
queue_7 = rstore_tail(queue_5,index_6),
inference(modus_ponens,[status(thm)],[1854,1853]) ).
tff(1856,plain,
rstore_tail(queue_5,index_6) = queue_7,
inference(symmetry,[status(thm)],[1855]) ).
tff(1857,plain,
rstore_tail(queue_5,index_6) = q1,
inference(transitivity,[status(thm)],[1856,1852]) ).
tff(1858,plain,
rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1)) = rstore_seq(q1,earray_79),
inference(monotonicity,[status(thm)],[1857,1848]) ).
tff(1859,plain,
rstore_seq(q1,earray_79) = rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1)),
inference(symmetry,[status(thm)],[1858]) ).
tff(1860,plain,
rselect_head(rstore_seq(q1,earray_79)) = rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))),
inference(monotonicity,[status(thm)],[1859]) ).
tff(1861,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_seq(q1,earray_79)),
inference(symmetry,[status(thm)],[1860]) ).
tff(1862,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_tail(queue_5,index_6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1863,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(unit_resolution,[status(thm)],[1862,85]) ).
tff(1864,plain,
rselect_head(rstore_tail(queue_5,index_6)) = rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))),
inference(symmetry,[status(thm)],[1863]) ).
tff(1865,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1866,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(1867,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[1866,1865]) ).
tff(1868,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[1867]) ).
tff(1869,plain,
( ( queue_5 = rstore_seq(q0,earray_4) )
<=> ( queue_5 = rstore_seq(q0,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1870,axiom,
queue_5 = rstore_seq(q0,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp335) ).
tff(1871,plain,
queue_5 = rstore_seq(q0,earray_4),
inference(modus_ponens,[status(thm)],[1870,1869]) ).
tff(1872,plain,
rstore_seq(q0,earray_4) = queue_5,
inference(symmetry,[status(thm)],[1871]) ).
tff(1873,plain,
rstore_tail(rstore_seq(q0,earray_4),s(index_3)) = rstore_tail(queue_5,index_6),
inference(monotonicity,[status(thm)],[1872,1868]) ).
tff(1874,plain,
rstore_tail(queue_5,index_6) = rstore_tail(rstore_seq(q0,earray_4),s(index_3)),
inference(symmetry,[status(thm)],[1873]) ).
tff(1875,plain,
rselect_head(rstore_tail(queue_5,index_6)) = rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(monotonicity,[status(thm)],[1874]) ).
tff(1876,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(symmetry,[status(thm)],[1875]) ).
tff(1877,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1878,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)),
inference(unit_resolution,[status(thm)],[1877,58]) ).
tff(1879,plain,
rselect_head(rstore_seq(q0,earray_4)) = rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(symmetry,[status(thm)],[1878]) ).
tff(1880,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1881,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp82) ).
tff(1882,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[1881,1880]) ).
tff(1883,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[1882]) ).
tff(1884,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1885,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp353) ).
tff(1886,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[1885,1884]) ).
tff(1887,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[1886]) ).
tff(1888,plain,
( ( queue_1 = rstore_head(q,index_0) )
<=> ( queue_1 = rstore_head(q,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1889,axiom,
queue_1 = rstore_head(q,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(1890,plain,
queue_1 = rstore_head(q,index_0),
inference(modus_ponens,[status(thm)],[1889,1888]) ).
tff(1891,plain,
rstore_head(q,index_0) = queue_1,
inference(symmetry,[status(thm)],[1890]) ).
tff(1892,plain,
rstore_head(q,index_0) = q0,
inference(transitivity,[status(thm)],[1891,1887]) ).
tff(1893,plain,
rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0)) = rstore_seq(q0,earray_4),
inference(monotonicity,[status(thm)],[1892,1883]) ).
tff(1894,plain,
rstore_seq(q0,earray_4) = rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0)),
inference(symmetry,[status(thm)],[1893]) ).
tff(1895,plain,
rselect_head(rstore_seq(q0,earray_4)) = rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))),
inference(monotonicity,[status(thm)],[1894]) ).
tff(1896,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_seq(q0,earray_4)),
inference(symmetry,[status(thm)],[1895]) ).
tff(1897,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1898,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)),
inference(unit_resolution,[status(thm)],[1897,85]) ).
tff(1899,plain,
rselect_head(rstore_head(q,index_0)) = rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))),
inference(symmetry,[status(thm)],[1898]) ).
tff(1900,plain,
( ( index_0 = rselect_tail(q) )
<=> ( index_0 = rselect_tail(q) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1901,axiom,
index_0 = rselect_tail(q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(1902,plain,
index_0 = rselect_tail(q),
inference(modus_ponens,[status(thm)],[1901,1900]) ).
tff(1903,plain,
rselect_tail(q) = index_0,
inference(symmetry,[status(thm)],[1902]) ).
tff(1904,plain,
rstore_head(q,rselect_tail(q)) = rstore_head(q,index_0),
inference(monotonicity,[status(thm)],[1903]) ).
tff(1905,plain,
rstore_head(q,index_0) = rstore_head(q,rselect_tail(q)),
inference(symmetry,[status(thm)],[1904]) ).
tff(1906,plain,
rselect_head(rstore_head(q,index_0)) = rselect_head(rstore_head(q,rselect_tail(q))),
inference(monotonicity,[status(thm)],[1905]) ).
tff(1907,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_head(rstore_head(q,index_0)),
inference(symmetry,[status(thm)],[1906]) ).
tff(1908,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1909,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1908,173]) ).
tff(1910,plain,
rselect_tail(q) = rselect_head(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1909]) ).
tff(1911,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1912,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(quant_intro,[status(thm)],[1911]) ).
tff(1913,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1914,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_tail_head) ).
tff(1915,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[1914,1913]) ).
tff(1916,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(skolemize,[status(sab)],[1915]) ).
tff(1917,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[1916,1912]) ).
tff(1918,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1919,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1918,1917]) ).
tff(1920,plain,
rstore_head(q,rselect_tail(q)) = q0,
inference(transitivity,[status(thm)],[1904,1891,1887]) ).
tff(1921,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q0),
inference(monotonicity,[status(thm)],[1920]) ).
tff(1922,plain,
rselect_tail(q0) = rselect_tail(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1921]) ).
tff(1923,plain,
( ( index_3 = rselect_tail(q0) )
<=> ( index_3 = rselect_tail(q0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1924,axiom,
index_3 = rselect_tail(q0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(1925,plain,
index_3 = rselect_tail(q0),
inference(modus_ponens,[status(thm)],[1924,1923]) ).
tff(1926,plain,
index_3 = index_158,
inference(transitivity,[status(thm)],[1925,1922,1919,1910,1907,1899,1896,1879,1876,1864,1861,1844,1841,1829,1826,1809,1806,1789]) ).
tff(1927,plain,
s(index_3) = s(index_158),
inference(monotonicity,[status(thm)],[1926]) ).
tff(1928,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1929,plain,
rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3),
inference(unit_resolution,[status(thm)],[1928,26]) ).
tff(1930,plain,
q1 = rstore_tail(rstore_seq(q0,earray_4),s(index_3)),
inference(transitivity,[status(thm)],[1851,1855,1874]) ).
tff(1931,plain,
rselect_tail(q1) = rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(monotonicity,[status(thm)],[1930]) ).
tff(1932,plain,
( ( index_78 = rselect_tail(q1) )
<=> ( index_78 = rselect_tail(q1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1933,axiom,
index_78 = rselect_tail(q1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(1934,plain,
index_78 = rselect_tail(q1),
inference(modus_ponens,[status(thm)],[1933,1932]) ).
tff(1935,plain,
index_78 = s(rselect_head(queue_157)),
inference(transitivity,[status(thm)],[1934,1931,1929,1927,1793]) ).
tff(1936,plain,
s(index_78) = s(s(rselect_head(queue_157))),
inference(monotonicity,[status(thm)],[1935]) ).
tff(1937,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = s(index_78) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1938,plain,
rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = s(index_78),
inference(unit_resolution,[status(thm)],[1937,26]) ).
tff(1939,plain,
q2 = rstore_tail(rstore_seq(q1,earray_79),s(index_78)),
inference(transitivity,[status(thm)],[1816,1820,1839]) ).
tff(1940,plain,
rselect_tail(q2) = rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(monotonicity,[status(thm)],[1939]) ).
tff(1941,plain,
( ( index_153 = rselect_tail(q2) )
<=> ( index_153 = rselect_tail(q2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1942,axiom,
index_153 = rselect_tail(q2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(1943,plain,
index_153 = rselect_tail(q2),
inference(modus_ponens,[status(thm)],[1942,1941]) ).
tff(1944,plain,
index_153 = s(rselect_head(queue_325)),
inference(transitivity,[status(thm)],[1943,1940,1938,1936,1792,1668]) ).
tff(1945,plain,
s(index_153) = s(s(rselect_head(queue_325))),
inference(monotonicity,[status(thm)],[1944]) ).
tff(1946,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1947,plain,
rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = s(index_153),
inference(unit_resolution,[status(thm)],[1946,26]) ).
tff(1948,plain,
rselect_tail(rstore_tail(queue_155,index_156)) = rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[1803]) ).
tff(1949,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_tail(rstore_tail(queue_155,index_156)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1950,plain,
rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_tail(rstore_tail(queue_155,index_156)),
inference(unit_resolution,[status(thm)],[1949,1917]) ).
tff(1951,plain,
rstore_head(queue_157,index_159) = rstore_head(rstore_tail(queue_155,index_156),s(index_158)),
inference(symmetry,[status(thm)],[1781]) ).
tff(1952,plain,
q3 = rstore_head(rstore_tail(queue_155,index_156),s(index_158)),
inference(transitivity,[status(thm)],[1761,1765,1951]) ).
tff(1953,plain,
rselect_tail(q3) = rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))),
inference(monotonicity,[status(thm)],[1952]) ).
tff(1954,plain,
( ( index_234 = rselect_tail(q3) )
<=> ( index_234 = rselect_tail(q3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1955,axiom,
index_234 = rselect_tail(q3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(1956,plain,
index_234 = rselect_tail(q3),
inference(modus_ponens,[status(thm)],[1955,1954]) ).
tff(1957,plain,
index_234 = s(rselect_head(queue_346)),
inference(transitivity,[status(thm)],[1956,1953,1950,1948,1947,1945,1667,1543]) ).
tff(1958,plain,
s(index_234) = s(s(rselect_head(queue_346))),
inference(monotonicity,[status(thm)],[1957]) ).
tff(1959,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q3,earray_235),s(index_234))) = s(index_234) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1960,plain,
rselect_tail(rstore_tail(rstore_seq(q3,earray_235),s(index_234))) = s(index_234),
inference(unit_resolution,[status(thm)],[1959,26]) ).
tff(1961,plain,
q4 = rstore_tail(rstore_seq(q3,earray_235),s(index_234)),
inference(transitivity,[status(thm)],[1726,1730,1749]) ).
tff(1962,plain,
rselect_tail(q4) = rselect_tail(rstore_tail(rstore_seq(q3,earray_235),s(index_234))),
inference(monotonicity,[status(thm)],[1961]) ).
tff(1963,plain,
( ( index_309 = rselect_tail(q4) )
<=> ( index_309 = rselect_tail(q4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1964,axiom,
index_309 = rselect_tail(q4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(1965,plain,
index_309 = rselect_tail(q4),
inference(modus_ponens,[status(thm)],[1964,1963]) ).
tff(1966,plain,
index_309 = s(rselect_head(queue_25)),
inference(transitivity,[status(thm)],[1965,1962,1960,1958,1542,1418]) ).
tff(1967,plain,
s(index_309) = s(s(rselect_head(queue_25))),
inference(monotonicity,[status(thm)],[1966]) ).
tff(1968,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q4,earray_310),s(index_309))) = s(index_309) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1969,plain,
rselect_tail(rstore_tail(rstore_seq(q4,earray_310),s(index_309))) = s(index_309),
inference(unit_resolution,[status(thm)],[1968,26]) ).
tff(1970,plain,
q5 = rstore_tail(rstore_seq(q4,earray_310),s(index_309)),
inference(transitivity,[status(thm)],[1691,1695,1714]) ).
tff(1971,plain,
rselect_tail(q5) = rselect_tail(rstore_tail(rstore_seq(q4,earray_310),s(index_309))),
inference(monotonicity,[status(thm)],[1970]) ).
tff(1972,plain,
( ( index_321 = rselect_tail(q5) )
<=> ( index_321 = rselect_tail(q5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1973,axiom,
index_321 = rselect_tail(q5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(1974,plain,
index_321 = rselect_tail(q5),
inference(modus_ponens,[status(thm)],[1973,1972]) ).
tff(1975,plain,
index_321 = s(rselect_head(queue_46)),
inference(transitivity,[status(thm)],[1974,1971,1969,1967,1417,1293]) ).
tff(1976,plain,
s(index_321) = s(s(rselect_head(queue_46))),
inference(monotonicity,[status(thm)],[1975]) ).
tff(1977,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q5,earray_322),s(index_321))) = s(index_321) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1978,plain,
rselect_tail(rstore_tail(rstore_seq(q5,earray_322),s(index_321))) = s(index_321),
inference(unit_resolution,[status(thm)],[1977,26]) ).
tff(1979,plain,
rselect_tail(rstore_tail(queue_323,index_324)) = rselect_tail(rstore_tail(rstore_seq(q5,earray_322),s(index_321))),
inference(monotonicity,[status(thm)],[1678]) ).
tff(1980,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_323,index_324),s(index_326))) = rselect_tail(rstore_tail(queue_323,index_324)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1981,plain,
rselect_tail(rstore_head(rstore_tail(queue_323,index_324),s(index_326))) = rselect_tail(rstore_tail(queue_323,index_324)),
inference(unit_resolution,[status(thm)],[1980,1917]) ).
tff(1982,plain,
rstore_head(queue_325,index_327) = rstore_head(rstore_tail(queue_323,index_324),s(index_326)),
inference(symmetry,[status(thm)],[1656]) ).
tff(1983,plain,
q6 = rstore_head(rstore_tail(queue_323,index_324),s(index_326)),
inference(transitivity,[status(thm)],[1636,1640,1982]) ).
tff(1984,plain,
rselect_tail(q6) = rselect_tail(rstore_head(rstore_tail(queue_323,index_324),s(index_326))),
inference(monotonicity,[status(thm)],[1983]) ).
tff(1985,plain,
( ( index_330 = rselect_tail(q6) )
<=> ( index_330 = rselect_tail(q6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1986,axiom,
index_330 = rselect_tail(q6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(1987,plain,
index_330 = rselect_tail(q6),
inference(modus_ponens,[status(thm)],[1986,1985]) ).
tff(1988,plain,
index_330 = s(rselect_head(queue_67)),
inference(transitivity,[status(thm)],[1987,1984,1981,1979,1978,1976,1292,1184]) ).
tff(1989,plain,
s(index_330) = s(s(rselect_head(queue_67))),
inference(monotonicity,[status(thm)],[1988]) ).
tff(1990,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q6,earray_331),s(index_330))) = s(index_330) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1991,plain,
rselect_tail(rstore_tail(rstore_seq(q6,earray_331),s(index_330))) = s(index_330),
inference(unit_resolution,[status(thm)],[1990,26]) ).
tff(1992,plain,
q7 = rstore_tail(rstore_seq(q6,earray_331),s(index_330)),
inference(transitivity,[status(thm)],[1601,1605,1624]) ).
tff(1993,plain,
rselect_tail(q7) = rselect_tail(rstore_tail(rstore_seq(q6,earray_331),s(index_330))),
inference(monotonicity,[status(thm)],[1992]) ).
tff(1994,plain,
( ( index_336 = rselect_tail(q7) )
<=> ( index_336 = rselect_tail(q7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1995,axiom,
index_336 = rselect_tail(q7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(1996,plain,
index_336 = rselect_tail(q7),
inference(modus_ponens,[status(thm)],[1995,1994]) ).
tff(1997,plain,
index_336 = s(rselect_head(queue_94)),
inference(transitivity,[status(thm)],[1996,1993,1991,1989,1183,1059]) ).
tff(1998,plain,
s(index_336) = s(s(rselect_head(queue_94))),
inference(monotonicity,[status(thm)],[1997]) ).
tff(1999,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q7,earray_337),s(index_336))) = s(index_336) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2000,plain,
rselect_tail(rstore_tail(rstore_seq(q7,earray_337),s(index_336))) = s(index_336),
inference(unit_resolution,[status(thm)],[1999,26]) ).
tff(2001,plain,
q8 = rstore_tail(rstore_seq(q7,earray_337),s(index_336)),
inference(transitivity,[status(thm)],[1566,1570,1589]) ).
tff(2002,plain,
rselect_tail(q8) = rselect_tail(rstore_tail(rstore_seq(q7,earray_337),s(index_336))),
inference(monotonicity,[status(thm)],[2001]) ).
tff(2003,plain,
( ( index_342 = rselect_tail(q8) )
<=> ( index_342 = rselect_tail(q8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2004,axiom,
index_342 = rselect_tail(q8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(2005,plain,
index_342 = rselect_tail(q8),
inference(modus_ponens,[status(thm)],[2004,2003]) ).
tff(2006,plain,
index_342 = s(rselect_head(queue_115)),
inference(transitivity,[status(thm)],[2005,2002,2000,1998,1058,934]) ).
tff(2007,plain,
s(index_342) = s(s(rselect_head(queue_115))),
inference(monotonicity,[status(thm)],[2006]) ).
tff(2008,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q8,earray_343),s(index_342))) = s(index_342) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2009,plain,
rselect_tail(rstore_tail(rstore_seq(q8,earray_343),s(index_342))) = s(index_342),
inference(unit_resolution,[status(thm)],[2008,26]) ).
tff(2010,plain,
rselect_tail(rstore_tail(queue_344,index_345)) = rselect_tail(rstore_tail(rstore_seq(q8,earray_343),s(index_342))),
inference(monotonicity,[status(thm)],[1553]) ).
tff(2011,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_344,index_345),s(index_347))) = rselect_tail(rstore_tail(queue_344,index_345)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2012,plain,
rselect_tail(rstore_head(rstore_tail(queue_344,index_345),s(index_347))) = rselect_tail(rstore_tail(queue_344,index_345)),
inference(unit_resolution,[status(thm)],[2011,1917]) ).
tff(2013,plain,
rstore_head(queue_346,index_348) = rstore_head(rstore_tail(queue_344,index_345),s(index_347)),
inference(symmetry,[status(thm)],[1531]) ).
tff(2014,plain,
q9 = rstore_head(rstore_tail(queue_344,index_345),s(index_347)),
inference(transitivity,[status(thm)],[1511,1515,2013]) ).
tff(2015,plain,
rselect_tail(q9) = rselect_tail(rstore_head(rstore_tail(queue_344,index_345),s(index_347))),
inference(monotonicity,[status(thm)],[2014]) ).
tff(2016,plain,
( ( index_9 = rselect_tail(q9) )
<=> ( index_9 = rselect_tail(q9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2017,axiom,
index_9 = rselect_tail(q9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(2018,plain,
index_9 = rselect_tail(q9),
inference(modus_ponens,[status(thm)],[2017,2016]) ).
tff(2019,plain,
index_9 = s(rselect_head(queue_136)),
inference(transitivity,[status(thm)],[2018,2015,2012,2010,2009,2007,933,809]) ).
tff(2020,plain,
s(index_9) = s(s(rselect_head(queue_136))),
inference(monotonicity,[status(thm)],[2019]) ).
tff(2021,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2022,plain,
rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9),
inference(unit_resolution,[status(thm)],[2021,26]) ).
tff(2023,plain,
q10 = rstore_tail(rstore_seq(q9,earray_10),s(index_9)),
inference(transitivity,[status(thm)],[1476,1480,1499]) ).
tff(2024,plain,
rselect_tail(q10) = rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(monotonicity,[status(thm)],[2023]) ).
tff(2025,plain,
( ( index_15 = rselect_tail(q10) )
<=> ( index_15 = rselect_tail(q10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2026,axiom,
index_15 = rselect_tail(q10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(2027,plain,
index_15 = rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2026,2025]) ).
tff(2028,plain,
index_15 = s(rselect_head(queue_166)),
inference(transitivity,[status(thm)],[2027,2024,2022,2020,808,684]) ).
tff(2029,plain,
s(index_15) = s(s(rselect_head(queue_166))),
inference(monotonicity,[status(thm)],[2028]) ).
tff(2030,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2031,plain,
rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15),
inference(unit_resolution,[status(thm)],[2030,26]) ).
tff(2032,plain,
q11 = rstore_tail(rstore_seq(q10,earray_16),s(index_15)),
inference(transitivity,[status(thm)],[1441,1445,1464]) ).
tff(2033,plain,
rselect_tail(q11) = rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(monotonicity,[status(thm)],[2032]) ).
tff(2034,plain,
( ( index_21 = rselect_tail(q11) )
<=> ( index_21 = rselect_tail(q11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2035,axiom,
index_21 = rselect_tail(q11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(2036,plain,
index_21 = rselect_tail(q11),
inference(modus_ponens,[status(thm)],[2035,2034]) ).
tff(2037,plain,
index_21 = s(rselect_head(queue_187)),
inference(transitivity,[status(thm)],[2036,2033,2031,2029,683,559]) ).
tff(2038,plain,
s(index_21) = s(s(rselect_head(queue_187))),
inference(monotonicity,[status(thm)],[2037]) ).
tff(2039,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2040,plain,
rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21),
inference(unit_resolution,[status(thm)],[2039,26]) ).
tff(2041,plain,
rselect_tail(rstore_tail(queue_23,index_24)) = rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[1428]) ).
tff(2042,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_tail(rstore_tail(queue_23,index_24)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2043,plain,
rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_tail(rstore_tail(queue_23,index_24)),
inference(unit_resolution,[status(thm)],[2042,1917]) ).
tff(2044,plain,
rstore_head(queue_25,index_27) = rstore_head(rstore_tail(queue_23,index_24),s(index_26)),
inference(symmetry,[status(thm)],[1406]) ).
tff(2045,plain,
q12 = rstore_head(rstore_tail(queue_23,index_24),s(index_26)),
inference(transitivity,[status(thm)],[1386,1390,2044]) ).
tff(2046,plain,
rselect_tail(q12) = rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(monotonicity,[status(thm)],[2045]) ).
tff(2047,plain,
( ( index_30 = rselect_tail(q12) )
<=> ( index_30 = rselect_tail(q12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2048,axiom,
index_30 = rselect_tail(q12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(2049,plain,
index_30 = rselect_tail(q12),
inference(modus_ponens,[status(thm)],[2048,2047]) ).
tff(2050,plain,
index_30 = s(rselect_head(queue_208)),
inference(transitivity,[status(thm)],[2049,2046,2043,2041,2040,2038,558,434]) ).
tff(2051,plain,
s(index_30) = s(s(rselect_head(queue_208))),
inference(monotonicity,[status(thm)],[2050]) ).
tff(2052,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = s(index_30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2053,plain,
rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = s(index_30),
inference(unit_resolution,[status(thm)],[2052,26]) ).
tff(2054,plain,
q13 = rstore_tail(rstore_seq(q12,earray_31),s(index_30)),
inference(transitivity,[status(thm)],[1351,1355,1374]) ).
tff(2055,plain,
rselect_tail(q13) = rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(monotonicity,[status(thm)],[2054]) ).
tff(2056,plain,
( ( index_36 = rselect_tail(q13) )
<=> ( index_36 = rselect_tail(q13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2057,axiom,
index_36 = rselect_tail(q13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(2058,plain,
index_36 = rselect_tail(q13),
inference(modus_ponens,[status(thm)],[2057,2056]) ).
tff(2059,plain,
index_36 = s(rselect_head(queue_229)),
inference(transitivity,[status(thm)],[2058,2055,2053,2051,433,309]) ).
tff(2060,plain,
s(index_36) = s(s(rselect_head(queue_229))),
inference(monotonicity,[status(thm)],[2059]) ).
tff(2061,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = s(index_36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2062,plain,
rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = s(index_36),
inference(unit_resolution,[status(thm)],[2061,26]) ).
tff(2063,plain,
q14 = rstore_tail(rstore_seq(q13,earray_37),s(index_36)),
inference(transitivity,[status(thm)],[1316,1320,1339]) ).
tff(2064,plain,
rselect_tail(q14) = rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(monotonicity,[status(thm)],[2063]) ).
tff(2065,plain,
( ( index_42 = rselect_tail(q14) )
<=> ( index_42 = rselect_tail(q14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2066,axiom,
index_42 = rselect_tail(q14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(2067,plain,
index_42 = rselect_tail(q14),
inference(modus_ponens,[status(thm)],[2066,2065]) ).
tff(2068,plain,
index_42 = s(rselect_head(queue_256)),
inference(transitivity,[status(thm)],[2067,2064,2062,2060,308,184]) ).
tff(2069,plain,
s(index_42) = s(s(rselect_head(queue_256))),
inference(monotonicity,[status(thm)],[2068]) ).
tff(2070,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = s(index_42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2071,plain,
rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = s(index_42),
inference(unit_resolution,[status(thm)],[2070,26]) ).
tff(2072,plain,
rselect_tail(rstore_tail(queue_44,index_45)) = rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(monotonicity,[status(thm)],[1303]) ).
tff(2073,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_tail(rstore_tail(queue_44,index_45)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2074,plain,
rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_tail(rstore_tail(queue_44,index_45)),
inference(unit_resolution,[status(thm)],[2073,1917]) ).
tff(2075,plain,
rstore_head(queue_46,index_48) = rstore_head(rstore_tail(queue_44,index_45),s(index_47)),
inference(symmetry,[status(thm)],[1281]) ).
tff(2076,plain,
q15 = rstore_head(rstore_tail(queue_44,index_45),s(index_47)),
inference(transitivity,[status(thm)],[1261,1265,2075]) ).
tff(2077,plain,
rselect_tail(q15) = rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(monotonicity,[status(thm)],[2076]) ).
tff(2078,plain,
( ( index_51 = rselect_tail(q15) )
<=> ( index_51 = rselect_tail(q15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2079,axiom,
index_51 = rselect_tail(q15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(2080,plain,
index_51 = rselect_tail(q15),
inference(modus_ponens,[status(thm)],[2079,2078]) ).
tff(2081,plain,
index_51 = s(rselect_head(queue_277)),
inference(transitivity,[status(thm)],[2080,2077,2074,2072,2071,2069,183,35]) ).
tff(2082,plain,
s(index_51) = s(s(rselect_head(queue_277))),
inference(monotonicity,[status(thm)],[2081]) ).
tff(2083,plain,
s(s(rselect_head(queue_277))) = s(index_51),
inference(symmetry,[status(thm)],[2082]) ).
tff(2084,plain,
( ( index_299 = rselect_head(queue_298) )
<=> ( index_299 = rselect_head(queue_298) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2085,axiom,
index_299 = rselect_head(queue_298),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(2086,plain,
index_299 = rselect_head(queue_298),
inference(modus_ponens,[status(thm)],[2085,2084]) ).
tff(2087,plain,
rselect_head(queue_298) = index_299,
inference(symmetry,[status(thm)],[2086]) ).
tff(2088,plain,
( ( index_297 = s(index_294) )
<=> ( index_297 = s(index_294) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2089,axiom,
index_297 = s(index_294),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(2090,plain,
index_297 = s(index_294),
inference(modus_ponens,[status(thm)],[2089,2088]) ).
tff(2091,plain,
s(index_294) = index_297,
inference(symmetry,[status(thm)],[2090]) ).
tff(2092,plain,
( ( queue_296 = rstore_seq(q47,earray_295) )
<=> ( queue_296 = rstore_seq(q47,earray_295) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2093,axiom,
queue_296 = rstore_seq(q47,earray_295),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp309) ).
tff(2094,plain,
queue_296 = rstore_seq(q47,earray_295),
inference(modus_ponens,[status(thm)],[2093,2092]) ).
tff(2095,plain,
rstore_seq(q47,earray_295) = queue_296,
inference(symmetry,[status(thm)],[2094]) ).
tff(2096,plain,
rstore_tail(rstore_seq(q47,earray_295),s(index_294)) = rstore_tail(queue_296,index_297),
inference(monotonicity,[status(thm)],[2095,2091]) ).
tff(2097,plain,
rstore_tail(queue_296,index_297) = rstore_tail(rstore_seq(q47,earray_295),s(index_294)),
inference(symmetry,[status(thm)],[2096]) ).
tff(2098,plain,
( ( queue_298 = rstore_tail(queue_296,index_297) )
<=> ( queue_298 = rstore_tail(queue_296,index_297) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2099,axiom,
queue_298 = rstore_tail(queue_296,index_297),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp310) ).
tff(2100,plain,
queue_298 = rstore_tail(queue_296,index_297),
inference(modus_ponens,[status(thm)],[2099,2098]) ).
tff(2101,plain,
queue_298 = rstore_tail(rstore_seq(q47,earray_295),s(index_294)),
inference(transitivity,[status(thm)],[2100,2097]) ).
tff(2102,plain,
rselect_head(queue_298) = rselect_head(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(monotonicity,[status(thm)],[2101]) ).
tff(2103,plain,
rselect_head(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_head(queue_298),
inference(symmetry,[status(thm)],[2102]) ).
tff(2104,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_head(rstore_seq(q47,earray_295)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2105,plain,
rselect_head(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_head(rstore_seq(q47,earray_295)),
inference(unit_resolution,[status(thm)],[2104,58]) ).
tff(2106,plain,
rselect_head(rstore_seq(q47,earray_295)) = rselect_head(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(symmetry,[status(thm)],[2105]) ).
tff(2107,plain,
( ( earray_295 = store(earray_293,index_294,e47) )
<=> ( earray_295 = store(earray_293,index_294,e47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2108,axiom,
earray_295 = store(earray_293,index_294,e47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(2109,plain,
earray_295 = store(earray_293,index_294,e47),
inference(modus_ponens,[status(thm)],[2108,2107]) ).
tff(2110,plain,
store(earray_293,index_294,e47) = earray_295,
inference(symmetry,[status(thm)],[2109]) ).
tff(2111,plain,
( ( q47 = queue_292 )
<=> ( q47 = queue_292 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2112,axiom,
q47 = queue_292,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp395) ).
tff(2113,plain,
q47 = queue_292,
inference(modus_ponens,[status(thm)],[2112,2111]) ).
tff(2114,plain,
queue_292 = q47,
inference(symmetry,[status(thm)],[2113]) ).
tff(2115,plain,
( ( queue_292 = rstore_tail(queue_290,index_291) )
<=> ( queue_292 = rstore_tail(queue_290,index_291) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2116,axiom,
queue_292 = rstore_tail(queue_290,index_291),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp308) ).
tff(2117,plain,
queue_292 = rstore_tail(queue_290,index_291),
inference(modus_ponens,[status(thm)],[2116,2115]) ).
tff(2118,plain,
rstore_tail(queue_290,index_291) = queue_292,
inference(symmetry,[status(thm)],[2117]) ).
tff(2119,plain,
rstore_tail(queue_290,index_291) = q47,
inference(transitivity,[status(thm)],[2118,2114]) ).
tff(2120,plain,
rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47)) = rstore_seq(q47,earray_295),
inference(monotonicity,[status(thm)],[2119,2110]) ).
tff(2121,plain,
rstore_seq(q47,earray_295) = rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47)),
inference(symmetry,[status(thm)],[2120]) ).
tff(2122,plain,
rselect_head(rstore_seq(q47,earray_295)) = rselect_head(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))),
inference(monotonicity,[status(thm)],[2121]) ).
tff(2123,plain,
rselect_head(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = rselect_head(rstore_seq(q47,earray_295)),
inference(symmetry,[status(thm)],[2122]) ).
tff(2124,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = rselect_head(rstore_tail(queue_290,index_291)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2125,plain,
rselect_head(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = rselect_head(rstore_tail(queue_290,index_291)),
inference(unit_resolution,[status(thm)],[2124,85]) ).
tff(2126,plain,
rselect_head(rstore_tail(queue_290,index_291)) = rselect_head(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))),
inference(symmetry,[status(thm)],[2125]) ).
tff(2127,plain,
( ( index_291 = s(index_288) )
<=> ( index_291 = s(index_288) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2128,axiom,
index_291 = s(index_288),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(2129,plain,
index_291 = s(index_288),
inference(modus_ponens,[status(thm)],[2128,2127]) ).
tff(2130,plain,
s(index_288) = index_291,
inference(symmetry,[status(thm)],[2129]) ).
tff(2131,plain,
( ( queue_290 = rstore_seq(q46,earray_289) )
<=> ( queue_290 = rstore_seq(q46,earray_289) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2132,axiom,
queue_290 = rstore_seq(q46,earray_289),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp307) ).
tff(2133,plain,
queue_290 = rstore_seq(q46,earray_289),
inference(modus_ponens,[status(thm)],[2132,2131]) ).
tff(2134,plain,
rstore_seq(q46,earray_289) = queue_290,
inference(symmetry,[status(thm)],[2133]) ).
tff(2135,plain,
rstore_tail(rstore_seq(q46,earray_289),s(index_288)) = rstore_tail(queue_290,index_291),
inference(monotonicity,[status(thm)],[2134,2130]) ).
tff(2136,plain,
rstore_tail(queue_290,index_291) = rstore_tail(rstore_seq(q46,earray_289),s(index_288)),
inference(symmetry,[status(thm)],[2135]) ).
tff(2137,plain,
rselect_head(rstore_tail(queue_290,index_291)) = rselect_head(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(monotonicity,[status(thm)],[2136]) ).
tff(2138,plain,
rselect_head(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_head(rstore_tail(queue_290,index_291)),
inference(symmetry,[status(thm)],[2137]) ).
tff(2139,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_head(rstore_seq(q46,earray_289)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2140,plain,
rselect_head(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_head(rstore_seq(q46,earray_289)),
inference(unit_resolution,[status(thm)],[2139,58]) ).
tff(2141,plain,
rselect_head(rstore_seq(q46,earray_289)) = rselect_head(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(symmetry,[status(thm)],[2140]) ).
tff(2142,plain,
( ( earray_289 = store(earray_287,index_288,e46) )
<=> ( earray_289 = store(earray_287,index_288,e46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2143,axiom,
earray_289 = store(earray_287,index_288,e46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(2144,plain,
earray_289 = store(earray_287,index_288,e46),
inference(modus_ponens,[status(thm)],[2143,2142]) ).
tff(2145,plain,
store(earray_287,index_288,e46) = earray_289,
inference(symmetry,[status(thm)],[2144]) ).
tff(2146,plain,
( ( q46 = queue_286 )
<=> ( q46 = queue_286 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2147,axiom,
q46 = queue_286,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp394) ).
tff(2148,plain,
q46 = queue_286,
inference(modus_ponens,[status(thm)],[2147,2146]) ).
tff(2149,plain,
queue_286 = q46,
inference(symmetry,[status(thm)],[2148]) ).
tff(2150,plain,
( ( queue_286 = rstore_tail(queue_284,index_285) )
<=> ( queue_286 = rstore_tail(queue_284,index_285) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2151,axiom,
queue_286 = rstore_tail(queue_284,index_285),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp306) ).
tff(2152,plain,
queue_286 = rstore_tail(queue_284,index_285),
inference(modus_ponens,[status(thm)],[2151,2150]) ).
tff(2153,plain,
rstore_tail(queue_284,index_285) = queue_286,
inference(symmetry,[status(thm)],[2152]) ).
tff(2154,plain,
rstore_tail(queue_284,index_285) = q46,
inference(transitivity,[status(thm)],[2153,2149]) ).
tff(2155,plain,
rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46)) = rstore_seq(q46,earray_289),
inference(monotonicity,[status(thm)],[2154,2145]) ).
tff(2156,plain,
rstore_seq(q46,earray_289) = rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46)),
inference(symmetry,[status(thm)],[2155]) ).
tff(2157,plain,
rselect_head(rstore_seq(q46,earray_289)) = rselect_head(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))),
inference(monotonicity,[status(thm)],[2156]) ).
tff(2158,plain,
rselect_head(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = rselect_head(rstore_seq(q46,earray_289)),
inference(symmetry,[status(thm)],[2157]) ).
tff(2159,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = rselect_head(rstore_tail(queue_284,index_285)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2160,plain,
rselect_head(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = rselect_head(rstore_tail(queue_284,index_285)),
inference(unit_resolution,[status(thm)],[2159,85]) ).
tff(2161,plain,
rselect_head(rstore_tail(queue_284,index_285)) = rselect_head(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))),
inference(symmetry,[status(thm)],[2160]) ).
tff(2162,plain,
( ( index_285 = s(index_282) )
<=> ( index_285 = s(index_282) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2163,axiom,
index_285 = s(index_282),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(2164,plain,
index_285 = s(index_282),
inference(modus_ponens,[status(thm)],[2163,2162]) ).
tff(2165,plain,
s(index_282) = index_285,
inference(symmetry,[status(thm)],[2164]) ).
tff(2166,plain,
( ( queue_284 = rstore_seq(q45,earray_283) )
<=> ( queue_284 = rstore_seq(q45,earray_283) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2167,axiom,
queue_284 = rstore_seq(q45,earray_283),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp305) ).
tff(2168,plain,
queue_284 = rstore_seq(q45,earray_283),
inference(modus_ponens,[status(thm)],[2167,2166]) ).
tff(2169,plain,
rstore_seq(q45,earray_283) = queue_284,
inference(symmetry,[status(thm)],[2168]) ).
tff(2170,plain,
rstore_tail(rstore_seq(q45,earray_283),s(index_282)) = rstore_tail(queue_284,index_285),
inference(monotonicity,[status(thm)],[2169,2165]) ).
tff(2171,plain,
rstore_tail(queue_284,index_285) = rstore_tail(rstore_seq(q45,earray_283),s(index_282)),
inference(symmetry,[status(thm)],[2170]) ).
tff(2172,plain,
rselect_head(rstore_tail(queue_284,index_285)) = rselect_head(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(monotonicity,[status(thm)],[2171]) ).
tff(2173,plain,
rselect_head(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_head(rstore_tail(queue_284,index_285)),
inference(symmetry,[status(thm)],[2172]) ).
tff(2174,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_head(rstore_seq(q45,earray_283)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2175,plain,
rselect_head(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_head(rstore_seq(q45,earray_283)),
inference(unit_resolution,[status(thm)],[2174,58]) ).
tff(2176,plain,
rselect_head(rstore_seq(q45,earray_283)) = rselect_head(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(symmetry,[status(thm)],[2175]) ).
tff(2177,plain,
( ( earray_283 = store(earray_281,index_282,e45) )
<=> ( earray_283 = store(earray_281,index_282,e45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2178,axiom,
earray_283 = store(earray_281,index_282,e45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp58) ).
tff(2179,plain,
earray_283 = store(earray_281,index_282,e45),
inference(modus_ponens,[status(thm)],[2178,2177]) ).
tff(2180,plain,
store(earray_281,index_282,e45) = earray_283,
inference(symmetry,[status(thm)],[2179]) ).
tff(2181,plain,
( ( q45 = queue_280 )
<=> ( q45 = queue_280 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2182,axiom,
q45 = queue_280,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp393) ).
tff(2183,plain,
q45 = queue_280,
inference(modus_ponens,[status(thm)],[2182,2181]) ).
tff(2184,plain,
queue_280 = q45,
inference(symmetry,[status(thm)],[2183]) ).
tff(2185,plain,
( ( queue_280 = rstore_head(queue_277,index_279) )
<=> ( queue_280 = rstore_head(queue_277,index_279) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2186,axiom,
queue_280 = rstore_head(queue_277,index_279),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp304) ).
tff(2187,plain,
queue_280 = rstore_head(queue_277,index_279),
inference(modus_ponens,[status(thm)],[2186,2185]) ).
tff(2188,plain,
rstore_head(queue_277,index_279) = queue_280,
inference(symmetry,[status(thm)],[2187]) ).
tff(2189,plain,
rstore_head(queue_277,index_279) = q45,
inference(transitivity,[status(thm)],[2188,2184]) ).
tff(2190,plain,
rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45)) = rstore_seq(q45,earray_283),
inference(monotonicity,[status(thm)],[2189,2180]) ).
tff(2191,plain,
rselect_head(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = rselect_head(rstore_seq(q45,earray_283)),
inference(monotonicity,[status(thm)],[2190]) ).
tff(2192,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = rselect_head(rstore_head(queue_277,index_279)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2193,plain,
rselect_head(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = rselect_head(rstore_head(queue_277,index_279)),
inference(unit_resolution,[status(thm)],[2192,85]) ).
tff(2194,plain,
rselect_head(rstore_head(queue_277,index_279)) = rselect_head(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))),
inference(symmetry,[status(thm)],[2193]) ).
tff(2195,plain,
( ( index_279 = s(index_278) )
<=> ( index_279 = s(index_278) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2196,axiom,
index_279 = s(index_278),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(2197,plain,
index_279 = s(index_278),
inference(modus_ponens,[status(thm)],[2196,2195]) ).
tff(2198,plain,
s(index_278) = index_279,
inference(symmetry,[status(thm)],[2197]) ).
tff(2199,plain,
rstore_tail(queue_275,index_276) = queue_277,
inference(symmetry,[status(thm)],[48]) ).
tff(2200,plain,
rstore_head(rstore_tail(queue_275,index_276),s(index_278)) = rstore_head(queue_277,index_279),
inference(monotonicity,[status(thm)],[2199,2198]) ).
tff(2201,plain,
rselect_head(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_head(rstore_head(queue_277,index_279)),
inference(monotonicity,[status(thm)],[2200]) ).
tff(2202,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = s(index_278) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2203,plain,
rselect_head(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = s(index_278),
inference(unit_resolution,[status(thm)],[2202,173]) ).
tff(2204,plain,
s(index_278) = rselect_head(rstore_head(rstore_tail(queue_275,index_276),s(index_278))),
inference(symmetry,[status(thm)],[2203]) ).
tff(2205,plain,
s(rselect_head(queue_277)) = index_299,
inference(transitivity,[status(thm)],[34,2204,2201,2194,2191,2176,2173,2161,2158,2141,2138,2126,2123,2106,2103,2087]) ).
tff(2206,plain,
s(s(rselect_head(queue_277))) = s(index_299),
inference(monotonicity,[status(thm)],[2205]) ).
tff(2207,plain,
s(index_299) = s(s(rselect_head(queue_277))),
inference(symmetry,[status(thm)],[2206]) ).
tff(2208,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = s(index_299) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2209,plain,
rselect_head(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = s(index_299),
inference(unit_resolution,[status(thm)],[2208,173]) ).
tff(2210,plain,
( ( index_300 = s(index_299) )
<=> ( index_300 = s(index_299) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2211,axiom,
index_300 = s(index_299),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(2212,plain,
index_300 = s(index_299),
inference(modus_ponens,[status(thm)],[2211,2210]) ).
tff(2213,plain,
s(index_299) = index_300,
inference(symmetry,[status(thm)],[2212]) ).
tff(2214,plain,
rstore_tail(queue_296,index_297) = queue_298,
inference(symmetry,[status(thm)],[2100]) ).
tff(2215,plain,
rstore_head(rstore_tail(queue_296,index_297),s(index_299)) = rstore_head(queue_298,index_300),
inference(monotonicity,[status(thm)],[2214,2213]) ).
tff(2216,plain,
rselect_head(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_head(rstore_head(queue_298,index_300)),
inference(monotonicity,[status(thm)],[2215]) ).
tff(2217,plain,
rselect_head(rstore_head(queue_298,index_300)) = rselect_head(rstore_head(rstore_tail(queue_296,index_297),s(index_299))),
inference(symmetry,[status(thm)],[2216]) ).
tff(2218,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = rselect_head(rstore_head(queue_298,index_300)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2219,plain,
rselect_head(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = rselect_head(rstore_head(queue_298,index_300)),
inference(unit_resolution,[status(thm)],[2218,85]) ).
tff(2220,plain,
( ( earray_304 = store(earray_302,index_303,e48) )
<=> ( earray_304 = store(earray_302,index_303,e48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2221,axiom,
earray_304 = store(earray_302,index_303,e48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(2222,plain,
earray_304 = store(earray_302,index_303,e48),
inference(modus_ponens,[status(thm)],[2221,2220]) ).
tff(2223,plain,
store(earray_302,index_303,e48) = earray_304,
inference(symmetry,[status(thm)],[2222]) ).
tff(2224,plain,
( ( q48 = queue_301 )
<=> ( q48 = queue_301 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2225,axiom,
q48 = queue_301,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp396) ).
tff(2226,plain,
q48 = queue_301,
inference(modus_ponens,[status(thm)],[2225,2224]) ).
tff(2227,plain,
queue_301 = q48,
inference(symmetry,[status(thm)],[2226]) ).
tff(2228,plain,
( ( queue_301 = rstore_head(queue_298,index_300) )
<=> ( queue_301 = rstore_head(queue_298,index_300) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2229,axiom,
queue_301 = rstore_head(queue_298,index_300),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp311) ).
tff(2230,plain,
queue_301 = rstore_head(queue_298,index_300),
inference(modus_ponens,[status(thm)],[2229,2228]) ).
tff(2231,plain,
rstore_head(queue_298,index_300) = queue_301,
inference(symmetry,[status(thm)],[2230]) ).
tff(2232,plain,
rstore_head(queue_298,index_300) = q48,
inference(transitivity,[status(thm)],[2231,2227]) ).
tff(2233,plain,
rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48)) = rstore_seq(q48,earray_304),
inference(monotonicity,[status(thm)],[2232,2223]) ).
tff(2234,plain,
rselect_head(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = rselect_head(rstore_seq(q48,earray_304)),
inference(monotonicity,[status(thm)],[2233]) ).
tff(2235,plain,
rselect_head(rstore_seq(q48,earray_304)) = rselect_head(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))),
inference(symmetry,[status(thm)],[2234]) ).
tff(2236,plain,
rselect_head(rstore_seq(q48,earray_304)) = rselect_tail(q16),
inference(transitivity,[status(thm)],[2235,2219,2217,2209,2207,2083,29,19]) ).
tff(2237,plain,
( ( index_57 = rselect_tail(q16) )
<=> ( index_57 = rselect_tail(q16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2238,axiom,
index_57 = rselect_tail(q16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(2239,plain,
index_57 = rselect_tail(q16),
inference(modus_ponens,[status(thm)],[2238,2237]) ).
tff(2240,plain,
rselect_tail(q16) = index_57,
inference(symmetry,[status(thm)],[2239]) ).
tff(2241,plain,
s(rselect_tail(q16)) = s(index_57),
inference(monotonicity,[status(thm)],[2240]) ).
tff(2242,plain,
s(index_57) = s(rselect_tail(q16)),
inference(symmetry,[status(thm)],[2241]) ).
tff(2243,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2244,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = s(index_57),
inference(unit_resolution,[status(thm)],[2243,26]) ).
tff(2245,plain,
rstore_tail(rstore_seq(q16,earray_58),s(index_57)) = q17,
inference(transitivity,[status(thm)],[1229,1212,1208]) ).
tff(2246,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_tail(q17),
inference(monotonicity,[status(thm)],[2245]) ).
tff(2247,plain,
rselect_tail(q17) = rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[2246]) ).
tff(2248,plain,
rselect_tail(q17) = s(rselect_tail(q16)),
inference(transitivity,[status(thm)],[2247,2244,2242]) ).
tff(2249,plain,
( ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(rselect_tail(q16)) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2248,2236]) ).
tff(2250,plain,
( ( s(rselect_tail(q16)) = rselect_tail(q16) )
<=> ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2249]) ).
tff(2251,plain,
( ( s(rselect_tail(q16)) != rselect_tail(q16) )
<=> ( rselect_tail(q17) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2250]) ).
tff(2252,plain,
^ [X: $i] :
refl(( ( s(X) != X )
<=> ( s(X) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2253,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(quant_intro,[status(thm)],[2252]) ).
tff(2254,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2255,axiom,
! [X: $i] : ( s(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as1) ).
tff(2256,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[2255,2254]) ).
tff(2257,plain,
! [X: $i] : ( s(X) != X ),
inference(skolemize,[status(sab)],[2256]) ).
tff(2258,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[2257,2253]) ).
tff(2259,plain,
( ~ ! [X: $i] : ( s(X) != X )
| ( s(rselect_tail(q16)) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2260,plain,
s(rselect_tail(q16)) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2259,2258]) ).
tff(2261,plain,
rselect_tail(q17) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2260,2251]) ).
tff(2262,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(2263,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(2264,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(2265,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[2264,2263]) ).
tff(2266,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[2265]) ).
tff(2267,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[2266,2262]) ).
tff(2268,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(rselect_seq(q16),rselect_tail(q16),e16),rselect_tail(q16)) = e16 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2269,plain,
select(store(rselect_seq(q16),rselect_tail(q16),e16),rselect_tail(q16)) = e16,
inference(unit_resolution,[status(thm)],[2268,2267]) ).
tff(2270,plain,
( ( earray_56 = rselect_seq(q16) )
<=> ( earray_56 = rselect_seq(q16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2271,axiom,
earray_56 = rselect_seq(q16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(2272,plain,
earray_56 = rselect_seq(q16),
inference(modus_ponens,[status(thm)],[2271,2270]) ).
tff(2273,plain,
rselect_seq(q16) = earray_56,
inference(symmetry,[status(thm)],[2272]) ).
tff(2274,plain,
store(rselect_seq(q16),rselect_tail(q16),e16) = store(earray_56,index_57,e16),
inference(monotonicity,[status(thm)],[2273,2240]) ).
tff(2275,plain,
store(earray_56,index_57,e16) = store(rselect_seq(q16),rselect_tail(q16),e16),
inference(symmetry,[status(thm)],[2274]) ).
tff(2276,plain,
select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) = select(store(rselect_seq(q16),rselect_tail(q16),e16),rselect_tail(q16)),
inference(monotonicity,[status(thm)],[2275,2236]) ).
tff(2277,plain,
select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) = e16,
inference(transitivity,[status(thm)],[2276,2269]) ).
tff(2278,plain,
( ( elem_352 = select(earray_350,index_351) )
<=> ( elem_352 = select(earray_350,index_351) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2279,axiom,
elem_352 = select(earray_350,index_351),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(2280,plain,
elem_352 = select(earray_350,index_351),
inference(modus_ponens,[status(thm)],[2279,2278]) ).
tff(2281,plain,
select(earray_350,index_351) = elem_352,
inference(symmetry,[status(thm)],[2280]) ).
tff(2282,plain,
( ( index_351 = rselect_head(q50) )
<=> ( index_351 = rselect_head(q50) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2283,axiom,
index_351 = rselect_head(q50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(2284,plain,
index_351 = rselect_head(q50),
inference(modus_ponens,[status(thm)],[2283,2282]) ).
tff(2285,plain,
rselect_head(q50) = index_351,
inference(symmetry,[status(thm)],[2284]) ).
tff(2286,plain,
( ( index_318 = s(index_315) )
<=> ( index_318 = s(index_315) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2287,axiom,
index_318 = s(index_315),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(2288,plain,
index_318 = s(index_315),
inference(modus_ponens,[status(thm)],[2287,2286]) ).
tff(2289,plain,
s(index_315) = index_318,
inference(symmetry,[status(thm)],[2288]) ).
tff(2290,plain,
( ( queue_317 = rstore_seq(q49,earray_316) )
<=> ( queue_317 = rstore_seq(q49,earray_316) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2291,axiom,
queue_317 = rstore_seq(q49,earray_316),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp316) ).
tff(2292,plain,
queue_317 = rstore_seq(q49,earray_316),
inference(modus_ponens,[status(thm)],[2291,2290]) ).
tff(2293,plain,
rstore_seq(q49,earray_316) = queue_317,
inference(symmetry,[status(thm)],[2292]) ).
tff(2294,plain,
rstore_tail(rstore_seq(q49,earray_316),s(index_315)) = rstore_tail(queue_317,index_318),
inference(monotonicity,[status(thm)],[2293,2289]) ).
tff(2295,plain,
rstore_tail(queue_317,index_318) = rstore_tail(rstore_seq(q49,earray_316),s(index_315)),
inference(symmetry,[status(thm)],[2294]) ).
tff(2296,plain,
( ( queue_319 = rstore_tail(queue_317,index_318) )
<=> ( queue_319 = rstore_tail(queue_317,index_318) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2297,axiom,
queue_319 = rstore_tail(queue_317,index_318),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp317) ).
tff(2298,plain,
queue_319 = rstore_tail(queue_317,index_318),
inference(modus_ponens,[status(thm)],[2297,2296]) ).
tff(2299,plain,
( ( q50 = queue_319 )
<=> ( q50 = queue_319 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2300,axiom,
q50 = queue_319,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp399) ).
tff(2301,plain,
q50 = queue_319,
inference(modus_ponens,[status(thm)],[2300,2299]) ).
tff(2302,plain,
q50 = rstore_tail(rstore_seq(q49,earray_316),s(index_315)),
inference(transitivity,[status(thm)],[2301,2298,2295]) ).
tff(2303,plain,
rselect_head(q50) = rselect_head(rstore_tail(rstore_seq(q49,earray_316),s(index_315))),
inference(monotonicity,[status(thm)],[2302]) ).
tff(2304,plain,
rselect_head(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_head(q50),
inference(symmetry,[status(thm)],[2303]) ).
tff(2305,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_head(rstore_seq(q49,earray_316)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2306,plain,
rselect_head(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_head(rstore_seq(q49,earray_316)),
inference(unit_resolution,[status(thm)],[2305,58]) ).
tff(2307,plain,
rselect_head(rstore_seq(q49,earray_316)) = rselect_head(rstore_tail(rstore_seq(q49,earray_316),s(index_315))),
inference(symmetry,[status(thm)],[2306]) ).
tff(2308,plain,
( ( earray_316 = store(earray_314,index_315,e49) )
<=> ( earray_316 = store(earray_314,index_315,e49) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2309,axiom,
earray_316 = store(earray_314,index_315,e49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(2310,plain,
earray_316 = store(earray_314,index_315,e49),
inference(modus_ponens,[status(thm)],[2309,2308]) ).
tff(2311,plain,
store(earray_314,index_315,e49) = earray_316,
inference(symmetry,[status(thm)],[2310]) ).
tff(2312,plain,
( ( q49 = queue_307 )
<=> ( q49 = queue_307 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2313,axiom,
q49 = queue_307,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp397) ).
tff(2314,plain,
q49 = queue_307,
inference(modus_ponens,[status(thm)],[2313,2312]) ).
tff(2315,plain,
queue_307 = q49,
inference(symmetry,[status(thm)],[2314]) ).
tff(2316,plain,
( ( queue_307 = rstore_tail(queue_305,index_306) )
<=> ( queue_307 = rstore_tail(queue_305,index_306) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2317,axiom,
queue_307 = rstore_tail(queue_305,index_306),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp313) ).
tff(2318,plain,
queue_307 = rstore_tail(queue_305,index_306),
inference(modus_ponens,[status(thm)],[2317,2316]) ).
tff(2319,plain,
rstore_tail(queue_305,index_306) = queue_307,
inference(symmetry,[status(thm)],[2318]) ).
tff(2320,plain,
rstore_tail(queue_305,index_306) = q49,
inference(transitivity,[status(thm)],[2319,2315]) ).
tff(2321,plain,
rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49)) = rstore_seq(q49,earray_316),
inference(monotonicity,[status(thm)],[2320,2311]) ).
tff(2322,plain,
rstore_seq(q49,earray_316) = rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49)),
inference(symmetry,[status(thm)],[2321]) ).
tff(2323,plain,
rselect_head(rstore_seq(q49,earray_316)) = rselect_head(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))),
inference(monotonicity,[status(thm)],[2322]) ).
tff(2324,plain,
rselect_head(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = rselect_head(rstore_seq(q49,earray_316)),
inference(symmetry,[status(thm)],[2323]) ).
tff(2325,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = rselect_head(rstore_tail(queue_305,index_306)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2326,plain,
rselect_head(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = rselect_head(rstore_tail(queue_305,index_306)),
inference(unit_resolution,[status(thm)],[2325,85]) ).
tff(2327,plain,
rselect_head(rstore_tail(queue_305,index_306)) = rselect_head(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))),
inference(symmetry,[status(thm)],[2326]) ).
tff(2328,plain,
( ( index_306 = s(index_303) )
<=> ( index_306 = s(index_303) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2329,axiom,
index_306 = s(index_303),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(2330,plain,
index_306 = s(index_303),
inference(modus_ponens,[status(thm)],[2329,2328]) ).
tff(2331,plain,
s(index_303) = index_306,
inference(symmetry,[status(thm)],[2330]) ).
tff(2332,plain,
( ( queue_305 = rstore_seq(q48,earray_304) )
<=> ( queue_305 = rstore_seq(q48,earray_304) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2333,axiom,
queue_305 = rstore_seq(q48,earray_304),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp312) ).
tff(2334,plain,
queue_305 = rstore_seq(q48,earray_304),
inference(modus_ponens,[status(thm)],[2333,2332]) ).
tff(2335,plain,
rstore_seq(q48,earray_304) = queue_305,
inference(symmetry,[status(thm)],[2334]) ).
tff(2336,plain,
rstore_tail(rstore_seq(q48,earray_304),s(index_303)) = rstore_tail(queue_305,index_306),
inference(monotonicity,[status(thm)],[2335,2331]) ).
tff(2337,plain,
rstore_tail(queue_305,index_306) = rstore_tail(rstore_seq(q48,earray_304),s(index_303)),
inference(symmetry,[status(thm)],[2336]) ).
tff(2338,plain,
rselect_head(rstore_tail(queue_305,index_306)) = rselect_head(rstore_tail(rstore_seq(q48,earray_304),s(index_303))),
inference(monotonicity,[status(thm)],[2337]) ).
tff(2339,plain,
rselect_head(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_head(rstore_tail(queue_305,index_306)),
inference(symmetry,[status(thm)],[2338]) ).
tff(2340,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2341,plain,
rselect_head(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_head(rstore_seq(q48,earray_304)),
inference(unit_resolution,[status(thm)],[2340,58]) ).
tff(2342,plain,
rselect_head(rstore_seq(q48,earray_304)) = rselect_head(rstore_tail(rstore_seq(q48,earray_304),s(index_303))),
inference(symmetry,[status(thm)],[2341]) ).
tff(2343,plain,
rselect_head(rstore_seq(q48,earray_304)) = index_351,
inference(transitivity,[status(thm)],[2342,2339,2327,2324,2307,2304,2285]) ).
tff(2344,plain,
( ( earray_350 = rselect_seq(q50) )
<=> ( earray_350 = rselect_seq(q50) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2345,axiom,
earray_350 = rselect_seq(q50),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp80) ).
tff(2346,plain,
earray_350 = rselect_seq(q50),
inference(modus_ponens,[status(thm)],[2345,2344]) ).
tff(2347,plain,
rselect_seq(q50) = earray_350,
inference(symmetry,[status(thm)],[2346]) ).
tff(2348,plain,
rselect_seq(q50) = rselect_seq(rstore_tail(rstore_seq(q49,earray_316),s(index_315))),
inference(monotonicity,[status(thm)],[2302]) ).
tff(2349,plain,
rselect_seq(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_seq(q50),
inference(symmetry,[status(thm)],[2348]) ).
tff(2350,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) )),
inference(bind,[status(th)],[]) ).
tff(2351,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(quant_intro,[status(thm)],[2350]) ).
tff(2352,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2353,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_seq_tail) ).
tff(2354,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[2353,2352]) ).
tff(2355,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(skolemize,[status(sab)],[2354]) ).
tff(2356,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[2355,2351]) ).
tff(2357,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_seq(rstore_seq(q49,earray_316)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2358,plain,
rselect_seq(rstore_tail(rstore_seq(q49,earray_316),s(index_315))) = rselect_seq(rstore_seq(q49,earray_316)),
inference(unit_resolution,[status(thm)],[2357,2356]) ).
tff(2359,plain,
rselect_seq(rstore_seq(q49,earray_316)) = rselect_seq(rstore_tail(rstore_seq(q49,earray_316),s(index_315))),
inference(symmetry,[status(thm)],[2358]) ).
tff(2360,plain,
rselect_seq(rstore_seq(q49,earray_316)) = rselect_seq(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))),
inference(monotonicity,[status(thm)],[2322]) ).
tff(2361,plain,
rselect_seq(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = rselect_seq(rstore_seq(q49,earray_316)),
inference(symmetry,[status(thm)],[2360]) ).
tff(2362,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_seq(A,E)) = E )
<=> ( rselect_seq(rstore_seq(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(2363,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[2362]) ).
tff(2364,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2365,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_seq) ).
tff(2366,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[2365,2364]) ).
tff(2367,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(skolemize,[status(sab)],[2366]) ).
tff(2368,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[2367,2363]) ).
tff(2369,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = store(earray_314,index_315,e49) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2370,plain,
rselect_seq(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))) = store(earray_314,index_315,e49),
inference(unit_resolution,[status(thm)],[2369,2368]) ).
tff(2371,plain,
store(earray_314,index_315,e49) = rselect_seq(rstore_seq(rstore_tail(queue_305,index_306),store(earray_314,index_315,e49))),
inference(symmetry,[status(thm)],[2370]) ).
tff(2372,plain,
( ( index_315 = rselect_tail(q49) )
<=> ( index_315 = rselect_tail(q49) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2373,axiom,
index_315 = rselect_tail(q49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(2374,plain,
index_315 = rselect_tail(q49),
inference(modus_ponens,[status(thm)],[2373,2372]) ).
tff(2375,plain,
rselect_tail(q49) = index_315,
inference(symmetry,[status(thm)],[2374]) ).
tff(2376,plain,
( ( earray_314 = rselect_seq(q49) )
<=> ( earray_314 = rselect_seq(q49) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2377,axiom,
earray_314 = rselect_seq(q49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp69) ).
tff(2378,plain,
earray_314 = rselect_seq(q49),
inference(modus_ponens,[status(thm)],[2377,2376]) ).
tff(2379,plain,
rselect_seq(q49) = earray_314,
inference(symmetry,[status(thm)],[2378]) ).
tff(2380,plain,
q49 = rstore_tail(rstore_seq(q48,earray_304),s(index_303)),
inference(transitivity,[status(thm)],[2314,2318,2337]) ).
tff(2381,plain,
rselect_seq(q49) = rselect_seq(rstore_tail(rstore_seq(q48,earray_304),s(index_303))),
inference(monotonicity,[status(thm)],[2380]) ).
tff(2382,plain,
rselect_seq(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_seq(q49),
inference(symmetry,[status(thm)],[2381]) ).
tff(2383,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_seq(rstore_seq(q48,earray_304)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2384,plain,
rselect_seq(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_seq(rstore_seq(q48,earray_304)),
inference(unit_resolution,[status(thm)],[2383,2356]) ).
tff(2385,plain,
rselect_seq(rstore_seq(q48,earray_304)) = rselect_seq(rstore_tail(rstore_seq(q48,earray_304),s(index_303))),
inference(symmetry,[status(thm)],[2384]) ).
tff(2386,plain,
rstore_seq(q48,earray_304) = rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48)),
inference(symmetry,[status(thm)],[2233]) ).
tff(2387,plain,
rselect_seq(rstore_seq(q48,earray_304)) = rselect_seq(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))),
inference(monotonicity,[status(thm)],[2386]) ).
tff(2388,plain,
rselect_seq(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = rselect_seq(rstore_seq(q48,earray_304)),
inference(symmetry,[status(thm)],[2387]) ).
tff(2389,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = store(earray_302,index_303,e48) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2390,plain,
rselect_seq(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))) = store(earray_302,index_303,e48),
inference(unit_resolution,[status(thm)],[2389,2368]) ).
tff(2391,plain,
store(earray_302,index_303,e48) = rselect_seq(rstore_seq(rstore_head(queue_298,index_300),store(earray_302,index_303,e48))),
inference(symmetry,[status(thm)],[2390]) ).
tff(2392,plain,
store(earray_302,index_303,e48) = earray_314,
inference(transitivity,[status(thm)],[2391,2388,2385,2382,2379]) ).
tff(2393,plain,
store(store(earray_302,index_303,e48),rselect_tail(q49),e49) = store(earray_314,index_315,e49),
inference(monotonicity,[status(thm)],[2392,2375]) ).
tff(2394,plain,
store(store(earray_302,index_303,e48),rselect_tail(q49),e49) = earray_350,
inference(transitivity,[status(thm)],[2393,2371,2361,2359,2349,2347]) ).
tff(2395,plain,
select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(earray_350,index_351),
inference(monotonicity,[status(thm)],[2394,2343]) ).
tff(2396,plain,
( ( index_303 = rselect_tail(q48) )
<=> ( index_303 = rselect_tail(q48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2397,axiom,
index_303 = rselect_tail(q48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(2398,plain,
index_303 = rselect_tail(q48),
inference(modus_ponens,[status(thm)],[2397,2396]) ).
tff(2399,plain,
rselect_tail(q48) = index_303,
inference(symmetry,[status(thm)],[2398]) ).
tff(2400,plain,
rstore_head(rstore_tail(queue_296,index_297),s(index_299)) = q48,
inference(transitivity,[status(thm)],[2215,2231,2227]) ).
tff(2401,plain,
rselect_tail(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_tail(q48),
inference(monotonicity,[status(thm)],[2400]) ).
tff(2402,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_tail(rstore_tail(queue_296,index_297)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2403,plain,
rselect_tail(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_tail(rstore_tail(queue_296,index_297)),
inference(unit_resolution,[status(thm)],[2402,1917]) ).
tff(2404,plain,
rselect_tail(rstore_tail(queue_296,index_297)) = rselect_tail(rstore_head(rstore_tail(queue_296,index_297),s(index_299))),
inference(symmetry,[status(thm)],[2403]) ).
tff(2405,plain,
rselect_tail(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_tail(rstore_tail(queue_296,index_297)),
inference(monotonicity,[status(thm)],[2096]) ).
tff(2406,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = s(index_294) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2407,plain,
rselect_tail(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = s(index_294),
inference(unit_resolution,[status(thm)],[2406,26]) ).
tff(2408,plain,
s(index_294) = rselect_tail(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(symmetry,[status(thm)],[2407]) ).
tff(2409,plain,
( ( index_294 = rselect_tail(q47) )
<=> ( index_294 = rselect_tail(q47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2410,axiom,
index_294 = rselect_tail(q47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(2411,plain,
index_294 = rselect_tail(q47),
inference(modus_ponens,[status(thm)],[2410,2409]) ).
tff(2412,plain,
rselect_tail(q47) = index_294,
inference(symmetry,[status(thm)],[2411]) ).
tff(2413,plain,
rstore_tail(rstore_seq(q46,earray_289),s(index_288)) = q47,
inference(transitivity,[status(thm)],[2135,2118,2114]) ).
tff(2414,plain,
rselect_tail(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_tail(q47),
inference(monotonicity,[status(thm)],[2413]) ).
tff(2415,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = s(index_288) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2416,plain,
rselect_tail(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = s(index_288),
inference(unit_resolution,[status(thm)],[2415,26]) ).
tff(2417,plain,
s(index_288) = rselect_tail(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(symmetry,[status(thm)],[2416]) ).
tff(2418,plain,
( ( index_288 = rselect_tail(q46) )
<=> ( index_288 = rselect_tail(q46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2419,axiom,
index_288 = rselect_tail(q46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(2420,plain,
index_288 = rselect_tail(q46),
inference(modus_ponens,[status(thm)],[2419,2418]) ).
tff(2421,plain,
rselect_tail(q46) = index_288,
inference(symmetry,[status(thm)],[2420]) ).
tff(2422,plain,
rstore_tail(rstore_seq(q45,earray_283),s(index_282)) = q46,
inference(transitivity,[status(thm)],[2170,2153,2149]) ).
tff(2423,plain,
rselect_tail(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_tail(q46),
inference(monotonicity,[status(thm)],[2422]) ).
tff(2424,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = s(index_282) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2425,plain,
rselect_tail(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = s(index_282),
inference(unit_resolution,[status(thm)],[2424,26]) ).
tff(2426,plain,
s(index_282) = rselect_tail(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(symmetry,[status(thm)],[2425]) ).
tff(2427,plain,
( ( index_282 = rselect_tail(q45) )
<=> ( index_282 = rselect_tail(q45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2428,axiom,
index_282 = rselect_tail(q45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(2429,plain,
index_282 = rselect_tail(q45),
inference(modus_ponens,[status(thm)],[2428,2427]) ).
tff(2430,plain,
rselect_tail(q45) = index_282,
inference(symmetry,[status(thm)],[2429]) ).
tff(2431,plain,
rstore_head(rstore_tail(queue_275,index_276),s(index_278)) = q45,
inference(transitivity,[status(thm)],[2200,2188,2184]) ).
tff(2432,plain,
rselect_tail(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_tail(q45),
inference(monotonicity,[status(thm)],[2431]) ).
tff(2433,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_tail(rstore_tail(queue_275,index_276)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2434,plain,
rselect_tail(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_tail(rstore_tail(queue_275,index_276)),
inference(unit_resolution,[status(thm)],[2433,1917]) ).
tff(2435,plain,
rselect_tail(rstore_tail(queue_275,index_276)) = rselect_tail(rstore_head(rstore_tail(queue_275,index_276),s(index_278))),
inference(symmetry,[status(thm)],[2434]) ).
tff(2436,plain,
rselect_tail(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_tail(rstore_tail(queue_275,index_276)),
inference(monotonicity,[status(thm)],[44]) ).
tff(2437,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = s(index_273) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2438,plain,
rselect_tail(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = s(index_273),
inference(unit_resolution,[status(thm)],[2437,26]) ).
tff(2439,plain,
s(index_273) = rselect_tail(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(symmetry,[status(thm)],[2438]) ).
tff(2440,plain,
( ( index_273 = rselect_tail(q44) )
<=> ( index_273 = rselect_tail(q44) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2441,axiom,
index_273 = rselect_tail(q44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(2442,plain,
index_273 = rselect_tail(q44),
inference(modus_ponens,[status(thm)],[2441,2440]) ).
tff(2443,plain,
rselect_tail(q44) = index_273,
inference(symmetry,[status(thm)],[2442]) ).
tff(2444,plain,
rstore_tail(rstore_seq(q43,earray_268),s(index_267)) = q44,
inference(transitivity,[status(thm)],[97,73,69]) ).
tff(2445,plain,
rselect_tail(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_tail(q44),
inference(monotonicity,[status(thm)],[2444]) ).
tff(2446,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = s(index_267) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2447,plain,
rselect_tail(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = s(index_267),
inference(unit_resolution,[status(thm)],[2446,26]) ).
tff(2448,plain,
s(index_267) = rselect_tail(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(symmetry,[status(thm)],[2447]) ).
tff(2449,plain,
( ( index_267 = rselect_tail(q43) )
<=> ( index_267 = rselect_tail(q43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2450,axiom,
index_267 = rselect_tail(q43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(2451,plain,
index_267 = rselect_tail(q43),
inference(modus_ponens,[status(thm)],[2450,2449]) ).
tff(2452,plain,
rselect_tail(q43) = index_267,
inference(symmetry,[status(thm)],[2451]) ).
tff(2453,plain,
rstore_tail(rstore_seq(q42,earray_262),s(index_261)) = q43,
inference(transitivity,[status(thm)],[132,115,111]) ).
tff(2454,plain,
rselect_tail(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_tail(q43),
inference(monotonicity,[status(thm)],[2453]) ).
tff(2455,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = s(index_261) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2456,plain,
rselect_tail(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = s(index_261),
inference(unit_resolution,[status(thm)],[2455,26]) ).
tff(2457,plain,
s(index_261) = rselect_tail(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(symmetry,[status(thm)],[2456]) ).
tff(2458,plain,
( ( index_261 = rselect_tail(q42) )
<=> ( index_261 = rselect_tail(q42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2459,axiom,
index_261 = rselect_tail(q42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(2460,plain,
index_261 = rselect_tail(q42),
inference(modus_ponens,[status(thm)],[2459,2458]) ).
tff(2461,plain,
rselect_tail(q42) = index_261,
inference(symmetry,[status(thm)],[2460]) ).
tff(2462,plain,
rstore_head(rstore_tail(queue_254,index_255),s(index_257)) = q42,
inference(transitivity,[status(thm)],[165,150,146]) ).
tff(2463,plain,
rselect_tail(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_tail(q42),
inference(monotonicity,[status(thm)],[2462]) ).
tff(2464,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_tail(rstore_tail(queue_254,index_255)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2465,plain,
rselect_tail(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_tail(rstore_tail(queue_254,index_255)),
inference(unit_resolution,[status(thm)],[2464,1917]) ).
tff(2466,plain,
rselect_tail(rstore_tail(queue_254,index_255)) = rselect_tail(rstore_head(rstore_tail(queue_254,index_255),s(index_257))),
inference(symmetry,[status(thm)],[2465]) ).
tff(2467,plain,
rselect_tail(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_tail(rstore_tail(queue_254,index_255)),
inference(monotonicity,[status(thm)],[193]) ).
tff(2468,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = s(index_252) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2469,plain,
rselect_tail(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = s(index_252),
inference(unit_resolution,[status(thm)],[2468,26]) ).
tff(2470,plain,
s(index_252) = rselect_tail(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(symmetry,[status(thm)],[2469]) ).
tff(2471,plain,
( ( index_252 = rselect_tail(q41) )
<=> ( index_252 = rselect_tail(q41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2472,axiom,
index_252 = rselect_tail(q41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(2473,plain,
index_252 = rselect_tail(q41),
inference(modus_ponens,[status(thm)],[2472,2471]) ).
tff(2474,plain,
rselect_tail(q41) = index_252,
inference(symmetry,[status(thm)],[2473]) ).
tff(2475,plain,
rstore_tail(rstore_seq(q40,earray_247),s(index_246)) = q41,
inference(transitivity,[status(thm)],[229,212,208]) ).
tff(2476,plain,
rselect_tail(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_tail(q41),
inference(monotonicity,[status(thm)],[2475]) ).
tff(2477,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = s(index_246) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2478,plain,
rselect_tail(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = s(index_246),
inference(unit_resolution,[status(thm)],[2477,26]) ).
tff(2479,plain,
s(index_246) = rselect_tail(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(symmetry,[status(thm)],[2478]) ).
tff(2480,plain,
( ( index_246 = rselect_tail(q40) )
<=> ( index_246 = rselect_tail(q40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2481,axiom,
index_246 = rselect_tail(q40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(2482,plain,
index_246 = rselect_tail(q40),
inference(modus_ponens,[status(thm)],[2481,2480]) ).
tff(2483,plain,
rselect_tail(q40) = index_246,
inference(symmetry,[status(thm)],[2482]) ).
tff(2484,plain,
rstore_tail(rstore_seq(q39,earray_241),s(index_240)) = q40,
inference(transitivity,[status(thm)],[264,247,243]) ).
tff(2485,plain,
rselect_tail(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_tail(q40),
inference(monotonicity,[status(thm)],[2484]) ).
tff(2486,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = s(index_240) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2487,plain,
rselect_tail(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = s(index_240),
inference(unit_resolution,[status(thm)],[2486,26]) ).
tff(2488,plain,
s(index_240) = rselect_tail(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(symmetry,[status(thm)],[2487]) ).
tff(2489,plain,
( ( index_240 = rselect_tail(q39) )
<=> ( index_240 = rselect_tail(q39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2490,axiom,
index_240 = rselect_tail(q39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(2491,plain,
index_240 = rselect_tail(q39),
inference(modus_ponens,[status(thm)],[2490,2489]) ).
tff(2492,plain,
rselect_tail(q39) = index_240,
inference(symmetry,[status(thm)],[2491]) ).
tff(2493,plain,
rstore_head(rstore_tail(queue_227,index_228),s(index_230)) = q39,
inference(transitivity,[status(thm)],[297,282,278]) ).
tff(2494,plain,
rselect_tail(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_tail(q39),
inference(monotonicity,[status(thm)],[2493]) ).
tff(2495,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_tail(rstore_tail(queue_227,index_228)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2496,plain,
rselect_tail(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_tail(rstore_tail(queue_227,index_228)),
inference(unit_resolution,[status(thm)],[2495,1917]) ).
tff(2497,plain,
rselect_tail(rstore_tail(queue_227,index_228)) = rselect_tail(rstore_head(rstore_tail(queue_227,index_228),s(index_230))),
inference(symmetry,[status(thm)],[2496]) ).
tff(2498,plain,
rselect_tail(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_tail(rstore_tail(queue_227,index_228)),
inference(monotonicity,[status(thm)],[318]) ).
tff(2499,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = s(index_225) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2500,plain,
rselect_tail(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = s(index_225),
inference(unit_resolution,[status(thm)],[2499,26]) ).
tff(2501,plain,
s(index_225) = rselect_tail(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(symmetry,[status(thm)],[2500]) ).
tff(2502,plain,
( ( index_225 = rselect_tail(q38) )
<=> ( index_225 = rselect_tail(q38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2503,axiom,
index_225 = rselect_tail(q38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(2504,plain,
index_225 = rselect_tail(q38),
inference(modus_ponens,[status(thm)],[2503,2502]) ).
tff(2505,plain,
rselect_tail(q38) = index_225,
inference(symmetry,[status(thm)],[2504]) ).
tff(2506,plain,
rstore_tail(rstore_seq(q37,earray_220),s(index_219)) = q38,
inference(transitivity,[status(thm)],[354,337,333]) ).
tff(2507,plain,
rselect_tail(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_tail(q38),
inference(monotonicity,[status(thm)],[2506]) ).
tff(2508,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = s(index_219) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2509,plain,
rselect_tail(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = s(index_219),
inference(unit_resolution,[status(thm)],[2508,26]) ).
tff(2510,plain,
s(index_219) = rselect_tail(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(symmetry,[status(thm)],[2509]) ).
tff(2511,plain,
( ( index_219 = rselect_tail(q37) )
<=> ( index_219 = rselect_tail(q37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2512,axiom,
index_219 = rselect_tail(q37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(2513,plain,
index_219 = rselect_tail(q37),
inference(modus_ponens,[status(thm)],[2512,2511]) ).
tff(2514,plain,
rselect_tail(q37) = index_219,
inference(symmetry,[status(thm)],[2513]) ).
tff(2515,plain,
rstore_tail(rstore_seq(q36,earray_214),s(index_213)) = q37,
inference(transitivity,[status(thm)],[389,372,368]) ).
tff(2516,plain,
rselect_tail(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_tail(q37),
inference(monotonicity,[status(thm)],[2515]) ).
tff(2517,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = s(index_213) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2518,plain,
rselect_tail(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = s(index_213),
inference(unit_resolution,[status(thm)],[2517,26]) ).
tff(2519,plain,
s(index_213) = rselect_tail(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(symmetry,[status(thm)],[2518]) ).
tff(2520,plain,
( ( index_213 = rselect_tail(q36) )
<=> ( index_213 = rselect_tail(q36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2521,axiom,
index_213 = rselect_tail(q36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(2522,plain,
index_213 = rselect_tail(q36),
inference(modus_ponens,[status(thm)],[2521,2520]) ).
tff(2523,plain,
rselect_tail(q36) = index_213,
inference(symmetry,[status(thm)],[2522]) ).
tff(2524,plain,
rstore_head(rstore_tail(queue_206,index_207),s(index_209)) = q36,
inference(transitivity,[status(thm)],[422,407,403]) ).
tff(2525,plain,
rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(q36),
inference(monotonicity,[status(thm)],[2524]) ).
tff(2526,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(rstore_tail(queue_206,index_207)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2527,plain,
rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(rstore_tail(queue_206,index_207)),
inference(unit_resolution,[status(thm)],[2526,1917]) ).
tff(2528,plain,
rselect_tail(rstore_tail(queue_206,index_207)) = rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[2527]) ).
tff(2529,plain,
rselect_tail(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_tail(rstore_tail(queue_206,index_207)),
inference(monotonicity,[status(thm)],[443]) ).
tff(2530,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = s(index_204) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2531,plain,
rselect_tail(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = s(index_204),
inference(unit_resolution,[status(thm)],[2530,26]) ).
tff(2532,plain,
s(index_204) = rselect_tail(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[2531]) ).
tff(2533,plain,
( ( index_204 = rselect_tail(q35) )
<=> ( index_204 = rselect_tail(q35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2534,axiom,
index_204 = rselect_tail(q35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(2535,plain,
index_204 = rselect_tail(q35),
inference(modus_ponens,[status(thm)],[2534,2533]) ).
tff(2536,plain,
rselect_tail(q35) = index_204,
inference(symmetry,[status(thm)],[2535]) ).
tff(2537,plain,
rstore_tail(rstore_seq(q34,earray_199),s(index_198)) = q35,
inference(transitivity,[status(thm)],[479,462,458]) ).
tff(2538,plain,
rselect_tail(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_tail(q35),
inference(monotonicity,[status(thm)],[2537]) ).
tff(2539,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = s(index_198) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2540,plain,
rselect_tail(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = s(index_198),
inference(unit_resolution,[status(thm)],[2539,26]) ).
tff(2541,plain,
s(index_198) = rselect_tail(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(symmetry,[status(thm)],[2540]) ).
tff(2542,plain,
( ( index_198 = rselect_tail(q34) )
<=> ( index_198 = rselect_tail(q34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2543,axiom,
index_198 = rselect_tail(q34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(2544,plain,
index_198 = rselect_tail(q34),
inference(modus_ponens,[status(thm)],[2543,2542]) ).
tff(2545,plain,
rselect_tail(q34) = index_198,
inference(symmetry,[status(thm)],[2544]) ).
tff(2546,plain,
rstore_tail(rstore_seq(q33,earray_193),s(index_192)) = q34,
inference(transitivity,[status(thm)],[514,497,493]) ).
tff(2547,plain,
rselect_tail(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_tail(q34),
inference(monotonicity,[status(thm)],[2546]) ).
tff(2548,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = s(index_192) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2549,plain,
rselect_tail(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = s(index_192),
inference(unit_resolution,[status(thm)],[2548,26]) ).
tff(2550,plain,
s(index_192) = rselect_tail(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(symmetry,[status(thm)],[2549]) ).
tff(2551,plain,
( ( index_192 = rselect_tail(q33) )
<=> ( index_192 = rselect_tail(q33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2552,axiom,
index_192 = rselect_tail(q33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(2553,plain,
index_192 = rselect_tail(q33),
inference(modus_ponens,[status(thm)],[2552,2551]) ).
tff(2554,plain,
rselect_tail(q33) = index_192,
inference(symmetry,[status(thm)],[2553]) ).
tff(2555,plain,
rstore_head(rstore_tail(queue_185,index_186),s(index_188)) = q33,
inference(transitivity,[status(thm)],[547,532,528]) ).
tff(2556,plain,
rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_tail(q33),
inference(monotonicity,[status(thm)],[2555]) ).
tff(2557,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_tail(rstore_tail(queue_185,index_186)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2558,plain,
rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_tail(rstore_tail(queue_185,index_186)),
inference(unit_resolution,[status(thm)],[2557,1917]) ).
tff(2559,plain,
rselect_tail(rstore_tail(queue_185,index_186)) = rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(symmetry,[status(thm)],[2558]) ).
tff(2560,plain,
rselect_tail(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_tail(rstore_tail(queue_185,index_186)),
inference(monotonicity,[status(thm)],[568]) ).
tff(2561,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2562,plain,
rselect_tail(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = s(index_183),
inference(unit_resolution,[status(thm)],[2561,26]) ).
tff(2563,plain,
s(index_183) = rselect_tail(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[2562]) ).
tff(2564,plain,
( ( index_183 = rselect_tail(q32) )
<=> ( index_183 = rselect_tail(q32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2565,axiom,
index_183 = rselect_tail(q32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(2566,plain,
index_183 = rselect_tail(q32),
inference(modus_ponens,[status(thm)],[2565,2564]) ).
tff(2567,plain,
rselect_tail(q32) = index_183,
inference(symmetry,[status(thm)],[2566]) ).
tff(2568,plain,
rstore_tail(rstore_seq(q31,earray_178),s(index_177)) = q32,
inference(transitivity,[status(thm)],[604,587,583]) ).
tff(2569,plain,
rselect_tail(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_tail(q32),
inference(monotonicity,[status(thm)],[2568]) ).
tff(2570,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2571,plain,
rselect_tail(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = s(index_177),
inference(unit_resolution,[status(thm)],[2570,26]) ).
tff(2572,plain,
s(index_177) = rselect_tail(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[2571]) ).
tff(2573,plain,
( ( index_177 = rselect_tail(q31) )
<=> ( index_177 = rselect_tail(q31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2574,axiom,
index_177 = rselect_tail(q31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(2575,plain,
index_177 = rselect_tail(q31),
inference(modus_ponens,[status(thm)],[2574,2573]) ).
tff(2576,plain,
rselect_tail(q31) = index_177,
inference(symmetry,[status(thm)],[2575]) ).
tff(2577,plain,
rstore_tail(rstore_seq(q30,earray_172),s(index_171)) = q31,
inference(transitivity,[status(thm)],[639,622,618]) ).
tff(2578,plain,
rselect_tail(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_tail(q31),
inference(monotonicity,[status(thm)],[2577]) ).
tff(2579,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2580,plain,
rselect_tail(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = s(index_171),
inference(unit_resolution,[status(thm)],[2579,26]) ).
tff(2581,plain,
s(index_171) = rselect_tail(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(symmetry,[status(thm)],[2580]) ).
tff(2582,plain,
( ( index_171 = rselect_tail(q30) )
<=> ( index_171 = rselect_tail(q30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2583,axiom,
index_171 = rselect_tail(q30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(2584,plain,
index_171 = rselect_tail(q30),
inference(modus_ponens,[status(thm)],[2583,2582]) ).
tff(2585,plain,
rselect_tail(q30) = index_171,
inference(symmetry,[status(thm)],[2584]) ).
tff(2586,plain,
rstore_head(rstore_tail(queue_164,index_165),s(index_167)) = q30,
inference(transitivity,[status(thm)],[672,657,653]) ).
tff(2587,plain,
rselect_tail(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_tail(q30),
inference(monotonicity,[status(thm)],[2586]) ).
tff(2588,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_tail(rstore_tail(queue_164,index_165)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2589,plain,
rselect_tail(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_tail(rstore_tail(queue_164,index_165)),
inference(unit_resolution,[status(thm)],[2588,1917]) ).
tff(2590,plain,
rselect_tail(rstore_tail(queue_164,index_165)) = rselect_tail(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[2589]) ).
tff(2591,plain,
rselect_tail(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_tail(rstore_tail(queue_164,index_165)),
inference(monotonicity,[status(thm)],[693]) ).
tff(2592,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = s(index_162) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2593,plain,
rselect_tail(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = s(index_162),
inference(unit_resolution,[status(thm)],[2592,26]) ).
tff(2594,plain,
s(index_162) = rselect_tail(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(symmetry,[status(thm)],[2593]) ).
tff(2595,plain,
( ( index_162 = rselect_tail(q29) )
<=> ( index_162 = rselect_tail(q29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2596,axiom,
index_162 = rselect_tail(q29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(2597,plain,
index_162 = rselect_tail(q29),
inference(modus_ponens,[status(thm)],[2596,2595]) ).
tff(2598,plain,
rselect_tail(q29) = index_162,
inference(symmetry,[status(thm)],[2597]) ).
tff(2599,plain,
rstore_tail(rstore_seq(q28,earray_148),s(index_147)) = q29,
inference(transitivity,[status(thm)],[729,712,708]) ).
tff(2600,plain,
rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_tail(q29),
inference(monotonicity,[status(thm)],[2599]) ).
tff(2601,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2602,plain,
rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = s(index_147),
inference(unit_resolution,[status(thm)],[2601,26]) ).
tff(2603,plain,
s(index_147) = rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[2602]) ).
tff(2604,plain,
( ( index_147 = rselect_tail(q28) )
<=> ( index_147 = rselect_tail(q28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2605,axiom,
index_147 = rselect_tail(q28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(2606,plain,
index_147 = rselect_tail(q28),
inference(modus_ponens,[status(thm)],[2605,2604]) ).
tff(2607,plain,
rselect_tail(q28) = index_147,
inference(symmetry,[status(thm)],[2606]) ).
tff(2608,plain,
rstore_tail(rstore_seq(q27,earray_142),s(index_141)) = q28,
inference(transitivity,[status(thm)],[764,747,743]) ).
tff(2609,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_tail(q28),
inference(monotonicity,[status(thm)],[2608]) ).
tff(2610,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2611,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = s(index_141),
inference(unit_resolution,[status(thm)],[2610,26]) ).
tff(2612,plain,
s(index_141) = rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[2611]) ).
tff(2613,plain,
( ( index_141 = rselect_tail(q27) )
<=> ( index_141 = rselect_tail(q27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2614,axiom,
index_141 = rselect_tail(q27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(2615,plain,
index_141 = rselect_tail(q27),
inference(modus_ponens,[status(thm)],[2614,2613]) ).
tff(2616,plain,
rselect_tail(q27) = index_141,
inference(symmetry,[status(thm)],[2615]) ).
tff(2617,plain,
rstore_head(rstore_tail(queue_134,index_135),s(index_137)) = q27,
inference(transitivity,[status(thm)],[797,782,778]) ).
tff(2618,plain,
rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(q27),
inference(monotonicity,[status(thm)],[2617]) ).
tff(2619,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(rstore_tail(queue_134,index_135)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2620,plain,
rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(rstore_tail(queue_134,index_135)),
inference(unit_resolution,[status(thm)],[2619,1917]) ).
tff(2621,plain,
rselect_tail(rstore_tail(queue_134,index_135)) = rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[2620]) ).
tff(2622,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_tail(rstore_tail(queue_134,index_135)),
inference(monotonicity,[status(thm)],[818]) ).
tff(2623,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = s(index_132) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2624,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = s(index_132),
inference(unit_resolution,[status(thm)],[2623,26]) ).
tff(2625,plain,
s(index_132) = rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[2624]) ).
tff(2626,plain,
( ( index_132 = rselect_tail(q26) )
<=> ( index_132 = rselect_tail(q26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2627,axiom,
index_132 = rselect_tail(q26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(2628,plain,
index_132 = rselect_tail(q26),
inference(modus_ponens,[status(thm)],[2627,2626]) ).
tff(2629,plain,
rselect_tail(q26) = index_132,
inference(symmetry,[status(thm)],[2628]) ).
tff(2630,plain,
rstore_tail(rstore_seq(q25,earray_127),s(index_126)) = q26,
inference(transitivity,[status(thm)],[854,837,833]) ).
tff(2631,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_tail(q26),
inference(monotonicity,[status(thm)],[2630]) ).
tff(2632,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = s(index_126) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2633,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = s(index_126),
inference(unit_resolution,[status(thm)],[2632,26]) ).
tff(2634,plain,
s(index_126) = rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[2633]) ).
tff(2635,plain,
( ( index_126 = rselect_tail(q25) )
<=> ( index_126 = rselect_tail(q25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2636,axiom,
index_126 = rselect_tail(q25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(2637,plain,
index_126 = rselect_tail(q25),
inference(modus_ponens,[status(thm)],[2636,2635]) ).
tff(2638,plain,
rselect_tail(q25) = index_126,
inference(symmetry,[status(thm)],[2637]) ).
tff(2639,plain,
rstore_tail(rstore_seq(q24,earray_121),s(index_120)) = q25,
inference(transitivity,[status(thm)],[889,872,868]) ).
tff(2640,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_tail(q25),
inference(monotonicity,[status(thm)],[2639]) ).
tff(2641,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = s(index_120) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2642,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = s(index_120),
inference(unit_resolution,[status(thm)],[2641,26]) ).
tff(2643,plain,
s(index_120) = rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[2642]) ).
tff(2644,plain,
( ( index_120 = rselect_tail(q24) )
<=> ( index_120 = rselect_tail(q24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2645,axiom,
index_120 = rselect_tail(q24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(2646,plain,
index_120 = rselect_tail(q24),
inference(modus_ponens,[status(thm)],[2645,2644]) ).
tff(2647,plain,
rselect_tail(q24) = index_120,
inference(symmetry,[status(thm)],[2646]) ).
tff(2648,plain,
rstore_head(rstore_tail(queue_113,index_114),s(index_116)) = q24,
inference(transitivity,[status(thm)],[922,907,903]) ).
tff(2649,plain,
rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(q24),
inference(monotonicity,[status(thm)],[2648]) ).
tff(2650,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(rstore_tail(queue_113,index_114)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2651,plain,
rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(rstore_tail(queue_113,index_114)),
inference(unit_resolution,[status(thm)],[2650,1917]) ).
tff(2652,plain,
rselect_tail(rstore_tail(queue_113,index_114)) = rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[2651]) ).
tff(2653,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_tail(rstore_tail(queue_113,index_114)),
inference(monotonicity,[status(thm)],[943]) ).
tff(2654,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2655,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = s(index_111),
inference(unit_resolution,[status(thm)],[2654,26]) ).
tff(2656,plain,
s(index_111) = rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[2655]) ).
tff(2657,plain,
( ( index_111 = rselect_tail(q23) )
<=> ( index_111 = rselect_tail(q23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2658,axiom,
index_111 = rselect_tail(q23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(2659,plain,
index_111 = rselect_tail(q23),
inference(modus_ponens,[status(thm)],[2658,2657]) ).
tff(2660,plain,
rselect_tail(q23) = index_111,
inference(symmetry,[status(thm)],[2659]) ).
tff(2661,plain,
rstore_tail(rstore_seq(q22,earray_106),s(index_105)) = q23,
inference(transitivity,[status(thm)],[979,962,958]) ).
tff(2662,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_tail(q23),
inference(monotonicity,[status(thm)],[2661]) ).
tff(2663,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2664,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = s(index_105),
inference(unit_resolution,[status(thm)],[2663,26]) ).
tff(2665,plain,
s(index_105) = rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[2664]) ).
tff(2666,plain,
( ( index_105 = rselect_tail(q22) )
<=> ( index_105 = rselect_tail(q22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2667,axiom,
index_105 = rselect_tail(q22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(2668,plain,
index_105 = rselect_tail(q22),
inference(modus_ponens,[status(thm)],[2667,2666]) ).
tff(2669,plain,
rselect_tail(q22) = index_105,
inference(symmetry,[status(thm)],[2668]) ).
tff(2670,plain,
rstore_tail(rstore_seq(q21,earray_100),s(index_99)) = q22,
inference(transitivity,[status(thm)],[1014,997,993]) ).
tff(2671,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_tail(q22),
inference(monotonicity,[status(thm)],[2670]) ).
tff(2672,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2673,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = s(index_99),
inference(unit_resolution,[status(thm)],[2672,26]) ).
tff(2674,plain,
s(index_99) = rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[2673]) ).
tff(2675,plain,
( ( index_99 = rselect_tail(q21) )
<=> ( index_99 = rselect_tail(q21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2676,axiom,
index_99 = rselect_tail(q21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(2677,plain,
index_99 = rselect_tail(q21),
inference(modus_ponens,[status(thm)],[2676,2675]) ).
tff(2678,plain,
rselect_tail(q21) = index_99,
inference(symmetry,[status(thm)],[2677]) ).
tff(2679,plain,
rstore_head(rstore_tail(queue_92,index_93),s(index_95)) = q21,
inference(transitivity,[status(thm)],[1047,1032,1028]) ).
tff(2680,plain,
rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(q21),
inference(monotonicity,[status(thm)],[2679]) ).
tff(2681,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(rstore_tail(queue_92,index_93)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2682,plain,
rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(rstore_tail(queue_92,index_93)),
inference(unit_resolution,[status(thm)],[2681,1917]) ).
tff(2683,plain,
rselect_tail(rstore_tail(queue_92,index_93)) = rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[2682]) ).
tff(2684,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_tail(rstore_tail(queue_92,index_93)),
inference(monotonicity,[status(thm)],[1068]) ).
tff(2685,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = s(index_90) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2686,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = s(index_90),
inference(unit_resolution,[status(thm)],[2685,26]) ).
tff(2687,plain,
s(index_90) = rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[2686]) ).
tff(2688,plain,
( ( index_90 = rselect_tail(q20) )
<=> ( index_90 = rselect_tail(q20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2689,axiom,
index_90 = rselect_tail(q20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(2690,plain,
index_90 = rselect_tail(q20),
inference(modus_ponens,[status(thm)],[2689,2688]) ).
tff(2691,plain,
rselect_tail(q20) = index_90,
inference(symmetry,[status(thm)],[2690]) ).
tff(2692,plain,
rstore_tail(rstore_seq(q19,earray_85),s(index_84)) = q20,
inference(transitivity,[status(thm)],[1104,1087,1083]) ).
tff(2693,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_tail(q20),
inference(monotonicity,[status(thm)],[2692]) ).
tff(2694,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = s(index_84) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2695,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = s(index_84),
inference(unit_resolution,[status(thm)],[2694,26]) ).
tff(2696,plain,
s(index_84) = rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[2695]) ).
tff(2697,plain,
( ( index_84 = rselect_tail(q19) )
<=> ( index_84 = rselect_tail(q19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2698,axiom,
index_84 = rselect_tail(q19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(2699,plain,
index_84 = rselect_tail(q19),
inference(modus_ponens,[status(thm)],[2698,2697]) ).
tff(2700,plain,
rselect_tail(q19) = index_84,
inference(symmetry,[status(thm)],[2699]) ).
tff(2701,plain,
rstore_tail(rstore_seq(q18,earray_73),s(index_72)) = q19,
inference(transitivity,[status(thm)],[1139,1122,1118]) ).
tff(2702,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_tail(q19),
inference(monotonicity,[status(thm)],[2701]) ).
tff(2703,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = s(index_72) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2704,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = s(index_72),
inference(unit_resolution,[status(thm)],[2703,26]) ).
tff(2705,plain,
s(index_72) = rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[2704]) ).
tff(2706,plain,
( ( index_72 = rselect_tail(q18) )
<=> ( index_72 = rselect_tail(q18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2707,axiom,
index_72 = rselect_tail(q18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(2708,plain,
index_72 = rselect_tail(q18),
inference(modus_ponens,[status(thm)],[2707,2706]) ).
tff(2709,plain,
rselect_tail(q18) = index_72,
inference(symmetry,[status(thm)],[2708]) ).
tff(2710,plain,
rstore_head(rstore_tail(queue_65,index_66),s(index_68)) = q18,
inference(transitivity,[status(thm)],[1172,1157,1153]) ).
tff(2711,plain,
rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(q18),
inference(monotonicity,[status(thm)],[2710]) ).
tff(2712,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(rstore_tail(queue_65,index_66)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2713,plain,
rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(rstore_tail(queue_65,index_66)),
inference(unit_resolution,[status(thm)],[2712,1917]) ).
tff(2714,plain,
rselect_tail(rstore_tail(queue_65,index_66)) = rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[2713]) ).
tff(2715,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_tail(rstore_tail(queue_65,index_66)),
inference(monotonicity,[status(thm)],[1193]) ).
tff(2716,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2717,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = s(index_63),
inference(unit_resolution,[status(thm)],[2716,26]) ).
tff(2718,plain,
s(index_63) = rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[2717]) ).
tff(2719,plain,
( ( index_63 = rselect_tail(q17) )
<=> ( index_63 = rselect_tail(q17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2720,axiom,
index_63 = rselect_tail(q17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(2721,plain,
index_63 = rselect_tail(q17),
inference(modus_ponens,[status(thm)],[2720,2719]) ).
tff(2722,plain,
rselect_tail(q17) = index_63,
inference(symmetry,[status(thm)],[2721]) ).
tff(2723,plain,
s(index_57) = rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[2244]) ).
tff(2724,plain,
s(rselect_tail(q16)) = index_63,
inference(transitivity,[status(thm)],[2241,2723,2246,2722]) ).
tff(2725,plain,
s(s(rselect_tail(q16))) = s(index_63),
inference(monotonicity,[status(thm)],[2724]) ).
tff(2726,plain,
s(s(rselect_tail(q16))) = index_72,
inference(transitivity,[status(thm)],[2725,2718,2715,2714,2711,2709]) ).
tff(2727,plain,
s(s(s(rselect_tail(q16)))) = s(index_72),
inference(monotonicity,[status(thm)],[2726]) ).
tff(2728,plain,
s(s(s(rselect_tail(q16)))) = index_84,
inference(transitivity,[status(thm)],[2727,2705,2702,2700]) ).
tff(2729,plain,
s(s(s(s(rselect_tail(q16))))) = s(index_84),
inference(monotonicity,[status(thm)],[2728]) ).
tff(2730,plain,
s(s(s(s(rselect_tail(q16))))) = index_90,
inference(transitivity,[status(thm)],[2729,2696,2693,2691]) ).
tff(2731,plain,
s(s(s(s(s(rselect_tail(q16)))))) = s(index_90),
inference(monotonicity,[status(thm)],[2730]) ).
tff(2732,plain,
s(s(s(s(s(rselect_tail(q16)))))) = index_99,
inference(transitivity,[status(thm)],[2731,2687,2684,2683,2680,2678]) ).
tff(2733,plain,
s(s(s(s(s(s(rselect_tail(q16))))))) = s(index_99),
inference(monotonicity,[status(thm)],[2732]) ).
tff(2734,plain,
s(s(s(s(s(s(rselect_tail(q16))))))) = index_105,
inference(transitivity,[status(thm)],[2733,2674,2671,2669]) ).
tff(2735,plain,
s(s(s(s(s(s(s(rselect_tail(q16)))))))) = s(index_105),
inference(monotonicity,[status(thm)],[2734]) ).
tff(2736,plain,
s(s(s(s(s(s(s(rselect_tail(q16)))))))) = index_111,
inference(transitivity,[status(thm)],[2735,2665,2662,2660]) ).
tff(2737,plain,
s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) = s(index_111),
inference(monotonicity,[status(thm)],[2736]) ).
tff(2738,plain,
s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) = index_120,
inference(transitivity,[status(thm)],[2737,2656,2653,2652,2649,2647]) ).
tff(2739,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) = s(index_120),
inference(monotonicity,[status(thm)],[2738]) ).
tff(2740,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) = index_126,
inference(transitivity,[status(thm)],[2739,2643,2640,2638]) ).
tff(2741,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) = s(index_126),
inference(monotonicity,[status(thm)],[2740]) ).
tff(2742,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) = index_132,
inference(transitivity,[status(thm)],[2741,2634,2631,2629]) ).
tff(2743,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) = s(index_132),
inference(monotonicity,[status(thm)],[2742]) ).
tff(2744,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) = index_141,
inference(transitivity,[status(thm)],[2743,2625,2622,2621,2618,2616]) ).
tff(2745,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) = s(index_141),
inference(monotonicity,[status(thm)],[2744]) ).
tff(2746,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) = index_147,
inference(transitivity,[status(thm)],[2745,2612,2609,2607]) ).
tff(2747,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) = s(index_147),
inference(monotonicity,[status(thm)],[2746]) ).
tff(2748,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) = index_162,
inference(transitivity,[status(thm)],[2747,2603,2600,2598]) ).
tff(2749,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) = s(index_162),
inference(monotonicity,[status(thm)],[2748]) ).
tff(2750,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) = index_171,
inference(transitivity,[status(thm)],[2749,2594,2591,2590,2587,2585]) ).
tff(2751,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) = s(index_171),
inference(monotonicity,[status(thm)],[2750]) ).
tff(2752,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) = index_177,
inference(transitivity,[status(thm)],[2751,2581,2578,2576]) ).
tff(2753,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) = s(index_177),
inference(monotonicity,[status(thm)],[2752]) ).
tff(2754,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) = index_183,
inference(transitivity,[status(thm)],[2753,2572,2569,2567]) ).
tff(2755,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) = s(index_183),
inference(monotonicity,[status(thm)],[2754]) ).
tff(2756,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) = index_192,
inference(transitivity,[status(thm)],[2755,2563,2560,2559,2556,2554]) ).
tff(2757,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) = s(index_192),
inference(monotonicity,[status(thm)],[2756]) ).
tff(2758,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) = index_198,
inference(transitivity,[status(thm)],[2757,2550,2547,2545]) ).
tff(2759,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) = s(index_198),
inference(monotonicity,[status(thm)],[2758]) ).
tff(2760,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) = index_204,
inference(transitivity,[status(thm)],[2759,2541,2538,2536]) ).
tff(2761,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) = s(index_204),
inference(monotonicity,[status(thm)],[2760]) ).
tff(2762,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) = index_213,
inference(transitivity,[status(thm)],[2761,2532,2529,2528,2525,2523]) ).
tff(2763,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) = s(index_213),
inference(monotonicity,[status(thm)],[2762]) ).
tff(2764,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) = index_219,
inference(transitivity,[status(thm)],[2763,2519,2516,2514]) ).
tff(2765,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) = s(index_219),
inference(monotonicity,[status(thm)],[2764]) ).
tff(2766,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) = index_225,
inference(transitivity,[status(thm)],[2765,2510,2507,2505]) ).
tff(2767,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) = s(index_225),
inference(monotonicity,[status(thm)],[2766]) ).
tff(2768,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) = index_240,
inference(transitivity,[status(thm)],[2767,2501,2498,2497,2494,2492]) ).
tff(2769,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(rselect_tail(q16))))))))))))))))))))))))) = s(index_240),
inference(monotonicity,[status(thm)],[2768]) ).
tff(2770,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(rselect_tail(q16))))))))))))))))))))))))) = index_246,
inference(transitivity,[status(thm)],[2769,2488,2485,2483]) ).
tff(2771,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(rselect_tail(q16)))))))))))))))))))))))))) = s(index_246),
inference(monotonicity,[status(thm)],[2770]) ).
tff(2772,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(rselect_tail(q16)))))))))))))))))))))))))) = index_252,
inference(transitivity,[status(thm)],[2771,2479,2476,2474]) ).
tff(2773,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(rselect_tail(q16))))))))))))))))))))))))))) = s(index_252),
inference(monotonicity,[status(thm)],[2772]) ).
tff(2774,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(rselect_tail(q16))))))))))))))))))))))))))) = index_261,
inference(transitivity,[status(thm)],[2773,2470,2467,2466,2463,2461]) ).
tff(2775,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(rselect_tail(q16)))))))))))))))))))))))))))) = s(index_261),
inference(monotonicity,[status(thm)],[2774]) ).
tff(2776,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(rselect_tail(q16)))))))))))))))))))))))))))) = index_267,
inference(transitivity,[status(thm)],[2775,2457,2454,2452]) ).
tff(2777,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(rselect_tail(q16))))))))))))))))))))))))))))) = s(index_267),
inference(monotonicity,[status(thm)],[2776]) ).
tff(2778,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(rselect_tail(q16))))))))))))))))))))))))))))) = index_273,
inference(transitivity,[status(thm)],[2777,2448,2445,2443]) ).
tff(2779,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(rselect_tail(q16)))))))))))))))))))))))))))))) = s(index_273),
inference(monotonicity,[status(thm)],[2778]) ).
tff(2780,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(rselect_tail(q16)))))))))))))))))))))))))))))) = index_282,
inference(transitivity,[status(thm)],[2779,2439,2436,2435,2432,2430]) ).
tff(2781,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(rselect_tail(q16))))))))))))))))))))))))))))))) = s(index_282),
inference(monotonicity,[status(thm)],[2780]) ).
tff(2782,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(rselect_tail(q16))))))))))))))))))))))))))))))) = index_288,
inference(transitivity,[status(thm)],[2781,2426,2423,2421]) ).
tff(2783,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(rselect_tail(q16)))))))))))))))))))))))))))))))) = s(index_288),
inference(monotonicity,[status(thm)],[2782]) ).
tff(2784,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(rselect_tail(q16)))))))))))))))))))))))))))))))) = index_294,
inference(transitivity,[status(thm)],[2783,2417,2414,2412]) ).
tff(2785,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(rselect_tail(q16))))))))))))))))))))))))))))))))) = s(index_294),
inference(monotonicity,[status(thm)],[2784]) ).
tff(2786,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(rselect_tail(q16))))))))))))))))))))))))))))))))) = index_303,
inference(transitivity,[status(thm)],[2785,2408,2405,2404,2401,2399]) ).
tff(2787,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(rselect_tail(q16)))))))))))))))))))))))))))))))))) = s(index_303),
inference(monotonicity,[status(thm)],[2786]) ).
tff(2788,plain,
s(index_303) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2787]) ).
tff(2789,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = s(index_303) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2790,plain,
rselect_tail(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = s(index_303),
inference(unit_resolution,[status(thm)],[2789,26]) ).
tff(2791,plain,
rstore_tail(rstore_seq(q48,earray_304),s(index_303)) = q49,
inference(transitivity,[status(thm)],[2336,2319,2315]) ).
tff(2792,plain,
rselect_tail(rstore_tail(rstore_seq(q48,earray_304),s(index_303))) = rselect_tail(q49),
inference(monotonicity,[status(thm)],[2791]) ).
tff(2793,plain,
rselect_tail(q49) = rselect_tail(rstore_tail(rstore_seq(q48,earray_304),s(index_303))),
inference(symmetry,[status(thm)],[2792]) ).
tff(2794,plain,
rselect_tail(q49) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[2793,2790,2788]) ).
tff(2795,plain,
( ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2794,2236]) ).
tff(2796,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(rselect_tail(q16)))))))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2795]) ).
tff(2797,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(rselect_tail(q16)))))))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q49) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2796]) ).
tff(2798,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(2799,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)],[2798]) ).
tff(2800,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(2801,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(2802,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)],[2801,2800]) ).
tff(2803,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)],[2802]) ).
tff(2804,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)],[2803,2799]) ).
tff(2805,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(rselect_tail(q16)))))))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2806,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(rselect_tail(q16)))))))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2805,2804]) ).
tff(2807,plain,
rselect_tail(q49) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2806,2797]) ).
tff(2808,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(2809,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(2810,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(2811,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)],[2810,2809]) ).
tff(2812,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(skolemize,[status(sab)],[2811]) ).
tff(2813,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)],[2812,2808]) ).
tff(2814,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2815,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2816,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[2815,2814]) ).
tff(2817,plain,
( ( rselect_tail(q49) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[2816,2813]) ).
tff(2818,plain,
select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[2817,2807]) ).
tff(2819,plain,
select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_302,index_303,e48),rselect_tail(q49),e49),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[2818]) ).
tff(2820,plain,
( ( earray_302 = rselect_seq(q48) )
<=> ( earray_302 = rselect_seq(q48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2821,axiom,
earray_302 = rselect_seq(q48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp64) ).
tff(2822,plain,
earray_302 = rselect_seq(q48),
inference(modus_ponens,[status(thm)],[2821,2820]) ).
tff(2823,plain,
rselect_seq(q48) = earray_302,
inference(symmetry,[status(thm)],[2822]) ).
tff(2824,plain,
rstore_head(queue_298,index_300) = rstore_head(rstore_tail(queue_296,index_297),s(index_299)),
inference(symmetry,[status(thm)],[2215]) ).
tff(2825,plain,
q48 = rstore_head(rstore_tail(queue_296,index_297),s(index_299)),
inference(transitivity,[status(thm)],[2226,2230,2824]) ).
tff(2826,plain,
rselect_seq(q48) = rselect_seq(rstore_head(rstore_tail(queue_296,index_297),s(index_299))),
inference(monotonicity,[status(thm)],[2825]) ).
tff(2827,plain,
rselect_seq(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_seq(q48),
inference(symmetry,[status(thm)],[2826]) ).
tff(2828,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) )),
inference(bind,[status(th)],[]) ).
tff(2829,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) ),
inference(quant_intro,[status(thm)],[2828]) ).
tff(2830,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2831,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_seq_head) ).
tff(2832,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[2831,2830]) ).
tff(2833,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(skolemize,[status(sab)],[2832]) ).
tff(2834,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[2833,2829]) ).
tff(2835,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_seq(rstore_tail(queue_296,index_297)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2836,plain,
rselect_seq(rstore_head(rstore_tail(queue_296,index_297),s(index_299))) = rselect_seq(rstore_tail(queue_296,index_297)),
inference(unit_resolution,[status(thm)],[2835,2834]) ).
tff(2837,plain,
rselect_seq(rstore_tail(queue_296,index_297)) = rselect_seq(rstore_head(rstore_tail(queue_296,index_297),s(index_299))),
inference(symmetry,[status(thm)],[2836]) ).
tff(2838,plain,
rselect_seq(rstore_tail(queue_296,index_297)) = rselect_seq(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(monotonicity,[status(thm)],[2097]) ).
tff(2839,plain,
rselect_seq(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_seq(rstore_tail(queue_296,index_297)),
inference(symmetry,[status(thm)],[2838]) ).
tff(2840,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_seq(rstore_seq(q47,earray_295)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2841,plain,
rselect_seq(rstore_tail(rstore_seq(q47,earray_295),s(index_294))) = rselect_seq(rstore_seq(q47,earray_295)),
inference(unit_resolution,[status(thm)],[2840,2356]) ).
tff(2842,plain,
rselect_seq(rstore_seq(q47,earray_295)) = rselect_seq(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(symmetry,[status(thm)],[2841]) ).
tff(2843,plain,
rselect_seq(rstore_seq(q47,earray_295)) = rselect_seq(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))),
inference(monotonicity,[status(thm)],[2121]) ).
tff(2844,plain,
rselect_seq(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = rselect_seq(rstore_seq(q47,earray_295)),
inference(symmetry,[status(thm)],[2843]) ).
tff(2845,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = store(earray_293,index_294,e47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2846,plain,
rselect_seq(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))) = store(earray_293,index_294,e47),
inference(unit_resolution,[status(thm)],[2845,2368]) ).
tff(2847,plain,
store(earray_293,index_294,e47) = rselect_seq(rstore_seq(rstore_tail(queue_290,index_291),store(earray_293,index_294,e47))),
inference(symmetry,[status(thm)],[2846]) ).
tff(2848,plain,
store(earray_293,index_294,e47) = earray_302,
inference(transitivity,[status(thm)],[2847,2844,2842,2839,2837,2827,2823]) ).
tff(2849,plain,
store(store(earray_293,index_294,e47),rselect_tail(q48),e48) = store(earray_302,index_303,e48),
inference(monotonicity,[status(thm)],[2848,2399]) ).
tff(2850,plain,
select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_302,index_303,e48),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[2849]) ).
tff(2851,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(rselect_tail(q16))))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2785]) ).
tff(2852,plain,
rselect_tail(rstore_tail(queue_296,index_297)) = rselect_tail(rstore_tail(rstore_seq(q47,earray_295),s(index_294))),
inference(symmetry,[status(thm)],[2405]) ).
tff(2853,plain,
rselect_tail(q48) = rselect_tail(rstore_head(rstore_tail(queue_296,index_297),s(index_299))),
inference(symmetry,[status(thm)],[2401]) ).
tff(2854,plain,
rselect_tail(q48) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[2853,2403,2852,2407,2851]) ).
tff(2855,plain,
( ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2854,2236]) ).
tff(2856,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(rselect_tail(q16))))))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2855]) ).
tff(2857,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(rselect_tail(q16))))))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q48) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2856]) ).
tff(2858,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(2859,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)],[2858]) ).
tff(2860,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(2861,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(2862,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)],[2861,2860]) ).
tff(2863,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)],[2862]) ).
tff(2864,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)],[2863,2859]) ).
tff(2865,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(rselect_tail(q16))))))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2866,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(rselect_tail(q16))))))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2865,2864]) ).
tff(2867,plain,
rselect_tail(q48) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2866,2857]) ).
tff(2868,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
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) ) )
| ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) ) ),
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) ) )
| ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[2869,2868]) ).
tff(2871,plain,
( ( rselect_tail(q48) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[2870,2813]) ).
tff(2872,plain,
select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[2871,2867]) ).
tff(2873,plain,
select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_293,index_294,e47),rselect_tail(q48),e48),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[2872]) ).
tff(2874,plain,
( ( earray_293 = rselect_seq(q47) )
<=> ( earray_293 = rselect_seq(q47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2875,axiom,
earray_293 = rselect_seq(q47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp62) ).
tff(2876,plain,
earray_293 = rselect_seq(q47),
inference(modus_ponens,[status(thm)],[2875,2874]) ).
tff(2877,plain,
rselect_seq(q47) = earray_293,
inference(symmetry,[status(thm)],[2876]) ).
tff(2878,plain,
q47 = rstore_tail(rstore_seq(q46,earray_289),s(index_288)),
inference(transitivity,[status(thm)],[2113,2117,2136]) ).
tff(2879,plain,
rselect_seq(q47) = rselect_seq(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(monotonicity,[status(thm)],[2878]) ).
tff(2880,plain,
rselect_seq(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_seq(q47),
inference(symmetry,[status(thm)],[2879]) ).
tff(2881,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_seq(rstore_seq(q46,earray_289)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2882,plain,
rselect_seq(rstore_tail(rstore_seq(q46,earray_289),s(index_288))) = rselect_seq(rstore_seq(q46,earray_289)),
inference(unit_resolution,[status(thm)],[2881,2356]) ).
tff(2883,plain,
rselect_seq(rstore_seq(q46,earray_289)) = rselect_seq(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(symmetry,[status(thm)],[2882]) ).
tff(2884,plain,
rselect_seq(rstore_seq(q46,earray_289)) = rselect_seq(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))),
inference(monotonicity,[status(thm)],[2156]) ).
tff(2885,plain,
rselect_seq(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = rselect_seq(rstore_seq(q46,earray_289)),
inference(symmetry,[status(thm)],[2884]) ).
tff(2886,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = store(earray_287,index_288,e46) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2887,plain,
rselect_seq(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))) = store(earray_287,index_288,e46),
inference(unit_resolution,[status(thm)],[2886,2368]) ).
tff(2888,plain,
store(earray_287,index_288,e46) = rselect_seq(rstore_seq(rstore_tail(queue_284,index_285),store(earray_287,index_288,e46))),
inference(symmetry,[status(thm)],[2887]) ).
tff(2889,plain,
store(earray_287,index_288,e46) = earray_293,
inference(transitivity,[status(thm)],[2888,2885,2883,2880,2877]) ).
tff(2890,plain,
store(store(earray_287,index_288,e46),rselect_tail(q47),e47) = store(earray_293,index_294,e47),
inference(monotonicity,[status(thm)],[2889,2412]) ).
tff(2891,plain,
select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_293,index_294,e47),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[2890]) ).
tff(2892,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(rselect_tail(q16)))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2783]) ).
tff(2893,plain,
rselect_tail(q47) = rselect_tail(rstore_tail(rstore_seq(q46,earray_289),s(index_288))),
inference(symmetry,[status(thm)],[2414]) ).
tff(2894,plain,
rselect_tail(q47) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[2893,2416,2892]) ).
tff(2895,plain,
( ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2894,2236]) ).
tff(2896,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(rselect_tail(q16)))))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2895]) ).
tff(2897,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(rselect_tail(q16)))))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q47) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2896]) ).
tff(2898,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(2899,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)],[2898]) ).
tff(2900,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(2901,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(2902,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)],[2901,2900]) ).
tff(2903,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)],[2902]) ).
tff(2904,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)],[2903,2899]) ).
tff(2905,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(rselect_tail(q16)))))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2906,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(rselect_tail(q16)))))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2905,2904]) ).
tff(2907,plain,
rselect_tail(q47) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2906,2897]) ).
tff(2908,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2909,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2910,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[2909,2908]) ).
tff(2911,plain,
( ( rselect_tail(q47) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[2910,2813]) ).
tff(2912,plain,
select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[2911,2907]) ).
tff(2913,plain,
select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_287,index_288,e46),rselect_tail(q47),e47),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[2912]) ).
tff(2914,plain,
( ( earray_287 = rselect_seq(q46) )
<=> ( earray_287 = rselect_seq(q46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2915,axiom,
earray_287 = rselect_seq(q46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp59) ).
tff(2916,plain,
earray_287 = rselect_seq(q46),
inference(modus_ponens,[status(thm)],[2915,2914]) ).
tff(2917,plain,
rselect_seq(q46) = earray_287,
inference(symmetry,[status(thm)],[2916]) ).
tff(2918,plain,
q46 = rstore_tail(rstore_seq(q45,earray_283),s(index_282)),
inference(transitivity,[status(thm)],[2148,2152,2171]) ).
tff(2919,plain,
rselect_seq(q46) = rselect_seq(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(monotonicity,[status(thm)],[2918]) ).
tff(2920,plain,
rselect_seq(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_seq(q46),
inference(symmetry,[status(thm)],[2919]) ).
tff(2921,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_seq(rstore_seq(q45,earray_283)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2922,plain,
rselect_seq(rstore_tail(rstore_seq(q45,earray_283),s(index_282))) = rselect_seq(rstore_seq(q45,earray_283)),
inference(unit_resolution,[status(thm)],[2921,2356]) ).
tff(2923,plain,
rselect_seq(rstore_seq(q45,earray_283)) = rselect_seq(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(symmetry,[status(thm)],[2922]) ).
tff(2924,plain,
rstore_seq(q45,earray_283) = rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45)),
inference(symmetry,[status(thm)],[2190]) ).
tff(2925,plain,
rselect_seq(rstore_seq(q45,earray_283)) = rselect_seq(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))),
inference(monotonicity,[status(thm)],[2924]) ).
tff(2926,plain,
rselect_seq(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = rselect_seq(rstore_seq(q45,earray_283)),
inference(symmetry,[status(thm)],[2925]) ).
tff(2927,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = store(earray_281,index_282,e45) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2928,plain,
rselect_seq(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))) = store(earray_281,index_282,e45),
inference(unit_resolution,[status(thm)],[2927,2368]) ).
tff(2929,plain,
store(earray_281,index_282,e45) = rselect_seq(rstore_seq(rstore_head(queue_277,index_279),store(earray_281,index_282,e45))),
inference(symmetry,[status(thm)],[2928]) ).
tff(2930,plain,
store(earray_281,index_282,e45) = earray_287,
inference(transitivity,[status(thm)],[2929,2926,2923,2920,2917]) ).
tff(2931,plain,
store(store(earray_281,index_282,e45),rselect_tail(q46),e46) = store(earray_287,index_288,e46),
inference(monotonicity,[status(thm)],[2930,2421]) ).
tff(2932,plain,
select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_287,index_288,e46),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[2931]) ).
tff(2933,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(rselect_tail(q16))))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2781]) ).
tff(2934,plain,
rselect_tail(q46) = rselect_tail(rstore_tail(rstore_seq(q45,earray_283),s(index_282))),
inference(symmetry,[status(thm)],[2423]) ).
tff(2935,plain,
rselect_tail(q46) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[2934,2425,2933]) ).
tff(2936,plain,
( ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2935,2236]) ).
tff(2937,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(rselect_tail(q16))))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2936]) ).
tff(2938,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(rselect_tail(q16))))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q46) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2937]) ).
tff(2939,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(2940,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)],[2939]) ).
tff(2941,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(2942,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(2943,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)],[2942,2941]) ).
tff(2944,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)],[2943]) ).
tff(2945,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)],[2944,2940]) ).
tff(2946,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(rselect_tail(q16))))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2947,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(rselect_tail(q16))))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2946,2945]) ).
tff(2948,plain,
rselect_tail(q46) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2947,2938]) ).
tff(2949,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2950,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2951,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[2950,2949]) ).
tff(2952,plain,
( ( rselect_tail(q46) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[2951,2813]) ).
tff(2953,plain,
select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[2952,2948]) ).
tff(2954,plain,
select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_281,index_282,e45),rselect_tail(q46),e46),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[2953]) ).
tff(2955,plain,
( ( earray_281 = rselect_seq(q45) )
<=> ( earray_281 = rselect_seq(q45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2956,axiom,
earray_281 = rselect_seq(q45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp57) ).
tff(2957,plain,
earray_281 = rselect_seq(q45),
inference(modus_ponens,[status(thm)],[2956,2955]) ).
tff(2958,plain,
rselect_seq(q45) = earray_281,
inference(symmetry,[status(thm)],[2957]) ).
tff(2959,plain,
rstore_head(queue_277,index_279) = rstore_head(rstore_tail(queue_275,index_276),s(index_278)),
inference(symmetry,[status(thm)],[2200]) ).
tff(2960,plain,
q45 = rstore_head(rstore_tail(queue_275,index_276),s(index_278)),
inference(transitivity,[status(thm)],[2183,2187,2959]) ).
tff(2961,plain,
rselect_seq(q45) = rselect_seq(rstore_head(rstore_tail(queue_275,index_276),s(index_278))),
inference(monotonicity,[status(thm)],[2960]) ).
tff(2962,plain,
rselect_seq(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_seq(q45),
inference(symmetry,[status(thm)],[2961]) ).
tff(2963,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_seq(rstore_tail(queue_275,index_276)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2964,plain,
rselect_seq(rstore_head(rstore_tail(queue_275,index_276),s(index_278))) = rselect_seq(rstore_tail(queue_275,index_276)),
inference(unit_resolution,[status(thm)],[2963,2834]) ).
tff(2965,plain,
rselect_seq(rstore_tail(queue_275,index_276)) = rselect_seq(rstore_head(rstore_tail(queue_275,index_276),s(index_278))),
inference(symmetry,[status(thm)],[2964]) ).
tff(2966,plain,
rselect_seq(rstore_tail(queue_275,index_276)) = rselect_seq(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(monotonicity,[status(thm)],[45]) ).
tff(2967,plain,
rselect_seq(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_seq(rstore_tail(queue_275,index_276)),
inference(symmetry,[status(thm)],[2966]) ).
tff(2968,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_seq(rstore_seq(q44,earray_274)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2969,plain,
rselect_seq(rstore_tail(rstore_seq(q44,earray_274),s(index_273))) = rselect_seq(rstore_seq(q44,earray_274)),
inference(unit_resolution,[status(thm)],[2968,2356]) ).
tff(2970,plain,
rselect_seq(rstore_seq(q44,earray_274)) = rselect_seq(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(symmetry,[status(thm)],[2969]) ).
tff(2971,plain,
rselect_seq(rstore_seq(q44,earray_274)) = rselect_seq(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))),
inference(monotonicity,[status(thm)],[76]) ).
tff(2972,plain,
rselect_seq(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = rselect_seq(rstore_seq(q44,earray_274)),
inference(symmetry,[status(thm)],[2971]) ).
tff(2973,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = store(earray_272,index_273,e44) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2974,plain,
rselect_seq(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))) = store(earray_272,index_273,e44),
inference(unit_resolution,[status(thm)],[2973,2368]) ).
tff(2975,plain,
store(earray_272,index_273,e44) = rselect_seq(rstore_seq(rstore_tail(queue_269,index_270),store(earray_272,index_273,e44))),
inference(symmetry,[status(thm)],[2974]) ).
tff(2976,plain,
store(earray_272,index_273,e44) = earray_281,
inference(transitivity,[status(thm)],[2975,2972,2970,2967,2965,2962,2958]) ).
tff(2977,plain,
store(store(earray_272,index_273,e44),rselect_tail(q45),e45) = store(earray_281,index_282,e45),
inference(monotonicity,[status(thm)],[2976,2430]) ).
tff(2978,plain,
select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_281,index_282,e45),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[2977]) ).
tff(2979,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(rselect_tail(q16)))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2779]) ).
tff(2980,plain,
rselect_tail(rstore_tail(queue_275,index_276)) = rselect_tail(rstore_tail(rstore_seq(q44,earray_274),s(index_273))),
inference(symmetry,[status(thm)],[2436]) ).
tff(2981,plain,
rselect_tail(q45) = rselect_tail(rstore_head(rstore_tail(queue_275,index_276),s(index_278))),
inference(symmetry,[status(thm)],[2432]) ).
tff(2982,plain,
rselect_tail(q45) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[2981,2434,2980,2438,2979]) ).
tff(2983,plain,
( ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[2982,2236]) ).
tff(2984,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(rselect_tail(q16)))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[2983]) ).
tff(2985,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(rselect_tail(q16)))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q45) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[2984]) ).
tff(2986,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(2987,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)],[2986]) ).
tff(2988,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(2989,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(2990,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)],[2989,2988]) ).
tff(2991,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)],[2990]) ).
tff(2992,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)],[2991,2987]) ).
tff(2993,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(rselect_tail(q16)))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2994,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(rselect_tail(q16)))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[2993,2992]) ).
tff(2995,plain,
rselect_tail(q45) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[2994,2985]) ).
tff(2996,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2997,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2998,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[2997,2996]) ).
tff(2999,plain,
( ( rselect_tail(q45) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[2998,2813]) ).
tff(3000,plain,
select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[2999,2995]) ).
tff(3001,plain,
select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_272,index_273,e44),rselect_tail(q45),e45),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3000]) ).
tff(3002,plain,
( ( earray_272 = rselect_seq(q44) )
<=> ( earray_272 = rselect_seq(q44) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3003,axiom,
earray_272 = rselect_seq(q44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp55) ).
tff(3004,plain,
earray_272 = rselect_seq(q44),
inference(modus_ponens,[status(thm)],[3003,3002]) ).
tff(3005,plain,
rselect_seq(q44) = earray_272,
inference(symmetry,[status(thm)],[3004]) ).
tff(3006,plain,
q44 = rstore_tail(rstore_seq(q43,earray_268),s(index_267)),
inference(transitivity,[status(thm)],[68,72,98]) ).
tff(3007,plain,
rselect_seq(q44) = rselect_seq(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(monotonicity,[status(thm)],[3006]) ).
tff(3008,plain,
rselect_seq(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_seq(q44),
inference(symmetry,[status(thm)],[3007]) ).
tff(3009,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_seq(rstore_seq(q43,earray_268)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3010,plain,
rselect_seq(rstore_tail(rstore_seq(q43,earray_268),s(index_267))) = rselect_seq(rstore_seq(q43,earray_268)),
inference(unit_resolution,[status(thm)],[3009,2356]) ).
tff(3011,plain,
rselect_seq(rstore_seq(q43,earray_268)) = rselect_seq(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(symmetry,[status(thm)],[3010]) ).
tff(3012,plain,
rselect_seq(rstore_seq(q43,earray_268)) = rselect_seq(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))),
inference(monotonicity,[status(thm)],[118]) ).
tff(3013,plain,
rselect_seq(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = rselect_seq(rstore_seq(q43,earray_268)),
inference(symmetry,[status(thm)],[3012]) ).
tff(3014,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = store(earray_266,index_267,e43) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3015,plain,
rselect_seq(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))) = store(earray_266,index_267,e43),
inference(unit_resolution,[status(thm)],[3014,2368]) ).
tff(3016,plain,
store(earray_266,index_267,e43) = rselect_seq(rstore_seq(rstore_tail(queue_263,index_264),store(earray_266,index_267,e43))),
inference(symmetry,[status(thm)],[3015]) ).
tff(3017,plain,
store(earray_266,index_267,e43) = earray_272,
inference(transitivity,[status(thm)],[3016,3013,3011,3008,3005]) ).
tff(3018,plain,
store(store(earray_266,index_267,e43),rselect_tail(q44),e44) = store(earray_272,index_273,e44),
inference(monotonicity,[status(thm)],[3017,2443]) ).
tff(3019,plain,
select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_272,index_273,e44),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3018]) ).
tff(3020,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(rselect_tail(q16))))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2777]) ).
tff(3021,plain,
rselect_tail(q44) = rselect_tail(rstore_tail(rstore_seq(q43,earray_268),s(index_267))),
inference(symmetry,[status(thm)],[2445]) ).
tff(3022,plain,
rselect_tail(q44) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3021,2447,3020]) ).
tff(3023,plain,
( ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3022,2236]) ).
tff(3024,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(rselect_tail(q16))))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3023]) ).
tff(3025,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(rselect_tail(q16))))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q44) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3024]) ).
tff(3026,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(3027,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)],[3026]) ).
tff(3028,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(3029,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(3030,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)],[3029,3028]) ).
tff(3031,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)],[3030]) ).
tff(3032,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)],[3031,3027]) ).
tff(3033,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(rselect_tail(q16))))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3034,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(rselect_tail(q16))))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3033,3032]) ).
tff(3035,plain,
rselect_tail(q44) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3034,3025]) ).
tff(3036,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3037,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3038,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3037,3036]) ).
tff(3039,plain,
( ( rselect_tail(q44) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3038,2813]) ).
tff(3040,plain,
select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3039,3035]) ).
tff(3041,plain,
select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_266,index_267,e43),rselect_tail(q44),e44),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3040]) ).
tff(3042,plain,
( ( earray_266 = rselect_seq(q43) )
<=> ( earray_266 = rselect_seq(q43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3043,axiom,
earray_266 = rselect_seq(q43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp53) ).
tff(3044,plain,
earray_266 = rselect_seq(q43),
inference(modus_ponens,[status(thm)],[3043,3042]) ).
tff(3045,plain,
rselect_seq(q43) = earray_266,
inference(symmetry,[status(thm)],[3044]) ).
tff(3046,plain,
q43 = rstore_tail(rstore_seq(q42,earray_262),s(index_261)),
inference(transitivity,[status(thm)],[110,114,133]) ).
tff(3047,plain,
rselect_seq(q43) = rselect_seq(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(monotonicity,[status(thm)],[3046]) ).
tff(3048,plain,
rselect_seq(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_seq(q43),
inference(symmetry,[status(thm)],[3047]) ).
tff(3049,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_seq(rstore_seq(q42,earray_262)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3050,plain,
rselect_seq(rstore_tail(rstore_seq(q42,earray_262),s(index_261))) = rselect_seq(rstore_seq(q42,earray_262)),
inference(unit_resolution,[status(thm)],[3049,2356]) ).
tff(3051,plain,
rselect_seq(rstore_seq(q42,earray_262)) = rselect_seq(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(symmetry,[status(thm)],[3050]) ).
tff(3052,plain,
rstore_seq(q42,earray_262) = rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42)),
inference(symmetry,[status(thm)],[152]) ).
tff(3053,plain,
rselect_seq(rstore_seq(q42,earray_262)) = rselect_seq(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))),
inference(monotonicity,[status(thm)],[3052]) ).
tff(3054,plain,
rselect_seq(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = rselect_seq(rstore_seq(q42,earray_262)),
inference(symmetry,[status(thm)],[3053]) ).
tff(3055,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = store(earray_260,index_261,e42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3056,plain,
rselect_seq(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))) = store(earray_260,index_261,e42),
inference(unit_resolution,[status(thm)],[3055,2368]) ).
tff(3057,plain,
store(earray_260,index_261,e42) = rselect_seq(rstore_seq(rstore_head(queue_256,index_258),store(earray_260,index_261,e42))),
inference(symmetry,[status(thm)],[3056]) ).
tff(3058,plain,
store(earray_260,index_261,e42) = earray_266,
inference(transitivity,[status(thm)],[3057,3054,3051,3048,3045]) ).
tff(3059,plain,
store(store(earray_260,index_261,e42),rselect_tail(q43),e43) = store(earray_266,index_267,e43),
inference(monotonicity,[status(thm)],[3058,2452]) ).
tff(3060,plain,
select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_266,index_267,e43),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3059]) ).
tff(3061,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(rselect_tail(q16)))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2775]) ).
tff(3062,plain,
rselect_tail(q43) = rselect_tail(rstore_tail(rstore_seq(q42,earray_262),s(index_261))),
inference(symmetry,[status(thm)],[2454]) ).
tff(3063,plain,
rselect_tail(q43) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3062,2456,3061]) ).
tff(3064,plain,
( ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3063,2236]) ).
tff(3065,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(rselect_tail(q16)))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3064]) ).
tff(3066,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(rselect_tail(q16)))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q43) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3065]) ).
tff(3067,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(3068,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)],[3067]) ).
tff(3069,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(3070,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(3071,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)],[3070,3069]) ).
tff(3072,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)],[3071]) ).
tff(3073,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)],[3072,3068]) ).
tff(3074,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(rselect_tail(q16)))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3075,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(rselect_tail(q16)))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3074,3073]) ).
tff(3076,plain,
rselect_tail(q43) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3075,3066]) ).
tff(3077,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3078,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3079,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3078,3077]) ).
tff(3080,plain,
( ( rselect_tail(q43) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3079,2813]) ).
tff(3081,plain,
select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3080,3076]) ).
tff(3082,plain,
select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_260,index_261,e42),rselect_tail(q43),e43),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3081]) ).
tff(3083,plain,
( ( earray_260 = rselect_seq(q42) )
<=> ( earray_260 = rselect_seq(q42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3084,axiom,
earray_260 = rselect_seq(q42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp51) ).
tff(3085,plain,
earray_260 = rselect_seq(q42),
inference(modus_ponens,[status(thm)],[3084,3083]) ).
tff(3086,plain,
rselect_seq(q42) = earray_260,
inference(symmetry,[status(thm)],[3085]) ).
tff(3087,plain,
rstore_head(queue_256,index_258) = rstore_head(rstore_tail(queue_254,index_255),s(index_257)),
inference(symmetry,[status(thm)],[165]) ).
tff(3088,plain,
q42 = rstore_head(rstore_tail(queue_254,index_255),s(index_257)),
inference(transitivity,[status(thm)],[145,149,3087]) ).
tff(3089,plain,
rselect_seq(q42) = rselect_seq(rstore_head(rstore_tail(queue_254,index_255),s(index_257))),
inference(monotonicity,[status(thm)],[3088]) ).
tff(3090,plain,
rselect_seq(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_seq(q42),
inference(symmetry,[status(thm)],[3089]) ).
tff(3091,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_seq(rstore_tail(queue_254,index_255)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3092,plain,
rselect_seq(rstore_head(rstore_tail(queue_254,index_255),s(index_257))) = rselect_seq(rstore_tail(queue_254,index_255)),
inference(unit_resolution,[status(thm)],[3091,2834]) ).
tff(3093,plain,
rselect_seq(rstore_tail(queue_254,index_255)) = rselect_seq(rstore_head(rstore_tail(queue_254,index_255),s(index_257))),
inference(symmetry,[status(thm)],[3092]) ).
tff(3094,plain,
rselect_seq(rstore_tail(queue_254,index_255)) = rselect_seq(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(monotonicity,[status(thm)],[194]) ).
tff(3095,plain,
rselect_seq(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_seq(rstore_tail(queue_254,index_255)),
inference(symmetry,[status(thm)],[3094]) ).
tff(3096,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_seq(rstore_seq(q41,earray_253)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3097,plain,
rselect_seq(rstore_tail(rstore_seq(q41,earray_253),s(index_252))) = rselect_seq(rstore_seq(q41,earray_253)),
inference(unit_resolution,[status(thm)],[3096,2356]) ).
tff(3098,plain,
rselect_seq(rstore_seq(q41,earray_253)) = rselect_seq(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(symmetry,[status(thm)],[3097]) ).
tff(3099,plain,
rselect_seq(rstore_seq(q41,earray_253)) = rselect_seq(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))),
inference(monotonicity,[status(thm)],[215]) ).
tff(3100,plain,
rselect_seq(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = rselect_seq(rstore_seq(q41,earray_253)),
inference(symmetry,[status(thm)],[3099]) ).
tff(3101,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = store(earray_251,index_252,e41) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3102,plain,
rselect_seq(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))) = store(earray_251,index_252,e41),
inference(unit_resolution,[status(thm)],[3101,2368]) ).
tff(3103,plain,
store(earray_251,index_252,e41) = rselect_seq(rstore_seq(rstore_tail(queue_248,index_249),store(earray_251,index_252,e41))),
inference(symmetry,[status(thm)],[3102]) ).
tff(3104,plain,
store(earray_251,index_252,e41) = earray_260,
inference(transitivity,[status(thm)],[3103,3100,3098,3095,3093,3090,3086]) ).
tff(3105,plain,
store(store(earray_251,index_252,e41),rselect_tail(q42),e42) = store(earray_260,index_261,e42),
inference(monotonicity,[status(thm)],[3104,2461]) ).
tff(3106,plain,
select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_260,index_261,e42),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3105]) ).
tff(3107,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(rselect_tail(q16))))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2773]) ).
tff(3108,plain,
rselect_tail(rstore_tail(queue_254,index_255)) = rselect_tail(rstore_tail(rstore_seq(q41,earray_253),s(index_252))),
inference(symmetry,[status(thm)],[2467]) ).
tff(3109,plain,
rselect_tail(q42) = rselect_tail(rstore_head(rstore_tail(queue_254,index_255),s(index_257))),
inference(symmetry,[status(thm)],[2463]) ).
tff(3110,plain,
rselect_tail(q42) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3109,2465,3108,2469,3107]) ).
tff(3111,plain,
( ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3110,2236]) ).
tff(3112,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(rselect_tail(q16))))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3111]) ).
tff(3113,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(rselect_tail(q16))))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q42) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3112]) ).
tff(3114,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(3115,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)],[3114]) ).
tff(3116,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(3117,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(3118,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)],[3117,3116]) ).
tff(3119,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)],[3118]) ).
tff(3120,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)],[3119,3115]) ).
tff(3121,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(rselect_tail(q16))))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3122,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(rselect_tail(q16))))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3121,3120]) ).
tff(3123,plain,
rselect_tail(q42) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3122,3113]) ).
tff(3124,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3125,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3126,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3125,3124]) ).
tff(3127,plain,
( ( rselect_tail(q42) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3126,2813]) ).
tff(3128,plain,
select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3127,3123]) ).
tff(3129,plain,
select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_251,index_252,e41),rselect_tail(q42),e42),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3128]) ).
tff(3130,plain,
( ( earray_251 = rselect_seq(q41) )
<=> ( earray_251 = rselect_seq(q41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3131,axiom,
earray_251 = rselect_seq(q41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp49) ).
tff(3132,plain,
earray_251 = rselect_seq(q41),
inference(modus_ponens,[status(thm)],[3131,3130]) ).
tff(3133,plain,
rselect_seq(q41) = earray_251,
inference(symmetry,[status(thm)],[3132]) ).
tff(3134,plain,
q41 = rstore_tail(rstore_seq(q40,earray_247),s(index_246)),
inference(transitivity,[status(thm)],[207,211,230]) ).
tff(3135,plain,
rselect_seq(q41) = rselect_seq(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(monotonicity,[status(thm)],[3134]) ).
tff(3136,plain,
rselect_seq(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_seq(q41),
inference(symmetry,[status(thm)],[3135]) ).
tff(3137,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_seq(rstore_seq(q40,earray_247)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3138,plain,
rselect_seq(rstore_tail(rstore_seq(q40,earray_247),s(index_246))) = rselect_seq(rstore_seq(q40,earray_247)),
inference(unit_resolution,[status(thm)],[3137,2356]) ).
tff(3139,plain,
rselect_seq(rstore_seq(q40,earray_247)) = rselect_seq(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(symmetry,[status(thm)],[3138]) ).
tff(3140,plain,
rselect_seq(rstore_seq(q40,earray_247)) = rselect_seq(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))),
inference(monotonicity,[status(thm)],[250]) ).
tff(3141,plain,
rselect_seq(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = rselect_seq(rstore_seq(q40,earray_247)),
inference(symmetry,[status(thm)],[3140]) ).
tff(3142,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = store(earray_245,index_246,e40) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3143,plain,
rselect_seq(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))) = store(earray_245,index_246,e40),
inference(unit_resolution,[status(thm)],[3142,2368]) ).
tff(3144,plain,
store(earray_245,index_246,e40) = rselect_seq(rstore_seq(rstore_tail(queue_242,index_243),store(earray_245,index_246,e40))),
inference(symmetry,[status(thm)],[3143]) ).
tff(3145,plain,
store(earray_245,index_246,e40) = earray_251,
inference(transitivity,[status(thm)],[3144,3141,3139,3136,3133]) ).
tff(3146,plain,
store(store(earray_245,index_246,e40),rselect_tail(q41),e41) = store(earray_251,index_252,e41),
inference(monotonicity,[status(thm)],[3145,2474]) ).
tff(3147,plain,
select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_251,index_252,e41),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3146]) ).
tff(3148,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(rselect_tail(q16)))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2771]) ).
tff(3149,plain,
rselect_tail(q41) = rselect_tail(rstore_tail(rstore_seq(q40,earray_247),s(index_246))),
inference(symmetry,[status(thm)],[2476]) ).
tff(3150,plain,
rselect_tail(q41) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3149,2478,3148]) ).
tff(3151,plain,
( ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3150,2236]) ).
tff(3152,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(rselect_tail(q16)))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3151]) ).
tff(3153,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(rselect_tail(q16)))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q41) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3152]) ).
tff(3154,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(3155,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)],[3154]) ).
tff(3156,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(3157,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(3158,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)],[3157,3156]) ).
tff(3159,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)],[3158]) ).
tff(3160,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)],[3159,3155]) ).
tff(3161,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(rselect_tail(q16)))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3162,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(rselect_tail(q16)))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3161,3160]) ).
tff(3163,plain,
rselect_tail(q41) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3162,3153]) ).
tff(3164,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3165,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3166,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3165,3164]) ).
tff(3167,plain,
( ( rselect_tail(q41) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3166,2813]) ).
tff(3168,plain,
select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3167,3163]) ).
tff(3169,plain,
select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_245,index_246,e40),rselect_tail(q41),e41),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3168]) ).
tff(3170,plain,
( ( earray_245 = rselect_seq(q40) )
<=> ( earray_245 = rselect_seq(q40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3171,axiom,
earray_245 = rselect_seq(q40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp47) ).
tff(3172,plain,
earray_245 = rselect_seq(q40),
inference(modus_ponens,[status(thm)],[3171,3170]) ).
tff(3173,plain,
rselect_seq(q40) = earray_245,
inference(symmetry,[status(thm)],[3172]) ).
tff(3174,plain,
q40 = rstore_tail(rstore_seq(q39,earray_241),s(index_240)),
inference(transitivity,[status(thm)],[242,246,265]) ).
tff(3175,plain,
rselect_seq(q40) = rselect_seq(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(monotonicity,[status(thm)],[3174]) ).
tff(3176,plain,
rselect_seq(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_seq(q40),
inference(symmetry,[status(thm)],[3175]) ).
tff(3177,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_seq(rstore_seq(q39,earray_241)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3178,plain,
rselect_seq(rstore_tail(rstore_seq(q39,earray_241),s(index_240))) = rselect_seq(rstore_seq(q39,earray_241)),
inference(unit_resolution,[status(thm)],[3177,2356]) ).
tff(3179,plain,
rselect_seq(rstore_seq(q39,earray_241)) = rselect_seq(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(symmetry,[status(thm)],[3178]) ).
tff(3180,plain,
rstore_seq(q39,earray_241) = rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39)),
inference(symmetry,[status(thm)],[284]) ).
tff(3181,plain,
rselect_seq(rstore_seq(q39,earray_241)) = rselect_seq(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))),
inference(monotonicity,[status(thm)],[3180]) ).
tff(3182,plain,
rselect_seq(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = rselect_seq(rstore_seq(q39,earray_241)),
inference(symmetry,[status(thm)],[3181]) ).
tff(3183,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = store(earray_239,index_240,e39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3184,plain,
rselect_seq(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))) = store(earray_239,index_240,e39),
inference(unit_resolution,[status(thm)],[3183,2368]) ).
tff(3185,plain,
store(earray_239,index_240,e39) = rselect_seq(rstore_seq(rstore_head(queue_229,index_231),store(earray_239,index_240,e39))),
inference(symmetry,[status(thm)],[3184]) ).
tff(3186,plain,
store(earray_239,index_240,e39) = earray_245,
inference(transitivity,[status(thm)],[3185,3182,3179,3176,3173]) ).
tff(3187,plain,
store(store(earray_239,index_240,e39),rselect_tail(q40),e40) = store(earray_245,index_246,e40),
inference(monotonicity,[status(thm)],[3186,2483]) ).
tff(3188,plain,
select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_245,index_246,e40),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3187]) ).
tff(3189,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(rselect_tail(q16))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2769]) ).
tff(3190,plain,
rselect_tail(q40) = rselect_tail(rstore_tail(rstore_seq(q39,earray_241),s(index_240))),
inference(symmetry,[status(thm)],[2485]) ).
tff(3191,plain,
rselect_tail(q40) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3190,2487,3189]) ).
tff(3192,plain,
( ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3191,2236]) ).
tff(3193,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(rselect_tail(q16))))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3192]) ).
tff(3194,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(rselect_tail(q16))))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q40) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3193]) ).
tff(3195,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(3196,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)],[3195]) ).
tff(3197,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(3198,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(3199,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)],[3198,3197]) ).
tff(3200,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)],[3199]) ).
tff(3201,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)],[3200,3196]) ).
tff(3202,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(rselect_tail(q16))))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3203,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(rselect_tail(q16))))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3202,3201]) ).
tff(3204,plain,
rselect_tail(q40) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3203,3194]) ).
tff(3205,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3206,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3207,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3206,3205]) ).
tff(3208,plain,
( ( rselect_tail(q40) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3207,2813]) ).
tff(3209,plain,
select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3208,3204]) ).
tff(3210,plain,
select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_239,index_240,e39),rselect_tail(q40),e40),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3209]) ).
tff(3211,plain,
( ( earray_239 = rselect_seq(q39) )
<=> ( earray_239 = rselect_seq(q39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3212,axiom,
earray_239 = rselect_seq(q39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(3213,plain,
earray_239 = rselect_seq(q39),
inference(modus_ponens,[status(thm)],[3212,3211]) ).
tff(3214,plain,
rselect_seq(q39) = earray_239,
inference(symmetry,[status(thm)],[3213]) ).
tff(3215,plain,
rstore_head(queue_229,index_231) = rstore_head(rstore_tail(queue_227,index_228),s(index_230)),
inference(symmetry,[status(thm)],[297]) ).
tff(3216,plain,
q39 = rstore_head(rstore_tail(queue_227,index_228),s(index_230)),
inference(transitivity,[status(thm)],[277,281,3215]) ).
tff(3217,plain,
rselect_seq(q39) = rselect_seq(rstore_head(rstore_tail(queue_227,index_228),s(index_230))),
inference(monotonicity,[status(thm)],[3216]) ).
tff(3218,plain,
rselect_seq(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_seq(q39),
inference(symmetry,[status(thm)],[3217]) ).
tff(3219,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_seq(rstore_tail(queue_227,index_228)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3220,plain,
rselect_seq(rstore_head(rstore_tail(queue_227,index_228),s(index_230))) = rselect_seq(rstore_tail(queue_227,index_228)),
inference(unit_resolution,[status(thm)],[3219,2834]) ).
tff(3221,plain,
rselect_seq(rstore_tail(queue_227,index_228)) = rselect_seq(rstore_head(rstore_tail(queue_227,index_228),s(index_230))),
inference(symmetry,[status(thm)],[3220]) ).
tff(3222,plain,
rselect_seq(rstore_tail(queue_227,index_228)) = rselect_seq(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(monotonicity,[status(thm)],[319]) ).
tff(3223,plain,
rselect_seq(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_seq(rstore_tail(queue_227,index_228)),
inference(symmetry,[status(thm)],[3222]) ).
tff(3224,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_seq(rstore_seq(q38,earray_226)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3225,plain,
rselect_seq(rstore_tail(rstore_seq(q38,earray_226),s(index_225))) = rselect_seq(rstore_seq(q38,earray_226)),
inference(unit_resolution,[status(thm)],[3224,2356]) ).
tff(3226,plain,
rselect_seq(rstore_seq(q38,earray_226)) = rselect_seq(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(symmetry,[status(thm)],[3225]) ).
tff(3227,plain,
rselect_seq(rstore_seq(q38,earray_226)) = rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))),
inference(monotonicity,[status(thm)],[340]) ).
tff(3228,plain,
rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = rselect_seq(rstore_seq(q38,earray_226)),
inference(symmetry,[status(thm)],[3227]) ).
tff(3229,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = store(earray_224,index_225,e38) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3230,plain,
rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))) = store(earray_224,index_225,e38),
inference(unit_resolution,[status(thm)],[3229,2368]) ).
tff(3231,plain,
store(earray_224,index_225,e38) = rselect_seq(rstore_seq(rstore_tail(queue_221,index_222),store(earray_224,index_225,e38))),
inference(symmetry,[status(thm)],[3230]) ).
tff(3232,plain,
store(earray_224,index_225,e38) = earray_239,
inference(transitivity,[status(thm)],[3231,3228,3226,3223,3221,3218,3214]) ).
tff(3233,plain,
store(store(earray_224,index_225,e38),rselect_tail(q39),e39) = store(earray_239,index_240,e39),
inference(monotonicity,[status(thm)],[3232,2492]) ).
tff(3234,plain,
select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_239,index_240,e39),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3233]) ).
tff(3235,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(rselect_tail(q16)))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2767]) ).
tff(3236,plain,
rselect_tail(rstore_tail(queue_227,index_228)) = rselect_tail(rstore_tail(rstore_seq(q38,earray_226),s(index_225))),
inference(symmetry,[status(thm)],[2498]) ).
tff(3237,plain,
rselect_tail(q39) = rselect_tail(rstore_head(rstore_tail(queue_227,index_228),s(index_230))),
inference(symmetry,[status(thm)],[2494]) ).
tff(3238,plain,
rselect_tail(q39) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3237,2496,3236,2500,3235]) ).
tff(3239,plain,
( ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3238,2236]) ).
tff(3240,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3239]) ).
tff(3241,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q39) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3240]) ).
tff(3242,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(3243,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)],[3242]) ).
tff(3244,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(3245,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(3246,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)],[3245,3244]) ).
tff(3247,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)],[3246]) ).
tff(3248,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)],[3247,3243]) ).
tff(3249,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(rselect_tail(q16)))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3250,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3249,3248]) ).
tff(3251,plain,
rselect_tail(q39) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3250,3241]) ).
tff(3252,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3253,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3254,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3253,3252]) ).
tff(3255,plain,
( ( rselect_tail(q39) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3254,2813]) ).
tff(3256,plain,
select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3255,3251]) ).
tff(3257,plain,
select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_224,index_225,e38),rselect_tail(q39),e39),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3256]) ).
tff(3258,plain,
( ( earray_224 = rselect_seq(q38) )
<=> ( earray_224 = rselect_seq(q38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3259,axiom,
earray_224 = rselect_seq(q38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(3260,plain,
earray_224 = rselect_seq(q38),
inference(modus_ponens,[status(thm)],[3259,3258]) ).
tff(3261,plain,
rselect_seq(q38) = earray_224,
inference(symmetry,[status(thm)],[3260]) ).
tff(3262,plain,
q38 = rstore_tail(rstore_seq(q37,earray_220),s(index_219)),
inference(transitivity,[status(thm)],[332,336,355]) ).
tff(3263,plain,
rselect_seq(q38) = rselect_seq(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(monotonicity,[status(thm)],[3262]) ).
tff(3264,plain,
rselect_seq(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_seq(q38),
inference(symmetry,[status(thm)],[3263]) ).
tff(3265,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_seq(rstore_seq(q37,earray_220)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3266,plain,
rselect_seq(rstore_tail(rstore_seq(q37,earray_220),s(index_219))) = rselect_seq(rstore_seq(q37,earray_220)),
inference(unit_resolution,[status(thm)],[3265,2356]) ).
tff(3267,plain,
rselect_seq(rstore_seq(q37,earray_220)) = rselect_seq(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(symmetry,[status(thm)],[3266]) ).
tff(3268,plain,
rselect_seq(rstore_seq(q37,earray_220)) = rselect_seq(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))),
inference(monotonicity,[status(thm)],[375]) ).
tff(3269,plain,
rselect_seq(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = rselect_seq(rstore_seq(q37,earray_220)),
inference(symmetry,[status(thm)],[3268]) ).
tff(3270,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = store(earray_218,index_219,e37) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3271,plain,
rselect_seq(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))) = store(earray_218,index_219,e37),
inference(unit_resolution,[status(thm)],[3270,2368]) ).
tff(3272,plain,
store(earray_218,index_219,e37) = rselect_seq(rstore_seq(rstore_tail(queue_215,index_216),store(earray_218,index_219,e37))),
inference(symmetry,[status(thm)],[3271]) ).
tff(3273,plain,
store(earray_218,index_219,e37) = earray_224,
inference(transitivity,[status(thm)],[3272,3269,3267,3264,3261]) ).
tff(3274,plain,
store(store(earray_218,index_219,e37),rselect_tail(q38),e38) = store(earray_224,index_225,e38),
inference(monotonicity,[status(thm)],[3273,2505]) ).
tff(3275,plain,
select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_224,index_225,e38),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3274]) ).
tff(3276,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(rselect_tail(q16))))))))))))))))))))))),
inference(symmetry,[status(thm)],[2765]) ).
tff(3277,plain,
rselect_tail(q38) = rselect_tail(rstore_tail(rstore_seq(q37,earray_220),s(index_219))),
inference(symmetry,[status(thm)],[2507]) ).
tff(3278,plain,
rselect_tail(q38) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3277,2509,3276]) ).
tff(3279,plain,
( ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3278,2236]) ).
tff(3280,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3279]) ).
tff(3281,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q38) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3280]) ).
tff(3282,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(3283,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)],[3282]) ).
tff(3284,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(3285,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(3286,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)],[3285,3284]) ).
tff(3287,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)],[3286]) ).
tff(3288,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)],[3287,3283]) ).
tff(3289,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(rselect_tail(q16))))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3290,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3289,3288]) ).
tff(3291,plain,
rselect_tail(q38) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3290,3281]) ).
tff(3292,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3293,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3294,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3293,3292]) ).
tff(3295,plain,
( ( rselect_tail(q38) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3294,2813]) ).
tff(3296,plain,
select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3295,3291]) ).
tff(3297,plain,
select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_218,index_219,e37),rselect_tail(q38),e38),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3296]) ).
tff(3298,plain,
( ( earray_218 = rselect_seq(q37) )
<=> ( earray_218 = rselect_seq(q37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3299,axiom,
earray_218 = rselect_seq(q37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp38) ).
tff(3300,plain,
earray_218 = rselect_seq(q37),
inference(modus_ponens,[status(thm)],[3299,3298]) ).
tff(3301,plain,
rselect_seq(q37) = earray_218,
inference(symmetry,[status(thm)],[3300]) ).
tff(3302,plain,
q37 = rstore_tail(rstore_seq(q36,earray_214),s(index_213)),
inference(transitivity,[status(thm)],[367,371,390]) ).
tff(3303,plain,
rselect_seq(q37) = rselect_seq(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(monotonicity,[status(thm)],[3302]) ).
tff(3304,plain,
rselect_seq(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_seq(q37),
inference(symmetry,[status(thm)],[3303]) ).
tff(3305,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_seq(rstore_seq(q36,earray_214)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3306,plain,
rselect_seq(rstore_tail(rstore_seq(q36,earray_214),s(index_213))) = rselect_seq(rstore_seq(q36,earray_214)),
inference(unit_resolution,[status(thm)],[3305,2356]) ).
tff(3307,plain,
rselect_seq(rstore_seq(q36,earray_214)) = rselect_seq(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(symmetry,[status(thm)],[3306]) ).
tff(3308,plain,
rstore_seq(q36,earray_214) = rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36)),
inference(symmetry,[status(thm)],[409]) ).
tff(3309,plain,
rselect_seq(rstore_seq(q36,earray_214)) = rselect_seq(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))),
inference(monotonicity,[status(thm)],[3308]) ).
tff(3310,plain,
rselect_seq(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = rselect_seq(rstore_seq(q36,earray_214)),
inference(symmetry,[status(thm)],[3309]) ).
tff(3311,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = store(earray_212,index_213,e36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3312,plain,
rselect_seq(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))) = store(earray_212,index_213,e36),
inference(unit_resolution,[status(thm)],[3311,2368]) ).
tff(3313,plain,
store(earray_212,index_213,e36) = rselect_seq(rstore_seq(rstore_head(queue_208,index_210),store(earray_212,index_213,e36))),
inference(symmetry,[status(thm)],[3312]) ).
tff(3314,plain,
store(earray_212,index_213,e36) = earray_218,
inference(transitivity,[status(thm)],[3313,3310,3307,3304,3301]) ).
tff(3315,plain,
store(store(earray_212,index_213,e36),rselect_tail(q37),e37) = store(earray_218,index_219,e37),
inference(monotonicity,[status(thm)],[3314,2514]) ).
tff(3316,plain,
select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_218,index_219,e37),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3315]) ).
tff(3317,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(rselect_tail(q16)))))))))))))))))))))),
inference(symmetry,[status(thm)],[2763]) ).
tff(3318,plain,
rselect_tail(q37) = rselect_tail(rstore_tail(rstore_seq(q36,earray_214),s(index_213))),
inference(symmetry,[status(thm)],[2516]) ).
tff(3319,plain,
rselect_tail(q37) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))),
inference(transitivity,[status(thm)],[3318,2518,3317]) ).
tff(3320,plain,
( ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3319,2236]) ).
tff(3321,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3320]) ).
tff(3322,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q37) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3321]) ).
tff(3323,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(3324,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)],[3323]) ).
tff(3325,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(3326,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(3327,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)],[3326,3325]) ).
tff(3328,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)],[3327]) ).
tff(3329,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)],[3328,3324]) ).
tff(3330,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(rselect_tail(q16)))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3331,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3330,3329]) ).
tff(3332,plain,
rselect_tail(q37) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3331,3322]) ).
tff(3333,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3334,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3335,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3334,3333]) ).
tff(3336,plain,
( ( rselect_tail(q37) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3335,2813]) ).
tff(3337,plain,
select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3336,3332]) ).
tff(3338,plain,
select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_212,index_213,e36),rselect_tail(q37),e37),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3337]) ).
tff(3339,plain,
( ( earray_212 = rselect_seq(q36) )
<=> ( earray_212 = rselect_seq(q36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3340,axiom,
earray_212 = rselect_seq(q36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp36) ).
tff(3341,plain,
earray_212 = rselect_seq(q36),
inference(modus_ponens,[status(thm)],[3340,3339]) ).
tff(3342,plain,
rselect_seq(q36) = earray_212,
inference(symmetry,[status(thm)],[3341]) ).
tff(3343,plain,
rstore_head(queue_208,index_210) = rstore_head(rstore_tail(queue_206,index_207),s(index_209)),
inference(symmetry,[status(thm)],[422]) ).
tff(3344,plain,
q36 = rstore_head(rstore_tail(queue_206,index_207),s(index_209)),
inference(transitivity,[status(thm)],[402,406,3343]) ).
tff(3345,plain,
rselect_seq(q36) = rselect_seq(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(monotonicity,[status(thm)],[3344]) ).
tff(3346,plain,
rselect_seq(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_seq(q36),
inference(symmetry,[status(thm)],[3345]) ).
tff(3347,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_seq(rstore_tail(queue_206,index_207)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3348,plain,
rselect_seq(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_seq(rstore_tail(queue_206,index_207)),
inference(unit_resolution,[status(thm)],[3347,2834]) ).
tff(3349,plain,
rselect_seq(rstore_tail(queue_206,index_207)) = rselect_seq(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[3348]) ).
tff(3350,plain,
rselect_seq(rstore_tail(queue_206,index_207)) = rselect_seq(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(monotonicity,[status(thm)],[444]) ).
tff(3351,plain,
rselect_seq(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_seq(rstore_tail(queue_206,index_207)),
inference(symmetry,[status(thm)],[3350]) ).
tff(3352,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_seq(rstore_seq(q35,earray_205)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3353,plain,
rselect_seq(rstore_tail(rstore_seq(q35,earray_205),s(index_204))) = rselect_seq(rstore_seq(q35,earray_205)),
inference(unit_resolution,[status(thm)],[3352,2356]) ).
tff(3354,plain,
rselect_seq(rstore_seq(q35,earray_205)) = rselect_seq(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[3353]) ).
tff(3355,plain,
rselect_seq(rstore_seq(q35,earray_205)) = rselect_seq(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))),
inference(monotonicity,[status(thm)],[465]) ).
tff(3356,plain,
rselect_seq(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = rselect_seq(rstore_seq(q35,earray_205)),
inference(symmetry,[status(thm)],[3355]) ).
tff(3357,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = store(earray_203,index_204,e35) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3358,plain,
rselect_seq(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))) = store(earray_203,index_204,e35),
inference(unit_resolution,[status(thm)],[3357,2368]) ).
tff(3359,plain,
store(earray_203,index_204,e35) = rselect_seq(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e35))),
inference(symmetry,[status(thm)],[3358]) ).
tff(3360,plain,
store(earray_203,index_204,e35) = earray_212,
inference(transitivity,[status(thm)],[3359,3356,3354,3351,3349,3346,3342]) ).
tff(3361,plain,
store(store(earray_203,index_204,e35),rselect_tail(q36),e36) = store(earray_212,index_213,e36),
inference(monotonicity,[status(thm)],[3360,2523]) ).
tff(3362,plain,
select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_212,index_213,e36),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3361]) ).
tff(3363,plain,
s(index_204) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))),
inference(symmetry,[status(thm)],[2761]) ).
tff(3364,plain,
rselect_tail(rstore_tail(queue_206,index_207)) = rselect_tail(rstore_tail(rstore_seq(q35,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[2529]) ).
tff(3365,plain,
rselect_tail(q36) = rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[2525]) ).
tff(3366,plain,
rselect_tail(q36) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))),
inference(transitivity,[status(thm)],[3365,2527,3364,2531,3363]) ).
tff(3367,plain,
( ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3366,2236]) ).
tff(3368,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3367]) ).
tff(3369,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q36) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3368]) ).
tff(3370,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(3371,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)],[3370]) ).
tff(3372,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(3373,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(3374,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)],[3373,3372]) ).
tff(3375,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)],[3374]) ).
tff(3376,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)],[3375,3371]) ).
tff(3377,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(rselect_tail(q16))))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3378,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3377,3376]) ).
tff(3379,plain,
rselect_tail(q36) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3378,3369]) ).
tff(3380,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3381,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3382,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3381,3380]) ).
tff(3383,plain,
( ( rselect_tail(q36) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3382,2813]) ).
tff(3384,plain,
select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3383,3379]) ).
tff(3385,plain,
select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_203,index_204,e35),rselect_tail(q36),e36),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3384]) ).
tff(3386,plain,
( ( earray_203 = rselect_seq(q35) )
<=> ( earray_203 = rselect_seq(q35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3387,axiom,
earray_203 = rselect_seq(q35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp34) ).
tff(3388,plain,
earray_203 = rselect_seq(q35),
inference(modus_ponens,[status(thm)],[3387,3386]) ).
tff(3389,plain,
rselect_seq(q35) = earray_203,
inference(symmetry,[status(thm)],[3388]) ).
tff(3390,plain,
q35 = rstore_tail(rstore_seq(q34,earray_199),s(index_198)),
inference(transitivity,[status(thm)],[457,461,480]) ).
tff(3391,plain,
rselect_seq(q35) = rselect_seq(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(monotonicity,[status(thm)],[3390]) ).
tff(3392,plain,
rselect_seq(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_seq(q35),
inference(symmetry,[status(thm)],[3391]) ).
tff(3393,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_seq(rstore_seq(q34,earray_199)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3394,plain,
rselect_seq(rstore_tail(rstore_seq(q34,earray_199),s(index_198))) = rselect_seq(rstore_seq(q34,earray_199)),
inference(unit_resolution,[status(thm)],[3393,2356]) ).
tff(3395,plain,
rselect_seq(rstore_seq(q34,earray_199)) = rselect_seq(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(symmetry,[status(thm)],[3394]) ).
tff(3396,plain,
rselect_seq(rstore_seq(q34,earray_199)) = rselect_seq(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))),
inference(monotonicity,[status(thm)],[500]) ).
tff(3397,plain,
rselect_seq(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = rselect_seq(rstore_seq(q34,earray_199)),
inference(symmetry,[status(thm)],[3396]) ).
tff(3398,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = store(earray_197,index_198,e34) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3399,plain,
rselect_seq(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))) = store(earray_197,index_198,e34),
inference(unit_resolution,[status(thm)],[3398,2368]) ).
tff(3400,plain,
store(earray_197,index_198,e34) = rselect_seq(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e34))),
inference(symmetry,[status(thm)],[3399]) ).
tff(3401,plain,
store(earray_197,index_198,e34) = earray_203,
inference(transitivity,[status(thm)],[3400,3397,3395,3392,3389]) ).
tff(3402,plain,
store(store(earray_197,index_198,e34),rselect_tail(q35),e35) = store(earray_203,index_204,e35),
inference(monotonicity,[status(thm)],[3401,2536]) ).
tff(3403,plain,
select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_203,index_204,e35),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3402]) ).
tff(3404,plain,
s(index_198) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))),
inference(symmetry,[status(thm)],[2759]) ).
tff(3405,plain,
rselect_tail(q35) = rselect_tail(rstore_tail(rstore_seq(q34,earray_199),s(index_198))),
inference(symmetry,[status(thm)],[2538]) ).
tff(3406,plain,
rselect_tail(q35) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))),
inference(transitivity,[status(thm)],[3405,2540,3404]) ).
tff(3407,plain,
( ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3406,2236]) ).
tff(3408,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3407]) ).
tff(3409,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q35) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3408]) ).
tff(3410,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(3411,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)],[3410]) ).
tff(3412,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(3413,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(3414,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)],[3413,3412]) ).
tff(3415,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)],[3414]) ).
tff(3416,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)],[3415,3411]) ).
tff(3417,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(rselect_tail(q16)))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3418,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3417,3416]) ).
tff(3419,plain,
rselect_tail(q35) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3418,3409]) ).
tff(3420,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3421,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3422,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3421,3420]) ).
tff(3423,plain,
( ( rselect_tail(q35) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3422,2813]) ).
tff(3424,plain,
select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3423,3419]) ).
tff(3425,plain,
select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_197,index_198,e34),rselect_tail(q35),e35),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3424]) ).
tff(3426,plain,
( ( earray_197 = rselect_seq(q34) )
<=> ( earray_197 = rselect_seq(q34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3427,axiom,
earray_197 = rselect_seq(q34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp30) ).
tff(3428,plain,
earray_197 = rselect_seq(q34),
inference(modus_ponens,[status(thm)],[3427,3426]) ).
tff(3429,plain,
rselect_seq(q34) = earray_197,
inference(symmetry,[status(thm)],[3428]) ).
tff(3430,plain,
q34 = rstore_tail(rstore_seq(q33,earray_193),s(index_192)),
inference(transitivity,[status(thm)],[492,496,515]) ).
tff(3431,plain,
rselect_seq(q34) = rselect_seq(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(monotonicity,[status(thm)],[3430]) ).
tff(3432,plain,
rselect_seq(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_seq(q34),
inference(symmetry,[status(thm)],[3431]) ).
tff(3433,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_seq(rstore_seq(q33,earray_193)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3434,plain,
rselect_seq(rstore_tail(rstore_seq(q33,earray_193),s(index_192))) = rselect_seq(rstore_seq(q33,earray_193)),
inference(unit_resolution,[status(thm)],[3433,2356]) ).
tff(3435,plain,
rselect_seq(rstore_seq(q33,earray_193)) = rselect_seq(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(symmetry,[status(thm)],[3434]) ).
tff(3436,plain,
rstore_seq(q33,earray_193) = rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33)),
inference(symmetry,[status(thm)],[534]) ).
tff(3437,plain,
rselect_seq(rstore_seq(q33,earray_193)) = rselect_seq(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))),
inference(monotonicity,[status(thm)],[3436]) ).
tff(3438,plain,
rselect_seq(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = rselect_seq(rstore_seq(q33,earray_193)),
inference(symmetry,[status(thm)],[3437]) ).
tff(3439,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = store(earray_191,index_192,e33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3440,plain,
rselect_seq(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))) = store(earray_191,index_192,e33),
inference(unit_resolution,[status(thm)],[3439,2368]) ).
tff(3441,plain,
store(earray_191,index_192,e33) = rselect_seq(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e33))),
inference(symmetry,[status(thm)],[3440]) ).
tff(3442,plain,
store(earray_191,index_192,e33) = earray_197,
inference(transitivity,[status(thm)],[3441,3438,3435,3432,3429]) ).
tff(3443,plain,
store(store(earray_191,index_192,e33),rselect_tail(q34),e34) = store(earray_197,index_198,e34),
inference(monotonicity,[status(thm)],[3442,2545]) ).
tff(3444,plain,
select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_197,index_198,e34),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3443]) ).
tff(3445,plain,
s(index_192) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))),
inference(symmetry,[status(thm)],[2757]) ).
tff(3446,plain,
rselect_tail(q34) = rselect_tail(rstore_tail(rstore_seq(q33,earray_193),s(index_192))),
inference(symmetry,[status(thm)],[2547]) ).
tff(3447,plain,
rselect_tail(q34) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))),
inference(transitivity,[status(thm)],[3446,2549,3445]) ).
tff(3448,plain,
( ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3447,2236]) ).
tff(3449,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3448]) ).
tff(3450,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q34) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3449]) ).
tff(3451,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(3452,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)],[3451]) ).
tff(3453,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(3454,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(3455,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)],[3454,3453]) ).
tff(3456,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)],[3455]) ).
tff(3457,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)],[3456,3452]) ).
tff(3458,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(rselect_tail(q16))))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3459,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3458,3457]) ).
tff(3460,plain,
rselect_tail(q34) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3459,3450]) ).
tff(3461,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3462,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3463,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3462,3461]) ).
tff(3464,plain,
( ( rselect_tail(q34) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3463,2813]) ).
tff(3465,plain,
select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3464,3460]) ).
tff(3466,plain,
select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_191,index_192,e33),rselect_tail(q34),e34),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3465]) ).
tff(3467,plain,
( ( earray_191 = rselect_seq(q33) )
<=> ( earray_191 = rselect_seq(q33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3468,axiom,
earray_191 = rselect_seq(q33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp28) ).
tff(3469,plain,
earray_191 = rselect_seq(q33),
inference(modus_ponens,[status(thm)],[3468,3467]) ).
tff(3470,plain,
rselect_seq(q33) = earray_191,
inference(symmetry,[status(thm)],[3469]) ).
tff(3471,plain,
rstore_head(queue_187,index_189) = rstore_head(rstore_tail(queue_185,index_186),s(index_188)),
inference(symmetry,[status(thm)],[547]) ).
tff(3472,plain,
q33 = rstore_head(rstore_tail(queue_185,index_186),s(index_188)),
inference(transitivity,[status(thm)],[527,531,3471]) ).
tff(3473,plain,
rselect_seq(q33) = rselect_seq(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(monotonicity,[status(thm)],[3472]) ).
tff(3474,plain,
rselect_seq(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_seq(q33),
inference(symmetry,[status(thm)],[3473]) ).
tff(3475,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_seq(rstore_tail(queue_185,index_186)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3476,plain,
rselect_seq(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_seq(rstore_tail(queue_185,index_186)),
inference(unit_resolution,[status(thm)],[3475,2834]) ).
tff(3477,plain,
rselect_seq(rstore_tail(queue_185,index_186)) = rselect_seq(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(symmetry,[status(thm)],[3476]) ).
tff(3478,plain,
rselect_seq(rstore_tail(queue_185,index_186)) = rselect_seq(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[569]) ).
tff(3479,plain,
rselect_seq(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_seq(rstore_tail(queue_185,index_186)),
inference(symmetry,[status(thm)],[3478]) ).
tff(3480,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_seq(rstore_seq(q32,earray_184)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3481,plain,
rselect_seq(rstore_tail(rstore_seq(q32,earray_184),s(index_183))) = rselect_seq(rstore_seq(q32,earray_184)),
inference(unit_resolution,[status(thm)],[3480,2356]) ).
tff(3482,plain,
rselect_seq(rstore_seq(q32,earray_184)) = rselect_seq(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[3481]) ).
tff(3483,plain,
rselect_seq(rstore_seq(q32,earray_184)) = rselect_seq(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))),
inference(monotonicity,[status(thm)],[590]) ).
tff(3484,plain,
rselect_seq(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = rselect_seq(rstore_seq(q32,earray_184)),
inference(symmetry,[status(thm)],[3483]) ).
tff(3485,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = store(earray_182,index_183,e32) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3486,plain,
rselect_seq(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))) = store(earray_182,index_183,e32),
inference(unit_resolution,[status(thm)],[3485,2368]) ).
tff(3487,plain,
store(earray_182,index_183,e32) = rselect_seq(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e32))),
inference(symmetry,[status(thm)],[3486]) ).
tff(3488,plain,
store(earray_182,index_183,e32) = earray_191,
inference(transitivity,[status(thm)],[3487,3484,3482,3479,3477,3474,3470]) ).
tff(3489,plain,
store(store(earray_182,index_183,e32),rselect_tail(q33),e33) = store(earray_191,index_192,e33),
inference(monotonicity,[status(thm)],[3488,2554]) ).
tff(3490,plain,
select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_191,index_192,e33),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3489]) ).
tff(3491,plain,
s(index_183) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))),
inference(symmetry,[status(thm)],[2755]) ).
tff(3492,plain,
rselect_tail(rstore_tail(queue_185,index_186)) = rselect_tail(rstore_tail(rstore_seq(q32,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[2560]) ).
tff(3493,plain,
rselect_tail(q33) = rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(symmetry,[status(thm)],[2556]) ).
tff(3494,plain,
rselect_tail(q33) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))),
inference(transitivity,[status(thm)],[3493,2558,3492,2562,3491]) ).
tff(3495,plain,
( ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3494,2236]) ).
tff(3496,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3495]) ).
tff(3497,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q33) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3496]) ).
tff(3498,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(3499,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)],[3498]) ).
tff(3500,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(3501,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(3502,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)],[3501,3500]) ).
tff(3503,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)],[3502]) ).
tff(3504,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)],[3503,3499]) ).
tff(3505,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(rselect_tail(q16)))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3506,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3505,3504]) ).
tff(3507,plain,
rselect_tail(q33) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3506,3497]) ).
tff(3508,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3509,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3510,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3509,3508]) ).
tff(3511,plain,
( ( rselect_tail(q33) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3510,2813]) ).
tff(3512,plain,
select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3511,3507]) ).
tff(3513,plain,
select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_182,index_183,e32),rselect_tail(q33),e33),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3512]) ).
tff(3514,plain,
( ( earray_182 = rselect_seq(q32) )
<=> ( earray_182 = rselect_seq(q32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3515,axiom,
earray_182 = rselect_seq(q32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp26) ).
tff(3516,plain,
earray_182 = rselect_seq(q32),
inference(modus_ponens,[status(thm)],[3515,3514]) ).
tff(3517,plain,
rselect_seq(q32) = earray_182,
inference(symmetry,[status(thm)],[3516]) ).
tff(3518,plain,
q32 = rstore_tail(rstore_seq(q31,earray_178),s(index_177)),
inference(transitivity,[status(thm)],[582,586,605]) ).
tff(3519,plain,
rselect_seq(q32) = rselect_seq(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[3518]) ).
tff(3520,plain,
rselect_seq(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_seq(q32),
inference(symmetry,[status(thm)],[3519]) ).
tff(3521,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_seq(rstore_seq(q31,earray_178)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3522,plain,
rselect_seq(rstore_tail(rstore_seq(q31,earray_178),s(index_177))) = rselect_seq(rstore_seq(q31,earray_178)),
inference(unit_resolution,[status(thm)],[3521,2356]) ).
tff(3523,plain,
rselect_seq(rstore_seq(q31,earray_178)) = rselect_seq(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[3522]) ).
tff(3524,plain,
rselect_seq(rstore_seq(q31,earray_178)) = rselect_seq(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))),
inference(monotonicity,[status(thm)],[625]) ).
tff(3525,plain,
rselect_seq(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = rselect_seq(rstore_seq(q31,earray_178)),
inference(symmetry,[status(thm)],[3524]) ).
tff(3526,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = store(earray_176,index_177,e31) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3527,plain,
rselect_seq(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))) = store(earray_176,index_177,e31),
inference(unit_resolution,[status(thm)],[3526,2368]) ).
tff(3528,plain,
store(earray_176,index_177,e31) = rselect_seq(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e31))),
inference(symmetry,[status(thm)],[3527]) ).
tff(3529,plain,
store(earray_176,index_177,e31) = earray_182,
inference(transitivity,[status(thm)],[3528,3525,3523,3520,3517]) ).
tff(3530,plain,
store(store(earray_176,index_177,e31),rselect_tail(q32),e32) = store(earray_182,index_183,e32),
inference(monotonicity,[status(thm)],[3529,2567]) ).
tff(3531,plain,
select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_182,index_183,e32),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3530]) ).
tff(3532,plain,
s(index_177) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))),
inference(symmetry,[status(thm)],[2753]) ).
tff(3533,plain,
rselect_tail(q32) = rselect_tail(rstore_tail(rstore_seq(q31,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[2569]) ).
tff(3534,plain,
rselect_tail(q32) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))),
inference(transitivity,[status(thm)],[3533,2571,3532]) ).
tff(3535,plain,
( ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3534,2236]) ).
tff(3536,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3535]) ).
tff(3537,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q32) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3536]) ).
tff(3538,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(3539,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)],[3538]) ).
tff(3540,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(3541,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(3542,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)],[3541,3540]) ).
tff(3543,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)],[3542]) ).
tff(3544,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)],[3543,3539]) ).
tff(3545,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(rselect_tail(q16))))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3546,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3545,3544]) ).
tff(3547,plain,
rselect_tail(q32) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3546,3537]) ).
tff(3548,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3549,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3550,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3549,3548]) ).
tff(3551,plain,
( ( rselect_tail(q32) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3550,2813]) ).
tff(3552,plain,
select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3551,3547]) ).
tff(3553,plain,
select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_176,index_177,e31),rselect_tail(q32),e32),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3552]) ).
tff(3554,plain,
( ( earray_176 = rselect_seq(q31) )
<=> ( earray_176 = rselect_seq(q31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3555,axiom,
earray_176 = rselect_seq(q31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp24) ).
tff(3556,plain,
earray_176 = rselect_seq(q31),
inference(modus_ponens,[status(thm)],[3555,3554]) ).
tff(3557,plain,
rselect_seq(q31) = earray_176,
inference(symmetry,[status(thm)],[3556]) ).
tff(3558,plain,
q31 = rstore_tail(rstore_seq(q30,earray_172),s(index_171)),
inference(transitivity,[status(thm)],[617,621,640]) ).
tff(3559,plain,
rselect_seq(q31) = rselect_seq(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[3558]) ).
tff(3560,plain,
rselect_seq(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_seq(q31),
inference(symmetry,[status(thm)],[3559]) ).
tff(3561,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_seq(rstore_seq(q30,earray_172)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3562,plain,
rselect_seq(rstore_tail(rstore_seq(q30,earray_172),s(index_171))) = rselect_seq(rstore_seq(q30,earray_172)),
inference(unit_resolution,[status(thm)],[3561,2356]) ).
tff(3563,plain,
rselect_seq(rstore_seq(q30,earray_172)) = rselect_seq(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(symmetry,[status(thm)],[3562]) ).
tff(3564,plain,
rstore_seq(q30,earray_172) = rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30)),
inference(symmetry,[status(thm)],[659]) ).
tff(3565,plain,
rselect_seq(rstore_seq(q30,earray_172)) = rselect_seq(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))),
inference(monotonicity,[status(thm)],[3564]) ).
tff(3566,plain,
rselect_seq(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = rselect_seq(rstore_seq(q30,earray_172)),
inference(symmetry,[status(thm)],[3565]) ).
tff(3567,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = store(earray_170,index_171,e30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3568,plain,
rselect_seq(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))) = store(earray_170,index_171,e30),
inference(unit_resolution,[status(thm)],[3567,2368]) ).
tff(3569,plain,
store(earray_170,index_171,e30) = rselect_seq(rstore_seq(rstore_head(queue_166,index_168),store(earray_170,index_171,e30))),
inference(symmetry,[status(thm)],[3568]) ).
tff(3570,plain,
store(earray_170,index_171,e30) = earray_176,
inference(transitivity,[status(thm)],[3569,3566,3563,3560,3557]) ).
tff(3571,plain,
store(store(earray_170,index_171,e30),rselect_tail(q31),e31) = store(earray_176,index_177,e31),
inference(monotonicity,[status(thm)],[3570,2576]) ).
tff(3572,plain,
select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_176,index_177,e31),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3571]) ).
tff(3573,plain,
s(index_171) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))),
inference(symmetry,[status(thm)],[2751]) ).
tff(3574,plain,
rselect_tail(q31) = rselect_tail(rstore_tail(rstore_seq(q30,earray_172),s(index_171))),
inference(symmetry,[status(thm)],[2578]) ).
tff(3575,plain,
rselect_tail(q31) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))),
inference(transitivity,[status(thm)],[3574,2580,3573]) ).
tff(3576,plain,
( ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3575,2236]) ).
tff(3577,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3576]) ).
tff(3578,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q31) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3577]) ).
tff(3579,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(3580,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)],[3579]) ).
tff(3581,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(3582,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(3583,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)],[3582,3581]) ).
tff(3584,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3583]) ).
tff(3585,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)],[3584,3580]) ).
tff(3586,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(rselect_tail(q16)))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3587,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3586,3585]) ).
tff(3588,plain,
rselect_tail(q31) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3587,3578]) ).
tff(3589,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3590,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3591,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3590,3589]) ).
tff(3592,plain,
( ( rselect_tail(q31) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3591,2813]) ).
tff(3593,plain,
select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3592,3588]) ).
tff(3594,plain,
select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_170,index_171,e30),rselect_tail(q31),e31),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3593]) ).
tff(3595,plain,
( ( earray_170 = rselect_seq(q30) )
<=> ( earray_170 = rselect_seq(q30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3596,axiom,
earray_170 = rselect_seq(q30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(3597,plain,
earray_170 = rselect_seq(q30),
inference(modus_ponens,[status(thm)],[3596,3595]) ).
tff(3598,plain,
rselect_seq(q30) = earray_170,
inference(symmetry,[status(thm)],[3597]) ).
tff(3599,plain,
rstore_head(queue_166,index_168) = rstore_head(rstore_tail(queue_164,index_165),s(index_167)),
inference(symmetry,[status(thm)],[672]) ).
tff(3600,plain,
q30 = rstore_head(rstore_tail(queue_164,index_165),s(index_167)),
inference(transitivity,[status(thm)],[652,656,3599]) ).
tff(3601,plain,
rselect_seq(q30) = rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(monotonicity,[status(thm)],[3600]) ).
tff(3602,plain,
rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(q30),
inference(symmetry,[status(thm)],[3601]) ).
tff(3603,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(rstore_tail(queue_164,index_165)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3604,plain,
rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(rstore_tail(queue_164,index_165)),
inference(unit_resolution,[status(thm)],[3603,2834]) ).
tff(3605,plain,
rselect_seq(rstore_tail(queue_164,index_165)) = rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[3604]) ).
tff(3606,plain,
rselect_seq(rstore_tail(queue_164,index_165)) = rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(monotonicity,[status(thm)],[694]) ).
tff(3607,plain,
rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_tail(queue_164,index_165)),
inference(symmetry,[status(thm)],[3606]) ).
tff(3608,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_seq(q29,earray_163)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3609,plain,
rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_seq(q29,earray_163)),
inference(unit_resolution,[status(thm)],[3608,2356]) ).
tff(3610,plain,
rselect_seq(rstore_seq(q29,earray_163)) = rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(symmetry,[status(thm)],[3609]) ).
tff(3611,plain,
rselect_seq(rstore_seq(q29,earray_163)) = rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(monotonicity,[status(thm)],[715]) ).
tff(3612,plain,
rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_seq(rstore_seq(q29,earray_163)),
inference(symmetry,[status(thm)],[3611]) ).
tff(3613,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = store(earray_161,index_162,e29) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3614,plain,
rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = store(earray_161,index_162,e29),
inference(unit_resolution,[status(thm)],[3613,2368]) ).
tff(3615,plain,
store(earray_161,index_162,e29) = rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(symmetry,[status(thm)],[3614]) ).
tff(3616,plain,
store(earray_161,index_162,e29) = earray_170,
inference(transitivity,[status(thm)],[3615,3612,3610,3607,3605,3602,3598]) ).
tff(3617,plain,
store(store(earray_161,index_162,e29),rselect_tail(q30),e30) = store(earray_170,index_171,e30),
inference(monotonicity,[status(thm)],[3616,2585]) ).
tff(3618,plain,
select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_170,index_171,e30),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3617]) ).
tff(3619,plain,
s(index_162) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))),
inference(symmetry,[status(thm)],[2749]) ).
tff(3620,plain,
rselect_tail(rstore_tail(queue_164,index_165)) = rselect_tail(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(symmetry,[status(thm)],[2591]) ).
tff(3621,plain,
rselect_tail(q30) = rselect_tail(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[2587]) ).
tff(3622,plain,
rselect_tail(q30) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))),
inference(transitivity,[status(thm)],[3621,2589,3620,2593,3619]) ).
tff(3623,plain,
( ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3622,2236]) ).
tff(3624,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3623]) ).
tff(3625,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q30) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3624]) ).
tff(3626,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(3627,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)],[3626]) ).
tff(3628,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(3629,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(3630,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3629,3628]) ).
tff(3631,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(skolemize,[status(sab)],[3630]) ).
tff(3632,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3631,3627]) ).
tff(3633,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(rselect_tail(q16))))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3634,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3633,3632]) ).
tff(3635,plain,
rselect_tail(q30) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3634,3625]) ).
tff(3636,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3637,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3638,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3637,3636]) ).
tff(3639,plain,
( ( rselect_tail(q30) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3638,2813]) ).
tff(3640,plain,
select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3639,3635]) ).
tff(3641,plain,
select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_161,index_162,e29),rselect_tail(q30),e30),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3640]) ).
tff(3642,plain,
( ( earray_161 = rselect_seq(q29) )
<=> ( earray_161 = rselect_seq(q29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3643,axiom,
earray_161 = rselect_seq(q29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(3644,plain,
earray_161 = rselect_seq(q29),
inference(modus_ponens,[status(thm)],[3643,3642]) ).
tff(3645,plain,
rselect_seq(q29) = earray_161,
inference(symmetry,[status(thm)],[3644]) ).
tff(3646,plain,
q29 = rstore_tail(rstore_seq(q28,earray_148),s(index_147)),
inference(transitivity,[status(thm)],[707,711,730]) ).
tff(3647,plain,
rselect_seq(q29) = rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[3646]) ).
tff(3648,plain,
rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(q29),
inference(symmetry,[status(thm)],[3647]) ).
tff(3649,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(rstore_seq(q28,earray_148)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3650,plain,
rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(rstore_seq(q28,earray_148)),
inference(unit_resolution,[status(thm)],[3649,2356]) ).
tff(3651,plain,
rselect_seq(rstore_seq(q28,earray_148)) = rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[3650]) ).
tff(3652,plain,
rselect_seq(rstore_seq(q28,earray_148)) = rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(monotonicity,[status(thm)],[750]) ).
tff(3653,plain,
rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_seq(rstore_seq(q28,earray_148)),
inference(symmetry,[status(thm)],[3652]) ).
tff(3654,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = store(earray_146,index_147,e28) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3655,plain,
rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = store(earray_146,index_147,e28),
inference(unit_resolution,[status(thm)],[3654,2368]) ).
tff(3656,plain,
store(earray_146,index_147,e28) = rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(symmetry,[status(thm)],[3655]) ).
tff(3657,plain,
store(earray_146,index_147,e28) = earray_161,
inference(transitivity,[status(thm)],[3656,3653,3651,3648,3645]) ).
tff(3658,plain,
store(store(earray_146,index_147,e28),rselect_tail(q29),e29) = store(earray_161,index_162,e29),
inference(monotonicity,[status(thm)],[3657,2598]) ).
tff(3659,plain,
select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_161,index_162,e29),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3658]) ).
tff(3660,plain,
s(index_147) = s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))),
inference(symmetry,[status(thm)],[2747]) ).
tff(3661,plain,
rselect_tail(q29) = rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[2600]) ).
tff(3662,plain,
rselect_tail(q29) = s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))),
inference(transitivity,[status(thm)],[3661,2602,3660]) ).
tff(3663,plain,
( ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3662,2236]) ).
tff(3664,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3663]) ).
tff(3665,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q29) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3664]) ).
tff(3666,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(3667,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)],[3666]) ).
tff(3668,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(3669,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(3670,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3669,3668]) ).
tff(3671,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(skolemize,[status(sab)],[3670]) ).
tff(3672,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3671,3667]) ).
tff(3673,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(rselect_tail(q16)))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3674,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3673,3672]) ).
tff(3675,plain,
rselect_tail(q29) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3674,3665]) ).
tff(3676,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3677,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3678,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3677,3676]) ).
tff(3679,plain,
( ( rselect_tail(q29) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3678,2813]) ).
tff(3680,plain,
select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3679,3675]) ).
tff(3681,plain,
select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3680]) ).
tff(3682,plain,
( ( earray_146 = rselect_seq(q28) )
<=> ( earray_146 = rselect_seq(q28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3683,axiom,
earray_146 = rselect_seq(q28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(3684,plain,
earray_146 = rselect_seq(q28),
inference(modus_ponens,[status(thm)],[3683,3682]) ).
tff(3685,plain,
rselect_seq(q28) = earray_146,
inference(symmetry,[status(thm)],[3684]) ).
tff(3686,plain,
q28 = rstore_tail(rstore_seq(q27,earray_142),s(index_141)),
inference(transitivity,[status(thm)],[742,746,765]) ).
tff(3687,plain,
rselect_seq(q28) = rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[3686]) ).
tff(3688,plain,
rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(q28),
inference(symmetry,[status(thm)],[3687]) ).
tff(3689,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(rstore_seq(q27,earray_142)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3690,plain,
rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(rstore_seq(q27,earray_142)),
inference(unit_resolution,[status(thm)],[3689,2356]) ).
tff(3691,plain,
rselect_seq(rstore_seq(q27,earray_142)) = rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[3690]) ).
tff(3692,plain,
rstore_seq(q27,earray_142) = rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27)),
inference(symmetry,[status(thm)],[784]) ).
tff(3693,plain,
rselect_seq(rstore_seq(q27,earray_142)) = rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(monotonicity,[status(thm)],[3692]) ).
tff(3694,plain,
rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_seq(rstore_seq(q27,earray_142)),
inference(symmetry,[status(thm)],[3693]) ).
tff(3695,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = store(earray_140,index_141,e27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3696,plain,
rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = store(earray_140,index_141,e27),
inference(unit_resolution,[status(thm)],[3695,2368]) ).
tff(3697,plain,
store(earray_140,index_141,e27) = rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(symmetry,[status(thm)],[3696]) ).
tff(3698,plain,
store(earray_140,index_141,e27) = earray_146,
inference(transitivity,[status(thm)],[3697,3694,3691,3688,3685]) ).
tff(3699,plain,
store(store(earray_140,index_141,e27),rselect_tail(q28),e28) = store(earray_146,index_147,e28),
inference(monotonicity,[status(thm)],[3698,2607]) ).
tff(3700,plain,
select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_146,index_147,e28),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3699]) ).
tff(3701,plain,
s(index_141) = s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))),
inference(symmetry,[status(thm)],[2745]) ).
tff(3702,plain,
rselect_tail(q28) = rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[2609]) ).
tff(3703,plain,
rselect_tail(q28) = s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))),
inference(transitivity,[status(thm)],[3702,2611,3701]) ).
tff(3704,plain,
( ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3703,2236]) ).
tff(3705,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3704]) ).
tff(3706,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q28) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3705]) ).
tff(3707,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(3708,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)],[3707]) ).
tff(3709,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(3710,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(3711,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3710,3709]) ).
tff(3712,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(skolemize,[status(sab)],[3711]) ).
tff(3713,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3712,3708]) ).
tff(3714,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(rselect_tail(q16))))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3715,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3714,3713]) ).
tff(3716,plain,
rselect_tail(q28) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3715,3706]) ).
tff(3717,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3718,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3719,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3718,3717]) ).
tff(3720,plain,
( ( rselect_tail(q28) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3719,2813]) ).
tff(3721,plain,
select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3720,3716]) ).
tff(3722,plain,
select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3721]) ).
tff(3723,plain,
( ( earray_140 = rselect_seq(q27) )
<=> ( earray_140 = rselect_seq(q27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3724,axiom,
earray_140 = rselect_seq(q27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(3725,plain,
earray_140 = rselect_seq(q27),
inference(modus_ponens,[status(thm)],[3724,3723]) ).
tff(3726,plain,
rselect_seq(q27) = earray_140,
inference(symmetry,[status(thm)],[3725]) ).
tff(3727,plain,
rstore_head(queue_136,index_138) = rstore_head(rstore_tail(queue_134,index_135),s(index_137)),
inference(symmetry,[status(thm)],[797]) ).
tff(3728,plain,
q27 = rstore_head(rstore_tail(queue_134,index_135),s(index_137)),
inference(transitivity,[status(thm)],[777,781,3727]) ).
tff(3729,plain,
rselect_seq(q27) = rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(monotonicity,[status(thm)],[3728]) ).
tff(3730,plain,
rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(q27),
inference(symmetry,[status(thm)],[3729]) ).
tff(3731,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(rstore_tail(queue_134,index_135)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3732,plain,
rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(rstore_tail(queue_134,index_135)),
inference(unit_resolution,[status(thm)],[3731,2834]) ).
tff(3733,plain,
rselect_seq(rstore_tail(queue_134,index_135)) = rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[3732]) ).
tff(3734,plain,
rselect_seq(rstore_tail(queue_134,index_135)) = rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(monotonicity,[status(thm)],[819]) ).
tff(3735,plain,
rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_tail(queue_134,index_135)),
inference(symmetry,[status(thm)],[3734]) ).
tff(3736,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_seq(q26,earray_133)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3737,plain,
rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_seq(q26,earray_133)),
inference(unit_resolution,[status(thm)],[3736,2356]) ).
tff(3738,plain,
rselect_seq(rstore_seq(q26,earray_133)) = rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[3737]) ).
tff(3739,plain,
rselect_seq(rstore_seq(q26,earray_133)) = rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(monotonicity,[status(thm)],[840]) ).
tff(3740,plain,
rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_seq(rstore_seq(q26,earray_133)),
inference(symmetry,[status(thm)],[3739]) ).
tff(3741,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = store(earray_131,index_132,e26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3742,plain,
rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = store(earray_131,index_132,e26),
inference(unit_resolution,[status(thm)],[3741,2368]) ).
tff(3743,plain,
store(earray_131,index_132,e26) = rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(symmetry,[status(thm)],[3742]) ).
tff(3744,plain,
store(earray_131,index_132,e26) = earray_140,
inference(transitivity,[status(thm)],[3743,3740,3738,3735,3733,3730,3726]) ).
tff(3745,plain,
store(store(earray_131,index_132,e26),rselect_tail(q27),e27) = store(earray_140,index_141,e27),
inference(monotonicity,[status(thm)],[3744,2616]) ).
tff(3746,plain,
select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_140,index_141,e27),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3745]) ).
tff(3747,plain,
s(index_132) = s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))),
inference(symmetry,[status(thm)],[2743]) ).
tff(3748,plain,
rselect_tail(rstore_tail(queue_134,index_135)) = rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[2622]) ).
tff(3749,plain,
rselect_tail(q27) = rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[2618]) ).
tff(3750,plain,
rselect_tail(q27) = s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))),
inference(transitivity,[status(thm)],[3749,2620,3748,2624,3747]) ).
tff(3751,plain,
( ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3750,2236]) ).
tff(3752,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3751]) ).
tff(3753,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q27) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3752]) ).
tff(3754,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(3755,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)],[3754]) ).
tff(3756,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(3757,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(3758,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3757,3756]) ).
tff(3759,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(skolemize,[status(sab)],[3758]) ).
tff(3760,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3759,3755]) ).
tff(3761,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(rselect_tail(q16)))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3762,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3761,3760]) ).
tff(3763,plain,
rselect_tail(q27) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3762,3753]) ).
tff(3764,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3765,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3766,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3765,3764]) ).
tff(3767,plain,
( ( rselect_tail(q27) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3766,2813]) ).
tff(3768,plain,
select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3767,3763]) ).
tff(3769,plain,
select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3768]) ).
tff(3770,plain,
( ( earray_131 = rselect_seq(q26) )
<=> ( earray_131 = rselect_seq(q26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3771,axiom,
earray_131 = rselect_seq(q26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(3772,plain,
earray_131 = rselect_seq(q26),
inference(modus_ponens,[status(thm)],[3771,3770]) ).
tff(3773,plain,
rselect_seq(q26) = earray_131,
inference(symmetry,[status(thm)],[3772]) ).
tff(3774,plain,
q26 = rstore_tail(rstore_seq(q25,earray_127),s(index_126)),
inference(transitivity,[status(thm)],[832,836,855]) ).
tff(3775,plain,
rselect_seq(q26) = rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(monotonicity,[status(thm)],[3774]) ).
tff(3776,plain,
rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(q26),
inference(symmetry,[status(thm)],[3775]) ).
tff(3777,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(rstore_seq(q25,earray_127)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3778,plain,
rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(rstore_seq(q25,earray_127)),
inference(unit_resolution,[status(thm)],[3777,2356]) ).
tff(3779,plain,
rselect_seq(rstore_seq(q25,earray_127)) = rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[3778]) ).
tff(3780,plain,
rselect_seq(rstore_seq(q25,earray_127)) = rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(monotonicity,[status(thm)],[875]) ).
tff(3781,plain,
rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_seq(rstore_seq(q25,earray_127)),
inference(symmetry,[status(thm)],[3780]) ).
tff(3782,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = store(earray_125,index_126,e25) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3783,plain,
rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = store(earray_125,index_126,e25),
inference(unit_resolution,[status(thm)],[3782,2368]) ).
tff(3784,plain,
store(earray_125,index_126,e25) = rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(symmetry,[status(thm)],[3783]) ).
tff(3785,plain,
store(earray_125,index_126,e25) = earray_131,
inference(transitivity,[status(thm)],[3784,3781,3779,3776,3773]) ).
tff(3786,plain,
store(store(earray_125,index_126,e25),rselect_tail(q26),e26) = store(earray_131,index_132,e26),
inference(monotonicity,[status(thm)],[3785,2629]) ).
tff(3787,plain,
select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_131,index_132,e26),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3786]) ).
tff(3788,plain,
s(index_126) = s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))),
inference(symmetry,[status(thm)],[2741]) ).
tff(3789,plain,
rselect_tail(q26) = rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[2631]) ).
tff(3790,plain,
rselect_tail(q26) = s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))),
inference(transitivity,[status(thm)],[3789,2633,3788]) ).
tff(3791,plain,
( ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3790,2236]) ).
tff(3792,plain,
( ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3791]) ).
tff(3793,plain,
( ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q26) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3792]) ).
tff(3794,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(3795,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)],[3794]) ).
tff(3796,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(3797,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as10) ).
tff(3798,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[3797,3796]) ).
tff(3799,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(skolemize,[status(sab)],[3798]) ).
tff(3800,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[3799,3795]) ).
tff(3801,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(rselect_tail(q16))))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3802,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q16))))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3801,3800]) ).
tff(3803,plain,
rselect_tail(q26) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3802,3793]) ).
tff(3804,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3805,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3806,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3805,3804]) ).
tff(3807,plain,
( ( rselect_tail(q26) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3806,2813]) ).
tff(3808,plain,
select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3807,3803]) ).
tff(3809,plain,
select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3808]) ).
tff(3810,plain,
( ( earray_125 = rselect_seq(q25) )
<=> ( earray_125 = rselect_seq(q25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3811,axiom,
earray_125 = rselect_seq(q25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(3812,plain,
earray_125 = rselect_seq(q25),
inference(modus_ponens,[status(thm)],[3811,3810]) ).
tff(3813,plain,
rselect_seq(q25) = earray_125,
inference(symmetry,[status(thm)],[3812]) ).
tff(3814,plain,
q25 = rstore_tail(rstore_seq(q24,earray_121),s(index_120)),
inference(transitivity,[status(thm)],[867,871,890]) ).
tff(3815,plain,
rselect_seq(q25) = rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(monotonicity,[status(thm)],[3814]) ).
tff(3816,plain,
rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(q25),
inference(symmetry,[status(thm)],[3815]) ).
tff(3817,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(rstore_seq(q24,earray_121)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3818,plain,
rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(rstore_seq(q24,earray_121)),
inference(unit_resolution,[status(thm)],[3817,2356]) ).
tff(3819,plain,
rselect_seq(rstore_seq(q24,earray_121)) = rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[3818]) ).
tff(3820,plain,
rstore_seq(q24,earray_121) = rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24)),
inference(symmetry,[status(thm)],[909]) ).
tff(3821,plain,
rselect_seq(rstore_seq(q24,earray_121)) = rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(monotonicity,[status(thm)],[3820]) ).
tff(3822,plain,
rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_seq(rstore_seq(q24,earray_121)),
inference(symmetry,[status(thm)],[3821]) ).
tff(3823,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = store(earray_119,index_120,e24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3824,plain,
rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = store(earray_119,index_120,e24),
inference(unit_resolution,[status(thm)],[3823,2368]) ).
tff(3825,plain,
store(earray_119,index_120,e24) = rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(symmetry,[status(thm)],[3824]) ).
tff(3826,plain,
store(earray_119,index_120,e24) = earray_125,
inference(transitivity,[status(thm)],[3825,3822,3819,3816,3813]) ).
tff(3827,plain,
store(store(earray_119,index_120,e24),rselect_tail(q25),e25) = store(earray_125,index_126,e25),
inference(monotonicity,[status(thm)],[3826,2638]) ).
tff(3828,plain,
select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_125,index_126,e25),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3827]) ).
tff(3829,plain,
s(index_120) = s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))),
inference(symmetry,[status(thm)],[2739]) ).
tff(3830,plain,
rselect_tail(q25) = rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[2640]) ).
tff(3831,plain,
rselect_tail(q25) = s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))),
inference(transitivity,[status(thm)],[3830,2642,3829]) ).
tff(3832,plain,
( ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3831,2236]) ).
tff(3833,plain,
( ( s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3832]) ).
tff(3834,plain,
( ( s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q25) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3833]) ).
tff(3835,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(3836,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)],[3835]) ).
tff(3837,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(3838,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as9) ).
tff(3839,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[3838,3837]) ).
tff(3840,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(skolemize,[status(sab)],[3839]) ).
tff(3841,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[3840,3836]) ).
tff(3842,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3843,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q16)))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3842,3841]) ).
tff(3844,plain,
rselect_tail(q25) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3843,3834]) ).
tff(3845,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3846,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3847,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3846,3845]) ).
tff(3848,plain,
( ( rselect_tail(q25) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3847,2813]) ).
tff(3849,plain,
select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3848,3844]) ).
tff(3850,plain,
select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3849]) ).
tff(3851,plain,
( ( earray_119 = rselect_seq(q24) )
<=> ( earray_119 = rselect_seq(q24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3852,axiom,
earray_119 = rselect_seq(q24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(3853,plain,
earray_119 = rselect_seq(q24),
inference(modus_ponens,[status(thm)],[3852,3851]) ).
tff(3854,plain,
rselect_seq(q24) = earray_119,
inference(symmetry,[status(thm)],[3853]) ).
tff(3855,plain,
rstore_head(queue_115,index_117) = rstore_head(rstore_tail(queue_113,index_114),s(index_116)),
inference(symmetry,[status(thm)],[922]) ).
tff(3856,plain,
q24 = rstore_head(rstore_tail(queue_113,index_114),s(index_116)),
inference(transitivity,[status(thm)],[902,906,3855]) ).
tff(3857,plain,
rselect_seq(q24) = rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(monotonicity,[status(thm)],[3856]) ).
tff(3858,plain,
rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(q24),
inference(symmetry,[status(thm)],[3857]) ).
tff(3859,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(rstore_tail(queue_113,index_114)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3860,plain,
rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(rstore_tail(queue_113,index_114)),
inference(unit_resolution,[status(thm)],[3859,2834]) ).
tff(3861,plain,
rselect_seq(rstore_tail(queue_113,index_114)) = rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[3860]) ).
tff(3862,plain,
rselect_seq(rstore_tail(queue_113,index_114)) = rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(monotonicity,[status(thm)],[944]) ).
tff(3863,plain,
rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_tail(queue_113,index_114)),
inference(symmetry,[status(thm)],[3862]) ).
tff(3864,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_seq(q23,earray_112)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3865,plain,
rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_seq(q23,earray_112)),
inference(unit_resolution,[status(thm)],[3864,2356]) ).
tff(3866,plain,
rselect_seq(rstore_seq(q23,earray_112)) = rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[3865]) ).
tff(3867,plain,
rselect_seq(rstore_seq(q23,earray_112)) = rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(monotonicity,[status(thm)],[965]) ).
tff(3868,plain,
rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_seq(rstore_seq(q23,earray_112)),
inference(symmetry,[status(thm)],[3867]) ).
tff(3869,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = store(earray_110,index_111,e23) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3870,plain,
rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = store(earray_110,index_111,e23),
inference(unit_resolution,[status(thm)],[3869,2368]) ).
tff(3871,plain,
store(earray_110,index_111,e23) = rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(symmetry,[status(thm)],[3870]) ).
tff(3872,plain,
store(earray_110,index_111,e23) = earray_119,
inference(transitivity,[status(thm)],[3871,3868,3866,3863,3861,3858,3854]) ).
tff(3873,plain,
store(store(earray_110,index_111,e23),rselect_tail(q24),e24) = store(earray_119,index_120,e24),
inference(monotonicity,[status(thm)],[3872,2647]) ).
tff(3874,plain,
select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_119,index_120,e24),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3873]) ).
tff(3875,plain,
s(index_111) = s(s(s(s(s(s(s(s(rselect_tail(q16))))))))),
inference(symmetry,[status(thm)],[2737]) ).
tff(3876,plain,
rselect_tail(rstore_tail(queue_113,index_114)) = rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[2653]) ).
tff(3877,plain,
rselect_tail(q24) = rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[2649]) ).
tff(3878,plain,
rselect_tail(q24) = s(s(s(s(s(s(s(s(rselect_tail(q16))))))))),
inference(transitivity,[status(thm)],[3877,2651,3876,2655,3875]) ).
tff(3879,plain,
( ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3878,2236]) ).
tff(3880,plain,
( ( s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3879]) ).
tff(3881,plain,
( ( s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q24) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3880]) ).
tff(3882,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(3883,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)],[3882]) ).
tff(3884,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(3885,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as8) ).
tff(3886,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[3885,3884]) ).
tff(3887,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(skolemize,[status(sab)],[3886]) ).
tff(3888,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[3887,3883]) ).
tff(3889,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
| ( s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3890,plain,
s(s(s(s(s(s(s(s(rselect_tail(q16))))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3889,3888]) ).
tff(3891,plain,
rselect_tail(q24) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3890,3881]) ).
tff(3892,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3893,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3894,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3893,3892]) ).
tff(3895,plain,
( ( rselect_tail(q24) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3894,2813]) ).
tff(3896,plain,
select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3895,3891]) ).
tff(3897,plain,
select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3896]) ).
tff(3898,plain,
( ( earray_110 = rselect_seq(q23) )
<=> ( earray_110 = rselect_seq(q23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3899,axiom,
earray_110 = rselect_seq(q23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(3900,plain,
earray_110 = rselect_seq(q23),
inference(modus_ponens,[status(thm)],[3899,3898]) ).
tff(3901,plain,
rselect_seq(q23) = earray_110,
inference(symmetry,[status(thm)],[3900]) ).
tff(3902,plain,
q23 = rstore_tail(rstore_seq(q22,earray_106),s(index_105)),
inference(transitivity,[status(thm)],[957,961,980]) ).
tff(3903,plain,
rselect_seq(q23) = rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[3902]) ).
tff(3904,plain,
rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(q23),
inference(symmetry,[status(thm)],[3903]) ).
tff(3905,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(rstore_seq(q22,earray_106)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3906,plain,
rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(rstore_seq(q22,earray_106)),
inference(unit_resolution,[status(thm)],[3905,2356]) ).
tff(3907,plain,
rselect_seq(rstore_seq(q22,earray_106)) = rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[3906]) ).
tff(3908,plain,
rselect_seq(rstore_seq(q22,earray_106)) = rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(monotonicity,[status(thm)],[1000]) ).
tff(3909,plain,
rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_seq(rstore_seq(q22,earray_106)),
inference(symmetry,[status(thm)],[3908]) ).
tff(3910,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = store(earray_104,index_105,e22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3911,plain,
rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = store(earray_104,index_105,e22),
inference(unit_resolution,[status(thm)],[3910,2368]) ).
tff(3912,plain,
store(earray_104,index_105,e22) = rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(symmetry,[status(thm)],[3911]) ).
tff(3913,plain,
store(earray_104,index_105,e22) = earray_110,
inference(transitivity,[status(thm)],[3912,3909,3907,3904,3901]) ).
tff(3914,plain,
store(store(earray_104,index_105,e22),rselect_tail(q23),e23) = store(earray_110,index_111,e23),
inference(monotonicity,[status(thm)],[3913,2660]) ).
tff(3915,plain,
select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_110,index_111,e23),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3914]) ).
tff(3916,plain,
s(index_105) = s(s(s(s(s(s(s(rselect_tail(q16)))))))),
inference(symmetry,[status(thm)],[2735]) ).
tff(3917,plain,
rselect_tail(q23) = rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[2662]) ).
tff(3918,plain,
rselect_tail(q23) = s(s(s(s(s(s(s(rselect_tail(q16)))))))),
inference(transitivity,[status(thm)],[3917,2664,3916]) ).
tff(3919,plain,
( ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(s(rselect_tail(q16)))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3918,2236]) ).
tff(3920,plain,
( ( s(s(s(s(s(s(s(rselect_tail(q16)))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3919]) ).
tff(3921,plain,
( ( s(s(s(s(s(s(s(rselect_tail(q16)))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q23) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3920]) ).
tff(3922,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(3923,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)],[3922]) ).
tff(3924,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(3925,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as7) ).
tff(3926,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[3925,3924]) ).
tff(3927,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(skolemize,[status(sab)],[3926]) ).
tff(3928,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[3927,3923]) ).
tff(3929,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
| ( s(s(s(s(s(s(s(rselect_tail(q16)))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3930,plain,
s(s(s(s(s(s(s(rselect_tail(q16)))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3929,3928]) ).
tff(3931,plain,
rselect_tail(q23) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3930,3921]) ).
tff(3932,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3933,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3934,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3933,3932]) ).
tff(3935,plain,
( ( rselect_tail(q23) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3934,2813]) ).
tff(3936,plain,
select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3935,3931]) ).
tff(3937,plain,
select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3936]) ).
tff(3938,plain,
( ( earray_104 = rselect_seq(q22) )
<=> ( earray_104 = rselect_seq(q22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3939,axiom,
earray_104 = rselect_seq(q22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(3940,plain,
earray_104 = rselect_seq(q22),
inference(modus_ponens,[status(thm)],[3939,3938]) ).
tff(3941,plain,
rselect_seq(q22) = earray_104,
inference(symmetry,[status(thm)],[3940]) ).
tff(3942,plain,
q22 = rstore_tail(rstore_seq(q21,earray_100),s(index_99)),
inference(transitivity,[status(thm)],[992,996,1015]) ).
tff(3943,plain,
rselect_seq(q22) = rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[3942]) ).
tff(3944,plain,
rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(q22),
inference(symmetry,[status(thm)],[3943]) ).
tff(3945,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(rstore_seq(q21,earray_100)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3946,plain,
rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(rstore_seq(q21,earray_100)),
inference(unit_resolution,[status(thm)],[3945,2356]) ).
tff(3947,plain,
rselect_seq(rstore_seq(q21,earray_100)) = rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[3946]) ).
tff(3948,plain,
rstore_seq(q21,earray_100) = rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21)),
inference(symmetry,[status(thm)],[1034]) ).
tff(3949,plain,
rselect_seq(rstore_seq(q21,earray_100)) = rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(monotonicity,[status(thm)],[3948]) ).
tff(3950,plain,
rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_seq(rstore_seq(q21,earray_100)),
inference(symmetry,[status(thm)],[3949]) ).
tff(3951,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = store(earray_98,index_99,e21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3952,plain,
rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = store(earray_98,index_99,e21),
inference(unit_resolution,[status(thm)],[3951,2368]) ).
tff(3953,plain,
store(earray_98,index_99,e21) = rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(symmetry,[status(thm)],[3952]) ).
tff(3954,plain,
store(earray_98,index_99,e21) = earray_104,
inference(transitivity,[status(thm)],[3953,3950,3947,3944,3941]) ).
tff(3955,plain,
store(store(earray_98,index_99,e21),rselect_tail(q22),e22) = store(earray_104,index_105,e22),
inference(monotonicity,[status(thm)],[3954,2669]) ).
tff(3956,plain,
select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_104,index_105,e22),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[3955]) ).
tff(3957,plain,
s(index_99) = s(s(s(s(s(s(rselect_tail(q16))))))),
inference(symmetry,[status(thm)],[2733]) ).
tff(3958,plain,
rselect_tail(q22) = rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[2671]) ).
tff(3959,plain,
rselect_tail(q22) = s(s(s(s(s(s(rselect_tail(q16))))))),
inference(transitivity,[status(thm)],[3958,2673,3957]) ).
tff(3960,plain,
( ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(s(rselect_tail(q16))))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[3959,2236]) ).
tff(3961,plain,
( ( s(s(s(s(s(s(rselect_tail(q16))))))) = rselect_tail(q16) )
<=> ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[3960]) ).
tff(3962,plain,
( ( s(s(s(s(s(s(rselect_tail(q16))))))) != rselect_tail(q16) )
<=> ( rselect_tail(q22) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[3961]) ).
tff(3963,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(3964,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)],[3963]) ).
tff(3965,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(3966,axiom,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as6) ).
tff(3967,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[3966,3965]) ).
tff(3968,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(skolemize,[status(sab)],[3967]) ).
tff(3969,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[3968,3964]) ).
tff(3970,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
| ( s(s(s(s(s(s(rselect_tail(q16))))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3971,plain,
s(s(s(s(s(s(rselect_tail(q16))))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[3970,3969]) ).
tff(3972,plain,
rselect_tail(q22) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[3971,3962]) ).
tff(3973,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3974,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3975,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[3974,3973]) ).
tff(3976,plain,
( ( rselect_tail(q22) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[3975,2813]) ).
tff(3977,plain,
select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[3976,3972]) ).
tff(3978,plain,
select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[3977]) ).
tff(3979,plain,
( ( earray_98 = rselect_seq(q21) )
<=> ( earray_98 = rselect_seq(q21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3980,axiom,
earray_98 = rselect_seq(q21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(3981,plain,
earray_98 = rselect_seq(q21),
inference(modus_ponens,[status(thm)],[3980,3979]) ).
tff(3982,plain,
rselect_seq(q21) = earray_98,
inference(symmetry,[status(thm)],[3981]) ).
tff(3983,plain,
rstore_head(queue_94,index_96) = rstore_head(rstore_tail(queue_92,index_93),s(index_95)),
inference(symmetry,[status(thm)],[1047]) ).
tff(3984,plain,
q21 = rstore_head(rstore_tail(queue_92,index_93),s(index_95)),
inference(transitivity,[status(thm)],[1027,1031,3983]) ).
tff(3985,plain,
rselect_seq(q21) = rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(monotonicity,[status(thm)],[3984]) ).
tff(3986,plain,
rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(q21),
inference(symmetry,[status(thm)],[3985]) ).
tff(3987,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(rstore_tail(queue_92,index_93)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3988,plain,
rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(rstore_tail(queue_92,index_93)),
inference(unit_resolution,[status(thm)],[3987,2834]) ).
tff(3989,plain,
rselect_seq(rstore_tail(queue_92,index_93)) = rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[3988]) ).
tff(3990,plain,
rselect_seq(rstore_tail(queue_92,index_93)) = rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(monotonicity,[status(thm)],[1069]) ).
tff(3991,plain,
rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_tail(queue_92,index_93)),
inference(symmetry,[status(thm)],[3990]) ).
tff(3992,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_seq(q20,earray_91)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3993,plain,
rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_seq(q20,earray_91)),
inference(unit_resolution,[status(thm)],[3992,2356]) ).
tff(3994,plain,
rselect_seq(rstore_seq(q20,earray_91)) = rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[3993]) ).
tff(3995,plain,
rselect_seq(rstore_seq(q20,earray_91)) = rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(monotonicity,[status(thm)],[1090]) ).
tff(3996,plain,
rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_seq(rstore_seq(q20,earray_91)),
inference(symmetry,[status(thm)],[3995]) ).
tff(3997,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = store(earray_89,index_90,e20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3998,plain,
rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = store(earray_89,index_90,e20),
inference(unit_resolution,[status(thm)],[3997,2368]) ).
tff(3999,plain,
store(earray_89,index_90,e20) = rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(symmetry,[status(thm)],[3998]) ).
tff(4000,plain,
store(earray_89,index_90,e20) = earray_98,
inference(transitivity,[status(thm)],[3999,3996,3994,3991,3989,3986,3982]) ).
tff(4001,plain,
store(store(earray_89,index_90,e20),rselect_tail(q21),e21) = store(earray_98,index_99,e21),
inference(monotonicity,[status(thm)],[4000,2678]) ).
tff(4002,plain,
select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_98,index_99,e21),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[4001]) ).
tff(4003,plain,
s(index_90) = s(s(s(s(s(rselect_tail(q16)))))),
inference(symmetry,[status(thm)],[2731]) ).
tff(4004,plain,
rselect_tail(rstore_tail(queue_92,index_93)) = rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[2684]) ).
tff(4005,plain,
rselect_tail(q21) = rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[2680]) ).
tff(4006,plain,
rselect_tail(q21) = s(s(s(s(s(rselect_tail(q16)))))),
inference(transitivity,[status(thm)],[4005,2682,4004,2686,4003]) ).
tff(4007,plain,
( ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(s(rselect_tail(q16)))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[4006,2236]) ).
tff(4008,plain,
( ( s(s(s(s(s(rselect_tail(q16)))))) = rselect_tail(q16) )
<=> ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[4007]) ).
tff(4009,plain,
( ( s(s(s(s(s(rselect_tail(q16)))))) != rselect_tail(q16) )
<=> ( rselect_tail(q21) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[4008]) ).
tff(4010,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(X))))) != X )
<=> ( s(s(s(s(s(X))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4011,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(quant_intro,[status(thm)],[4010]) ).
tff(4012,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4013,axiom,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as5) ).
tff(4014,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[4013,4012]) ).
tff(4015,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(skolemize,[status(sab)],[4014]) ).
tff(4016,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[4015,4011]) ).
tff(4017,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(X))))) != X )
| ( s(s(s(s(s(rselect_tail(q16)))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4018,plain,
s(s(s(s(s(rselect_tail(q16)))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[4017,4016]) ).
tff(4019,plain,
rselect_tail(q21) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[4018,4009]) ).
tff(4020,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4021,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4022,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[4021,4020]) ).
tff(4023,plain,
( ( rselect_tail(q21) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[4022,2813]) ).
tff(4024,plain,
select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[4023,4019]) ).
tff(4025,plain,
select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[4024]) ).
tff(4026,plain,
( ( earray_89 = rselect_seq(q20) )
<=> ( earray_89 = rselect_seq(q20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4027,axiom,
earray_89 = rselect_seq(q20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(4028,plain,
earray_89 = rselect_seq(q20),
inference(modus_ponens,[status(thm)],[4027,4026]) ).
tff(4029,plain,
rselect_seq(q20) = earray_89,
inference(symmetry,[status(thm)],[4028]) ).
tff(4030,plain,
q20 = rstore_tail(rstore_seq(q19,earray_85),s(index_84)),
inference(transitivity,[status(thm)],[1082,1086,1105]) ).
tff(4031,plain,
rselect_seq(q20) = rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(monotonicity,[status(thm)],[4030]) ).
tff(4032,plain,
rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(q20),
inference(symmetry,[status(thm)],[4031]) ).
tff(4033,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(rstore_seq(q19,earray_85)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4034,plain,
rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(rstore_seq(q19,earray_85)),
inference(unit_resolution,[status(thm)],[4033,2356]) ).
tff(4035,plain,
rselect_seq(rstore_seq(q19,earray_85)) = rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[4034]) ).
tff(4036,plain,
rselect_seq(rstore_seq(q19,earray_85)) = rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(monotonicity,[status(thm)],[1125]) ).
tff(4037,plain,
rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_seq(rstore_seq(q19,earray_85)),
inference(symmetry,[status(thm)],[4036]) ).
tff(4038,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = store(earray_83,index_84,e19) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4039,plain,
rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = store(earray_83,index_84,e19),
inference(unit_resolution,[status(thm)],[4038,2368]) ).
tff(4040,plain,
store(earray_83,index_84,e19) = rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(symmetry,[status(thm)],[4039]) ).
tff(4041,plain,
store(earray_83,index_84,e19) = earray_89,
inference(transitivity,[status(thm)],[4040,4037,4035,4032,4029]) ).
tff(4042,plain,
store(store(earray_83,index_84,e19),rselect_tail(q20),e20) = store(earray_89,index_90,e20),
inference(monotonicity,[status(thm)],[4041,2691]) ).
tff(4043,plain,
select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_89,index_90,e20),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[4042]) ).
tff(4044,plain,
s(index_84) = s(s(s(s(rselect_tail(q16))))),
inference(symmetry,[status(thm)],[2729]) ).
tff(4045,plain,
rselect_tail(q20) = rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[2693]) ).
tff(4046,plain,
rselect_tail(q20) = s(s(s(s(rselect_tail(q16))))),
inference(transitivity,[status(thm)],[4045,2695,4044]) ).
tff(4047,plain,
( ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(s(rselect_tail(q16))))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[4046,2236]) ).
tff(4048,plain,
( ( s(s(s(s(rselect_tail(q16))))) = rselect_tail(q16) )
<=> ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[4047]) ).
tff(4049,plain,
( ( s(s(s(s(rselect_tail(q16))))) != rselect_tail(q16) )
<=> ( rselect_tail(q20) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[4048]) ).
tff(4050,plain,
^ [X: $i] :
refl(( ( s(s(s(s(X)))) != X )
<=> ( s(s(s(s(X)))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4051,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(quant_intro,[status(thm)],[4050]) ).
tff(4052,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4053,axiom,
! [X: $i] : ( s(s(s(s(X)))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as4) ).
tff(4054,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[4053,4052]) ).
tff(4055,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(skolemize,[status(sab)],[4054]) ).
tff(4056,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[4055,4051]) ).
tff(4057,plain,
( ~ ! [X: $i] : ( s(s(s(s(X)))) != X )
| ( s(s(s(s(rselect_tail(q16))))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4058,plain,
s(s(s(s(rselect_tail(q16))))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[4057,4056]) ).
tff(4059,plain,
rselect_tail(q20) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[4058,4049]) ).
tff(4060,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4062,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[4061,4060]) ).
tff(4063,plain,
( ( rselect_tail(q20) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[4062,2813]) ).
tff(4064,plain,
select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[4063,4059]) ).
tff(4065,plain,
select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[4064]) ).
tff(4066,plain,
( ( earray_83 = rselect_seq(q19) )
<=> ( earray_83 = rselect_seq(q19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4067,axiom,
earray_83 = rselect_seq(q19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(4068,plain,
earray_83 = rselect_seq(q19),
inference(modus_ponens,[status(thm)],[4067,4066]) ).
tff(4069,plain,
rselect_seq(q19) = earray_83,
inference(symmetry,[status(thm)],[4068]) ).
tff(4070,plain,
q19 = rstore_tail(rstore_seq(q18,earray_73),s(index_72)),
inference(transitivity,[status(thm)],[1117,1121,1140]) ).
tff(4071,plain,
rselect_seq(q19) = rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(monotonicity,[status(thm)],[4070]) ).
tff(4072,plain,
rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(q19),
inference(symmetry,[status(thm)],[4071]) ).
tff(4073,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(rstore_seq(q18,earray_73)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4074,plain,
rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(rstore_seq(q18,earray_73)),
inference(unit_resolution,[status(thm)],[4073,2356]) ).
tff(4075,plain,
rselect_seq(rstore_seq(q18,earray_73)) = rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[4074]) ).
tff(4076,plain,
rstore_seq(q18,earray_73) = rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18)),
inference(symmetry,[status(thm)],[1159]) ).
tff(4077,plain,
rselect_seq(rstore_seq(q18,earray_73)) = rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(monotonicity,[status(thm)],[4076]) ).
tff(4078,plain,
rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_seq(rstore_seq(q18,earray_73)),
inference(symmetry,[status(thm)],[4077]) ).
tff(4079,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = store(earray_71,index_72,e18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4080,plain,
rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = store(earray_71,index_72,e18),
inference(unit_resolution,[status(thm)],[4079,2368]) ).
tff(4081,plain,
store(earray_71,index_72,e18) = rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(symmetry,[status(thm)],[4080]) ).
tff(4082,plain,
store(earray_71,index_72,e18) = earray_83,
inference(transitivity,[status(thm)],[4081,4078,4075,4072,4069]) ).
tff(4083,plain,
store(store(earray_71,index_72,e18),rselect_tail(q19),e19) = store(earray_83,index_84,e19),
inference(monotonicity,[status(thm)],[4082,2700]) ).
tff(4084,plain,
select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_83,index_84,e19),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[4083]) ).
tff(4085,plain,
s(index_72) = s(s(s(rselect_tail(q16)))),
inference(symmetry,[status(thm)],[2727]) ).
tff(4086,plain,
rselect_tail(q19) = rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[2702]) ).
tff(4087,plain,
rselect_tail(q19) = s(s(s(rselect_tail(q16)))),
inference(transitivity,[status(thm)],[4086,2704,4085]) ).
tff(4088,plain,
( ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(s(rselect_tail(q16)))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[4087,2236]) ).
tff(4089,plain,
( ( s(s(s(rselect_tail(q16)))) = rselect_tail(q16) )
<=> ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[4088]) ).
tff(4090,plain,
( ( s(s(s(rselect_tail(q16)))) != rselect_tail(q16) )
<=> ( rselect_tail(q19) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[4089]) ).
tff(4091,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) != X )
<=> ( s(s(s(X))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4092,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(quant_intro,[status(thm)],[4091]) ).
tff(4093,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4094,axiom,
! [X: $i] : ( s(s(s(X))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as3) ).
tff(4095,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[4094,4093]) ).
tff(4096,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(skolemize,[status(sab)],[4095]) ).
tff(4097,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[4096,4092]) ).
tff(4098,plain,
( ~ ! [X: $i] : ( s(s(s(X))) != X )
| ( s(s(s(rselect_tail(q16)))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4099,plain,
s(s(s(rselect_tail(q16)))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[4098,4097]) ).
tff(4100,plain,
rselect_tail(q19) != rselect_head(rstore_seq(q48,earray_304)),
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) ) )
| ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
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) ) )
| ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) ) ),
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) ) )
| ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[4102,4101]) ).
tff(4104,plain,
( ( rselect_tail(q19) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[4103,2813]) ).
tff(4105,plain,
select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[4104,4100]) ).
tff(4106,plain,
select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[4105]) ).
tff(4107,plain,
( ( earray_71 = rselect_seq(q18) )
<=> ( earray_71 = rselect_seq(q18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4108,axiom,
earray_71 = rselect_seq(q18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(4109,plain,
earray_71 = rselect_seq(q18),
inference(modus_ponens,[status(thm)],[4108,4107]) ).
tff(4110,plain,
rselect_seq(q18) = earray_71,
inference(symmetry,[status(thm)],[4109]) ).
tff(4111,plain,
rstore_head(queue_67,index_69) = rstore_head(rstore_tail(queue_65,index_66),s(index_68)),
inference(symmetry,[status(thm)],[1172]) ).
tff(4112,plain,
q18 = rstore_head(rstore_tail(queue_65,index_66),s(index_68)),
inference(transitivity,[status(thm)],[1152,1156,4111]) ).
tff(4113,plain,
rselect_seq(q18) = rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(monotonicity,[status(thm)],[4112]) ).
tff(4114,plain,
rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(q18),
inference(symmetry,[status(thm)],[4113]) ).
tff(4115,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(rstore_tail(queue_65,index_66)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4116,plain,
rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(rstore_tail(queue_65,index_66)),
inference(unit_resolution,[status(thm)],[4115,2834]) ).
tff(4117,plain,
rselect_seq(rstore_tail(queue_65,index_66)) = rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[4116]) ).
tff(4118,plain,
rselect_seq(rstore_tail(queue_65,index_66)) = rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[1194]) ).
tff(4119,plain,
rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_tail(queue_65,index_66)),
inference(symmetry,[status(thm)],[4118]) ).
tff(4120,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_seq(q17,earray_64)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4121,plain,
rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_seq(q17,earray_64)),
inference(unit_resolution,[status(thm)],[4120,2356]) ).
tff(4122,plain,
rselect_seq(rstore_seq(q17,earray_64)) = rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[4121]) ).
tff(4123,plain,
rselect_seq(rstore_seq(q17,earray_64)) = rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(monotonicity,[status(thm)],[1215]) ).
tff(4124,plain,
rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_seq(rstore_seq(q17,earray_64)),
inference(symmetry,[status(thm)],[4123]) ).
tff(4125,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = store(earray_62,index_63,e17) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4126,plain,
rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = store(earray_62,index_63,e17),
inference(unit_resolution,[status(thm)],[4125,2368]) ).
tff(4127,plain,
store(earray_62,index_63,e17) = rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(symmetry,[status(thm)],[4126]) ).
tff(4128,plain,
store(earray_62,index_63,e17) = earray_71,
inference(transitivity,[status(thm)],[4127,4124,4122,4119,4117,4114,4110]) ).
tff(4129,plain,
store(store(earray_62,index_63,e17),rselect_tail(q18),e18) = store(earray_71,index_72,e18),
inference(monotonicity,[status(thm)],[4128,2709]) ).
tff(4130,plain,
select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_71,index_72,e18),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[4129]) ).
tff(4131,plain,
s(index_63) = s(s(rselect_tail(q16))),
inference(symmetry,[status(thm)],[2725]) ).
tff(4132,plain,
rselect_tail(rstore_tail(queue_65,index_66)) = rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[2715]) ).
tff(4133,plain,
rselect_tail(q18) = rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[2711]) ).
tff(4134,plain,
rselect_tail(q18) = s(s(rselect_tail(q16))),
inference(transitivity,[status(thm)],[4133,2713,4132,2717,4131]) ).
tff(4135,plain,
( ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
<=> ( s(s(rselect_tail(q16))) = rselect_tail(q16) ) ),
inference(monotonicity,[status(thm)],[4134,2236]) ).
tff(4136,plain,
( ( s(s(rselect_tail(q16))) = rselect_tail(q16) )
<=> ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(symmetry,[status(thm)],[4135]) ).
tff(4137,plain,
( ( s(s(rselect_tail(q16))) != rselect_tail(q16) )
<=> ( rselect_tail(q18) != rselect_head(rstore_seq(q48,earray_304)) ) ),
inference(monotonicity,[status(thm)],[4136]) ).
tff(4138,plain,
^ [X: $i] :
refl(( ( s(s(X)) != X )
<=> ( s(s(X)) != X ) )),
inference(bind,[status(th)],[]) ).
tff(4139,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(quant_intro,[status(thm)],[4138]) ).
tff(4140,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4141,axiom,
! [X: $i] : ( s(s(X)) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as2) ).
tff(4142,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[4141,4140]) ).
tff(4143,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(skolemize,[status(sab)],[4142]) ).
tff(4144,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[4143,4139]) ).
tff(4145,plain,
( ~ ! [X: $i] : ( s(s(X)) != X )
| ( s(s(rselect_tail(q16))) != rselect_tail(q16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4146,plain,
s(s(rselect_tail(q16))) != rselect_tail(q16),
inference(unit_resolution,[status(thm)],[4145,4144]) ).
tff(4147,plain,
rselect_tail(q18) != rselect_head(rstore_seq(q48,earray_304)),
inference(modus_ponens,[status(thm)],[4146,4137]) ).
tff(4148,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4149,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4150,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[4149,4148]) ).
tff(4151,plain,
( ( rselect_tail(q18) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[4150,2813]) ).
tff(4152,plain,
select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))),
inference(unit_resolution,[status(thm)],[4151,4147]) ).
tff(4153,plain,
select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_head(rstore_seq(q48,earray_304))),
inference(symmetry,[status(thm)],[4152]) ).
tff(4154,plain,
( ( earray_62 = rselect_seq(q17) )
<=> ( earray_62 = rselect_seq(q17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4155,axiom,
earray_62 = rselect_seq(q17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(4156,plain,
earray_62 = rselect_seq(q17),
inference(modus_ponens,[status(thm)],[4155,4154]) ).
tff(4157,plain,
rselect_seq(q17) = earray_62,
inference(symmetry,[status(thm)],[4156]) ).
tff(4158,plain,
q17 = rstore_tail(rstore_seq(q16,earray_58),s(index_57)),
inference(transitivity,[status(thm)],[1207,1211,1230]) ).
tff(4159,plain,
rselect_seq(q17) = rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[4158]) ).
tff(4160,plain,
rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(q17),
inference(symmetry,[status(thm)],[4159]) ).
tff(4161,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(rstore_seq(q16,earray_58)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4162,plain,
rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(rstore_seq(q16,earray_58)),
inference(unit_resolution,[status(thm)],[4161,2356]) ).
tff(4163,plain,
rselect_seq(rstore_seq(q16,earray_58)) = rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[4162]) ).
tff(4164,plain,
rselect_seq(rstore_seq(q16,earray_58)) = rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(monotonicity,[status(thm)],[1244]) ).
tff(4165,plain,
rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_seq(rstore_seq(q16,earray_58)),
inference(symmetry,[status(thm)],[4164]) ).
tff(4166,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = store(earray_56,index_57,e16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4167,plain,
rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = store(earray_56,index_57,e16),
inference(unit_resolution,[status(thm)],[4166,2368]) ).
tff(4168,plain,
store(earray_56,index_57,e16) = rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(symmetry,[status(thm)],[4167]) ).
tff(4169,plain,
store(earray_56,index_57,e16) = earray_62,
inference(transitivity,[status(thm)],[4168,4165,4163,4160,4157]) ).
tff(4170,plain,
store(store(earray_56,index_57,e16),rselect_tail(q17),e17) = store(earray_62,index_63,e17),
inference(monotonicity,[status(thm)],[4169,2722]) ).
tff(4171,plain,
select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_62,index_63,e17),rselect_head(rstore_seq(q48,earray_304))),
inference(monotonicity,[status(thm)],[4170]) ).
tff(4172,plain,
select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = elem_352,
inference(transitivity,[status(thm)],[4171,4153,4130,4106,4084,4065,4043,4025,4002,3978,3956,3937,3915,3897,3874,3850,3828,3809,3787,3769,3746,3722,3700,3681,3659,3641,3618,3594,3572,3553,3531,3513,3490,3466,3444,3425,3403,3385,3362,3338,3316,3297,3275,3257,3234,3210,3188,3169,3147,3129,3106,3082,3060,3041,3019,3001,2978,2954,2932,2913,2891,2873,2850,2819,2395,2281]) ).
tff(4173,plain,
( ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) )
<=> ( elem_352 = e16 ) ),
inference(monotonicity,[status(thm)],[4172,2277]) ).
tff(4174,plain,
( ( elem_352 = e16 )
<=> ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(symmetry,[status(thm)],[4173]) ).
tff(4175,plain,
( ( elem_352 != e16 )
<=> ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) != select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(monotonicity,[status(thm)],[4174]) ).
tff(4176,plain,
( ( elem_352 != e16 )
<=> ( elem_352 != e16 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4177,axiom,
elem_352 != e16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(4178,plain,
elem_352 != e16,
inference(modus_ponens,[status(thm)],[4177,4176]) ).
tff(4179,plain,
select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) != select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))),
inference(modus_ponens,[status(thm)],[4178,4175]) ).
tff(4180,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4181,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(4182,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(modus_ponens,[status(thm)],[4181,4180]) ).
tff(4183,plain,
( ( rselect_tail(q17) = rselect_head(rstore_seq(q48,earray_304)) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_head(rstore_seq(q48,earray_304))) = select(store(earray_56,index_57,e16),rselect_head(rstore_seq(q48,earray_304))) ) ),
inference(unit_resolution,[status(thm)],[4182,2813]) ).
tff(4184,plain,
$false,
inference(unit_resolution,[status(thm)],[4183,4179,2261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV568-1.050 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 10:24:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.31/1.52 % SZS status Unsatisfiable
% 1.31/1.52 % SZS output start Proof
% See solution above
% 1.52/1.74 % E exiting
%------------------------------------------------------------------------------