%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV569-1.040 : 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 05:35:39 AM UTC 2025
% Result : Unsatisfiable 6.91s 7.10s
% Output : Proof 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 1184
% Syntax : Number of formulae : 3946 (2791 unt; 0 typ; 0 def)
% Number of atoms : 6887 (6860 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 4168 (1253 ~;2258 |; 0 &)
% ( 657 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 28 ( 3 avg)
% Number of FOOLs : 26 ( 26 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 : 372 ( 372 usr; 369 con; 0-3 aty)
% Number of variables : 3366 (3340 !; 0 ?;3366 :)
% Comments :
%------------------------------------------------------------------------------
tff(s_type,type,
s: $i > $i ).
tff(index_230_type,type,
index_230: $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(head_type,type,
head: $i ).
tff(queue_229_type,type,
queue_229: $i ).
tff(seq_type,type,
seq: $i ).
tff(q14_type,type,
q14: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e14_type,type,
e14: $i ).
tff(e13_type,type,
e13: $i ).
tff(elem_283_type,type,
elem_283: $i ).
tff(tail_type,type,
tail: $i ).
tff(q13_type,type,
q13: $i ).
tff(index_30_type,type,
index_30: $i ).
tff(earray_31_type,type,
earray_31: $i ).
tff(q12_type,type,
q12: $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(q11_type,type,
q11: $i ).
tff(index_21_type,type,
index_21: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(index_24_type,type,
index_24: $i ).
tff(queue_23_type,type,
queue_23: $i ).
tff(index_26_type,type,
index_26: $i ).
tff(index_27_type,type,
index_27: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(queue_28_type,type,
queue_28: $i ).
tff(index_225_type,type,
index_225: $i ).
tff(earray_226_type,type,
earray_226: $i ).
tff(q38_type,type,
q38: $i ).
tff(index_228_type,type,
index_228: $i ).
tff(queue_227_type,type,
queue_227: $i ).
tff(q39_type,type,
q39: $i ).
tff(index_222_type,type,
index_222: $i ).
tff(queue_221_type,type,
queue_221: $i ).
tff(e38_type,type,
e38: $i ).
tff(earray_224_type,type,
earray_224: $i ).
tff(queue_223_type,type,
queue_223: $i ).
tff(queue_232_type,type,
queue_232: $i ).
tff(index_231_type,type,
index_231: $i ).
tff(index_219_type,type,
index_219: $i ).
tff(earray_220_type,type,
earray_220: $i ).
tff(q37_type,type,
q37: $i ).
tff(index_216_type,type,
index_216: $i ).
tff(queue_215_type,type,
queue_215: $i ).
tff(e37_type,type,
e37: $i ).
tff(earray_218_type,type,
earray_218: $i ).
tff(queue_217_type,type,
queue_217: $i ).
tff(index_213_type,type,
index_213: $i ).
tff(earray_214_type,type,
earray_214: $i ).
tff(q36_type,type,
q36: $i ).
tff(index_210_type,type,
index_210: $i ).
tff(queue_208_type,type,
queue_208: $i ).
tff(e36_type,type,
e36: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(queue_211_type,type,
queue_211: $i ).
tff(index_209_type,type,
index_209: $i ).
tff(index_207_type,type,
index_207: $i ).
tff(queue_206_type,type,
queue_206: $i ).
tff(q10_type,type,
q10: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(earray_205_type,type,
earray_205: $i ).
tff(q35_type,type,
q35: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(queue_200_type,type,
queue_200: $i ).
tff(e35_type,type,
e35: $i ).
tff(earray_203_type,type,
earray_203: $i ).
tff(queue_202_type,type,
queue_202: $i ).
tff(index_198_type,type,
index_198: $i ).
tff(earray_199_type,type,
earray_199: $i ).
tff(q34_type,type,
q34: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(queue_194_type,type,
queue_194: $i ).
tff(e34_type,type,
e34: $i ).
tff(earray_197_type,type,
earray_197: $i ).
tff(queue_196_type,type,
queue_196: $i ).
tff(index_192_type,type,
index_192: $i ).
tff(earray_193_type,type,
earray_193: $i ).
tff(q33_type,type,
q33: $i ).
tff(index_189_type,type,
index_189: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(e33_type,type,
e33: $i ).
tff(earray_191_type,type,
earray_191: $i ).
tff(queue_190_type,type,
queue_190: $i ).
tff(index_188_type,type,
index_188: $i ).
tff(index_186_type,type,
index_186: $i ).
tff(queue_185_type,type,
queue_185: $i ).
tff(q9_type,type,
q9: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(q32_type,type,
q32: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $i ).
tff(e32_type,type,
e32: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(queue_181_type,type,
queue_181: $i ).
tff(index_177_type,type,
index_177: $i ).
tff(earray_178_type,type,
earray_178: $i ).
tff(q31_type,type,
q31: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $i ).
tff(e31_type,type,
e31: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(queue_175_type,type,
queue_175: $i ).
tff(index_171_type,type,
index_171: $i ).
tff(earray_172_type,type,
earray_172: $i ).
tff(q30_type,type,
q30: $i ).
tff(index_168_type,type,
index_168: $i ).
tff(queue_166_type,type,
queue_166: $i ).
tff(e30_type,type,
e30: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(queue_169_type,type,
queue_169: $i ).
tff(index_167_type,type,
index_167: $i ).
tff(index_165_type,type,
index_165: $i ).
tff(queue_164_type,type,
queue_164: $i ).
tff(q8_type,type,
q8: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(earray_163_type,type,
earray_163: $i ).
tff(q29_type,type,
q29: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $i ).
tff(e29_type,type,
e29: $i ).
tff(earray_161_type,type,
earray_161: $i ).
tff(queue_151_type,type,
queue_151: $i ).
tff(index_147_type,type,
index_147: $i ).
tff(earray_148_type,type,
earray_148: $i ).
tff(q28_type,type,
q28: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $i ).
tff(e28_type,type,
e28: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(queue_145_type,type,
queue_145: $i ).
tff(index_141_type,type,
index_141: $i ).
tff(earray_142_type,type,
earray_142: $i ).
tff(q27_type,type,
q27: $i ).
tff(index_138_type,type,
index_138: $i ).
tff(queue_136_type,type,
queue_136: $i ).
tff(e27_type,type,
e27: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(queue_139_type,type,
queue_139: $i ).
tff(index_137_type,type,
index_137: $i ).
tff(index_135_type,type,
index_135: $i ).
tff(queue_134_type,type,
queue_134: $i ).
tff(q7_type,type,
q7: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(earray_133_type,type,
earray_133: $i ).
tff(q26_type,type,
q26: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(queue_128_type,type,
queue_128: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_131_type,type,
earray_131: $i ).
tff(queue_130_type,type,
queue_130: $i ).
tff(index_126_type,type,
index_126: $i ).
tff(earray_127_type,type,
earray_127: $i ).
tff(q25_type,type,
q25: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(queue_122_type,type,
queue_122: $i ).
tff(e25_type,type,
e25: $i ).
tff(earray_125_type,type,
earray_125: $i ).
tff(queue_124_type,type,
queue_124: $i ).
tff(index_120_type,type,
index_120: $i ).
tff(earray_121_type,type,
earray_121: $i ).
tff(q24_type,type,
q24: $i ).
tff(index_117_type,type,
index_117: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(e24_type,type,
e24: $i ).
tff(earray_119_type,type,
earray_119: $i ).
tff(queue_118_type,type,
queue_118: $i ).
tff(index_116_type,type,
index_116: $i ).
tff(index_114_type,type,
index_114: $i ).
tff(queue_113_type,type,
queue_113: $i ).
tff(q6_type,type,
q6: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(q23_type,type,
q23: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(queue_109_type,type,
queue_109: $i ).
tff(index_105_type,type,
index_105: $i ).
tff(earray_106_type,type,
earray_106: $i ).
tff(q22_type,type,
q22: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $i ).
tff(e22_type,type,
e22: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(queue_103_type,type,
queue_103: $i ).
tff(index_99_type,type,
index_99: $i ).
tff(earray_100_type,type,
earray_100: $i ).
tff(q21_type,type,
q21: $i ).
tff(index_96_type,type,
index_96: $i ).
tff(queue_94_type,type,
queue_94: $i ).
tff(e21_type,type,
e21: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(queue_97_type,type,
queue_97: $i ).
tff(index_95_type,type,
index_95: $i ).
tff(index_93_type,type,
index_93: $i ).
tff(queue_92_type,type,
queue_92: $i ).
tff(q5_type,type,
q5: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(earray_91_type,type,
earray_91: $i ).
tff(q20_type,type,
q20: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(queue_86_type,type,
queue_86: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_89_type,type,
earray_89: $i ).
tff(queue_88_type,type,
queue_88: $i ).
tff(index_84_type,type,
index_84: $i ).
tff(earray_85_type,type,
earray_85: $i ).
tff(q19_type,type,
q19: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(queue_74_type,type,
queue_74: $i ).
tff(e19_type,type,
e19: $i ).
tff(earray_83_type,type,
earray_83: $i ).
tff(queue_76_type,type,
queue_76: $i ).
tff(index_72_type,type,
index_72: $i ).
tff(earray_73_type,type,
earray_73: $i ).
tff(q18_type,type,
q18: $i ).
tff(index_69_type,type,
index_69: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(e18_type,type,
e18: $i ).
tff(earray_71_type,type,
earray_71: $i ).
tff(queue_70_type,type,
queue_70: $i ).
tff(index_68_type,type,
index_68: $i ).
tff(index_66_type,type,
index_66: $i ).
tff(queue_65_type,type,
queue_65: $i ).
tff(q4_type,type,
q4: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(q17_type,type,
q17: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $i ).
tff(e17_type,type,
e17: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(queue_61_type,type,
queue_61: $i ).
tff(index_57_type,type,
index_57: $i ).
tff(earray_58_type,type,
earray_58: $i ).
tff(q16_type,type,
q16: $i ).
tff(index_54_type,type,
index_54: $i ).
tff(queue_53_type,type,
queue_53: $i ).
tff(e16_type,type,
e16: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(queue_55_type,type,
queue_55: $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_48_type,type,
index_48: $i ).
tff(queue_46_type,type,
queue_46: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_50_type,type,
earray_50: $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(q3_type,type,
q3: $i ).
tff(index_42_type,type,
index_42: $i ).
tff(earray_43_type,type,
earray_43: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(queue_38_type,type,
queue_38: $i ).
tff(earray_41_type,type,
earray_41: $i ).
tff(queue_40_type,type,
queue_40: $i ).
tff(index_36_type,type,
index_36: $i ).
tff(earray_37_type,type,
earray_37: $i ).
tff(earray_35_type,type,
earray_35: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_29_type,type,
earray_29: $i ).
tff(q2_type,type,
q2: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(e11_type,type,
e11: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(index_15_type,type,
index_15: $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(index_9_type,type,
index_9: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(index_279_type,type,
index_279: $i ).
tff(queue_277_type,type,
queue_277: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(queue_280_type,type,
queue_280: $i ).
tff(index_278_type,type,
index_278: $i ).
tff(index_276_type,type,
index_276: $i ).
tff(queue_275_type,type,
queue_275: $i ).
tff(q1_type,type,
q1: $i ).
tff(index_273_type,type,
index_273: $i ).
tff(earray_274_type,type,
earray_274: $i ).
tff(index_270_type,type,
index_270: $i ).
tff(queue_269_type,type,
queue_269: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_272_type,type,
earray_272: $i ).
tff(queue_271_type,type,
queue_271: $i ).
tff(index_267_type,type,
index_267: $i ).
tff(earray_268_type,type,
earray_268: $i ).
tff(index_264_type,type,
index_264: $i ).
tff(queue_263_type,type,
queue_263: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_266_type,type,
earray_266: $i ).
tff(queue_265_type,type,
queue_265: $i ).
tff(index_261_type,type,
index_261: $i ).
tff(earray_262_type,type,
earray_262: $i ).
tff(index_258_type,type,
index_258: $i ).
tff(queue_256_type,type,
queue_256: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_260_type,type,
earray_260: $i ).
tff(queue_259_type,type,
queue_259: $i ).
tff(index_257_type,type,
index_257: $i ).
tff(index_255_type,type,
index_255: $i ).
tff(queue_254_type,type,
queue_254: $i ).
tff(q0_type,type,
q0: $i ).
tff(index_252_type,type,
index_252: $i ).
tff(earray_253_type,type,
earray_253: $i ).
tff(index_249_type,type,
index_249: $i ).
tff(queue_248_type,type,
queue_248: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_251_type,type,
earray_251: $i ).
tff(queue_250_type,type,
queue_250: $i ).
tff(index_246_type,type,
index_246: $i ).
tff(earray_247_type,type,
earray_247: $i ).
tff(index_237_type,type,
index_237: $i ).
tff(queue_236_type,type,
queue_236: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_245_type,type,
earray_245: $i ).
tff(queue_238_type,type,
queue_238: $i ).
tff(index_234_type,type,
index_234: $i ).
tff(earray_235_type,type,
earray_235: $i ).
tff(index_159_type,type,
index_159: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_233_type,type,
earray_233: $i ).
tff(queue_160_type,type,
queue_160: $i ).
tff(index_158_type,type,
index_158: $i ).
tff(index_156_type,type,
index_156: $i ).
tff(queue_155_type,type,
queue_155: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(index_153_type,type,
index_153: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(queue_80_type,type,
queue_80: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(queue_82_type,type,
queue_82: $i ).
tff(index_78_type,type,
index_78: $i ).
tff(earray_79_type,type,
earray_79: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_77_type,type,
earray_77: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(q_type,type,
q: $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(index_282_type,type,
index_282: $i ).
tff(earray_281_type,type,
earray_281: $i ).
tff(q40_type,type,
q40: $i ).
tff(e39_type,type,
e39: $i ).
tff(index_240_type,type,
index_240: $i ).
tff(earray_241_type,type,
earray_241: $i ).
tff(queue_244_type,type,
queue_244: $i ).
tff(index_243_type,type,
index_243: $i ).
tff(queue_242_type,type,
queue_242: $i ).
tff(earray_239_type,type,
earray_239: $i ).
tff(1,plain,
( ( index_230 = select(queue_229,head) )
<=> ( index_230 = select(queue_229,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
index_230 = select(queue_229,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(3,plain,
index_230 = select(queue_229,head),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
select(queue_229,head) = index_230,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
s(select(queue_229,head)) = s(index_230),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
s(index_230) = s(select(queue_229,head)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
s(s(index_230)) = s(s(select(queue_229,head))),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
s(s(select(queue_229,head))) = s(s(index_230)),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( s(s(select(queue_229,head))) = s(index_230) )
<=> ( s(s(index_230)) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( s(s(index_230)) = s(index_230) )
<=> ( s(s(select(queue_229,head))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( s(s(index_230)) != s(index_230) )
<=> ( s(s(select(queue_229,head))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
refl(( ( s(X) != X )
<=> ( s(X) != X ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [X: $i] : ( s(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as1) ).
tff(16,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] : ( s(X) != X ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [X: $i] : ( s(X) != X )
| ( s(s(index_230)) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
s(s(index_230)) != s(index_230),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
s(s(select(queue_229,head))) != s(index_230),
inference(modus_ponens,[status(thm)],[20,11]) ).
tff(22,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(23,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(24,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(25,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(select(q13,seq),select(q13,tail),e13),select(q13,tail)) = e13 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
select(store(select(q13,seq),select(q13,tail),e13),select(q13,tail)) = e13,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ( index_33 = s(index_30) )
<=> ( index_33 = s(index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
index_33 = s(index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(32,plain,
index_33 = s(index_30),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
s(index_30) = index_33,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( queue_32 = store(q12,seq,earray_31) )
<=> ( queue_32 = store(q12,seq,earray_31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
queue_32 = store(q12,seq,earray_31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp259) ).
tff(36,plain,
queue_32 = store(q12,seq,earray_31),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
store(q12,seq,earray_31) = queue_32,
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
store(store(q12,seq,earray_31),tail,s(index_30)) = store(queue_32,tail,index_33),
inference(monotonicity,[status(thm)],[37,33]) ).
tff(39,plain,
store(queue_32,tail,index_33) = store(store(q12,seq,earray_31),tail,s(index_30)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ( queue_34 = store(queue_32,tail,index_33) )
<=> ( queue_34 = store(queue_32,tail,index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
queue_34 = store(queue_32,tail,index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp260) ).
tff(42,plain,
queue_34 = store(queue_32,tail,index_33),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
( ( q13 = queue_34 )
<=> ( q13 = queue_34 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
q13 = queue_34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp289) ).
tff(45,plain,
q13 = queue_34,
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
q13 = store(store(q12,seq,earray_31),tail,s(index_30)),
inference(transitivity,[status(thm)],[45,42,39]) ).
tff(47,plain,
select(q13,tail) = select(store(store(q12,seq,earray_31),tail,s(index_30)),tail),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),tail) = select(q13,tail),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),tail) = s(index_30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),tail) = s(index_30),
inference(unit_resolution,[status(thm)],[49,27]) ).
tff(51,plain,
s(index_30) = select(store(store(q12,seq,earray_31),tail,s(index_30)),tail),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( ( index_21 = select(q11,tail) )
<=> ( index_21 = select(q11,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
index_21 = select(q11,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(54,plain,
index_21 = select(q11,tail),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
select(q11,tail) = index_21,
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
s(select(q11,tail)) = s(index_21),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
s(index_21) = s(select(q11,tail)),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = s(index_21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = s(index_21),
inference(unit_resolution,[status(thm)],[58,27]) ).
tff(60,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(62,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( ( queue_23 = store(q11,seq,earray_22) )
<=> ( queue_23 = store(q11,seq,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
queue_23 = store(q11,seq,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(66,plain,
queue_23 = store(q11,seq,earray_22),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
store(q11,seq,earray_22) = queue_23,
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = store(queue_23,tail,index_24),
inference(monotonicity,[status(thm)],[67,63]) ).
tff(69,plain,
store(queue_23,tail,index_24) = store(store(q11,seq,earray_22),tail,s(index_21)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
select(store(queue_23,tail,index_24),tail) = select(store(store(q11,seq,earray_22),tail,s(index_21)),tail),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( head != tail )
<=> ( head != tail ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
head != tail,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_tail) ).
tff(73,plain,
head != tail,
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,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(75,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(76,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(77,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)],[76,75]) ).
tff(78,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,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)],[78,74]) ).
tff(80,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),tail) = select(store(queue_23,tail,index_24),tail),
inference(unit_resolution,[status(thm)],[82,79,73]) ).
tff(84,plain,
( ( index_27 = s(index_26) )
<=> ( index_27 = s(index_26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
index_27 = s(index_26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(86,plain,
index_27 = s(index_26),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
s(index_26) = index_27,
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ( queue_25 = store(queue_23,tail,index_24) )
<=> ( queue_25 = store(queue_23,tail,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
queue_25 = store(queue_23,tail,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp246) ).
tff(90,plain,
queue_25 = store(queue_23,tail,index_24),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
store(queue_23,tail,index_24) = queue_25,
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
store(store(queue_23,tail,index_24),head,s(index_26)) = store(queue_25,head,index_27),
inference(monotonicity,[status(thm)],[91,87]) ).
tff(93,plain,
store(queue_25,head,index_27) = store(store(queue_23,tail,index_24),head,s(index_26)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ( queue_28 = store(queue_25,head,index_27) )
<=> ( queue_28 = store(queue_25,head,index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
queue_28 = store(queue_25,head,index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp257) ).
tff(96,plain,
queue_28 = store(queue_25,head,index_27),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
( ( q12 = queue_28 )
<=> ( q12 = queue_28 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
q12 = queue_28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp288) ).
tff(99,plain,
q12 = queue_28,
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
q12 = store(store(queue_23,tail,index_24),head,s(index_26)),
inference(transitivity,[status(thm)],[99,96,93]) ).
tff(101,plain,
select(q12,tail) = select(store(store(queue_23,tail,index_24),head,s(index_26)),tail),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( index_30 = select(q12,tail) )
<=> ( index_30 = select(q12,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
index_30 = select(q12,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(104,plain,
index_30 = select(q12,tail),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
index_30 = s(select(q11,tail)),
inference(transitivity,[status(thm)],[104,101,83,70,59,57]) ).
tff(106,plain,
s(index_30) = s(s(select(q11,tail))),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
s(s(select(q11,tail))) = s(index_30),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ( queue_229 = store(queue_227,tail,index_228) )
<=> ( queue_229 = store(queue_227,tail,index_228) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,axiom,
queue_229 = store(queue_227,tail,index_228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(110,plain,
queue_229 = store(queue_227,tail,index_228),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
store(queue_227,tail,index_228) = queue_229,
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ( index_228 = s(index_225) )
<=> ( index_228 = s(index_225) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
index_228 = s(index_225),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(114,plain,
index_228 = s(index_225),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
s(index_225) = index_228,
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ( queue_227 = store(q38,seq,earray_226) )
<=> ( queue_227 = store(q38,seq,earray_226) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
queue_227 = store(q38,seq,earray_226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(118,plain,
queue_227 = store(q38,seq,earray_226),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
store(q38,seq,earray_226) = queue_227,
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
store(store(q38,seq,earray_226),tail,s(index_225)) = store(queue_227,tail,index_228),
inference(monotonicity,[status(thm)],[119,115]) ).
tff(121,plain,
store(store(q38,seq,earray_226),tail,s(index_225)) = queue_229,
inference(transitivity,[status(thm)],[120,111]) ).
tff(122,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(queue_229,head),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
( ( tail = head )
<=> ( head = tail ) ),
inference(commutativity,[status(thm)],[]) ).
tff(124,plain,
( ( head = tail )
<=> ( tail = head ) ),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ( head != tail )
<=> ( tail != head ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
tail != head,
inference(modus_ponens,[status(thm)],[73,125]) ).
tff(127,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
( ( tail = head )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head) ) ),
inference(unit_resolution,[status(thm)],[129,79]) ).
tff(131,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),head) = select(store(q38,seq,earray_226),head),
inference(unit_resolution,[status(thm)],[130,126]) ).
tff(132,plain,
select(store(q38,seq,earray_226),head) = select(store(store(q38,seq,earray_226),tail,s(index_225)),head),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ( earray_226 = store(earray_224,index_225,e38) )
<=> ( earray_226 = store(earray_224,index_225,e38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
earray_226 = store(earray_224,index_225,e38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp42) ).
tff(135,plain,
earray_226 = store(earray_224,index_225,e38),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
store(earray_224,index_225,e38) = earray_226,
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = store(earray_224,index_225,e38) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = store(earray_224,index_225,e38),
inference(unit_resolution,[status(thm)],[137,27]) ).
tff(139,plain,
( ( q38 = queue_223 )
<=> ( q38 = queue_223 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
q38 = queue_223,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp316) ).
tff(141,plain,
q38 = queue_223,
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
queue_223 = q38,
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
( ( queue_223 = store(queue_221,tail,index_222) )
<=> ( queue_223 = store(queue_221,tail,index_222) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
queue_223 = store(queue_221,tail,index_222),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(145,plain,
queue_223 = store(queue_221,tail,index_222),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
store(queue_221,tail,index_222) = queue_223,
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
store(queue_221,tail,index_222) = q38,
inference(transitivity,[status(thm)],[146,142]) ).
tff(148,plain,
store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)) = store(q38,seq,earray_226),
inference(monotonicity,[status(thm)],[147,136]) ).
tff(149,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq) = select(store(q38,seq,earray_226),seq),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
select(store(q38,seq,earray_226),seq) = select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ( tail != seq )
<=> ( tail != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,axiom,
tail != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_distinct_from_seq) ).
tff(153,plain,
tail != seq,
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq) ) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(q38,seq,earray_226),seq),
inference(unit_resolution,[status(thm)],[156,79,153]) ).
tff(158,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),seq) = select(store(queue_227,tail,index_228),seq),
inference(monotonicity,[status(thm)],[120]) ).
tff(159,plain,
select(store(queue_227,tail,index_228),seq) = select(store(store(q38,seq,earray_226),tail,s(index_225)),seq),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ( head != seq )
<=> ( head != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,axiom,
head != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_seq) ).
tff(162,plain,
head != seq,
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq) ) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(store(queue_227,tail,index_228),seq),
inference(unit_resolution,[status(thm)],[165,79,162]) ).
tff(167,plain,
( ( q39 = queue_232 )
<=> ( q39 = queue_232 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,axiom,
q39 = queue_232,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp317) ).
tff(169,plain,
q39 = queue_232,
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
queue_232 = q39,
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ( queue_232 = store(queue_229,head,index_231) )
<=> ( queue_232 = store(queue_229,head,index_231) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
queue_232 = store(queue_229,head,index_231),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(173,plain,
queue_232 = store(queue_229,head,index_231),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
store(queue_229,head,index_231) = queue_232,
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ( index_231 = s(index_230) )
<=> ( index_231 = s(index_230) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
index_231 = s(index_230),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(177,plain,
index_231 = s(index_230),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
s(index_230) = index_231,
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
store(store(queue_227,tail,index_228),head,s(index_230)) = store(queue_229,head,index_231),
inference(monotonicity,[status(thm)],[111,178]) ).
tff(180,plain,
store(store(queue_227,tail,index_228),head,s(index_230)) = q39,
inference(transitivity,[status(thm)],[179,174,170]) ).
tff(181,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),seq) = select(q39,seq),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
select(q39,seq) = select(store(store(queue_227,tail,index_228),head,s(index_230)),seq),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
select(q39,seq) = earray_226,
inference(transitivity,[status(thm)],[182,166,159,157,150,138,136]) ).
tff(184,plain,
store(store(queue_221,tail,index_222),seq,select(q39,seq)) = store(q38,seq,earray_226),
inference(monotonicity,[status(thm)],[147,183]) ).
tff(185,plain,
select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(q38,seq,earray_226),head),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( seq = head )
<=> ( head = seq ) ),
inference(commutativity,[status(thm)],[]) ).
tff(187,plain,
( ( head = seq )
<=> ( seq = head ) ),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
( ( head != seq )
<=> ( seq != head ) ),
inference(monotonicity,[status(thm)],[187]) ).
tff(189,plain,
seq != head,
inference(modus_ponens,[status(thm)],[162,188]) ).
tff(190,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(191,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
( ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(unit_resolution,[status(thm)],[192,79]) ).
tff(194,plain,
select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head) = select(store(queue_221,tail,index_222),head),
inference(unit_resolution,[status(thm)],[193,189]) ).
tff(195,plain,
select(store(queue_221,tail,index_222),head) = select(store(store(queue_221,tail,index_222),seq,select(q39,seq)),head),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ( index_222 = s(index_219) )
<=> ( index_222 = s(index_219) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,axiom,
index_222 = s(index_219),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(198,plain,
index_222 = s(index_219),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
s(index_219) = index_222,
inference(symmetry,[status(thm)],[198]) ).
tff(200,plain,
( ( queue_221 = store(q37,seq,earray_220) )
<=> ( queue_221 = store(q37,seq,earray_220) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
queue_221 = store(q37,seq,earray_220),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(202,plain,
queue_221 = store(q37,seq,earray_220),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
store(q37,seq,earray_220) = queue_221,
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
store(store(q37,seq,earray_220),tail,s(index_219)) = store(queue_221,tail,index_222),
inference(monotonicity,[status(thm)],[203,199]) ).
tff(205,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(queue_221,tail,index_222),head),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head) ) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),head) = select(store(q37,seq,earray_220),head),
inference(unit_resolution,[status(thm)],[208,79,126]) ).
tff(210,plain,
select(store(q37,seq,earray_220),head) = select(store(store(q37,seq,earray_220),tail,s(index_219)),head),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ( earray_220 = store(earray_218,index_219,e37) )
<=> ( earray_220 = store(earray_218,index_219,e37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,axiom,
earray_220 = store(earray_218,index_219,e37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp40) ).
tff(213,plain,
earray_220 = store(earray_218,index_219,e37),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
store(earray_218,index_219,e37) = earray_220,
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = store(earray_218,index_219,e37) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(216,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = store(earray_218,index_219,e37),
inference(unit_resolution,[status(thm)],[215,27]) ).
tff(217,plain,
( ( q37 = queue_217 )
<=> ( q37 = queue_217 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,axiom,
q37 = queue_217,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp315) ).
tff(219,plain,
q37 = queue_217,
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
queue_217 = q37,
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ( queue_217 = store(queue_215,tail,index_216) )
<=> ( queue_217 = store(queue_215,tail,index_216) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,axiom,
queue_217 = store(queue_215,tail,index_216),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(223,plain,
queue_217 = store(queue_215,tail,index_216),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
store(queue_215,tail,index_216) = queue_217,
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
store(queue_215,tail,index_216) = q37,
inference(transitivity,[status(thm)],[224,220]) ).
tff(226,plain,
store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)) = store(q37,seq,earray_220),
inference(monotonicity,[status(thm)],[225,214]) ).
tff(227,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq) = select(store(q37,seq,earray_220),seq),
inference(monotonicity,[status(thm)],[226]) ).
tff(228,plain,
select(store(q37,seq,earray_220),seq) = select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(230,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(231,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq) ) ),
inference(modus_ponens,[status(thm)],[230,229]) ).
tff(232,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(store(q37,seq,earray_220),seq),
inference(unit_resolution,[status(thm)],[231,79,153]) ).
tff(233,plain,
store(store(q37,seq,earray_220),tail,s(index_219)) = q38,
inference(transitivity,[status(thm)],[204,146,142]) ).
tff(234,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),seq) = select(q38,seq),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
select(q38,seq) = select(store(store(q37,seq,earray_220),tail,s(index_219)),seq),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
select(q38,seq) = earray_220,
inference(transitivity,[status(thm)],[235,232,228,216,214]) ).
tff(237,plain,
store(store(queue_215,tail,index_216),seq,select(q38,seq)) = store(q37,seq,earray_220),
inference(monotonicity,[status(thm)],[225,236]) ).
tff(238,plain,
select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(q37,seq,earray_220),head),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(241,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head) = select(store(queue_215,tail,index_216),head),
inference(unit_resolution,[status(thm)],[241,79,189]) ).
tff(243,plain,
select(store(queue_215,tail,index_216),head) = select(store(store(queue_215,tail,index_216),seq,select(q38,seq)),head),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ( index_216 = s(index_213) )
<=> ( index_216 = s(index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
index_216 = s(index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(246,plain,
index_216 = s(index_213),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
s(index_213) = index_216,
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
( ( queue_215 = store(q36,seq,earray_214) )
<=> ( queue_215 = store(q36,seq,earray_214) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(249,axiom,
queue_215 = store(q36,seq,earray_214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(250,plain,
queue_215 = store(q36,seq,earray_214),
inference(modus_ponens,[status(thm)],[249,248]) ).
tff(251,plain,
store(q36,seq,earray_214) = queue_215,
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
store(store(q36,seq,earray_214),tail,s(index_213)) = store(queue_215,tail,index_216),
inference(monotonicity,[status(thm)],[251,247]) ).
tff(253,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(queue_215,tail,index_216),head),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(255,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(256,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head) ) ),
inference(modus_ponens,[status(thm)],[255,254]) ).
tff(257,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),head) = select(store(q36,seq,earray_214),head),
inference(unit_resolution,[status(thm)],[256,79,126]) ).
tff(258,plain,
select(store(q36,seq,earray_214),head) = select(store(store(q36,seq,earray_214),tail,s(index_213)),head),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ( earray_214 = store(earray_212,index_213,e36) )
<=> ( earray_214 = store(earray_212,index_213,e36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
earray_214 = store(earray_212,index_213,e36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp37) ).
tff(261,plain,
earray_214 = store(earray_212,index_213,e36),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
store(earray_212,index_213,e36) = earray_214,
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = store(earray_212,index_213,e36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = store(earray_212,index_213,e36),
inference(unit_resolution,[status(thm)],[263,27]) ).
tff(265,plain,
( ( q36 = queue_211 )
<=> ( q36 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(266,axiom,
q36 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp314) ).
tff(267,plain,
q36 = queue_211,
inference(modus_ponens,[status(thm)],[266,265]) ).
tff(268,plain,
queue_211 = q36,
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ( queue_211 = store(queue_208,head,index_210) )
<=> ( queue_211 = store(queue_208,head,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,axiom,
queue_211 = store(queue_208,head,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(271,plain,
queue_211 = store(queue_208,head,index_210),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
store(queue_208,head,index_210) = queue_211,
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
store(queue_208,head,index_210) = q36,
inference(transitivity,[status(thm)],[272,268]) ).
tff(274,plain,
store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)) = store(q36,seq,earray_214),
inference(monotonicity,[status(thm)],[273,262]) ).
tff(275,plain,
select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq) = select(store(q36,seq,earray_214),seq),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
select(store(q36,seq,earray_214),seq) = select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(278,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(279,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq) ) ),
inference(modus_ponens,[status(thm)],[278,277]) ).
tff(280,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(store(q36,seq,earray_214),seq),
inference(unit_resolution,[status(thm)],[279,79,153]) ).
tff(281,plain,
store(store(q36,seq,earray_214),tail,s(index_213)) = q37,
inference(transitivity,[status(thm)],[252,224,220]) ).
tff(282,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),seq) = select(q37,seq),
inference(monotonicity,[status(thm)],[281]) ).
tff(283,plain,
select(q37,seq) = select(store(store(q36,seq,earray_214),tail,s(index_213)),seq),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
select(q37,seq) = earray_214,
inference(transitivity,[status(thm)],[283,280,276,264,262]) ).
tff(285,plain,
store(store(queue_208,head,index_210),seq,select(q37,seq)) = store(q36,seq,earray_214),
inference(monotonicity,[status(thm)],[273,284]) ).
tff(286,plain,
select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(q36,seq,earray_214),head),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(288,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head) ) ),
inference(modus_ponens,[status(thm)],[288,287]) ).
tff(290,plain,
select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head) = select(store(queue_208,head,index_210),head),
inference(unit_resolution,[status(thm)],[289,79,189]) ).
tff(291,plain,
select(store(queue_208,head,index_210),head) = select(store(store(queue_208,head,index_210),seq,select(q37,seq)),head),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
( ( index_210 = s(index_209) )
<=> ( index_210 = s(index_209) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(293,axiom,
index_210 = s(index_209),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(294,plain,
index_210 = s(index_209),
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
s(index_209) = index_210,
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ( queue_208 = store(queue_206,tail,index_207) )
<=> ( queue_208 = store(queue_206,tail,index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(297,axiom,
queue_208 = store(queue_206,tail,index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(298,plain,
queue_208 = store(queue_206,tail,index_207),
inference(modus_ponens,[status(thm)],[297,296]) ).
tff(299,plain,
store(queue_206,tail,index_207) = queue_208,
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
store(store(queue_206,tail,index_207),head,s(index_209)) = store(queue_208,head,index_210),
inference(monotonicity,[status(thm)],[299,295]) ).
tff(301,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = select(store(queue_208,head,index_210),head),
inference(monotonicity,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = s(index_209) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),head) = s(index_209),
inference(unit_resolution,[status(thm)],[302,27]) ).
tff(304,plain,
s(index_209) = select(store(store(queue_206,tail,index_207),head,s(index_209)),head),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
( ( index_209 = select(queue_208,head) )
<=> ( index_209 = select(queue_208,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(306,axiom,
index_209 = select(queue_208,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(307,plain,
index_209 = select(queue_208,head),
inference(modus_ponens,[status(thm)],[306,305]) ).
tff(308,plain,
select(queue_208,head) = index_209,
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
( ( index_207 = s(index_204) )
<=> ( index_207 = s(index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,axiom,
index_207 = s(index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(311,plain,
index_207 = s(index_204),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
s(index_204) = index_207,
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
( ( queue_206 = store(q35,seq,earray_205) )
<=> ( queue_206 = store(q35,seq,earray_205) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,axiom,
queue_206 = store(q35,seq,earray_205),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(315,plain,
queue_206 = store(q35,seq,earray_205),
inference(modus_ponens,[status(thm)],[314,313]) ).
tff(316,plain,
store(q35,seq,earray_205) = queue_206,
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
store(store(q35,seq,earray_205),tail,s(index_204)) = store(queue_206,tail,index_207),
inference(monotonicity,[status(thm)],[316,312]) ).
tff(318,plain,
store(store(q35,seq,earray_205),tail,s(index_204)) = queue_208,
inference(transitivity,[status(thm)],[317,299]) ).
tff(319,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(queue_208,head),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(321,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(modus_ponens,[status(thm)],[321,320]) ).
tff(323,plain,
( ( tail = head )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head) ) ),
inference(unit_resolution,[status(thm)],[322,79]) ).
tff(324,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),head) = select(store(q35,seq,earray_205),head),
inference(unit_resolution,[status(thm)],[323,126]) ).
tff(325,plain,
select(store(q35,seq,earray_205),head) = select(store(store(q35,seq,earray_205),tail,s(index_204)),head),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
( ( earray_205 = store(earray_203,index_204,e35) )
<=> ( earray_205 = store(earray_203,index_204,e35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(327,axiom,
earray_205 = store(earray_203,index_204,e35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(328,plain,
earray_205 = store(earray_203,index_204,e35),
inference(modus_ponens,[status(thm)],[327,326]) ).
tff(329,plain,
store(earray_203,index_204,e35) = earray_205,
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = store(earray_203,index_204,e35) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(331,plain,
select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = store(earray_203,index_204,e35),
inference(unit_resolution,[status(thm)],[330,27]) ).
tff(332,plain,
( ( q35 = queue_202 )
<=> ( q35 = queue_202 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(333,axiom,
q35 = queue_202,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp313) ).
tff(334,plain,
q35 = queue_202,
inference(modus_ponens,[status(thm)],[333,332]) ).
tff(335,plain,
queue_202 = q35,
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ( queue_202 = store(queue_200,tail,index_201) )
<=> ( queue_202 = store(queue_200,tail,index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(337,axiom,
queue_202 = store(queue_200,tail,index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(338,plain,
queue_202 = store(queue_200,tail,index_201),
inference(modus_ponens,[status(thm)],[337,336]) ).
tff(339,plain,
store(queue_200,tail,index_201) = queue_202,
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
store(queue_200,tail,index_201) = q35,
inference(transitivity,[status(thm)],[339,335]) ).
tff(341,plain,
store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)) = store(q35,seq,earray_205),
inference(monotonicity,[status(thm)],[340,329]) ).
tff(342,plain,
select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq) = select(store(q35,seq,earray_205),seq),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
select(store(q35,seq,earray_205),seq) = select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq) ) ),
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(q35,seq,earray_205),seq),
inference(unit_resolution,[status(thm)],[346,79,153]) ).
tff(348,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),seq) = select(store(queue_206,tail,index_207),seq),
inference(monotonicity,[status(thm)],[317]) ).
tff(349,plain,
select(store(queue_206,tail,index_207),seq) = select(store(store(q35,seq,earray_205),tail,s(index_204)),seq),
inference(symmetry,[status(thm)],[348]) ).
tff(350,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(351,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq) ) ),
inference(modus_ponens,[status(thm)],[351,350]) ).
tff(353,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(store(queue_206,tail,index_207),seq),
inference(unit_resolution,[status(thm)],[352,79,162]) ).
tff(354,plain,
store(store(queue_206,tail,index_207),head,s(index_209)) = q36,
inference(transitivity,[status(thm)],[300,272,268]) ).
tff(355,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),seq) = select(q36,seq),
inference(monotonicity,[status(thm)],[354]) ).
tff(356,plain,
select(q36,seq) = select(store(store(queue_206,tail,index_207),head,s(index_209)),seq),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
select(q36,seq) = earray_205,
inference(transitivity,[status(thm)],[356,353,349,347,343,331,329]) ).
tff(358,plain,
store(store(queue_200,tail,index_201),seq,select(q36,seq)) = store(q35,seq,earray_205),
inference(monotonicity,[status(thm)],[340,357]) ).
tff(359,plain,
select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(q35,seq,earray_205),head),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(361,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(modus_ponens,[status(thm)],[361,360]) ).
tff(363,plain,
( ( seq = head )
| ( select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head) ) ),
inference(unit_resolution,[status(thm)],[362,79]) ).
tff(364,plain,
select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head) = select(store(queue_200,tail,index_201),head),
inference(unit_resolution,[status(thm)],[363,189]) ).
tff(365,plain,
select(store(queue_200,tail,index_201),head) = select(store(store(queue_200,tail,index_201),seq,select(q36,seq)),head),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
( ( index_201 = s(index_198) )
<=> ( index_201 = s(index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(367,axiom,
index_201 = s(index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(368,plain,
index_201 = s(index_198),
inference(modus_ponens,[status(thm)],[367,366]) ).
tff(369,plain,
s(index_198) = index_201,
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ( queue_200 = store(q34,seq,earray_199) )
<=> ( queue_200 = store(q34,seq,earray_199) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(371,axiom,
queue_200 = store(q34,seq,earray_199),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(372,plain,
queue_200 = store(q34,seq,earray_199),
inference(modus_ponens,[status(thm)],[371,370]) ).
tff(373,plain,
store(q34,seq,earray_199) = queue_200,
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
store(store(q34,seq,earray_199),tail,s(index_198)) = store(queue_200,tail,index_201),
inference(monotonicity,[status(thm)],[373,369]) ).
tff(375,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(queue_200,tail,index_201),head),
inference(monotonicity,[status(thm)],[374]) ).
tff(376,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(377,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(378,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head) ) ),
inference(modus_ponens,[status(thm)],[377,376]) ).
tff(379,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),head) = select(store(q34,seq,earray_199),head),
inference(unit_resolution,[status(thm)],[378,79,126]) ).
tff(380,plain,
select(store(q34,seq,earray_199),head) = select(store(store(q34,seq,earray_199),tail,s(index_198)),head),
inference(symmetry,[status(thm)],[379]) ).
tff(381,plain,
( ( earray_199 = store(earray_197,index_198,e34) )
<=> ( earray_199 = store(earray_197,index_198,e34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(382,axiom,
earray_199 = store(earray_197,index_198,e34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(383,plain,
earray_199 = store(earray_197,index_198,e34),
inference(modus_ponens,[status(thm)],[382,381]) ).
tff(384,plain,
store(earray_197,index_198,e34) = earray_199,
inference(symmetry,[status(thm)],[383]) ).
tff(385,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = store(earray_197,index_198,e34) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(386,plain,
select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = store(earray_197,index_198,e34),
inference(unit_resolution,[status(thm)],[385,27]) ).
tff(387,plain,
( ( q34 = queue_196 )
<=> ( q34 = queue_196 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,axiom,
q34 = queue_196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp312) ).
tff(389,plain,
q34 = queue_196,
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
queue_196 = q34,
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
( ( queue_196 = store(queue_194,tail,index_195) )
<=> ( queue_196 = store(queue_194,tail,index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(392,axiom,
queue_196 = store(queue_194,tail,index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(393,plain,
queue_196 = store(queue_194,tail,index_195),
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
store(queue_194,tail,index_195) = queue_196,
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
store(queue_194,tail,index_195) = q34,
inference(transitivity,[status(thm)],[394,390]) ).
tff(396,plain,
store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)) = store(q34,seq,earray_199),
inference(monotonicity,[status(thm)],[395,384]) ).
tff(397,plain,
select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq) = select(store(q34,seq,earray_199),seq),
inference(monotonicity,[status(thm)],[396]) ).
tff(398,plain,
select(store(q34,seq,earray_199),seq) = select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(400,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(401,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq) ) ),
inference(modus_ponens,[status(thm)],[400,399]) ).
tff(402,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(store(q34,seq,earray_199),seq),
inference(unit_resolution,[status(thm)],[401,79,153]) ).
tff(403,plain,
store(store(q34,seq,earray_199),tail,s(index_198)) = q35,
inference(transitivity,[status(thm)],[374,339,335]) ).
tff(404,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),seq) = select(q35,seq),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
select(q35,seq) = select(store(store(q34,seq,earray_199),tail,s(index_198)),seq),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
select(q35,seq) = earray_199,
inference(transitivity,[status(thm)],[405,402,398,386,384]) ).
tff(407,plain,
store(store(queue_194,tail,index_195),seq,select(q35,seq)) = store(q34,seq,earray_199),
inference(monotonicity,[status(thm)],[395,406]) ).
tff(408,plain,
select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(q34,seq,earray_199),head),
inference(monotonicity,[status(thm)],[407]) ).
tff(409,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(410,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(411,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head) ) ),
inference(modus_ponens,[status(thm)],[410,409]) ).
tff(412,plain,
select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head) = select(store(queue_194,tail,index_195),head),
inference(unit_resolution,[status(thm)],[411,79,189]) ).
tff(413,plain,
select(store(queue_194,tail,index_195),head) = select(store(store(queue_194,tail,index_195),seq,select(q35,seq)),head),
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
( ( index_195 = s(index_192) )
<=> ( index_195 = s(index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(415,axiom,
index_195 = s(index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(416,plain,
index_195 = s(index_192),
inference(modus_ponens,[status(thm)],[415,414]) ).
tff(417,plain,
s(index_192) = index_195,
inference(symmetry,[status(thm)],[416]) ).
tff(418,plain,
( ( queue_194 = store(q33,seq,earray_193) )
<=> ( queue_194 = store(q33,seq,earray_193) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(419,axiom,
queue_194 = store(q33,seq,earray_193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(420,plain,
queue_194 = store(q33,seq,earray_193),
inference(modus_ponens,[status(thm)],[419,418]) ).
tff(421,plain,
store(q33,seq,earray_193) = queue_194,
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
store(store(q33,seq,earray_193),tail,s(index_192)) = store(queue_194,tail,index_195),
inference(monotonicity,[status(thm)],[421,417]) ).
tff(423,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(queue_194,tail,index_195),head),
inference(monotonicity,[status(thm)],[422]) ).
tff(424,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(425,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(426,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head) ) ),
inference(modus_ponens,[status(thm)],[425,424]) ).
tff(427,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),head) = select(store(q33,seq,earray_193),head),
inference(unit_resolution,[status(thm)],[426,79,126]) ).
tff(428,plain,
select(store(q33,seq,earray_193),head) = select(store(store(q33,seq,earray_193),tail,s(index_192)),head),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
( ( earray_193 = store(earray_191,index_192,e33) )
<=> ( earray_193 = store(earray_191,index_192,e33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(430,axiom,
earray_193 = store(earray_191,index_192,e33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(431,plain,
earray_193 = store(earray_191,index_192,e33),
inference(modus_ponens,[status(thm)],[430,429]) ).
tff(432,plain,
store(earray_191,index_192,e33) = earray_193,
inference(symmetry,[status(thm)],[431]) ).
tff(433,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = store(earray_191,index_192,e33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(434,plain,
select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = store(earray_191,index_192,e33),
inference(unit_resolution,[status(thm)],[433,27]) ).
tff(435,plain,
( ( q33 = queue_190 )
<=> ( q33 = queue_190 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(436,axiom,
q33 = queue_190,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp311) ).
tff(437,plain,
q33 = queue_190,
inference(modus_ponens,[status(thm)],[436,435]) ).
tff(438,plain,
queue_190 = q33,
inference(symmetry,[status(thm)],[437]) ).
tff(439,plain,
( ( queue_190 = store(queue_187,head,index_189) )
<=> ( queue_190 = store(queue_187,head,index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(440,axiom,
queue_190 = store(queue_187,head,index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(441,plain,
queue_190 = store(queue_187,head,index_189),
inference(modus_ponens,[status(thm)],[440,439]) ).
tff(442,plain,
store(queue_187,head,index_189) = queue_190,
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
store(queue_187,head,index_189) = q33,
inference(transitivity,[status(thm)],[442,438]) ).
tff(444,plain,
store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)) = store(q33,seq,earray_193),
inference(monotonicity,[status(thm)],[443,432]) ).
tff(445,plain,
select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq) = select(store(q33,seq,earray_193),seq),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
select(store(q33,seq,earray_193),seq) = select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(448,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(449,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq) ) ),
inference(modus_ponens,[status(thm)],[448,447]) ).
tff(450,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(store(q33,seq,earray_193),seq),
inference(unit_resolution,[status(thm)],[449,79,153]) ).
tff(451,plain,
store(store(q33,seq,earray_193),tail,s(index_192)) = q34,
inference(transitivity,[status(thm)],[422,394,390]) ).
tff(452,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),seq) = select(q34,seq),
inference(monotonicity,[status(thm)],[451]) ).
tff(453,plain,
select(q34,seq) = select(store(store(q33,seq,earray_193),tail,s(index_192)),seq),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
select(q34,seq) = earray_193,
inference(transitivity,[status(thm)],[453,450,446,434,432]) ).
tff(455,plain,
store(store(queue_187,head,index_189),seq,select(q34,seq)) = store(q33,seq,earray_193),
inference(monotonicity,[status(thm)],[443,454]) ).
tff(456,plain,
select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(q33,seq,earray_193),head),
inference(monotonicity,[status(thm)],[455]) ).
tff(457,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(458,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(459,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head) ) ),
inference(modus_ponens,[status(thm)],[458,457]) ).
tff(460,plain,
select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head) = select(store(queue_187,head,index_189),head),
inference(unit_resolution,[status(thm)],[459,79,189]) ).
tff(461,plain,
select(store(queue_187,head,index_189),head) = select(store(store(queue_187,head,index_189),seq,select(q34,seq)),head),
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
( ( index_189 = s(index_188) )
<=> ( index_189 = s(index_188) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(463,axiom,
index_189 = s(index_188),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(464,plain,
index_189 = s(index_188),
inference(modus_ponens,[status(thm)],[463,462]) ).
tff(465,plain,
s(index_188) = index_189,
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
( ( queue_187 = store(queue_185,tail,index_186) )
<=> ( queue_187 = store(queue_185,tail,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(467,axiom,
queue_187 = store(queue_185,tail,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(468,plain,
queue_187 = store(queue_185,tail,index_186),
inference(modus_ponens,[status(thm)],[467,466]) ).
tff(469,plain,
store(queue_185,tail,index_186) = queue_187,
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
store(store(queue_185,tail,index_186),head,s(index_188)) = store(queue_187,head,index_189),
inference(monotonicity,[status(thm)],[469,465]) ).
tff(471,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = select(store(queue_187,head,index_189),head),
inference(monotonicity,[status(thm)],[470]) ).
tff(472,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = s(index_188) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(473,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),head) = s(index_188),
inference(unit_resolution,[status(thm)],[472,27]) ).
tff(474,plain,
s(index_188) = select(store(store(queue_185,tail,index_186),head,s(index_188)),head),
inference(symmetry,[status(thm)],[473]) ).
tff(475,plain,
( ( index_188 = select(queue_187,head) )
<=> ( index_188 = select(queue_187,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(476,axiom,
index_188 = select(queue_187,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(477,plain,
index_188 = select(queue_187,head),
inference(modus_ponens,[status(thm)],[476,475]) ).
tff(478,plain,
select(queue_187,head) = index_188,
inference(symmetry,[status(thm)],[477]) ).
tff(479,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(480,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(481,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[480,479]) ).
tff(482,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[481]) ).
tff(483,plain,
( ( queue_185 = store(q32,seq,earray_184) )
<=> ( queue_185 = store(q32,seq,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(484,axiom,
queue_185 = store(q32,seq,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(485,plain,
queue_185 = store(q32,seq,earray_184),
inference(modus_ponens,[status(thm)],[484,483]) ).
tff(486,plain,
store(q32,seq,earray_184) = queue_185,
inference(symmetry,[status(thm)],[485]) ).
tff(487,plain,
store(store(q32,seq,earray_184),tail,s(index_183)) = store(queue_185,tail,index_186),
inference(monotonicity,[status(thm)],[486,482]) ).
tff(488,plain,
store(store(q32,seq,earray_184),tail,s(index_183)) = queue_187,
inference(transitivity,[status(thm)],[487,469]) ).
tff(489,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(queue_187,head),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(491,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(modus_ponens,[status(thm)],[491,490]) ).
tff(493,plain,
( ( tail = head )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head) ) ),
inference(unit_resolution,[status(thm)],[492,79]) ).
tff(494,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),head) = select(store(q32,seq,earray_184),head),
inference(unit_resolution,[status(thm)],[493,126]) ).
tff(495,plain,
select(store(q32,seq,earray_184),head) = select(store(store(q32,seq,earray_184),tail,s(index_183)),head),
inference(symmetry,[status(thm)],[494]) ).
tff(496,plain,
( ( earray_184 = store(earray_182,index_183,e32) )
<=> ( earray_184 = store(earray_182,index_183,e32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(497,axiom,
earray_184 = store(earray_182,index_183,e32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(498,plain,
earray_184 = store(earray_182,index_183,e32),
inference(modus_ponens,[status(thm)],[497,496]) ).
tff(499,plain,
store(earray_182,index_183,e32) = earray_184,
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = store(earray_182,index_183,e32) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(501,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = store(earray_182,index_183,e32),
inference(unit_resolution,[status(thm)],[500,27]) ).
tff(502,plain,
( ( q32 = queue_181 )
<=> ( q32 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(503,axiom,
q32 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp310) ).
tff(504,plain,
q32 = queue_181,
inference(modus_ponens,[status(thm)],[503,502]) ).
tff(505,plain,
queue_181 = q32,
inference(symmetry,[status(thm)],[504]) ).
tff(506,plain,
( ( queue_181 = store(queue_179,tail,index_180) )
<=> ( queue_181 = store(queue_179,tail,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(507,axiom,
queue_181 = store(queue_179,tail,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(508,plain,
queue_181 = store(queue_179,tail,index_180),
inference(modus_ponens,[status(thm)],[507,506]) ).
tff(509,plain,
store(queue_179,tail,index_180) = queue_181,
inference(symmetry,[status(thm)],[508]) ).
tff(510,plain,
store(queue_179,tail,index_180) = q32,
inference(transitivity,[status(thm)],[509,505]) ).
tff(511,plain,
store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)) = store(q32,seq,earray_184),
inference(monotonicity,[status(thm)],[510,499]) ).
tff(512,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq) = select(store(q32,seq,earray_184),seq),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
select(store(q32,seq,earray_184),seq) = select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(515,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(516,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq) ) ),
inference(modus_ponens,[status(thm)],[515,514]) ).
tff(517,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(q32,seq,earray_184),seq),
inference(unit_resolution,[status(thm)],[516,79,153]) ).
tff(518,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),seq) = select(store(queue_185,tail,index_186),seq),
inference(monotonicity,[status(thm)],[487]) ).
tff(519,plain,
select(store(queue_185,tail,index_186),seq) = select(store(store(q32,seq,earray_184),tail,s(index_183)),seq),
inference(symmetry,[status(thm)],[518]) ).
tff(520,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(521,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(522,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq) ) ),
inference(modus_ponens,[status(thm)],[521,520]) ).
tff(523,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(store(queue_185,tail,index_186),seq),
inference(unit_resolution,[status(thm)],[522,79,162]) ).
tff(524,plain,
store(store(queue_185,tail,index_186),head,s(index_188)) = q33,
inference(transitivity,[status(thm)],[470,442,438]) ).
tff(525,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),seq) = select(q33,seq),
inference(monotonicity,[status(thm)],[524]) ).
tff(526,plain,
select(q33,seq) = select(store(store(queue_185,tail,index_186),head,s(index_188)),seq),
inference(symmetry,[status(thm)],[525]) ).
tff(527,plain,
select(q33,seq) = earray_184,
inference(transitivity,[status(thm)],[526,523,519,517,513,501,499]) ).
tff(528,plain,
store(store(queue_179,tail,index_180),seq,select(q33,seq)) = store(q32,seq,earray_184),
inference(monotonicity,[status(thm)],[510,527]) ).
tff(529,plain,
select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(q32,seq,earray_184),head),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(531,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(532,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(modus_ponens,[status(thm)],[531,530]) ).
tff(533,plain,
( ( seq = head )
| ( select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(unit_resolution,[status(thm)],[532,79]) ).
tff(534,plain,
select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head) = select(store(queue_179,tail,index_180),head),
inference(unit_resolution,[status(thm)],[533,189]) ).
tff(535,plain,
select(store(queue_179,tail,index_180),head) = select(store(store(queue_179,tail,index_180),seq,select(q33,seq)),head),
inference(symmetry,[status(thm)],[534]) ).
tff(536,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(537,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(538,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[537,536]) ).
tff(539,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[538]) ).
tff(540,plain,
( ( queue_179 = store(q31,seq,earray_178) )
<=> ( queue_179 = store(q31,seq,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(541,axiom,
queue_179 = store(q31,seq,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(542,plain,
queue_179 = store(q31,seq,earray_178),
inference(modus_ponens,[status(thm)],[541,540]) ).
tff(543,plain,
store(q31,seq,earray_178) = queue_179,
inference(symmetry,[status(thm)],[542]) ).
tff(544,plain,
store(store(q31,seq,earray_178),tail,s(index_177)) = store(queue_179,tail,index_180),
inference(monotonicity,[status(thm)],[543,539]) ).
tff(545,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(queue_179,tail,index_180),head),
inference(monotonicity,[status(thm)],[544]) ).
tff(546,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(547,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(548,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head) ) ),
inference(modus_ponens,[status(thm)],[547,546]) ).
tff(549,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),head) = select(store(q31,seq,earray_178),head),
inference(unit_resolution,[status(thm)],[548,79,126]) ).
tff(550,plain,
select(store(q31,seq,earray_178),head) = select(store(store(q31,seq,earray_178),tail,s(index_177)),head),
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
( ( earray_178 = store(earray_176,index_177,e31) )
<=> ( earray_178 = store(earray_176,index_177,e31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(552,axiom,
earray_178 = store(earray_176,index_177,e31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(553,plain,
earray_178 = store(earray_176,index_177,e31),
inference(modus_ponens,[status(thm)],[552,551]) ).
tff(554,plain,
store(earray_176,index_177,e31) = earray_178,
inference(symmetry,[status(thm)],[553]) ).
tff(555,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = store(earray_176,index_177,e31) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(556,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = store(earray_176,index_177,e31),
inference(unit_resolution,[status(thm)],[555,27]) ).
tff(557,plain,
( ( q31 = queue_175 )
<=> ( q31 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(558,axiom,
q31 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp309) ).
tff(559,plain,
q31 = queue_175,
inference(modus_ponens,[status(thm)],[558,557]) ).
tff(560,plain,
queue_175 = q31,
inference(symmetry,[status(thm)],[559]) ).
tff(561,plain,
( ( queue_175 = store(queue_173,tail,index_174) )
<=> ( queue_175 = store(queue_173,tail,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(562,axiom,
queue_175 = store(queue_173,tail,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(563,plain,
queue_175 = store(queue_173,tail,index_174),
inference(modus_ponens,[status(thm)],[562,561]) ).
tff(564,plain,
store(queue_173,tail,index_174) = queue_175,
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
store(queue_173,tail,index_174) = q31,
inference(transitivity,[status(thm)],[564,560]) ).
tff(566,plain,
store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)) = store(q31,seq,earray_178),
inference(monotonicity,[status(thm)],[565,554]) ).
tff(567,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq) = select(store(q31,seq,earray_178),seq),
inference(monotonicity,[status(thm)],[566]) ).
tff(568,plain,
select(store(q31,seq,earray_178),seq) = select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq),
inference(symmetry,[status(thm)],[567]) ).
tff(569,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(570,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(571,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq) ) ),
inference(modus_ponens,[status(thm)],[570,569]) ).
tff(572,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(store(q31,seq,earray_178),seq),
inference(unit_resolution,[status(thm)],[571,79,153]) ).
tff(573,plain,
store(store(q31,seq,earray_178),tail,s(index_177)) = q32,
inference(transitivity,[status(thm)],[544,509,505]) ).
tff(574,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),seq) = select(q32,seq),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
select(q32,seq) = select(store(store(q31,seq,earray_178),tail,s(index_177)),seq),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
select(q32,seq) = earray_178,
inference(transitivity,[status(thm)],[575,572,568,556,554]) ).
tff(577,plain,
store(store(queue_173,tail,index_174),seq,select(q32,seq)) = store(q31,seq,earray_178),
inference(monotonicity,[status(thm)],[565,576]) ).
tff(578,plain,
select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(q31,seq,earray_178),head),
inference(monotonicity,[status(thm)],[577]) ).
tff(579,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(580,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(581,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(modus_ponens,[status(thm)],[580,579]) ).
tff(582,plain,
select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head) = select(store(queue_173,tail,index_174),head),
inference(unit_resolution,[status(thm)],[581,79,189]) ).
tff(583,plain,
select(store(queue_173,tail,index_174),head) = select(store(store(queue_173,tail,index_174),seq,select(q32,seq)),head),
inference(symmetry,[status(thm)],[582]) ).
tff(584,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(585,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(586,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[585,584]) ).
tff(587,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[586]) ).
tff(588,plain,
( ( queue_173 = store(q30,seq,earray_172) )
<=> ( queue_173 = store(q30,seq,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(589,axiom,
queue_173 = store(q30,seq,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(590,plain,
queue_173 = store(q30,seq,earray_172),
inference(modus_ponens,[status(thm)],[589,588]) ).
tff(591,plain,
store(q30,seq,earray_172) = queue_173,
inference(symmetry,[status(thm)],[590]) ).
tff(592,plain,
store(store(q30,seq,earray_172),tail,s(index_171)) = store(queue_173,tail,index_174),
inference(monotonicity,[status(thm)],[591,587]) ).
tff(593,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(queue_173,tail,index_174),head),
inference(monotonicity,[status(thm)],[592]) ).
tff(594,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(595,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(596,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head) ) ),
inference(modus_ponens,[status(thm)],[595,594]) ).
tff(597,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),head) = select(store(q30,seq,earray_172),head),
inference(unit_resolution,[status(thm)],[596,79,126]) ).
tff(598,plain,
select(store(q30,seq,earray_172),head) = select(store(store(q30,seq,earray_172),tail,s(index_171)),head),
inference(symmetry,[status(thm)],[597]) ).
tff(599,plain,
( ( earray_172 = store(earray_170,index_171,e30) )
<=> ( earray_172 = store(earray_170,index_171,e30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(600,axiom,
earray_172 = store(earray_170,index_171,e30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(601,plain,
earray_172 = store(earray_170,index_171,e30),
inference(modus_ponens,[status(thm)],[600,599]) ).
tff(602,plain,
store(earray_170,index_171,e30) = earray_172,
inference(symmetry,[status(thm)],[601]) ).
tff(603,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = store(earray_170,index_171,e30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(604,plain,
select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = store(earray_170,index_171,e30),
inference(unit_resolution,[status(thm)],[603,27]) ).
tff(605,plain,
( ( q30 = queue_169 )
<=> ( q30 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(606,axiom,
q30 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp308) ).
tff(607,plain,
q30 = queue_169,
inference(modus_ponens,[status(thm)],[606,605]) ).
tff(608,plain,
queue_169 = q30,
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
( ( queue_169 = store(queue_166,head,index_168) )
<=> ( queue_169 = store(queue_166,head,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(610,axiom,
queue_169 = store(queue_166,head,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(611,plain,
queue_169 = store(queue_166,head,index_168),
inference(modus_ponens,[status(thm)],[610,609]) ).
tff(612,plain,
store(queue_166,head,index_168) = queue_169,
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
store(queue_166,head,index_168) = q30,
inference(transitivity,[status(thm)],[612,608]) ).
tff(614,plain,
store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)) = store(q30,seq,earray_172),
inference(monotonicity,[status(thm)],[613,602]) ).
tff(615,plain,
select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq) = select(store(q30,seq,earray_172),seq),
inference(monotonicity,[status(thm)],[614]) ).
tff(616,plain,
select(store(q30,seq,earray_172),seq) = select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq),
inference(symmetry,[status(thm)],[615]) ).
tff(617,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(618,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(619,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq) ) ),
inference(modus_ponens,[status(thm)],[618,617]) ).
tff(620,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(store(q30,seq,earray_172),seq),
inference(unit_resolution,[status(thm)],[619,79,153]) ).
tff(621,plain,
store(store(q30,seq,earray_172),tail,s(index_171)) = q31,
inference(transitivity,[status(thm)],[592,564,560]) ).
tff(622,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),seq) = select(q31,seq),
inference(monotonicity,[status(thm)],[621]) ).
tff(623,plain,
select(q31,seq) = select(store(store(q30,seq,earray_172),tail,s(index_171)),seq),
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
select(q31,seq) = earray_172,
inference(transitivity,[status(thm)],[623,620,616,604,602]) ).
tff(625,plain,
store(store(queue_166,head,index_168),seq,select(q31,seq)) = store(q30,seq,earray_172),
inference(monotonicity,[status(thm)],[613,624]) ).
tff(626,plain,
select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(q30,seq,earray_172),head),
inference(monotonicity,[status(thm)],[625]) ).
tff(627,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(628,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(629,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head) ) ),
inference(modus_ponens,[status(thm)],[628,627]) ).
tff(630,plain,
select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head) = select(store(queue_166,head,index_168),head),
inference(unit_resolution,[status(thm)],[629,79,189]) ).
tff(631,plain,
select(store(queue_166,head,index_168),head) = select(store(store(queue_166,head,index_168),seq,select(q31,seq)),head),
inference(symmetry,[status(thm)],[630]) ).
tff(632,plain,
( ( index_168 = s(index_167) )
<=> ( index_168 = s(index_167) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(633,axiom,
index_168 = s(index_167),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(634,plain,
index_168 = s(index_167),
inference(modus_ponens,[status(thm)],[633,632]) ).
tff(635,plain,
s(index_167) = index_168,
inference(symmetry,[status(thm)],[634]) ).
tff(636,plain,
( ( queue_166 = store(queue_164,tail,index_165) )
<=> ( queue_166 = store(queue_164,tail,index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(637,axiom,
queue_166 = store(queue_164,tail,index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(638,plain,
queue_166 = store(queue_164,tail,index_165),
inference(modus_ponens,[status(thm)],[637,636]) ).
tff(639,plain,
store(queue_164,tail,index_165) = queue_166,
inference(symmetry,[status(thm)],[638]) ).
tff(640,plain,
store(store(queue_164,tail,index_165),head,s(index_167)) = store(queue_166,head,index_168),
inference(monotonicity,[status(thm)],[639,635]) ).
tff(641,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = select(store(queue_166,head,index_168),head),
inference(monotonicity,[status(thm)],[640]) ).
tff(642,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = s(index_167) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(643,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),head) = s(index_167),
inference(unit_resolution,[status(thm)],[642,27]) ).
tff(644,plain,
s(index_167) = select(store(store(queue_164,tail,index_165),head,s(index_167)),head),
inference(symmetry,[status(thm)],[643]) ).
tff(645,plain,
( ( index_167 = select(queue_166,head) )
<=> ( index_167 = select(queue_166,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(646,axiom,
index_167 = select(queue_166,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(647,plain,
index_167 = select(queue_166,head),
inference(modus_ponens,[status(thm)],[646,645]) ).
tff(648,plain,
select(queue_166,head) = index_167,
inference(symmetry,[status(thm)],[647]) ).
tff(649,plain,
( ( index_165 = s(index_162) )
<=> ( index_165 = s(index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(650,axiom,
index_165 = s(index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(651,plain,
index_165 = s(index_162),
inference(modus_ponens,[status(thm)],[650,649]) ).
tff(652,plain,
s(index_162) = index_165,
inference(symmetry,[status(thm)],[651]) ).
tff(653,plain,
( ( queue_164 = store(q29,seq,earray_163) )
<=> ( queue_164 = store(q29,seq,earray_163) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(654,axiom,
queue_164 = store(q29,seq,earray_163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(655,plain,
queue_164 = store(q29,seq,earray_163),
inference(modus_ponens,[status(thm)],[654,653]) ).
tff(656,plain,
store(q29,seq,earray_163) = queue_164,
inference(symmetry,[status(thm)],[655]) ).
tff(657,plain,
store(store(q29,seq,earray_163),tail,s(index_162)) = store(queue_164,tail,index_165),
inference(monotonicity,[status(thm)],[656,652]) ).
tff(658,plain,
store(store(q29,seq,earray_163),tail,s(index_162)) = queue_166,
inference(transitivity,[status(thm)],[657,639]) ).
tff(659,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(queue_166,head),
inference(monotonicity,[status(thm)],[658]) ).
tff(660,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(661,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(662,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(modus_ponens,[status(thm)],[661,660]) ).
tff(663,plain,
( ( tail = head )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head) ) ),
inference(unit_resolution,[status(thm)],[662,79]) ).
tff(664,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),head) = select(store(q29,seq,earray_163),head),
inference(unit_resolution,[status(thm)],[663,126]) ).
tff(665,plain,
select(store(q29,seq,earray_163),head) = select(store(store(q29,seq,earray_163),tail,s(index_162)),head),
inference(symmetry,[status(thm)],[664]) ).
tff(666,plain,
( ( earray_163 = store(earray_161,index_162,e29) )
<=> ( earray_163 = store(earray_161,index_162,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(667,axiom,
earray_163 = store(earray_161,index_162,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp21) ).
tff(668,plain,
earray_163 = store(earray_161,index_162,e29),
inference(modus_ponens,[status(thm)],[667,666]) ).
tff(669,plain,
store(earray_161,index_162,e29) = earray_163,
inference(symmetry,[status(thm)],[668]) ).
tff(670,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = store(earray_161,index_162,e29) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(671,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = store(earray_161,index_162,e29),
inference(unit_resolution,[status(thm)],[670,27]) ).
tff(672,plain,
( ( q29 = queue_151 )
<=> ( q29 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(673,axiom,
q29 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp306) ).
tff(674,plain,
q29 = queue_151,
inference(modus_ponens,[status(thm)],[673,672]) ).
tff(675,plain,
queue_151 = q29,
inference(symmetry,[status(thm)],[674]) ).
tff(676,plain,
( ( queue_151 = store(queue_149,tail,index_150) )
<=> ( queue_151 = store(queue_149,tail,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(677,axiom,
queue_151 = store(queue_149,tail,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(678,plain,
queue_151 = store(queue_149,tail,index_150),
inference(modus_ponens,[status(thm)],[677,676]) ).
tff(679,plain,
store(queue_149,tail,index_150) = queue_151,
inference(symmetry,[status(thm)],[678]) ).
tff(680,plain,
store(queue_149,tail,index_150) = q29,
inference(transitivity,[status(thm)],[679,675]) ).
tff(681,plain,
store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)) = store(q29,seq,earray_163),
inference(monotonicity,[status(thm)],[680,669]) ).
tff(682,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq) = select(store(q29,seq,earray_163),seq),
inference(monotonicity,[status(thm)],[681]) ).
tff(683,plain,
select(store(q29,seq,earray_163),seq) = select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(685,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(686,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq) ) ),
inference(modus_ponens,[status(thm)],[685,684]) ).
tff(687,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(q29,seq,earray_163),seq),
inference(unit_resolution,[status(thm)],[686,79,153]) ).
tff(688,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),seq) = select(store(queue_164,tail,index_165),seq),
inference(monotonicity,[status(thm)],[657]) ).
tff(689,plain,
select(store(queue_164,tail,index_165),seq) = select(store(store(q29,seq,earray_163),tail,s(index_162)),seq),
inference(symmetry,[status(thm)],[688]) ).
tff(690,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(691,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(692,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq) ) ),
inference(modus_ponens,[status(thm)],[691,690]) ).
tff(693,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(store(queue_164,tail,index_165),seq),
inference(unit_resolution,[status(thm)],[692,79,162]) ).
tff(694,plain,
store(store(queue_164,tail,index_165),head,s(index_167)) = q30,
inference(transitivity,[status(thm)],[640,612,608]) ).
tff(695,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),seq) = select(q30,seq),
inference(monotonicity,[status(thm)],[694]) ).
tff(696,plain,
select(q30,seq) = select(store(store(queue_164,tail,index_165),head,s(index_167)),seq),
inference(symmetry,[status(thm)],[695]) ).
tff(697,plain,
select(q30,seq) = earray_163,
inference(transitivity,[status(thm)],[696,693,689,687,683,671,669]) ).
tff(698,plain,
store(store(queue_149,tail,index_150),seq,select(q30,seq)) = store(q29,seq,earray_163),
inference(monotonicity,[status(thm)],[680,697]) ).
tff(699,plain,
select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(q29,seq,earray_163),head),
inference(monotonicity,[status(thm)],[698]) ).
tff(700,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(701,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(702,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(modus_ponens,[status(thm)],[701,700]) ).
tff(703,plain,
( ( seq = head )
| ( select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(unit_resolution,[status(thm)],[702,79]) ).
tff(704,plain,
select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head) = select(store(queue_149,tail,index_150),head),
inference(unit_resolution,[status(thm)],[703,189]) ).
tff(705,plain,
select(store(queue_149,tail,index_150),head) = select(store(store(queue_149,tail,index_150),seq,select(q30,seq)),head),
inference(symmetry,[status(thm)],[704]) ).
tff(706,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(707,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(708,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[707,706]) ).
tff(709,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[708]) ).
tff(710,plain,
( ( queue_149 = store(q28,seq,earray_148) )
<=> ( queue_149 = store(q28,seq,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(711,axiom,
queue_149 = store(q28,seq,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(712,plain,
queue_149 = store(q28,seq,earray_148),
inference(modus_ponens,[status(thm)],[711,710]) ).
tff(713,plain,
store(q28,seq,earray_148) = queue_149,
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
store(store(q28,seq,earray_148),tail,s(index_147)) = store(queue_149,tail,index_150),
inference(monotonicity,[status(thm)],[713,709]) ).
tff(715,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(queue_149,tail,index_150),head),
inference(monotonicity,[status(thm)],[714]) ).
tff(716,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(717,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(718,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head) ) ),
inference(modus_ponens,[status(thm)],[717,716]) ).
tff(719,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),head) = select(store(q28,seq,earray_148),head),
inference(unit_resolution,[status(thm)],[718,79,126]) ).
tff(720,plain,
select(store(q28,seq,earray_148),head) = select(store(store(q28,seq,earray_148),tail,s(index_147)),head),
inference(symmetry,[status(thm)],[719]) ).
tff(721,plain,
( ( earray_148 = store(earray_146,index_147,e28) )
<=> ( earray_148 = store(earray_146,index_147,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(722,axiom,
earray_148 = store(earray_146,index_147,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(723,plain,
earray_148 = store(earray_146,index_147,e28),
inference(modus_ponens,[status(thm)],[722,721]) ).
tff(724,plain,
store(earray_146,index_147,e28) = earray_148,
inference(symmetry,[status(thm)],[723]) ).
tff(725,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = store(earray_146,index_147,e28) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(726,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = store(earray_146,index_147,e28),
inference(unit_resolution,[status(thm)],[725,27]) ).
tff(727,plain,
( ( q28 = queue_145 )
<=> ( q28 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(728,axiom,
q28 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp305) ).
tff(729,plain,
q28 = queue_145,
inference(modus_ponens,[status(thm)],[728,727]) ).
tff(730,plain,
queue_145 = q28,
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
( ( queue_145 = store(queue_143,tail,index_144) )
<=> ( queue_145 = store(queue_143,tail,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(732,axiom,
queue_145 = store(queue_143,tail,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(733,plain,
queue_145 = store(queue_143,tail,index_144),
inference(modus_ponens,[status(thm)],[732,731]) ).
tff(734,plain,
store(queue_143,tail,index_144) = queue_145,
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
store(queue_143,tail,index_144) = q28,
inference(transitivity,[status(thm)],[734,730]) ).
tff(736,plain,
store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)) = store(q28,seq,earray_148),
inference(monotonicity,[status(thm)],[735,724]) ).
tff(737,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq) = select(store(q28,seq,earray_148),seq),
inference(monotonicity,[status(thm)],[736]) ).
tff(738,plain,
select(store(q28,seq,earray_148),seq) = select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(740,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(741,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq) ) ),
inference(modus_ponens,[status(thm)],[740,739]) ).
tff(742,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(store(q28,seq,earray_148),seq),
inference(unit_resolution,[status(thm)],[741,79,153]) ).
tff(743,plain,
store(store(q28,seq,earray_148),tail,s(index_147)) = q29,
inference(transitivity,[status(thm)],[714,679,675]) ).
tff(744,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),seq) = select(q29,seq),
inference(monotonicity,[status(thm)],[743]) ).
tff(745,plain,
select(q29,seq) = select(store(store(q28,seq,earray_148),tail,s(index_147)),seq),
inference(symmetry,[status(thm)],[744]) ).
tff(746,plain,
select(q29,seq) = earray_148,
inference(transitivity,[status(thm)],[745,742,738,726,724]) ).
tff(747,plain,
store(store(queue_143,tail,index_144),seq,select(q29,seq)) = store(q28,seq,earray_148),
inference(monotonicity,[status(thm)],[735,746]) ).
tff(748,plain,
select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(q28,seq,earray_148),head),
inference(monotonicity,[status(thm)],[747]) ).
tff(749,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(750,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(751,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(modus_ponens,[status(thm)],[750,749]) ).
tff(752,plain,
select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head) = select(store(queue_143,tail,index_144),head),
inference(unit_resolution,[status(thm)],[751,79,189]) ).
tff(753,plain,
select(store(queue_143,tail,index_144),head) = select(store(store(queue_143,tail,index_144),seq,select(q29,seq)),head),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(755,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(756,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[755,754]) ).
tff(757,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[756]) ).
tff(758,plain,
( ( queue_143 = store(q27,seq,earray_142) )
<=> ( queue_143 = store(q27,seq,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(759,axiom,
queue_143 = store(q27,seq,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(760,plain,
queue_143 = store(q27,seq,earray_142),
inference(modus_ponens,[status(thm)],[759,758]) ).
tff(761,plain,
store(q27,seq,earray_142) = queue_143,
inference(symmetry,[status(thm)],[760]) ).
tff(762,plain,
store(store(q27,seq,earray_142),tail,s(index_141)) = store(queue_143,tail,index_144),
inference(monotonicity,[status(thm)],[761,757]) ).
tff(763,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(queue_143,tail,index_144),head),
inference(monotonicity,[status(thm)],[762]) ).
tff(764,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(765,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(766,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head) ) ),
inference(modus_ponens,[status(thm)],[765,764]) ).
tff(767,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),head) = select(store(q27,seq,earray_142),head),
inference(unit_resolution,[status(thm)],[766,79,126]) ).
tff(768,plain,
select(store(q27,seq,earray_142),head) = select(store(store(q27,seq,earray_142),tail,s(index_141)),head),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
( ( earray_142 = store(earray_140,index_141,e27) )
<=> ( earray_142 = store(earray_140,index_141,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(770,axiom,
earray_142 = store(earray_140,index_141,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp14) ).
tff(771,plain,
earray_142 = store(earray_140,index_141,e27),
inference(modus_ponens,[status(thm)],[770,769]) ).
tff(772,plain,
store(earray_140,index_141,e27) = earray_142,
inference(symmetry,[status(thm)],[771]) ).
tff(773,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = store(earray_140,index_141,e27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(774,plain,
select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = store(earray_140,index_141,e27),
inference(unit_resolution,[status(thm)],[773,27]) ).
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',hyp304) ).
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 = store(queue_136,head,index_138) )
<=> ( queue_139 = store(queue_136,head,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(780,axiom,
queue_139 = store(queue_136,head,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(781,plain,
queue_139 = store(queue_136,head,index_138),
inference(modus_ponens,[status(thm)],[780,779]) ).
tff(782,plain,
store(queue_136,head,index_138) = queue_139,
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
store(queue_136,head,index_138) = q27,
inference(transitivity,[status(thm)],[782,778]) ).
tff(784,plain,
store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)) = store(q27,seq,earray_142),
inference(monotonicity,[status(thm)],[783,772]) ).
tff(785,plain,
select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq) = select(store(q27,seq,earray_142),seq),
inference(monotonicity,[status(thm)],[784]) ).
tff(786,plain,
select(store(q27,seq,earray_142),seq) = select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq),
inference(symmetry,[status(thm)],[785]) ).
tff(787,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(788,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(789,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq) ) ),
inference(modus_ponens,[status(thm)],[788,787]) ).
tff(790,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(store(q27,seq,earray_142),seq),
inference(unit_resolution,[status(thm)],[789,79,153]) ).
tff(791,plain,
store(store(q27,seq,earray_142),tail,s(index_141)) = q28,
inference(transitivity,[status(thm)],[762,734,730]) ).
tff(792,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),seq) = select(q28,seq),
inference(monotonicity,[status(thm)],[791]) ).
tff(793,plain,
select(q28,seq) = select(store(store(q27,seq,earray_142),tail,s(index_141)),seq),
inference(symmetry,[status(thm)],[792]) ).
tff(794,plain,
select(q28,seq) = earray_142,
inference(transitivity,[status(thm)],[793,790,786,774,772]) ).
tff(795,plain,
store(store(queue_136,head,index_138),seq,select(q28,seq)) = store(q27,seq,earray_142),
inference(monotonicity,[status(thm)],[783,794]) ).
tff(796,plain,
select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(q27,seq,earray_142),head),
inference(monotonicity,[status(thm)],[795]) ).
tff(797,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(798,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(799,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head) ) ),
inference(modus_ponens,[status(thm)],[798,797]) ).
tff(800,plain,
select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head) = select(store(queue_136,head,index_138),head),
inference(unit_resolution,[status(thm)],[799,79,189]) ).
tff(801,plain,
select(store(queue_136,head,index_138),head) = select(store(store(queue_136,head,index_138),seq,select(q28,seq)),head),
inference(symmetry,[status(thm)],[800]) ).
tff(802,plain,
( ( index_138 = s(index_137) )
<=> ( index_138 = s(index_137) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(803,axiom,
index_138 = s(index_137),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(804,plain,
index_138 = s(index_137),
inference(modus_ponens,[status(thm)],[803,802]) ).
tff(805,plain,
s(index_137) = index_138,
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
( ( queue_136 = store(queue_134,tail,index_135) )
<=> ( queue_136 = store(queue_134,tail,index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(807,axiom,
queue_136 = store(queue_134,tail,index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(808,plain,
queue_136 = store(queue_134,tail,index_135),
inference(modus_ponens,[status(thm)],[807,806]) ).
tff(809,plain,
store(queue_134,tail,index_135) = queue_136,
inference(symmetry,[status(thm)],[808]) ).
tff(810,plain,
store(store(queue_134,tail,index_135),head,s(index_137)) = store(queue_136,head,index_138),
inference(monotonicity,[status(thm)],[809,805]) ).
tff(811,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = select(store(queue_136,head,index_138),head),
inference(monotonicity,[status(thm)],[810]) ).
tff(812,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = s(index_137) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(813,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),head) = s(index_137),
inference(unit_resolution,[status(thm)],[812,27]) ).
tff(814,plain,
s(index_137) = select(store(store(queue_134,tail,index_135),head,s(index_137)),head),
inference(symmetry,[status(thm)],[813]) ).
tff(815,plain,
( ( index_137 = select(queue_136,head) )
<=> ( index_137 = select(queue_136,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(816,axiom,
index_137 = select(queue_136,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(817,plain,
index_137 = select(queue_136,head),
inference(modus_ponens,[status(thm)],[816,815]) ).
tff(818,plain,
select(queue_136,head) = index_137,
inference(symmetry,[status(thm)],[817]) ).
tff(819,plain,
( ( index_135 = s(index_132) )
<=> ( index_135 = s(index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(820,axiom,
index_135 = s(index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(821,plain,
index_135 = s(index_132),
inference(modus_ponens,[status(thm)],[820,819]) ).
tff(822,plain,
s(index_132) = index_135,
inference(symmetry,[status(thm)],[821]) ).
tff(823,plain,
( ( queue_134 = store(q26,seq,earray_133) )
<=> ( queue_134 = store(q26,seq,earray_133) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(824,axiom,
queue_134 = store(q26,seq,earray_133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(825,plain,
queue_134 = store(q26,seq,earray_133),
inference(modus_ponens,[status(thm)],[824,823]) ).
tff(826,plain,
store(q26,seq,earray_133) = queue_134,
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
store(store(q26,seq,earray_133),tail,s(index_132)) = store(queue_134,tail,index_135),
inference(monotonicity,[status(thm)],[826,822]) ).
tff(828,plain,
store(store(q26,seq,earray_133),tail,s(index_132)) = queue_136,
inference(transitivity,[status(thm)],[827,809]) ).
tff(829,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(queue_136,head),
inference(monotonicity,[status(thm)],[828]) ).
tff(830,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(831,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(832,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(modus_ponens,[status(thm)],[831,830]) ).
tff(833,plain,
( ( tail = head )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head) ) ),
inference(unit_resolution,[status(thm)],[832,79]) ).
tff(834,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),head) = select(store(q26,seq,earray_133),head),
inference(unit_resolution,[status(thm)],[833,126]) ).
tff(835,plain,
select(store(q26,seq,earray_133),head) = select(store(store(q26,seq,earray_133),tail,s(index_132)),head),
inference(symmetry,[status(thm)],[834]) ).
tff(836,plain,
( ( earray_133 = store(earray_131,index_132,e26) )
<=> ( earray_133 = store(earray_131,index_132,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(837,axiom,
earray_133 = store(earray_131,index_132,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(838,plain,
earray_133 = store(earray_131,index_132,e26),
inference(modus_ponens,[status(thm)],[837,836]) ).
tff(839,plain,
store(earray_131,index_132,e26) = earray_133,
inference(symmetry,[status(thm)],[838]) ).
tff(840,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = store(earray_131,index_132,e26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(841,plain,
select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = store(earray_131,index_132,e26),
inference(unit_resolution,[status(thm)],[840,27]) ).
tff(842,plain,
( ( q26 = queue_130 )
<=> ( q26 = queue_130 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(843,axiom,
q26 = queue_130,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp303) ).
tff(844,plain,
q26 = queue_130,
inference(modus_ponens,[status(thm)],[843,842]) ).
tff(845,plain,
queue_130 = q26,
inference(symmetry,[status(thm)],[844]) ).
tff(846,plain,
( ( queue_130 = store(queue_128,tail,index_129) )
<=> ( queue_130 = store(queue_128,tail,index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(847,axiom,
queue_130 = store(queue_128,tail,index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(848,plain,
queue_130 = store(queue_128,tail,index_129),
inference(modus_ponens,[status(thm)],[847,846]) ).
tff(849,plain,
store(queue_128,tail,index_129) = queue_130,
inference(symmetry,[status(thm)],[848]) ).
tff(850,plain,
store(queue_128,tail,index_129) = q26,
inference(transitivity,[status(thm)],[849,845]) ).
tff(851,plain,
store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)) = store(q26,seq,earray_133),
inference(monotonicity,[status(thm)],[850,839]) ).
tff(852,plain,
select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq) = select(store(q26,seq,earray_133),seq),
inference(monotonicity,[status(thm)],[851]) ).
tff(853,plain,
select(store(q26,seq,earray_133),seq) = select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq),
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(855,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(856,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq) ) ),
inference(modus_ponens,[status(thm)],[855,854]) ).
tff(857,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(q26,seq,earray_133),seq),
inference(unit_resolution,[status(thm)],[856,79,153]) ).
tff(858,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),seq) = select(store(queue_134,tail,index_135),seq),
inference(monotonicity,[status(thm)],[827]) ).
tff(859,plain,
select(store(queue_134,tail,index_135),seq) = select(store(store(q26,seq,earray_133),tail,s(index_132)),seq),
inference(symmetry,[status(thm)],[858]) ).
tff(860,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(861,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(862,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq) ) ),
inference(modus_ponens,[status(thm)],[861,860]) ).
tff(863,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(store(queue_134,tail,index_135),seq),
inference(unit_resolution,[status(thm)],[862,79,162]) ).
tff(864,plain,
store(store(queue_134,tail,index_135),head,s(index_137)) = q27,
inference(transitivity,[status(thm)],[810,782,778]) ).
tff(865,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),seq) = select(q27,seq),
inference(monotonicity,[status(thm)],[864]) ).
tff(866,plain,
select(q27,seq) = select(store(store(queue_134,tail,index_135),head,s(index_137)),seq),
inference(symmetry,[status(thm)],[865]) ).
tff(867,plain,
select(q27,seq) = earray_133,
inference(transitivity,[status(thm)],[866,863,859,857,853,841,839]) ).
tff(868,plain,
store(store(queue_128,tail,index_129),seq,select(q27,seq)) = store(q26,seq,earray_133),
inference(monotonicity,[status(thm)],[850,867]) ).
tff(869,plain,
select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(q26,seq,earray_133),head),
inference(monotonicity,[status(thm)],[868]) ).
tff(870,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(871,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(872,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(modus_ponens,[status(thm)],[871,870]) ).
tff(873,plain,
( ( seq = head )
| ( select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head) ) ),
inference(unit_resolution,[status(thm)],[872,79]) ).
tff(874,plain,
select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head) = select(store(queue_128,tail,index_129),head),
inference(unit_resolution,[status(thm)],[873,189]) ).
tff(875,plain,
select(store(queue_128,tail,index_129),head) = select(store(store(queue_128,tail,index_129),seq,select(q27,seq)),head),
inference(symmetry,[status(thm)],[874]) ).
tff(876,plain,
( ( index_129 = s(index_126) )
<=> ( index_129 = s(index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(877,axiom,
index_129 = s(index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(878,plain,
index_129 = s(index_126),
inference(modus_ponens,[status(thm)],[877,876]) ).
tff(879,plain,
s(index_126) = index_129,
inference(symmetry,[status(thm)],[878]) ).
tff(880,plain,
( ( queue_128 = store(q25,seq,earray_127) )
<=> ( queue_128 = store(q25,seq,earray_127) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(881,axiom,
queue_128 = store(q25,seq,earray_127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(882,plain,
queue_128 = store(q25,seq,earray_127),
inference(modus_ponens,[status(thm)],[881,880]) ).
tff(883,plain,
store(q25,seq,earray_127) = queue_128,
inference(symmetry,[status(thm)],[882]) ).
tff(884,plain,
store(store(q25,seq,earray_127),tail,s(index_126)) = store(queue_128,tail,index_129),
inference(monotonicity,[status(thm)],[883,879]) ).
tff(885,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(queue_128,tail,index_129),head),
inference(monotonicity,[status(thm)],[884]) ).
tff(886,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(887,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(888,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head) ) ),
inference(modus_ponens,[status(thm)],[887,886]) ).
tff(889,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),head) = select(store(q25,seq,earray_127),head),
inference(unit_resolution,[status(thm)],[888,79,126]) ).
tff(890,plain,
select(store(q25,seq,earray_127),head) = select(store(store(q25,seq,earray_127),tail,s(index_126)),head),
inference(symmetry,[status(thm)],[889]) ).
tff(891,plain,
( ( earray_127 = store(earray_125,index_126,e25) )
<=> ( earray_127 = store(earray_125,index_126,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(892,axiom,
earray_127 = store(earray_125,index_126,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(893,plain,
earray_127 = store(earray_125,index_126,e25),
inference(modus_ponens,[status(thm)],[892,891]) ).
tff(894,plain,
store(earray_125,index_126,e25) = earray_127,
inference(symmetry,[status(thm)],[893]) ).
tff(895,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = store(earray_125,index_126,e25) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(896,plain,
select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = store(earray_125,index_126,e25),
inference(unit_resolution,[status(thm)],[895,27]) ).
tff(897,plain,
( ( q25 = queue_124 )
<=> ( q25 = queue_124 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(898,axiom,
q25 = queue_124,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp302) ).
tff(899,plain,
q25 = queue_124,
inference(modus_ponens,[status(thm)],[898,897]) ).
tff(900,plain,
queue_124 = q25,
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
( ( queue_124 = store(queue_122,tail,index_123) )
<=> ( queue_124 = store(queue_122,tail,index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(902,axiom,
queue_124 = store(queue_122,tail,index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(903,plain,
queue_124 = store(queue_122,tail,index_123),
inference(modus_ponens,[status(thm)],[902,901]) ).
tff(904,plain,
store(queue_122,tail,index_123) = queue_124,
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
store(queue_122,tail,index_123) = q25,
inference(transitivity,[status(thm)],[904,900]) ).
tff(906,plain,
store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)) = store(q25,seq,earray_127),
inference(monotonicity,[status(thm)],[905,894]) ).
tff(907,plain,
select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq) = select(store(q25,seq,earray_127),seq),
inference(monotonicity,[status(thm)],[906]) ).
tff(908,plain,
select(store(q25,seq,earray_127),seq) = select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq),
inference(symmetry,[status(thm)],[907]) ).
tff(909,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(910,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(911,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq) ) ),
inference(modus_ponens,[status(thm)],[910,909]) ).
tff(912,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(store(q25,seq,earray_127),seq),
inference(unit_resolution,[status(thm)],[911,79,153]) ).
tff(913,plain,
store(store(q25,seq,earray_127),tail,s(index_126)) = q26,
inference(transitivity,[status(thm)],[884,849,845]) ).
tff(914,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),seq) = select(q26,seq),
inference(monotonicity,[status(thm)],[913]) ).
tff(915,plain,
select(q26,seq) = select(store(store(q25,seq,earray_127),tail,s(index_126)),seq),
inference(symmetry,[status(thm)],[914]) ).
tff(916,plain,
select(q26,seq) = earray_127,
inference(transitivity,[status(thm)],[915,912,908,896,894]) ).
tff(917,plain,
store(store(queue_122,tail,index_123),seq,select(q26,seq)) = store(q25,seq,earray_127),
inference(monotonicity,[status(thm)],[905,916]) ).
tff(918,plain,
select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(q25,seq,earray_127),head),
inference(monotonicity,[status(thm)],[917]) ).
tff(919,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(920,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(921,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head) ) ),
inference(modus_ponens,[status(thm)],[920,919]) ).
tff(922,plain,
select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head) = select(store(queue_122,tail,index_123),head),
inference(unit_resolution,[status(thm)],[921,79,189]) ).
tff(923,plain,
select(store(queue_122,tail,index_123),head) = select(store(store(queue_122,tail,index_123),seq,select(q26,seq)),head),
inference(symmetry,[status(thm)],[922]) ).
tff(924,plain,
( ( index_123 = s(index_120) )
<=> ( index_123 = s(index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(925,axiom,
index_123 = s(index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(926,plain,
index_123 = s(index_120),
inference(modus_ponens,[status(thm)],[925,924]) ).
tff(927,plain,
s(index_120) = index_123,
inference(symmetry,[status(thm)],[926]) ).
tff(928,plain,
( ( queue_122 = store(q24,seq,earray_121) )
<=> ( queue_122 = store(q24,seq,earray_121) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(929,axiom,
queue_122 = store(q24,seq,earray_121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(930,plain,
queue_122 = store(q24,seq,earray_121),
inference(modus_ponens,[status(thm)],[929,928]) ).
tff(931,plain,
store(q24,seq,earray_121) = queue_122,
inference(symmetry,[status(thm)],[930]) ).
tff(932,plain,
store(store(q24,seq,earray_121),tail,s(index_120)) = store(queue_122,tail,index_123),
inference(monotonicity,[status(thm)],[931,927]) ).
tff(933,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(queue_122,tail,index_123),head),
inference(monotonicity,[status(thm)],[932]) ).
tff(934,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(935,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(936,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head) ) ),
inference(modus_ponens,[status(thm)],[935,934]) ).
tff(937,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),head) = select(store(q24,seq,earray_121),head),
inference(unit_resolution,[status(thm)],[936,79,126]) ).
tff(938,plain,
select(store(q24,seq,earray_121),head) = select(store(store(q24,seq,earray_121),tail,s(index_120)),head),
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
( ( earray_121 = store(earray_119,index_120,e24) )
<=> ( earray_121 = store(earray_119,index_120,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(940,axiom,
earray_121 = store(earray_119,index_120,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(941,plain,
earray_121 = store(earray_119,index_120,e24),
inference(modus_ponens,[status(thm)],[940,939]) ).
tff(942,plain,
store(earray_119,index_120,e24) = earray_121,
inference(symmetry,[status(thm)],[941]) ).
tff(943,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = store(earray_119,index_120,e24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(944,plain,
select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = store(earray_119,index_120,e24),
inference(unit_resolution,[status(thm)],[943,27]) ).
tff(945,plain,
( ( q24 = queue_118 )
<=> ( q24 = queue_118 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(946,axiom,
q24 = queue_118,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp301) ).
tff(947,plain,
q24 = queue_118,
inference(modus_ponens,[status(thm)],[946,945]) ).
tff(948,plain,
queue_118 = q24,
inference(symmetry,[status(thm)],[947]) ).
tff(949,plain,
( ( queue_118 = store(queue_115,head,index_117) )
<=> ( queue_118 = store(queue_115,head,index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(950,axiom,
queue_118 = store(queue_115,head,index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(951,plain,
queue_118 = store(queue_115,head,index_117),
inference(modus_ponens,[status(thm)],[950,949]) ).
tff(952,plain,
store(queue_115,head,index_117) = queue_118,
inference(symmetry,[status(thm)],[951]) ).
tff(953,plain,
store(queue_115,head,index_117) = q24,
inference(transitivity,[status(thm)],[952,948]) ).
tff(954,plain,
store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)) = store(q24,seq,earray_121),
inference(monotonicity,[status(thm)],[953,942]) ).
tff(955,plain,
select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq) = select(store(q24,seq,earray_121),seq),
inference(monotonicity,[status(thm)],[954]) ).
tff(956,plain,
select(store(q24,seq,earray_121),seq) = select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(958,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(959,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq) ) ),
inference(modus_ponens,[status(thm)],[958,957]) ).
tff(960,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(store(q24,seq,earray_121),seq),
inference(unit_resolution,[status(thm)],[959,79,153]) ).
tff(961,plain,
store(store(q24,seq,earray_121),tail,s(index_120)) = q25,
inference(transitivity,[status(thm)],[932,904,900]) ).
tff(962,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),seq) = select(q25,seq),
inference(monotonicity,[status(thm)],[961]) ).
tff(963,plain,
select(q25,seq) = select(store(store(q24,seq,earray_121),tail,s(index_120)),seq),
inference(symmetry,[status(thm)],[962]) ).
tff(964,plain,
select(q25,seq) = earray_121,
inference(transitivity,[status(thm)],[963,960,956,944,942]) ).
tff(965,plain,
store(store(queue_115,head,index_117),seq,select(q25,seq)) = store(q24,seq,earray_121),
inference(monotonicity,[status(thm)],[953,964]) ).
tff(966,plain,
select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(q24,seq,earray_121),head),
inference(monotonicity,[status(thm)],[965]) ).
tff(967,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(968,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(969,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head) ) ),
inference(modus_ponens,[status(thm)],[968,967]) ).
tff(970,plain,
select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head) = select(store(queue_115,head,index_117),head),
inference(unit_resolution,[status(thm)],[969,79,189]) ).
tff(971,plain,
select(store(queue_115,head,index_117),head) = select(store(store(queue_115,head,index_117),seq,select(q25,seq)),head),
inference(symmetry,[status(thm)],[970]) ).
tff(972,plain,
( ( index_117 = s(index_116) )
<=> ( index_117 = s(index_116) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(973,axiom,
index_117 = s(index_116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(974,plain,
index_117 = s(index_116),
inference(modus_ponens,[status(thm)],[973,972]) ).
tff(975,plain,
s(index_116) = index_117,
inference(symmetry,[status(thm)],[974]) ).
tff(976,plain,
( ( queue_115 = store(queue_113,tail,index_114) )
<=> ( queue_115 = store(queue_113,tail,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(977,axiom,
queue_115 = store(queue_113,tail,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(978,plain,
queue_115 = store(queue_113,tail,index_114),
inference(modus_ponens,[status(thm)],[977,976]) ).
tff(979,plain,
store(queue_113,tail,index_114) = queue_115,
inference(symmetry,[status(thm)],[978]) ).
tff(980,plain,
store(store(queue_113,tail,index_114),head,s(index_116)) = store(queue_115,head,index_117),
inference(monotonicity,[status(thm)],[979,975]) ).
tff(981,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = select(store(queue_115,head,index_117),head),
inference(monotonicity,[status(thm)],[980]) ).
tff(982,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = s(index_116) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(983,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),head) = s(index_116),
inference(unit_resolution,[status(thm)],[982,27]) ).
tff(984,plain,
s(index_116) = select(store(store(queue_113,tail,index_114),head,s(index_116)),head),
inference(symmetry,[status(thm)],[983]) ).
tff(985,plain,
( ( index_116 = select(queue_115,head) )
<=> ( index_116 = select(queue_115,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(986,axiom,
index_116 = select(queue_115,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(987,plain,
index_116 = select(queue_115,head),
inference(modus_ponens,[status(thm)],[986,985]) ).
tff(988,plain,
select(queue_115,head) = index_116,
inference(symmetry,[status(thm)],[987]) ).
tff(989,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(990,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(991,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[990,989]) ).
tff(992,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[991]) ).
tff(993,plain,
( ( queue_113 = store(q23,seq,earray_112) )
<=> ( queue_113 = store(q23,seq,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(994,axiom,
queue_113 = store(q23,seq,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(995,plain,
queue_113 = store(q23,seq,earray_112),
inference(modus_ponens,[status(thm)],[994,993]) ).
tff(996,plain,
store(q23,seq,earray_112) = queue_113,
inference(symmetry,[status(thm)],[995]) ).
tff(997,plain,
store(store(q23,seq,earray_112),tail,s(index_111)) = store(queue_113,tail,index_114),
inference(monotonicity,[status(thm)],[996,992]) ).
tff(998,plain,
store(store(q23,seq,earray_112),tail,s(index_111)) = queue_115,
inference(transitivity,[status(thm)],[997,979]) ).
tff(999,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(queue_115,head),
inference(monotonicity,[status(thm)],[998]) ).
tff(1000,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1001,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1002,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(modus_ponens,[status(thm)],[1001,1000]) ).
tff(1003,plain,
( ( tail = head )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head) ) ),
inference(unit_resolution,[status(thm)],[1002,79]) ).
tff(1004,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),head) = select(store(q23,seq,earray_112),head),
inference(unit_resolution,[status(thm)],[1003,126]) ).
tff(1005,plain,
select(store(q23,seq,earray_112),head) = select(store(store(q23,seq,earray_112),tail,s(index_111)),head),
inference(symmetry,[status(thm)],[1004]) ).
tff(1006,plain,
( ( earray_112 = store(earray_110,index_111,e23) )
<=> ( earray_112 = store(earray_110,index_111,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1007,axiom,
earray_112 = store(earray_110,index_111,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(1008,plain,
earray_112 = store(earray_110,index_111,e23),
inference(modus_ponens,[status(thm)],[1007,1006]) ).
tff(1009,plain,
store(earray_110,index_111,e23) = earray_112,
inference(symmetry,[status(thm)],[1008]) ).
tff(1010,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = store(earray_110,index_111,e23) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1011,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = store(earray_110,index_111,e23),
inference(unit_resolution,[status(thm)],[1010,27]) ).
tff(1012,plain,
( ( q23 = queue_109 )
<=> ( q23 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1013,axiom,
q23 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp300) ).
tff(1014,plain,
q23 = queue_109,
inference(modus_ponens,[status(thm)],[1013,1012]) ).
tff(1015,plain,
queue_109 = q23,
inference(symmetry,[status(thm)],[1014]) ).
tff(1016,plain,
( ( queue_109 = store(queue_107,tail,index_108) )
<=> ( queue_109 = store(queue_107,tail,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1017,axiom,
queue_109 = store(queue_107,tail,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(1018,plain,
queue_109 = store(queue_107,tail,index_108),
inference(modus_ponens,[status(thm)],[1017,1016]) ).
tff(1019,plain,
store(queue_107,tail,index_108) = queue_109,
inference(symmetry,[status(thm)],[1018]) ).
tff(1020,plain,
store(queue_107,tail,index_108) = q23,
inference(transitivity,[status(thm)],[1019,1015]) ).
tff(1021,plain,
store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)) = store(q23,seq,earray_112),
inference(monotonicity,[status(thm)],[1020,1009]) ).
tff(1022,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq) = select(store(q23,seq,earray_112),seq),
inference(monotonicity,[status(thm)],[1021]) ).
tff(1023,plain,
select(store(q23,seq,earray_112),seq) = select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq),
inference(symmetry,[status(thm)],[1022]) ).
tff(1024,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1025,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1026,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq) ) ),
inference(modus_ponens,[status(thm)],[1025,1024]) ).
tff(1027,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(q23,seq,earray_112),seq),
inference(unit_resolution,[status(thm)],[1026,79,153]) ).
tff(1028,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),seq) = select(store(queue_113,tail,index_114),seq),
inference(monotonicity,[status(thm)],[997]) ).
tff(1029,plain,
select(store(queue_113,tail,index_114),seq) = select(store(store(q23,seq,earray_112),tail,s(index_111)),seq),
inference(symmetry,[status(thm)],[1028]) ).
tff(1030,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1031,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1032,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq) ) ),
inference(modus_ponens,[status(thm)],[1031,1030]) ).
tff(1033,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(store(queue_113,tail,index_114),seq),
inference(unit_resolution,[status(thm)],[1032,79,162]) ).
tff(1034,plain,
store(store(queue_113,tail,index_114),head,s(index_116)) = q24,
inference(transitivity,[status(thm)],[980,952,948]) ).
tff(1035,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),seq) = select(q24,seq),
inference(monotonicity,[status(thm)],[1034]) ).
tff(1036,plain,
select(q24,seq) = select(store(store(queue_113,tail,index_114),head,s(index_116)),seq),
inference(symmetry,[status(thm)],[1035]) ).
tff(1037,plain,
select(q24,seq) = earray_112,
inference(transitivity,[status(thm)],[1036,1033,1029,1027,1023,1011,1009]) ).
tff(1038,plain,
store(store(queue_107,tail,index_108),seq,select(q24,seq)) = store(q23,seq,earray_112),
inference(monotonicity,[status(thm)],[1020,1037]) ).
tff(1039,plain,
select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(q23,seq,earray_112),head),
inference(monotonicity,[status(thm)],[1038]) ).
tff(1040,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1041,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1042,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(modus_ponens,[status(thm)],[1041,1040]) ).
tff(1043,plain,
( ( seq = head )
| ( select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(unit_resolution,[status(thm)],[1042,79]) ).
tff(1044,plain,
select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head) = select(store(queue_107,tail,index_108),head),
inference(unit_resolution,[status(thm)],[1043,189]) ).
tff(1045,plain,
select(store(queue_107,tail,index_108),head) = select(store(store(queue_107,tail,index_108),seq,select(q24,seq)),head),
inference(symmetry,[status(thm)],[1044]) ).
tff(1046,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1047,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp85) ).
tff(1048,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[1047,1046]) ).
tff(1049,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[1048]) ).
tff(1050,plain,
( ( queue_107 = store(q22,seq,earray_106) )
<=> ( queue_107 = store(q22,seq,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1051,axiom,
queue_107 = store(q22,seq,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(1052,plain,
queue_107 = store(q22,seq,earray_106),
inference(modus_ponens,[status(thm)],[1051,1050]) ).
tff(1053,plain,
store(q22,seq,earray_106) = queue_107,
inference(symmetry,[status(thm)],[1052]) ).
tff(1054,plain,
store(store(q22,seq,earray_106),tail,s(index_105)) = store(queue_107,tail,index_108),
inference(monotonicity,[status(thm)],[1053,1049]) ).
tff(1055,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(queue_107,tail,index_108),head),
inference(monotonicity,[status(thm)],[1054]) ).
tff(1056,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1057,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1058,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head) ) ),
inference(modus_ponens,[status(thm)],[1057,1056]) ).
tff(1059,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),head) = select(store(q22,seq,earray_106),head),
inference(unit_resolution,[status(thm)],[1058,79,126]) ).
tff(1060,plain,
select(store(q22,seq,earray_106),head) = select(store(store(q22,seq,earray_106),tail,s(index_105)),head),
inference(symmetry,[status(thm)],[1059]) ).
tff(1061,plain,
( ( earray_106 = store(earray_104,index_105,e22) )
<=> ( earray_106 = store(earray_104,index_105,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1062,axiom,
earray_106 = store(earray_104,index_105,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(1063,plain,
earray_106 = store(earray_104,index_105,e22),
inference(modus_ponens,[status(thm)],[1062,1061]) ).
tff(1064,plain,
store(earray_104,index_105,e22) = earray_106,
inference(symmetry,[status(thm)],[1063]) ).
tff(1065,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = store(earray_104,index_105,e22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1066,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = store(earray_104,index_105,e22),
inference(unit_resolution,[status(thm)],[1065,27]) ).
tff(1067,plain,
( ( q22 = queue_103 )
<=> ( q22 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1068,axiom,
q22 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp299) ).
tff(1069,plain,
q22 = queue_103,
inference(modus_ponens,[status(thm)],[1068,1067]) ).
tff(1070,plain,
queue_103 = q22,
inference(symmetry,[status(thm)],[1069]) ).
tff(1071,plain,
( ( queue_103 = store(queue_101,tail,index_102) )
<=> ( queue_103 = store(queue_101,tail,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1072,axiom,
queue_103 = store(queue_101,tail,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(1073,plain,
queue_103 = store(queue_101,tail,index_102),
inference(modus_ponens,[status(thm)],[1072,1071]) ).
tff(1074,plain,
store(queue_101,tail,index_102) = queue_103,
inference(symmetry,[status(thm)],[1073]) ).
tff(1075,plain,
store(queue_101,tail,index_102) = q22,
inference(transitivity,[status(thm)],[1074,1070]) ).
tff(1076,plain,
store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)) = store(q22,seq,earray_106),
inference(monotonicity,[status(thm)],[1075,1064]) ).
tff(1077,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq) = select(store(q22,seq,earray_106),seq),
inference(monotonicity,[status(thm)],[1076]) ).
tff(1078,plain,
select(store(q22,seq,earray_106),seq) = select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq),
inference(symmetry,[status(thm)],[1077]) ).
tff(1079,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1080,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1081,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq) ) ),
inference(modus_ponens,[status(thm)],[1080,1079]) ).
tff(1082,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(store(q22,seq,earray_106),seq),
inference(unit_resolution,[status(thm)],[1081,79,153]) ).
tff(1083,plain,
store(store(q22,seq,earray_106),tail,s(index_105)) = q23,
inference(transitivity,[status(thm)],[1054,1019,1015]) ).
tff(1084,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),seq) = select(q23,seq),
inference(monotonicity,[status(thm)],[1083]) ).
tff(1085,plain,
select(q23,seq) = select(store(store(q22,seq,earray_106),tail,s(index_105)),seq),
inference(symmetry,[status(thm)],[1084]) ).
tff(1086,plain,
select(q23,seq) = earray_106,
inference(transitivity,[status(thm)],[1085,1082,1078,1066,1064]) ).
tff(1087,plain,
store(store(queue_101,tail,index_102),seq,select(q23,seq)) = store(q22,seq,earray_106),
inference(monotonicity,[status(thm)],[1075,1086]) ).
tff(1088,plain,
select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(q22,seq,earray_106),head),
inference(monotonicity,[status(thm)],[1087]) ).
tff(1089,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1090,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1091,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(modus_ponens,[status(thm)],[1090,1089]) ).
tff(1092,plain,
select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head) = select(store(queue_101,tail,index_102),head),
inference(unit_resolution,[status(thm)],[1091,79,189]) ).
tff(1093,plain,
select(store(queue_101,tail,index_102),head) = select(store(store(queue_101,tail,index_102),seq,select(q23,seq)),head),
inference(symmetry,[status(thm)],[1092]) ).
tff(1094,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1095,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp83) ).
tff(1096,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[1095,1094]) ).
tff(1097,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[1096]) ).
tff(1098,plain,
( ( queue_101 = store(q21,seq,earray_100) )
<=> ( queue_101 = store(q21,seq,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1099,axiom,
queue_101 = store(q21,seq,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(1100,plain,
queue_101 = store(q21,seq,earray_100),
inference(modus_ponens,[status(thm)],[1099,1098]) ).
tff(1101,plain,
store(q21,seq,earray_100) = queue_101,
inference(symmetry,[status(thm)],[1100]) ).
tff(1102,plain,
store(store(q21,seq,earray_100),tail,s(index_99)) = store(queue_101,tail,index_102),
inference(monotonicity,[status(thm)],[1101,1097]) ).
tff(1103,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(queue_101,tail,index_102),head),
inference(monotonicity,[status(thm)],[1102]) ).
tff(1104,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1105,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1106,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head) ) ),
inference(modus_ponens,[status(thm)],[1105,1104]) ).
tff(1107,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),head) = select(store(q21,seq,earray_100),head),
inference(unit_resolution,[status(thm)],[1106,79,126]) ).
tff(1108,plain,
select(store(q21,seq,earray_100),head) = select(store(store(q21,seq,earray_100),tail,s(index_99)),head),
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
( ( earray_100 = store(earray_98,index_99,e21) )
<=> ( earray_100 = store(earray_98,index_99,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1110,axiom,
earray_100 = store(earray_98,index_99,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(1111,plain,
earray_100 = store(earray_98,index_99,e21),
inference(modus_ponens,[status(thm)],[1110,1109]) ).
tff(1112,plain,
store(earray_98,index_99,e21) = earray_100,
inference(symmetry,[status(thm)],[1111]) ).
tff(1113,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = store(earray_98,index_99,e21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1114,plain,
select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = store(earray_98,index_99,e21),
inference(unit_resolution,[status(thm)],[1113,27]) ).
tff(1115,plain,
( ( q21 = queue_97 )
<=> ( q21 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1116,axiom,
q21 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp298) ).
tff(1117,plain,
q21 = queue_97,
inference(modus_ponens,[status(thm)],[1116,1115]) ).
tff(1118,plain,
queue_97 = q21,
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
( ( queue_97 = store(queue_94,head,index_96) )
<=> ( queue_97 = store(queue_94,head,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1120,axiom,
queue_97 = store(queue_94,head,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp283) ).
tff(1121,plain,
queue_97 = store(queue_94,head,index_96),
inference(modus_ponens,[status(thm)],[1120,1119]) ).
tff(1122,plain,
store(queue_94,head,index_96) = queue_97,
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
store(queue_94,head,index_96) = q21,
inference(transitivity,[status(thm)],[1122,1118]) ).
tff(1124,plain,
store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)) = store(q21,seq,earray_100),
inference(monotonicity,[status(thm)],[1123,1112]) ).
tff(1125,plain,
select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq) = select(store(q21,seq,earray_100),seq),
inference(monotonicity,[status(thm)],[1124]) ).
tff(1126,plain,
select(store(q21,seq,earray_100),seq) = select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq),
inference(symmetry,[status(thm)],[1125]) ).
tff(1127,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1128,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1129,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq) ) ),
inference(modus_ponens,[status(thm)],[1128,1127]) ).
tff(1130,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(store(q21,seq,earray_100),seq),
inference(unit_resolution,[status(thm)],[1129,79,153]) ).
tff(1131,plain,
store(store(q21,seq,earray_100),tail,s(index_99)) = q22,
inference(transitivity,[status(thm)],[1102,1074,1070]) ).
tff(1132,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),seq) = select(q22,seq),
inference(monotonicity,[status(thm)],[1131]) ).
tff(1133,plain,
select(q22,seq) = select(store(store(q21,seq,earray_100),tail,s(index_99)),seq),
inference(symmetry,[status(thm)],[1132]) ).
tff(1134,plain,
select(q22,seq) = earray_100,
inference(transitivity,[status(thm)],[1133,1130,1126,1114,1112]) ).
tff(1135,plain,
store(store(queue_94,head,index_96),seq,select(q22,seq)) = store(q21,seq,earray_100),
inference(monotonicity,[status(thm)],[1123,1134]) ).
tff(1136,plain,
select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(q21,seq,earray_100),head),
inference(monotonicity,[status(thm)],[1135]) ).
tff(1137,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1138,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1139,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head) ) ),
inference(modus_ponens,[status(thm)],[1138,1137]) ).
tff(1140,plain,
select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head) = select(store(queue_94,head,index_96),head),
inference(unit_resolution,[status(thm)],[1139,79,189]) ).
tff(1141,plain,
select(store(queue_94,head,index_96),head) = select(store(store(queue_94,head,index_96),seq,select(q22,seq)),head),
inference(symmetry,[status(thm)],[1140]) ).
tff(1142,plain,
( ( index_96 = s(index_95) )
<=> ( index_96 = s(index_95) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1143,axiom,
index_96 = s(index_95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(1144,plain,
index_96 = s(index_95),
inference(modus_ponens,[status(thm)],[1143,1142]) ).
tff(1145,plain,
s(index_95) = index_96,
inference(symmetry,[status(thm)],[1144]) ).
tff(1146,plain,
( ( queue_94 = store(queue_92,tail,index_93) )
<=> ( queue_94 = store(queue_92,tail,index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1147,axiom,
queue_94 = store(queue_92,tail,index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp282) ).
tff(1148,plain,
queue_94 = store(queue_92,tail,index_93),
inference(modus_ponens,[status(thm)],[1147,1146]) ).
tff(1149,plain,
store(queue_92,tail,index_93) = queue_94,
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
store(store(queue_92,tail,index_93),head,s(index_95)) = store(queue_94,head,index_96),
inference(monotonicity,[status(thm)],[1149,1145]) ).
tff(1151,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = select(store(queue_94,head,index_96),head),
inference(monotonicity,[status(thm)],[1150]) ).
tff(1152,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = s(index_95) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1153,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),head) = s(index_95),
inference(unit_resolution,[status(thm)],[1152,27]) ).
tff(1154,plain,
s(index_95) = select(store(store(queue_92,tail,index_93),head,s(index_95)),head),
inference(symmetry,[status(thm)],[1153]) ).
tff(1155,plain,
( ( index_95 = select(queue_94,head) )
<=> ( index_95 = select(queue_94,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1156,axiom,
index_95 = select(queue_94,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(1157,plain,
index_95 = select(queue_94,head),
inference(modus_ponens,[status(thm)],[1156,1155]) ).
tff(1158,plain,
select(queue_94,head) = index_95,
inference(symmetry,[status(thm)],[1157]) ).
tff(1159,plain,
( ( index_93 = s(index_90) )
<=> ( index_93 = s(index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1160,axiom,
index_93 = s(index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(1161,plain,
index_93 = s(index_90),
inference(modus_ponens,[status(thm)],[1160,1159]) ).
tff(1162,plain,
s(index_90) = index_93,
inference(symmetry,[status(thm)],[1161]) ).
tff(1163,plain,
( ( queue_92 = store(q20,seq,earray_91) )
<=> ( queue_92 = store(q20,seq,earray_91) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1164,axiom,
queue_92 = store(q20,seq,earray_91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp281) ).
tff(1165,plain,
queue_92 = store(q20,seq,earray_91),
inference(modus_ponens,[status(thm)],[1164,1163]) ).
tff(1166,plain,
store(q20,seq,earray_91) = queue_92,
inference(symmetry,[status(thm)],[1165]) ).
tff(1167,plain,
store(store(q20,seq,earray_91),tail,s(index_90)) = store(queue_92,tail,index_93),
inference(monotonicity,[status(thm)],[1166,1162]) ).
tff(1168,plain,
store(store(q20,seq,earray_91),tail,s(index_90)) = queue_94,
inference(transitivity,[status(thm)],[1167,1149]) ).
tff(1169,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(queue_94,head),
inference(monotonicity,[status(thm)],[1168]) ).
tff(1170,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1171,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1172,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(modus_ponens,[status(thm)],[1171,1170]) ).
tff(1173,plain,
( ( tail = head )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head) ) ),
inference(unit_resolution,[status(thm)],[1172,79]) ).
tff(1174,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),head) = select(store(q20,seq,earray_91),head),
inference(unit_resolution,[status(thm)],[1173,126]) ).
tff(1175,plain,
select(store(q20,seq,earray_91),head) = select(store(store(q20,seq,earray_91),tail,s(index_90)),head),
inference(symmetry,[status(thm)],[1174]) ).
tff(1176,plain,
( ( earray_91 = store(earray_89,index_90,e20) )
<=> ( earray_91 = store(earray_89,index_90,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1177,axiom,
earray_91 = store(earray_89,index_90,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp79) ).
tff(1178,plain,
earray_91 = store(earray_89,index_90,e20),
inference(modus_ponens,[status(thm)],[1177,1176]) ).
tff(1179,plain,
store(earray_89,index_90,e20) = earray_91,
inference(symmetry,[status(thm)],[1178]) ).
tff(1180,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = store(earray_89,index_90,e20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1181,plain,
select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = store(earray_89,index_90,e20),
inference(unit_resolution,[status(thm)],[1180,27]) ).
tff(1182,plain,
( ( q20 = queue_88 )
<=> ( q20 = queue_88 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1183,axiom,
q20 = queue_88,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp297) ).
tff(1184,plain,
q20 = queue_88,
inference(modus_ponens,[status(thm)],[1183,1182]) ).
tff(1185,plain,
queue_88 = q20,
inference(symmetry,[status(thm)],[1184]) ).
tff(1186,plain,
( ( queue_88 = store(queue_86,tail,index_87) )
<=> ( queue_88 = store(queue_86,tail,index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1187,axiom,
queue_88 = store(queue_86,tail,index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp280) ).
tff(1188,plain,
queue_88 = store(queue_86,tail,index_87),
inference(modus_ponens,[status(thm)],[1187,1186]) ).
tff(1189,plain,
store(queue_86,tail,index_87) = queue_88,
inference(symmetry,[status(thm)],[1188]) ).
tff(1190,plain,
store(queue_86,tail,index_87) = q20,
inference(transitivity,[status(thm)],[1189,1185]) ).
tff(1191,plain,
store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)) = store(q20,seq,earray_91),
inference(monotonicity,[status(thm)],[1190,1179]) ).
tff(1192,plain,
select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq) = select(store(q20,seq,earray_91),seq),
inference(monotonicity,[status(thm)],[1191]) ).
tff(1193,plain,
select(store(q20,seq,earray_91),seq) = select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq),
inference(symmetry,[status(thm)],[1192]) ).
tff(1194,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1195,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1196,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq) ) ),
inference(modus_ponens,[status(thm)],[1195,1194]) ).
tff(1197,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(q20,seq,earray_91),seq),
inference(unit_resolution,[status(thm)],[1196,79,153]) ).
tff(1198,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),seq) = select(store(queue_92,tail,index_93),seq),
inference(monotonicity,[status(thm)],[1167]) ).
tff(1199,plain,
select(store(queue_92,tail,index_93),seq) = select(store(store(q20,seq,earray_91),tail,s(index_90)),seq),
inference(symmetry,[status(thm)],[1198]) ).
tff(1200,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1201,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1202,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq) ) ),
inference(modus_ponens,[status(thm)],[1201,1200]) ).
tff(1203,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(store(queue_92,tail,index_93),seq),
inference(unit_resolution,[status(thm)],[1202,79,162]) ).
tff(1204,plain,
store(store(queue_92,tail,index_93),head,s(index_95)) = q21,
inference(transitivity,[status(thm)],[1150,1122,1118]) ).
tff(1205,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),seq) = select(q21,seq),
inference(monotonicity,[status(thm)],[1204]) ).
tff(1206,plain,
select(q21,seq) = select(store(store(queue_92,tail,index_93),head,s(index_95)),seq),
inference(symmetry,[status(thm)],[1205]) ).
tff(1207,plain,
select(q21,seq) = earray_91,
inference(transitivity,[status(thm)],[1206,1203,1199,1197,1193,1181,1179]) ).
tff(1208,plain,
store(store(queue_86,tail,index_87),seq,select(q21,seq)) = store(q20,seq,earray_91),
inference(monotonicity,[status(thm)],[1190,1207]) ).
tff(1209,plain,
select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(q20,seq,earray_91),head),
inference(monotonicity,[status(thm)],[1208]) ).
tff(1210,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1211,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1212,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(modus_ponens,[status(thm)],[1211,1210]) ).
tff(1213,plain,
( ( seq = head )
| ( select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head) ) ),
inference(unit_resolution,[status(thm)],[1212,79]) ).
tff(1214,plain,
select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head) = select(store(queue_86,tail,index_87),head),
inference(unit_resolution,[status(thm)],[1213,189]) ).
tff(1215,plain,
select(store(queue_86,tail,index_87),head) = select(store(store(queue_86,tail,index_87),seq,select(q21,seq)),head),
inference(symmetry,[status(thm)],[1214]) ).
tff(1216,plain,
( ( index_87 = s(index_84) )
<=> ( index_87 = s(index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1217,axiom,
index_87 = s(index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(1218,plain,
index_87 = s(index_84),
inference(modus_ponens,[status(thm)],[1217,1216]) ).
tff(1219,plain,
s(index_84) = index_87,
inference(symmetry,[status(thm)],[1218]) ).
tff(1220,plain,
( ( queue_86 = store(q19,seq,earray_85) )
<=> ( queue_86 = store(q19,seq,earray_85) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1221,axiom,
queue_86 = store(q19,seq,earray_85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp279) ).
tff(1222,plain,
queue_86 = store(q19,seq,earray_85),
inference(modus_ponens,[status(thm)],[1221,1220]) ).
tff(1223,plain,
store(q19,seq,earray_85) = queue_86,
inference(symmetry,[status(thm)],[1222]) ).
tff(1224,plain,
store(store(q19,seq,earray_85),tail,s(index_84)) = store(queue_86,tail,index_87),
inference(monotonicity,[status(thm)],[1223,1219]) ).
tff(1225,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(queue_86,tail,index_87),head),
inference(monotonicity,[status(thm)],[1224]) ).
tff(1226,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1227,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1228,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head) ) ),
inference(modus_ponens,[status(thm)],[1227,1226]) ).
tff(1229,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),head) = select(store(q19,seq,earray_85),head),
inference(unit_resolution,[status(thm)],[1228,79,126]) ).
tff(1230,plain,
select(store(q19,seq,earray_85),head) = select(store(store(q19,seq,earray_85),tail,s(index_84)),head),
inference(symmetry,[status(thm)],[1229]) ).
tff(1231,plain,
( ( earray_85 = store(earray_83,index_84,e19) )
<=> ( earray_85 = store(earray_83,index_84,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1232,axiom,
earray_85 = store(earray_83,index_84,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp77) ).
tff(1233,plain,
earray_85 = store(earray_83,index_84,e19),
inference(modus_ponens,[status(thm)],[1232,1231]) ).
tff(1234,plain,
store(earray_83,index_84,e19) = earray_85,
inference(symmetry,[status(thm)],[1233]) ).
tff(1235,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = store(earray_83,index_84,e19) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1236,plain,
select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = store(earray_83,index_84,e19),
inference(unit_resolution,[status(thm)],[1235,27]) ).
tff(1237,plain,
( ( q19 = queue_76 )
<=> ( q19 = queue_76 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1238,axiom,
q19 = queue_76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp295) ).
tff(1239,plain,
q19 = queue_76,
inference(modus_ponens,[status(thm)],[1238,1237]) ).
tff(1240,plain,
queue_76 = q19,
inference(symmetry,[status(thm)],[1239]) ).
tff(1241,plain,
( ( queue_76 = store(queue_74,tail,index_75) )
<=> ( queue_76 = store(queue_74,tail,index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1242,axiom,
queue_76 = store(queue_74,tail,index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp276) ).
tff(1243,plain,
queue_76 = store(queue_74,tail,index_75),
inference(modus_ponens,[status(thm)],[1242,1241]) ).
tff(1244,plain,
store(queue_74,tail,index_75) = queue_76,
inference(symmetry,[status(thm)],[1243]) ).
tff(1245,plain,
store(queue_74,tail,index_75) = q19,
inference(transitivity,[status(thm)],[1244,1240]) ).
tff(1246,plain,
store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)) = store(q19,seq,earray_85),
inference(monotonicity,[status(thm)],[1245,1234]) ).
tff(1247,plain,
select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq) = select(store(q19,seq,earray_85),seq),
inference(monotonicity,[status(thm)],[1246]) ).
tff(1248,plain,
select(store(q19,seq,earray_85),seq) = select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq),
inference(symmetry,[status(thm)],[1247]) ).
tff(1249,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1250,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1251,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq) ) ),
inference(modus_ponens,[status(thm)],[1250,1249]) ).
tff(1252,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(store(q19,seq,earray_85),seq),
inference(unit_resolution,[status(thm)],[1251,79,153]) ).
tff(1253,plain,
store(store(q19,seq,earray_85),tail,s(index_84)) = q20,
inference(transitivity,[status(thm)],[1224,1189,1185]) ).
tff(1254,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),seq) = select(q20,seq),
inference(monotonicity,[status(thm)],[1253]) ).
tff(1255,plain,
select(q20,seq) = select(store(store(q19,seq,earray_85),tail,s(index_84)),seq),
inference(symmetry,[status(thm)],[1254]) ).
tff(1256,plain,
select(q20,seq) = earray_85,
inference(transitivity,[status(thm)],[1255,1252,1248,1236,1234]) ).
tff(1257,plain,
store(store(queue_74,tail,index_75),seq,select(q20,seq)) = store(q19,seq,earray_85),
inference(monotonicity,[status(thm)],[1245,1256]) ).
tff(1258,plain,
select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(q19,seq,earray_85),head),
inference(monotonicity,[status(thm)],[1257]) ).
tff(1259,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1260,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1261,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head) ) ),
inference(modus_ponens,[status(thm)],[1260,1259]) ).
tff(1262,plain,
select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head) = select(store(queue_74,tail,index_75),head),
inference(unit_resolution,[status(thm)],[1261,79,189]) ).
tff(1263,plain,
select(store(queue_74,tail,index_75),head) = select(store(store(queue_74,tail,index_75),seq,select(q20,seq)),head),
inference(symmetry,[status(thm)],[1262]) ).
tff(1264,plain,
( ( index_75 = s(index_72) )
<=> ( index_75 = s(index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1265,axiom,
index_75 = s(index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(1266,plain,
index_75 = s(index_72),
inference(modus_ponens,[status(thm)],[1265,1264]) ).
tff(1267,plain,
s(index_72) = index_75,
inference(symmetry,[status(thm)],[1266]) ).
tff(1268,plain,
( ( queue_74 = store(q18,seq,earray_73) )
<=> ( queue_74 = store(q18,seq,earray_73) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1269,axiom,
queue_74 = store(q18,seq,earray_73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp275) ).
tff(1270,plain,
queue_74 = store(q18,seq,earray_73),
inference(modus_ponens,[status(thm)],[1269,1268]) ).
tff(1271,plain,
store(q18,seq,earray_73) = queue_74,
inference(symmetry,[status(thm)],[1270]) ).
tff(1272,plain,
store(store(q18,seq,earray_73),tail,s(index_72)) = store(queue_74,tail,index_75),
inference(monotonicity,[status(thm)],[1271,1267]) ).
tff(1273,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(queue_74,tail,index_75),head),
inference(monotonicity,[status(thm)],[1272]) ).
tff(1274,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1275,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1276,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head) ) ),
inference(modus_ponens,[status(thm)],[1275,1274]) ).
tff(1277,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),head) = select(store(q18,seq,earray_73),head),
inference(unit_resolution,[status(thm)],[1276,79,126]) ).
tff(1278,plain,
select(store(q18,seq,earray_73),head) = select(store(store(q18,seq,earray_73),tail,s(index_72)),head),
inference(symmetry,[status(thm)],[1277]) ).
tff(1279,plain,
( ( earray_73 = store(earray_71,index_72,e18) )
<=> ( earray_73 = store(earray_71,index_72,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1280,axiom,
earray_73 = store(earray_71,index_72,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(1281,plain,
earray_73 = store(earray_71,index_72,e18),
inference(modus_ponens,[status(thm)],[1280,1279]) ).
tff(1282,plain,
store(earray_71,index_72,e18) = earray_73,
inference(symmetry,[status(thm)],[1281]) ).
tff(1283,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = store(earray_71,index_72,e18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1284,plain,
select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = store(earray_71,index_72,e18),
inference(unit_resolution,[status(thm)],[1283,27]) ).
tff(1285,plain,
( ( q18 = queue_70 )
<=> ( q18 = queue_70 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1286,axiom,
q18 = queue_70,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp294) ).
tff(1287,plain,
q18 = queue_70,
inference(modus_ponens,[status(thm)],[1286,1285]) ).
tff(1288,plain,
queue_70 = q18,
inference(symmetry,[status(thm)],[1287]) ).
tff(1289,plain,
( ( queue_70 = store(queue_67,head,index_69) )
<=> ( queue_70 = store(queue_67,head,index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1290,axiom,
queue_70 = store(queue_67,head,index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp274) ).
tff(1291,plain,
queue_70 = store(queue_67,head,index_69),
inference(modus_ponens,[status(thm)],[1290,1289]) ).
tff(1292,plain,
store(queue_67,head,index_69) = queue_70,
inference(symmetry,[status(thm)],[1291]) ).
tff(1293,plain,
store(queue_67,head,index_69) = q18,
inference(transitivity,[status(thm)],[1292,1288]) ).
tff(1294,plain,
store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)) = store(q18,seq,earray_73),
inference(monotonicity,[status(thm)],[1293,1282]) ).
tff(1295,plain,
select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq) = select(store(q18,seq,earray_73),seq),
inference(monotonicity,[status(thm)],[1294]) ).
tff(1296,plain,
select(store(q18,seq,earray_73),seq) = select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq),
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1298,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1299,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq) ) ),
inference(modus_ponens,[status(thm)],[1298,1297]) ).
tff(1300,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(store(q18,seq,earray_73),seq),
inference(unit_resolution,[status(thm)],[1299,79,153]) ).
tff(1301,plain,
store(store(q18,seq,earray_73),tail,s(index_72)) = q19,
inference(transitivity,[status(thm)],[1272,1244,1240]) ).
tff(1302,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),seq) = select(q19,seq),
inference(monotonicity,[status(thm)],[1301]) ).
tff(1303,plain,
select(q19,seq) = select(store(store(q18,seq,earray_73),tail,s(index_72)),seq),
inference(symmetry,[status(thm)],[1302]) ).
tff(1304,plain,
select(q19,seq) = earray_73,
inference(transitivity,[status(thm)],[1303,1300,1296,1284,1282]) ).
tff(1305,plain,
store(store(queue_67,head,index_69),seq,select(q19,seq)) = store(q18,seq,earray_73),
inference(monotonicity,[status(thm)],[1293,1304]) ).
tff(1306,plain,
select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(q18,seq,earray_73),head),
inference(monotonicity,[status(thm)],[1305]) ).
tff(1307,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1308,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1309,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head) ) ),
inference(modus_ponens,[status(thm)],[1308,1307]) ).
tff(1310,plain,
select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head) = select(store(queue_67,head,index_69),head),
inference(unit_resolution,[status(thm)],[1309,79,189]) ).
tff(1311,plain,
select(store(queue_67,head,index_69),head) = select(store(store(queue_67,head,index_69),seq,select(q19,seq)),head),
inference(symmetry,[status(thm)],[1310]) ).
tff(1312,plain,
( ( index_69 = s(index_68) )
<=> ( index_69 = s(index_68) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1313,axiom,
index_69 = s(index_68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(1314,plain,
index_69 = s(index_68),
inference(modus_ponens,[status(thm)],[1313,1312]) ).
tff(1315,plain,
s(index_68) = index_69,
inference(symmetry,[status(thm)],[1314]) ).
tff(1316,plain,
( ( queue_67 = store(queue_65,tail,index_66) )
<=> ( queue_67 = store(queue_65,tail,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1317,axiom,
queue_67 = store(queue_65,tail,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp272) ).
tff(1318,plain,
queue_67 = store(queue_65,tail,index_66),
inference(modus_ponens,[status(thm)],[1317,1316]) ).
tff(1319,plain,
store(queue_65,tail,index_66) = queue_67,
inference(symmetry,[status(thm)],[1318]) ).
tff(1320,plain,
store(store(queue_65,tail,index_66),head,s(index_68)) = store(queue_67,head,index_69),
inference(monotonicity,[status(thm)],[1319,1315]) ).
tff(1321,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = select(store(queue_67,head,index_69),head),
inference(monotonicity,[status(thm)],[1320]) ).
tff(1322,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = s(index_68) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1323,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),head) = s(index_68),
inference(unit_resolution,[status(thm)],[1322,27]) ).
tff(1324,plain,
s(index_68) = select(store(store(queue_65,tail,index_66),head,s(index_68)),head),
inference(symmetry,[status(thm)],[1323]) ).
tff(1325,plain,
( ( index_68 = select(queue_67,head) )
<=> ( index_68 = select(queue_67,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1326,axiom,
index_68 = select(queue_67,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(1327,plain,
index_68 = select(queue_67,head),
inference(modus_ponens,[status(thm)],[1326,1325]) ).
tff(1328,plain,
select(queue_67,head) = index_68,
inference(symmetry,[status(thm)],[1327]) ).
tff(1329,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1330,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(1331,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[1330,1329]) ).
tff(1332,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[1331]) ).
tff(1333,plain,
( ( queue_65 = store(q17,seq,earray_64) )
<=> ( queue_65 = store(q17,seq,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1334,axiom,
queue_65 = store(q17,seq,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp271) ).
tff(1335,plain,
queue_65 = store(q17,seq,earray_64),
inference(modus_ponens,[status(thm)],[1334,1333]) ).
tff(1336,plain,
store(q17,seq,earray_64) = queue_65,
inference(symmetry,[status(thm)],[1335]) ).
tff(1337,plain,
store(store(q17,seq,earray_64),tail,s(index_63)) = store(queue_65,tail,index_66),
inference(monotonicity,[status(thm)],[1336,1332]) ).
tff(1338,plain,
store(store(q17,seq,earray_64),tail,s(index_63)) = queue_67,
inference(transitivity,[status(thm)],[1337,1319]) ).
tff(1339,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(queue_67,head),
inference(monotonicity,[status(thm)],[1338]) ).
tff(1340,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1341,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1342,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(modus_ponens,[status(thm)],[1341,1340]) ).
tff(1343,plain,
( ( tail = head )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head) ) ),
inference(unit_resolution,[status(thm)],[1342,79]) ).
tff(1344,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),head) = select(store(q17,seq,earray_64),head),
inference(unit_resolution,[status(thm)],[1343,126]) ).
tff(1345,plain,
select(store(q17,seq,earray_64),head) = select(store(store(q17,seq,earray_64),tail,s(index_63)),head),
inference(symmetry,[status(thm)],[1344]) ).
tff(1346,plain,
( ( earray_64 = store(earray_62,index_63,e17) )
<=> ( earray_64 = store(earray_62,index_63,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1347,axiom,
earray_64 = store(earray_62,index_63,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(1348,plain,
earray_64 = store(earray_62,index_63,e17),
inference(modus_ponens,[status(thm)],[1347,1346]) ).
tff(1349,plain,
store(earray_62,index_63,e17) = earray_64,
inference(symmetry,[status(thm)],[1348]) ).
tff(1350,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = store(earray_62,index_63,e17) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1351,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = store(earray_62,index_63,e17),
inference(unit_resolution,[status(thm)],[1350,27]) ).
tff(1352,plain,
( ( q17 = queue_61 )
<=> ( q17 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1353,axiom,
q17 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp293) ).
tff(1354,plain,
q17 = queue_61,
inference(modus_ponens,[status(thm)],[1353,1352]) ).
tff(1355,plain,
queue_61 = q17,
inference(symmetry,[status(thm)],[1354]) ).
tff(1356,plain,
( ( queue_61 = store(queue_59,tail,index_60) )
<=> ( queue_61 = store(queue_59,tail,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1357,axiom,
queue_61 = store(queue_59,tail,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp270) ).
tff(1358,plain,
queue_61 = store(queue_59,tail,index_60),
inference(modus_ponens,[status(thm)],[1357,1356]) ).
tff(1359,plain,
store(queue_59,tail,index_60) = queue_61,
inference(symmetry,[status(thm)],[1358]) ).
tff(1360,plain,
store(queue_59,tail,index_60) = q17,
inference(transitivity,[status(thm)],[1359,1355]) ).
tff(1361,plain,
store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)) = store(q17,seq,earray_64),
inference(monotonicity,[status(thm)],[1360,1349]) ).
tff(1362,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq) = select(store(q17,seq,earray_64),seq),
inference(monotonicity,[status(thm)],[1361]) ).
tff(1363,plain,
select(store(q17,seq,earray_64),seq) = select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq),
inference(symmetry,[status(thm)],[1362]) ).
tff(1364,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1365,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1366,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq) ) ),
inference(modus_ponens,[status(thm)],[1365,1364]) ).
tff(1367,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(q17,seq,earray_64),seq),
inference(unit_resolution,[status(thm)],[1366,79,153]) ).
tff(1368,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),seq) = select(store(queue_65,tail,index_66),seq),
inference(monotonicity,[status(thm)],[1337]) ).
tff(1369,plain,
select(store(queue_65,tail,index_66),seq) = select(store(store(q17,seq,earray_64),tail,s(index_63)),seq),
inference(symmetry,[status(thm)],[1368]) ).
tff(1370,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1371,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1372,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq) ) ),
inference(modus_ponens,[status(thm)],[1371,1370]) ).
tff(1373,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(store(queue_65,tail,index_66),seq),
inference(unit_resolution,[status(thm)],[1372,79,162]) ).
tff(1374,plain,
store(store(queue_65,tail,index_66),head,s(index_68)) = q18,
inference(transitivity,[status(thm)],[1320,1292,1288]) ).
tff(1375,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),seq) = select(q18,seq),
inference(monotonicity,[status(thm)],[1374]) ).
tff(1376,plain,
select(q18,seq) = select(store(store(queue_65,tail,index_66),head,s(index_68)),seq),
inference(symmetry,[status(thm)],[1375]) ).
tff(1377,plain,
select(q18,seq) = earray_64,
inference(transitivity,[status(thm)],[1376,1373,1369,1367,1363,1351,1349]) ).
tff(1378,plain,
store(store(queue_59,tail,index_60),seq,select(q18,seq)) = store(q17,seq,earray_64),
inference(monotonicity,[status(thm)],[1360,1377]) ).
tff(1379,plain,
select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(q17,seq,earray_64),head),
inference(monotonicity,[status(thm)],[1378]) ).
tff(1380,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1381,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1382,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(modus_ponens,[status(thm)],[1381,1380]) ).
tff(1383,plain,
( ( seq = head )
| ( select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(unit_resolution,[status(thm)],[1382,79]) ).
tff(1384,plain,
select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head) = select(store(queue_59,tail,index_60),head),
inference(unit_resolution,[status(thm)],[1383,189]) ).
tff(1385,plain,
select(store(queue_59,tail,index_60),head) = select(store(store(queue_59,tail,index_60),seq,select(q18,seq)),head),
inference(symmetry,[status(thm)],[1384]) ).
tff(1386,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1387,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(1388,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[1387,1386]) ).
tff(1389,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[1388]) ).
tff(1390,plain,
( ( queue_59 = store(q16,seq,earray_58) )
<=> ( queue_59 = store(q16,seq,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1391,axiom,
queue_59 = store(q16,seq,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp269) ).
tff(1392,plain,
queue_59 = store(q16,seq,earray_58),
inference(modus_ponens,[status(thm)],[1391,1390]) ).
tff(1393,plain,
store(q16,seq,earray_58) = queue_59,
inference(symmetry,[status(thm)],[1392]) ).
tff(1394,plain,
store(store(q16,seq,earray_58),tail,s(index_57)) = store(queue_59,tail,index_60),
inference(monotonicity,[status(thm)],[1393,1389]) ).
tff(1395,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(queue_59,tail,index_60),head),
inference(monotonicity,[status(thm)],[1394]) ).
tff(1396,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1397,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1398,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head) ) ),
inference(modus_ponens,[status(thm)],[1397,1396]) ).
tff(1399,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),head) = select(store(q16,seq,earray_58),head),
inference(unit_resolution,[status(thm)],[1398,79,126]) ).
tff(1400,plain,
select(store(q16,seq,earray_58),head) = select(store(store(q16,seq,earray_58),tail,s(index_57)),head),
inference(symmetry,[status(thm)],[1399]) ).
tff(1401,plain,
( ( earray_58 = store(earray_56,index_57,e16) )
<=> ( earray_58 = store(earray_56,index_57,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1402,axiom,
earray_58 = store(earray_56,index_57,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(1403,plain,
earray_58 = store(earray_56,index_57,e16),
inference(modus_ponens,[status(thm)],[1402,1401]) ).
tff(1404,plain,
store(earray_56,index_57,e16) = earray_58,
inference(symmetry,[status(thm)],[1403]) ).
tff(1405,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = store(earray_56,index_57,e16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1406,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = store(earray_56,index_57,e16),
inference(unit_resolution,[status(thm)],[1405,27]) ).
tff(1407,plain,
( ( q16 = queue_55 )
<=> ( q16 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1408,axiom,
q16 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp292) ).
tff(1409,plain,
q16 = queue_55,
inference(modus_ponens,[status(thm)],[1408,1407]) ).
tff(1410,plain,
queue_55 = q16,
inference(symmetry,[status(thm)],[1409]) ).
tff(1411,plain,
( ( queue_55 = store(queue_53,tail,index_54) )
<=> ( queue_55 = store(queue_53,tail,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1412,axiom,
queue_55 = store(queue_53,tail,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp268) ).
tff(1413,plain,
queue_55 = store(queue_53,tail,index_54),
inference(modus_ponens,[status(thm)],[1412,1411]) ).
tff(1414,plain,
store(queue_53,tail,index_54) = queue_55,
inference(symmetry,[status(thm)],[1413]) ).
tff(1415,plain,
store(queue_53,tail,index_54) = q16,
inference(transitivity,[status(thm)],[1414,1410]) ).
tff(1416,plain,
store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)) = store(q16,seq,earray_58),
inference(monotonicity,[status(thm)],[1415,1404]) ).
tff(1417,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq) = select(store(q16,seq,earray_58),seq),
inference(monotonicity,[status(thm)],[1416]) ).
tff(1418,plain,
select(store(q16,seq,earray_58),seq) = select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq),
inference(symmetry,[status(thm)],[1417]) ).
tff(1419,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1420,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1421,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq) ) ),
inference(modus_ponens,[status(thm)],[1420,1419]) ).
tff(1422,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(store(q16,seq,earray_58),seq),
inference(unit_resolution,[status(thm)],[1421,79,153]) ).
tff(1423,plain,
store(store(q16,seq,earray_58),tail,s(index_57)) = q17,
inference(transitivity,[status(thm)],[1394,1359,1355]) ).
tff(1424,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),seq) = select(q17,seq),
inference(monotonicity,[status(thm)],[1423]) ).
tff(1425,plain,
select(q17,seq) = select(store(store(q16,seq,earray_58),tail,s(index_57)),seq),
inference(symmetry,[status(thm)],[1424]) ).
tff(1426,plain,
select(q17,seq) = earray_58,
inference(transitivity,[status(thm)],[1425,1422,1418,1406,1404]) ).
tff(1427,plain,
store(store(queue_53,tail,index_54),seq,select(q17,seq)) = store(q16,seq,earray_58),
inference(monotonicity,[status(thm)],[1415,1426]) ).
tff(1428,plain,
select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(q16,seq,earray_58),head),
inference(monotonicity,[status(thm)],[1427]) ).
tff(1429,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1430,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1431,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(modus_ponens,[status(thm)],[1430,1429]) ).
tff(1432,plain,
select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head) = select(store(queue_53,tail,index_54),head),
inference(unit_resolution,[status(thm)],[1431,79,189]) ).
tff(1433,plain,
select(store(queue_53,tail,index_54),head) = select(store(store(queue_53,tail,index_54),seq,select(q17,seq)),head),
inference(symmetry,[status(thm)],[1432]) ).
tff(1434,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1435,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(1436,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[1435,1434]) ).
tff(1437,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[1436]) ).
tff(1438,plain,
( ( queue_53 = store(q15,seq,earray_52) )
<=> ( queue_53 = store(q15,seq,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1439,axiom,
queue_53 = store(q15,seq,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp267) ).
tff(1440,plain,
queue_53 = store(q15,seq,earray_52),
inference(modus_ponens,[status(thm)],[1439,1438]) ).
tff(1441,plain,
store(q15,seq,earray_52) = queue_53,
inference(symmetry,[status(thm)],[1440]) ).
tff(1442,plain,
store(store(q15,seq,earray_52),tail,s(index_51)) = store(queue_53,tail,index_54),
inference(monotonicity,[status(thm)],[1441,1437]) ).
tff(1443,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(queue_53,tail,index_54),head),
inference(monotonicity,[status(thm)],[1442]) ).
tff(1444,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1445,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1446,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head) ) ),
inference(modus_ponens,[status(thm)],[1445,1444]) ).
tff(1447,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),head) = select(store(q15,seq,earray_52),head),
inference(unit_resolution,[status(thm)],[1446,79,126]) ).
tff(1448,plain,
select(store(q15,seq,earray_52),head) = select(store(store(q15,seq,earray_52),tail,s(index_51)),head),
inference(symmetry,[status(thm)],[1447]) ).
tff(1449,plain,
( ( earray_52 = store(earray_50,index_51,e15) )
<=> ( earray_52 = store(earray_50,index_51,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1450,axiom,
earray_52 = store(earray_50,index_51,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp66) ).
tff(1451,plain,
earray_52 = store(earray_50,index_51,e15),
inference(modus_ponens,[status(thm)],[1450,1449]) ).
tff(1452,plain,
store(earray_50,index_51,e15) = earray_52,
inference(symmetry,[status(thm)],[1451]) ).
tff(1453,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = store(earray_50,index_51,e15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1454,plain,
select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = store(earray_50,index_51,e15),
inference(unit_resolution,[status(thm)],[1453,27]) ).
tff(1455,plain,
( ( q15 = queue_49 )
<=> ( q15 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1456,axiom,
q15 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp291) ).
tff(1457,plain,
q15 = queue_49,
inference(modus_ponens,[status(thm)],[1456,1455]) ).
tff(1458,plain,
queue_49 = q15,
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
( ( queue_49 = store(queue_46,head,index_48) )
<=> ( queue_49 = store(queue_46,head,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1460,axiom,
queue_49 = store(queue_46,head,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp265) ).
tff(1461,plain,
queue_49 = store(queue_46,head,index_48),
inference(modus_ponens,[status(thm)],[1460,1459]) ).
tff(1462,plain,
store(queue_46,head,index_48) = queue_49,
inference(symmetry,[status(thm)],[1461]) ).
tff(1463,plain,
store(queue_46,head,index_48) = q15,
inference(transitivity,[status(thm)],[1462,1458]) ).
tff(1464,plain,
store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)) = store(q15,seq,earray_52),
inference(monotonicity,[status(thm)],[1463,1452]) ).
tff(1465,plain,
select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq) = select(store(q15,seq,earray_52),seq),
inference(monotonicity,[status(thm)],[1464]) ).
tff(1466,plain,
select(store(q15,seq,earray_52),seq) = select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq),
inference(symmetry,[status(thm)],[1465]) ).
tff(1467,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1468,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1469,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq) ) ),
inference(modus_ponens,[status(thm)],[1468,1467]) ).
tff(1470,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(store(q15,seq,earray_52),seq),
inference(unit_resolution,[status(thm)],[1469,79,153]) ).
tff(1471,plain,
store(store(q15,seq,earray_52),tail,s(index_51)) = q16,
inference(transitivity,[status(thm)],[1442,1414,1410]) ).
tff(1472,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),seq) = select(q16,seq),
inference(monotonicity,[status(thm)],[1471]) ).
tff(1473,plain,
select(q16,seq) = select(store(store(q15,seq,earray_52),tail,s(index_51)),seq),
inference(symmetry,[status(thm)],[1472]) ).
tff(1474,plain,
select(q16,seq) = earray_52,
inference(transitivity,[status(thm)],[1473,1470,1466,1454,1452]) ).
tff(1475,plain,
store(store(queue_46,head,index_48),seq,select(q16,seq)) = store(q15,seq,earray_52),
inference(monotonicity,[status(thm)],[1463,1474]) ).
tff(1476,plain,
select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(q15,seq,earray_52),head),
inference(monotonicity,[status(thm)],[1475]) ).
tff(1477,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1478,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1479,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head) ) ),
inference(modus_ponens,[status(thm)],[1478,1477]) ).
tff(1480,plain,
select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head) = select(store(queue_46,head,index_48),head),
inference(unit_resolution,[status(thm)],[1479,79,189]) ).
tff(1481,plain,
select(store(queue_46,head,index_48),head) = select(store(store(queue_46,head,index_48),seq,select(q16,seq)),head),
inference(symmetry,[status(thm)],[1480]) ).
tff(1482,plain,
( ( index_48 = s(index_47) )
<=> ( index_48 = s(index_47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1483,axiom,
index_48 = s(index_47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(1484,plain,
index_48 = s(index_47),
inference(modus_ponens,[status(thm)],[1483,1482]) ).
tff(1485,plain,
s(index_47) = index_48,
inference(symmetry,[status(thm)],[1484]) ).
tff(1486,plain,
( ( queue_46 = store(queue_44,tail,index_45) )
<=> ( queue_46 = store(queue_44,tail,index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1487,axiom,
queue_46 = store(queue_44,tail,index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp264) ).
tff(1488,plain,
queue_46 = store(queue_44,tail,index_45),
inference(modus_ponens,[status(thm)],[1487,1486]) ).
tff(1489,plain,
store(queue_44,tail,index_45) = queue_46,
inference(symmetry,[status(thm)],[1488]) ).
tff(1490,plain,
store(store(queue_44,tail,index_45),head,s(index_47)) = store(queue_46,head,index_48),
inference(monotonicity,[status(thm)],[1489,1485]) ).
tff(1491,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = select(store(queue_46,head,index_48),head),
inference(monotonicity,[status(thm)],[1490]) ).
tff(1492,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = s(index_47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1493,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),head) = s(index_47),
inference(unit_resolution,[status(thm)],[1492,27]) ).
tff(1494,plain,
s(index_47) = select(store(store(queue_44,tail,index_45),head,s(index_47)),head),
inference(symmetry,[status(thm)],[1493]) ).
tff(1495,plain,
( ( index_47 = select(queue_46,head) )
<=> ( index_47 = select(queue_46,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1496,axiom,
index_47 = select(queue_46,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(1497,plain,
index_47 = select(queue_46,head),
inference(modus_ponens,[status(thm)],[1496,1495]) ).
tff(1498,plain,
select(queue_46,head) = index_47,
inference(symmetry,[status(thm)],[1497]) ).
tff(1499,plain,
( ( index_45 = s(index_42) )
<=> ( index_45 = s(index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1500,axiom,
index_45 = s(index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(1501,plain,
index_45 = s(index_42),
inference(modus_ponens,[status(thm)],[1500,1499]) ).
tff(1502,plain,
s(index_42) = index_45,
inference(symmetry,[status(thm)],[1501]) ).
tff(1503,plain,
( ( queue_44 = store(q14,seq,earray_43) )
<=> ( queue_44 = store(q14,seq,earray_43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1504,axiom,
queue_44 = store(q14,seq,earray_43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp263) ).
tff(1505,plain,
queue_44 = store(q14,seq,earray_43),
inference(modus_ponens,[status(thm)],[1504,1503]) ).
tff(1506,plain,
store(q14,seq,earray_43) = queue_44,
inference(symmetry,[status(thm)],[1505]) ).
tff(1507,plain,
store(store(q14,seq,earray_43),tail,s(index_42)) = store(queue_44,tail,index_45),
inference(monotonicity,[status(thm)],[1506,1502]) ).
tff(1508,plain,
store(store(q14,seq,earray_43),tail,s(index_42)) = queue_46,
inference(transitivity,[status(thm)],[1507,1489]) ).
tff(1509,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(queue_46,head),
inference(monotonicity,[status(thm)],[1508]) ).
tff(1510,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1511,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1512,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(modus_ponens,[status(thm)],[1511,1510]) ).
tff(1513,plain,
( ( tail = head )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head) ) ),
inference(unit_resolution,[status(thm)],[1512,79]) ).
tff(1514,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),head) = select(store(q14,seq,earray_43),head),
inference(unit_resolution,[status(thm)],[1513,126]) ).
tff(1515,plain,
select(store(q14,seq,earray_43),head) = select(store(store(q14,seq,earray_43),tail,s(index_42)),head),
inference(symmetry,[status(thm)],[1514]) ).
tff(1516,plain,
( ( earray_43 = store(earray_41,index_42,e14) )
<=> ( earray_43 = store(earray_41,index_42,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1517,axiom,
earray_43 = store(earray_41,index_42,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp64) ).
tff(1518,plain,
earray_43 = store(earray_41,index_42,e14),
inference(modus_ponens,[status(thm)],[1517,1516]) ).
tff(1519,plain,
store(earray_41,index_42,e14) = earray_43,
inference(symmetry,[status(thm)],[1518]) ).
tff(1520,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = store(earray_41,index_42,e14) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1521,plain,
select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = store(earray_41,index_42,e14),
inference(unit_resolution,[status(thm)],[1520,27]) ).
tff(1522,plain,
( ( q14 = queue_40 )
<=> ( q14 = queue_40 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1523,axiom,
q14 = queue_40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp290) ).
tff(1524,plain,
q14 = queue_40,
inference(modus_ponens,[status(thm)],[1523,1522]) ).
tff(1525,plain,
queue_40 = q14,
inference(symmetry,[status(thm)],[1524]) ).
tff(1526,plain,
( ( queue_40 = store(queue_38,tail,index_39) )
<=> ( queue_40 = store(queue_38,tail,index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1527,axiom,
queue_40 = store(queue_38,tail,index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp262) ).
tff(1528,plain,
queue_40 = store(queue_38,tail,index_39),
inference(modus_ponens,[status(thm)],[1527,1526]) ).
tff(1529,plain,
store(queue_38,tail,index_39) = queue_40,
inference(symmetry,[status(thm)],[1528]) ).
tff(1530,plain,
store(queue_38,tail,index_39) = q14,
inference(transitivity,[status(thm)],[1529,1525]) ).
tff(1531,plain,
store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)) = store(q14,seq,earray_43),
inference(monotonicity,[status(thm)],[1530,1519]) ).
tff(1532,plain,
select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq) = select(store(q14,seq,earray_43),seq),
inference(monotonicity,[status(thm)],[1531]) ).
tff(1533,plain,
select(store(q14,seq,earray_43),seq) = select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq),
inference(symmetry,[status(thm)],[1532]) ).
tff(1534,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1535,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1536,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq) ) ),
inference(modus_ponens,[status(thm)],[1535,1534]) ).
tff(1537,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(q14,seq,earray_43),seq),
inference(unit_resolution,[status(thm)],[1536,79,153]) ).
tff(1538,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),seq) = select(store(queue_44,tail,index_45),seq),
inference(monotonicity,[status(thm)],[1507]) ).
tff(1539,plain,
select(store(queue_44,tail,index_45),seq) = select(store(store(q14,seq,earray_43),tail,s(index_42)),seq),
inference(symmetry,[status(thm)],[1538]) ).
tff(1540,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1541,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1542,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq) ) ),
inference(modus_ponens,[status(thm)],[1541,1540]) ).
tff(1543,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(store(queue_44,tail,index_45),seq),
inference(unit_resolution,[status(thm)],[1542,79,162]) ).
tff(1544,plain,
store(store(queue_44,tail,index_45),head,s(index_47)) = q15,
inference(transitivity,[status(thm)],[1490,1462,1458]) ).
tff(1545,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),seq) = select(q15,seq),
inference(monotonicity,[status(thm)],[1544]) ).
tff(1546,plain,
select(q15,seq) = select(store(store(queue_44,tail,index_45),head,s(index_47)),seq),
inference(symmetry,[status(thm)],[1545]) ).
tff(1547,plain,
select(q15,seq) = earray_43,
inference(transitivity,[status(thm)],[1546,1543,1539,1537,1533,1521,1519]) ).
tff(1548,plain,
store(store(queue_38,tail,index_39),seq,select(q15,seq)) = store(q14,seq,earray_43),
inference(monotonicity,[status(thm)],[1530,1547]) ).
tff(1549,plain,
select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(q14,seq,earray_43),head),
inference(monotonicity,[status(thm)],[1548]) ).
tff(1550,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1551,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1552,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(modus_ponens,[status(thm)],[1551,1550]) ).
tff(1553,plain,
( ( seq = head )
| ( select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head) ) ),
inference(unit_resolution,[status(thm)],[1552,79]) ).
tff(1554,plain,
select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head) = select(store(queue_38,tail,index_39),head),
inference(unit_resolution,[status(thm)],[1553,189]) ).
tff(1555,plain,
select(store(queue_38,tail,index_39),head) = select(store(store(queue_38,tail,index_39),seq,select(q15,seq)),head),
inference(symmetry,[status(thm)],[1554]) ).
tff(1556,plain,
( ( index_39 = s(index_36) )
<=> ( index_39 = s(index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1557,axiom,
index_39 = s(index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(1558,plain,
index_39 = s(index_36),
inference(modus_ponens,[status(thm)],[1557,1556]) ).
tff(1559,plain,
s(index_36) = index_39,
inference(symmetry,[status(thm)],[1558]) ).
tff(1560,plain,
( ( queue_38 = store(q13,seq,earray_37) )
<=> ( queue_38 = store(q13,seq,earray_37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1561,axiom,
queue_38 = store(q13,seq,earray_37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp261) ).
tff(1562,plain,
queue_38 = store(q13,seq,earray_37),
inference(modus_ponens,[status(thm)],[1561,1560]) ).
tff(1563,plain,
store(q13,seq,earray_37) = queue_38,
inference(symmetry,[status(thm)],[1562]) ).
tff(1564,plain,
store(store(q13,seq,earray_37),tail,s(index_36)) = store(queue_38,tail,index_39),
inference(monotonicity,[status(thm)],[1563,1559]) ).
tff(1565,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(queue_38,tail,index_39),head),
inference(monotonicity,[status(thm)],[1564]) ).
tff(1566,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1567,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1568,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head) ) ),
inference(modus_ponens,[status(thm)],[1567,1566]) ).
tff(1569,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),head) = select(store(q13,seq,earray_37),head),
inference(unit_resolution,[status(thm)],[1568,79,126]) ).
tff(1570,plain,
select(store(q13,seq,earray_37),head) = select(store(store(q13,seq,earray_37),tail,s(index_36)),head),
inference(symmetry,[status(thm)],[1569]) ).
tff(1571,plain,
( ( earray_37 = store(earray_35,index_36,e13) )
<=> ( earray_37 = store(earray_35,index_36,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1572,axiom,
earray_37 = store(earray_35,index_36,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp61) ).
tff(1573,plain,
earray_37 = store(earray_35,index_36,e13),
inference(modus_ponens,[status(thm)],[1572,1571]) ).
tff(1574,plain,
store(earray_35,index_36,e13) = earray_37,
inference(symmetry,[status(thm)],[1573]) ).
tff(1575,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = store(earray_35,index_36,e13) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1576,plain,
select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = store(earray_35,index_36,e13),
inference(unit_resolution,[status(thm)],[1575,27]) ).
tff(1577,plain,
queue_34 = q13,
inference(symmetry,[status(thm)],[45]) ).
tff(1578,plain,
store(queue_32,tail,index_33) = queue_34,
inference(symmetry,[status(thm)],[42]) ).
tff(1579,plain,
store(queue_32,tail,index_33) = q13,
inference(transitivity,[status(thm)],[1578,1577]) ).
tff(1580,plain,
store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)) = store(q13,seq,earray_37),
inference(monotonicity,[status(thm)],[1579,1574]) ).
tff(1581,plain,
select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq) = select(store(q13,seq,earray_37),seq),
inference(monotonicity,[status(thm)],[1580]) ).
tff(1582,plain,
select(store(q13,seq,earray_37),seq) = select(store(store(queue_32,tail,index_33),seq,store(earray_35,index_36,e13)),seq),
inference(symmetry,[status(thm)],[1581]) ).
tff(1583,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1584,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1585,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq) ) ),
inference(modus_ponens,[status(thm)],[1584,1583]) ).
tff(1586,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(store(q13,seq,earray_37),seq),
inference(unit_resolution,[status(thm)],[1585,79,153]) ).
tff(1587,plain,
store(store(q13,seq,earray_37),tail,s(index_36)) = q14,
inference(transitivity,[status(thm)],[1564,1529,1525]) ).
tff(1588,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),seq) = select(q14,seq),
inference(monotonicity,[status(thm)],[1587]) ).
tff(1589,plain,
select(q14,seq) = select(store(store(q13,seq,earray_37),tail,s(index_36)),seq),
inference(symmetry,[status(thm)],[1588]) ).
tff(1590,plain,
select(q14,seq) = earray_37,
inference(transitivity,[status(thm)],[1589,1586,1582,1576,1574]) ).
tff(1591,plain,
store(store(queue_32,tail,index_33),seq,select(q14,seq)) = store(q13,seq,earray_37),
inference(monotonicity,[status(thm)],[1579,1590]) ).
tff(1592,plain,
select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(q13,seq,earray_37),head),
inference(monotonicity,[status(thm)],[1591]) ).
tff(1593,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1594,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1595,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head) ) ),
inference(modus_ponens,[status(thm)],[1594,1593]) ).
tff(1596,plain,
select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head) = select(store(queue_32,tail,index_33),head),
inference(unit_resolution,[status(thm)],[1595,79,189]) ).
tff(1597,plain,
select(store(queue_32,tail,index_33),head) = select(store(store(queue_32,tail,index_33),seq,select(q14,seq)),head),
inference(symmetry,[status(thm)],[1596]) ).
tff(1598,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(queue_32,tail,index_33),head),
inference(monotonicity,[status(thm)],[38]) ).
tff(1599,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1600,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1601,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head) ) ),
inference(modus_ponens,[status(thm)],[1600,1599]) ).
tff(1602,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),head) = select(store(q12,seq,earray_31),head),
inference(unit_resolution,[status(thm)],[1601,79,126]) ).
tff(1603,plain,
select(store(q12,seq,earray_31),head) = select(store(store(q12,seq,earray_31),tail,s(index_30)),head),
inference(symmetry,[status(thm)],[1602]) ).
tff(1604,plain,
( ( earray_31 = store(earray_29,index_30,e12) )
<=> ( earray_31 = store(earray_29,index_30,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1605,axiom,
earray_31 = store(earray_29,index_30,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp59) ).
tff(1606,plain,
earray_31 = store(earray_29,index_30,e12),
inference(modus_ponens,[status(thm)],[1605,1604]) ).
tff(1607,plain,
store(earray_29,index_30,e12) = earray_31,
inference(symmetry,[status(thm)],[1606]) ).
tff(1608,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = store(earray_29,index_30,e12) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1609,plain,
select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = store(earray_29,index_30,e12),
inference(unit_resolution,[status(thm)],[1608,27]) ).
tff(1610,plain,
queue_28 = q12,
inference(symmetry,[status(thm)],[99]) ).
tff(1611,plain,
store(queue_25,head,index_27) = queue_28,
inference(symmetry,[status(thm)],[96]) ).
tff(1612,plain,
store(queue_25,head,index_27) = q12,
inference(transitivity,[status(thm)],[1611,1610]) ).
tff(1613,plain,
store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)) = store(q12,seq,earray_31),
inference(monotonicity,[status(thm)],[1612,1607]) ).
tff(1614,plain,
select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq) = select(store(q12,seq,earray_31),seq),
inference(monotonicity,[status(thm)],[1613]) ).
tff(1615,plain,
select(store(q12,seq,earray_31),seq) = select(store(store(queue_25,head,index_27),seq,store(earray_29,index_30,e12)),seq),
inference(symmetry,[status(thm)],[1614]) ).
tff(1616,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1617,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1618,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq) ) ),
inference(modus_ponens,[status(thm)],[1617,1616]) ).
tff(1619,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(store(q12,seq,earray_31),seq),
inference(unit_resolution,[status(thm)],[1618,79,153]) ).
tff(1620,plain,
store(store(q12,seq,earray_31),tail,s(index_30)) = q13,
inference(transitivity,[status(thm)],[38,1578,1577]) ).
tff(1621,plain,
select(store(store(q12,seq,earray_31),tail,s(index_30)),seq) = select(q13,seq),
inference(monotonicity,[status(thm)],[1620]) ).
tff(1622,plain,
select(q13,seq) = select(store(store(q12,seq,earray_31),tail,s(index_30)),seq),
inference(symmetry,[status(thm)],[1621]) ).
tff(1623,plain,
select(q13,seq) = earray_31,
inference(transitivity,[status(thm)],[1622,1619,1615,1609,1607]) ).
tff(1624,plain,
store(store(queue_25,head,index_27),seq,select(q13,seq)) = store(q12,seq,earray_31),
inference(monotonicity,[status(thm)],[1612,1623]) ).
tff(1625,plain,
select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(q12,seq,earray_31),head),
inference(monotonicity,[status(thm)],[1624]) ).
tff(1626,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1627,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1628,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head) ) ),
inference(modus_ponens,[status(thm)],[1627,1626]) ).
tff(1629,plain,
select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head) = select(store(queue_25,head,index_27),head),
inference(unit_resolution,[status(thm)],[1628,79,189]) ).
tff(1630,plain,
select(store(queue_25,head,index_27),head) = select(store(store(queue_25,head,index_27),seq,select(q13,seq)),head),
inference(symmetry,[status(thm)],[1629]) ).
tff(1631,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = select(store(queue_25,head,index_27),head),
inference(monotonicity,[status(thm)],[92]) ).
tff(1632,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = s(index_26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1633,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),head) = s(index_26),
inference(unit_resolution,[status(thm)],[1632,27]) ).
tff(1634,plain,
s(index_26) = select(store(store(queue_23,tail,index_24),head,s(index_26)),head),
inference(symmetry,[status(thm)],[1633]) ).
tff(1635,plain,
( ( index_26 = select(queue_25,head) )
<=> ( index_26 = select(queue_25,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1636,axiom,
index_26 = select(queue_25,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(1637,plain,
index_26 = select(queue_25,head),
inference(modus_ponens,[status(thm)],[1636,1635]) ).
tff(1638,plain,
select(queue_25,head) = index_26,
inference(symmetry,[status(thm)],[1637]) ).
tff(1639,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = queue_25,
inference(transitivity,[status(thm)],[68,91]) ).
tff(1640,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(queue_25,head),
inference(monotonicity,[status(thm)],[1639]) ).
tff(1641,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1642,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1643,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(modus_ponens,[status(thm)],[1642,1641]) ).
tff(1644,plain,
( ( tail = head )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(unit_resolution,[status(thm)],[1643,79]) ).
tff(1645,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),head) = select(store(q11,seq,earray_22),head),
inference(unit_resolution,[status(thm)],[1644,126]) ).
tff(1646,plain,
select(store(q11,seq,earray_22),head) = select(store(store(q11,seq,earray_22),tail,s(index_21)),head),
inference(symmetry,[status(thm)],[1645]) ).
tff(1647,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1648,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(1649,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[1648,1647]) ).
tff(1650,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[1649]) ).
tff(1651,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = store(earray_20,index_21,e11) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1652,plain,
select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = store(earray_20,index_21,e11),
inference(unit_resolution,[status(thm)],[1651,27]) ).
tff(1653,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1654,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp287) ).
tff(1655,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[1654,1653]) ).
tff(1656,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[1655]) ).
tff(1657,plain,
( ( queue_19 = store(queue_17,tail,index_18) )
<=> ( queue_19 = store(queue_17,tail,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1658,axiom,
queue_19 = store(queue_17,tail,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(1659,plain,
queue_19 = store(queue_17,tail,index_18),
inference(modus_ponens,[status(thm)],[1658,1657]) ).
tff(1660,plain,
store(queue_17,tail,index_18) = queue_19,
inference(symmetry,[status(thm)],[1659]) ).
tff(1661,plain,
store(queue_17,tail,index_18) = q11,
inference(transitivity,[status(thm)],[1660,1656]) ).
tff(1662,plain,
store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[1661,1650]) ).
tff(1663,plain,
select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq) = select(store(q11,seq,earray_22),seq),
inference(monotonicity,[status(thm)],[1662]) ).
tff(1664,plain,
select(store(q11,seq,earray_22),seq) = select(store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)),seq),
inference(symmetry,[status(thm)],[1663]) ).
tff(1665,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1666,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1667,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq) ) ),
inference(modus_ponens,[status(thm)],[1666,1665]) ).
tff(1668,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(q11,seq,earray_22),seq),
inference(unit_resolution,[status(thm)],[1667,79,153]) ).
tff(1669,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(store(queue_23,tail,index_24),seq),
inference(monotonicity,[status(thm)],[68]) ).
tff(1670,plain,
select(store(queue_23,tail,index_24),seq) = select(store(store(q11,seq,earray_22),tail,s(index_21)),seq),
inference(symmetry,[status(thm)],[1669]) ).
tff(1671,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1672,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1673,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq) ) ),
inference(modus_ponens,[status(thm)],[1672,1671]) ).
tff(1674,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(store(queue_23,tail,index_24),seq),
inference(unit_resolution,[status(thm)],[1673,79,162]) ).
tff(1675,plain,
store(store(queue_23,tail,index_24),head,s(index_26)) = q12,
inference(transitivity,[status(thm)],[92,1611,1610]) ).
tff(1676,plain,
select(store(store(queue_23,tail,index_24),head,s(index_26)),seq) = select(q12,seq),
inference(monotonicity,[status(thm)],[1675]) ).
tff(1677,plain,
select(q12,seq) = select(store(store(queue_23,tail,index_24),head,s(index_26)),seq),
inference(symmetry,[status(thm)],[1676]) ).
tff(1678,plain,
select(q12,seq) = earray_22,
inference(transitivity,[status(thm)],[1677,1674,1670,1668,1664,1652,1650]) ).
tff(1679,plain,
store(store(queue_17,tail,index_18),seq,select(q12,seq)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[1661,1678]) ).
tff(1680,plain,
select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(q11,seq,earray_22),head),
inference(monotonicity,[status(thm)],[1679]) ).
tff(1681,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1682,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1683,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(modus_ponens,[status(thm)],[1682,1681]) ).
tff(1684,plain,
( ( seq = head )
| ( select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head) ) ),
inference(unit_resolution,[status(thm)],[1683,79]) ).
tff(1685,plain,
select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head) = select(store(queue_17,tail,index_18),head),
inference(unit_resolution,[status(thm)],[1684,189]) ).
tff(1686,plain,
select(store(queue_17,tail,index_18),head) = select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head),
inference(symmetry,[status(thm)],[1685]) ).
tff(1687,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1688,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(1689,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[1688,1687]) ).
tff(1690,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[1689]) ).
tff(1691,plain,
( ( queue_17 = store(q10,seq,earray_16) )
<=> ( queue_17 = store(q10,seq,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1692,axiom,
queue_17 = store(q10,seq,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(1693,plain,
queue_17 = store(q10,seq,earray_16),
inference(modus_ponens,[status(thm)],[1692,1691]) ).
tff(1694,plain,
store(q10,seq,earray_16) = queue_17,
inference(symmetry,[status(thm)],[1693]) ).
tff(1695,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = store(queue_17,tail,index_18),
inference(monotonicity,[status(thm)],[1694,1690]) ).
tff(1696,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(queue_17,tail,index_18),head),
inference(monotonicity,[status(thm)],[1695]) ).
tff(1697,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1698,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1699,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(modus_ponens,[status(thm)],[1698,1697]) ).
tff(1700,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),head) = select(store(q10,seq,earray_16),head),
inference(unit_resolution,[status(thm)],[1699,79,126]) ).
tff(1701,plain,
select(store(q10,seq,earray_16),head) = select(store(store(q10,seq,earray_16),tail,s(index_15)),head),
inference(symmetry,[status(thm)],[1700]) ).
tff(1702,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1703,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp19) ).
tff(1704,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[1703,1702]) ).
tff(1705,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[1704]) ).
tff(1706,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = store(earray_14,index_15,e10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1707,plain,
select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = store(earray_14,index_15,e10),
inference(unit_resolution,[status(thm)],[1706,27]) ).
tff(1708,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1709,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp286) ).
tff(1710,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[1709,1708]) ).
tff(1711,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[1710]) ).
tff(1712,plain,
( ( queue_13 = store(queue_11,tail,index_12) )
<=> ( queue_13 = store(queue_11,tail,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1713,axiom,
queue_13 = store(queue_11,tail,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(1714,plain,
queue_13 = store(queue_11,tail,index_12),
inference(modus_ponens,[status(thm)],[1713,1712]) ).
tff(1715,plain,
store(queue_11,tail,index_12) = queue_13,
inference(symmetry,[status(thm)],[1714]) ).
tff(1716,plain,
store(queue_11,tail,index_12) = q10,
inference(transitivity,[status(thm)],[1715,1711]) ).
tff(1717,plain,
store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[1716,1705]) ).
tff(1718,plain,
select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq) = select(store(q10,seq,earray_16),seq),
inference(monotonicity,[status(thm)],[1717]) ).
tff(1719,plain,
select(store(q10,seq,earray_16),seq) = select(store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)),seq),
inference(symmetry,[status(thm)],[1718]) ).
tff(1720,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1721,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1722,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ),
inference(modus_ponens,[status(thm)],[1721,1720]) ).
tff(1723,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq),
inference(unit_resolution,[status(thm)],[1722,79,153]) ).
tff(1724,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = q11,
inference(transitivity,[status(thm)],[1695,1660,1656]) ).
tff(1725,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(q11,seq),
inference(monotonicity,[status(thm)],[1724]) ).
tff(1726,plain,
select(q11,seq) = select(store(store(q10,seq,earray_16),tail,s(index_15)),seq),
inference(symmetry,[status(thm)],[1725]) ).
tff(1727,plain,
select(q11,seq) = earray_16,
inference(transitivity,[status(thm)],[1726,1723,1719,1707,1705]) ).
tff(1728,plain,
store(store(queue_11,tail,index_12),seq,select(q11,seq)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[1716,1727]) ).
tff(1729,plain,
select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(q10,seq,earray_16),head),
inference(monotonicity,[status(thm)],[1728]) ).
tff(1730,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1731,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1732,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head) ) ),
inference(modus_ponens,[status(thm)],[1731,1730]) ).
tff(1733,plain,
select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head) = select(store(queue_11,tail,index_12),head),
inference(unit_resolution,[status(thm)],[1732,79,189]) ).
tff(1734,plain,
select(store(queue_11,tail,index_12),head) = select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head),
inference(symmetry,[status(thm)],[1733]) ).
tff(1735,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1736,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(1737,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[1736,1735]) ).
tff(1738,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[1737]) ).
tff(1739,plain,
( ( queue_11 = store(q9,seq,earray_10) )
<=> ( queue_11 = store(q9,seq,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1740,axiom,
queue_11 = store(q9,seq,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(1741,plain,
queue_11 = store(q9,seq,earray_10),
inference(modus_ponens,[status(thm)],[1740,1739]) ).
tff(1742,plain,
store(q9,seq,earray_10) = queue_11,
inference(symmetry,[status(thm)],[1741]) ).
tff(1743,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = store(queue_11,tail,index_12),
inference(monotonicity,[status(thm)],[1742,1738]) ).
tff(1744,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(queue_11,tail,index_12),head),
inference(monotonicity,[status(thm)],[1743]) ).
tff(1745,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1746,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1747,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(modus_ponens,[status(thm)],[1746,1745]) ).
tff(1748,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),head) = select(store(q9,seq,earray_10),head),
inference(unit_resolution,[status(thm)],[1747,79,126]) ).
tff(1749,plain,
select(store(q9,seq,earray_10),head) = select(store(store(q9,seq,earray_10),tail,s(index_9)),head),
inference(symmetry,[status(thm)],[1748]) ).
tff(1750,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1751,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(1752,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[1751,1750]) ).
tff(1753,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[1752]) ).
tff(1754,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_277,head,index_279),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1755,plain,
select(store(store(queue_277,head,index_279),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9),
inference(unit_resolution,[status(thm)],[1754,27]) ).
tff(1756,plain,
( ( q9 = queue_280 )
<=> ( q9 = queue_280 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1757,axiom,
q9 = queue_280,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp324) ).
tff(1758,plain,
q9 = queue_280,
inference(modus_ponens,[status(thm)],[1757,1756]) ).
tff(1759,plain,
queue_280 = q9,
inference(symmetry,[status(thm)],[1758]) ).
tff(1760,plain,
( ( queue_280 = store(queue_277,head,index_279) )
<=> ( queue_280 = store(queue_277,head,index_279) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1761,axiom,
queue_280 = store(queue_277,head,index_279),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp258) ).
tff(1762,plain,
queue_280 = store(queue_277,head,index_279),
inference(modus_ponens,[status(thm)],[1761,1760]) ).
tff(1763,plain,
store(queue_277,head,index_279) = queue_280,
inference(symmetry,[status(thm)],[1762]) ).
tff(1764,plain,
store(queue_277,head,index_279) = q9,
inference(transitivity,[status(thm)],[1763,1759]) ).
tff(1765,plain,
store(store(queue_277,head,index_279),seq,store(earray_8,index_9,e9)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[1764,1753]) ).
tff(1766,plain,
select(store(store(queue_277,head,index_279),seq,store(earray_8,index_9,e9)),seq) = select(store(q9,seq,earray_10),seq),
inference(monotonicity,[status(thm)],[1765]) ).
tff(1767,plain,
select(store(q9,seq,earray_10),seq) = select(store(store(queue_277,head,index_279),seq,store(earray_8,index_9,e9)),seq),
inference(symmetry,[status(thm)],[1766]) ).
tff(1768,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1769,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1770,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq) ) ),
inference(modus_ponens,[status(thm)],[1769,1768]) ).
tff(1771,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(store(q9,seq,earray_10),seq),
inference(unit_resolution,[status(thm)],[1770,79,153]) ).
tff(1772,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = q10,
inference(transitivity,[status(thm)],[1743,1715,1711]) ).
tff(1773,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(q10,seq),
inference(monotonicity,[status(thm)],[1772]) ).
tff(1774,plain,
select(q10,seq) = select(store(store(q9,seq,earray_10),tail,s(index_9)),seq),
inference(symmetry,[status(thm)],[1773]) ).
tff(1775,plain,
select(q10,seq) = earray_10,
inference(transitivity,[status(thm)],[1774,1771,1767,1755,1753]) ).
tff(1776,plain,
store(store(queue_277,head,index_279),seq,select(q10,seq)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[1764,1775]) ).
tff(1777,plain,
select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(q9,seq,earray_10),head),
inference(monotonicity,[status(thm)],[1776]) ).
tff(1778,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(queue_277,head,index_279),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(queue_277,head,index_279),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1779,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(queue_277,head,index_279),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1780,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(queue_277,head,index_279),head) ) ),
inference(modus_ponens,[status(thm)],[1779,1778]) ).
tff(1781,plain,
select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head) = select(store(queue_277,head,index_279),head),
inference(unit_resolution,[status(thm)],[1780,79,189]) ).
tff(1782,plain,
select(store(queue_277,head,index_279),head) = select(store(store(queue_277,head,index_279),seq,select(q10,seq)),head),
inference(symmetry,[status(thm)],[1781]) ).
tff(1783,plain,
( ( index_279 = s(index_278) )
<=> ( index_279 = s(index_278) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1784,axiom,
index_279 = s(index_278),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(1785,plain,
index_279 = s(index_278),
inference(modus_ponens,[status(thm)],[1784,1783]) ).
tff(1786,plain,
s(index_278) = index_279,
inference(symmetry,[status(thm)],[1785]) ).
tff(1787,plain,
( ( queue_277 = store(queue_275,tail,index_276) )
<=> ( queue_277 = store(queue_275,tail,index_276) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1788,axiom,
queue_277 = store(queue_275,tail,index_276),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp256) ).
tff(1789,plain,
queue_277 = store(queue_275,tail,index_276),
inference(modus_ponens,[status(thm)],[1788,1787]) ).
tff(1790,plain,
store(queue_275,tail,index_276) = queue_277,
inference(symmetry,[status(thm)],[1789]) ).
tff(1791,plain,
store(store(queue_275,tail,index_276),head,s(index_278)) = store(queue_277,head,index_279),
inference(monotonicity,[status(thm)],[1790,1786]) ).
tff(1792,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = select(store(queue_277,head,index_279),head),
inference(monotonicity,[status(thm)],[1791]) ).
tff(1793,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = s(index_278) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1794,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),head) = s(index_278),
inference(unit_resolution,[status(thm)],[1793,27]) ).
tff(1795,plain,
s(index_278) = select(store(store(queue_275,tail,index_276),head,s(index_278)),head),
inference(symmetry,[status(thm)],[1794]) ).
tff(1796,plain,
( ( index_278 = select(queue_277,head) )
<=> ( index_278 = select(queue_277,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1797,axiom,
index_278 = select(queue_277,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(1798,plain,
index_278 = select(queue_277,head),
inference(modus_ponens,[status(thm)],[1797,1796]) ).
tff(1799,plain,
select(queue_277,head) = index_278,
inference(symmetry,[status(thm)],[1798]) ).
tff(1800,plain,
( ( index_276 = s(index_273) )
<=> ( index_276 = s(index_273) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1801,axiom,
index_276 = s(index_273),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(1802,plain,
index_276 = s(index_273),
inference(modus_ponens,[status(thm)],[1801,1800]) ).
tff(1803,plain,
s(index_273) = index_276,
inference(symmetry,[status(thm)],[1802]) ).
tff(1804,plain,
( ( queue_275 = store(q8,seq,earray_274) )
<=> ( queue_275 = store(q8,seq,earray_274) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1805,axiom,
queue_275 = store(q8,seq,earray_274),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp255) ).
tff(1806,plain,
queue_275 = store(q8,seq,earray_274),
inference(modus_ponens,[status(thm)],[1805,1804]) ).
tff(1807,plain,
store(q8,seq,earray_274) = queue_275,
inference(symmetry,[status(thm)],[1806]) ).
tff(1808,plain,
store(store(q8,seq,earray_274),tail,s(index_273)) = store(queue_275,tail,index_276),
inference(monotonicity,[status(thm)],[1807,1803]) ).
tff(1809,plain,
store(store(q8,seq,earray_274),tail,s(index_273)) = queue_277,
inference(transitivity,[status(thm)],[1808,1790]) ).
tff(1810,plain,
select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(queue_277,head),
inference(monotonicity,[status(thm)],[1809]) ).
tff(1811,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1812,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1813,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head) ) ),
inference(modus_ponens,[status(thm)],[1812,1811]) ).
tff(1814,plain,
( ( tail = head )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head) ) ),
inference(unit_resolution,[status(thm)],[1813,79]) ).
tff(1815,plain,
select(store(store(q8,seq,earray_274),tail,s(index_273)),head) = select(store(q8,seq,earray_274),head),
inference(unit_resolution,[status(thm)],[1814,126]) ).
tff(1816,plain,
select(store(q8,seq,earray_274),head) = select(store(store(q8,seq,earray_274),tail,s(index_273)),head),
inference(symmetry,[status(thm)],[1815]) ).
tff(1817,plain,
( ( earray_274 = store(earray_272,index_273,e8) )
<=> ( earray_274 = store(earray_272,index_273,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1818,axiom,
earray_274 = store(earray_272,index_273,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(1819,plain,
earray_274 = store(earray_272,index_273,e8),
inference(modus_ponens,[status(thm)],[1818,1817]) ).
tff(1820,plain,
store(earray_272,index_273,e8) = earray_274,
inference(symmetry,[status(thm)],[1819]) ).
tff(1821,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e8)),seq) = store(earray_272,index_273,e8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1822,plain,
select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e8)),seq) = store(earray_272,index_273,e8),
inference(unit_resolution,[status(thm)],[1821,27]) ).
tff(1823,plain,
( ( q8 = queue_271 )
<=> ( q8 = queue_271 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1824,axiom,
q8 = queue_271,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp323) ).
tff(1825,plain,
q8 = queue_271,
inference(modus_ponens,[status(thm)],[1824,1823]) ).
tff(1826,plain,
queue_271 = q8,
inference(symmetry,[status(thm)],[1825]) ).
tff(1827,plain,
( ( queue_271 = store(queue_269,tail,index_270) )
<=> ( queue_271 = store(queue_269,tail,index_270) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1828,axiom,
queue_271 = store(queue_269,tail,index_270),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp254) ).
tff(1829,plain,
queue_271 = store(queue_269,tail,index_270),
inference(modus_ponens,[status(thm)],[1828,1827]) ).
tff(1830,plain,
store(queue_269,tail,index_270) = queue_271,
inference(symmetry,[status(thm)],[1829]) ).
tff(1831,plain,
store(queue_269,tail,index_270) = q8,
inference(transitivity,[status(thm)],[1830,1826]) ).
tff(1832,plain,
store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e8)) = store(q8,seq,earray_274),
inference(monotonicity,[status(thm)],[1831,1820]) ).
tff(1833,plain,
select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e8)),seq) = select(store(q8,seq,earray_274),seq),
inference(monotonicity,[status(thm)],[1832]) ).
tff(1834,plain,
select(store(q8,seq,earray_274),seq) = select(store(store(queue_269,tail,index_270),seq,store(earray_272,index_273,e8)),seq),
inference(symmetry,[status(thm)],[1833]) ).
tff(1835,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(q8,seq,earray_274),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(q8,seq,earray_274),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1836,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(q8,seq,earray_274),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1837,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(q8,seq,earray_274),seq) ) ),
inference(modus_ponens,[status(thm)],[1836,1835]) ).
tff(1838,plain,
select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(q8,seq,earray_274),seq),
inference(unit_resolution,[status(thm)],[1837,79,153]) ).
tff(1839,plain,
select(store(store(q8,seq,earray_274),tail,s(index_273)),seq) = select(store(queue_275,tail,index_276),seq),
inference(monotonicity,[status(thm)],[1808]) ).
tff(1840,plain,
select(store(queue_275,tail,index_276),seq) = select(store(store(q8,seq,earray_274),tail,s(index_273)),seq),
inference(symmetry,[status(thm)],[1839]) ).
tff(1841,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1842,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1843,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq) ) ),
inference(modus_ponens,[status(thm)],[1842,1841]) ).
tff(1844,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(store(queue_275,tail,index_276),seq),
inference(unit_resolution,[status(thm)],[1843,79,162]) ).
tff(1845,plain,
store(store(queue_275,tail,index_276),head,s(index_278)) = q9,
inference(transitivity,[status(thm)],[1791,1763,1759]) ).
tff(1846,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),seq) = select(q9,seq),
inference(monotonicity,[status(thm)],[1845]) ).
tff(1847,plain,
select(q9,seq) = select(store(store(queue_275,tail,index_276),head,s(index_278)),seq),
inference(symmetry,[status(thm)],[1846]) ).
tff(1848,plain,
select(q9,seq) = earray_274,
inference(transitivity,[status(thm)],[1847,1844,1840,1838,1834,1822,1820]) ).
tff(1849,plain,
store(store(queue_269,tail,index_270),seq,select(q9,seq)) = store(q8,seq,earray_274),
inference(monotonicity,[status(thm)],[1831,1848]) ).
tff(1850,plain,
select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(q8,seq,earray_274),head),
inference(monotonicity,[status(thm)],[1849]) ).
tff(1851,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1852,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1853,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(modus_ponens,[status(thm)],[1852,1851]) ).
tff(1854,plain,
( ( seq = head )
| ( select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head) ) ),
inference(unit_resolution,[status(thm)],[1853,79]) ).
tff(1855,plain,
select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head) = select(store(queue_269,tail,index_270),head),
inference(unit_resolution,[status(thm)],[1854,189]) ).
tff(1856,plain,
select(store(queue_269,tail,index_270),head) = select(store(store(queue_269,tail,index_270),seq,select(q9,seq)),head),
inference(symmetry,[status(thm)],[1855]) ).
tff(1857,plain,
( ( index_270 = s(index_267) )
<=> ( index_270 = s(index_267) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1858,axiom,
index_270 = s(index_267),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(1859,plain,
index_270 = s(index_267),
inference(modus_ponens,[status(thm)],[1858,1857]) ).
tff(1860,plain,
s(index_267) = index_270,
inference(symmetry,[status(thm)],[1859]) ).
tff(1861,plain,
( ( queue_269 = store(q7,seq,earray_268) )
<=> ( queue_269 = store(q7,seq,earray_268) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1862,axiom,
queue_269 = store(q7,seq,earray_268),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp253) ).
tff(1863,plain,
queue_269 = store(q7,seq,earray_268),
inference(modus_ponens,[status(thm)],[1862,1861]) ).
tff(1864,plain,
store(q7,seq,earray_268) = queue_269,
inference(symmetry,[status(thm)],[1863]) ).
tff(1865,plain,
store(store(q7,seq,earray_268),tail,s(index_267)) = store(queue_269,tail,index_270),
inference(monotonicity,[status(thm)],[1864,1860]) ).
tff(1866,plain,
select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(queue_269,tail,index_270),head),
inference(monotonicity,[status(thm)],[1865]) ).
tff(1867,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(q7,seq,earray_268),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(q7,seq,earray_268),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1868,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(q7,seq,earray_268),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1869,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(q7,seq,earray_268),head) ) ),
inference(modus_ponens,[status(thm)],[1868,1867]) ).
tff(1870,plain,
select(store(store(q7,seq,earray_268),tail,s(index_267)),head) = select(store(q7,seq,earray_268),head),
inference(unit_resolution,[status(thm)],[1869,79,126]) ).
tff(1871,plain,
select(store(q7,seq,earray_268),head) = select(store(store(q7,seq,earray_268),tail,s(index_267)),head),
inference(symmetry,[status(thm)],[1870]) ).
tff(1872,plain,
( ( earray_268 = store(earray_266,index_267,e7) )
<=> ( earray_268 = store(earray_266,index_267,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1873,axiom,
earray_268 = store(earray_266,index_267,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(1874,plain,
earray_268 = store(earray_266,index_267,e7),
inference(modus_ponens,[status(thm)],[1873,1872]) ).
tff(1875,plain,
store(earray_266,index_267,e7) = earray_268,
inference(symmetry,[status(thm)],[1874]) ).
tff(1876,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e7)),seq) = store(earray_266,index_267,e7) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1877,plain,
select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e7)),seq) = store(earray_266,index_267,e7),
inference(unit_resolution,[status(thm)],[1876,27]) ).
tff(1878,plain,
( ( q7 = queue_265 )
<=> ( q7 = queue_265 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1879,axiom,
q7 = queue_265,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp322) ).
tff(1880,plain,
q7 = queue_265,
inference(modus_ponens,[status(thm)],[1879,1878]) ).
tff(1881,plain,
queue_265 = q7,
inference(symmetry,[status(thm)],[1880]) ).
tff(1882,plain,
( ( queue_265 = store(queue_263,tail,index_264) )
<=> ( queue_265 = store(queue_263,tail,index_264) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1883,axiom,
queue_265 = store(queue_263,tail,index_264),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp252) ).
tff(1884,plain,
queue_265 = store(queue_263,tail,index_264),
inference(modus_ponens,[status(thm)],[1883,1882]) ).
tff(1885,plain,
store(queue_263,tail,index_264) = queue_265,
inference(symmetry,[status(thm)],[1884]) ).
tff(1886,plain,
store(queue_263,tail,index_264) = q7,
inference(transitivity,[status(thm)],[1885,1881]) ).
tff(1887,plain,
store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e7)) = store(q7,seq,earray_268),
inference(monotonicity,[status(thm)],[1886,1875]) ).
tff(1888,plain,
select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e7)),seq) = select(store(q7,seq,earray_268),seq),
inference(monotonicity,[status(thm)],[1887]) ).
tff(1889,plain,
select(store(q7,seq,earray_268),seq) = select(store(store(queue_263,tail,index_264),seq,store(earray_266,index_267,e7)),seq),
inference(symmetry,[status(thm)],[1888]) ).
tff(1890,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(store(q7,seq,earray_268),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(store(q7,seq,earray_268),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1891,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(store(q7,seq,earray_268),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1892,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(store(q7,seq,earray_268),seq) ) ),
inference(modus_ponens,[status(thm)],[1891,1890]) ).
tff(1893,plain,
select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(store(q7,seq,earray_268),seq),
inference(unit_resolution,[status(thm)],[1892,79,153]) ).
tff(1894,plain,
store(store(q7,seq,earray_268),tail,s(index_267)) = q8,
inference(transitivity,[status(thm)],[1865,1830,1826]) ).
tff(1895,plain,
select(store(store(q7,seq,earray_268),tail,s(index_267)),seq) = select(q8,seq),
inference(monotonicity,[status(thm)],[1894]) ).
tff(1896,plain,
select(q8,seq) = select(store(store(q7,seq,earray_268),tail,s(index_267)),seq),
inference(symmetry,[status(thm)],[1895]) ).
tff(1897,plain,
select(q8,seq) = earray_268,
inference(transitivity,[status(thm)],[1896,1893,1889,1877,1875]) ).
tff(1898,plain,
store(store(queue_263,tail,index_264),seq,select(q8,seq)) = store(q7,seq,earray_268),
inference(monotonicity,[status(thm)],[1886,1897]) ).
tff(1899,plain,
select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(q7,seq,earray_268),head),
inference(monotonicity,[status(thm)],[1898]) ).
tff(1900,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(queue_263,tail,index_264),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(queue_263,tail,index_264),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1901,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(queue_263,tail,index_264),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1902,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(queue_263,tail,index_264),head) ) ),
inference(modus_ponens,[status(thm)],[1901,1900]) ).
tff(1903,plain,
select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head) = select(store(queue_263,tail,index_264),head),
inference(unit_resolution,[status(thm)],[1902,79,189]) ).
tff(1904,plain,
select(store(queue_263,tail,index_264),head) = select(store(store(queue_263,tail,index_264),seq,select(q8,seq)),head),
inference(symmetry,[status(thm)],[1903]) ).
tff(1905,plain,
( ( index_264 = s(index_261) )
<=> ( index_264 = s(index_261) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1906,axiom,
index_264 = s(index_261),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(1907,plain,
index_264 = s(index_261),
inference(modus_ponens,[status(thm)],[1906,1905]) ).
tff(1908,plain,
s(index_261) = index_264,
inference(symmetry,[status(thm)],[1907]) ).
tff(1909,plain,
( ( queue_263 = store(q6,seq,earray_262) )
<=> ( queue_263 = store(q6,seq,earray_262) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1910,axiom,
queue_263 = store(q6,seq,earray_262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp251) ).
tff(1911,plain,
queue_263 = store(q6,seq,earray_262),
inference(modus_ponens,[status(thm)],[1910,1909]) ).
tff(1912,plain,
store(q6,seq,earray_262) = queue_263,
inference(symmetry,[status(thm)],[1911]) ).
tff(1913,plain,
store(store(q6,seq,earray_262),tail,s(index_261)) = store(queue_263,tail,index_264),
inference(monotonicity,[status(thm)],[1912,1908]) ).
tff(1914,plain,
select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(queue_263,tail,index_264),head),
inference(monotonicity,[status(thm)],[1913]) ).
tff(1915,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(q6,seq,earray_262),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(q6,seq,earray_262),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1916,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(q6,seq,earray_262),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1917,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(q6,seq,earray_262),head) ) ),
inference(modus_ponens,[status(thm)],[1916,1915]) ).
tff(1918,plain,
select(store(store(q6,seq,earray_262),tail,s(index_261)),head) = select(store(q6,seq,earray_262),head),
inference(unit_resolution,[status(thm)],[1917,79,126]) ).
tff(1919,plain,
select(store(q6,seq,earray_262),head) = select(store(store(q6,seq,earray_262),tail,s(index_261)),head),
inference(symmetry,[status(thm)],[1918]) ).
tff(1920,plain,
( ( earray_262 = store(earray_260,index_261,e6) )
<=> ( earray_262 = store(earray_260,index_261,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1921,axiom,
earray_262 = store(earray_260,index_261,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(1922,plain,
earray_262 = store(earray_260,index_261,e6),
inference(modus_ponens,[status(thm)],[1921,1920]) ).
tff(1923,plain,
store(earray_260,index_261,e6) = earray_262,
inference(symmetry,[status(thm)],[1922]) ).
tff(1924,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e6)),seq) = store(earray_260,index_261,e6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1925,plain,
select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e6)),seq) = store(earray_260,index_261,e6),
inference(unit_resolution,[status(thm)],[1924,27]) ).
tff(1926,plain,
( ( q6 = queue_259 )
<=> ( q6 = queue_259 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1927,axiom,
q6 = queue_259,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp321) ).
tff(1928,plain,
q6 = queue_259,
inference(modus_ponens,[status(thm)],[1927,1926]) ).
tff(1929,plain,
queue_259 = q6,
inference(symmetry,[status(thm)],[1928]) ).
tff(1930,plain,
( ( queue_259 = store(queue_256,head,index_258) )
<=> ( queue_259 = store(queue_256,head,index_258) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1931,axiom,
queue_259 = store(queue_256,head,index_258),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp250) ).
tff(1932,plain,
queue_259 = store(queue_256,head,index_258),
inference(modus_ponens,[status(thm)],[1931,1930]) ).
tff(1933,plain,
store(queue_256,head,index_258) = queue_259,
inference(symmetry,[status(thm)],[1932]) ).
tff(1934,plain,
store(queue_256,head,index_258) = q6,
inference(transitivity,[status(thm)],[1933,1929]) ).
tff(1935,plain,
store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e6)) = store(q6,seq,earray_262),
inference(monotonicity,[status(thm)],[1934,1923]) ).
tff(1936,plain,
select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e6)),seq) = select(store(q6,seq,earray_262),seq),
inference(monotonicity,[status(thm)],[1935]) ).
tff(1937,plain,
select(store(q6,seq,earray_262),seq) = select(store(store(queue_256,head,index_258),seq,store(earray_260,index_261,e6)),seq),
inference(symmetry,[status(thm)],[1936]) ).
tff(1938,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(store(q6,seq,earray_262),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(store(q6,seq,earray_262),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1939,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(store(q6,seq,earray_262),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1940,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(store(q6,seq,earray_262),seq) ) ),
inference(modus_ponens,[status(thm)],[1939,1938]) ).
tff(1941,plain,
select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(store(q6,seq,earray_262),seq),
inference(unit_resolution,[status(thm)],[1940,79,153]) ).
tff(1942,plain,
store(store(q6,seq,earray_262),tail,s(index_261)) = q7,
inference(transitivity,[status(thm)],[1913,1885,1881]) ).
tff(1943,plain,
select(store(store(q6,seq,earray_262),tail,s(index_261)),seq) = select(q7,seq),
inference(monotonicity,[status(thm)],[1942]) ).
tff(1944,plain,
select(q7,seq) = select(store(store(q6,seq,earray_262),tail,s(index_261)),seq),
inference(symmetry,[status(thm)],[1943]) ).
tff(1945,plain,
select(q7,seq) = earray_262,
inference(transitivity,[status(thm)],[1944,1941,1937,1925,1923]) ).
tff(1946,plain,
store(store(queue_256,head,index_258),seq,select(q7,seq)) = store(q6,seq,earray_262),
inference(monotonicity,[status(thm)],[1934,1945]) ).
tff(1947,plain,
select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(q6,seq,earray_262),head),
inference(monotonicity,[status(thm)],[1946]) ).
tff(1948,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(queue_256,head,index_258),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(queue_256,head,index_258),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1949,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(queue_256,head,index_258),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1950,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(queue_256,head,index_258),head) ) ),
inference(modus_ponens,[status(thm)],[1949,1948]) ).
tff(1951,plain,
select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head) = select(store(queue_256,head,index_258),head),
inference(unit_resolution,[status(thm)],[1950,79,189]) ).
tff(1952,plain,
select(store(queue_256,head,index_258),head) = select(store(store(queue_256,head,index_258),seq,select(q7,seq)),head),
inference(symmetry,[status(thm)],[1951]) ).
tff(1953,plain,
( ( index_258 = s(index_257) )
<=> ( index_258 = s(index_257) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1954,axiom,
index_258 = s(index_257),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(1955,plain,
index_258 = s(index_257),
inference(modus_ponens,[status(thm)],[1954,1953]) ).
tff(1956,plain,
s(index_257) = index_258,
inference(symmetry,[status(thm)],[1955]) ).
tff(1957,plain,
( ( queue_256 = store(queue_254,tail,index_255) )
<=> ( queue_256 = store(queue_254,tail,index_255) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1958,axiom,
queue_256 = store(queue_254,tail,index_255),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp249) ).
tff(1959,plain,
queue_256 = store(queue_254,tail,index_255),
inference(modus_ponens,[status(thm)],[1958,1957]) ).
tff(1960,plain,
store(queue_254,tail,index_255) = queue_256,
inference(symmetry,[status(thm)],[1959]) ).
tff(1961,plain,
store(store(queue_254,tail,index_255),head,s(index_257)) = store(queue_256,head,index_258),
inference(monotonicity,[status(thm)],[1960,1956]) ).
tff(1962,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = select(store(queue_256,head,index_258),head),
inference(monotonicity,[status(thm)],[1961]) ).
tff(1963,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = s(index_257) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1964,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),head) = s(index_257),
inference(unit_resolution,[status(thm)],[1963,27]) ).
tff(1965,plain,
s(index_257) = select(store(store(queue_254,tail,index_255),head,s(index_257)),head),
inference(symmetry,[status(thm)],[1964]) ).
tff(1966,plain,
( ( index_257 = select(queue_256,head) )
<=> ( index_257 = select(queue_256,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1967,axiom,
index_257 = select(queue_256,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(1968,plain,
index_257 = select(queue_256,head),
inference(modus_ponens,[status(thm)],[1967,1966]) ).
tff(1969,plain,
select(queue_256,head) = index_257,
inference(symmetry,[status(thm)],[1968]) ).
tff(1970,plain,
( ( index_255 = s(index_252) )
<=> ( index_255 = s(index_252) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1971,axiom,
index_255 = s(index_252),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(1972,plain,
index_255 = s(index_252),
inference(modus_ponens,[status(thm)],[1971,1970]) ).
tff(1973,plain,
s(index_252) = index_255,
inference(symmetry,[status(thm)],[1972]) ).
tff(1974,plain,
( ( queue_254 = store(q5,seq,earray_253) )
<=> ( queue_254 = store(q5,seq,earray_253) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1975,axiom,
queue_254 = store(q5,seq,earray_253),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp248) ).
tff(1976,plain,
queue_254 = store(q5,seq,earray_253),
inference(modus_ponens,[status(thm)],[1975,1974]) ).
tff(1977,plain,
store(q5,seq,earray_253) = queue_254,
inference(symmetry,[status(thm)],[1976]) ).
tff(1978,plain,
store(store(q5,seq,earray_253),tail,s(index_252)) = store(queue_254,tail,index_255),
inference(monotonicity,[status(thm)],[1977,1973]) ).
tff(1979,plain,
store(store(q5,seq,earray_253),tail,s(index_252)) = queue_256,
inference(transitivity,[status(thm)],[1978,1960]) ).
tff(1980,plain,
select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(queue_256,head),
inference(monotonicity,[status(thm)],[1979]) ).
tff(1981,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1982,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1983,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head) ) ),
inference(modus_ponens,[status(thm)],[1982,1981]) ).
tff(1984,plain,
( ( tail = head )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head) ) ),
inference(unit_resolution,[status(thm)],[1983,79]) ).
tff(1985,plain,
select(store(store(q5,seq,earray_253),tail,s(index_252)),head) = select(store(q5,seq,earray_253),head),
inference(unit_resolution,[status(thm)],[1984,126]) ).
tff(1986,plain,
select(store(q5,seq,earray_253),head) = select(store(store(q5,seq,earray_253),tail,s(index_252)),head),
inference(symmetry,[status(thm)],[1985]) ).
tff(1987,plain,
( ( earray_253 = store(earray_251,index_252,e5) )
<=> ( earray_253 = store(earray_251,index_252,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1988,axiom,
earray_253 = store(earray_251,index_252,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(1989,plain,
earray_253 = store(earray_251,index_252,e5),
inference(modus_ponens,[status(thm)],[1988,1987]) ).
tff(1990,plain,
store(earray_251,index_252,e5) = earray_253,
inference(symmetry,[status(thm)],[1989]) ).
tff(1991,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e5)),seq) = store(earray_251,index_252,e5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1992,plain,
select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e5)),seq) = store(earray_251,index_252,e5),
inference(unit_resolution,[status(thm)],[1991,27]) ).
tff(1993,plain,
( ( q5 = queue_250 )
<=> ( q5 = queue_250 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1994,axiom,
q5 = queue_250,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp320) ).
tff(1995,plain,
q5 = queue_250,
inference(modus_ponens,[status(thm)],[1994,1993]) ).
tff(1996,plain,
queue_250 = q5,
inference(symmetry,[status(thm)],[1995]) ).
tff(1997,plain,
( ( queue_250 = store(queue_248,tail,index_249) )
<=> ( queue_250 = store(queue_248,tail,index_249) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1998,axiom,
queue_250 = store(queue_248,tail,index_249),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp247) ).
tff(1999,plain,
queue_250 = store(queue_248,tail,index_249),
inference(modus_ponens,[status(thm)],[1998,1997]) ).
tff(2000,plain,
store(queue_248,tail,index_249) = queue_250,
inference(symmetry,[status(thm)],[1999]) ).
tff(2001,plain,
store(queue_248,tail,index_249) = q5,
inference(transitivity,[status(thm)],[2000,1996]) ).
tff(2002,plain,
store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e5)) = store(q5,seq,earray_253),
inference(monotonicity,[status(thm)],[2001,1990]) ).
tff(2003,plain,
select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e5)),seq) = select(store(q5,seq,earray_253),seq),
inference(monotonicity,[status(thm)],[2002]) ).
tff(2004,plain,
select(store(q5,seq,earray_253),seq) = select(store(store(queue_248,tail,index_249),seq,store(earray_251,index_252,e5)),seq),
inference(symmetry,[status(thm)],[2003]) ).
tff(2005,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(q5,seq,earray_253),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(q5,seq,earray_253),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2006,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(q5,seq,earray_253),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2007,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(q5,seq,earray_253),seq) ) ),
inference(modus_ponens,[status(thm)],[2006,2005]) ).
tff(2008,plain,
select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(q5,seq,earray_253),seq),
inference(unit_resolution,[status(thm)],[2007,79,153]) ).
tff(2009,plain,
select(store(store(q5,seq,earray_253),tail,s(index_252)),seq) = select(store(queue_254,tail,index_255),seq),
inference(monotonicity,[status(thm)],[1978]) ).
tff(2010,plain,
select(store(queue_254,tail,index_255),seq) = select(store(store(q5,seq,earray_253),tail,s(index_252)),seq),
inference(symmetry,[status(thm)],[2009]) ).
tff(2011,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2012,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2013,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq) ) ),
inference(modus_ponens,[status(thm)],[2012,2011]) ).
tff(2014,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(store(queue_254,tail,index_255),seq),
inference(unit_resolution,[status(thm)],[2013,79,162]) ).
tff(2015,plain,
store(store(queue_254,tail,index_255),head,s(index_257)) = q6,
inference(transitivity,[status(thm)],[1961,1933,1929]) ).
tff(2016,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),seq) = select(q6,seq),
inference(monotonicity,[status(thm)],[2015]) ).
tff(2017,plain,
select(q6,seq) = select(store(store(queue_254,tail,index_255),head,s(index_257)),seq),
inference(symmetry,[status(thm)],[2016]) ).
tff(2018,plain,
select(q6,seq) = earray_253,
inference(transitivity,[status(thm)],[2017,2014,2010,2008,2004,1992,1990]) ).
tff(2019,plain,
store(store(queue_248,tail,index_249),seq,select(q6,seq)) = store(q5,seq,earray_253),
inference(monotonicity,[status(thm)],[2001,2018]) ).
tff(2020,plain,
select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(q5,seq,earray_253),head),
inference(monotonicity,[status(thm)],[2019]) ).
tff(2021,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2022,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2023,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(modus_ponens,[status(thm)],[2022,2021]) ).
tff(2024,plain,
( ( seq = head )
| ( select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head) ) ),
inference(unit_resolution,[status(thm)],[2023,79]) ).
tff(2025,plain,
select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head) = select(store(queue_248,tail,index_249),head),
inference(unit_resolution,[status(thm)],[2024,189]) ).
tff(2026,plain,
select(store(queue_248,tail,index_249),head) = select(store(store(queue_248,tail,index_249),seq,select(q6,seq)),head),
inference(symmetry,[status(thm)],[2025]) ).
tff(2027,plain,
( ( index_249 = s(index_246) )
<=> ( index_249 = s(index_246) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2028,axiom,
index_249 = s(index_246),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(2029,plain,
index_249 = s(index_246),
inference(modus_ponens,[status(thm)],[2028,2027]) ).
tff(2030,plain,
s(index_246) = index_249,
inference(symmetry,[status(thm)],[2029]) ).
tff(2031,plain,
( ( queue_248 = store(q4,seq,earray_247) )
<=> ( queue_248 = store(q4,seq,earray_247) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2032,axiom,
queue_248 = store(q4,seq,earray_247),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(2033,plain,
queue_248 = store(q4,seq,earray_247),
inference(modus_ponens,[status(thm)],[2032,2031]) ).
tff(2034,plain,
store(q4,seq,earray_247) = queue_248,
inference(symmetry,[status(thm)],[2033]) ).
tff(2035,plain,
store(store(q4,seq,earray_247),tail,s(index_246)) = store(queue_248,tail,index_249),
inference(monotonicity,[status(thm)],[2034,2030]) ).
tff(2036,plain,
select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(queue_248,tail,index_249),head),
inference(monotonicity,[status(thm)],[2035]) ).
tff(2037,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(q4,seq,earray_247),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(q4,seq,earray_247),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2038,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(q4,seq,earray_247),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2039,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(q4,seq,earray_247),head) ) ),
inference(modus_ponens,[status(thm)],[2038,2037]) ).
tff(2040,plain,
select(store(store(q4,seq,earray_247),tail,s(index_246)),head) = select(store(q4,seq,earray_247),head),
inference(unit_resolution,[status(thm)],[2039,79,126]) ).
tff(2041,plain,
select(store(q4,seq,earray_247),head) = select(store(store(q4,seq,earray_247),tail,s(index_246)),head),
inference(symmetry,[status(thm)],[2040]) ).
tff(2042,plain,
( ( earray_247 = store(earray_245,index_246,e4) )
<=> ( earray_247 = store(earray_245,index_246,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2043,axiom,
earray_247 = store(earray_245,index_246,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(2044,plain,
earray_247 = store(earray_245,index_246,e4),
inference(modus_ponens,[status(thm)],[2043,2042]) ).
tff(2045,plain,
store(earray_245,index_246,e4) = earray_247,
inference(symmetry,[status(thm)],[2044]) ).
tff(2046,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_236,tail,index_237),seq,store(earray_245,index_246,e4)),seq) = store(earray_245,index_246,e4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2047,plain,
select(store(store(queue_236,tail,index_237),seq,store(earray_245,index_246,e4)),seq) = store(earray_245,index_246,e4),
inference(unit_resolution,[status(thm)],[2046,27]) ).
tff(2048,plain,
( ( q4 = queue_238 )
<=> ( q4 = queue_238 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2049,axiom,
q4 = queue_238,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp318) ).
tff(2050,plain,
q4 = queue_238,
inference(modus_ponens,[status(thm)],[2049,2048]) ).
tff(2051,plain,
queue_238 = q4,
inference(symmetry,[status(thm)],[2050]) ).
tff(2052,plain,
( ( queue_238 = store(queue_236,tail,index_237) )
<=> ( queue_238 = store(queue_236,tail,index_237) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2053,axiom,
queue_238 = store(queue_236,tail,index_237),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(2054,plain,
queue_238 = store(queue_236,tail,index_237),
inference(modus_ponens,[status(thm)],[2053,2052]) ).
tff(2055,plain,
store(queue_236,tail,index_237) = queue_238,
inference(symmetry,[status(thm)],[2054]) ).
tff(2056,plain,
store(queue_236,tail,index_237) = q4,
inference(transitivity,[status(thm)],[2055,2051]) ).
tff(2057,plain,
store(store(queue_236,tail,index_237),seq,store(earray_245,index_246,e4)) = store(q4,seq,earray_247),
inference(monotonicity,[status(thm)],[2056,2045]) ).
tff(2058,plain,
select(store(store(queue_236,tail,index_237),seq,store(earray_245,index_246,e4)),seq) = select(store(q4,seq,earray_247),seq),
inference(monotonicity,[status(thm)],[2057]) ).
tff(2059,plain,
select(store(q4,seq,earray_247),seq) = select(store(store(queue_236,tail,index_237),seq,store(earray_245,index_246,e4)),seq),
inference(symmetry,[status(thm)],[2058]) ).
tff(2060,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(store(q4,seq,earray_247),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(store(q4,seq,earray_247),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(store(q4,seq,earray_247),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2062,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(store(q4,seq,earray_247),seq) ) ),
inference(modus_ponens,[status(thm)],[2061,2060]) ).
tff(2063,plain,
select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(store(q4,seq,earray_247),seq),
inference(unit_resolution,[status(thm)],[2062,79,153]) ).
tff(2064,plain,
store(store(q4,seq,earray_247),tail,s(index_246)) = q5,
inference(transitivity,[status(thm)],[2035,2000,1996]) ).
tff(2065,plain,
select(store(store(q4,seq,earray_247),tail,s(index_246)),seq) = select(q5,seq),
inference(monotonicity,[status(thm)],[2064]) ).
tff(2066,plain,
select(q5,seq) = select(store(store(q4,seq,earray_247),tail,s(index_246)),seq),
inference(symmetry,[status(thm)],[2065]) ).
tff(2067,plain,
select(q5,seq) = earray_247,
inference(transitivity,[status(thm)],[2066,2063,2059,2047,2045]) ).
tff(2068,plain,
store(store(queue_236,tail,index_237),seq,select(q5,seq)) = store(q4,seq,earray_247),
inference(monotonicity,[status(thm)],[2056,2067]) ).
tff(2069,plain,
select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(q4,seq,earray_247),head),
inference(monotonicity,[status(thm)],[2068]) ).
tff(2070,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2071,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2072,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head) ) ),
inference(modus_ponens,[status(thm)],[2071,2070]) ).
tff(2073,plain,
select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head) = select(store(queue_236,tail,index_237),head),
inference(unit_resolution,[status(thm)],[2072,79,189]) ).
tff(2074,plain,
select(store(queue_236,tail,index_237),head) = select(store(store(queue_236,tail,index_237),seq,select(q5,seq)),head),
inference(symmetry,[status(thm)],[2073]) ).
tff(2075,plain,
( ( index_237 = s(index_234) )
<=> ( index_237 = s(index_234) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2076,axiom,
index_237 = s(index_234),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(2077,plain,
index_237 = s(index_234),
inference(modus_ponens,[status(thm)],[2076,2075]) ).
tff(2078,plain,
s(index_234) = index_237,
inference(symmetry,[status(thm)],[2077]) ).
tff(2079,plain,
( ( queue_236 = store(q3,seq,earray_235) )
<=> ( queue_236 = store(q3,seq,earray_235) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2080,axiom,
queue_236 = store(q3,seq,earray_235),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(2081,plain,
queue_236 = store(q3,seq,earray_235),
inference(modus_ponens,[status(thm)],[2080,2079]) ).
tff(2082,plain,
store(q3,seq,earray_235) = queue_236,
inference(symmetry,[status(thm)],[2081]) ).
tff(2083,plain,
store(store(q3,seq,earray_235),tail,s(index_234)) = store(queue_236,tail,index_237),
inference(monotonicity,[status(thm)],[2082,2078]) ).
tff(2084,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(queue_236,tail,index_237),head),
inference(monotonicity,[status(thm)],[2083]) ).
tff(2085,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2086,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2087,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head) ) ),
inference(modus_ponens,[status(thm)],[2086,2085]) ).
tff(2088,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),head) = select(store(q3,seq,earray_235),head),
inference(unit_resolution,[status(thm)],[2087,79,126]) ).
tff(2089,plain,
select(store(q3,seq,earray_235),head) = select(store(store(q3,seq,earray_235),tail,s(index_234)),head),
inference(symmetry,[status(thm)],[2088]) ).
tff(2090,plain,
( ( earray_235 = store(earray_233,index_234,e3) )
<=> ( earray_235 = store(earray_233,index_234,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2091,axiom,
earray_235 = store(earray_233,index_234,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp44) ).
tff(2092,plain,
earray_235 = store(earray_233,index_234,e3),
inference(modus_ponens,[status(thm)],[2091,2090]) ).
tff(2093,plain,
store(earray_233,index_234,e3) = earray_235,
inference(symmetry,[status(thm)],[2092]) ).
tff(2094,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = store(earray_233,index_234,e3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2095,plain,
select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = store(earray_233,index_234,e3),
inference(unit_resolution,[status(thm)],[2094,27]) ).
tff(2096,plain,
( ( q3 = queue_160 )
<=> ( q3 = queue_160 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2097,axiom,
q3 = queue_160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp307) ).
tff(2098,plain,
q3 = queue_160,
inference(modus_ponens,[status(thm)],[2097,2096]) ).
tff(2099,plain,
queue_160 = q3,
inference(symmetry,[status(thm)],[2098]) ).
tff(2100,plain,
( ( queue_160 = store(queue_157,head,index_159) )
<=> ( queue_160 = store(queue_157,head,index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2101,axiom,
queue_160 = store(queue_157,head,index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(2102,plain,
queue_160 = store(queue_157,head,index_159),
inference(modus_ponens,[status(thm)],[2101,2100]) ).
tff(2103,plain,
store(queue_157,head,index_159) = queue_160,
inference(symmetry,[status(thm)],[2102]) ).
tff(2104,plain,
store(queue_157,head,index_159) = q3,
inference(transitivity,[status(thm)],[2103,2099]) ).
tff(2105,plain,
store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)) = store(q3,seq,earray_235),
inference(monotonicity,[status(thm)],[2104,2093]) ).
tff(2106,plain,
select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq) = select(store(q3,seq,earray_235),seq),
inference(monotonicity,[status(thm)],[2105]) ).
tff(2107,plain,
select(store(q3,seq,earray_235),seq) = select(store(store(queue_157,head,index_159),seq,store(earray_233,index_234,e3)),seq),
inference(symmetry,[status(thm)],[2106]) ).
tff(2108,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2109,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2110,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq) ) ),
inference(modus_ponens,[status(thm)],[2109,2108]) ).
tff(2111,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(store(q3,seq,earray_235),seq),
inference(unit_resolution,[status(thm)],[2110,79,153]) ).
tff(2112,plain,
store(store(q3,seq,earray_235),tail,s(index_234)) = q4,
inference(transitivity,[status(thm)],[2083,2055,2051]) ).
tff(2113,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),seq) = select(q4,seq),
inference(monotonicity,[status(thm)],[2112]) ).
tff(2114,plain,
select(q4,seq) = select(store(store(q3,seq,earray_235),tail,s(index_234)),seq),
inference(symmetry,[status(thm)],[2113]) ).
tff(2115,plain,
select(q4,seq) = earray_235,
inference(transitivity,[status(thm)],[2114,2111,2107,2095,2093]) ).
tff(2116,plain,
store(store(queue_157,head,index_159),seq,select(q4,seq)) = store(q3,seq,earray_235),
inference(monotonicity,[status(thm)],[2104,2115]) ).
tff(2117,plain,
select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(q3,seq,earray_235),head),
inference(monotonicity,[status(thm)],[2116]) ).
tff(2118,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2119,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2120,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head) ) ),
inference(modus_ponens,[status(thm)],[2119,2118]) ).
tff(2121,plain,
select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head) = select(store(queue_157,head,index_159),head),
inference(unit_resolution,[status(thm)],[2120,79,189]) ).
tff(2122,plain,
select(store(queue_157,head,index_159),head) = select(store(store(queue_157,head,index_159),seq,select(q4,seq)),head),
inference(symmetry,[status(thm)],[2121]) ).
tff(2123,plain,
( ( index_159 = s(index_158) )
<=> ( index_159 = s(index_158) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2124,axiom,
index_159 = s(index_158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(2125,plain,
index_159 = s(index_158),
inference(modus_ponens,[status(thm)],[2124,2123]) ).
tff(2126,plain,
s(index_158) = index_159,
inference(symmetry,[status(thm)],[2125]) ).
tff(2127,plain,
( ( queue_157 = store(queue_155,tail,index_156) )
<=> ( queue_157 = store(queue_155,tail,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2128,axiom,
queue_157 = store(queue_155,tail,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(2129,plain,
queue_157 = store(queue_155,tail,index_156),
inference(modus_ponens,[status(thm)],[2128,2127]) ).
tff(2130,plain,
store(queue_155,tail,index_156) = queue_157,
inference(symmetry,[status(thm)],[2129]) ).
tff(2131,plain,
store(store(queue_155,tail,index_156),head,s(index_158)) = store(queue_157,head,index_159),
inference(monotonicity,[status(thm)],[2130,2126]) ).
tff(2132,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = select(store(queue_157,head,index_159),head),
inference(monotonicity,[status(thm)],[2131]) ).
tff(2133,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = s(index_158) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2134,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),head) = s(index_158),
inference(unit_resolution,[status(thm)],[2133,27]) ).
tff(2135,plain,
s(index_158) = select(store(store(queue_155,tail,index_156),head,s(index_158)),head),
inference(symmetry,[status(thm)],[2134]) ).
tff(2136,plain,
( ( index_158 = select(queue_157,head) )
<=> ( index_158 = select(queue_157,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2137,axiom,
index_158 = select(queue_157,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(2138,plain,
index_158 = select(queue_157,head),
inference(modus_ponens,[status(thm)],[2137,2136]) ).
tff(2139,plain,
select(queue_157,head) = index_158,
inference(symmetry,[status(thm)],[2138]) ).
tff(2140,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2141,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(2142,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[2141,2140]) ).
tff(2143,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[2142]) ).
tff(2144,plain,
( ( queue_155 = store(q2,seq,earray_154) )
<=> ( queue_155 = store(q2,seq,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2145,axiom,
queue_155 = store(q2,seq,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(2146,plain,
queue_155 = store(q2,seq,earray_154),
inference(modus_ponens,[status(thm)],[2145,2144]) ).
tff(2147,plain,
store(q2,seq,earray_154) = queue_155,
inference(symmetry,[status(thm)],[2146]) ).
tff(2148,plain,
store(store(q2,seq,earray_154),tail,s(index_153)) = store(queue_155,tail,index_156),
inference(monotonicity,[status(thm)],[2147,2143]) ).
tff(2149,plain,
store(store(q2,seq,earray_154),tail,s(index_153)) = queue_157,
inference(transitivity,[status(thm)],[2148,2130]) ).
tff(2150,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(queue_157,head),
inference(monotonicity,[status(thm)],[2149]) ).
tff(2151,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2152,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2153,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(modus_ponens,[status(thm)],[2152,2151]) ).
tff(2154,plain,
( ( tail = head )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head) ) ),
inference(unit_resolution,[status(thm)],[2153,79]) ).
tff(2155,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),head) = select(store(q2,seq,earray_154),head),
inference(unit_resolution,[status(thm)],[2154,126]) ).
tff(2156,plain,
select(store(q2,seq,earray_154),head) = select(store(store(q2,seq,earray_154),tail,s(index_153)),head),
inference(symmetry,[status(thm)],[2155]) ).
tff(2157,plain,
( ( earray_154 = store(earray_152,index_153,e2) )
<=> ( earray_154 = store(earray_152,index_153,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2158,axiom,
earray_154 = store(earray_152,index_153,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(2159,plain,
earray_154 = store(earray_152,index_153,e2),
inference(modus_ponens,[status(thm)],[2158,2157]) ).
tff(2160,plain,
store(earray_152,index_153,e2) = earray_154,
inference(symmetry,[status(thm)],[2159]) ).
tff(2161,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = store(earray_152,index_153,e2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2162,plain,
select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = store(earray_152,index_153,e2),
inference(unit_resolution,[status(thm)],[2161,27]) ).
tff(2163,plain,
( ( q2 = queue_82 )
<=> ( q2 = queue_82 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2164,axiom,
q2 = queue_82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp296) ).
tff(2165,plain,
q2 = queue_82,
inference(modus_ponens,[status(thm)],[2164,2163]) ).
tff(2166,plain,
queue_82 = q2,
inference(symmetry,[status(thm)],[2165]) ).
tff(2167,plain,
( ( queue_82 = store(queue_80,tail,index_81) )
<=> ( queue_82 = store(queue_80,tail,index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2168,axiom,
queue_82 = store(queue_80,tail,index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp278) ).
tff(2169,plain,
queue_82 = store(queue_80,tail,index_81),
inference(modus_ponens,[status(thm)],[2168,2167]) ).
tff(2170,plain,
store(queue_80,tail,index_81) = queue_82,
inference(symmetry,[status(thm)],[2169]) ).
tff(2171,plain,
store(queue_80,tail,index_81) = q2,
inference(transitivity,[status(thm)],[2170,2166]) ).
tff(2172,plain,
store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)) = store(q2,seq,earray_154),
inference(monotonicity,[status(thm)],[2171,2160]) ).
tff(2173,plain,
select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq) = select(store(q2,seq,earray_154),seq),
inference(monotonicity,[status(thm)],[2172]) ).
tff(2174,plain,
select(store(q2,seq,earray_154),seq) = select(store(store(queue_80,tail,index_81),seq,store(earray_152,index_153,e2)),seq),
inference(symmetry,[status(thm)],[2173]) ).
tff(2175,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2176,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2177,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq) ) ),
inference(modus_ponens,[status(thm)],[2176,2175]) ).
tff(2178,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(q2,seq,earray_154),seq),
inference(unit_resolution,[status(thm)],[2177,79,153]) ).
tff(2179,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),seq) = select(store(queue_155,tail,index_156),seq),
inference(monotonicity,[status(thm)],[2148]) ).
tff(2180,plain,
select(store(queue_155,tail,index_156),seq) = select(store(store(q2,seq,earray_154),tail,s(index_153)),seq),
inference(symmetry,[status(thm)],[2179]) ).
tff(2181,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2182,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2183,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = seq )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq) ) ),
inference(modus_ponens,[status(thm)],[2182,2181]) ).
tff(2184,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(store(queue_155,tail,index_156),seq),
inference(unit_resolution,[status(thm)],[2183,79,162]) ).
tff(2185,plain,
store(store(queue_155,tail,index_156),head,s(index_158)) = q3,
inference(transitivity,[status(thm)],[2131,2103,2099]) ).
tff(2186,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),seq) = select(q3,seq),
inference(monotonicity,[status(thm)],[2185]) ).
tff(2187,plain,
select(q3,seq) = select(store(store(queue_155,tail,index_156),head,s(index_158)),seq),
inference(symmetry,[status(thm)],[2186]) ).
tff(2188,plain,
select(q3,seq) = earray_154,
inference(transitivity,[status(thm)],[2187,2184,2180,2178,2174,2162,2160]) ).
tff(2189,plain,
store(store(queue_80,tail,index_81),seq,select(q3,seq)) = store(q2,seq,earray_154),
inference(monotonicity,[status(thm)],[2171,2188]) ).
tff(2190,plain,
select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(q2,seq,earray_154),head),
inference(monotonicity,[status(thm)],[2189]) ).
tff(2191,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2192,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2193,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(modus_ponens,[status(thm)],[2192,2191]) ).
tff(2194,plain,
( ( seq = head )
| ( select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head) ) ),
inference(unit_resolution,[status(thm)],[2193,79]) ).
tff(2195,plain,
select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head) = select(store(queue_80,tail,index_81),head),
inference(unit_resolution,[status(thm)],[2194,189]) ).
tff(2196,plain,
select(store(queue_80,tail,index_81),head) = select(store(store(queue_80,tail,index_81),seq,select(q3,seq)),head),
inference(symmetry,[status(thm)],[2195]) ).
tff(2197,plain,
( ( index_81 = s(index_78) )
<=> ( index_81 = s(index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2198,axiom,
index_81 = s(index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(2199,plain,
index_81 = s(index_78),
inference(modus_ponens,[status(thm)],[2198,2197]) ).
tff(2200,plain,
s(index_78) = index_81,
inference(symmetry,[status(thm)],[2199]) ).
tff(2201,plain,
( ( queue_80 = store(q1,seq,earray_79) )
<=> ( queue_80 = store(q1,seq,earray_79) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2202,axiom,
queue_80 = store(q1,seq,earray_79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp277) ).
tff(2203,plain,
queue_80 = store(q1,seq,earray_79),
inference(modus_ponens,[status(thm)],[2202,2201]) ).
tff(2204,plain,
store(q1,seq,earray_79) = queue_80,
inference(symmetry,[status(thm)],[2203]) ).
tff(2205,plain,
store(store(q1,seq,earray_79),tail,s(index_78)) = store(queue_80,tail,index_81),
inference(monotonicity,[status(thm)],[2204,2200]) ).
tff(2206,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(queue_80,tail,index_81),head),
inference(monotonicity,[status(thm)],[2205]) ).
tff(2207,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2208,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2209,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head) ) ),
inference(modus_ponens,[status(thm)],[2208,2207]) ).
tff(2210,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),head) = select(store(q1,seq,earray_79),head),
inference(unit_resolution,[status(thm)],[2209,79,126]) ).
tff(2211,plain,
select(store(q1,seq,earray_79),head) = select(store(store(q1,seq,earray_79),tail,s(index_78)),head),
inference(symmetry,[status(thm)],[2210]) ).
tff(2212,plain,
( ( earray_79 = store(earray_77,index_78,e1) )
<=> ( earray_79 = store(earray_77,index_78,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2213,axiom,
earray_79 = store(earray_77,index_78,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(2214,plain,
earray_79 = store(earray_77,index_78,e1),
inference(modus_ponens,[status(thm)],[2213,2212]) ).
tff(2215,plain,
store(earray_77,index_78,e1) = earray_79,
inference(symmetry,[status(thm)],[2214]) ).
tff(2216,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = store(earray_77,index_78,e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2217,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = store(earray_77,index_78,e1),
inference(unit_resolution,[status(thm)],[2216,27]) ).
tff(2218,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2219,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp285) ).
tff(2220,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[2219,2218]) ).
tff(2221,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[2220]) ).
tff(2222,plain,
( ( queue_7 = store(queue_5,tail,index_6) )
<=> ( queue_7 = store(queue_5,tail,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2223,axiom,
queue_7 = store(queue_5,tail,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp273) ).
tff(2224,plain,
queue_7 = store(queue_5,tail,index_6),
inference(modus_ponens,[status(thm)],[2223,2222]) ).
tff(2225,plain,
store(queue_5,tail,index_6) = queue_7,
inference(symmetry,[status(thm)],[2224]) ).
tff(2226,plain,
store(queue_5,tail,index_6) = q1,
inference(transitivity,[status(thm)],[2225,2221]) ).
tff(2227,plain,
store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)) = store(q1,seq,earray_79),
inference(monotonicity,[status(thm)],[2226,2215]) ).
tff(2228,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq) = select(store(q1,seq,earray_79),seq),
inference(monotonicity,[status(thm)],[2227]) ).
tff(2229,plain,
select(store(q1,seq,earray_79),seq) = select(store(store(queue_5,tail,index_6),seq,store(earray_77,index_78,e1)),seq),
inference(symmetry,[status(thm)],[2228]) ).
tff(2230,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2231,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2232,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq) ) ),
inference(modus_ponens,[status(thm)],[2231,2230]) ).
tff(2233,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(store(q1,seq,earray_79),seq),
inference(unit_resolution,[status(thm)],[2232,79,153]) ).
tff(2234,plain,
store(store(q1,seq,earray_79),tail,s(index_78)) = q2,
inference(transitivity,[status(thm)],[2205,2170,2166]) ).
tff(2235,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),seq) = select(q2,seq),
inference(monotonicity,[status(thm)],[2234]) ).
tff(2236,plain,
select(q2,seq) = select(store(store(q1,seq,earray_79),tail,s(index_78)),seq),
inference(symmetry,[status(thm)],[2235]) ).
tff(2237,plain,
select(q2,seq) = earray_79,
inference(transitivity,[status(thm)],[2236,2233,2229,2217,2215]) ).
tff(2238,plain,
store(store(queue_5,tail,index_6),seq,select(q2,seq)) = store(q1,seq,earray_79),
inference(monotonicity,[status(thm)],[2226,2237]) ).
tff(2239,plain,
select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(q1,seq,earray_79),head),
inference(monotonicity,[status(thm)],[2238]) ).
tff(2240,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2241,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2242,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head) ) ),
inference(modus_ponens,[status(thm)],[2241,2240]) ).
tff(2243,plain,
select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(queue_5,tail,index_6),head),
inference(unit_resolution,[status(thm)],[2242,79,189]) ).
tff(2244,plain,
select(store(queue_5,tail,index_6),head) = select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head),
inference(symmetry,[status(thm)],[2243]) ).
tff(2245,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2246,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(2247,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[2246,2245]) ).
tff(2248,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[2247]) ).
tff(2249,plain,
( ( queue_5 = store(q0,seq,earray_4) )
<=> ( queue_5 = store(q0,seq,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2250,axiom,
queue_5 = store(q0,seq,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp266) ).
tff(2251,plain,
queue_5 = store(q0,seq,earray_4),
inference(modus_ponens,[status(thm)],[2250,2249]) ).
tff(2252,plain,
store(q0,seq,earray_4) = queue_5,
inference(symmetry,[status(thm)],[2251]) ).
tff(2253,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = store(queue_5,tail,index_6),
inference(monotonicity,[status(thm)],[2252,2248]) ).
tff(2254,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(queue_5,tail,index_6),head),
inference(monotonicity,[status(thm)],[2253]) ).
tff(2255,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2256,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2257,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head) ) ),
inference(modus_ponens,[status(thm)],[2256,2255]) ).
tff(2258,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),head) = select(store(q0,seq,earray_4),head),
inference(unit_resolution,[status(thm)],[2257,79,126]) ).
tff(2259,plain,
select(store(q0,seq,earray_4),head) = select(store(store(q0,seq,earray_4),tail,s(index_3)),head),
inference(symmetry,[status(thm)],[2258]) ).
tff(2260,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2261,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp62) ).
tff(2262,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[2261,2260]) ).
tff(2263,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[2262]) ).
tff(2264,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = store(earray_2,index_3,e0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2265,plain,
select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = store(earray_2,index_3,e0),
inference(unit_resolution,[status(thm)],[2264,27]) ).
tff(2266,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2267,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp284) ).
tff(2268,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[2267,2266]) ).
tff(2269,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[2268]) ).
tff(2270,plain,
( ( queue_1 = store(q,head,index_0) )
<=> ( queue_1 = store(q,head,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2271,axiom,
queue_1 = store(q,head,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(2272,plain,
queue_1 = store(q,head,index_0),
inference(modus_ponens,[status(thm)],[2271,2270]) ).
tff(2273,plain,
store(q,head,index_0) = queue_1,
inference(symmetry,[status(thm)],[2272]) ).
tff(2274,plain,
store(q,head,index_0) = q0,
inference(transitivity,[status(thm)],[2273,2269]) ).
tff(2275,plain,
store(store(q,head,index_0),seq,store(earray_2,index_3,e0)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[2274,2263]) ).
tff(2276,plain,
select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq) = select(store(q0,seq,earray_4),seq),
inference(monotonicity,[status(thm)],[2275]) ).
tff(2277,plain,
select(store(q0,seq,earray_4),seq) = select(store(store(q,head,index_0),seq,store(earray_2,index_3,e0)),seq),
inference(symmetry,[status(thm)],[2276]) ).
tff(2278,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2279,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2280,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq) ) ),
inference(modus_ponens,[status(thm)],[2279,2278]) ).
tff(2281,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(store(q0,seq,earray_4),seq),
inference(unit_resolution,[status(thm)],[2280,79,153]) ).
tff(2282,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = q1,
inference(transitivity,[status(thm)],[2253,2225,2221]) ).
tff(2283,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(q1,seq),
inference(monotonicity,[status(thm)],[2282]) ).
tff(2284,plain,
select(q1,seq) = select(store(store(q0,seq,earray_4),tail,s(index_3)),seq),
inference(symmetry,[status(thm)],[2283]) ).
tff(2285,plain,
select(q1,seq) = earray_4,
inference(transitivity,[status(thm)],[2284,2281,2277,2265,2263]) ).
tff(2286,plain,
store(store(q,head,index_0),seq,select(q1,seq)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[2274,2285]) ).
tff(2287,plain,
select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q0,seq,earray_4),head),
inference(monotonicity,[status(thm)],[2286]) ).
tff(2288,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2289,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2290,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head) ) ),
inference(modus_ponens,[status(thm)],[2289,2288]) ).
tff(2291,plain,
select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q,head,index_0),head),
inference(unit_resolution,[status(thm)],[2290,79,189]) ).
tff(2292,plain,
select(store(q,head,index_0),head) = select(store(store(q,head,index_0),seq,select(q1,seq)),head),
inference(symmetry,[status(thm)],[2291]) ).
tff(2293,plain,
( ( index_0 = select(q,tail) )
<=> ( index_0 = select(q,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2294,axiom,
index_0 = select(q,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp82) ).
tff(2295,plain,
index_0 = select(q,tail),
inference(modus_ponens,[status(thm)],[2294,2293]) ).
tff(2296,plain,
select(q,tail) = index_0,
inference(symmetry,[status(thm)],[2295]) ).
tff(2297,plain,
store(q,head,select(q,tail)) = store(q,head,index_0),
inference(monotonicity,[status(thm)],[2296]) ).
tff(2298,plain,
select(store(q,head,select(q,tail)),head) = select(store(q,head,index_0),head),
inference(monotonicity,[status(thm)],[2297]) ).
tff(2299,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(q,head,select(q,tail)),head) = select(q,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2300,plain,
select(store(q,head,select(q,tail)),head) = select(q,tail),
inference(unit_resolution,[status(thm)],[2299,27]) ).
tff(2301,plain,
select(q,tail) = select(store(q,head,select(q,tail)),head),
inference(symmetry,[status(thm)],[2300]) ).
tff(2302,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2303,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2304,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(q,head,select(q,tail)),tail) = select(q,tail) ) ),
inference(modus_ponens,[status(thm)],[2303,2302]) ).
tff(2305,plain,
select(store(q,head,select(q,tail)),tail) = select(q,tail),
inference(unit_resolution,[status(thm)],[2304,79,73]) ).
tff(2306,plain,
store(q,head,index_0) = store(q,head,select(q,tail)),
inference(symmetry,[status(thm)],[2297]) ).
tff(2307,plain,
q0 = store(q,head,select(q,tail)),
inference(transitivity,[status(thm)],[2268,2272,2306]) ).
tff(2308,plain,
select(q0,tail) = select(store(q,head,select(q,tail)),tail),
inference(monotonicity,[status(thm)],[2307]) ).
tff(2309,plain,
( ( index_3 = select(q0,tail) )
<=> ( index_3 = select(q0,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2310,axiom,
index_3 = select(q0,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(2311,plain,
index_3 = select(q0,tail),
inference(modus_ponens,[status(thm)],[2310,2309]) ).
tff(2312,plain,
index_3 = index_158,
inference(transitivity,[status(thm)],[2311,2308,2305,2301,2298,2292,2287,2259,2254,2244,2239,2211,2206,2196,2190,2156,2150,2139]) ).
tff(2313,plain,
s(index_3) = s(index_158),
inference(monotonicity,[status(thm)],[2312]) ).
tff(2314,plain,
select(q0,tail) = index_3,
inference(symmetry,[status(thm)],[2311]) ).
tff(2315,plain,
s(select(q0,tail)) = s(index_3),
inference(monotonicity,[status(thm)],[2314]) ).
tff(2316,plain,
s(select(q0,tail)) = index_257,
inference(transitivity,[status(thm)],[2315,2313,2135,2132,2122,2117,2089,2084,2074,2069,2041,2036,2026,2020,1986,1980,1969]) ).
tff(2317,plain,
s(s(select(q0,tail))) = s(index_257),
inference(monotonicity,[status(thm)],[2316]) ).
tff(2318,plain,
s(index_3) = s(select(q0,tail)),
inference(symmetry,[status(thm)],[2315]) ).
tff(2319,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = s(index_3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2320,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = s(index_3),
inference(unit_resolution,[status(thm)],[2319,27]) ).
tff(2321,plain,
store(queue_5,tail,index_6) = store(store(q0,seq,earray_4),tail,s(index_3)),
inference(symmetry,[status(thm)],[2253]) ).
tff(2322,plain,
q1 = store(store(q0,seq,earray_4),tail,s(index_3)),
inference(transitivity,[status(thm)],[2220,2224,2321]) ).
tff(2323,plain,
select(q1,tail) = select(store(store(q0,seq,earray_4),tail,s(index_3)),tail),
inference(monotonicity,[status(thm)],[2322]) ).
tff(2324,plain,
( ( index_78 = select(q1,tail) )
<=> ( index_78 = select(q1,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2325,axiom,
index_78 = select(q1,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(2326,plain,
index_78 = select(q1,tail),
inference(modus_ponens,[status(thm)],[2325,2324]) ).
tff(2327,plain,
index_78 = s(select(q0,tail)),
inference(transitivity,[status(thm)],[2326,2323,2320,2318]) ).
tff(2328,plain,
s(index_78) = s(s(select(q0,tail))),
inference(monotonicity,[status(thm)],[2327]) ).
tff(2329,plain,
select(q1,tail) = index_78,
inference(symmetry,[status(thm)],[2326]) ).
tff(2330,plain,
s(select(q1,tail)) = s(index_78),
inference(monotonicity,[status(thm)],[2329]) ).
tff(2331,plain,
s(select(q1,tail)) = index_278,
inference(transitivity,[status(thm)],[2330,2328,2317,1965,1962,1952,1947,1919,1914,1904,1899,1871,1866,1856,1850,1816,1810,1799]) ).
tff(2332,plain,
s(s(select(q1,tail))) = s(index_278),
inference(monotonicity,[status(thm)],[2331]) ).
tff(2333,plain,
s(index_78) = s(select(q1,tail)),
inference(symmetry,[status(thm)],[2330]) ).
tff(2334,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q1,seq,earray_79),tail,s(index_78)),tail) = s(index_78) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2335,plain,
select(store(store(q1,seq,earray_79),tail,s(index_78)),tail) = s(index_78),
inference(unit_resolution,[status(thm)],[2334,27]) ).
tff(2336,plain,
store(queue_80,tail,index_81) = store(store(q1,seq,earray_79),tail,s(index_78)),
inference(symmetry,[status(thm)],[2205]) ).
tff(2337,plain,
q2 = store(store(q1,seq,earray_79),tail,s(index_78)),
inference(transitivity,[status(thm)],[2165,2169,2336]) ).
tff(2338,plain,
select(q2,tail) = select(store(store(q1,seq,earray_79),tail,s(index_78)),tail),
inference(monotonicity,[status(thm)],[2337]) ).
tff(2339,plain,
( ( index_153 = select(q2,tail) )
<=> ( index_153 = select(q2,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2340,axiom,
index_153 = select(q2,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(2341,plain,
index_153 = select(q2,tail),
inference(modus_ponens,[status(thm)],[2340,2339]) ).
tff(2342,plain,
index_153 = s(select(q1,tail)),
inference(transitivity,[status(thm)],[2341,2338,2335,2333]) ).
tff(2343,plain,
s(index_153) = s(s(select(q1,tail))),
inference(monotonicity,[status(thm)],[2342]) ).
tff(2344,plain,
select(q2,tail) = index_153,
inference(symmetry,[status(thm)],[2341]) ).
tff(2345,plain,
s(select(q2,tail)) = s(index_153),
inference(monotonicity,[status(thm)],[2344]) ).
tff(2346,plain,
s(select(q2,tail)) = index_26,
inference(transitivity,[status(thm)],[2345,2343,2332,1795,1792,1782,1777,1749,1744,1734,1729,1701,1696,1686,1680,1646,1640,1638]) ).
tff(2347,plain,
s(s(select(q2,tail))) = s(index_26),
inference(monotonicity,[status(thm)],[2346]) ).
tff(2348,plain,
s(index_153) = s(select(q2,tail)),
inference(symmetry,[status(thm)],[2345]) ).
tff(2349,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q2,seq,earray_154),tail,s(index_153)),tail) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2350,plain,
select(store(store(q2,seq,earray_154),tail,s(index_153)),tail) = s(index_153),
inference(unit_resolution,[status(thm)],[2349,27]) ).
tff(2351,plain,
store(queue_155,tail,index_156) = store(store(q2,seq,earray_154),tail,s(index_153)),
inference(symmetry,[status(thm)],[2148]) ).
tff(2352,plain,
select(store(queue_155,tail,index_156),tail) = select(store(store(q2,seq,earray_154),tail,s(index_153)),tail),
inference(monotonicity,[status(thm)],[2351]) ).
tff(2353,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2354,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2355,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail) ) ),
inference(modus_ponens,[status(thm)],[2354,2353]) ).
tff(2356,plain,
select(store(store(queue_155,tail,index_156),head,s(index_158)),tail) = select(store(queue_155,tail,index_156),tail),
inference(unit_resolution,[status(thm)],[2355,79,73]) ).
tff(2357,plain,
store(queue_157,head,index_159) = store(store(queue_155,tail,index_156),head,s(index_158)),
inference(symmetry,[status(thm)],[2131]) ).
tff(2358,plain,
q3 = store(store(queue_155,tail,index_156),head,s(index_158)),
inference(transitivity,[status(thm)],[2098,2102,2357]) ).
tff(2359,plain,
select(q3,tail) = select(store(store(queue_155,tail,index_156),head,s(index_158)),tail),
inference(monotonicity,[status(thm)],[2358]) ).
tff(2360,plain,
( ( index_234 = select(q3,tail) )
<=> ( index_234 = select(q3,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2361,axiom,
index_234 = select(q3,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(2362,plain,
index_234 = select(q3,tail),
inference(modus_ponens,[status(thm)],[2361,2360]) ).
tff(2363,plain,
index_234 = s(select(q2,tail)),
inference(transitivity,[status(thm)],[2362,2359,2356,2352,2350,2348]) ).
tff(2364,plain,
s(index_234) = s(s(select(q2,tail))),
inference(monotonicity,[status(thm)],[2363]) ).
tff(2365,plain,
select(q3,tail) = index_234,
inference(symmetry,[status(thm)],[2362]) ).
tff(2366,plain,
s(select(q3,tail)) = s(index_234),
inference(monotonicity,[status(thm)],[2365]) ).
tff(2367,plain,
s(select(q3,tail)) = index_47,
inference(transitivity,[status(thm)],[2366,2364,2347,1634,1631,1630,1625,1603,1598,1597,1592,1570,1565,1555,1549,1515,1509,1498]) ).
tff(2368,plain,
s(s(select(q3,tail))) = s(index_47),
inference(monotonicity,[status(thm)],[2367]) ).
tff(2369,plain,
s(index_234) = s(select(q3,tail)),
inference(symmetry,[status(thm)],[2366]) ).
tff(2370,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q3,seq,earray_235),tail,s(index_234)),tail) = s(index_234) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2371,plain,
select(store(store(q3,seq,earray_235),tail,s(index_234)),tail) = s(index_234),
inference(unit_resolution,[status(thm)],[2370,27]) ).
tff(2372,plain,
store(queue_236,tail,index_237) = store(store(q3,seq,earray_235),tail,s(index_234)),
inference(symmetry,[status(thm)],[2083]) ).
tff(2373,plain,
q4 = store(store(q3,seq,earray_235),tail,s(index_234)),
inference(transitivity,[status(thm)],[2050,2054,2372]) ).
tff(2374,plain,
select(q4,tail) = select(store(store(q3,seq,earray_235),tail,s(index_234)),tail),
inference(monotonicity,[status(thm)],[2373]) ).
tff(2375,plain,
( ( index_246 = select(q4,tail) )
<=> ( index_246 = select(q4,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2376,axiom,
index_246 = select(q4,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(2377,plain,
index_246 = select(q4,tail),
inference(modus_ponens,[status(thm)],[2376,2375]) ).
tff(2378,plain,
index_246 = s(select(q3,tail)),
inference(transitivity,[status(thm)],[2377,2374,2371,2369]) ).
tff(2379,plain,
s(index_246) = s(s(select(q3,tail))),
inference(monotonicity,[status(thm)],[2378]) ).
tff(2380,plain,
select(q4,tail) = index_246,
inference(symmetry,[status(thm)],[2377]) ).
tff(2381,plain,
s(select(q4,tail)) = s(index_246),
inference(monotonicity,[status(thm)],[2380]) ).
tff(2382,plain,
s(select(q4,tail)) = index_68,
inference(transitivity,[status(thm)],[2381,2379,2368,1494,1491,1481,1476,1448,1443,1433,1428,1400,1395,1385,1379,1345,1339,1328]) ).
tff(2383,plain,
s(s(select(q4,tail))) = s(index_68),
inference(monotonicity,[status(thm)],[2382]) ).
tff(2384,plain,
s(index_246) = s(select(q4,tail)),
inference(symmetry,[status(thm)],[2381]) ).
tff(2385,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q4,seq,earray_247),tail,s(index_246)),tail) = s(index_246) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2386,plain,
select(store(store(q4,seq,earray_247),tail,s(index_246)),tail) = s(index_246),
inference(unit_resolution,[status(thm)],[2385,27]) ).
tff(2387,plain,
store(queue_248,tail,index_249) = store(store(q4,seq,earray_247),tail,s(index_246)),
inference(symmetry,[status(thm)],[2035]) ).
tff(2388,plain,
q5 = store(store(q4,seq,earray_247),tail,s(index_246)),
inference(transitivity,[status(thm)],[1995,1999,2387]) ).
tff(2389,plain,
select(q5,tail) = select(store(store(q4,seq,earray_247),tail,s(index_246)),tail),
inference(monotonicity,[status(thm)],[2388]) ).
tff(2390,plain,
( ( index_252 = select(q5,tail) )
<=> ( index_252 = select(q5,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2391,axiom,
index_252 = select(q5,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(2392,plain,
index_252 = select(q5,tail),
inference(modus_ponens,[status(thm)],[2391,2390]) ).
tff(2393,plain,
index_252 = s(select(q4,tail)),
inference(transitivity,[status(thm)],[2392,2389,2386,2384]) ).
tff(2394,plain,
s(index_252) = s(s(select(q4,tail))),
inference(monotonicity,[status(thm)],[2393]) ).
tff(2395,plain,
select(q5,tail) = index_252,
inference(symmetry,[status(thm)],[2392]) ).
tff(2396,plain,
s(select(q5,tail)) = s(index_252),
inference(monotonicity,[status(thm)],[2395]) ).
tff(2397,plain,
s(select(q5,tail)) = index_95,
inference(transitivity,[status(thm)],[2396,2394,2383,1324,1321,1311,1306,1278,1273,1263,1258,1230,1225,1215,1209,1175,1169,1158]) ).
tff(2398,plain,
s(s(select(q5,tail))) = s(index_95),
inference(monotonicity,[status(thm)],[2397]) ).
tff(2399,plain,
s(index_252) = s(select(q5,tail)),
inference(symmetry,[status(thm)],[2396]) ).
tff(2400,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q5,seq,earray_253),tail,s(index_252)),tail) = s(index_252) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2401,plain,
select(store(store(q5,seq,earray_253),tail,s(index_252)),tail) = s(index_252),
inference(unit_resolution,[status(thm)],[2400,27]) ).
tff(2402,plain,
store(queue_254,tail,index_255) = store(store(q5,seq,earray_253),tail,s(index_252)),
inference(symmetry,[status(thm)],[1978]) ).
tff(2403,plain,
select(store(queue_254,tail,index_255),tail) = select(store(store(q5,seq,earray_253),tail,s(index_252)),tail),
inference(monotonicity,[status(thm)],[2402]) ).
tff(2404,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2405,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2406,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail) ) ),
inference(modus_ponens,[status(thm)],[2405,2404]) ).
tff(2407,plain,
select(store(store(queue_254,tail,index_255),head,s(index_257)),tail) = select(store(queue_254,tail,index_255),tail),
inference(unit_resolution,[status(thm)],[2406,79,73]) ).
tff(2408,plain,
store(queue_256,head,index_258) = store(store(queue_254,tail,index_255),head,s(index_257)),
inference(symmetry,[status(thm)],[1961]) ).
tff(2409,plain,
q6 = store(store(queue_254,tail,index_255),head,s(index_257)),
inference(transitivity,[status(thm)],[1928,1932,2408]) ).
tff(2410,plain,
select(q6,tail) = select(store(store(queue_254,tail,index_255),head,s(index_257)),tail),
inference(monotonicity,[status(thm)],[2409]) ).
tff(2411,plain,
( ( index_261 = select(q6,tail) )
<=> ( index_261 = select(q6,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2412,axiom,
index_261 = select(q6,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(2413,plain,
index_261 = select(q6,tail),
inference(modus_ponens,[status(thm)],[2412,2411]) ).
tff(2414,plain,
index_261 = s(select(q5,tail)),
inference(transitivity,[status(thm)],[2413,2410,2407,2403,2401,2399]) ).
tff(2415,plain,
s(index_261) = s(s(select(q5,tail))),
inference(monotonicity,[status(thm)],[2414]) ).
tff(2416,plain,
select(q6,tail) = index_261,
inference(symmetry,[status(thm)],[2413]) ).
tff(2417,plain,
s(select(q6,tail)) = s(index_261),
inference(monotonicity,[status(thm)],[2416]) ).
tff(2418,plain,
s(select(q6,tail)) = index_116,
inference(transitivity,[status(thm)],[2417,2415,2398,1154,1151,1141,1136,1108,1103,1093,1088,1060,1055,1045,1039,1005,999,988]) ).
tff(2419,plain,
s(s(select(q6,tail))) = s(index_116),
inference(monotonicity,[status(thm)],[2418]) ).
tff(2420,plain,
s(index_261) = s(select(q6,tail)),
inference(symmetry,[status(thm)],[2417]) ).
tff(2421,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q6,seq,earray_262),tail,s(index_261)),tail) = s(index_261) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2422,plain,
select(store(store(q6,seq,earray_262),tail,s(index_261)),tail) = s(index_261),
inference(unit_resolution,[status(thm)],[2421,27]) ).
tff(2423,plain,
store(queue_263,tail,index_264) = store(store(q6,seq,earray_262),tail,s(index_261)),
inference(symmetry,[status(thm)],[1913]) ).
tff(2424,plain,
q7 = store(store(q6,seq,earray_262),tail,s(index_261)),
inference(transitivity,[status(thm)],[1880,1884,2423]) ).
tff(2425,plain,
select(q7,tail) = select(store(store(q6,seq,earray_262),tail,s(index_261)),tail),
inference(monotonicity,[status(thm)],[2424]) ).
tff(2426,plain,
( ( index_267 = select(q7,tail) )
<=> ( index_267 = select(q7,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2427,axiom,
index_267 = select(q7,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(2428,plain,
index_267 = select(q7,tail),
inference(modus_ponens,[status(thm)],[2427,2426]) ).
tff(2429,plain,
index_267 = s(select(q6,tail)),
inference(transitivity,[status(thm)],[2428,2425,2422,2420]) ).
tff(2430,plain,
s(index_267) = s(s(select(q6,tail))),
inference(monotonicity,[status(thm)],[2429]) ).
tff(2431,plain,
select(q7,tail) = index_267,
inference(symmetry,[status(thm)],[2428]) ).
tff(2432,plain,
s(select(q7,tail)) = s(index_267),
inference(monotonicity,[status(thm)],[2431]) ).
tff(2433,plain,
s(select(q7,tail)) = index_137,
inference(transitivity,[status(thm)],[2432,2430,2419,984,981,971,966,938,933,923,918,890,885,875,869,835,829,818]) ).
tff(2434,plain,
s(s(select(q7,tail))) = s(index_137),
inference(monotonicity,[status(thm)],[2433]) ).
tff(2435,plain,
s(index_267) = s(select(q7,tail)),
inference(symmetry,[status(thm)],[2432]) ).
tff(2436,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q7,seq,earray_268),tail,s(index_267)),tail) = s(index_267) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2437,plain,
select(store(store(q7,seq,earray_268),tail,s(index_267)),tail) = s(index_267),
inference(unit_resolution,[status(thm)],[2436,27]) ).
tff(2438,plain,
store(queue_269,tail,index_270) = store(store(q7,seq,earray_268),tail,s(index_267)),
inference(symmetry,[status(thm)],[1865]) ).
tff(2439,plain,
q8 = store(store(q7,seq,earray_268),tail,s(index_267)),
inference(transitivity,[status(thm)],[1825,1829,2438]) ).
tff(2440,plain,
select(q8,tail) = select(store(store(q7,seq,earray_268),tail,s(index_267)),tail),
inference(monotonicity,[status(thm)],[2439]) ).
tff(2441,plain,
( ( index_273 = select(q8,tail) )
<=> ( index_273 = select(q8,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2442,axiom,
index_273 = select(q8,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(2443,plain,
index_273 = select(q8,tail),
inference(modus_ponens,[status(thm)],[2442,2441]) ).
tff(2444,plain,
index_273 = s(select(q7,tail)),
inference(transitivity,[status(thm)],[2443,2440,2437,2435]) ).
tff(2445,plain,
s(index_273) = s(s(select(q7,tail))),
inference(monotonicity,[status(thm)],[2444]) ).
tff(2446,plain,
select(q8,tail) = index_273,
inference(symmetry,[status(thm)],[2443]) ).
tff(2447,plain,
s(select(q8,tail)) = s(index_273),
inference(monotonicity,[status(thm)],[2446]) ).
tff(2448,plain,
s(select(q8,tail)) = index_167,
inference(transitivity,[status(thm)],[2447,2445,2434,814,811,801,796,768,763,753,748,720,715,705,699,665,659,648]) ).
tff(2449,plain,
s(s(select(q8,tail))) = s(index_167),
inference(monotonicity,[status(thm)],[2448]) ).
tff(2450,plain,
s(index_273) = s(select(q8,tail)),
inference(symmetry,[status(thm)],[2447]) ).
tff(2451,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q8,seq,earray_274),tail,s(index_273)),tail) = s(index_273) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2452,plain,
select(store(store(q8,seq,earray_274),tail,s(index_273)),tail) = s(index_273),
inference(unit_resolution,[status(thm)],[2451,27]) ).
tff(2453,plain,
store(queue_275,tail,index_276) = store(store(q8,seq,earray_274),tail,s(index_273)),
inference(symmetry,[status(thm)],[1808]) ).
tff(2454,plain,
select(store(queue_275,tail,index_276),tail) = select(store(store(q8,seq,earray_274),tail,s(index_273)),tail),
inference(monotonicity,[status(thm)],[2453]) ).
tff(2455,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2456,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2457,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail) ) ),
inference(modus_ponens,[status(thm)],[2456,2455]) ).
tff(2458,plain,
select(store(store(queue_275,tail,index_276),head,s(index_278)),tail) = select(store(queue_275,tail,index_276),tail),
inference(unit_resolution,[status(thm)],[2457,79,73]) ).
tff(2459,plain,
store(queue_277,head,index_279) = store(store(queue_275,tail,index_276),head,s(index_278)),
inference(symmetry,[status(thm)],[1791]) ).
tff(2460,plain,
q9 = store(store(queue_275,tail,index_276),head,s(index_278)),
inference(transitivity,[status(thm)],[1758,1762,2459]) ).
tff(2461,plain,
select(q9,tail) = select(store(store(queue_275,tail,index_276),head,s(index_278)),tail),
inference(monotonicity,[status(thm)],[2460]) ).
tff(2462,plain,
( ( index_9 = select(q9,tail) )
<=> ( index_9 = select(q9,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2463,axiom,
index_9 = select(q9,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(2464,plain,
index_9 = select(q9,tail),
inference(modus_ponens,[status(thm)],[2463,2462]) ).
tff(2465,plain,
index_9 = s(select(q8,tail)),
inference(transitivity,[status(thm)],[2464,2461,2458,2454,2452,2450]) ).
tff(2466,plain,
s(index_9) = s(s(select(q8,tail))),
inference(monotonicity,[status(thm)],[2465]) ).
tff(2467,plain,
select(q9,tail) = index_9,
inference(symmetry,[status(thm)],[2464]) ).
tff(2468,plain,
s(select(q9,tail)) = s(index_9),
inference(monotonicity,[status(thm)],[2467]) ).
tff(2469,plain,
s(select(q9,tail)) = index_188,
inference(transitivity,[status(thm)],[2468,2466,2449,644,641,631,626,598,593,583,578,550,545,535,529,495,489,478]) ).
tff(2470,plain,
s(s(select(q9,tail))) = s(index_188),
inference(monotonicity,[status(thm)],[2469]) ).
tff(2471,plain,
s(index_9) = s(select(q9,tail)),
inference(symmetry,[status(thm)],[2468]) ).
tff(2472,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = s(index_9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2473,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = s(index_9),
inference(unit_resolution,[status(thm)],[2472,27]) ).
tff(2474,plain,
store(queue_11,tail,index_12) = store(store(q9,seq,earray_10),tail,s(index_9)),
inference(symmetry,[status(thm)],[1743]) ).
tff(2475,plain,
q10 = store(store(q9,seq,earray_10),tail,s(index_9)),
inference(transitivity,[status(thm)],[1710,1714,2474]) ).
tff(2476,plain,
select(q10,tail) = select(store(store(q9,seq,earray_10),tail,s(index_9)),tail),
inference(monotonicity,[status(thm)],[2475]) ).
tff(2477,plain,
( ( index_15 = select(q10,tail) )
<=> ( index_15 = select(q10,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2478,axiom,
index_15 = select(q10,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(2479,plain,
index_15 = select(q10,tail),
inference(modus_ponens,[status(thm)],[2478,2477]) ).
tff(2480,plain,
index_15 = s(select(q9,tail)),
inference(transitivity,[status(thm)],[2479,2476,2473,2471]) ).
tff(2481,plain,
s(index_15) = s(s(select(q9,tail))),
inference(monotonicity,[status(thm)],[2480]) ).
tff(2482,plain,
select(q10,tail) = index_15,
inference(symmetry,[status(thm)],[2479]) ).
tff(2483,plain,
s(select(q10,tail)) = s(index_15),
inference(monotonicity,[status(thm)],[2482]) ).
tff(2484,plain,
s(select(q10,tail)) = index_209,
inference(transitivity,[status(thm)],[2483,2481,2470,474,471,461,456,428,423,413,408,380,375,365,359,325,319,308]) ).
tff(2485,plain,
s(s(select(q10,tail))) = s(index_209),
inference(monotonicity,[status(thm)],[2484]) ).
tff(2486,plain,
s(index_15) = s(select(q10,tail)),
inference(symmetry,[status(thm)],[2483]) ).
tff(2487,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = s(index_15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2488,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = s(index_15),
inference(unit_resolution,[status(thm)],[2487,27]) ).
tff(2489,plain,
store(queue_17,tail,index_18) = store(store(q10,seq,earray_16),tail,s(index_15)),
inference(symmetry,[status(thm)],[1695]) ).
tff(2490,plain,
q11 = store(store(q10,seq,earray_16),tail,s(index_15)),
inference(transitivity,[status(thm)],[1655,1659,2489]) ).
tff(2491,plain,
select(q11,tail) = select(store(store(q10,seq,earray_16),tail,s(index_15)),tail),
inference(monotonicity,[status(thm)],[2490]) ).
tff(2492,plain,
index_21 = s(select(q10,tail)),
inference(transitivity,[status(thm)],[54,2491,2488,2486]) ).
tff(2493,plain,
s(index_21) = s(s(select(q10,tail))),
inference(monotonicity,[status(thm)],[2492]) ).
tff(2494,plain,
s(select(q11,tail)) = index_230,
inference(transitivity,[status(thm)],[56,2493,2485,304,301,291,286,258,253,243,238,210,205,195,185,132,122,4]) ).
tff(2495,plain,
s(s(select(q11,tail))) = s(index_230),
inference(monotonicity,[status(thm)],[2494]) ).
tff(2496,plain,
s(index_230) = s(s(select(q11,tail))),
inference(symmetry,[status(thm)],[2495]) ).
tff(2497,plain,
s(index_230) = select(q13,tail),
inference(transitivity,[status(thm)],[2496,107,51,48]) ).
tff(2498,plain,
( ( index_36 = select(q13,tail) )
<=> ( index_36 = select(q13,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2499,axiom,
index_36 = select(q13,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(2500,plain,
index_36 = select(q13,tail),
inference(modus_ponens,[status(thm)],[2499,2498]) ).
tff(2501,plain,
select(q13,tail) = index_36,
inference(symmetry,[status(thm)],[2500]) ).
tff(2502,plain,
( ( earray_35 = select(q13,seq) )
<=> ( earray_35 = select(q13,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2503,axiom,
earray_35 = select(q13,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(2504,plain,
earray_35 = select(q13,seq),
inference(modus_ponens,[status(thm)],[2503,2502]) ).
tff(2505,plain,
select(q13,seq) = earray_35,
inference(symmetry,[status(thm)],[2504]) ).
tff(2506,plain,
store(select(q13,seq),select(q13,tail),e13) = store(earray_35,index_36,e13),
inference(monotonicity,[status(thm)],[2505,2501]) ).
tff(2507,plain,
store(earray_35,index_36,e13) = store(select(q13,seq),select(q13,tail),e13),
inference(symmetry,[status(thm)],[2506]) ).
tff(2508,plain,
select(q14,seq) = store(select(q13,seq),select(q13,tail),e13),
inference(transitivity,[status(thm)],[1589,1586,1582,1576,2507]) ).
tff(2509,plain,
select(select(q14,seq),s(index_230)) = select(store(select(q13,seq),select(q13,tail),e13),select(q13,tail)),
inference(monotonicity,[status(thm)],[2508,2497]) ).
tff(2510,plain,
select(select(q14,seq),s(index_230)) = e13,
inference(transitivity,[status(thm)],[2509,29]) ).
tff(2511,plain,
( ( elem_283 = select(earray_281,index_282) )
<=> ( elem_283 = select(earray_281,index_282) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2512,axiom,
elem_283 = select(earray_281,index_282),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(2513,plain,
elem_283 = select(earray_281,index_282),
inference(modus_ponens,[status(thm)],[2512,2511]) ).
tff(2514,plain,
select(earray_281,index_282) = elem_283,
inference(symmetry,[status(thm)],[2513]) ).
tff(2515,plain,
( ( index_282 = select(q40,head) )
<=> ( index_282 = select(q40,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2516,axiom,
index_282 = select(q40,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(2517,plain,
index_282 = select(q40,head),
inference(modus_ponens,[status(thm)],[2516,2515]) ).
tff(2518,plain,
select(q40,head) = index_282,
inference(symmetry,[status(thm)],[2517]) ).
tff(2519,plain,
( ( earray_281 = select(q40,seq) )
<=> ( earray_281 = select(q40,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2520,axiom,
earray_281 = select(q40,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp57) ).
tff(2521,plain,
earray_281 = select(q40,seq),
inference(modus_ponens,[status(thm)],[2520,2519]) ).
tff(2522,plain,
select(q40,seq) = earray_281,
inference(symmetry,[status(thm)],[2521]) ).
tff(2523,plain,
( ( q40 = queue_244 )
<=> ( q40 = queue_244 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2524,axiom,
q40 = queue_244,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp319) ).
tff(2525,plain,
q40 = queue_244,
inference(modus_ponens,[status(thm)],[2524,2523]) ).
tff(2526,plain,
queue_244 = q40,
inference(symmetry,[status(thm)],[2525]) ).
tff(2527,plain,
( ( queue_244 = store(queue_242,tail,index_243) )
<=> ( queue_244 = store(queue_242,tail,index_243) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2528,axiom,
queue_244 = store(queue_242,tail,index_243),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(2529,plain,
queue_244 = store(queue_242,tail,index_243),
inference(modus_ponens,[status(thm)],[2528,2527]) ).
tff(2530,plain,
store(queue_242,tail,index_243) = queue_244,
inference(symmetry,[status(thm)],[2529]) ).
tff(2531,plain,
( ( index_243 = s(index_240) )
<=> ( index_243 = s(index_240) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2532,axiom,
index_243 = s(index_240),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(2533,plain,
index_243 = s(index_240),
inference(modus_ponens,[status(thm)],[2532,2531]) ).
tff(2534,plain,
s(index_240) = index_243,
inference(symmetry,[status(thm)],[2533]) ).
tff(2535,plain,
( ( queue_242 = store(q39,seq,earray_241) )
<=> ( queue_242 = store(q39,seq,earray_241) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2536,axiom,
queue_242 = store(q39,seq,earray_241),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(2537,plain,
queue_242 = store(q39,seq,earray_241),
inference(modus_ponens,[status(thm)],[2536,2535]) ).
tff(2538,plain,
store(q39,seq,earray_241) = queue_242,
inference(symmetry,[status(thm)],[2537]) ).
tff(2539,plain,
store(store(q39,seq,earray_241),tail,s(index_240)) = store(queue_242,tail,index_243),
inference(monotonicity,[status(thm)],[2538,2534]) ).
tff(2540,plain,
store(store(q39,seq,earray_241),tail,s(index_240)) = q40,
inference(transitivity,[status(thm)],[2539,2530,2526]) ).
tff(2541,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(q40,seq),
inference(monotonicity,[status(thm)],[2540]) ).
tff(2542,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2543,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2544,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq) ) ),
inference(modus_ponens,[status(thm)],[2543,2542]) ).
tff(2545,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),seq) = select(store(q39,seq,earray_241),seq),
inference(unit_resolution,[status(thm)],[2544,79,153]) ).
tff(2546,plain,
select(store(q39,seq,earray_241),seq) = select(store(store(q39,seq,earray_241),tail,s(index_240)),seq),
inference(symmetry,[status(thm)],[2545]) ).
tff(2547,plain,
( ( earray_241 = store(earray_239,index_240,e39) )
<=> ( earray_241 = store(earray_239,index_240,e39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2548,axiom,
earray_241 = store(earray_239,index_240,e39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(2549,plain,
earray_241 = store(earray_239,index_240,e39),
inference(modus_ponens,[status(thm)],[2548,2547]) ).
tff(2550,plain,
store(earray_239,index_240,e39) = earray_241,
inference(symmetry,[status(thm)],[2549]) ).
tff(2551,plain,
store(queue_229,head,index_231) = q39,
inference(transitivity,[status(thm)],[174,170]) ).
tff(2552,plain,
store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)) = store(q39,seq,earray_241),
inference(monotonicity,[status(thm)],[2551,2550]) ).
tff(2553,plain,
select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = select(store(q39,seq,earray_241),seq),
inference(monotonicity,[status(thm)],[2552]) ).
tff(2554,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = store(earray_239,index_240,e39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2555,plain,
select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq) = store(earray_239,index_240,e39),
inference(unit_resolution,[status(thm)],[2554,27]) ).
tff(2556,plain,
store(earray_239,index_240,e39) = select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq),
inference(symmetry,[status(thm)],[2555]) ).
tff(2557,plain,
( ( index_240 = select(q39,tail) )
<=> ( index_240 = select(q39,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2558,axiom,
index_240 = select(q39,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(2559,plain,
index_240 = select(q39,tail),
inference(modus_ponens,[status(thm)],[2558,2557]) ).
tff(2560,plain,
select(q39,tail) = index_240,
inference(symmetry,[status(thm)],[2559]) ).
tff(2561,plain,
store(queue_229,head,index_231) = store(store(queue_227,tail,index_228),head,s(index_230)),
inference(symmetry,[status(thm)],[179]) ).
tff(2562,plain,
q39 = store(store(queue_227,tail,index_228),head,s(index_230)),
inference(transitivity,[status(thm)],[169,173,2561]) ).
tff(2563,plain,
select(q39,tail) = select(store(store(queue_227,tail,index_228),head,s(index_230)),tail),
inference(monotonicity,[status(thm)],[2562]) ).
tff(2564,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(q39,tail),
inference(symmetry,[status(thm)],[2563]) ).
tff(2565,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2566,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2567,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail) ) ),
inference(modus_ponens,[status(thm)],[2566,2565]) ).
tff(2568,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),tail) = select(store(queue_227,tail,index_228),tail),
inference(unit_resolution,[status(thm)],[2567,79,73]) ).
tff(2569,plain,
select(store(queue_227,tail,index_228),tail) = select(store(store(queue_227,tail,index_228),head,s(index_230)),tail),
inference(symmetry,[status(thm)],[2568]) ).
tff(2570,plain,
store(queue_227,tail,index_228) = store(store(q38,seq,earray_226),tail,s(index_225)),
inference(symmetry,[status(thm)],[120]) ).
tff(2571,plain,
select(store(queue_227,tail,index_228),tail) = select(store(store(q38,seq,earray_226),tail,s(index_225)),tail),
inference(monotonicity,[status(thm)],[2570]) ).
tff(2572,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = select(store(queue_227,tail,index_228),tail),
inference(symmetry,[status(thm)],[2571]) ).
tff(2573,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = s(index_225) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2574,plain,
select(store(store(q38,seq,earray_226),tail,s(index_225)),tail) = s(index_225),
inference(unit_resolution,[status(thm)],[2573,27]) ).
tff(2575,plain,
s(index_225) = select(store(store(q38,seq,earray_226),tail,s(index_225)),tail),
inference(symmetry,[status(thm)],[2574]) ).
tff(2576,plain,
s(index_225) = index_240,
inference(transitivity,[status(thm)],[2575,2572,2569,2564,2560]) ).
tff(2577,plain,
( ( earray_239 = select(q39,seq) )
<=> ( earray_239 = select(q39,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2578,axiom,
earray_239 = select(q39,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(2579,plain,
earray_239 = select(q39,seq),
inference(modus_ponens,[status(thm)],[2578,2577]) ).
tff(2580,plain,
select(q39,seq) = earray_239,
inference(symmetry,[status(thm)],[2579]) ).
tff(2581,plain,
store(select(q39,seq),s(index_225),e39) = store(earray_239,index_240,e39),
inference(monotonicity,[status(thm)],[2580,2576]) ).
tff(2582,plain,
store(select(q39,seq),s(index_225),e39) = earray_281,
inference(transitivity,[status(thm)],[2581,2556,2553,2546,2541,2522]) ).
tff(2583,plain,
select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(earray_281,index_282),
inference(monotonicity,[status(thm)],[2582,2518]) ).
tff(2584,plain,
store(queue_242,tail,index_243) = store(store(q39,seq,earray_241),tail,s(index_240)),
inference(symmetry,[status(thm)],[2539]) ).
tff(2585,plain,
q40 = store(store(q39,seq,earray_241),tail,s(index_240)),
inference(transitivity,[status(thm)],[2525,2529,2584]) ).
tff(2586,plain,
select(q40,head) = select(store(store(q39,seq,earray_241),tail,s(index_240)),head),
inference(monotonicity,[status(thm)],[2585]) ).
tff(2587,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(q40,head),
inference(symmetry,[status(thm)],[2586]) ).
tff(2588,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2589,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2590,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ),
inference(modus_ponens,[status(thm)],[2589,2588]) ).
tff(2591,plain,
( ( tail = head )
| ( select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head) ) ),
inference(unit_resolution,[status(thm)],[2590,79]) ).
tff(2592,plain,
select(store(store(q39,seq,earray_241),tail,s(index_240)),head) = select(store(q39,seq,earray_241),head),
inference(unit_resolution,[status(thm)],[2591,126]) ).
tff(2593,plain,
select(store(q39,seq,earray_241),head) = select(store(store(q39,seq,earray_241),tail,s(index_240)),head),
inference(symmetry,[status(thm)],[2592]) ).
tff(2594,plain,
select(store(q39,seq,earray_241),seq) = select(store(store(queue_229,head,index_231),seq,store(earray_239,index_240,e39)),seq),
inference(symmetry,[status(thm)],[2553]) ).
tff(2595,plain,
select(q40,seq) = select(store(store(q39,seq,earray_241),tail,s(index_240)),seq),
inference(symmetry,[status(thm)],[2541]) ).
tff(2596,plain,
select(q40,seq) = earray_241,
inference(transitivity,[status(thm)],[2595,2545,2594,2555,2550]) ).
tff(2597,plain,
store(store(queue_229,head,index_231),seq,select(q40,seq)) = store(q39,seq,earray_241),
inference(monotonicity,[status(thm)],[2551,2596]) ).
tff(2598,plain,
store(q39,seq,earray_241) = store(store(queue_229,head,index_231),seq,select(q40,seq)),
inference(symmetry,[status(thm)],[2597]) ).
tff(2599,plain,
select(store(q39,seq,earray_241),head) = select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head),
inference(monotonicity,[status(thm)],[2598]) ).
tff(2600,plain,
select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(q39,seq,earray_241),head),
inference(symmetry,[status(thm)],[2599]) ).
tff(2601,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2602,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2603,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ),
inference(modus_ponens,[status(thm)],[2602,2601]) ).
tff(2604,plain,
( ( seq = head )
| ( select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head) ) ),
inference(unit_resolution,[status(thm)],[2603,79]) ).
tff(2605,plain,
select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head) = select(store(queue_229,head,index_231),head),
inference(unit_resolution,[status(thm)],[2604,189]) ).
tff(2606,plain,
select(store(queue_229,head,index_231),head) = select(store(store(queue_229,head,index_231),seq,select(q40,seq)),head),
inference(symmetry,[status(thm)],[2605]) ).
tff(2607,plain,
select(store(queue_229,head,index_231),head) = select(store(store(queue_227,tail,index_228),head,s(index_230)),head),
inference(monotonicity,[status(thm)],[2561]) ).
tff(2608,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = select(store(queue_229,head,index_231),head),
inference(symmetry,[status(thm)],[2607]) ).
tff(2609,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2610,plain,
select(store(store(queue_227,tail,index_228),head,s(index_230)),head) = s(index_230),
inference(unit_resolution,[status(thm)],[2609,27]) ).
tff(2611,plain,
s(index_230) = select(store(store(queue_227,tail,index_228),head,s(index_230)),head),
inference(symmetry,[status(thm)],[2610]) ).
tff(2612,plain,
select(q13,tail) = select(q40,head),
inference(transitivity,[status(thm)],[47,50,106,2495,2611,2608,2606,2600,2593,2587]) ).
tff(2613,plain,
( ( index_225 = select(q38,tail) )
<=> ( index_225 = select(q38,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2614,axiom,
index_225 = select(q38,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(2615,plain,
index_225 = select(q38,tail),
inference(modus_ponens,[status(thm)],[2614,2613]) ).
tff(2616,plain,
select(q38,tail) = index_225,
inference(symmetry,[status(thm)],[2615]) ).
tff(2617,plain,
store(queue_221,tail,index_222) = store(store(q37,seq,earray_220),tail,s(index_219)),
inference(symmetry,[status(thm)],[204]) ).
tff(2618,plain,
q38 = store(store(q37,seq,earray_220),tail,s(index_219)),
inference(transitivity,[status(thm)],[141,145,2617]) ).
tff(2619,plain,
select(q38,tail) = select(store(store(q37,seq,earray_220),tail,s(index_219)),tail),
inference(monotonicity,[status(thm)],[2618]) ).
tff(2620,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = select(q38,tail),
inference(symmetry,[status(thm)],[2619]) ).
tff(2621,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = s(index_219) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2622,plain,
select(store(store(q37,seq,earray_220),tail,s(index_219)),tail) = s(index_219),
inference(unit_resolution,[status(thm)],[2621,27]) ).
tff(2623,plain,
s(index_219) = select(store(store(q37,seq,earray_220),tail,s(index_219)),tail),
inference(symmetry,[status(thm)],[2622]) ).
tff(2624,plain,
( ( index_219 = select(q37,tail) )
<=> ( index_219 = select(q37,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2625,axiom,
index_219 = select(q37,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(2626,plain,
index_219 = select(q37,tail),
inference(modus_ponens,[status(thm)],[2625,2624]) ).
tff(2627,plain,
select(q37,tail) = index_219,
inference(symmetry,[status(thm)],[2626]) ).
tff(2628,plain,
s(select(q37,tail)) = s(index_219),
inference(monotonicity,[status(thm)],[2627]) ).
tff(2629,plain,
s(select(q37,tail)) = index_225,
inference(transitivity,[status(thm)],[2628,2623,2620,2616]) ).
tff(2630,plain,
s(s(select(q37,tail))) = s(index_225),
inference(monotonicity,[status(thm)],[2629]) ).
tff(2631,plain,
s(index_219) = s(select(q37,tail)),
inference(symmetry,[status(thm)],[2628]) ).
tff(2632,plain,
store(queue_215,tail,index_216) = store(store(q36,seq,earray_214),tail,s(index_213)),
inference(symmetry,[status(thm)],[252]) ).
tff(2633,plain,
q37 = store(store(q36,seq,earray_214),tail,s(index_213)),
inference(transitivity,[status(thm)],[219,223,2632]) ).
tff(2634,plain,
select(q37,tail) = select(store(store(q36,seq,earray_214),tail,s(index_213)),tail),
inference(monotonicity,[status(thm)],[2633]) ).
tff(2635,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = select(q37,tail),
inference(symmetry,[status(thm)],[2634]) ).
tff(2636,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = s(index_213) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2637,plain,
select(store(store(q36,seq,earray_214),tail,s(index_213)),tail) = s(index_213),
inference(unit_resolution,[status(thm)],[2636,27]) ).
tff(2638,plain,
s(index_213) = select(store(store(q36,seq,earray_214),tail,s(index_213)),tail),
inference(symmetry,[status(thm)],[2637]) ).
tff(2639,plain,
( ( index_213 = select(q36,tail) )
<=> ( index_213 = select(q36,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2640,axiom,
index_213 = select(q36,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(2641,plain,
index_213 = select(q36,tail),
inference(modus_ponens,[status(thm)],[2640,2639]) ).
tff(2642,plain,
select(q36,tail) = index_213,
inference(symmetry,[status(thm)],[2641]) ).
tff(2643,plain,
s(select(q36,tail)) = s(index_213),
inference(monotonicity,[status(thm)],[2642]) ).
tff(2644,plain,
s(select(q36,tail)) = index_219,
inference(transitivity,[status(thm)],[2643,2638,2635,2627]) ).
tff(2645,plain,
s(s(select(q36,tail))) = s(index_219),
inference(monotonicity,[status(thm)],[2644]) ).
tff(2646,plain,
s(index_213) = s(select(q36,tail)),
inference(symmetry,[status(thm)],[2643]) ).
tff(2647,plain,
store(queue_208,head,index_210) = store(store(queue_206,tail,index_207),head,s(index_209)),
inference(symmetry,[status(thm)],[300]) ).
tff(2648,plain,
q36 = store(store(queue_206,tail,index_207),head,s(index_209)),
inference(transitivity,[status(thm)],[267,271,2647]) ).
tff(2649,plain,
select(q36,tail) = select(store(store(queue_206,tail,index_207),head,s(index_209)),tail),
inference(monotonicity,[status(thm)],[2648]) ).
tff(2650,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(q36,tail),
inference(symmetry,[status(thm)],[2649]) ).
tff(2651,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2652,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2653,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail) ) ),
inference(modus_ponens,[status(thm)],[2652,2651]) ).
tff(2654,plain,
select(store(store(queue_206,tail,index_207),head,s(index_209)),tail) = select(store(queue_206,tail,index_207),tail),
inference(unit_resolution,[status(thm)],[2653,79,73]) ).
tff(2655,plain,
select(store(queue_206,tail,index_207),tail) = select(store(store(queue_206,tail,index_207),head,s(index_209)),tail),
inference(symmetry,[status(thm)],[2654]) ).
tff(2656,plain,
store(queue_206,tail,index_207) = store(store(q35,seq,earray_205),tail,s(index_204)),
inference(symmetry,[status(thm)],[317]) ).
tff(2657,plain,
select(store(queue_206,tail,index_207),tail) = select(store(store(q35,seq,earray_205),tail,s(index_204)),tail),
inference(monotonicity,[status(thm)],[2656]) ).
tff(2658,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = select(store(queue_206,tail,index_207),tail),
inference(symmetry,[status(thm)],[2657]) ).
tff(2659,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = s(index_204) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2660,plain,
select(store(store(q35,seq,earray_205),tail,s(index_204)),tail) = s(index_204),
inference(unit_resolution,[status(thm)],[2659,27]) ).
tff(2661,plain,
s(index_204) = select(store(store(q35,seq,earray_205),tail,s(index_204)),tail),
inference(symmetry,[status(thm)],[2660]) ).
tff(2662,plain,
( ( index_204 = select(q35,tail) )
<=> ( index_204 = select(q35,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2663,axiom,
index_204 = select(q35,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(2664,plain,
index_204 = select(q35,tail),
inference(modus_ponens,[status(thm)],[2663,2662]) ).
tff(2665,plain,
select(q35,tail) = index_204,
inference(symmetry,[status(thm)],[2664]) ).
tff(2666,plain,
s(select(q35,tail)) = s(index_204),
inference(monotonicity,[status(thm)],[2665]) ).
tff(2667,plain,
s(select(q35,tail)) = index_213,
inference(transitivity,[status(thm)],[2666,2661,2658,2655,2650,2642]) ).
tff(2668,plain,
s(s(select(q35,tail))) = s(index_213),
inference(monotonicity,[status(thm)],[2667]) ).
tff(2669,plain,
s(index_204) = s(select(q35,tail)),
inference(symmetry,[status(thm)],[2666]) ).
tff(2670,plain,
store(queue_200,tail,index_201) = store(store(q34,seq,earray_199),tail,s(index_198)),
inference(symmetry,[status(thm)],[374]) ).
tff(2671,plain,
q35 = store(store(q34,seq,earray_199),tail,s(index_198)),
inference(transitivity,[status(thm)],[334,338,2670]) ).
tff(2672,plain,
select(q35,tail) = select(store(store(q34,seq,earray_199),tail,s(index_198)),tail),
inference(monotonicity,[status(thm)],[2671]) ).
tff(2673,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = select(q35,tail),
inference(symmetry,[status(thm)],[2672]) ).
tff(2674,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = s(index_198) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2675,plain,
select(store(store(q34,seq,earray_199),tail,s(index_198)),tail) = s(index_198),
inference(unit_resolution,[status(thm)],[2674,27]) ).
tff(2676,plain,
s(index_198) = select(store(store(q34,seq,earray_199),tail,s(index_198)),tail),
inference(symmetry,[status(thm)],[2675]) ).
tff(2677,plain,
( ( index_198 = select(q34,tail) )
<=> ( index_198 = select(q34,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2678,axiom,
index_198 = select(q34,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(2679,plain,
index_198 = select(q34,tail),
inference(modus_ponens,[status(thm)],[2678,2677]) ).
tff(2680,plain,
select(q34,tail) = index_198,
inference(symmetry,[status(thm)],[2679]) ).
tff(2681,plain,
s(select(q34,tail)) = s(index_198),
inference(monotonicity,[status(thm)],[2680]) ).
tff(2682,plain,
s(select(q34,tail)) = index_204,
inference(transitivity,[status(thm)],[2681,2676,2673,2665]) ).
tff(2683,plain,
s(s(select(q34,tail))) = s(index_204),
inference(monotonicity,[status(thm)],[2682]) ).
tff(2684,plain,
s(index_198) = s(select(q34,tail)),
inference(symmetry,[status(thm)],[2681]) ).
tff(2685,plain,
store(queue_194,tail,index_195) = store(store(q33,seq,earray_193),tail,s(index_192)),
inference(symmetry,[status(thm)],[422]) ).
tff(2686,plain,
q34 = store(store(q33,seq,earray_193),tail,s(index_192)),
inference(transitivity,[status(thm)],[389,393,2685]) ).
tff(2687,plain,
select(q34,tail) = select(store(store(q33,seq,earray_193),tail,s(index_192)),tail),
inference(monotonicity,[status(thm)],[2686]) ).
tff(2688,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = select(q34,tail),
inference(symmetry,[status(thm)],[2687]) ).
tff(2689,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = s(index_192) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2690,plain,
select(store(store(q33,seq,earray_193),tail,s(index_192)),tail) = s(index_192),
inference(unit_resolution,[status(thm)],[2689,27]) ).
tff(2691,plain,
s(index_192) = select(store(store(q33,seq,earray_193),tail,s(index_192)),tail),
inference(symmetry,[status(thm)],[2690]) ).
tff(2692,plain,
( ( index_192 = select(q33,tail) )
<=> ( index_192 = select(q33,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2693,axiom,
index_192 = select(q33,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(2694,plain,
index_192 = select(q33,tail),
inference(modus_ponens,[status(thm)],[2693,2692]) ).
tff(2695,plain,
select(q33,tail) = index_192,
inference(symmetry,[status(thm)],[2694]) ).
tff(2696,plain,
s(select(q33,tail)) = s(index_192),
inference(monotonicity,[status(thm)],[2695]) ).
tff(2697,plain,
s(select(q33,tail)) = index_198,
inference(transitivity,[status(thm)],[2696,2691,2688,2680]) ).
tff(2698,plain,
s(s(select(q33,tail))) = s(index_198),
inference(monotonicity,[status(thm)],[2697]) ).
tff(2699,plain,
s(index_192) = s(select(q33,tail)),
inference(symmetry,[status(thm)],[2696]) ).
tff(2700,plain,
store(queue_187,head,index_189) = store(store(queue_185,tail,index_186),head,s(index_188)),
inference(symmetry,[status(thm)],[470]) ).
tff(2701,plain,
q33 = store(store(queue_185,tail,index_186),head,s(index_188)),
inference(transitivity,[status(thm)],[437,441,2700]) ).
tff(2702,plain,
select(q33,tail) = select(store(store(queue_185,tail,index_186),head,s(index_188)),tail),
inference(monotonicity,[status(thm)],[2701]) ).
tff(2703,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(q33,tail),
inference(symmetry,[status(thm)],[2702]) ).
tff(2704,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2705,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2706,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail) ) ),
inference(modus_ponens,[status(thm)],[2705,2704]) ).
tff(2707,plain,
select(store(store(queue_185,tail,index_186),head,s(index_188)),tail) = select(store(queue_185,tail,index_186),tail),
inference(unit_resolution,[status(thm)],[2706,79,73]) ).
tff(2708,plain,
select(store(queue_185,tail,index_186),tail) = select(store(store(queue_185,tail,index_186),head,s(index_188)),tail),
inference(symmetry,[status(thm)],[2707]) ).
tff(2709,plain,
store(queue_185,tail,index_186) = store(store(q32,seq,earray_184),tail,s(index_183)),
inference(symmetry,[status(thm)],[487]) ).
tff(2710,plain,
select(store(queue_185,tail,index_186),tail) = select(store(store(q32,seq,earray_184),tail,s(index_183)),tail),
inference(monotonicity,[status(thm)],[2709]) ).
tff(2711,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = select(store(queue_185,tail,index_186),tail),
inference(symmetry,[status(thm)],[2710]) ).
tff(2712,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2713,plain,
select(store(store(q32,seq,earray_184),tail,s(index_183)),tail) = s(index_183),
inference(unit_resolution,[status(thm)],[2712,27]) ).
tff(2714,plain,
s(index_183) = select(store(store(q32,seq,earray_184),tail,s(index_183)),tail),
inference(symmetry,[status(thm)],[2713]) ).
tff(2715,plain,
( ( index_183 = select(q32,tail) )
<=> ( index_183 = select(q32,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2716,axiom,
index_183 = select(q32,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(2717,plain,
index_183 = select(q32,tail),
inference(modus_ponens,[status(thm)],[2716,2715]) ).
tff(2718,plain,
select(q32,tail) = index_183,
inference(symmetry,[status(thm)],[2717]) ).
tff(2719,plain,
s(select(q32,tail)) = s(index_183),
inference(monotonicity,[status(thm)],[2718]) ).
tff(2720,plain,
s(select(q32,tail)) = index_192,
inference(transitivity,[status(thm)],[2719,2714,2711,2708,2703,2695]) ).
tff(2721,plain,
s(s(select(q32,tail))) = s(index_192),
inference(monotonicity,[status(thm)],[2720]) ).
tff(2722,plain,
s(index_183) = s(select(q32,tail)),
inference(symmetry,[status(thm)],[2719]) ).
tff(2723,plain,
store(queue_179,tail,index_180) = store(store(q31,seq,earray_178),tail,s(index_177)),
inference(symmetry,[status(thm)],[544]) ).
tff(2724,plain,
q32 = store(store(q31,seq,earray_178),tail,s(index_177)),
inference(transitivity,[status(thm)],[504,508,2723]) ).
tff(2725,plain,
select(q32,tail) = select(store(store(q31,seq,earray_178),tail,s(index_177)),tail),
inference(monotonicity,[status(thm)],[2724]) ).
tff(2726,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = select(q32,tail),
inference(symmetry,[status(thm)],[2725]) ).
tff(2727,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2728,plain,
select(store(store(q31,seq,earray_178),tail,s(index_177)),tail) = s(index_177),
inference(unit_resolution,[status(thm)],[2727,27]) ).
tff(2729,plain,
s(index_177) = select(store(store(q31,seq,earray_178),tail,s(index_177)),tail),
inference(symmetry,[status(thm)],[2728]) ).
tff(2730,plain,
( ( index_177 = select(q31,tail) )
<=> ( index_177 = select(q31,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2731,axiom,
index_177 = select(q31,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(2732,plain,
index_177 = select(q31,tail),
inference(modus_ponens,[status(thm)],[2731,2730]) ).
tff(2733,plain,
select(q31,tail) = index_177,
inference(symmetry,[status(thm)],[2732]) ).
tff(2734,plain,
s(select(q31,tail)) = s(index_177),
inference(monotonicity,[status(thm)],[2733]) ).
tff(2735,plain,
s(select(q31,tail)) = index_183,
inference(transitivity,[status(thm)],[2734,2729,2726,2718]) ).
tff(2736,plain,
s(s(select(q31,tail))) = s(index_183),
inference(monotonicity,[status(thm)],[2735]) ).
tff(2737,plain,
s(index_177) = s(select(q31,tail)),
inference(symmetry,[status(thm)],[2734]) ).
tff(2738,plain,
store(queue_173,tail,index_174) = store(store(q30,seq,earray_172),tail,s(index_171)),
inference(symmetry,[status(thm)],[592]) ).
tff(2739,plain,
q31 = store(store(q30,seq,earray_172),tail,s(index_171)),
inference(transitivity,[status(thm)],[559,563,2738]) ).
tff(2740,plain,
select(q31,tail) = select(store(store(q30,seq,earray_172),tail,s(index_171)),tail),
inference(monotonicity,[status(thm)],[2739]) ).
tff(2741,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = select(q31,tail),
inference(symmetry,[status(thm)],[2740]) ).
tff(2742,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2743,plain,
select(store(store(q30,seq,earray_172),tail,s(index_171)),tail) = s(index_171),
inference(unit_resolution,[status(thm)],[2742,27]) ).
tff(2744,plain,
s(index_171) = select(store(store(q30,seq,earray_172),tail,s(index_171)),tail),
inference(symmetry,[status(thm)],[2743]) ).
tff(2745,plain,
( ( index_171 = select(q30,tail) )
<=> ( index_171 = select(q30,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2746,axiom,
index_171 = select(q30,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(2747,plain,
index_171 = select(q30,tail),
inference(modus_ponens,[status(thm)],[2746,2745]) ).
tff(2748,plain,
select(q30,tail) = index_171,
inference(symmetry,[status(thm)],[2747]) ).
tff(2749,plain,
s(select(q30,tail)) = s(index_171),
inference(monotonicity,[status(thm)],[2748]) ).
tff(2750,plain,
s(select(q30,tail)) = index_177,
inference(transitivity,[status(thm)],[2749,2744,2741,2733]) ).
tff(2751,plain,
s(s(select(q30,tail))) = s(index_177),
inference(monotonicity,[status(thm)],[2750]) ).
tff(2752,plain,
s(index_171) = s(select(q30,tail)),
inference(symmetry,[status(thm)],[2749]) ).
tff(2753,plain,
store(queue_166,head,index_168) = store(store(queue_164,tail,index_165),head,s(index_167)),
inference(symmetry,[status(thm)],[640]) ).
tff(2754,plain,
q30 = store(store(queue_164,tail,index_165),head,s(index_167)),
inference(transitivity,[status(thm)],[607,611,2753]) ).
tff(2755,plain,
select(q30,tail) = select(store(store(queue_164,tail,index_165),head,s(index_167)),tail),
inference(monotonicity,[status(thm)],[2754]) ).
tff(2756,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(q30,tail),
inference(symmetry,[status(thm)],[2755]) ).
tff(2757,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2758,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2759,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail) ) ),
inference(modus_ponens,[status(thm)],[2758,2757]) ).
tff(2760,plain,
select(store(store(queue_164,tail,index_165),head,s(index_167)),tail) = select(store(queue_164,tail,index_165),tail),
inference(unit_resolution,[status(thm)],[2759,79,73]) ).
tff(2761,plain,
select(store(queue_164,tail,index_165),tail) = select(store(store(queue_164,tail,index_165),head,s(index_167)),tail),
inference(symmetry,[status(thm)],[2760]) ).
tff(2762,plain,
store(queue_164,tail,index_165) = store(store(q29,seq,earray_163),tail,s(index_162)),
inference(symmetry,[status(thm)],[657]) ).
tff(2763,plain,
select(store(queue_164,tail,index_165),tail) = select(store(store(q29,seq,earray_163),tail,s(index_162)),tail),
inference(monotonicity,[status(thm)],[2762]) ).
tff(2764,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = select(store(queue_164,tail,index_165),tail),
inference(symmetry,[status(thm)],[2763]) ).
tff(2765,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = s(index_162) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2766,plain,
select(store(store(q29,seq,earray_163),tail,s(index_162)),tail) = s(index_162),
inference(unit_resolution,[status(thm)],[2765,27]) ).
tff(2767,plain,
s(index_162) = select(store(store(q29,seq,earray_163),tail,s(index_162)),tail),
inference(symmetry,[status(thm)],[2766]) ).
tff(2768,plain,
( ( index_162 = select(q29,tail) )
<=> ( index_162 = select(q29,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2769,axiom,
index_162 = select(q29,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(2770,plain,
index_162 = select(q29,tail),
inference(modus_ponens,[status(thm)],[2769,2768]) ).
tff(2771,plain,
select(q29,tail) = index_162,
inference(symmetry,[status(thm)],[2770]) ).
tff(2772,plain,
s(select(q29,tail)) = s(index_162),
inference(monotonicity,[status(thm)],[2771]) ).
tff(2773,plain,
s(select(q29,tail)) = index_171,
inference(transitivity,[status(thm)],[2772,2767,2764,2761,2756,2748]) ).
tff(2774,plain,
s(s(select(q29,tail))) = s(index_171),
inference(monotonicity,[status(thm)],[2773]) ).
tff(2775,plain,
s(index_162) = s(select(q29,tail)),
inference(symmetry,[status(thm)],[2772]) ).
tff(2776,plain,
store(queue_149,tail,index_150) = store(store(q28,seq,earray_148),tail,s(index_147)),
inference(symmetry,[status(thm)],[714]) ).
tff(2777,plain,
q29 = store(store(q28,seq,earray_148),tail,s(index_147)),
inference(transitivity,[status(thm)],[674,678,2776]) ).
tff(2778,plain,
select(q29,tail) = select(store(store(q28,seq,earray_148),tail,s(index_147)),tail),
inference(monotonicity,[status(thm)],[2777]) ).
tff(2779,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = select(q29,tail),
inference(symmetry,[status(thm)],[2778]) ).
tff(2780,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2781,plain,
select(store(store(q28,seq,earray_148),tail,s(index_147)),tail) = s(index_147),
inference(unit_resolution,[status(thm)],[2780,27]) ).
tff(2782,plain,
s(index_147) = select(store(store(q28,seq,earray_148),tail,s(index_147)),tail),
inference(symmetry,[status(thm)],[2781]) ).
tff(2783,plain,
( ( index_147 = select(q28,tail) )
<=> ( index_147 = select(q28,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2784,axiom,
index_147 = select(q28,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(2785,plain,
index_147 = select(q28,tail),
inference(modus_ponens,[status(thm)],[2784,2783]) ).
tff(2786,plain,
select(q28,tail) = index_147,
inference(symmetry,[status(thm)],[2785]) ).
tff(2787,plain,
s(select(q28,tail)) = s(index_147),
inference(monotonicity,[status(thm)],[2786]) ).
tff(2788,plain,
s(select(q28,tail)) = index_162,
inference(transitivity,[status(thm)],[2787,2782,2779,2771]) ).
tff(2789,plain,
s(s(select(q28,tail))) = s(index_162),
inference(monotonicity,[status(thm)],[2788]) ).
tff(2790,plain,
s(index_147) = s(select(q28,tail)),
inference(symmetry,[status(thm)],[2787]) ).
tff(2791,plain,
store(queue_143,tail,index_144) = store(store(q27,seq,earray_142),tail,s(index_141)),
inference(symmetry,[status(thm)],[762]) ).
tff(2792,plain,
q28 = store(store(q27,seq,earray_142),tail,s(index_141)),
inference(transitivity,[status(thm)],[729,733,2791]) ).
tff(2793,plain,
select(q28,tail) = select(store(store(q27,seq,earray_142),tail,s(index_141)),tail),
inference(monotonicity,[status(thm)],[2792]) ).
tff(2794,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = select(q28,tail),
inference(symmetry,[status(thm)],[2793]) ).
tff(2795,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2796,plain,
select(store(store(q27,seq,earray_142),tail,s(index_141)),tail) = s(index_141),
inference(unit_resolution,[status(thm)],[2795,27]) ).
tff(2797,plain,
s(index_141) = select(store(store(q27,seq,earray_142),tail,s(index_141)),tail),
inference(symmetry,[status(thm)],[2796]) ).
tff(2798,plain,
( ( index_141 = select(q27,tail) )
<=> ( index_141 = select(q27,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2799,axiom,
index_141 = select(q27,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(2800,plain,
index_141 = select(q27,tail),
inference(modus_ponens,[status(thm)],[2799,2798]) ).
tff(2801,plain,
select(q27,tail) = index_141,
inference(symmetry,[status(thm)],[2800]) ).
tff(2802,plain,
s(select(q27,tail)) = s(index_141),
inference(monotonicity,[status(thm)],[2801]) ).
tff(2803,plain,
s(select(q27,tail)) = index_147,
inference(transitivity,[status(thm)],[2802,2797,2794,2786]) ).
tff(2804,plain,
s(s(select(q27,tail))) = s(index_147),
inference(monotonicity,[status(thm)],[2803]) ).
tff(2805,plain,
s(index_141) = s(select(q27,tail)),
inference(symmetry,[status(thm)],[2802]) ).
tff(2806,plain,
store(queue_136,head,index_138) = store(store(queue_134,tail,index_135),head,s(index_137)),
inference(symmetry,[status(thm)],[810]) ).
tff(2807,plain,
q27 = store(store(queue_134,tail,index_135),head,s(index_137)),
inference(transitivity,[status(thm)],[777,781,2806]) ).
tff(2808,plain,
select(q27,tail) = select(store(store(queue_134,tail,index_135),head,s(index_137)),tail),
inference(monotonicity,[status(thm)],[2807]) ).
tff(2809,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(q27,tail),
inference(symmetry,[status(thm)],[2808]) ).
tff(2810,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2811,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2812,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail) ) ),
inference(modus_ponens,[status(thm)],[2811,2810]) ).
tff(2813,plain,
select(store(store(queue_134,tail,index_135),head,s(index_137)),tail) = select(store(queue_134,tail,index_135),tail),
inference(unit_resolution,[status(thm)],[2812,79,73]) ).
tff(2814,plain,
select(store(queue_134,tail,index_135),tail) = select(store(store(queue_134,tail,index_135),head,s(index_137)),tail),
inference(symmetry,[status(thm)],[2813]) ).
tff(2815,plain,
store(queue_134,tail,index_135) = store(store(q26,seq,earray_133),tail,s(index_132)),
inference(symmetry,[status(thm)],[827]) ).
tff(2816,plain,
select(store(queue_134,tail,index_135),tail) = select(store(store(q26,seq,earray_133),tail,s(index_132)),tail),
inference(monotonicity,[status(thm)],[2815]) ).
tff(2817,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = select(store(queue_134,tail,index_135),tail),
inference(symmetry,[status(thm)],[2816]) ).
tff(2818,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = s(index_132) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2819,plain,
select(store(store(q26,seq,earray_133),tail,s(index_132)),tail) = s(index_132),
inference(unit_resolution,[status(thm)],[2818,27]) ).
tff(2820,plain,
s(index_132) = select(store(store(q26,seq,earray_133),tail,s(index_132)),tail),
inference(symmetry,[status(thm)],[2819]) ).
tff(2821,plain,
( ( index_132 = select(q26,tail) )
<=> ( index_132 = select(q26,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2822,axiom,
index_132 = select(q26,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp95) ).
tff(2823,plain,
index_132 = select(q26,tail),
inference(modus_ponens,[status(thm)],[2822,2821]) ).
tff(2824,plain,
select(q26,tail) = index_132,
inference(symmetry,[status(thm)],[2823]) ).
tff(2825,plain,
s(select(q26,tail)) = s(index_132),
inference(monotonicity,[status(thm)],[2824]) ).
tff(2826,plain,
s(select(q26,tail)) = index_141,
inference(transitivity,[status(thm)],[2825,2820,2817,2814,2809,2801]) ).
tff(2827,plain,
s(s(select(q26,tail))) = s(index_141),
inference(monotonicity,[status(thm)],[2826]) ).
tff(2828,plain,
s(index_132) = s(select(q26,tail)),
inference(symmetry,[status(thm)],[2825]) ).
tff(2829,plain,
store(queue_128,tail,index_129) = store(store(q25,seq,earray_127),tail,s(index_126)),
inference(symmetry,[status(thm)],[884]) ).
tff(2830,plain,
q26 = store(store(q25,seq,earray_127),tail,s(index_126)),
inference(transitivity,[status(thm)],[844,848,2829]) ).
tff(2831,plain,
select(q26,tail) = select(store(store(q25,seq,earray_127),tail,s(index_126)),tail),
inference(monotonicity,[status(thm)],[2830]) ).
tff(2832,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = select(q26,tail),
inference(symmetry,[status(thm)],[2831]) ).
tff(2833,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = s(index_126) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2834,plain,
select(store(store(q25,seq,earray_127),tail,s(index_126)),tail) = s(index_126),
inference(unit_resolution,[status(thm)],[2833,27]) ).
tff(2835,plain,
s(index_126) = select(store(store(q25,seq,earray_127),tail,s(index_126)),tail),
inference(symmetry,[status(thm)],[2834]) ).
tff(2836,plain,
( ( index_126 = select(q25,tail) )
<=> ( index_126 = select(q25,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2837,axiom,
index_126 = select(q25,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp93) ).
tff(2838,plain,
index_126 = select(q25,tail),
inference(modus_ponens,[status(thm)],[2837,2836]) ).
tff(2839,plain,
select(q25,tail) = index_126,
inference(symmetry,[status(thm)],[2838]) ).
tff(2840,plain,
s(select(q25,tail)) = s(index_126),
inference(monotonicity,[status(thm)],[2839]) ).
tff(2841,plain,
s(select(q25,tail)) = index_132,
inference(transitivity,[status(thm)],[2840,2835,2832,2824]) ).
tff(2842,plain,
s(s(select(q25,tail))) = s(index_132),
inference(monotonicity,[status(thm)],[2841]) ).
tff(2843,plain,
s(index_126) = s(select(q25,tail)),
inference(symmetry,[status(thm)],[2840]) ).
tff(2844,plain,
store(queue_122,tail,index_123) = store(store(q24,seq,earray_121),tail,s(index_120)),
inference(symmetry,[status(thm)],[932]) ).
tff(2845,plain,
q25 = store(store(q24,seq,earray_121),tail,s(index_120)),
inference(transitivity,[status(thm)],[899,903,2844]) ).
tff(2846,plain,
select(q25,tail) = select(store(store(q24,seq,earray_121),tail,s(index_120)),tail),
inference(monotonicity,[status(thm)],[2845]) ).
tff(2847,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = select(q25,tail),
inference(symmetry,[status(thm)],[2846]) ).
tff(2848,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = s(index_120) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2849,plain,
select(store(store(q24,seq,earray_121),tail,s(index_120)),tail) = s(index_120),
inference(unit_resolution,[status(thm)],[2848,27]) ).
tff(2850,plain,
s(index_120) = select(store(store(q24,seq,earray_121),tail,s(index_120)),tail),
inference(symmetry,[status(thm)],[2849]) ).
tff(2851,plain,
( ( index_120 = select(q24,tail) )
<=> ( index_120 = select(q24,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2852,axiom,
index_120 = select(q24,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(2853,plain,
index_120 = select(q24,tail),
inference(modus_ponens,[status(thm)],[2852,2851]) ).
tff(2854,plain,
select(q24,tail) = index_120,
inference(symmetry,[status(thm)],[2853]) ).
tff(2855,plain,
s(select(q24,tail)) = s(index_120),
inference(monotonicity,[status(thm)],[2854]) ).
tff(2856,plain,
s(select(q24,tail)) = index_126,
inference(transitivity,[status(thm)],[2855,2850,2847,2839]) ).
tff(2857,plain,
s(s(select(q24,tail))) = s(index_126),
inference(monotonicity,[status(thm)],[2856]) ).
tff(2858,plain,
s(index_120) = s(select(q24,tail)),
inference(symmetry,[status(thm)],[2855]) ).
tff(2859,plain,
store(queue_115,head,index_117) = store(store(queue_113,tail,index_114),head,s(index_116)),
inference(symmetry,[status(thm)],[980]) ).
tff(2860,plain,
q24 = store(store(queue_113,tail,index_114),head,s(index_116)),
inference(transitivity,[status(thm)],[947,951,2859]) ).
tff(2861,plain,
select(q24,tail) = select(store(store(queue_113,tail,index_114),head,s(index_116)),tail),
inference(monotonicity,[status(thm)],[2860]) ).
tff(2862,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(q24,tail),
inference(symmetry,[status(thm)],[2861]) ).
tff(2863,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2864,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2865,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail) ) ),
inference(modus_ponens,[status(thm)],[2864,2863]) ).
tff(2866,plain,
select(store(store(queue_113,tail,index_114),head,s(index_116)),tail) = select(store(queue_113,tail,index_114),tail),
inference(unit_resolution,[status(thm)],[2865,79,73]) ).
tff(2867,plain,
select(store(queue_113,tail,index_114),tail) = select(store(store(queue_113,tail,index_114),head,s(index_116)),tail),
inference(symmetry,[status(thm)],[2866]) ).
tff(2868,plain,
store(queue_113,tail,index_114) = store(store(q23,seq,earray_112),tail,s(index_111)),
inference(symmetry,[status(thm)],[997]) ).
tff(2869,plain,
select(store(queue_113,tail,index_114),tail) = select(store(store(q23,seq,earray_112),tail,s(index_111)),tail),
inference(monotonicity,[status(thm)],[2868]) ).
tff(2870,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = select(store(queue_113,tail,index_114),tail),
inference(symmetry,[status(thm)],[2869]) ).
tff(2871,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2872,plain,
select(store(store(q23,seq,earray_112),tail,s(index_111)),tail) = s(index_111),
inference(unit_resolution,[status(thm)],[2871,27]) ).
tff(2873,plain,
s(index_111) = select(store(store(q23,seq,earray_112),tail,s(index_111)),tail),
inference(symmetry,[status(thm)],[2872]) ).
tff(2874,plain,
( ( index_111 = select(q23,tail) )
<=> ( index_111 = select(q23,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2875,axiom,
index_111 = select(q23,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp86) ).
tff(2876,plain,
index_111 = select(q23,tail),
inference(modus_ponens,[status(thm)],[2875,2874]) ).
tff(2877,plain,
select(q23,tail) = index_111,
inference(symmetry,[status(thm)],[2876]) ).
tff(2878,plain,
s(select(q23,tail)) = s(index_111),
inference(monotonicity,[status(thm)],[2877]) ).
tff(2879,plain,
s(select(q23,tail)) = index_120,
inference(transitivity,[status(thm)],[2878,2873,2870,2867,2862,2854]) ).
tff(2880,plain,
s(s(select(q23,tail))) = s(index_120),
inference(monotonicity,[status(thm)],[2879]) ).
tff(2881,plain,
s(index_111) = s(select(q23,tail)),
inference(symmetry,[status(thm)],[2878]) ).
tff(2882,plain,
store(queue_107,tail,index_108) = store(store(q22,seq,earray_106),tail,s(index_105)),
inference(symmetry,[status(thm)],[1054]) ).
tff(2883,plain,
q23 = store(store(q22,seq,earray_106),tail,s(index_105)),
inference(transitivity,[status(thm)],[1014,1018,2882]) ).
tff(2884,plain,
select(q23,tail) = select(store(store(q22,seq,earray_106),tail,s(index_105)),tail),
inference(monotonicity,[status(thm)],[2883]) ).
tff(2885,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = select(q23,tail),
inference(symmetry,[status(thm)],[2884]) ).
tff(2886,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2887,plain,
select(store(store(q22,seq,earray_106),tail,s(index_105)),tail) = s(index_105),
inference(unit_resolution,[status(thm)],[2886,27]) ).
tff(2888,plain,
s(index_105) = select(store(store(q22,seq,earray_106),tail,s(index_105)),tail),
inference(symmetry,[status(thm)],[2887]) ).
tff(2889,plain,
( ( index_105 = select(q22,tail) )
<=> ( index_105 = select(q22,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2890,axiom,
index_105 = select(q22,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp84) ).
tff(2891,plain,
index_105 = select(q22,tail),
inference(modus_ponens,[status(thm)],[2890,2889]) ).
tff(2892,plain,
select(q22,tail) = index_105,
inference(symmetry,[status(thm)],[2891]) ).
tff(2893,plain,
s(select(q22,tail)) = s(index_105),
inference(monotonicity,[status(thm)],[2892]) ).
tff(2894,plain,
s(select(q22,tail)) = index_111,
inference(transitivity,[status(thm)],[2893,2888,2885,2877]) ).
tff(2895,plain,
s(s(select(q22,tail))) = s(index_111),
inference(monotonicity,[status(thm)],[2894]) ).
tff(2896,plain,
s(index_105) = s(select(q22,tail)),
inference(symmetry,[status(thm)],[2893]) ).
tff(2897,plain,
store(queue_101,tail,index_102) = store(store(q21,seq,earray_100),tail,s(index_99)),
inference(symmetry,[status(thm)],[1102]) ).
tff(2898,plain,
q22 = store(store(q21,seq,earray_100),tail,s(index_99)),
inference(transitivity,[status(thm)],[1069,1073,2897]) ).
tff(2899,plain,
select(q22,tail) = select(store(store(q21,seq,earray_100),tail,s(index_99)),tail),
inference(monotonicity,[status(thm)],[2898]) ).
tff(2900,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = select(q22,tail),
inference(symmetry,[status(thm)],[2899]) ).
tff(2901,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2902,plain,
select(store(store(q21,seq,earray_100),tail,s(index_99)),tail) = s(index_99),
inference(unit_resolution,[status(thm)],[2901,27]) ).
tff(2903,plain,
s(index_99) = select(store(store(q21,seq,earray_100),tail,s(index_99)),tail),
inference(symmetry,[status(thm)],[2902]) ).
tff(2904,plain,
( ( index_99 = select(q21,tail) )
<=> ( index_99 = select(q21,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2905,axiom,
index_99 = select(q21,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(2906,plain,
index_99 = select(q21,tail),
inference(modus_ponens,[status(thm)],[2905,2904]) ).
tff(2907,plain,
select(q21,tail) = index_99,
inference(symmetry,[status(thm)],[2906]) ).
tff(2908,plain,
s(select(q21,tail)) = s(index_99),
inference(monotonicity,[status(thm)],[2907]) ).
tff(2909,plain,
s(select(q21,tail)) = index_105,
inference(transitivity,[status(thm)],[2908,2903,2900,2892]) ).
tff(2910,plain,
s(s(select(q21,tail))) = s(index_105),
inference(monotonicity,[status(thm)],[2909]) ).
tff(2911,plain,
s(index_99) = s(select(q21,tail)),
inference(symmetry,[status(thm)],[2908]) ).
tff(2912,plain,
store(queue_94,head,index_96) = store(store(queue_92,tail,index_93),head,s(index_95)),
inference(symmetry,[status(thm)],[1150]) ).
tff(2913,plain,
q21 = store(store(queue_92,tail,index_93),head,s(index_95)),
inference(transitivity,[status(thm)],[1117,1121,2912]) ).
tff(2914,plain,
select(q21,tail) = select(store(store(queue_92,tail,index_93),head,s(index_95)),tail),
inference(monotonicity,[status(thm)],[2913]) ).
tff(2915,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(q21,tail),
inference(symmetry,[status(thm)],[2914]) ).
tff(2916,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2917,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2918,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail) ) ),
inference(modus_ponens,[status(thm)],[2917,2916]) ).
tff(2919,plain,
select(store(store(queue_92,tail,index_93),head,s(index_95)),tail) = select(store(queue_92,tail,index_93),tail),
inference(unit_resolution,[status(thm)],[2918,79,73]) ).
tff(2920,plain,
select(store(queue_92,tail,index_93),tail) = select(store(store(queue_92,tail,index_93),head,s(index_95)),tail),
inference(symmetry,[status(thm)],[2919]) ).
tff(2921,plain,
store(queue_92,tail,index_93) = store(store(q20,seq,earray_91),tail,s(index_90)),
inference(symmetry,[status(thm)],[1167]) ).
tff(2922,plain,
select(store(queue_92,tail,index_93),tail) = select(store(store(q20,seq,earray_91),tail,s(index_90)),tail),
inference(monotonicity,[status(thm)],[2921]) ).
tff(2923,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = select(store(queue_92,tail,index_93),tail),
inference(symmetry,[status(thm)],[2922]) ).
tff(2924,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = s(index_90) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2925,plain,
select(store(store(q20,seq,earray_91),tail,s(index_90)),tail) = s(index_90),
inference(unit_resolution,[status(thm)],[2924,27]) ).
tff(2926,plain,
s(index_90) = select(store(store(q20,seq,earray_91),tail,s(index_90)),tail),
inference(symmetry,[status(thm)],[2925]) ).
tff(2927,plain,
( ( index_90 = select(q20,tail) )
<=> ( index_90 = select(q20,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2928,axiom,
index_90 = select(q20,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(2929,plain,
index_90 = select(q20,tail),
inference(modus_ponens,[status(thm)],[2928,2927]) ).
tff(2930,plain,
select(q20,tail) = index_90,
inference(symmetry,[status(thm)],[2929]) ).
tff(2931,plain,
s(select(q20,tail)) = s(index_90),
inference(monotonicity,[status(thm)],[2930]) ).
tff(2932,plain,
s(select(q20,tail)) = index_99,
inference(transitivity,[status(thm)],[2931,2926,2923,2920,2915,2907]) ).
tff(2933,plain,
s(s(select(q20,tail))) = s(index_99),
inference(monotonicity,[status(thm)],[2932]) ).
tff(2934,plain,
s(index_90) = s(select(q20,tail)),
inference(symmetry,[status(thm)],[2931]) ).
tff(2935,plain,
store(queue_86,tail,index_87) = store(store(q19,seq,earray_85),tail,s(index_84)),
inference(symmetry,[status(thm)],[1224]) ).
tff(2936,plain,
q20 = store(store(q19,seq,earray_85),tail,s(index_84)),
inference(transitivity,[status(thm)],[1184,1188,2935]) ).
tff(2937,plain,
select(q20,tail) = select(store(store(q19,seq,earray_85),tail,s(index_84)),tail),
inference(monotonicity,[status(thm)],[2936]) ).
tff(2938,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = select(q20,tail),
inference(symmetry,[status(thm)],[2937]) ).
tff(2939,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = s(index_84) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2940,plain,
select(store(store(q19,seq,earray_85),tail,s(index_84)),tail) = s(index_84),
inference(unit_resolution,[status(thm)],[2939,27]) ).
tff(2941,plain,
s(index_84) = select(store(store(q19,seq,earray_85),tail,s(index_84)),tail),
inference(symmetry,[status(thm)],[2940]) ).
tff(2942,plain,
( ( index_84 = select(q19,tail) )
<=> ( index_84 = select(q19,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2943,axiom,
index_84 = select(q19,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(2944,plain,
index_84 = select(q19,tail),
inference(modus_ponens,[status(thm)],[2943,2942]) ).
tff(2945,plain,
select(q19,tail) = index_84,
inference(symmetry,[status(thm)],[2944]) ).
tff(2946,plain,
s(select(q19,tail)) = s(index_84),
inference(monotonicity,[status(thm)],[2945]) ).
tff(2947,plain,
s(select(q19,tail)) = index_90,
inference(transitivity,[status(thm)],[2946,2941,2938,2930]) ).
tff(2948,plain,
s(s(select(q19,tail))) = s(index_90),
inference(monotonicity,[status(thm)],[2947]) ).
tff(2949,plain,
s(index_84) = s(select(q19,tail)),
inference(symmetry,[status(thm)],[2946]) ).
tff(2950,plain,
( ( index_72 = select(q18,tail) )
<=> ( index_72 = select(q18,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2951,axiom,
index_72 = select(q18,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(2952,plain,
index_72 = select(q18,tail),
inference(modus_ponens,[status(thm)],[2951,2950]) ).
tff(2953,plain,
select(q18,tail) = index_72,
inference(symmetry,[status(thm)],[2952]) ).
tff(2954,plain,
s(select(q18,tail)) = s(index_72),
inference(monotonicity,[status(thm)],[2953]) ).
tff(2955,plain,
s(index_72) = s(select(q18,tail)),
inference(symmetry,[status(thm)],[2954]) ).
tff(2956,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = s(index_72) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2957,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = s(index_72),
inference(unit_resolution,[status(thm)],[2956,27]) ).
tff(2958,plain,
store(queue_74,tail,index_75) = store(store(q18,seq,earray_73),tail,s(index_72)),
inference(symmetry,[status(thm)],[1272]) ).
tff(2959,plain,
q19 = store(store(q18,seq,earray_73),tail,s(index_72)),
inference(transitivity,[status(thm)],[1239,1243,2958]) ).
tff(2960,plain,
select(q19,tail) = select(store(store(q18,seq,earray_73),tail,s(index_72)),tail),
inference(monotonicity,[status(thm)],[2959]) ).
tff(2961,plain,
index_84 = s(select(q18,tail)),
inference(transitivity,[status(thm)],[2944,2960,2957,2955]) ).
tff(2962,plain,
s(index_84) = s(s(select(q18,tail))),
inference(monotonicity,[status(thm)],[2961]) ).
tff(2963,plain,
s(s(select(q18,tail))) = s(index_84),
inference(symmetry,[status(thm)],[2962]) ).
tff(2964,plain,
( ( index_63 = select(q17,tail) )
<=> ( index_63 = select(q17,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2965,axiom,
index_63 = select(q17,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(2966,plain,
index_63 = select(q17,tail),
inference(modus_ponens,[status(thm)],[2965,2964]) ).
tff(2967,plain,
select(q17,tail) = index_63,
inference(symmetry,[status(thm)],[2966]) ).
tff(2968,plain,
s(select(q17,tail)) = s(index_63),
inference(monotonicity,[status(thm)],[2967]) ).
tff(2969,plain,
s(index_63) = s(select(q17,tail)),
inference(symmetry,[status(thm)],[2968]) ).
tff(2970,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2971,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = s(index_63),
inference(unit_resolution,[status(thm)],[2970,27]) ).
tff(2972,plain,
store(queue_65,tail,index_66) = store(store(q17,seq,earray_64),tail,s(index_63)),
inference(symmetry,[status(thm)],[1337]) ).
tff(2973,plain,
select(store(queue_65,tail,index_66),tail) = select(store(store(q17,seq,earray_64),tail,s(index_63)),tail),
inference(monotonicity,[status(thm)],[2972]) ).
tff(2974,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2975,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2976,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail) ) ),
inference(modus_ponens,[status(thm)],[2975,2974]) ).
tff(2977,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(store(queue_65,tail,index_66),tail),
inference(unit_resolution,[status(thm)],[2976,79,73]) ).
tff(2978,plain,
store(queue_67,head,index_69) = store(store(queue_65,tail,index_66),head,s(index_68)),
inference(symmetry,[status(thm)],[1320]) ).
tff(2979,plain,
q18 = store(store(queue_65,tail,index_66),head,s(index_68)),
inference(transitivity,[status(thm)],[1287,1291,2978]) ).
tff(2980,plain,
select(q18,tail) = select(store(store(queue_65,tail,index_66),head,s(index_68)),tail),
inference(monotonicity,[status(thm)],[2979]) ).
tff(2981,plain,
index_72 = s(select(q17,tail)),
inference(transitivity,[status(thm)],[2952,2980,2977,2973,2971,2969]) ).
tff(2982,plain,
s(index_72) = s(s(select(q17,tail))),
inference(monotonicity,[status(thm)],[2981]) ).
tff(2983,plain,
s(s(select(q17,tail))) = s(index_72),
inference(symmetry,[status(thm)],[2982]) ).
tff(2984,plain,
( ( index_57 = select(q16,tail) )
<=> ( index_57 = select(q16,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2985,axiom,
index_57 = select(q16,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(2986,plain,
index_57 = select(q16,tail),
inference(modus_ponens,[status(thm)],[2985,2984]) ).
tff(2987,plain,
select(q16,tail) = index_57,
inference(symmetry,[status(thm)],[2986]) ).
tff(2988,plain,
s(select(q16,tail)) = s(index_57),
inference(monotonicity,[status(thm)],[2987]) ).
tff(2989,plain,
s(index_57) = s(select(q16,tail)),
inference(symmetry,[status(thm)],[2988]) ).
tff(2990,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2991,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = s(index_57),
inference(unit_resolution,[status(thm)],[2990,27]) ).
tff(2992,plain,
store(queue_59,tail,index_60) = store(store(q16,seq,earray_58),tail,s(index_57)),
inference(symmetry,[status(thm)],[1394]) ).
tff(2993,plain,
q17 = store(store(q16,seq,earray_58),tail,s(index_57)),
inference(transitivity,[status(thm)],[1354,1358,2992]) ).
tff(2994,plain,
select(q17,tail) = select(store(store(q16,seq,earray_58),tail,s(index_57)),tail),
inference(monotonicity,[status(thm)],[2993]) ).
tff(2995,plain,
index_63 = s(select(q16,tail)),
inference(transitivity,[status(thm)],[2966,2994,2991,2989]) ).
tff(2996,plain,
s(index_63) = s(s(select(q16,tail))),
inference(monotonicity,[status(thm)],[2995]) ).
tff(2997,plain,
s(s(select(q16,tail))) = s(index_63),
inference(symmetry,[status(thm)],[2996]) ).
tff(2998,plain,
( ( index_51 = select(q15,tail) )
<=> ( index_51 = select(q15,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2999,axiom,
index_51 = select(q15,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(3000,plain,
index_51 = select(q15,tail),
inference(modus_ponens,[status(thm)],[2999,2998]) ).
tff(3001,plain,
select(q15,tail) = index_51,
inference(symmetry,[status(thm)],[3000]) ).
tff(3002,plain,
s(select(q15,tail)) = s(index_51),
inference(monotonicity,[status(thm)],[3001]) ).
tff(3003,plain,
s(index_51) = s(select(q15,tail)),
inference(symmetry,[status(thm)],[3002]) ).
tff(3004,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3005,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = s(index_51),
inference(unit_resolution,[status(thm)],[3004,27]) ).
tff(3006,plain,
store(queue_53,tail,index_54) = store(store(q15,seq,earray_52),tail,s(index_51)),
inference(symmetry,[status(thm)],[1442]) ).
tff(3007,plain,
q16 = store(store(q15,seq,earray_52),tail,s(index_51)),
inference(transitivity,[status(thm)],[1409,1413,3006]) ).
tff(3008,plain,
select(q16,tail) = select(store(store(q15,seq,earray_52),tail,s(index_51)),tail),
inference(monotonicity,[status(thm)],[3007]) ).
tff(3009,plain,
index_57 = s(select(q15,tail)),
inference(transitivity,[status(thm)],[2986,3008,3005,3003]) ).
tff(3010,plain,
s(index_57) = s(s(select(q15,tail))),
inference(monotonicity,[status(thm)],[3009]) ).
tff(3011,plain,
s(s(select(q15,tail))) = s(index_57),
inference(symmetry,[status(thm)],[3010]) ).
tff(3012,plain,
( ( index_42 = select(q14,tail) )
<=> ( index_42 = select(q14,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3013,axiom,
index_42 = select(q14,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(3014,plain,
index_42 = select(q14,tail),
inference(modus_ponens,[status(thm)],[3013,3012]) ).
tff(3015,plain,
select(q14,tail) = index_42,
inference(symmetry,[status(thm)],[3014]) ).
tff(3016,plain,
s(select(q14,tail)) = s(index_42),
inference(monotonicity,[status(thm)],[3015]) ).
tff(3017,plain,
s(index_42) = s(select(q14,tail)),
inference(symmetry,[status(thm)],[3016]) ).
tff(3018,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q14,seq,earray_43),tail,s(index_42)),tail) = s(index_42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3019,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),tail) = s(index_42),
inference(unit_resolution,[status(thm)],[3018,27]) ).
tff(3020,plain,
store(queue_44,tail,index_45) = store(store(q14,seq,earray_43),tail,s(index_42)),
inference(symmetry,[status(thm)],[1507]) ).
tff(3021,plain,
select(store(queue_44,tail,index_45),tail) = select(store(store(q14,seq,earray_43),tail,s(index_42)),tail),
inference(monotonicity,[status(thm)],[3020]) ).
tff(3022,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3023,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3024,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( head = tail )
| ( select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail) ) ),
inference(modus_ponens,[status(thm)],[3023,3022]) ).
tff(3025,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(store(queue_44,tail,index_45),tail),
inference(unit_resolution,[status(thm)],[3024,79,73]) ).
tff(3026,plain,
store(queue_46,head,index_48) = store(store(queue_44,tail,index_45),head,s(index_47)),
inference(symmetry,[status(thm)],[1490]) ).
tff(3027,plain,
q15 = store(store(queue_44,tail,index_45),head,s(index_47)),
inference(transitivity,[status(thm)],[1457,1461,3026]) ).
tff(3028,plain,
select(q15,tail) = select(store(store(queue_44,tail,index_45),head,s(index_47)),tail),
inference(monotonicity,[status(thm)],[3027]) ).
tff(3029,plain,
index_51 = s(select(q14,tail)),
inference(transitivity,[status(thm)],[3000,3028,3025,3021,3019,3017]) ).
tff(3030,plain,
s(index_51) = s(s(select(q14,tail))),
inference(monotonicity,[status(thm)],[3029]) ).
tff(3031,plain,
s(s(select(q14,tail))) = s(index_51),
inference(symmetry,[status(thm)],[3030]) ).
tff(3032,plain,
s(select(q13,tail)) = s(index_36),
inference(monotonicity,[status(thm)],[2501]) ).
tff(3033,plain,
s(index_36) = s(select(q13,tail)),
inference(symmetry,[status(thm)],[3032]) ).
tff(3034,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q13,seq,earray_37),tail,s(index_36)),tail) = s(index_36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3035,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),tail) = s(index_36),
inference(unit_resolution,[status(thm)],[3034,27]) ).
tff(3036,plain,
store(queue_38,tail,index_39) = store(store(q13,seq,earray_37),tail,s(index_36)),
inference(symmetry,[status(thm)],[1564]) ).
tff(3037,plain,
q14 = store(store(q13,seq,earray_37),tail,s(index_36)),
inference(transitivity,[status(thm)],[1524,1528,3036]) ).
tff(3038,plain,
select(q14,tail) = select(store(store(q13,seq,earray_37),tail,s(index_36)),tail),
inference(monotonicity,[status(thm)],[3037]) ).
tff(3039,plain,
index_42 = s(select(q13,tail)),
inference(transitivity,[status(thm)],[3014,3038,3035,3033]) ).
tff(3040,plain,
s(index_42) = s(s(select(q13,tail))),
inference(monotonicity,[status(thm)],[3039]) ).
tff(3041,plain,
s(s(select(q13,tail))) = s(index_42),
inference(symmetry,[status(thm)],[3040]) ).
tff(3042,plain,
s(s(select(q13,tail))) = s(select(q14,tail)),
inference(transitivity,[status(thm)],[3041,3017]) ).
tff(3043,plain,
s(s(s(select(q13,tail)))) = s(s(select(q14,tail))),
inference(monotonicity,[status(thm)],[3042]) ).
tff(3044,plain,
s(s(s(select(q13,tail)))) = s(select(q15,tail)),
inference(transitivity,[status(thm)],[3043,3031,3003]) ).
tff(3045,plain,
s(s(s(s(select(q13,tail))))) = s(s(select(q15,tail))),
inference(monotonicity,[status(thm)],[3044]) ).
tff(3046,plain,
s(s(s(s(select(q13,tail))))) = s(select(q16,tail)),
inference(transitivity,[status(thm)],[3045,3011,2989]) ).
tff(3047,plain,
s(s(s(s(s(select(q13,tail)))))) = s(s(select(q16,tail))),
inference(monotonicity,[status(thm)],[3046]) ).
tff(3048,plain,
s(s(s(s(s(select(q13,tail)))))) = s(select(q17,tail)),
inference(transitivity,[status(thm)],[3047,2997,2969]) ).
tff(3049,plain,
s(s(s(s(s(s(select(q13,tail))))))) = s(s(select(q17,tail))),
inference(monotonicity,[status(thm)],[3048]) ).
tff(3050,plain,
s(s(s(s(s(s(select(q13,tail))))))) = s(select(q18,tail)),
inference(transitivity,[status(thm)],[3049,2983,2955]) ).
tff(3051,plain,
s(s(s(s(s(s(s(select(q13,tail)))))))) = s(s(select(q18,tail))),
inference(monotonicity,[status(thm)],[3050]) ).
tff(3052,plain,
s(s(s(s(s(s(s(select(q13,tail)))))))) = s(select(q19,tail)),
inference(transitivity,[status(thm)],[3051,2963,2949]) ).
tff(3053,plain,
s(s(s(s(s(s(s(s(select(q13,tail))))))))) = s(s(select(q19,tail))),
inference(monotonicity,[status(thm)],[3052]) ).
tff(3054,plain,
s(s(s(s(s(s(s(s(select(q13,tail))))))))) = s(select(q20,tail)),
inference(transitivity,[status(thm)],[3053,2948,2934]) ).
tff(3055,plain,
s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) = s(s(select(q20,tail))),
inference(monotonicity,[status(thm)],[3054]) ).
tff(3056,plain,
s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) = s(select(q21,tail)),
inference(transitivity,[status(thm)],[3055,2933,2911]) ).
tff(3057,plain,
s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) = s(s(select(q21,tail))),
inference(monotonicity,[status(thm)],[3056]) ).
tff(3058,plain,
s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) = s(select(q22,tail)),
inference(transitivity,[status(thm)],[3057,2910,2896]) ).
tff(3059,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) = s(s(select(q22,tail))),
inference(monotonicity,[status(thm)],[3058]) ).
tff(3060,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) = s(select(q23,tail)),
inference(transitivity,[status(thm)],[3059,2895,2881]) ).
tff(3061,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) = s(s(select(q23,tail))),
inference(monotonicity,[status(thm)],[3060]) ).
tff(3062,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) = s(select(q24,tail)),
inference(transitivity,[status(thm)],[3061,2880,2858]) ).
tff(3063,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) = s(s(select(q24,tail))),
inference(monotonicity,[status(thm)],[3062]) ).
tff(3064,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) = s(select(q25,tail)),
inference(transitivity,[status(thm)],[3063,2857,2843]) ).
tff(3065,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) = s(s(select(q25,tail))),
inference(monotonicity,[status(thm)],[3064]) ).
tff(3066,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) = s(select(q26,tail)),
inference(transitivity,[status(thm)],[3065,2842,2828]) ).
tff(3067,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) = s(s(select(q26,tail))),
inference(monotonicity,[status(thm)],[3066]) ).
tff(3068,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) = s(select(q27,tail)),
inference(transitivity,[status(thm)],[3067,2827,2805]) ).
tff(3069,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) = s(s(select(q27,tail))),
inference(monotonicity,[status(thm)],[3068]) ).
tff(3070,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) = s(select(q28,tail)),
inference(transitivity,[status(thm)],[3069,2804,2790]) ).
tff(3071,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) = s(s(select(q28,tail))),
inference(monotonicity,[status(thm)],[3070]) ).
tff(3072,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) = s(select(q29,tail)),
inference(transitivity,[status(thm)],[3071,2789,2775]) ).
tff(3073,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) = s(s(select(q29,tail))),
inference(monotonicity,[status(thm)],[3072]) ).
tff(3074,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) = s(select(q30,tail)),
inference(transitivity,[status(thm)],[3073,2774,2752]) ).
tff(3075,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) = s(s(select(q30,tail))),
inference(monotonicity,[status(thm)],[3074]) ).
tff(3076,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) = s(select(q31,tail)),
inference(transitivity,[status(thm)],[3075,2751,2737]) ).
tff(3077,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) = s(s(select(q31,tail))),
inference(monotonicity,[status(thm)],[3076]) ).
tff(3078,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) = s(select(q32,tail)),
inference(transitivity,[status(thm)],[3077,2736,2722]) ).
tff(3079,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) = s(s(select(q32,tail))),
inference(monotonicity,[status(thm)],[3078]) ).
tff(3080,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) = s(select(q33,tail)),
inference(transitivity,[status(thm)],[3079,2721,2699]) ).
tff(3081,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) = s(s(select(q33,tail))),
inference(monotonicity,[status(thm)],[3080]) ).
tff(3082,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) = s(select(q34,tail)),
inference(transitivity,[status(thm)],[3081,2698,2684]) ).
tff(3083,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) = s(s(select(q34,tail))),
inference(monotonicity,[status(thm)],[3082]) ).
tff(3084,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) = s(select(q35,tail)),
inference(transitivity,[status(thm)],[3083,2683,2669]) ).
tff(3085,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) = s(s(select(q35,tail))),
inference(monotonicity,[status(thm)],[3084]) ).
tff(3086,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) = s(select(q36,tail)),
inference(transitivity,[status(thm)],[3085,2668,2646]) ).
tff(3087,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) = s(s(select(q36,tail))),
inference(monotonicity,[status(thm)],[3086]) ).
tff(3088,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) = s(select(q37,tail)),
inference(transitivity,[status(thm)],[3087,2645,2631]) ).
tff(3089,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) = s(s(select(q37,tail))),
inference(monotonicity,[status(thm)],[3088]) ).
tff(3090,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) = s(index_225),
inference(transitivity,[status(thm)],[3089,2630]) ).
tff(3091,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_225) = select(q40,head) ) ),
inference(monotonicity,[status(thm)],[3090,2612]) ).
tff(3092,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_225) != select(q40,head) ) ),
inference(monotonicity,[status(thm)],[3091]) ).
tff(3093,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(3094,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)],[3093]) ).
tff(3095,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(3096,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(3097,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)],[3096,3095]) ).
tff(3098,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)],[3097]) ).
tff(3099,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)],[3098,3094]) ).
tff(3100,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3101,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3100,3099]) ).
tff(3102,plain,
s(index_225) != select(q40,head),
inference(modus_ponens,[status(thm)],[3101,3092]) ).
tff(3103,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q40,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q40,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3104,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q40,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3105,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_225) = select(q40,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)) ) ),
inference(modus_ponens,[status(thm)],[3104,3103]) ).
tff(3106,plain,
( ( s(index_225) = select(q40,head) )
| ( select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)) ) ),
inference(unit_resolution,[status(thm)],[3105,79]) ).
tff(3107,plain,
select(store(select(q39,seq),s(index_225),e39),select(q40,head)) = select(select(q39,seq),select(q40,head)),
inference(unit_resolution,[status(thm)],[3106,3102]) ).
tff(3108,plain,
select(select(q39,seq),select(q40,head)) = select(store(select(q39,seq),s(index_225),e39),select(q40,head)),
inference(symmetry,[status(thm)],[3107]) ).
tff(3109,plain,
s(index_230) = select(q40,head),
inference(transitivity,[status(thm)],[2611,2608,2606,2600,2593,2587]) ).
tff(3110,plain,
select(store(queue_227,tail,index_228),seq) = select(store(store(queue_227,tail,index_228),head,s(index_230)),seq),
inference(symmetry,[status(thm)],[166]) ).
tff(3111,plain,
select(store(q38,seq,earray_226),seq) = select(store(store(q38,seq,earray_226),tail,s(index_225)),seq),
inference(symmetry,[status(thm)],[157]) ).
tff(3112,plain,
store(earray_224,index_225,e38) = select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e38)),seq),
inference(symmetry,[status(thm)],[138]) ).
tff(3113,plain,
s(index_219) = index_225,
inference(transitivity,[status(thm)],[2623,2620,2616]) ).
tff(3114,plain,
( ( earray_224 = select(q38,seq) )
<=> ( earray_224 = select(q38,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3115,axiom,
earray_224 = select(q38,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(3116,plain,
earray_224 = select(q38,seq),
inference(modus_ponens,[status(thm)],[3115,3114]) ).
tff(3117,plain,
select(q38,seq) = earray_224,
inference(symmetry,[status(thm)],[3116]) ).
tff(3118,plain,
store(select(q38,seq),s(index_219),e38) = store(earray_224,index_225,e38),
inference(monotonicity,[status(thm)],[3117,3113]) ).
tff(3119,plain,
store(select(q38,seq),s(index_219),e38) = select(q39,seq),
inference(transitivity,[status(thm)],[3118,3112,149,3111,158,3110,181]) ).
tff(3120,plain,
select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q39,seq),select(q40,head)),
inference(monotonicity,[status(thm)],[3119,3109]) ).
tff(3121,plain,
s(s(select(q36,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3087]) ).
tff(3122,plain,
s(index_219) = s(s(select(q36,tail))),
inference(symmetry,[status(thm)],[2645]) ).
tff(3123,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(s(s(s(select(q13,tail)))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3122,3121]) ).
tff(3124,plain,
( ( s(index_219) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3123,2497]) ).
tff(3125,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_219) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3124]) ).
tff(3126,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_219) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3125]) ).
tff(3127,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(3128,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)],[3127]) ).
tff(3129,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(3130,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(3131,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)],[3130,3129]) ).
tff(3132,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)],[3131]) ).
tff(3133,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)],[3132,3128]) ).
tff(3134,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3135,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3134,3133]) ).
tff(3136,plain,
s(index_219) != s(index_230),
inference(modus_ponens,[status(thm)],[3135,3126]) ).
tff(3137,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = s(index_230) )
| ( select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = s(index_230) )
| ( select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3138,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = s(index_230) )
| ( select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3139,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_219) = s(index_230) )
| ( select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3138,3137]) ).
tff(3140,plain,
( ( s(index_219) = s(index_230) )
| ( select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3139,79]) ).
tff(3141,plain,
select(store(select(q38,seq),s(index_219),e38),s(index_230)) = select(select(q38,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3140,3136]) ).
tff(3142,plain,
select(select(q38,seq),s(index_230)) = select(store(select(q38,seq),s(index_219),e38),s(index_230)),
inference(symmetry,[status(thm)],[3141]) ).
tff(3143,plain,
select(store(q37,seq,earray_220),seq) = select(store(store(q37,seq,earray_220),tail,s(index_219)),seq),
inference(symmetry,[status(thm)],[232]) ).
tff(3144,plain,
store(earray_218,index_219,e37) = select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e37)),seq),
inference(symmetry,[status(thm)],[216]) ).
tff(3145,plain,
s(index_213) = index_219,
inference(transitivity,[status(thm)],[2638,2635,2627]) ).
tff(3146,plain,
( ( earray_218 = select(q37,seq) )
<=> ( earray_218 = select(q37,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3147,axiom,
earray_218 = select(q37,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp38) ).
tff(3148,plain,
earray_218 = select(q37,seq),
inference(modus_ponens,[status(thm)],[3147,3146]) ).
tff(3149,plain,
select(q37,seq) = earray_218,
inference(symmetry,[status(thm)],[3148]) ).
tff(3150,plain,
store(select(q37,seq),s(index_213),e37) = store(earray_218,index_219,e37),
inference(monotonicity,[status(thm)],[3149,3145]) ).
tff(3151,plain,
store(select(q37,seq),s(index_213),e37) = select(q38,seq),
inference(transitivity,[status(thm)],[3150,3144,227,3143,234]) ).
tff(3152,plain,
select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q38,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3151]) ).
tff(3153,plain,
s(s(select(q35,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3085]) ).
tff(3154,plain,
s(index_213) = s(s(select(q35,tail))),
inference(symmetry,[status(thm)],[2668]) ).
tff(3155,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(s(s(s(select(q13,tail))))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3154,3153]) ).
tff(3156,plain,
( ( s(index_213) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3155,2497]) ).
tff(3157,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_213) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3156]) ).
tff(3158,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_213) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3157]) ).
tff(3159,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(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(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)],[3159]) ).
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(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(3162,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(3163,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)],[3162,3161]) ).
tff(3164,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)],[3163]) ).
tff(3165,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)],[3164,3160]) ).
tff(3166,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3167,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3166,3165]) ).
tff(3168,plain,
s(index_213) != s(index_230),
inference(modus_ponens,[status(thm)],[3167,3158]) ).
tff(3169,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = s(index_230) )
| ( select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = s(index_230) )
| ( select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3170,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = s(index_230) )
| ( select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3171,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_213) = s(index_230) )
| ( select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3170,3169]) ).
tff(3172,plain,
( ( s(index_213) = s(index_230) )
| ( select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3171,79]) ).
tff(3173,plain,
select(store(select(q37,seq),s(index_213),e37),s(index_230)) = select(select(q37,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3172,3168]) ).
tff(3174,plain,
select(select(q37,seq),s(index_230)) = select(store(select(q37,seq),s(index_213),e37),s(index_230)),
inference(symmetry,[status(thm)],[3173]) ).
tff(3175,plain,
select(store(q36,seq,earray_214),seq) = select(store(store(q36,seq,earray_214),tail,s(index_213)),seq),
inference(symmetry,[status(thm)],[280]) ).
tff(3176,plain,
store(earray_212,index_213,e36) = select(store(store(queue_208,head,index_210),seq,store(earray_212,index_213,e36)),seq),
inference(symmetry,[status(thm)],[264]) ).
tff(3177,plain,
s(index_204) = index_213,
inference(transitivity,[status(thm)],[2661,2658,2655,2650,2642]) ).
tff(3178,plain,
( ( earray_212 = select(q36,seq) )
<=> ( earray_212 = select(q36,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3179,axiom,
earray_212 = select(q36,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp36) ).
tff(3180,plain,
earray_212 = select(q36,seq),
inference(modus_ponens,[status(thm)],[3179,3178]) ).
tff(3181,plain,
select(q36,seq) = earray_212,
inference(symmetry,[status(thm)],[3180]) ).
tff(3182,plain,
store(select(q36,seq),s(index_204),e36) = store(earray_212,index_213,e36),
inference(monotonicity,[status(thm)],[3181,3177]) ).
tff(3183,plain,
store(select(q36,seq),s(index_204),e36) = select(q37,seq),
inference(transitivity,[status(thm)],[3182,3176,275,3175,282]) ).
tff(3184,plain,
select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q37,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3183]) ).
tff(3185,plain,
s(s(select(q34,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3083]) ).
tff(3186,plain,
s(index_204) = s(s(select(q34,tail))),
inference(symmetry,[status(thm)],[2683]) ).
tff(3187,plain,
s(index_204) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3186,3185]) ).
tff(3188,plain,
( ( s(index_204) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3187,2497]) ).
tff(3189,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_204) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3188]) ).
tff(3190,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_204) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3189]) ).
tff(3191,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(3192,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)],[3191]) ).
tff(3193,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(3194,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(3195,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)],[3194,3193]) ).
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(X))))))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[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(X))))))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3196,3192]) ).
tff(3198,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3199,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3198,3197]) ).
tff(3200,plain,
s(index_204) != s(index_230),
inference(modus_ponens,[status(thm)],[3199,3190]) ).
tff(3201,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = s(index_230) )
| ( select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = s(index_230) )
| ( select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3202,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = s(index_230) )
| ( select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3203,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_204) = s(index_230) )
| ( select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3202,3201]) ).
tff(3204,plain,
( ( s(index_204) = s(index_230) )
| ( select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3203,79]) ).
tff(3205,plain,
select(store(select(q36,seq),s(index_204),e36),s(index_230)) = select(select(q36,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3204,3200]) ).
tff(3206,plain,
select(select(q36,seq),s(index_230)) = select(store(select(q36,seq),s(index_204),e36),s(index_230)),
inference(symmetry,[status(thm)],[3205]) ).
tff(3207,plain,
select(store(queue_206,tail,index_207),seq) = select(store(store(queue_206,tail,index_207),head,s(index_209)),seq),
inference(symmetry,[status(thm)],[353]) ).
tff(3208,plain,
select(store(q35,seq,earray_205),seq) = select(store(store(q35,seq,earray_205),tail,s(index_204)),seq),
inference(symmetry,[status(thm)],[347]) ).
tff(3209,plain,
store(earray_203,index_204,e35) = select(store(store(queue_200,tail,index_201),seq,store(earray_203,index_204,e35)),seq),
inference(symmetry,[status(thm)],[331]) ).
tff(3210,plain,
s(index_198) = index_204,
inference(transitivity,[status(thm)],[2676,2673,2665]) ).
tff(3211,plain,
( ( earray_203 = select(q35,seq) )
<=> ( earray_203 = select(q35,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3212,axiom,
earray_203 = select(q35,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp34) ).
tff(3213,plain,
earray_203 = select(q35,seq),
inference(modus_ponens,[status(thm)],[3212,3211]) ).
tff(3214,plain,
select(q35,seq) = earray_203,
inference(symmetry,[status(thm)],[3213]) ).
tff(3215,plain,
store(select(q35,seq),s(index_198),e35) = store(earray_203,index_204,e35),
inference(monotonicity,[status(thm)],[3214,3210]) ).
tff(3216,plain,
store(select(q35,seq),s(index_198),e35) = select(q36,seq),
inference(transitivity,[status(thm)],[3215,3209,342,3208,348,3207,355]) ).
tff(3217,plain,
select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q36,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3216]) ).
tff(3218,plain,
s(s(select(q33,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))),
inference(symmetry,[status(thm)],[3081]) ).
tff(3219,plain,
s(index_198) = s(s(select(q33,tail))),
inference(symmetry,[status(thm)],[2698]) ).
tff(3220,plain,
s(index_198) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))),
inference(transitivity,[status(thm)],[3219,3218]) ).
tff(3221,plain,
( ( s(index_198) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3220,2497]) ).
tff(3222,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_198) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3221]) ).
tff(3223,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_198) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3222]) ).
tff(3224,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(3225,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)],[3224]) ).
tff(3226,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(3227,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(3228,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)],[3227,3226]) ).
tff(3229,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)],[3228]) ).
tff(3230,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)],[3229,3225]) ).
tff(3231,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3232,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3231,3230]) ).
tff(3233,plain,
s(index_198) != s(index_230),
inference(modus_ponens,[status(thm)],[3232,3223]) ).
tff(3234,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = s(index_230) )
| ( select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = s(index_230) )
| ( select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3235,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = s(index_230) )
| ( select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3236,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_198) = s(index_230) )
| ( select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3235,3234]) ).
tff(3237,plain,
( ( s(index_198) = s(index_230) )
| ( select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3236,79]) ).
tff(3238,plain,
select(store(select(q35,seq),s(index_198),e35),s(index_230)) = select(select(q35,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3237,3233]) ).
tff(3239,plain,
select(select(q35,seq),s(index_230)) = select(store(select(q35,seq),s(index_198),e35),s(index_230)),
inference(symmetry,[status(thm)],[3238]) ).
tff(3240,plain,
select(store(q34,seq,earray_199),seq) = select(store(store(q34,seq,earray_199),tail,s(index_198)),seq),
inference(symmetry,[status(thm)],[402]) ).
tff(3241,plain,
store(earray_197,index_198,e34) = select(store(store(queue_194,tail,index_195),seq,store(earray_197,index_198,e34)),seq),
inference(symmetry,[status(thm)],[386]) ).
tff(3242,plain,
s(index_192) = index_198,
inference(transitivity,[status(thm)],[2691,2688,2680]) ).
tff(3243,plain,
( ( earray_197 = select(q34,seq) )
<=> ( earray_197 = select(q34,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3244,axiom,
earray_197 = select(q34,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp30) ).
tff(3245,plain,
earray_197 = select(q34,seq),
inference(modus_ponens,[status(thm)],[3244,3243]) ).
tff(3246,plain,
select(q34,seq) = earray_197,
inference(symmetry,[status(thm)],[3245]) ).
tff(3247,plain,
store(select(q34,seq),s(index_192),e34) = store(earray_197,index_198,e34),
inference(monotonicity,[status(thm)],[3246,3242]) ).
tff(3248,plain,
store(select(q34,seq),s(index_192),e34) = select(q35,seq),
inference(transitivity,[status(thm)],[3247,3241,397,3240,404]) ).
tff(3249,plain,
select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q35,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3248]) ).
tff(3250,plain,
s(s(select(q32,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))),
inference(symmetry,[status(thm)],[3079]) ).
tff(3251,plain,
s(index_192) = s(s(select(q32,tail))),
inference(symmetry,[status(thm)],[2721]) ).
tff(3252,plain,
s(index_192) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))),
inference(transitivity,[status(thm)],[3251,3250]) ).
tff(3253,plain,
( ( s(index_192) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3252,2497]) ).
tff(3254,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_192) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3253]) ).
tff(3255,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_192) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3254]) ).
tff(3256,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(3257,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)],[3256]) ).
tff(3258,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(3259,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(3260,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)],[3259,3258]) ).
tff(3261,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)],[3260]) ).
tff(3262,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)],[3261,3257]) ).
tff(3263,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3264,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3263,3262]) ).
tff(3265,plain,
s(index_192) != s(index_230),
inference(modus_ponens,[status(thm)],[3264,3255]) ).
tff(3266,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = s(index_230) )
| ( select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = s(index_230) )
| ( select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3267,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = s(index_230) )
| ( select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3268,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_192) = s(index_230) )
| ( select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3267,3266]) ).
tff(3269,plain,
( ( s(index_192) = s(index_230) )
| ( select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3268,79]) ).
tff(3270,plain,
select(store(select(q34,seq),s(index_192),e34),s(index_230)) = select(select(q34,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3269,3265]) ).
tff(3271,plain,
select(select(q34,seq),s(index_230)) = select(store(select(q34,seq),s(index_192),e34),s(index_230)),
inference(symmetry,[status(thm)],[3270]) ).
tff(3272,plain,
select(store(q33,seq,earray_193),seq) = select(store(store(q33,seq,earray_193),tail,s(index_192)),seq),
inference(symmetry,[status(thm)],[450]) ).
tff(3273,plain,
store(earray_191,index_192,e33) = select(store(store(queue_187,head,index_189),seq,store(earray_191,index_192,e33)),seq),
inference(symmetry,[status(thm)],[434]) ).
tff(3274,plain,
s(index_183) = index_192,
inference(transitivity,[status(thm)],[2714,2711,2708,2703,2695]) ).
tff(3275,plain,
( ( earray_191 = select(q33,seq) )
<=> ( earray_191 = select(q33,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3276,axiom,
earray_191 = select(q33,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp28) ).
tff(3277,plain,
earray_191 = select(q33,seq),
inference(modus_ponens,[status(thm)],[3276,3275]) ).
tff(3278,plain,
select(q33,seq) = earray_191,
inference(symmetry,[status(thm)],[3277]) ).
tff(3279,plain,
store(select(q33,seq),s(index_183),e33) = store(earray_191,index_192,e33),
inference(monotonicity,[status(thm)],[3278,3274]) ).
tff(3280,plain,
store(select(q33,seq),s(index_183),e33) = select(q34,seq),
inference(transitivity,[status(thm)],[3279,3273,445,3272,452]) ).
tff(3281,plain,
select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q34,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3280]) ).
tff(3282,plain,
s(s(select(q31,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))),
inference(symmetry,[status(thm)],[3077]) ).
tff(3283,plain,
s(index_183) = s(s(select(q31,tail))),
inference(symmetry,[status(thm)],[2736]) ).
tff(3284,plain,
s(index_183) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))),
inference(transitivity,[status(thm)],[3283,3282]) ).
tff(3285,plain,
( ( s(index_183) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3284,2497]) ).
tff(3286,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_183) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3285]) ).
tff(3287,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_183) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3286]) ).
tff(3288,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(3289,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)],[3288]) ).
tff(3290,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(3291,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(3292,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)],[3291,3290]) ).
tff(3293,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)],[3292]) ).
tff(3294,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)],[3293,3289]) ).
tff(3295,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3296,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3295,3294]) ).
tff(3297,plain,
s(index_183) != s(index_230),
inference(modus_ponens,[status(thm)],[3296,3287]) ).
tff(3298,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = s(index_230) )
| ( select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = s(index_230) )
| ( select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3299,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = s(index_230) )
| ( select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3300,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_183) = s(index_230) )
| ( select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3299,3298]) ).
tff(3301,plain,
( ( s(index_183) = s(index_230) )
| ( select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3300,79]) ).
tff(3302,plain,
select(store(select(q33,seq),s(index_183),e33),s(index_230)) = select(select(q33,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3301,3297]) ).
tff(3303,plain,
select(select(q33,seq),s(index_230)) = select(store(select(q33,seq),s(index_183),e33),s(index_230)),
inference(symmetry,[status(thm)],[3302]) ).
tff(3304,plain,
select(store(queue_185,tail,index_186),seq) = select(store(store(queue_185,tail,index_186),head,s(index_188)),seq),
inference(symmetry,[status(thm)],[523]) ).
tff(3305,plain,
select(store(q32,seq,earray_184),seq) = select(store(store(q32,seq,earray_184),tail,s(index_183)),seq),
inference(symmetry,[status(thm)],[517]) ).
tff(3306,plain,
store(earray_182,index_183,e32) = select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e32)),seq),
inference(symmetry,[status(thm)],[501]) ).
tff(3307,plain,
s(index_177) = index_183,
inference(transitivity,[status(thm)],[2729,2726,2718]) ).
tff(3308,plain,
( ( earray_182 = select(q32,seq) )
<=> ( earray_182 = select(q32,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3309,axiom,
earray_182 = select(q32,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp26) ).
tff(3310,plain,
earray_182 = select(q32,seq),
inference(modus_ponens,[status(thm)],[3309,3308]) ).
tff(3311,plain,
select(q32,seq) = earray_182,
inference(symmetry,[status(thm)],[3310]) ).
tff(3312,plain,
store(select(q32,seq),s(index_177),e32) = store(earray_182,index_183,e32),
inference(monotonicity,[status(thm)],[3311,3307]) ).
tff(3313,plain,
store(select(q32,seq),s(index_177),e32) = select(q33,seq),
inference(transitivity,[status(thm)],[3312,3306,512,3305,518,3304,525]) ).
tff(3314,plain,
select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q33,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3313]) ).
tff(3315,plain,
s(s(select(q30,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))),
inference(symmetry,[status(thm)],[3075]) ).
tff(3316,plain,
s(index_177) = s(s(select(q30,tail))),
inference(symmetry,[status(thm)],[2751]) ).
tff(3317,plain,
s(index_177) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))),
inference(transitivity,[status(thm)],[3316,3315]) ).
tff(3318,plain,
( ( s(index_177) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3317,2497]) ).
tff(3319,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_177) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3318]) ).
tff(3320,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_177) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3319]) ).
tff(3321,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(3322,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)],[3321]) ).
tff(3323,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(3324,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(3325,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)],[3324,3323]) ).
tff(3326,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)],[3325]) ).
tff(3327,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)],[3326,3322]) ).
tff(3328,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3329,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3328,3327]) ).
tff(3330,plain,
s(index_177) != s(index_230),
inference(modus_ponens,[status(thm)],[3329,3320]) ).
tff(3331,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = s(index_230) )
| ( select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = s(index_230) )
| ( select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3332,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = s(index_230) )
| ( select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3333,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_177) = s(index_230) )
| ( select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3332,3331]) ).
tff(3334,plain,
( ( s(index_177) = s(index_230) )
| ( select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3333,79]) ).
tff(3335,plain,
select(store(select(q32,seq),s(index_177),e32),s(index_230)) = select(select(q32,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3334,3330]) ).
tff(3336,plain,
select(select(q32,seq),s(index_230)) = select(store(select(q32,seq),s(index_177),e32),s(index_230)),
inference(symmetry,[status(thm)],[3335]) ).
tff(3337,plain,
select(store(q31,seq,earray_178),seq) = select(store(store(q31,seq,earray_178),tail,s(index_177)),seq),
inference(symmetry,[status(thm)],[572]) ).
tff(3338,plain,
store(earray_176,index_177,e31) = select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e31)),seq),
inference(symmetry,[status(thm)],[556]) ).
tff(3339,plain,
s(index_171) = index_177,
inference(transitivity,[status(thm)],[2744,2741,2733]) ).
tff(3340,plain,
( ( earray_176 = select(q31,seq) )
<=> ( earray_176 = select(q31,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3341,axiom,
earray_176 = select(q31,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp24) ).
tff(3342,plain,
earray_176 = select(q31,seq),
inference(modus_ponens,[status(thm)],[3341,3340]) ).
tff(3343,plain,
select(q31,seq) = earray_176,
inference(symmetry,[status(thm)],[3342]) ).
tff(3344,plain,
store(select(q31,seq),s(index_171),e31) = store(earray_176,index_177,e31),
inference(monotonicity,[status(thm)],[3343,3339]) ).
tff(3345,plain,
store(select(q31,seq),s(index_171),e31) = select(q32,seq),
inference(transitivity,[status(thm)],[3344,3338,567,3337,574]) ).
tff(3346,plain,
select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q32,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3345]) ).
tff(3347,plain,
s(s(select(q29,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))),
inference(symmetry,[status(thm)],[3073]) ).
tff(3348,plain,
s(index_171) = s(s(select(q29,tail))),
inference(symmetry,[status(thm)],[2774]) ).
tff(3349,plain,
s(index_171) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))),
inference(transitivity,[status(thm)],[3348,3347]) ).
tff(3350,plain,
( ( s(index_171) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3349,2497]) ).
tff(3351,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) = select(q13,tail) )
<=> ( s(index_171) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3350]) ).
tff(3352,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) != select(q13,tail) )
<=> ( s(index_171) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3351]) ).
tff(3353,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(3354,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)],[3353]) ).
tff(3355,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(3356,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(3357,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)],[3356,3355]) ).
tff(3358,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)],[3357]) ).
tff(3359,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)],[3358,3354]) ).
tff(3360,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3361,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3360,3359]) ).
tff(3362,plain,
s(index_171) != s(index_230),
inference(modus_ponens,[status(thm)],[3361,3352]) ).
tff(3363,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = s(index_230) )
| ( select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = s(index_230) )
| ( select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3364,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = s(index_230) )
| ( select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3365,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_171) = s(index_230) )
| ( select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3364,3363]) ).
tff(3366,plain,
( ( s(index_171) = s(index_230) )
| ( select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3365,79]) ).
tff(3367,plain,
select(store(select(q31,seq),s(index_171),e31),s(index_230)) = select(select(q31,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3366,3362]) ).
tff(3368,plain,
select(select(q31,seq),s(index_230)) = select(store(select(q31,seq),s(index_171),e31),s(index_230)),
inference(symmetry,[status(thm)],[3367]) ).
tff(3369,plain,
select(store(q30,seq,earray_172),seq) = select(store(store(q30,seq,earray_172),tail,s(index_171)),seq),
inference(symmetry,[status(thm)],[620]) ).
tff(3370,plain,
store(earray_170,index_171,e30) = select(store(store(queue_166,head,index_168),seq,store(earray_170,index_171,e30)),seq),
inference(symmetry,[status(thm)],[604]) ).
tff(3371,plain,
s(index_162) = index_171,
inference(transitivity,[status(thm)],[2767,2764,2761,2756,2748]) ).
tff(3372,plain,
( ( earray_170 = select(q30,seq) )
<=> ( earray_170 = select(q30,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3373,axiom,
earray_170 = select(q30,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(3374,plain,
earray_170 = select(q30,seq),
inference(modus_ponens,[status(thm)],[3373,3372]) ).
tff(3375,plain,
select(q30,seq) = earray_170,
inference(symmetry,[status(thm)],[3374]) ).
tff(3376,plain,
store(select(q30,seq),s(index_162),e30) = store(earray_170,index_171,e30),
inference(monotonicity,[status(thm)],[3375,3371]) ).
tff(3377,plain,
store(select(q30,seq),s(index_162),e30) = select(q31,seq),
inference(transitivity,[status(thm)],[3376,3370,615,3369,622]) ).
tff(3378,plain,
select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q31,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3377]) ).
tff(3379,plain,
s(s(select(q28,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))),
inference(symmetry,[status(thm)],[3071]) ).
tff(3380,plain,
s(index_162) = s(s(select(q28,tail))),
inference(symmetry,[status(thm)],[2789]) ).
tff(3381,plain,
s(index_162) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))),
inference(transitivity,[status(thm)],[3380,3379]) ).
tff(3382,plain,
( ( s(index_162) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3381,2497]) ).
tff(3383,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) = select(q13,tail) )
<=> ( s(index_162) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3382]) ).
tff(3384,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) != select(q13,tail) )
<=> ( s(index_162) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3383]) ).
tff(3385,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(3386,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)],[3385]) ).
tff(3387,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(3388,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(3389,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)],[3388,3387]) ).
tff(3390,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)],[3389]) ).
tff(3391,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)],[3390,3386]) ).
tff(3392,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3393,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3392,3391]) ).
tff(3394,plain,
s(index_162) != s(index_230),
inference(modus_ponens,[status(thm)],[3393,3384]) ).
tff(3395,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = s(index_230) )
| ( select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = s(index_230) )
| ( select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3396,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = s(index_230) )
| ( select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3397,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_162) = s(index_230) )
| ( select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3396,3395]) ).
tff(3398,plain,
( ( s(index_162) = s(index_230) )
| ( select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3397,79]) ).
tff(3399,plain,
select(store(select(q30,seq),s(index_162),e30),s(index_230)) = select(select(q30,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3398,3394]) ).
tff(3400,plain,
select(select(q30,seq),s(index_230)) = select(store(select(q30,seq),s(index_162),e30),s(index_230)),
inference(symmetry,[status(thm)],[3399]) ).
tff(3401,plain,
select(store(queue_164,tail,index_165),seq) = select(store(store(queue_164,tail,index_165),head,s(index_167)),seq),
inference(symmetry,[status(thm)],[693]) ).
tff(3402,plain,
select(store(q29,seq,earray_163),seq) = select(store(store(q29,seq,earray_163),tail,s(index_162)),seq),
inference(symmetry,[status(thm)],[687]) ).
tff(3403,plain,
store(earray_161,index_162,e29) = select(store(store(queue_149,tail,index_150),seq,store(earray_161,index_162,e29)),seq),
inference(symmetry,[status(thm)],[671]) ).
tff(3404,plain,
s(index_147) = index_162,
inference(transitivity,[status(thm)],[2782,2779,2771]) ).
tff(3405,plain,
( ( earray_161 = select(q29,seq) )
<=> ( earray_161 = select(q29,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3406,axiom,
earray_161 = select(q29,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(3407,plain,
earray_161 = select(q29,seq),
inference(modus_ponens,[status(thm)],[3406,3405]) ).
tff(3408,plain,
select(q29,seq) = earray_161,
inference(symmetry,[status(thm)],[3407]) ).
tff(3409,plain,
store(select(q29,seq),s(index_147),e29) = store(earray_161,index_162,e29),
inference(monotonicity,[status(thm)],[3408,3404]) ).
tff(3410,plain,
store(select(q29,seq),s(index_147),e29) = select(q30,seq),
inference(transitivity,[status(thm)],[3409,3403,682,3402,688,3401,695]) ).
tff(3411,plain,
select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q30,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3410]) ).
tff(3412,plain,
s(s(select(q27,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))),
inference(symmetry,[status(thm)],[3069]) ).
tff(3413,plain,
s(index_147) = s(s(select(q27,tail))),
inference(symmetry,[status(thm)],[2804]) ).
tff(3414,plain,
s(index_147) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))),
inference(transitivity,[status(thm)],[3413,3412]) ).
tff(3415,plain,
( ( s(index_147) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3414,2497]) ).
tff(3416,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) = select(q13,tail) )
<=> ( s(index_147) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3415]) ).
tff(3417,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) != select(q13,tail) )
<=> ( s(index_147) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3416]) ).
tff(3418,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(3419,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)],[3418]) ).
tff(3420,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(3421,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(3422,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)],[3421,3420]) ).
tff(3423,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)],[3422]) ).
tff(3424,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)],[3423,3419]) ).
tff(3425,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3426,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3425,3424]) ).
tff(3427,plain,
s(index_147) != s(index_230),
inference(modus_ponens,[status(thm)],[3426,3417]) ).
tff(3428,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = s(index_230) )
| ( select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = s(index_230) )
| ( select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3429,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = s(index_230) )
| ( select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3430,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_147) = s(index_230) )
| ( select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3429,3428]) ).
tff(3431,plain,
( ( s(index_147) = s(index_230) )
| ( select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3430,79]) ).
tff(3432,plain,
select(store(select(q29,seq),s(index_147),e29),s(index_230)) = select(select(q29,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3431,3427]) ).
tff(3433,plain,
select(select(q29,seq),s(index_230)) = select(store(select(q29,seq),s(index_147),e29),s(index_230)),
inference(symmetry,[status(thm)],[3432]) ).
tff(3434,plain,
select(store(q28,seq,earray_148),seq) = select(store(store(q28,seq,earray_148),tail,s(index_147)),seq),
inference(symmetry,[status(thm)],[742]) ).
tff(3435,plain,
store(earray_146,index_147,e28) = select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e28)),seq),
inference(symmetry,[status(thm)],[726]) ).
tff(3436,plain,
s(index_141) = index_147,
inference(transitivity,[status(thm)],[2797,2794,2786]) ).
tff(3437,plain,
( ( earray_146 = select(q28,seq) )
<=> ( earray_146 = select(q28,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3438,axiom,
earray_146 = select(q28,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(3439,plain,
earray_146 = select(q28,seq),
inference(modus_ponens,[status(thm)],[3438,3437]) ).
tff(3440,plain,
select(q28,seq) = earray_146,
inference(symmetry,[status(thm)],[3439]) ).
tff(3441,plain,
store(select(q28,seq),s(index_141),e28) = store(earray_146,index_147,e28),
inference(monotonicity,[status(thm)],[3440,3436]) ).
tff(3442,plain,
store(select(q28,seq),s(index_141),e28) = select(q29,seq),
inference(transitivity,[status(thm)],[3441,3435,737,3434,744]) ).
tff(3443,plain,
select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q29,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3442]) ).
tff(3444,plain,
s(s(select(q26,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))),
inference(symmetry,[status(thm)],[3067]) ).
tff(3445,plain,
s(index_141) = s(s(select(q26,tail))),
inference(symmetry,[status(thm)],[2827]) ).
tff(3446,plain,
s(index_141) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))),
inference(transitivity,[status(thm)],[3445,3444]) ).
tff(3447,plain,
( ( s(index_141) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3446,2497]) ).
tff(3448,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) = select(q13,tail) )
<=> ( s(index_141) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3447]) ).
tff(3449,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) != select(q13,tail) )
<=> ( s(index_141) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3448]) ).
tff(3450,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(3451,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)],[3450]) ).
tff(3452,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(3453,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(3454,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)],[3453,3452]) ).
tff(3455,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(skolemize,[status(sab)],[3454]) ).
tff(3456,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)],[3455,3451]) ).
tff(3457,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3458,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3457,3456]) ).
tff(3459,plain,
s(index_141) != s(index_230),
inference(modus_ponens,[status(thm)],[3458,3449]) ).
tff(3460,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = s(index_230) )
| ( select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = s(index_230) )
| ( select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3461,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = s(index_230) )
| ( select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3462,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_141) = s(index_230) )
| ( select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3461,3460]) ).
tff(3463,plain,
( ( s(index_141) = s(index_230) )
| ( select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3462,79]) ).
tff(3464,plain,
select(store(select(q28,seq),s(index_141),e28),s(index_230)) = select(select(q28,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3463,3459]) ).
tff(3465,plain,
select(select(q28,seq),s(index_230)) = select(store(select(q28,seq),s(index_141),e28),s(index_230)),
inference(symmetry,[status(thm)],[3464]) ).
tff(3466,plain,
select(store(q27,seq,earray_142),seq) = select(store(store(q27,seq,earray_142),tail,s(index_141)),seq),
inference(symmetry,[status(thm)],[790]) ).
tff(3467,plain,
store(earray_140,index_141,e27) = select(store(store(queue_136,head,index_138),seq,store(earray_140,index_141,e27)),seq),
inference(symmetry,[status(thm)],[774]) ).
tff(3468,plain,
s(index_132) = index_141,
inference(transitivity,[status(thm)],[2820,2817,2814,2809,2801]) ).
tff(3469,plain,
( ( earray_140 = select(q27,seq) )
<=> ( earray_140 = select(q27,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3470,axiom,
earray_140 = select(q27,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(3471,plain,
earray_140 = select(q27,seq),
inference(modus_ponens,[status(thm)],[3470,3469]) ).
tff(3472,plain,
select(q27,seq) = earray_140,
inference(symmetry,[status(thm)],[3471]) ).
tff(3473,plain,
store(select(q27,seq),s(index_132),e27) = store(earray_140,index_141,e27),
inference(monotonicity,[status(thm)],[3472,3468]) ).
tff(3474,plain,
store(select(q27,seq),s(index_132),e27) = select(q28,seq),
inference(transitivity,[status(thm)],[3473,3467,785,3466,792]) ).
tff(3475,plain,
select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q28,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3474]) ).
tff(3476,plain,
s(s(select(q25,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))),
inference(symmetry,[status(thm)],[3065]) ).
tff(3477,plain,
s(index_132) = s(s(select(q25,tail))),
inference(symmetry,[status(thm)],[2842]) ).
tff(3478,plain,
s(index_132) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))),
inference(transitivity,[status(thm)],[3477,3476]) ).
tff(3479,plain,
( ( s(index_132) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3478,2497]) ).
tff(3480,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) = select(q13,tail) )
<=> ( s(index_132) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3479]) ).
tff(3481,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) != select(q13,tail) )
<=> ( s(index_132) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3480]) ).
tff(3482,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(3483,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)],[3482]) ).
tff(3484,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(3485,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(3486,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3485,3484]) ).
tff(3487,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(skolemize,[status(sab)],[3486]) ).
tff(3488,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3487,3483]) ).
tff(3489,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3490,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3489,3488]) ).
tff(3491,plain,
s(index_132) != s(index_230),
inference(modus_ponens,[status(thm)],[3490,3481]) ).
tff(3492,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = s(index_230) )
| ( select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = s(index_230) )
| ( select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3493,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = s(index_230) )
| ( select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3494,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_132) = s(index_230) )
| ( select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3493,3492]) ).
tff(3495,plain,
( ( s(index_132) = s(index_230) )
| ( select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3494,79]) ).
tff(3496,plain,
select(store(select(q27,seq),s(index_132),e27),s(index_230)) = select(select(q27,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3495,3491]) ).
tff(3497,plain,
select(select(q27,seq),s(index_230)) = select(store(select(q27,seq),s(index_132),e27),s(index_230)),
inference(symmetry,[status(thm)],[3496]) ).
tff(3498,plain,
select(store(queue_134,tail,index_135),seq) = select(store(store(queue_134,tail,index_135),head,s(index_137)),seq),
inference(symmetry,[status(thm)],[863]) ).
tff(3499,plain,
select(store(q26,seq,earray_133),seq) = select(store(store(q26,seq,earray_133),tail,s(index_132)),seq),
inference(symmetry,[status(thm)],[857]) ).
tff(3500,plain,
store(earray_131,index_132,e26) = select(store(store(queue_128,tail,index_129),seq,store(earray_131,index_132,e26)),seq),
inference(symmetry,[status(thm)],[841]) ).
tff(3501,plain,
s(index_126) = index_132,
inference(transitivity,[status(thm)],[2835,2832,2824]) ).
tff(3502,plain,
( ( earray_131 = select(q26,seq) )
<=> ( earray_131 = select(q26,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3503,axiom,
earray_131 = select(q26,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(3504,plain,
earray_131 = select(q26,seq),
inference(modus_ponens,[status(thm)],[3503,3502]) ).
tff(3505,plain,
select(q26,seq) = earray_131,
inference(symmetry,[status(thm)],[3504]) ).
tff(3506,plain,
store(select(q26,seq),s(index_126),e26) = store(earray_131,index_132,e26),
inference(monotonicity,[status(thm)],[3505,3501]) ).
tff(3507,plain,
store(select(q26,seq),s(index_126),e26) = select(q27,seq),
inference(transitivity,[status(thm)],[3506,3500,852,3499,858,3498,865]) ).
tff(3508,plain,
select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q27,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3507]) ).
tff(3509,plain,
s(s(select(q24,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))),
inference(symmetry,[status(thm)],[3063]) ).
tff(3510,plain,
s(index_126) = s(s(select(q24,tail))),
inference(symmetry,[status(thm)],[2857]) ).
tff(3511,plain,
s(index_126) = s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))),
inference(transitivity,[status(thm)],[3510,3509]) ).
tff(3512,plain,
( ( s(index_126) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3511,2497]) ).
tff(3513,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) = select(q13,tail) )
<=> ( s(index_126) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3512]) ).
tff(3514,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) != select(q13,tail) )
<=> ( s(index_126) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3513]) ).
tff(3515,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(3516,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)],[3515]) ).
tff(3517,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(3518,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(3519,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3518,3517]) ).
tff(3520,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(skolemize,[status(sab)],[3519]) ).
tff(3521,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3520,3516]) ).
tff(3522,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3523,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3522,3521]) ).
tff(3524,plain,
s(index_126) != s(index_230),
inference(modus_ponens,[status(thm)],[3523,3514]) ).
tff(3525,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_126) = s(index_230) )
| ( select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_126) = s(index_230) )
| ( select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3526,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_126) = s(index_230) )
| ( select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3527,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_126) = s(index_230) )
| ( select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3526,3525]) ).
tff(3528,plain,
( ( s(index_126) = s(index_230) )
| ( select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3527,79]) ).
tff(3529,plain,
select(store(select(q26,seq),s(index_126),e26),s(index_230)) = select(select(q26,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3528,3524]) ).
tff(3530,plain,
select(select(q26,seq),s(index_230)) = select(store(select(q26,seq),s(index_126),e26),s(index_230)),
inference(symmetry,[status(thm)],[3529]) ).
tff(3531,plain,
select(store(q25,seq,earray_127),seq) = select(store(store(q25,seq,earray_127),tail,s(index_126)),seq),
inference(symmetry,[status(thm)],[912]) ).
tff(3532,plain,
store(earray_125,index_126,e25) = select(store(store(queue_122,tail,index_123),seq,store(earray_125,index_126,e25)),seq),
inference(symmetry,[status(thm)],[896]) ).
tff(3533,plain,
s(index_120) = index_126,
inference(transitivity,[status(thm)],[2850,2847,2839]) ).
tff(3534,plain,
( ( earray_125 = select(q25,seq) )
<=> ( earray_125 = select(q25,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3535,axiom,
earray_125 = select(q25,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(3536,plain,
earray_125 = select(q25,seq),
inference(modus_ponens,[status(thm)],[3535,3534]) ).
tff(3537,plain,
select(q25,seq) = earray_125,
inference(symmetry,[status(thm)],[3536]) ).
tff(3538,plain,
store(select(q25,seq),s(index_120),e25) = store(earray_125,index_126,e25),
inference(monotonicity,[status(thm)],[3537,3533]) ).
tff(3539,plain,
store(select(q25,seq),s(index_120),e25) = select(q26,seq),
inference(transitivity,[status(thm)],[3538,3532,907,3531,914]) ).
tff(3540,plain,
select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q26,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3539]) ).
tff(3541,plain,
s(s(select(q23,tail))) = s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))),
inference(symmetry,[status(thm)],[3061]) ).
tff(3542,plain,
s(index_120) = s(s(select(q23,tail))),
inference(symmetry,[status(thm)],[2880]) ).
tff(3543,plain,
s(index_120) = s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))),
inference(transitivity,[status(thm)],[3542,3541]) ).
tff(3544,plain,
( ( s(index_120) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3543,2497]) ).
tff(3545,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) = select(q13,tail) )
<=> ( s(index_120) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3544]) ).
tff(3546,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) != select(q13,tail) )
<=> ( s(index_120) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3545]) ).
tff(3547,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(3548,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)],[3547]) ).
tff(3549,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(3550,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(3551,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3550,3549]) ).
tff(3552,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(skolemize,[status(sab)],[3551]) ).
tff(3553,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[3552,3548]) ).
tff(3554,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3555,plain,
s(s(s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3554,3553]) ).
tff(3556,plain,
s(index_120) != s(index_230),
inference(modus_ponens,[status(thm)],[3555,3546]) ).
tff(3557,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_120) = s(index_230) )
| ( select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_120) = s(index_230) )
| ( select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3558,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_120) = s(index_230) )
| ( select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3559,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_120) = s(index_230) )
| ( select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3558,3557]) ).
tff(3560,plain,
( ( s(index_120) = s(index_230) )
| ( select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3559,79]) ).
tff(3561,plain,
select(store(select(q25,seq),s(index_120),e25),s(index_230)) = select(select(q25,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3560,3556]) ).
tff(3562,plain,
select(select(q25,seq),s(index_230)) = select(store(select(q25,seq),s(index_120),e25),s(index_230)),
inference(symmetry,[status(thm)],[3561]) ).
tff(3563,plain,
select(store(q24,seq,earray_121),seq) = select(store(store(q24,seq,earray_121),tail,s(index_120)),seq),
inference(symmetry,[status(thm)],[960]) ).
tff(3564,plain,
store(earray_119,index_120,e24) = select(store(store(queue_115,head,index_117),seq,store(earray_119,index_120,e24)),seq),
inference(symmetry,[status(thm)],[944]) ).
tff(3565,plain,
s(index_111) = index_120,
inference(transitivity,[status(thm)],[2873,2870,2867,2862,2854]) ).
tff(3566,plain,
( ( earray_119 = select(q24,seq) )
<=> ( earray_119 = select(q24,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3567,axiom,
earray_119 = select(q24,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(3568,plain,
earray_119 = select(q24,seq),
inference(modus_ponens,[status(thm)],[3567,3566]) ).
tff(3569,plain,
select(q24,seq) = earray_119,
inference(symmetry,[status(thm)],[3568]) ).
tff(3570,plain,
store(select(q24,seq),s(index_111),e24) = store(earray_119,index_120,e24),
inference(monotonicity,[status(thm)],[3569,3565]) ).
tff(3571,plain,
store(select(q24,seq),s(index_111),e24) = select(q25,seq),
inference(transitivity,[status(thm)],[3570,3564,955,3563,962]) ).
tff(3572,plain,
select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q25,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3571]) ).
tff(3573,plain,
s(s(select(q22,tail))) = s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))),
inference(symmetry,[status(thm)],[3059]) ).
tff(3574,plain,
s(index_111) = s(s(select(q22,tail))),
inference(symmetry,[status(thm)],[2895]) ).
tff(3575,plain,
s(index_111) = s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))),
inference(transitivity,[status(thm)],[3574,3573]) ).
tff(3576,plain,
( ( s(index_111) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3575,2497]) ).
tff(3577,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) = select(q13,tail) )
<=> ( s(index_111) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3576]) ).
tff(3578,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) != select(q13,tail) )
<=> ( s(index_111) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3577]) ).
tff(3579,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(3580,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)],[3579]) ).
tff(3581,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(3582,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(3583,plain,
! [X: $i] : ( 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(X))))))))))) != X ),
inference(skolemize,[status(sab)],[3583]) ).
tff(3585,plain,
! [X: $i] : ( 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(X))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3587,plain,
s(s(s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3586,3585]) ).
tff(3588,plain,
s(index_111) != s(index_230),
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) ) )
| ( s(index_111) = s(index_230) )
| ( select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_111) = s(index_230) )
| ( select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)) ) ) ),
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) ) )
| ( s(index_111) = s(index_230) )
| ( select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)) ) ),
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) ) )
| ( s(index_111) = s(index_230) )
| ( select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3590,3589]) ).
tff(3592,plain,
( ( s(index_111) = s(index_230) )
| ( select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3591,79]) ).
tff(3593,plain,
select(store(select(q24,seq),s(index_111),e24),s(index_230)) = select(select(q24,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3592,3588]) ).
tff(3594,plain,
select(select(q24,seq),s(index_230)) = select(store(select(q24,seq),s(index_111),e24),s(index_230)),
inference(symmetry,[status(thm)],[3593]) ).
tff(3595,plain,
select(store(queue_113,tail,index_114),seq) = select(store(store(queue_113,tail,index_114),head,s(index_116)),seq),
inference(symmetry,[status(thm)],[1033]) ).
tff(3596,plain,
select(store(q23,seq,earray_112),seq) = select(store(store(q23,seq,earray_112),tail,s(index_111)),seq),
inference(symmetry,[status(thm)],[1027]) ).
tff(3597,plain,
store(earray_110,index_111,e23) = select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e23)),seq),
inference(symmetry,[status(thm)],[1011]) ).
tff(3598,plain,
s(index_105) = index_111,
inference(transitivity,[status(thm)],[2888,2885,2877]) ).
tff(3599,plain,
( ( earray_110 = select(q23,seq) )
<=> ( earray_110 = select(q23,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3600,axiom,
earray_110 = select(q23,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(3601,plain,
earray_110 = select(q23,seq),
inference(modus_ponens,[status(thm)],[3600,3599]) ).
tff(3602,plain,
select(q23,seq) = earray_110,
inference(symmetry,[status(thm)],[3601]) ).
tff(3603,plain,
store(select(q23,seq),s(index_105),e23) = store(earray_110,index_111,e23),
inference(monotonicity,[status(thm)],[3602,3598]) ).
tff(3604,plain,
store(select(q23,seq),s(index_105),e23) = select(q24,seq),
inference(transitivity,[status(thm)],[3603,3597,1022,3596,1028,3595,1035]) ).
tff(3605,plain,
select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q24,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3604]) ).
tff(3606,plain,
s(s(select(q21,tail))) = s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))),
inference(symmetry,[status(thm)],[3057]) ).
tff(3607,plain,
s(index_105) = s(s(select(q21,tail))),
inference(symmetry,[status(thm)],[2910]) ).
tff(3608,plain,
s(index_105) = s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))),
inference(transitivity,[status(thm)],[3607,3606]) ).
tff(3609,plain,
( ( s(index_105) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3608,2497]) ).
tff(3610,plain,
( ( s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) = select(q13,tail) )
<=> ( s(index_105) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3609]) ).
tff(3611,plain,
( ( s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) != select(q13,tail) )
<=> ( s(index_105) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3610]) ).
tff(3612,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(3613,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)],[3612]) ).
tff(3614,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(3615,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as10) ).
tff(3616,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[3615,3614]) ).
tff(3617,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(skolemize,[status(sab)],[3616]) ).
tff(3618,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[3617,3613]) ).
tff(3619,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(select(q13,tail))))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3620,plain,
s(s(s(s(s(s(s(s(s(s(select(q13,tail))))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3619,3618]) ).
tff(3621,plain,
s(index_105) != s(index_230),
inference(modus_ponens,[status(thm)],[3620,3611]) ).
tff(3622,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_105) = s(index_230) )
| ( select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_105) = s(index_230) )
| ( select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3623,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_105) = s(index_230) )
| ( select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3624,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_105) = s(index_230) )
| ( select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3623,3622]) ).
tff(3625,plain,
( ( s(index_105) = s(index_230) )
| ( select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3624,79]) ).
tff(3626,plain,
select(store(select(q23,seq),s(index_105),e23),s(index_230)) = select(select(q23,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3625,3621]) ).
tff(3627,plain,
select(select(q23,seq),s(index_230)) = select(store(select(q23,seq),s(index_105),e23),s(index_230)),
inference(symmetry,[status(thm)],[3626]) ).
tff(3628,plain,
select(store(q22,seq,earray_106),seq) = select(store(store(q22,seq,earray_106),tail,s(index_105)),seq),
inference(symmetry,[status(thm)],[1082]) ).
tff(3629,plain,
store(earray_104,index_105,e22) = select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e22)),seq),
inference(symmetry,[status(thm)],[1066]) ).
tff(3630,plain,
s(index_99) = index_105,
inference(transitivity,[status(thm)],[2903,2900,2892]) ).
tff(3631,plain,
( ( earray_104 = select(q22,seq) )
<=> ( earray_104 = select(q22,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3632,axiom,
earray_104 = select(q22,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(3633,plain,
earray_104 = select(q22,seq),
inference(modus_ponens,[status(thm)],[3632,3631]) ).
tff(3634,plain,
select(q22,seq) = earray_104,
inference(symmetry,[status(thm)],[3633]) ).
tff(3635,plain,
store(select(q22,seq),s(index_99),e22) = store(earray_104,index_105,e22),
inference(monotonicity,[status(thm)],[3634,3630]) ).
tff(3636,plain,
store(select(q22,seq),s(index_99),e22) = select(q23,seq),
inference(transitivity,[status(thm)],[3635,3629,1077,3628,1084]) ).
tff(3637,plain,
select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q23,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3636]) ).
tff(3638,plain,
s(s(select(q20,tail))) = s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))),
inference(symmetry,[status(thm)],[3055]) ).
tff(3639,plain,
s(index_99) = s(s(select(q20,tail))),
inference(symmetry,[status(thm)],[2933]) ).
tff(3640,plain,
s(index_99) = s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))),
inference(transitivity,[status(thm)],[3639,3638]) ).
tff(3641,plain,
( ( s(index_99) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3640,2497]) ).
tff(3642,plain,
( ( s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) = select(q13,tail) )
<=> ( s(index_99) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3641]) ).
tff(3643,plain,
( ( s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) != select(q13,tail) )
<=> ( s(index_99) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3642]) ).
tff(3644,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(3645,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)],[3644]) ).
tff(3646,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(3647,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as9) ).
tff(3648,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[3647,3646]) ).
tff(3649,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(skolemize,[status(sab)],[3648]) ).
tff(3650,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[3649,3645]) ).
tff(3651,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3652,plain,
s(s(s(s(s(s(s(s(s(select(q13,tail)))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3651,3650]) ).
tff(3653,plain,
s(index_99) != s(index_230),
inference(modus_ponens,[status(thm)],[3652,3643]) ).
tff(3654,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_99) = s(index_230) )
| ( select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_99) = s(index_230) )
| ( select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3655,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_99) = s(index_230) )
| ( select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3656,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_99) = s(index_230) )
| ( select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3655,3654]) ).
tff(3657,plain,
( ( s(index_99) = s(index_230) )
| ( select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3656,79]) ).
tff(3658,plain,
select(store(select(q22,seq),s(index_99),e22),s(index_230)) = select(select(q22,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3657,3653]) ).
tff(3659,plain,
select(select(q22,seq),s(index_230)) = select(store(select(q22,seq),s(index_99),e22),s(index_230)),
inference(symmetry,[status(thm)],[3658]) ).
tff(3660,plain,
select(store(q21,seq,earray_100),seq) = select(store(store(q21,seq,earray_100),tail,s(index_99)),seq),
inference(symmetry,[status(thm)],[1130]) ).
tff(3661,plain,
store(earray_98,index_99,e21) = select(store(store(queue_94,head,index_96),seq,store(earray_98,index_99,e21)),seq),
inference(symmetry,[status(thm)],[1114]) ).
tff(3662,plain,
s(index_90) = index_99,
inference(transitivity,[status(thm)],[2926,2923,2920,2915,2907]) ).
tff(3663,plain,
( ( earray_98 = select(q21,seq) )
<=> ( earray_98 = select(q21,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3664,axiom,
earray_98 = select(q21,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp80) ).
tff(3665,plain,
earray_98 = select(q21,seq),
inference(modus_ponens,[status(thm)],[3664,3663]) ).
tff(3666,plain,
select(q21,seq) = earray_98,
inference(symmetry,[status(thm)],[3665]) ).
tff(3667,plain,
store(select(q21,seq),s(index_90),e21) = store(earray_98,index_99,e21),
inference(monotonicity,[status(thm)],[3666,3662]) ).
tff(3668,plain,
store(select(q21,seq),s(index_90),e21) = select(q22,seq),
inference(transitivity,[status(thm)],[3667,3661,1125,3660,1132]) ).
tff(3669,plain,
select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q22,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3668]) ).
tff(3670,plain,
s(s(select(q19,tail))) = s(s(s(s(s(s(s(s(select(q13,tail))))))))),
inference(symmetry,[status(thm)],[3053]) ).
tff(3671,plain,
s(index_90) = s(s(select(q19,tail))),
inference(symmetry,[status(thm)],[2948]) ).
tff(3672,plain,
s(index_90) = s(s(s(s(s(s(s(s(select(q13,tail))))))))),
inference(transitivity,[status(thm)],[3671,3670]) ).
tff(3673,plain,
( ( s(index_90) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(select(q13,tail))))))))) = select(q13,tail) ) ),
inference(monotonicity,[status(thm)],[3672,2497]) ).
tff(3674,plain,
( ( s(s(s(s(s(s(s(s(select(q13,tail))))))))) = select(q13,tail) )
<=> ( s(index_90) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3673]) ).
tff(3675,plain,
( ( s(s(s(s(s(s(s(s(select(q13,tail))))))))) != select(q13,tail) )
<=> ( s(index_90) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3674]) ).
tff(3676,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(3677,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)],[3676]) ).
tff(3678,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(3679,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as8) ).
tff(3680,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[3679,3678]) ).
tff(3681,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(skolemize,[status(sab)],[3680]) ).
tff(3682,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[3681,3677]) ).
tff(3683,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
| ( s(s(s(s(s(s(s(s(select(q13,tail))))))))) != select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3684,plain,
s(s(s(s(s(s(s(s(select(q13,tail))))))))) != select(q13,tail),
inference(unit_resolution,[status(thm)],[3683,3682]) ).
tff(3685,plain,
s(index_90) != s(index_230),
inference(modus_ponens,[status(thm)],[3684,3675]) ).
tff(3686,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_90) = s(index_230) )
| ( select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_90) = s(index_230) )
| ( select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3687,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_90) = s(index_230) )
| ( select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3688,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(index_90) = s(index_230) )
| ( select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3687,3686]) ).
tff(3689,plain,
( ( s(index_90) = s(index_230) )
| ( select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3688,79]) ).
tff(3690,plain,
select(store(select(q21,seq),s(index_90),e21),s(index_230)) = select(select(q21,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3689,3685]) ).
tff(3691,plain,
select(select(q21,seq),s(index_230)) = select(store(select(q21,seq),s(index_90),e21),s(index_230)),
inference(symmetry,[status(thm)],[3690]) ).
tff(3692,plain,
select(store(queue_92,tail,index_93),seq) = select(store(store(queue_92,tail,index_93),head,s(index_95)),seq),
inference(symmetry,[status(thm)],[1203]) ).
tff(3693,plain,
select(store(q20,seq,earray_91),seq) = select(store(store(q20,seq,earray_91),tail,s(index_90)),seq),
inference(symmetry,[status(thm)],[1197]) ).
tff(3694,plain,
store(earray_89,index_90,e20) = select(store(store(queue_86,tail,index_87),seq,store(earray_89,index_90,e20)),seq),
inference(symmetry,[status(thm)],[1181]) ).
tff(3695,plain,
select(q12,tail) = index_30,
inference(symmetry,[status(thm)],[104]) ).
tff(3696,plain,
s(select(q12,tail)) = s(index_30),
inference(monotonicity,[status(thm)],[3695]) ).
tff(3697,plain,
s(select(q12,tail)) = s(select(queue_229,head)),
inference(transitivity,[status(thm)],[3696,106,2495,6]) ).
tff(3698,plain,
s(s(select(q12,tail))) = s(s(select(queue_229,head))),
inference(monotonicity,[status(thm)],[3697]) ).
tff(3699,plain,
s(index_30) = s(select(q12,tail)),
inference(symmetry,[status(thm)],[3696]) ).
tff(3700,plain,
index_36 = s(select(q12,tail)),
inference(transitivity,[status(thm)],[2500,47,50,3699]) ).
tff(3701,plain,
s(index_36) = s(s(select(q12,tail))),
inference(monotonicity,[status(thm)],[3700]) ).
tff(3702,plain,
s(select(q13,tail)) = s(s(select(queue_229,head))),
inference(transitivity,[status(thm)],[3032,3701,3698]) ).
tff(3703,plain,
s(s(select(q13,tail))) = s(s(s(select(queue_229,head)))),
inference(monotonicity,[status(thm)],[3702]) ).
tff(3704,plain,
s(select(q14,tail)) = s(s(s(select(queue_229,head)))),
inference(transitivity,[status(thm)],[3016,3040,3703]) ).
tff(3705,plain,
s(s(select(q14,tail))) = s(s(s(s(select(queue_229,head))))),
inference(monotonicity,[status(thm)],[3704]) ).
tff(3706,plain,
s(select(q15,tail)) = s(s(s(s(select(queue_229,head))))),
inference(transitivity,[status(thm)],[3002,3030,3705]) ).
tff(3707,plain,
s(s(select(q15,tail))) = s(s(s(s(s(select(queue_229,head)))))),
inference(monotonicity,[status(thm)],[3706]) ).
tff(3708,plain,
s(select(q16,tail)) = s(s(s(s(s(select(queue_229,head)))))),
inference(transitivity,[status(thm)],[2988,3010,3707]) ).
tff(3709,plain,
s(s(select(q16,tail))) = s(s(s(s(s(s(select(queue_229,head))))))),
inference(monotonicity,[status(thm)],[3708]) ).
tff(3710,plain,
s(select(q17,tail)) = s(s(s(s(s(s(select(queue_229,head))))))),
inference(transitivity,[status(thm)],[2968,2996,3709]) ).
tff(3711,plain,
s(s(select(q17,tail))) = s(s(s(s(s(s(s(select(queue_229,head)))))))),
inference(monotonicity,[status(thm)],[3710]) ).
tff(3712,plain,
s(select(q18,tail)) = s(s(s(s(s(s(s(select(queue_229,head)))))))),
inference(transitivity,[status(thm)],[2954,2982,3711]) ).
tff(3713,plain,
s(s(select(q18,tail))) = s(s(s(s(s(s(s(s(select(queue_229,head))))))))),
inference(monotonicity,[status(thm)],[3712]) ).
tff(3714,plain,
s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(s(select(q18,tail))),
inference(symmetry,[status(thm)],[3713]) ).
tff(3715,plain,
s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = index_90,
inference(transitivity,[status(thm)],[3714,2963,2941,2938,2930]) ).
tff(3716,plain,
( ( earray_89 = select(q20,seq) )
<=> ( earray_89 = select(q20,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3717,axiom,
earray_89 = select(q20,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(3718,plain,
earray_89 = select(q20,seq),
inference(modus_ponens,[status(thm)],[3717,3716]) ).
tff(3719,plain,
select(q20,seq) = earray_89,
inference(symmetry,[status(thm)],[3718]) ).
tff(3720,plain,
store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20) = store(earray_89,index_90,e20),
inference(monotonicity,[status(thm)],[3719,3715]) ).
tff(3721,plain,
store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20) = select(q21,seq),
inference(transitivity,[status(thm)],[3720,3694,1192,3693,1198,3692,1205]) ).
tff(3722,plain,
select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q21,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3721]) ).
tff(3723,plain,
s(s(s(index_230))) = s(s(s(select(queue_229,head)))),
inference(monotonicity,[status(thm)],[7]) ).
tff(3724,plain,
s(s(s(s(index_230)))) = s(s(s(s(select(queue_229,head))))),
inference(monotonicity,[status(thm)],[3723]) ).
tff(3725,plain,
s(s(s(s(s(index_230))))) = s(s(s(s(s(select(queue_229,head)))))),
inference(monotonicity,[status(thm)],[3724]) ).
tff(3726,plain,
s(s(s(s(s(s(index_230)))))) = s(s(s(s(s(s(select(queue_229,head))))))),
inference(monotonicity,[status(thm)],[3725]) ).
tff(3727,plain,
s(s(s(s(s(s(s(index_230))))))) = s(s(s(s(s(s(s(select(queue_229,head)))))))),
inference(monotonicity,[status(thm)],[3726]) ).
tff(3728,plain,
s(s(s(s(s(s(s(s(index_230)))))))) = s(s(s(s(s(s(s(s(select(queue_229,head))))))))),
inference(monotonicity,[status(thm)],[3727]) ).
tff(3729,plain,
s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(s(s(s(s(s(s(s(index_230)))))))),
inference(symmetry,[status(thm)],[3728]) ).
tff(3730,plain,
( ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(index_230)))))))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3729]) ).
tff(3731,plain,
( ( s(s(s(s(s(s(s(s(index_230)))))))) = s(index_230) )
<=> ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3730]) ).
tff(3732,plain,
( ( s(s(s(s(s(s(s(s(index_230)))))))) != s(index_230) )
<=> ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3731]) ).
tff(3733,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(3734,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)],[3733]) ).
tff(3735,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(3736,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as7) ).
tff(3737,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[3736,3735]) ).
tff(3738,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(skolemize,[status(sab)],[3737]) ).
tff(3739,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[3738,3734]) ).
tff(3740,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
| ( s(s(s(s(s(s(s(s(index_230)))))))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3741,plain,
s(s(s(s(s(s(s(s(index_230)))))))) != s(index_230),
inference(unit_resolution,[status(thm)],[3740,3739]) ).
tff(3742,plain,
s(s(s(s(s(s(s(s(select(queue_229,head))))))))) != s(index_230),
inference(modus_ponens,[status(thm)],[3741,3732]) ).
tff(3743,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
| ( select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
| ( select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3744,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
| ( select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3745,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
| ( select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3744,3743]) ).
tff(3746,plain,
( ( s(s(s(s(s(s(s(s(select(queue_229,head))))))))) = s(index_230) )
| ( select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3745,79]) ).
tff(3747,plain,
select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)) = select(select(q20,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3746,3742]) ).
tff(3748,plain,
select(select(q20,seq),s(index_230)) = select(store(select(q20,seq),s(s(s(s(s(s(s(s(select(queue_229,head))))))))),e20),s(index_230)),
inference(symmetry,[status(thm)],[3747]) ).
tff(3749,plain,
select(store(q19,seq,earray_85),seq) = select(store(store(q19,seq,earray_85),tail,s(index_84)),seq),
inference(symmetry,[status(thm)],[1252]) ).
tff(3750,plain,
store(earray_83,index_84,e19) = select(store(store(queue_74,tail,index_75),seq,store(earray_83,index_84,e19)),seq),
inference(symmetry,[status(thm)],[1236]) ).
tff(3751,plain,
select(store(store(q18,seq,earray_73),tail,s(index_72)),tail) = select(q19,tail),
inference(symmetry,[status(thm)],[2960]) ).
tff(3752,plain,
s(index_72) = select(store(store(q18,seq,earray_73),tail,s(index_72)),tail),
inference(symmetry,[status(thm)],[2957]) ).
tff(3753,plain,
s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(s(select(q17,tail))),
inference(symmetry,[status(thm)],[3711]) ).
tff(3754,plain,
s(s(s(s(s(s(s(select(queue_229,head)))))))) = index_84,
inference(transitivity,[status(thm)],[3753,2983,3752,3751,2945]) ).
tff(3755,plain,
( ( earray_83 = select(q19,seq) )
<=> ( earray_83 = select(q19,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3756,axiom,
earray_83 = select(q19,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(3757,plain,
earray_83 = select(q19,seq),
inference(modus_ponens,[status(thm)],[3756,3755]) ).
tff(3758,plain,
select(q19,seq) = earray_83,
inference(symmetry,[status(thm)],[3757]) ).
tff(3759,plain,
store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19) = store(earray_83,index_84,e19),
inference(monotonicity,[status(thm)],[3758,3754]) ).
tff(3760,plain,
store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19) = select(q20,seq),
inference(transitivity,[status(thm)],[3759,3750,1247,3749,1254]) ).
tff(3761,plain,
select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q20,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3760]) ).
tff(3762,plain,
s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(s(s(s(s(s(s(index_230))))))),
inference(symmetry,[status(thm)],[3727]) ).
tff(3763,plain,
( ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
<=> ( s(s(s(s(s(s(s(index_230))))))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3762]) ).
tff(3764,plain,
( ( s(s(s(s(s(s(s(index_230))))))) = s(index_230) )
<=> ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3763]) ).
tff(3765,plain,
( ( s(s(s(s(s(s(s(index_230))))))) != s(index_230) )
<=> ( s(s(s(s(s(s(s(select(queue_229,head)))))))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3764]) ).
tff(3766,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(3767,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)],[3766]) ).
tff(3768,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(3769,axiom,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as6) ).
tff(3770,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[3769,3768]) ).
tff(3771,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(skolemize,[status(sab)],[3770]) ).
tff(3772,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[3771,3767]) ).
tff(3773,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
| ( s(s(s(s(s(s(s(index_230))))))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3774,plain,
s(s(s(s(s(s(s(index_230))))))) != s(index_230),
inference(unit_resolution,[status(thm)],[3773,3772]) ).
tff(3775,plain,
s(s(s(s(s(s(s(select(queue_229,head)))))))) != s(index_230),
inference(modus_ponens,[status(thm)],[3774,3765]) ).
tff(3776,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
| ( select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
| ( select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3777,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
| ( select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3778,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
| ( select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3777,3776]) ).
tff(3779,plain,
( ( s(s(s(s(s(s(s(select(queue_229,head)))))))) = s(index_230) )
| ( select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3778,79]) ).
tff(3780,plain,
select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)) = select(select(q19,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3779,3775]) ).
tff(3781,plain,
select(select(q19,seq),s(index_230)) = select(store(select(q19,seq),s(s(s(s(s(s(s(select(queue_229,head)))))))),e19),s(index_230)),
inference(symmetry,[status(thm)],[3780]) ).
tff(3782,plain,
select(store(q18,seq,earray_73),seq) = select(store(store(q18,seq,earray_73),tail,s(index_72)),seq),
inference(symmetry,[status(thm)],[1300]) ).
tff(3783,plain,
store(earray_71,index_72,e18) = select(store(store(queue_67,head,index_69),seq,store(earray_71,index_72,e18)),seq),
inference(symmetry,[status(thm)],[1284]) ).
tff(3784,plain,
select(store(store(queue_65,tail,index_66),head,s(index_68)),tail) = select(q18,tail),
inference(symmetry,[status(thm)],[2980]) ).
tff(3785,plain,
select(store(queue_65,tail,index_66),tail) = select(store(store(queue_65,tail,index_66),head,s(index_68)),tail),
inference(symmetry,[status(thm)],[2977]) ).
tff(3786,plain,
select(store(store(q17,seq,earray_64),tail,s(index_63)),tail) = select(store(queue_65,tail,index_66),tail),
inference(symmetry,[status(thm)],[2973]) ).
tff(3787,plain,
s(index_63) = select(store(store(q17,seq,earray_64),tail,s(index_63)),tail),
inference(symmetry,[status(thm)],[2971]) ).
tff(3788,plain,
s(s(s(s(s(s(select(queue_229,head))))))) = s(s(select(q16,tail))),
inference(symmetry,[status(thm)],[3709]) ).
tff(3789,plain,
s(s(s(s(s(s(select(queue_229,head))))))) = index_72,
inference(transitivity,[status(thm)],[3788,2997,3787,3786,3785,3784,2953]) ).
tff(3790,plain,
( ( earray_71 = select(q18,seq) )
<=> ( earray_71 = select(q18,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3791,axiom,
earray_71 = select(q18,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp71) ).
tff(3792,plain,
earray_71 = select(q18,seq),
inference(modus_ponens,[status(thm)],[3791,3790]) ).
tff(3793,plain,
select(q18,seq) = earray_71,
inference(symmetry,[status(thm)],[3792]) ).
tff(3794,plain,
store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18) = store(earray_71,index_72,e18),
inference(monotonicity,[status(thm)],[3793,3789]) ).
tff(3795,plain,
store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18) = select(q19,seq),
inference(transitivity,[status(thm)],[3794,3783,1295,3782,1302]) ).
tff(3796,plain,
select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q19,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3795]) ).
tff(3797,plain,
s(s(s(s(s(s(select(queue_229,head))))))) = s(s(s(s(s(s(index_230)))))),
inference(symmetry,[status(thm)],[3726]) ).
tff(3798,plain,
( ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
<=> ( s(s(s(s(s(s(index_230)))))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3797]) ).
tff(3799,plain,
( ( s(s(s(s(s(s(index_230)))))) = s(index_230) )
<=> ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3798]) ).
tff(3800,plain,
( ( s(s(s(s(s(s(index_230)))))) != s(index_230) )
<=> ( s(s(s(s(s(s(select(queue_229,head))))))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3799]) ).
tff(3801,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(X))))) != X )
<=> ( s(s(s(s(s(X))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3802,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(quant_intro,[status(thm)],[3801]) ).
tff(3803,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3804,axiom,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as5) ).
tff(3805,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[3804,3803]) ).
tff(3806,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(skolemize,[status(sab)],[3805]) ).
tff(3807,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[3806,3802]) ).
tff(3808,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(X))))) != X )
| ( s(s(s(s(s(s(index_230)))))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3809,plain,
s(s(s(s(s(s(index_230)))))) != s(index_230),
inference(unit_resolution,[status(thm)],[3808,3807]) ).
tff(3810,plain,
s(s(s(s(s(s(select(queue_229,head))))))) != s(index_230),
inference(modus_ponens,[status(thm)],[3809,3800]) ).
tff(3811,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
| ( select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
| ( select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3812,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
| ( select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3813,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
| ( select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3812,3811]) ).
tff(3814,plain,
( ( s(s(s(s(s(s(select(queue_229,head))))))) = s(index_230) )
| ( select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3813,79]) ).
tff(3815,plain,
select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)) = select(select(q18,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3814,3810]) ).
tff(3816,plain,
select(select(q18,seq),s(index_230)) = select(store(select(q18,seq),s(s(s(s(s(s(select(queue_229,head))))))),e18),s(index_230)),
inference(symmetry,[status(thm)],[3815]) ).
tff(3817,plain,
select(store(queue_65,tail,index_66),seq) = select(store(store(queue_65,tail,index_66),head,s(index_68)),seq),
inference(symmetry,[status(thm)],[1373]) ).
tff(3818,plain,
select(store(q17,seq,earray_64),seq) = select(store(store(q17,seq,earray_64),tail,s(index_63)),seq),
inference(symmetry,[status(thm)],[1367]) ).
tff(3819,plain,
store(earray_62,index_63,e17) = select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e17)),seq),
inference(symmetry,[status(thm)],[1351]) ).
tff(3820,plain,
select(store(store(q16,seq,earray_58),tail,s(index_57)),tail) = select(q17,tail),
inference(symmetry,[status(thm)],[2994]) ).
tff(3821,plain,
s(index_57) = select(store(store(q16,seq,earray_58),tail,s(index_57)),tail),
inference(symmetry,[status(thm)],[2991]) ).
tff(3822,plain,
s(s(s(s(s(select(queue_229,head)))))) = s(s(select(q15,tail))),
inference(symmetry,[status(thm)],[3707]) ).
tff(3823,plain,
s(s(s(s(s(select(queue_229,head)))))) = index_63,
inference(transitivity,[status(thm)],[3822,3011,3821,3820,2967]) ).
tff(3824,plain,
( ( earray_62 = select(q17,seq) )
<=> ( earray_62 = select(q17,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3825,axiom,
earray_62 = select(q17,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp69) ).
tff(3826,plain,
earray_62 = select(q17,seq),
inference(modus_ponens,[status(thm)],[3825,3824]) ).
tff(3827,plain,
select(q17,seq) = earray_62,
inference(symmetry,[status(thm)],[3826]) ).
tff(3828,plain,
store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17) = store(earray_62,index_63,e17),
inference(monotonicity,[status(thm)],[3827,3823]) ).
tff(3829,plain,
store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17) = select(q18,seq),
inference(transitivity,[status(thm)],[3828,3819,1362,3818,1368,3817,1375]) ).
tff(3830,plain,
select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q18,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3829]) ).
tff(3831,plain,
s(s(s(s(s(select(queue_229,head)))))) = s(s(s(s(s(index_230))))),
inference(symmetry,[status(thm)],[3725]) ).
tff(3832,plain,
( ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
<=> ( s(s(s(s(s(index_230))))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3831]) ).
tff(3833,plain,
( ( s(s(s(s(s(index_230))))) = s(index_230) )
<=> ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3832]) ).
tff(3834,plain,
( ( s(s(s(s(s(index_230))))) != s(index_230) )
<=> ( s(s(s(s(s(select(queue_229,head)))))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3833]) ).
tff(3835,plain,
^ [X: $i] :
refl(( ( s(s(s(s(X)))) != X )
<=> ( s(s(s(s(X)))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3836,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(quant_intro,[status(thm)],[3835]) ).
tff(3837,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3838,axiom,
! [X: $i] : ( s(s(s(s(X)))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as4) ).
tff(3839,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[3838,3837]) ).
tff(3840,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(skolemize,[status(sab)],[3839]) ).
tff(3841,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[3840,3836]) ).
tff(3842,plain,
( ~ ! [X: $i] : ( s(s(s(s(X)))) != X )
| ( s(s(s(s(s(index_230))))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3843,plain,
s(s(s(s(s(index_230))))) != s(index_230),
inference(unit_resolution,[status(thm)],[3842,3841]) ).
tff(3844,plain,
s(s(s(s(s(select(queue_229,head)))))) != s(index_230),
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) ) )
| ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
| ( select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
| ( select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)) ) ) ),
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) ) )
| ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
| ( select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)) ) ),
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) ) )
| ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
| ( select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3846,3845]) ).
tff(3848,plain,
( ( s(s(s(s(s(select(queue_229,head)))))) = s(index_230) )
| ( select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3847,79]) ).
tff(3849,plain,
select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)) = select(select(q17,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3848,3844]) ).
tff(3850,plain,
select(select(q17,seq),s(index_230)) = select(store(select(q17,seq),s(s(s(s(s(select(queue_229,head)))))),e17),s(index_230)),
inference(symmetry,[status(thm)],[3849]) ).
tff(3851,plain,
select(store(q16,seq,earray_58),seq) = select(store(store(q16,seq,earray_58),tail,s(index_57)),seq),
inference(symmetry,[status(thm)],[1422]) ).
tff(3852,plain,
store(earray_56,index_57,e16) = select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e16)),seq),
inference(symmetry,[status(thm)],[1406]) ).
tff(3853,plain,
select(store(store(q15,seq,earray_52),tail,s(index_51)),tail) = select(q16,tail),
inference(symmetry,[status(thm)],[3008]) ).
tff(3854,plain,
s(index_51) = select(store(store(q15,seq,earray_52),tail,s(index_51)),tail),
inference(symmetry,[status(thm)],[3005]) ).
tff(3855,plain,
s(s(s(s(select(queue_229,head))))) = s(s(select(q14,tail))),
inference(symmetry,[status(thm)],[3705]) ).
tff(3856,plain,
s(s(s(s(select(queue_229,head))))) = index_57,
inference(transitivity,[status(thm)],[3855,3031,3854,3853,2987]) ).
tff(3857,plain,
( ( earray_56 = select(q16,seq) )
<=> ( earray_56 = select(q16,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3858,axiom,
earray_56 = select(q16,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp67) ).
tff(3859,plain,
earray_56 = select(q16,seq),
inference(modus_ponens,[status(thm)],[3858,3857]) ).
tff(3860,plain,
select(q16,seq) = earray_56,
inference(symmetry,[status(thm)],[3859]) ).
tff(3861,plain,
store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16) = store(earray_56,index_57,e16),
inference(monotonicity,[status(thm)],[3860,3856]) ).
tff(3862,plain,
store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16) = select(q17,seq),
inference(transitivity,[status(thm)],[3861,3852,1417,3851,1424]) ).
tff(3863,plain,
select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q17,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3862]) ).
tff(3864,plain,
s(s(s(s(select(queue_229,head))))) = s(s(s(s(index_230)))),
inference(symmetry,[status(thm)],[3724]) ).
tff(3865,plain,
( ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
<=> ( s(s(s(s(index_230)))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3864]) ).
tff(3866,plain,
( ( s(s(s(s(index_230)))) = s(index_230) )
<=> ( s(s(s(s(select(queue_229,head))))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3865]) ).
tff(3867,plain,
( ( s(s(s(s(index_230)))) != s(index_230) )
<=> ( s(s(s(s(select(queue_229,head))))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3866]) ).
tff(3868,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) != X )
<=> ( s(s(s(X))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3869,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(quant_intro,[status(thm)],[3868]) ).
tff(3870,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3871,axiom,
! [X: $i] : ( s(s(s(X))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as3) ).
tff(3872,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[3871,3870]) ).
tff(3873,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(skolemize,[status(sab)],[3872]) ).
tff(3874,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[3873,3869]) ).
tff(3875,plain,
( ~ ! [X: $i] : ( s(s(s(X))) != X )
| ( s(s(s(s(index_230)))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3876,plain,
s(s(s(s(index_230)))) != s(index_230),
inference(unit_resolution,[status(thm)],[3875,3874]) ).
tff(3877,plain,
s(s(s(s(select(queue_229,head))))) != s(index_230),
inference(modus_ponens,[status(thm)],[3876,3867]) ).
tff(3878,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
| ( select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
| ( select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3879,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
| ( select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3880,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
| ( select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3879,3878]) ).
tff(3881,plain,
( ( s(s(s(s(select(queue_229,head))))) = s(index_230) )
| ( select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3880,79]) ).
tff(3882,plain,
select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)) = select(select(q16,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3881,3877]) ).
tff(3883,plain,
select(select(q16,seq),s(index_230)) = select(store(select(q16,seq),s(s(s(s(select(queue_229,head))))),e16),s(index_230)),
inference(symmetry,[status(thm)],[3882]) ).
tff(3884,plain,
select(store(q15,seq,earray_52),seq) = select(store(store(q15,seq,earray_52),tail,s(index_51)),seq),
inference(symmetry,[status(thm)],[1470]) ).
tff(3885,plain,
store(earray_50,index_51,e15) = select(store(store(queue_46,head,index_48),seq,store(earray_50,index_51,e15)),seq),
inference(symmetry,[status(thm)],[1454]) ).
tff(3886,plain,
select(store(store(queue_44,tail,index_45),head,s(index_47)),tail) = select(q15,tail),
inference(symmetry,[status(thm)],[3028]) ).
tff(3887,plain,
select(store(queue_44,tail,index_45),tail) = select(store(store(queue_44,tail,index_45),head,s(index_47)),tail),
inference(symmetry,[status(thm)],[3025]) ).
tff(3888,plain,
select(store(store(q14,seq,earray_43),tail,s(index_42)),tail) = select(store(queue_44,tail,index_45),tail),
inference(symmetry,[status(thm)],[3021]) ).
tff(3889,plain,
s(index_42) = select(store(store(q14,seq,earray_43),tail,s(index_42)),tail),
inference(symmetry,[status(thm)],[3019]) ).
tff(3890,plain,
s(s(s(select(queue_229,head)))) = s(s(select(q13,tail))),
inference(symmetry,[status(thm)],[3703]) ).
tff(3891,plain,
s(s(s(select(queue_229,head)))) = index_51,
inference(transitivity,[status(thm)],[3890,3041,3889,3888,3887,3886,3001]) ).
tff(3892,plain,
( ( earray_50 = select(q15,seq) )
<=> ( earray_50 = select(q15,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3893,axiom,
earray_50 = select(q15,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(3894,plain,
earray_50 = select(q15,seq),
inference(modus_ponens,[status(thm)],[3893,3892]) ).
tff(3895,plain,
select(q15,seq) = earray_50,
inference(symmetry,[status(thm)],[3894]) ).
tff(3896,plain,
store(select(q15,seq),s(s(s(select(queue_229,head)))),e15) = store(earray_50,index_51,e15),
inference(monotonicity,[status(thm)],[3895,3891]) ).
tff(3897,plain,
store(select(q15,seq),s(s(s(select(queue_229,head)))),e15) = select(q16,seq),
inference(transitivity,[status(thm)],[3896,3885,1465,3884,1472]) ).
tff(3898,plain,
select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q16,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3897]) ).
tff(3899,plain,
s(s(s(select(queue_229,head)))) = s(s(s(index_230))),
inference(symmetry,[status(thm)],[3723]) ).
tff(3900,plain,
( ( s(s(s(select(queue_229,head)))) = s(index_230) )
<=> ( s(s(s(index_230))) = s(index_230) ) ),
inference(monotonicity,[status(thm)],[3899]) ).
tff(3901,plain,
( ( s(s(s(index_230))) = s(index_230) )
<=> ( s(s(s(select(queue_229,head)))) = s(index_230) ) ),
inference(symmetry,[status(thm)],[3900]) ).
tff(3902,plain,
( ( s(s(s(index_230))) != s(index_230) )
<=> ( s(s(s(select(queue_229,head)))) != s(index_230) ) ),
inference(monotonicity,[status(thm)],[3901]) ).
tff(3903,plain,
^ [X: $i] :
refl(( ( s(s(X)) != X )
<=> ( s(s(X)) != X ) )),
inference(bind,[status(th)],[]) ).
tff(3904,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(quant_intro,[status(thm)],[3903]) ).
tff(3905,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3906,axiom,
! [X: $i] : ( s(s(X)) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as2) ).
tff(3907,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[3906,3905]) ).
tff(3908,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(skolemize,[status(sab)],[3907]) ).
tff(3909,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[3908,3904]) ).
tff(3910,plain,
( ~ ! [X: $i] : ( s(s(X)) != X )
| ( s(s(s(index_230))) != s(index_230) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3911,plain,
s(s(s(index_230))) != s(index_230),
inference(unit_resolution,[status(thm)],[3910,3909]) ).
tff(3912,plain,
s(s(s(select(queue_229,head)))) != s(index_230),
inference(modus_ponens,[status(thm)],[3911,3902]) ).
tff(3913,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_229,head)))) = s(index_230) )
| ( select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_229,head)))) = s(index_230) )
| ( select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3914,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_229,head)))) = s(index_230) )
| ( select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3915,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(s(select(queue_229,head)))) = s(index_230) )
| ( select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3914,3913]) ).
tff(3916,plain,
( ( s(s(s(select(queue_229,head)))) = s(index_230) )
| ( select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3915,79]) ).
tff(3917,plain,
select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)) = select(select(q15,seq),s(index_230)),
inference(unit_resolution,[status(thm)],[3916,3912]) ).
tff(3918,plain,
select(select(q15,seq),s(index_230)) = select(store(select(q15,seq),s(s(s(select(queue_229,head)))),e15),s(index_230)),
inference(symmetry,[status(thm)],[3917]) ).
tff(3919,plain,
select(store(queue_44,tail,index_45),seq) = select(store(store(queue_44,tail,index_45),head,s(index_47)),seq),
inference(symmetry,[status(thm)],[1543]) ).
tff(3920,plain,
select(store(q14,seq,earray_43),seq) = select(store(store(q14,seq,earray_43),tail,s(index_42)),seq),
inference(symmetry,[status(thm)],[1537]) ).
tff(3921,plain,
store(earray_41,index_42,e14) = select(store(store(queue_38,tail,index_39),seq,store(earray_41,index_42,e14)),seq),
inference(symmetry,[status(thm)],[1521]) ).
tff(3922,plain,
select(store(store(q13,seq,earray_37),tail,s(index_36)),tail) = select(q14,tail),
inference(symmetry,[status(thm)],[3038]) ).
tff(3923,plain,
s(index_36) = select(store(store(q13,seq,earray_37),tail,s(index_36)),tail),
inference(symmetry,[status(thm)],[3035]) ).
tff(3924,plain,
s(s(select(q12,tail))) = s(index_36),
inference(symmetry,[status(thm)],[3701]) ).
tff(3925,plain,
s(s(select(queue_229,head))) = s(s(select(q12,tail))),
inference(symmetry,[status(thm)],[3698]) ).
tff(3926,plain,
s(s(select(queue_229,head))) = index_42,
inference(transitivity,[status(thm)],[3925,3924,3923,3922,3015]) ).
tff(3927,plain,
( ( earray_41 = select(q14,seq) )
<=> ( earray_41 = select(q14,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3928,axiom,
earray_41 = select(q14,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(3929,plain,
earray_41 = select(q14,seq),
inference(modus_ponens,[status(thm)],[3928,3927]) ).
tff(3930,plain,
select(q14,seq) = earray_41,
inference(symmetry,[status(thm)],[3929]) ).
tff(3931,plain,
store(select(q14,seq),s(s(select(queue_229,head))),e14) = store(earray_41,index_42,e14),
inference(monotonicity,[status(thm)],[3930,3926]) ).
tff(3932,plain,
store(select(q14,seq),s(s(select(queue_229,head))),e14) = select(q15,seq),
inference(transitivity,[status(thm)],[3931,3921,1532,3920,1538,3919,1545]) ).
tff(3933,plain,
select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q15,seq),s(index_230)),
inference(monotonicity,[status(thm)],[3932]) ).
tff(3934,plain,
select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = elem_283,
inference(transitivity,[status(thm)],[3933,3918,3898,3883,3863,3850,3830,3816,3796,3781,3761,3748,3722,3691,3669,3659,3637,3627,3605,3594,3572,3562,3540,3530,3508,3497,3475,3465,3443,3433,3411,3400,3378,3368,3346,3336,3314,3303,3281,3271,3249,3239,3217,3206,3184,3174,3152,3142,3120,3108,2583,2514]) ).
tff(3935,plain,
( ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) )
<=> ( elem_283 = e13 ) ),
inference(monotonicity,[status(thm)],[3934,2510]) ).
tff(3936,plain,
( ( elem_283 = e13 )
<=> ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) ),
inference(symmetry,[status(thm)],[3935]) ).
tff(3937,plain,
( ( elem_283 != e13 )
<=> ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) != select(select(q14,seq),s(index_230)) ) ),
inference(monotonicity,[status(thm)],[3936]) ).
tff(3938,plain,
( ( elem_283 != e13 )
<=> ( elem_283 != e13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3939,axiom,
elem_283 != e13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(3940,plain,
elem_283 != e13,
inference(modus_ponens,[status(thm)],[3939,3938]) ).
tff(3941,plain,
select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) != select(select(q14,seq),s(index_230)),
inference(modus_ponens,[status(thm)],[3940,3937]) ).
tff(3942,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_229,head))) = s(index_230) )
| ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_229,head))) = s(index_230) )
| ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3943,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_229,head))) = s(index_230) )
| ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3944,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( s(s(select(queue_229,head))) = s(index_230) )
| ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) ),
inference(modus_ponens,[status(thm)],[3943,3942]) ).
tff(3945,plain,
( ( s(s(select(queue_229,head))) = s(index_230) )
| ( select(store(select(q14,seq),s(s(select(queue_229,head))),e14),s(index_230)) = select(select(q14,seq),s(index_230)) ) ),
inference(unit_resolution,[status(thm)],[3944,79]) ).
tff(3946,plain,
$false,
inference(unit_resolution,[status(thm)],[3945,3941,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV569-1.040 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 10:24:03 EDT 2025
% 0.13/0.33 % CPUTime :
% 6.91/7.10 % SZS status Unsatisfiable
% 6.91/7.10 % SZS output start Proof
% See solution above
% 7.20/7.40 % E exiting
%------------------------------------------------------------------------------