%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV571-1.043 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:35:43 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 947
% Syntax : Number of formulae : 3095 (2284 unt; 0 typ; 0 def)
% Number of atoms : 5212 (5210 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 2787 ( 671 ~;1699 |; 0 &)
% ( 417 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 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 : 361 ( 361 usr; 357 con; 0-3 aty)
% Number of variables : 2456 (2455 !; 0 ?;2456 :)
% Comments :
%------------------------------------------------------------------------------
tff(elem_265_type,type,
elem_265: $i ).
tff(elem_262_type,type,
elem_262: $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(index_264_type,type,
index_264: $i ).
tff(earray_260_type,type,
earray_260: $i ).
tff(tail_type,type,
tail: $i ).
tff(q42_type,type,
q42: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e42_type,type,
e42: $i ).
tff(seq_type,type,
seq: $i ).
tff(p_type,type,
p: $i > $i ).
tff(s_type,type,
s: $i > $i ).
tff(index_225_type,type,
index_225: $i ).
tff(earray_226_type,type,
earray_226: $i ).
tff(q43_type,type,
q43: $i ).
tff(index_228_type,type,
index_228: $i ).
tff(queue_227_type,type,
queue_227: $i ).
tff(queue_229_type,type,
queue_229: $i ).
tff(index_263_type,type,
index_263: $i ).
tff(earray_224_type,type,
earray_224: $i ).
tff(index_222_type,type,
index_222: $i ).
tff(queue_221_type,type,
queue_221: $i ).
tff(queue_223_type,type,
queue_223: $i ).
tff(index_261_type,type,
index_261: $i ).
tff(index_219_type,type,
index_219: $i ).
tff(earray_220_type,type,
earray_220: $i ).
tff(q41_type,type,
q41: $i ).
tff(q39_type,type,
q39: $i ).
tff(index_213_type,type,
index_213: $i ).
tff(q40_type,type,
q40: $i ).
tff(index_207_type,type,
index_207: $i ).
tff(earray_208_type,type,
earray_208: $i ).
tff(index_210_type,type,
index_210: $i ).
tff(queue_209_type,type,
queue_209: $i ).
tff(queue_211_type,type,
queue_211: $i ).
tff(earray_214_type,type,
earray_214: $i ).
tff(index_216_type,type,
index_216: $i ).
tff(queue_215_type,type,
queue_215: $i ).
tff(queue_217_type,type,
queue_217: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(earray_196_type,type,
earray_196: $i ).
tff(q38_type,type,
q38: $i ).
tff(index_198_type,type,
index_198: $i ).
tff(queue_197_type,type,
queue_197: $i ).
tff(queue_199_type,type,
queue_199: $i ).
tff(q36_type,type,
q36: $i ).
tff(index_189_type,type,
index_189: $i ).
tff(q37_type,type,
q37: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(index_186_type,type,
index_186: $i ).
tff(queue_185_type,type,
queue_185: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(earray_190_type,type,
earray_190: $i ).
tff(index_192_type,type,
index_192: $i ).
tff(queue_191_type,type,
queue_191: $i ).
tff(queue_193_type,type,
queue_193: $i ).
tff(index_177_type,type,
index_177: $i ).
tff(earray_178_type,type,
earray_178: $i ).
tff(q35_type,type,
q35: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $i ).
tff(queue_181_type,type,
queue_181: $i ).
tff(q33_type,type,
q33: $i ).
tff(index_171_type,type,
index_171: $i ).
tff(q34_type,type,
q34: $i ).
tff(index_165_type,type,
index_165: $i ).
tff(earray_166_type,type,
earray_166: $i ).
tff(index_168_type,type,
index_168: $i ).
tff(queue_167_type,type,
queue_167: $i ).
tff(queue_169_type,type,
queue_169: $i ).
tff(earray_172_type,type,
earray_172: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $i ).
tff(queue_175_type,type,
queue_175: $i ).
tff(index_159_type,type,
index_159: $i ).
tff(earray_160_type,type,
earray_160: $i ).
tff(q32_type,type,
q32: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(queue_161_type,type,
queue_161: $i ).
tff(queue_163_type,type,
queue_163: $i ).
tff(q30_type,type,
q30: $i ).
tff(index_153_type,type,
index_153: $i ).
tff(q31_type,type,
q31: $i ).
tff(index_147_type,type,
index_147: $i ).
tff(earray_148_type,type,
earray_148: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $i ).
tff(queue_151_type,type,
queue_151: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(index_156_type,type,
index_156: $i ).
tff(queue_155_type,type,
queue_155: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(index_141_type,type,
index_141: $i ).
tff(earray_142_type,type,
earray_142: $i ).
tff(q29_type,type,
q29: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $i ).
tff(queue_145_type,type,
queue_145: $i ).
tff(q27_type,type,
q27: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(q28_type,type,
q28: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(earray_124_type,type,
earray_124: $i ).
tff(index_126_type,type,
index_126: $i ).
tff(queue_125_type,type,
queue_125: $i ).
tff(queue_127_type,type,
queue_127: $i ).
tff(earray_130_type,type,
earray_130: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(queue_131_type,type,
queue_131: $i ).
tff(queue_133_type,type,
queue_133: $i ).
tff(index_117_type,type,
index_117: $i ).
tff(earray_118_type,type,
earray_118: $i ).
tff(q26_type,type,
q26: $i ).
tff(index_120_type,type,
index_120: $i ).
tff(queue_119_type,type,
queue_119: $i ).
tff(queue_121_type,type,
queue_121: $i ).
tff(q24_type,type,
q24: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(q25_type,type,
q25: $i ).
tff(index_105_type,type,
index_105: $i ).
tff(earray_106_type,type,
earray_106: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $i ).
tff(queue_109_type,type,
queue_109: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(index_114_type,type,
index_114: $i ).
tff(queue_113_type,type,
queue_113: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(index_99_type,type,
index_99: $i ).
tff(earray_100_type,type,
earray_100: $i ).
tff(q23_type,type,
q23: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $i ).
tff(queue_103_type,type,
queue_103: $i ).
tff(q21_type,type,
q21: $i ).
tff(index_93_type,type,
index_93: $i ).
tff(q22_type,type,
q22: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(earray_88_type,type,
earray_88: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(queue_89_type,type,
queue_89: $i ).
tff(queue_91_type,type,
queue_91: $i ).
tff(earray_94_type,type,
earray_94: $i ).
tff(index_96_type,type,
index_96: $i ).
tff(queue_95_type,type,
queue_95: $i ).
tff(queue_97_type,type,
queue_97: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(earray_82_type,type,
earray_82: $i ).
tff(q20_type,type,
q20: $i ).
tff(index_84_type,type,
index_84: $i ).
tff(queue_83_type,type,
queue_83: $i ).
tff(queue_85_type,type,
queue_85: $i ).
tff(q18_type,type,
q18: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(q19_type,type,
q19: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(index_66_type,type,
index_66: $i ).
tff(queue_65_type,type,
queue_65: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(earray_76_type,type,
earray_76: $i ).
tff(index_78_type,type,
index_78: $i ).
tff(queue_77_type,type,
queue_77: $i ).
tff(queue_79_type,type,
queue_79: $i ).
tff(index_57_type,type,
index_57: $i ).
tff(earray_58_type,type,
earray_58: $i ).
tff(q17_type,type,
q17: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $i ).
tff(queue_61_type,type,
queue_61: $i ).
tff(q15_type,type,
q15: $i ).
tff(index_51_type,type,
index_51: $i ).
tff(q16_type,type,
q16: $i ).
tff(index_45_type,type,
index_45: $i ).
tff(earray_46_type,type,
earray_46: $i ).
tff(index_48_type,type,
index_48: $i ).
tff(queue_47_type,type,
queue_47: $i ).
tff(queue_49_type,type,
queue_49: $i ).
tff(earray_52_type,type,
earray_52: $i ).
tff(index_54_type,type,
index_54: $i ).
tff(queue_53_type,type,
queue_53: $i ).
tff(queue_55_type,type,
queue_55: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(earray_40_type,type,
earray_40: $i ).
tff(q14_type,type,
q14: $i ).
tff(index_42_type,type,
index_42: $i ).
tff(queue_41_type,type,
queue_41: $i ).
tff(queue_43_type,type,
queue_43: $i ).
tff(q12_type,type,
q12: $i ).
tff(index_33_type,type,
index_33: $i ).
tff(q13_type,type,
q13: $i ).
tff(index_27_type,type,
index_27: $i ).
tff(earray_28_type,type,
earray_28: $i ).
tff(queue_31_type,type,
queue_31: $i ).
tff(index_30_type,type,
index_30: $i ).
tff(queue_29_type,type,
queue_29: $i ).
tff(earray_34_type,type,
earray_34: $i ).
tff(queue_37_type,type,
queue_37: $i ).
tff(index_36_type,type,
index_36: $i ).
tff(queue_35_type,type,
queue_35: $i ).
tff(index_21_type,type,
index_21: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(q11_type,type,
q11: $i ).
tff(index_24_type,type,
index_24: $i ).
tff(queue_23_type,type,
queue_23: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(q9_type,type,
q9: $i ).
tff(index_15_type,type,
index_15: $i ).
tff(q10_type,type,
q10: $i ).
tff(index_9_type,type,
index_9: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(index_255_type,type,
index_255: $i ).
tff(earray_256_type,type,
earray_256: $i ).
tff(q8_type,type,
q8: $i ).
tff(index_258_type,type,
index_258: $i ).
tff(queue_257_type,type,
queue_257: $i ).
tff(queue_259_type,type,
queue_259: $i ).
tff(q6_type,type,
q6: $i ).
tff(index_249_type,type,
index_249: $i ).
tff(q7_type,type,
q7: $i ).
tff(index_243_type,type,
index_243: $i ).
tff(earray_244_type,type,
earray_244: $i ).
tff(queue_247_type,type,
queue_247: $i ).
tff(index_246_type,type,
index_246: $i ).
tff(queue_245_type,type,
queue_245: $i ).
tff(earray_250_type,type,
earray_250: $i ).
tff(queue_253_type,type,
queue_253: $i ).
tff(index_252_type,type,
index_252: $i ).
tff(queue_251_type,type,
queue_251: $i ).
tff(index_237_type,type,
index_237: $i ).
tff(earray_238_type,type,
earray_238: $i ).
tff(q5_type,type,
q5: $i ).
tff(index_240_type,type,
index_240: $i ).
tff(queue_239_type,type,
queue_239: $i ).
tff(queue_241_type,type,
queue_241: $i ).
tff(q3_type,type,
q3: $i ).
tff(index_231_type,type,
index_231: $i ).
tff(q4_type,type,
q4: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(earray_202_type,type,
earray_202: $i ).
tff(queue_205_type,type,
queue_205: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(queue_203_type,type,
queue_203: $i ).
tff(earray_232_type,type,
earray_232: $i ).
tff(queue_235_type,type,
queue_235: $i ).
tff(index_234_type,type,
index_234: $i ).
tff(queue_233_type,type,
queue_233: $i ).
tff(index_135_type,type,
index_135: $i ).
tff(earray_136_type,type,
earray_136: $i ).
tff(q2_type,type,
q2: $i ).
tff(index_138_type,type,
index_138: $i ).
tff(queue_137_type,type,
queue_137: $i ).
tff(queue_139_type,type,
queue_139: $i ).
tff(q0_type,type,
q0: $i ).
tff(index_69_type,type,
index_69: $i ).
tff(q1_type,type,
q1: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(earray_70_type,type,
earray_70: $i ).
tff(queue_73_type,type,
queue_73: $i ).
tff(index_72_type,type,
index_72: $i ).
tff(queue_71_type,type,
queue_71: $i ).
tff(q_type,type,
q: $i ).
tff(head_type,type,
head: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_68_type,type,
earray_68: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_134_type,type,
earray_134: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_200_type,type,
earray_200: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_230_type,type,
earray_230: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_236_type,type,
earray_236: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_242_type,type,
earray_242: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_248_type,type,
earray_248: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_254_type,type,
earray_254: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(e11_type,type,
e11: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_26_type,type,
earray_26: $i ).
tff(e13_type,type,
e13: $i ).
tff(earray_32_type,type,
earray_32: $i ).
tff(e14_type,type,
e14: $i ).
tff(earray_38_type,type,
earray_38: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_44_type,type,
earray_44: $i ).
tff(e16_type,type,
e16: $i ).
tff(earray_50_type,type,
earray_50: $i ).
tff(e17_type,type,
e17: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(e18_type,type,
e18: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(e19_type,type,
e19: $i ).
tff(earray_74_type,type,
earray_74: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_80_type,type,
earray_80: $i ).
tff(e21_type,type,
e21: $i ).
tff(earray_86_type,type,
earray_86: $i ).
tff(e22_type,type,
e22: $i ).
tff(earray_92_type,type,
earray_92: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(e24_type,type,
e24: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(e25_type,type,
e25: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_116_type,type,
earray_116: $i ).
tff(e27_type,type,
e27: $i ).
tff(earray_122_type,type,
earray_122: $i ).
tff(e28_type,type,
e28: $i ).
tff(earray_128_type,type,
earray_128: $i ).
tff(e29_type,type,
e29: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(e30_type,type,
e30: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(e31_type,type,
e31: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(e32_type,type,
e32: $i ).
tff(earray_158_type,type,
earray_158: $i ).
tff(e33_type,type,
e33: $i ).
tff(earray_164_type,type,
earray_164: $i ).
tff(e34_type,type,
e34: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(e35_type,type,
e35: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(e36_type,type,
e36: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(e37_type,type,
e37: $i ).
tff(earray_188_type,type,
earray_188: $i ).
tff(e38_type,type,
e38: $i ).
tff(earray_194_type,type,
earray_194: $i ).
tff(e39_type,type,
e39: $i ).
tff(earray_206_type,type,
earray_206: $i ).
tff(e40_type,type,
e40: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(e41_type,type,
e41: $i ).
tff(earray_218_type,type,
earray_218: $i ).
tff(1,plain,
( ( elem_265 = select(earray_260,index_264) )
<=> ( elem_265 = select(earray_260,index_264) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
elem_265 = select(earray_260,index_264),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(3,plain,
elem_265 = select(earray_260,index_264),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
select(earray_260,index_264) = elem_265,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] : ( p(s(X)) = X )
<=> ! [X: $i] : ( p(s(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ! [X: $i] : ( p(s(X)) = X )
<=> ! [X: $i] : ( p(s(X)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] : ( p(s(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ps) ).
tff(8,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] : ( p(s(X)) = X ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [X: $i] : ( p(s(X)) = X )
| ( p(s(select(q42,tail))) = select(q42,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
p(s(select(q42,tail))) = select(q42,tail),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
( ( index_225 = select(q42,tail) )
<=> ( index_225 = select(q42,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
index_225 = select(q42,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(15,plain,
index_225 = select(q42,tail),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
select(q42,tail) = index_225,
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
s(select(q42,tail)) = s(index_225),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
s(index_225) = s(select(q42,tail)),
inference(symmetry,[status(thm)],[17]) ).
tff(19,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(20,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(21,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(22,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),tail) = s(index_225) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
select(store(store(q42,seq,earray_226),tail,s(index_225)),tail) = s(index_225),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ( index_228 = s(index_225) )
<=> ( index_228 = s(index_225) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
index_228 = s(index_225),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(29,plain,
index_228 = s(index_225),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
s(index_225) = index_228,
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ( queue_227 = store(q42,seq,earray_226) )
<=> ( queue_227 = store(q42,seq,earray_226) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
queue_227 = store(q42,seq,earray_226),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(33,plain,
queue_227 = store(q42,seq,earray_226),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
store(q42,seq,earray_226) = queue_227,
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
store(store(q42,seq,earray_226),tail,s(index_225)) = store(queue_227,tail,index_228),
inference(monotonicity,[status(thm)],[34,30]) ).
tff(36,plain,
store(queue_227,tail,index_228) = store(store(q42,seq,earray_226),tail,s(index_225)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ( queue_229 = store(queue_227,tail,index_228) )
<=> ( queue_229 = store(queue_227,tail,index_228) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
queue_229 = store(queue_227,tail,index_228),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(39,plain,
queue_229 = store(queue_227,tail,index_228),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( q43 = queue_229 )
<=> ( q43 = queue_229 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
q43 = queue_229,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp304) ).
tff(42,plain,
q43 = queue_229,
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
q43 = store(store(q42,seq,earray_226),tail,s(index_225)),
inference(transitivity,[status(thm)],[42,39,36]) ).
tff(44,plain,
select(q43,tail) = select(store(store(q42,seq,earray_226),tail,s(index_225)),tail),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( index_263 = select(q43,tail) )
<=> ( index_263 = select(q43,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
index_263 = select(q43,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(47,plain,
index_263 = select(q43,tail),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( s(index_264) = index_263 )
<=> ( s(index_264) = index_263 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
s(index_264) = index_263,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(50,plain,
s(index_264) = index_263,
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
s(index_264) = s(select(q42,tail)),
inference(transitivity,[status(thm)],[50,47,44,26,18]) ).
tff(52,plain,
p(s(index_264)) = p(s(select(q42,tail))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( ~ ! [X: $i] : ( p(s(X)) = X )
| ( p(s(index_264)) = index_264 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
p(s(index_264)) = index_264,
inference(unit_resolution,[status(thm)],[53,10]) ).
tff(55,plain,
index_264 = p(s(index_264)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
index_264 = select(q42,tail),
inference(transitivity,[status(thm)],[55,52,12]) ).
tff(57,plain,
( ( earray_224 = select(q42,seq) )
<=> ( earray_224 = select(q42,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
earray_224 = select(q42,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp47) ).
tff(59,plain,
earray_224 = select(q42,seq),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
select(q42,seq) = earray_224,
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
store(select(q42,seq),select(q42,tail),e42) = store(earray_224,index_225,e42),
inference(monotonicity,[status(thm)],[60,16]) ).
tff(62,plain,
store(earray_224,index_225,e42) = store(select(q42,seq),select(q42,tail),e42),
inference(symmetry,[status(thm)],[61]) ).
tff(63,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,e42)),seq) = store(earray_224,index_225,e42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e42)),seq) = store(earray_224,index_225,e42),
inference(unit_resolution,[status(thm)],[63,24]) ).
tff(65,plain,
( ( earray_226 = store(earray_224,index_225,e42) )
<=> ( earray_226 = store(earray_224,index_225,e42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
earray_226 = store(earray_224,index_225,e42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(67,plain,
earray_226 = store(earray_224,index_225,e42),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
store(earray_224,index_225,e42) = earray_226,
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ( q42 = queue_223 )
<=> ( q42 = queue_223 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
q42 = queue_223,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp303) ).
tff(71,plain,
q42 = queue_223,
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
queue_223 = q42,
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ( queue_223 = store(queue_221,tail,index_222) )
<=> ( queue_223 = store(queue_221,tail,index_222) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
queue_223 = store(queue_221,tail,index_222),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(75,plain,
queue_223 = store(queue_221,tail,index_222),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
store(queue_221,tail,index_222) = queue_223,
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
store(queue_221,tail,index_222) = q42,
inference(transitivity,[status(thm)],[76,72]) ).
tff(78,plain,
store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e42)) = store(q42,seq,earray_226),
inference(monotonicity,[status(thm)],[77,68]) ).
tff(79,plain,
select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e42)),seq) = select(store(q42,seq,earray_226),seq),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
select(store(q42,seq,earray_226),seq) = select(store(store(queue_221,tail,index_222),seq,store(earray_224,index_225,e42)),seq),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ( tail != seq )
<=> ( tail != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
tail != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tail_distinct_from_seq) ).
tff(83,plain,
tail != seq,
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,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(85,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(86,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(87,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)],[86,85]) ).
tff(88,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,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)],[88,84]) ).
tff(90,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),seq) = select(store(q42,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(q42,seq,earray_226),tail,s(index_225)),seq) = select(store(q42,seq,earray_226),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),seq) = select(store(q42,seq,earray_226),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),seq) = select(store(q42,seq,earray_226),seq) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
select(store(store(q42,seq,earray_226),tail,s(index_225)),seq) = select(store(q42,seq,earray_226),seq),
inference(unit_resolution,[status(thm)],[92,89,83]) ).
tff(94,plain,
queue_229 = q43,
inference(symmetry,[status(thm)],[42]) ).
tff(95,plain,
store(queue_227,tail,index_228) = queue_229,
inference(symmetry,[status(thm)],[39]) ).
tff(96,plain,
store(store(q42,seq,earray_226),tail,s(index_225)) = q43,
inference(transitivity,[status(thm)],[35,95,94]) ).
tff(97,plain,
select(store(store(q42,seq,earray_226),tail,s(index_225)),seq) = select(q43,seq),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
select(q43,seq) = select(store(store(q42,seq,earray_226),tail,s(index_225)),seq),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ( earray_260 = select(q43,seq) )
<=> ( earray_260 = select(q43,seq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
earray_260 = select(q43,seq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(101,plain,
earray_260 = select(q43,seq),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
earray_260 = store(select(q42,seq),select(q42,tail),e42),
inference(transitivity,[status(thm)],[101,98,93,80,64,62]) ).
tff(103,plain,
select(earray_260,index_264) = select(store(select(q42,seq),select(q42,tail),e42),select(q42,tail)),
inference(monotonicity,[status(thm)],[102,56]) ).
tff(104,plain,
select(store(select(q42,seq),select(q42,tail),e42),select(q42,tail)) = select(earray_260,index_264),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ( index_222 = s(index_219) )
<=> ( index_222 = s(index_219) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
index_222 = s(index_219),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(107,plain,
index_222 = s(index_219),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
s(index_219) = index_222,
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ( queue_221 = store(q41,seq,earray_220) )
<=> ( queue_221 = store(q41,seq,earray_220) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
queue_221 = store(q41,seq,earray_220),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(111,plain,
queue_221 = store(q41,seq,earray_220),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
store(q41,seq,earray_220) = queue_221,
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
store(store(q41,seq,earray_220),tail,s(index_219)) = store(queue_221,tail,index_222),
inference(monotonicity,[status(thm)],[112,108]) ).
tff(114,plain,
store(queue_221,tail,index_222) = store(store(q41,seq,earray_220),tail,s(index_219)),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
q42 = store(store(q41,seq,earray_220),tail,s(index_219)),
inference(transitivity,[status(thm)],[71,75,114]) ).
tff(116,plain,
select(q42,tail) = select(store(store(q41,seq,earray_220),tail,s(index_219)),tail),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
select(store(store(q41,seq,earray_220),tail,s(index_219)),tail) = select(q42,tail),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q41,seq,earray_220),tail,s(index_219)),tail) = s(index_219) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
select(store(store(q41,seq,earray_220),tail,s(index_219)),tail) = s(index_219),
inference(unit_resolution,[status(thm)],[118,24]) ).
tff(120,plain,
s(index_219) = select(store(store(q41,seq,earray_220),tail,s(index_219)),tail),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ( index_213 = select(q40,tail) )
<=> ( index_213 = select(q40,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
index_213 = select(q40,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(123,plain,
index_213 = select(q40,tail),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
select(q40,tail) = index_213,
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
( ( index_210 = s(index_207) )
<=> ( index_210 = s(index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
index_210 = s(index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(127,plain,
index_210 = s(index_207),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
s(index_207) = index_210,
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ( queue_209 = store(q39,seq,earray_208) )
<=> ( queue_209 = store(q39,seq,earray_208) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(130,axiom,
queue_209 = store(q39,seq,earray_208),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(131,plain,
queue_209 = store(q39,seq,earray_208),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
store(q39,seq,earray_208) = queue_209,
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
store(store(q39,seq,earray_208),tail,s(index_207)) = store(queue_209,tail,index_210),
inference(monotonicity,[status(thm)],[132,128]) ).
tff(134,plain,
store(queue_209,tail,index_210) = store(store(q39,seq,earray_208),tail,s(index_207)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ( queue_211 = store(queue_209,tail,index_210) )
<=> ( queue_211 = store(queue_209,tail,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
queue_211 = store(queue_209,tail,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(137,plain,
queue_211 = store(queue_209,tail,index_210),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ( q40 = queue_211 )
<=> ( q40 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,axiom,
q40 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp301) ).
tff(140,plain,
q40 = queue_211,
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
q40 = store(store(q39,seq,earray_208),tail,s(index_207)),
inference(transitivity,[status(thm)],[140,137,134]) ).
tff(142,plain,
select(q40,tail) = select(store(store(q39,seq,earray_208),tail,s(index_207)),tail),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
select(store(store(q39,seq,earray_208),tail,s(index_207)),tail) = select(q40,tail),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q39,seq,earray_208),tail,s(index_207)),tail) = s(index_207) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
select(store(store(q39,seq,earray_208),tail,s(index_207)),tail) = s(index_207),
inference(unit_resolution,[status(thm)],[144,24]) ).
tff(146,plain,
s(index_207) = select(store(store(q39,seq,earray_208),tail,s(index_207)),tail),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ( index_207 = select(q39,tail) )
<=> ( index_207 = select(q39,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,axiom,
index_207 = select(q39,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(149,plain,
index_207 = select(q39,tail),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
select(q39,tail) = index_207,
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
s(select(q39,tail)) = s(index_207),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
s(select(q39,tail)) = index_213,
inference(transitivity,[status(thm)],[151,146,143,124]) ).
tff(153,plain,
s(s(select(q39,tail))) = s(index_213),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
s(index_213) = s(s(select(q39,tail))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q40,seq,earray_214),tail,s(index_213)),tail) = s(index_213) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
select(store(store(q40,seq,earray_214),tail,s(index_213)),tail) = s(index_213),
inference(unit_resolution,[status(thm)],[155,24]) ).
tff(157,plain,
( ( index_216 = s(index_213) )
<=> ( index_216 = s(index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,axiom,
index_216 = s(index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(159,plain,
index_216 = s(index_213),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
s(index_213) = index_216,
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ( queue_215 = store(q40,seq,earray_214) )
<=> ( queue_215 = store(q40,seq,earray_214) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
queue_215 = store(q40,seq,earray_214),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(163,plain,
queue_215 = store(q40,seq,earray_214),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
store(q40,seq,earray_214) = queue_215,
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
store(store(q40,seq,earray_214),tail,s(index_213)) = store(queue_215,tail,index_216),
inference(monotonicity,[status(thm)],[164,160]) ).
tff(166,plain,
store(queue_215,tail,index_216) = store(store(q40,seq,earray_214),tail,s(index_213)),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ( queue_217 = store(queue_215,tail,index_216) )
<=> ( queue_217 = store(queue_215,tail,index_216) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,axiom,
queue_217 = store(queue_215,tail,index_216),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(169,plain,
queue_217 = store(queue_215,tail,index_216),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( ( q41 = queue_217 )
<=> ( q41 = queue_217 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
q41 = queue_217,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp302) ).
tff(172,plain,
q41 = queue_217,
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
q41 = store(store(q40,seq,earray_214),tail,s(index_213)),
inference(transitivity,[status(thm)],[172,169,166]) ).
tff(174,plain,
select(q41,tail) = select(store(store(q40,seq,earray_214),tail,s(index_213)),tail),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
( ( index_219 = select(q41,tail) )
<=> ( index_219 = select(q41,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
index_219 = select(q41,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(177,plain,
index_219 = select(q41,tail),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
index_219 = s(s(select(q39,tail))),
inference(transitivity,[status(thm)],[177,174,156,154]) ).
tff(179,plain,
s(index_219) = s(s(s(select(q39,tail)))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
s(s(s(select(q39,tail)))) = s(index_219),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) = X )
<=> ( s(s(s(X))) = X ) )),
inference(bind,[status(th)],[]) ).
tff(182,plain,
( ! [X: $i] : ( s(s(s(X))) = X )
<=> ! [X: $i] : ( s(s(s(X))) = X ) ),
inference(quant_intro,[status(thm)],[181]) ).
tff(183,plain,
( ! [X: $i] : ( s(s(s(X))) = X )
<=> ! [X: $i] : ( s(s(s(X))) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,axiom,
! [X: $i] : ( s(s(s(X))) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',circular) ).
tff(185,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(modus_ponens,[status(thm)],[184,183]) ).
tff(186,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(skolemize,[status(sab)],[185]) ).
tff(187,plain,
! [X: $i] : ( s(s(s(X))) = X ),
inference(modus_ponens,[status(thm)],[186,182]) ).
tff(188,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q39,tail)))) = select(q39,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
s(s(s(select(q39,tail)))) = select(q39,tail),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
select(q39,tail) = s(s(s(select(q39,tail)))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ( index_198 = s(index_195) )
<=> ( index_198 = s(index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,axiom,
index_198 = s(index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(193,plain,
index_198 = s(index_195),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
s(index_195) = index_198,
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
( ( queue_197 = store(q38,seq,earray_196) )
<=> ( queue_197 = store(q38,seq,earray_196) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
queue_197 = store(q38,seq,earray_196),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(197,plain,
queue_197 = store(q38,seq,earray_196),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
store(q38,seq,earray_196) = queue_197,
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
store(store(q38,seq,earray_196),tail,s(index_195)) = store(queue_197,tail,index_198),
inference(monotonicity,[status(thm)],[198,194]) ).
tff(200,plain,
store(queue_197,tail,index_198) = store(store(q38,seq,earray_196),tail,s(index_195)),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
( ( queue_199 = store(queue_197,tail,index_198) )
<=> ( queue_199 = store(queue_197,tail,index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,axiom,
queue_199 = store(queue_197,tail,index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(203,plain,
queue_199 = store(queue_197,tail,index_198),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
( ( q39 = queue_199 )
<=> ( q39 = queue_199 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,axiom,
q39 = queue_199,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp299) ).
tff(206,plain,
q39 = queue_199,
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
q39 = store(store(q38,seq,earray_196),tail,s(index_195)),
inference(transitivity,[status(thm)],[206,203,200]) ).
tff(208,plain,
select(q39,tail) = select(store(store(q38,seq,earray_196),tail,s(index_195)),tail),
inference(monotonicity,[status(thm)],[207]) ).
tff(209,plain,
select(store(store(q38,seq,earray_196),tail,s(index_195)),tail) = select(q39,tail),
inference(symmetry,[status(thm)],[208]) ).
tff(210,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q38,seq,earray_196),tail,s(index_195)),tail) = s(index_195) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
select(store(store(q38,seq,earray_196),tail,s(index_195)),tail) = s(index_195),
inference(unit_resolution,[status(thm)],[210,24]) ).
tff(212,plain,
s(index_195) = select(store(store(q38,seq,earray_196),tail,s(index_195)),tail),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
( ( index_189 = select(q37,tail) )
<=> ( index_189 = select(q37,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(214,axiom,
index_189 = select(q37,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(215,plain,
index_189 = select(q37,tail),
inference(modus_ponens,[status(thm)],[214,213]) ).
tff(216,plain,
select(q37,tail) = index_189,
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(219,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ( queue_185 = store(q36,seq,earray_184) )
<=> ( queue_185 = store(q36,seq,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,axiom,
queue_185 = store(q36,seq,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(223,plain,
queue_185 = store(q36,seq,earray_184),
inference(modus_ponens,[status(thm)],[222,221]) ).
tff(224,plain,
store(q36,seq,earray_184) = queue_185,
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
store(store(q36,seq,earray_184),tail,s(index_183)) = store(queue_185,tail,index_186),
inference(monotonicity,[status(thm)],[224,220]) ).
tff(226,plain,
store(queue_185,tail,index_186) = store(store(q36,seq,earray_184),tail,s(index_183)),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ( queue_187 = store(queue_185,tail,index_186) )
<=> ( queue_187 = store(queue_185,tail,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,axiom,
queue_187 = store(queue_185,tail,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(229,plain,
queue_187 = store(queue_185,tail,index_186),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
( ( q37 = queue_187 )
<=> ( q37 = queue_187 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,axiom,
q37 = queue_187,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp297) ).
tff(232,plain,
q37 = queue_187,
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
q37 = store(store(q36,seq,earray_184),tail,s(index_183)),
inference(transitivity,[status(thm)],[232,229,226]) ).
tff(234,plain,
select(q37,tail) = select(store(store(q36,seq,earray_184),tail,s(index_183)),tail),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
select(store(store(q36,seq,earray_184),tail,s(index_183)),tail) = select(q37,tail),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q36,seq,earray_184),tail,s(index_183)),tail) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
select(store(store(q36,seq,earray_184),tail,s(index_183)),tail) = s(index_183),
inference(unit_resolution,[status(thm)],[236,24]) ).
tff(238,plain,
s(index_183) = select(store(store(q36,seq,earray_184),tail,s(index_183)),tail),
inference(symmetry,[status(thm)],[237]) ).
tff(239,plain,
( ( index_183 = select(q36,tail) )
<=> ( index_183 = select(q36,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(240,axiom,
index_183 = select(q36,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(241,plain,
index_183 = select(q36,tail),
inference(modus_ponens,[status(thm)],[240,239]) ).
tff(242,plain,
select(q36,tail) = index_183,
inference(symmetry,[status(thm)],[241]) ).
tff(243,plain,
s(select(q36,tail)) = s(index_183),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
s(select(q36,tail)) = index_189,
inference(transitivity,[status(thm)],[243,238,235,216]) ).
tff(245,plain,
s(s(select(q36,tail))) = s(index_189),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
s(index_189) = s(s(select(q36,tail))),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q37,seq,earray_190),tail,s(index_189)),tail) = s(index_189) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(248,plain,
select(store(store(q37,seq,earray_190),tail,s(index_189)),tail) = s(index_189),
inference(unit_resolution,[status(thm)],[247,24]) ).
tff(249,plain,
( ( index_192 = s(index_189) )
<=> ( index_192 = s(index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,axiom,
index_192 = s(index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(251,plain,
index_192 = s(index_189),
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
s(index_189) = index_192,
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
( ( queue_191 = store(q37,seq,earray_190) )
<=> ( queue_191 = store(q37,seq,earray_190) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,axiom,
queue_191 = store(q37,seq,earray_190),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(255,plain,
queue_191 = store(q37,seq,earray_190),
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
store(q37,seq,earray_190) = queue_191,
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
store(store(q37,seq,earray_190),tail,s(index_189)) = store(queue_191,tail,index_192),
inference(monotonicity,[status(thm)],[256,252]) ).
tff(258,plain,
store(queue_191,tail,index_192) = store(store(q37,seq,earray_190),tail,s(index_189)),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
( ( queue_193 = store(queue_191,tail,index_192) )
<=> ( queue_193 = store(queue_191,tail,index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,axiom,
queue_193 = store(queue_191,tail,index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(261,plain,
queue_193 = store(queue_191,tail,index_192),
inference(modus_ponens,[status(thm)],[260,259]) ).
tff(262,plain,
( ( q38 = queue_193 )
<=> ( q38 = queue_193 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(263,axiom,
q38 = queue_193,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp298) ).
tff(264,plain,
q38 = queue_193,
inference(modus_ponens,[status(thm)],[263,262]) ).
tff(265,plain,
q38 = store(store(q37,seq,earray_190),tail,s(index_189)),
inference(transitivity,[status(thm)],[264,261,258]) ).
tff(266,plain,
select(q38,tail) = select(store(store(q37,seq,earray_190),tail,s(index_189)),tail),
inference(monotonicity,[status(thm)],[265]) ).
tff(267,plain,
( ( index_195 = select(q38,tail) )
<=> ( index_195 = select(q38,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(268,axiom,
index_195 = select(q38,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(269,plain,
index_195 = select(q38,tail),
inference(modus_ponens,[status(thm)],[268,267]) ).
tff(270,plain,
index_195 = s(s(select(q36,tail))),
inference(transitivity,[status(thm)],[269,266,248,246]) ).
tff(271,plain,
s(index_195) = s(s(s(select(q36,tail)))),
inference(monotonicity,[status(thm)],[270]) ).
tff(272,plain,
s(s(s(select(q36,tail)))) = s(index_195),
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q36,tail)))) = select(q36,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(274,plain,
s(s(s(select(q36,tail)))) = select(q36,tail),
inference(unit_resolution,[status(thm)],[273,187]) ).
tff(275,plain,
select(q36,tail) = s(s(s(select(q36,tail)))),
inference(symmetry,[status(thm)],[274]) ).
tff(276,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(277,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(278,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[277,276]) ).
tff(279,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[278]) ).
tff(280,plain,
( ( queue_179 = store(q35,seq,earray_178) )
<=> ( queue_179 = store(q35,seq,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(281,axiom,
queue_179 = store(q35,seq,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(282,plain,
queue_179 = store(q35,seq,earray_178),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
store(q35,seq,earray_178) = queue_179,
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
store(store(q35,seq,earray_178),tail,s(index_177)) = store(queue_179,tail,index_180),
inference(monotonicity,[status(thm)],[283,279]) ).
tff(285,plain,
store(queue_179,tail,index_180) = store(store(q35,seq,earray_178),tail,s(index_177)),
inference(symmetry,[status(thm)],[284]) ).
tff(286,plain,
( ( queue_181 = store(queue_179,tail,index_180) )
<=> ( queue_181 = store(queue_179,tail,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(287,axiom,
queue_181 = store(queue_179,tail,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(288,plain,
queue_181 = store(queue_179,tail,index_180),
inference(modus_ponens,[status(thm)],[287,286]) ).
tff(289,plain,
( ( q36 = queue_181 )
<=> ( q36 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(290,axiom,
q36 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp296) ).
tff(291,plain,
q36 = queue_181,
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
q36 = store(store(q35,seq,earray_178),tail,s(index_177)),
inference(transitivity,[status(thm)],[291,288,285]) ).
tff(293,plain,
select(q36,tail) = select(store(store(q35,seq,earray_178),tail,s(index_177)),tail),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
select(store(store(q35,seq,earray_178),tail,s(index_177)),tail) = select(q36,tail),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q35,seq,earray_178),tail,s(index_177)),tail) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(296,plain,
select(store(store(q35,seq,earray_178),tail,s(index_177)),tail) = s(index_177),
inference(unit_resolution,[status(thm)],[295,24]) ).
tff(297,plain,
s(index_177) = select(store(store(q35,seq,earray_178),tail,s(index_177)),tail),
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
( ( index_171 = select(q34,tail) )
<=> ( index_171 = select(q34,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,axiom,
index_171 = select(q34,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(300,plain,
index_171 = select(q34,tail),
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
select(q34,tail) = index_171,
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ( index_168 = s(index_165) )
<=> ( index_168 = s(index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(303,axiom,
index_168 = s(index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(304,plain,
index_168 = s(index_165),
inference(modus_ponens,[status(thm)],[303,302]) ).
tff(305,plain,
s(index_165) = index_168,
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ( queue_167 = store(q33,seq,earray_166) )
<=> ( queue_167 = store(q33,seq,earray_166) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(307,axiom,
queue_167 = store(q33,seq,earray_166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(308,plain,
queue_167 = store(q33,seq,earray_166),
inference(modus_ponens,[status(thm)],[307,306]) ).
tff(309,plain,
store(q33,seq,earray_166) = queue_167,
inference(symmetry,[status(thm)],[308]) ).
tff(310,plain,
store(store(q33,seq,earray_166),tail,s(index_165)) = store(queue_167,tail,index_168),
inference(monotonicity,[status(thm)],[309,305]) ).
tff(311,plain,
store(queue_167,tail,index_168) = store(store(q33,seq,earray_166),tail,s(index_165)),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ( queue_169 = store(queue_167,tail,index_168) )
<=> ( queue_169 = store(queue_167,tail,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(313,axiom,
queue_169 = store(queue_167,tail,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(314,plain,
queue_169 = store(queue_167,tail,index_168),
inference(modus_ponens,[status(thm)],[313,312]) ).
tff(315,plain,
( ( q34 = queue_169 )
<=> ( q34 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(316,axiom,
q34 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp294) ).
tff(317,plain,
q34 = queue_169,
inference(modus_ponens,[status(thm)],[316,315]) ).
tff(318,plain,
q34 = store(store(q33,seq,earray_166),tail,s(index_165)),
inference(transitivity,[status(thm)],[317,314,311]) ).
tff(319,plain,
select(q34,tail) = select(store(store(q33,seq,earray_166),tail,s(index_165)),tail),
inference(monotonicity,[status(thm)],[318]) ).
tff(320,plain,
select(store(store(q33,seq,earray_166),tail,s(index_165)),tail) = select(q34,tail),
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q33,seq,earray_166),tail,s(index_165)),tail) = s(index_165) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(322,plain,
select(store(store(q33,seq,earray_166),tail,s(index_165)),tail) = s(index_165),
inference(unit_resolution,[status(thm)],[321,24]) ).
tff(323,plain,
s(index_165) = select(store(store(q33,seq,earray_166),tail,s(index_165)),tail),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
( ( index_165 = select(q33,tail) )
<=> ( index_165 = select(q33,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(325,axiom,
index_165 = select(q33,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(326,plain,
index_165 = select(q33,tail),
inference(modus_ponens,[status(thm)],[325,324]) ).
tff(327,plain,
select(q33,tail) = index_165,
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
s(select(q33,tail)) = s(index_165),
inference(monotonicity,[status(thm)],[327]) ).
tff(329,plain,
s(select(q33,tail)) = index_171,
inference(transitivity,[status(thm)],[328,323,320,301]) ).
tff(330,plain,
s(s(select(q33,tail))) = s(index_171),
inference(monotonicity,[status(thm)],[329]) ).
tff(331,plain,
s(index_171) = s(s(select(q33,tail))),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q34,seq,earray_172),tail,s(index_171)),tail) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(333,plain,
select(store(store(q34,seq,earray_172),tail,s(index_171)),tail) = s(index_171),
inference(unit_resolution,[status(thm)],[332,24]) ).
tff(334,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(335,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(336,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[335,334]) ).
tff(337,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[336]) ).
tff(338,plain,
( ( queue_173 = store(q34,seq,earray_172) )
<=> ( queue_173 = store(q34,seq,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(339,axiom,
queue_173 = store(q34,seq,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(340,plain,
queue_173 = store(q34,seq,earray_172),
inference(modus_ponens,[status(thm)],[339,338]) ).
tff(341,plain,
store(q34,seq,earray_172) = queue_173,
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
store(store(q34,seq,earray_172),tail,s(index_171)) = store(queue_173,tail,index_174),
inference(monotonicity,[status(thm)],[341,337]) ).
tff(343,plain,
store(queue_173,tail,index_174) = store(store(q34,seq,earray_172),tail,s(index_171)),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
( ( queue_175 = store(queue_173,tail,index_174) )
<=> ( queue_175 = store(queue_173,tail,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,axiom,
queue_175 = store(queue_173,tail,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(346,plain,
queue_175 = store(queue_173,tail,index_174),
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
( ( q35 = queue_175 )
<=> ( q35 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(348,axiom,
q35 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp295) ).
tff(349,plain,
q35 = queue_175,
inference(modus_ponens,[status(thm)],[348,347]) ).
tff(350,plain,
q35 = store(store(q34,seq,earray_172),tail,s(index_171)),
inference(transitivity,[status(thm)],[349,346,343]) ).
tff(351,plain,
select(q35,tail) = select(store(store(q34,seq,earray_172),tail,s(index_171)),tail),
inference(monotonicity,[status(thm)],[350]) ).
tff(352,plain,
( ( index_177 = select(q35,tail) )
<=> ( index_177 = select(q35,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(353,axiom,
index_177 = select(q35,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(354,plain,
index_177 = select(q35,tail),
inference(modus_ponens,[status(thm)],[353,352]) ).
tff(355,plain,
index_177 = s(s(select(q33,tail))),
inference(transitivity,[status(thm)],[354,351,333,331]) ).
tff(356,plain,
s(index_177) = s(s(s(select(q33,tail)))),
inference(monotonicity,[status(thm)],[355]) ).
tff(357,plain,
s(s(s(select(q33,tail)))) = s(index_177),
inference(symmetry,[status(thm)],[356]) ).
tff(358,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q33,tail)))) = select(q33,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(359,plain,
s(s(s(select(q33,tail)))) = select(q33,tail),
inference(unit_resolution,[status(thm)],[358,187]) ).
tff(360,plain,
select(q33,tail) = s(s(s(select(q33,tail)))),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
( ( index_162 = s(index_159) )
<=> ( index_162 = s(index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(362,axiom,
index_162 = s(index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(363,plain,
index_162 = s(index_159),
inference(modus_ponens,[status(thm)],[362,361]) ).
tff(364,plain,
s(index_159) = index_162,
inference(symmetry,[status(thm)],[363]) ).
tff(365,plain,
( ( queue_161 = store(q32,seq,earray_160) )
<=> ( queue_161 = store(q32,seq,earray_160) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(366,axiom,
queue_161 = store(q32,seq,earray_160),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(367,plain,
queue_161 = store(q32,seq,earray_160),
inference(modus_ponens,[status(thm)],[366,365]) ).
tff(368,plain,
store(q32,seq,earray_160) = queue_161,
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
store(store(q32,seq,earray_160),tail,s(index_159)) = store(queue_161,tail,index_162),
inference(monotonicity,[status(thm)],[368,364]) ).
tff(370,plain,
store(queue_161,tail,index_162) = store(store(q32,seq,earray_160),tail,s(index_159)),
inference(symmetry,[status(thm)],[369]) ).
tff(371,plain,
( ( queue_163 = store(queue_161,tail,index_162) )
<=> ( queue_163 = store(queue_161,tail,index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(372,axiom,
queue_163 = store(queue_161,tail,index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(373,plain,
queue_163 = store(queue_161,tail,index_162),
inference(modus_ponens,[status(thm)],[372,371]) ).
tff(374,plain,
( ( q33 = queue_163 )
<=> ( q33 = queue_163 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(375,axiom,
q33 = queue_163,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp293) ).
tff(376,plain,
q33 = queue_163,
inference(modus_ponens,[status(thm)],[375,374]) ).
tff(377,plain,
q33 = store(store(q32,seq,earray_160),tail,s(index_159)),
inference(transitivity,[status(thm)],[376,373,370]) ).
tff(378,plain,
select(q33,tail) = select(store(store(q32,seq,earray_160),tail,s(index_159)),tail),
inference(monotonicity,[status(thm)],[377]) ).
tff(379,plain,
select(store(store(q32,seq,earray_160),tail,s(index_159)),tail) = select(q33,tail),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q32,seq,earray_160),tail,s(index_159)),tail) = s(index_159) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
select(store(store(q32,seq,earray_160),tail,s(index_159)),tail) = s(index_159),
inference(unit_resolution,[status(thm)],[380,24]) ).
tff(382,plain,
s(index_159) = select(store(store(q32,seq,earray_160),tail,s(index_159)),tail),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ( index_153 = select(q31,tail) )
<=> ( index_153 = select(q31,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(384,axiom,
index_153 = select(q31,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(385,plain,
index_153 = select(q31,tail),
inference(modus_ponens,[status(thm)],[384,383]) ).
tff(386,plain,
select(q31,tail) = index_153,
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(389,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
( ( queue_149 = store(q30,seq,earray_148) )
<=> ( queue_149 = store(q30,seq,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(392,axiom,
queue_149 = store(q30,seq,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(393,plain,
queue_149 = store(q30,seq,earray_148),
inference(modus_ponens,[status(thm)],[392,391]) ).
tff(394,plain,
store(q30,seq,earray_148) = queue_149,
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
store(store(q30,seq,earray_148),tail,s(index_147)) = store(queue_149,tail,index_150),
inference(monotonicity,[status(thm)],[394,390]) ).
tff(396,plain,
store(queue_149,tail,index_150) = store(store(q30,seq,earray_148),tail,s(index_147)),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ( queue_151 = store(queue_149,tail,index_150) )
<=> ( queue_151 = store(queue_149,tail,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(398,axiom,
queue_151 = store(queue_149,tail,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(399,plain,
queue_151 = store(queue_149,tail,index_150),
inference(modus_ponens,[status(thm)],[398,397]) ).
tff(400,plain,
( ( q31 = queue_151 )
<=> ( q31 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(401,axiom,
q31 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp291) ).
tff(402,plain,
q31 = queue_151,
inference(modus_ponens,[status(thm)],[401,400]) ).
tff(403,plain,
q31 = store(store(q30,seq,earray_148),tail,s(index_147)),
inference(transitivity,[status(thm)],[402,399,396]) ).
tff(404,plain,
select(q31,tail) = select(store(store(q30,seq,earray_148),tail,s(index_147)),tail),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
select(store(store(q30,seq,earray_148),tail,s(index_147)),tail) = select(q31,tail),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q30,seq,earray_148),tail,s(index_147)),tail) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(407,plain,
select(store(store(q30,seq,earray_148),tail,s(index_147)),tail) = s(index_147),
inference(unit_resolution,[status(thm)],[406,24]) ).
tff(408,plain,
s(index_147) = select(store(store(q30,seq,earray_148),tail,s(index_147)),tail),
inference(symmetry,[status(thm)],[407]) ).
tff(409,plain,
( ( index_147 = select(q30,tail) )
<=> ( index_147 = select(q30,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(410,axiom,
index_147 = select(q30,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(411,plain,
index_147 = select(q30,tail),
inference(modus_ponens,[status(thm)],[410,409]) ).
tff(412,plain,
select(q30,tail) = index_147,
inference(symmetry,[status(thm)],[411]) ).
tff(413,plain,
s(select(q30,tail)) = s(index_147),
inference(monotonicity,[status(thm)],[412]) ).
tff(414,plain,
s(select(q30,tail)) = index_153,
inference(transitivity,[status(thm)],[413,408,405,386]) ).
tff(415,plain,
s(s(select(q30,tail))) = s(index_153),
inference(monotonicity,[status(thm)],[414]) ).
tff(416,plain,
s(index_153) = s(s(select(q30,tail))),
inference(symmetry,[status(thm)],[415]) ).
tff(417,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q31,seq,earray_154),tail,s(index_153)),tail) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(418,plain,
select(store(store(q31,seq,earray_154),tail,s(index_153)),tail) = s(index_153),
inference(unit_resolution,[status(thm)],[417,24]) ).
tff(419,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(420,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(421,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[420,419]) ).
tff(422,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
( ( queue_155 = store(q31,seq,earray_154) )
<=> ( queue_155 = store(q31,seq,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(424,axiom,
queue_155 = store(q31,seq,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(425,plain,
queue_155 = store(q31,seq,earray_154),
inference(modus_ponens,[status(thm)],[424,423]) ).
tff(426,plain,
store(q31,seq,earray_154) = queue_155,
inference(symmetry,[status(thm)],[425]) ).
tff(427,plain,
store(store(q31,seq,earray_154),tail,s(index_153)) = store(queue_155,tail,index_156),
inference(monotonicity,[status(thm)],[426,422]) ).
tff(428,plain,
store(queue_155,tail,index_156) = store(store(q31,seq,earray_154),tail,s(index_153)),
inference(symmetry,[status(thm)],[427]) ).
tff(429,plain,
( ( queue_157 = store(queue_155,tail,index_156) )
<=> ( queue_157 = store(queue_155,tail,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(430,axiom,
queue_157 = store(queue_155,tail,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(431,plain,
queue_157 = store(queue_155,tail,index_156),
inference(modus_ponens,[status(thm)],[430,429]) ).
tff(432,plain,
( ( q32 = queue_157 )
<=> ( q32 = queue_157 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(433,axiom,
q32 = queue_157,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp292) ).
tff(434,plain,
q32 = queue_157,
inference(modus_ponens,[status(thm)],[433,432]) ).
tff(435,plain,
q32 = store(store(q31,seq,earray_154),tail,s(index_153)),
inference(transitivity,[status(thm)],[434,431,428]) ).
tff(436,plain,
select(q32,tail) = select(store(store(q31,seq,earray_154),tail,s(index_153)),tail),
inference(monotonicity,[status(thm)],[435]) ).
tff(437,plain,
( ( index_159 = select(q32,tail) )
<=> ( index_159 = select(q32,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(438,axiom,
index_159 = select(q32,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(439,plain,
index_159 = select(q32,tail),
inference(modus_ponens,[status(thm)],[438,437]) ).
tff(440,plain,
index_159 = s(s(select(q30,tail))),
inference(transitivity,[status(thm)],[439,436,418,416]) ).
tff(441,plain,
s(index_159) = s(s(s(select(q30,tail)))),
inference(monotonicity,[status(thm)],[440]) ).
tff(442,plain,
s(s(s(select(q30,tail)))) = s(index_159),
inference(symmetry,[status(thm)],[441]) ).
tff(443,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q30,tail)))) = select(q30,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(444,plain,
s(s(s(select(q30,tail)))) = select(q30,tail),
inference(unit_resolution,[status(thm)],[443,187]) ).
tff(445,plain,
select(q30,tail) = s(s(s(select(q30,tail)))),
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(447,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(448,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[447,446]) ).
tff(449,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[448]) ).
tff(450,plain,
( ( queue_143 = store(q29,seq,earray_142) )
<=> ( queue_143 = store(q29,seq,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(451,axiom,
queue_143 = store(q29,seq,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(452,plain,
queue_143 = store(q29,seq,earray_142),
inference(modus_ponens,[status(thm)],[451,450]) ).
tff(453,plain,
store(q29,seq,earray_142) = queue_143,
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
store(store(q29,seq,earray_142),tail,s(index_141)) = store(queue_143,tail,index_144),
inference(monotonicity,[status(thm)],[453,449]) ).
tff(455,plain,
store(queue_143,tail,index_144) = store(store(q29,seq,earray_142),tail,s(index_141)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
( ( queue_145 = store(queue_143,tail,index_144) )
<=> ( queue_145 = store(queue_143,tail,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(457,axiom,
queue_145 = store(queue_143,tail,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(458,plain,
queue_145 = store(queue_143,tail,index_144),
inference(modus_ponens,[status(thm)],[457,456]) ).
tff(459,plain,
( ( q30 = queue_145 )
<=> ( q30 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(460,axiom,
q30 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp290) ).
tff(461,plain,
q30 = queue_145,
inference(modus_ponens,[status(thm)],[460,459]) ).
tff(462,plain,
q30 = store(store(q29,seq,earray_142),tail,s(index_141)),
inference(transitivity,[status(thm)],[461,458,455]) ).
tff(463,plain,
select(q30,tail) = select(store(store(q29,seq,earray_142),tail,s(index_141)),tail),
inference(monotonicity,[status(thm)],[462]) ).
tff(464,plain,
select(store(store(q29,seq,earray_142),tail,s(index_141)),tail) = select(q30,tail),
inference(symmetry,[status(thm)],[463]) ).
tff(465,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q29,seq,earray_142),tail,s(index_141)),tail) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(466,plain,
select(store(store(q29,seq,earray_142),tail,s(index_141)),tail) = s(index_141),
inference(unit_resolution,[status(thm)],[465,24]) ).
tff(467,plain,
s(index_141) = select(store(store(q29,seq,earray_142),tail,s(index_141)),tail),
inference(symmetry,[status(thm)],[466]) ).
tff(468,plain,
( ( index_129 = select(q28,tail) )
<=> ( index_129 = select(q28,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(469,axiom,
index_129 = select(q28,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(470,plain,
index_129 = select(q28,tail),
inference(modus_ponens,[status(thm)],[469,468]) ).
tff(471,plain,
select(q28,tail) = index_129,
inference(symmetry,[status(thm)],[470]) ).
tff(472,plain,
( ( index_126 = s(index_123) )
<=> ( index_126 = s(index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(473,axiom,
index_126 = s(index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(474,plain,
index_126 = s(index_123),
inference(modus_ponens,[status(thm)],[473,472]) ).
tff(475,plain,
s(index_123) = index_126,
inference(symmetry,[status(thm)],[474]) ).
tff(476,plain,
( ( queue_125 = store(q27,seq,earray_124) )
<=> ( queue_125 = store(q27,seq,earray_124) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(477,axiom,
queue_125 = store(q27,seq,earray_124),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(478,plain,
queue_125 = store(q27,seq,earray_124),
inference(modus_ponens,[status(thm)],[477,476]) ).
tff(479,plain,
store(q27,seq,earray_124) = queue_125,
inference(symmetry,[status(thm)],[478]) ).
tff(480,plain,
store(store(q27,seq,earray_124),tail,s(index_123)) = store(queue_125,tail,index_126),
inference(monotonicity,[status(thm)],[479,475]) ).
tff(481,plain,
store(queue_125,tail,index_126) = store(store(q27,seq,earray_124),tail,s(index_123)),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
( ( queue_127 = store(queue_125,tail,index_126) )
<=> ( queue_127 = store(queue_125,tail,index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(483,axiom,
queue_127 = store(queue_125,tail,index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(484,plain,
queue_127 = store(queue_125,tail,index_126),
inference(modus_ponens,[status(thm)],[483,482]) ).
tff(485,plain,
( ( q28 = queue_127 )
<=> ( q28 = queue_127 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(486,axiom,
q28 = queue_127,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp287) ).
tff(487,plain,
q28 = queue_127,
inference(modus_ponens,[status(thm)],[486,485]) ).
tff(488,plain,
q28 = store(store(q27,seq,earray_124),tail,s(index_123)),
inference(transitivity,[status(thm)],[487,484,481]) ).
tff(489,plain,
select(q28,tail) = select(store(store(q27,seq,earray_124),tail,s(index_123)),tail),
inference(monotonicity,[status(thm)],[488]) ).
tff(490,plain,
select(store(store(q27,seq,earray_124),tail,s(index_123)),tail) = select(q28,tail),
inference(symmetry,[status(thm)],[489]) ).
tff(491,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q27,seq,earray_124),tail,s(index_123)),tail) = s(index_123) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(492,plain,
select(store(store(q27,seq,earray_124),tail,s(index_123)),tail) = s(index_123),
inference(unit_resolution,[status(thm)],[491,24]) ).
tff(493,plain,
s(index_123) = select(store(store(q27,seq,earray_124),tail,s(index_123)),tail),
inference(symmetry,[status(thm)],[492]) ).
tff(494,plain,
( ( index_123 = select(q27,tail) )
<=> ( index_123 = select(q27,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(495,axiom,
index_123 = select(q27,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(496,plain,
index_123 = select(q27,tail),
inference(modus_ponens,[status(thm)],[495,494]) ).
tff(497,plain,
select(q27,tail) = index_123,
inference(symmetry,[status(thm)],[496]) ).
tff(498,plain,
s(select(q27,tail)) = s(index_123),
inference(monotonicity,[status(thm)],[497]) ).
tff(499,plain,
s(select(q27,tail)) = index_129,
inference(transitivity,[status(thm)],[498,493,490,471]) ).
tff(500,plain,
s(s(select(q27,tail))) = s(index_129),
inference(monotonicity,[status(thm)],[499]) ).
tff(501,plain,
s(index_129) = s(s(select(q27,tail))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q28,seq,earray_130),tail,s(index_129)),tail) = s(index_129) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(503,plain,
select(store(store(q28,seq,earray_130),tail,s(index_129)),tail) = s(index_129),
inference(unit_resolution,[status(thm)],[502,24]) ).
tff(504,plain,
( ( index_132 = s(index_129) )
<=> ( index_132 = s(index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(505,axiom,
index_132 = s(index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(506,plain,
index_132 = s(index_129),
inference(modus_ponens,[status(thm)],[505,504]) ).
tff(507,plain,
s(index_129) = index_132,
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
( ( queue_131 = store(q28,seq,earray_130) )
<=> ( queue_131 = store(q28,seq,earray_130) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(509,axiom,
queue_131 = store(q28,seq,earray_130),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(510,plain,
queue_131 = store(q28,seq,earray_130),
inference(modus_ponens,[status(thm)],[509,508]) ).
tff(511,plain,
store(q28,seq,earray_130) = queue_131,
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
store(store(q28,seq,earray_130),tail,s(index_129)) = store(queue_131,tail,index_132),
inference(monotonicity,[status(thm)],[511,507]) ).
tff(513,plain,
store(queue_131,tail,index_132) = store(store(q28,seq,earray_130),tail,s(index_129)),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ( queue_133 = store(queue_131,tail,index_132) )
<=> ( queue_133 = store(queue_131,tail,index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(515,axiom,
queue_133 = store(queue_131,tail,index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(516,plain,
queue_133 = store(queue_131,tail,index_132),
inference(modus_ponens,[status(thm)],[515,514]) ).
tff(517,plain,
( ( q29 = queue_133 )
<=> ( q29 = queue_133 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(518,axiom,
q29 = queue_133,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp288) ).
tff(519,plain,
q29 = queue_133,
inference(modus_ponens,[status(thm)],[518,517]) ).
tff(520,plain,
q29 = store(store(q28,seq,earray_130),tail,s(index_129)),
inference(transitivity,[status(thm)],[519,516,513]) ).
tff(521,plain,
select(q29,tail) = select(store(store(q28,seq,earray_130),tail,s(index_129)),tail),
inference(monotonicity,[status(thm)],[520]) ).
tff(522,plain,
( ( index_141 = select(q29,tail) )
<=> ( index_141 = select(q29,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(523,axiom,
index_141 = select(q29,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(524,plain,
index_141 = select(q29,tail),
inference(modus_ponens,[status(thm)],[523,522]) ).
tff(525,plain,
index_141 = s(s(select(q27,tail))),
inference(transitivity,[status(thm)],[524,521,503,501]) ).
tff(526,plain,
s(index_141) = s(s(s(select(q27,tail)))),
inference(monotonicity,[status(thm)],[525]) ).
tff(527,plain,
s(s(s(select(q27,tail)))) = s(index_141),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q27,tail)))) = select(q27,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(529,plain,
s(s(s(select(q27,tail)))) = select(q27,tail),
inference(unit_resolution,[status(thm)],[528,187]) ).
tff(530,plain,
select(q27,tail) = s(s(s(select(q27,tail)))),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ( index_120 = s(index_117) )
<=> ( index_120 = s(index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(532,axiom,
index_120 = s(index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(533,plain,
index_120 = s(index_117),
inference(modus_ponens,[status(thm)],[532,531]) ).
tff(534,plain,
s(index_117) = index_120,
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
( ( queue_119 = store(q26,seq,earray_118) )
<=> ( queue_119 = store(q26,seq,earray_118) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(536,axiom,
queue_119 = store(q26,seq,earray_118),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(537,plain,
queue_119 = store(q26,seq,earray_118),
inference(modus_ponens,[status(thm)],[536,535]) ).
tff(538,plain,
store(q26,seq,earray_118) = queue_119,
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
store(store(q26,seq,earray_118),tail,s(index_117)) = store(queue_119,tail,index_120),
inference(monotonicity,[status(thm)],[538,534]) ).
tff(540,plain,
store(queue_119,tail,index_120) = store(store(q26,seq,earray_118),tail,s(index_117)),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
( ( queue_121 = store(queue_119,tail,index_120) )
<=> ( queue_121 = store(queue_119,tail,index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(542,axiom,
queue_121 = store(queue_119,tail,index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(543,plain,
queue_121 = store(queue_119,tail,index_120),
inference(modus_ponens,[status(thm)],[542,541]) ).
tff(544,plain,
( ( q27 = queue_121 )
<=> ( q27 = queue_121 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(545,axiom,
q27 = queue_121,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp286) ).
tff(546,plain,
q27 = queue_121,
inference(modus_ponens,[status(thm)],[545,544]) ).
tff(547,plain,
q27 = store(store(q26,seq,earray_118),tail,s(index_117)),
inference(transitivity,[status(thm)],[546,543,540]) ).
tff(548,plain,
select(q27,tail) = select(store(store(q26,seq,earray_118),tail,s(index_117)),tail),
inference(monotonicity,[status(thm)],[547]) ).
tff(549,plain,
select(store(store(q26,seq,earray_118),tail,s(index_117)),tail) = select(q27,tail),
inference(symmetry,[status(thm)],[548]) ).
tff(550,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q26,seq,earray_118),tail,s(index_117)),tail) = s(index_117) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(551,plain,
select(store(store(q26,seq,earray_118),tail,s(index_117)),tail) = s(index_117),
inference(unit_resolution,[status(thm)],[550,24]) ).
tff(552,plain,
s(index_117) = select(store(store(q26,seq,earray_118),tail,s(index_117)),tail),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
( ( index_111 = select(q25,tail) )
<=> ( index_111 = select(q25,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(554,axiom,
index_111 = select(q25,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp93) ).
tff(555,plain,
index_111 = select(q25,tail),
inference(modus_ponens,[status(thm)],[554,553]) ).
tff(556,plain,
select(q25,tail) = index_111,
inference(symmetry,[status(thm)],[555]) ).
tff(557,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(558,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(559,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[558,557]) ).
tff(560,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[559]) ).
tff(561,plain,
( ( queue_107 = store(q24,seq,earray_106) )
<=> ( queue_107 = store(q24,seq,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(562,axiom,
queue_107 = store(q24,seq,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(563,plain,
queue_107 = store(q24,seq,earray_106),
inference(modus_ponens,[status(thm)],[562,561]) ).
tff(564,plain,
store(q24,seq,earray_106) = queue_107,
inference(symmetry,[status(thm)],[563]) ).
tff(565,plain,
store(store(q24,seq,earray_106),tail,s(index_105)) = store(queue_107,tail,index_108),
inference(monotonicity,[status(thm)],[564,560]) ).
tff(566,plain,
store(queue_107,tail,index_108) = store(store(q24,seq,earray_106),tail,s(index_105)),
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
( ( queue_109 = store(queue_107,tail,index_108) )
<=> ( queue_109 = store(queue_107,tail,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(568,axiom,
queue_109 = store(queue_107,tail,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(569,plain,
queue_109 = store(queue_107,tail,index_108),
inference(modus_ponens,[status(thm)],[568,567]) ).
tff(570,plain,
( ( q25 = queue_109 )
<=> ( q25 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(571,axiom,
q25 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp284) ).
tff(572,plain,
q25 = queue_109,
inference(modus_ponens,[status(thm)],[571,570]) ).
tff(573,plain,
q25 = store(store(q24,seq,earray_106),tail,s(index_105)),
inference(transitivity,[status(thm)],[572,569,566]) ).
tff(574,plain,
select(q25,tail) = select(store(store(q24,seq,earray_106),tail,s(index_105)),tail),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
select(store(store(q24,seq,earray_106),tail,s(index_105)),tail) = select(q25,tail),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q24,seq,earray_106),tail,s(index_105)),tail) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(577,plain,
select(store(store(q24,seq,earray_106),tail,s(index_105)),tail) = s(index_105),
inference(unit_resolution,[status(thm)],[576,24]) ).
tff(578,plain,
s(index_105) = select(store(store(q24,seq,earray_106),tail,s(index_105)),tail),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
( ( index_105 = select(q24,tail) )
<=> ( index_105 = select(q24,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(580,axiom,
index_105 = select(q24,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(581,plain,
index_105 = select(q24,tail),
inference(modus_ponens,[status(thm)],[580,579]) ).
tff(582,plain,
select(q24,tail) = index_105,
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
s(select(q24,tail)) = s(index_105),
inference(monotonicity,[status(thm)],[582]) ).
tff(584,plain,
s(select(q24,tail)) = index_111,
inference(transitivity,[status(thm)],[583,578,575,556]) ).
tff(585,plain,
s(s(select(q24,tail))) = s(index_111),
inference(monotonicity,[status(thm)],[584]) ).
tff(586,plain,
s(index_111) = s(s(select(q24,tail))),
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q25,seq,earray_112),tail,s(index_111)),tail) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(588,plain,
select(store(store(q25,seq,earray_112),tail,s(index_111)),tail) = s(index_111),
inference(unit_resolution,[status(thm)],[587,24]) ).
tff(589,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(590,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(591,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[590,589]) ).
tff(592,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[591]) ).
tff(593,plain,
( ( queue_113 = store(q25,seq,earray_112) )
<=> ( queue_113 = store(q25,seq,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(594,axiom,
queue_113 = store(q25,seq,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(595,plain,
queue_113 = store(q25,seq,earray_112),
inference(modus_ponens,[status(thm)],[594,593]) ).
tff(596,plain,
store(q25,seq,earray_112) = queue_113,
inference(symmetry,[status(thm)],[595]) ).
tff(597,plain,
store(store(q25,seq,earray_112),tail,s(index_111)) = store(queue_113,tail,index_114),
inference(monotonicity,[status(thm)],[596,592]) ).
tff(598,plain,
store(queue_113,tail,index_114) = store(store(q25,seq,earray_112),tail,s(index_111)),
inference(symmetry,[status(thm)],[597]) ).
tff(599,plain,
( ( queue_115 = store(queue_113,tail,index_114) )
<=> ( queue_115 = store(queue_113,tail,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(600,axiom,
queue_115 = store(queue_113,tail,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(601,plain,
queue_115 = store(queue_113,tail,index_114),
inference(modus_ponens,[status(thm)],[600,599]) ).
tff(602,plain,
( ( q26 = queue_115 )
<=> ( q26 = queue_115 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(603,axiom,
q26 = queue_115,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp285) ).
tff(604,plain,
q26 = queue_115,
inference(modus_ponens,[status(thm)],[603,602]) ).
tff(605,plain,
q26 = store(store(q25,seq,earray_112),tail,s(index_111)),
inference(transitivity,[status(thm)],[604,601,598]) ).
tff(606,plain,
select(q26,tail) = select(store(store(q25,seq,earray_112),tail,s(index_111)),tail),
inference(monotonicity,[status(thm)],[605]) ).
tff(607,plain,
( ( index_117 = select(q26,tail) )
<=> ( index_117 = select(q26,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(608,axiom,
index_117 = select(q26,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp95) ).
tff(609,plain,
index_117 = select(q26,tail),
inference(modus_ponens,[status(thm)],[608,607]) ).
tff(610,plain,
index_117 = s(s(select(q24,tail))),
inference(transitivity,[status(thm)],[609,606,588,586]) ).
tff(611,plain,
s(index_117) = s(s(s(select(q24,tail)))),
inference(monotonicity,[status(thm)],[610]) ).
tff(612,plain,
s(s(s(select(q24,tail)))) = s(index_117),
inference(symmetry,[status(thm)],[611]) ).
tff(613,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q24,tail)))) = select(q24,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(614,plain,
s(s(s(select(q24,tail)))) = select(q24,tail),
inference(unit_resolution,[status(thm)],[613,187]) ).
tff(615,plain,
select(q24,tail) = s(s(s(select(q24,tail)))),
inference(symmetry,[status(thm)],[614]) ).
tff(616,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(617,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(618,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[617,616]) ).
tff(619,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[618]) ).
tff(620,plain,
( ( queue_101 = store(q23,seq,earray_100) )
<=> ( queue_101 = store(q23,seq,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(621,axiom,
queue_101 = store(q23,seq,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(622,plain,
queue_101 = store(q23,seq,earray_100),
inference(modus_ponens,[status(thm)],[621,620]) ).
tff(623,plain,
store(q23,seq,earray_100) = queue_101,
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
store(store(q23,seq,earray_100),tail,s(index_99)) = store(queue_101,tail,index_102),
inference(monotonicity,[status(thm)],[623,619]) ).
tff(625,plain,
store(queue_101,tail,index_102) = store(store(q23,seq,earray_100),tail,s(index_99)),
inference(symmetry,[status(thm)],[624]) ).
tff(626,plain,
( ( queue_103 = store(queue_101,tail,index_102) )
<=> ( queue_103 = store(queue_101,tail,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(627,axiom,
queue_103 = store(queue_101,tail,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(628,plain,
queue_103 = store(queue_101,tail,index_102),
inference(modus_ponens,[status(thm)],[627,626]) ).
tff(629,plain,
( ( q24 = queue_103 )
<=> ( q24 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(630,axiom,
q24 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp283) ).
tff(631,plain,
q24 = queue_103,
inference(modus_ponens,[status(thm)],[630,629]) ).
tff(632,plain,
q24 = store(store(q23,seq,earray_100),tail,s(index_99)),
inference(transitivity,[status(thm)],[631,628,625]) ).
tff(633,plain,
select(q24,tail) = select(store(store(q23,seq,earray_100),tail,s(index_99)),tail),
inference(monotonicity,[status(thm)],[632]) ).
tff(634,plain,
select(store(store(q23,seq,earray_100),tail,s(index_99)),tail) = select(q24,tail),
inference(symmetry,[status(thm)],[633]) ).
tff(635,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q23,seq,earray_100),tail,s(index_99)),tail) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(636,plain,
select(store(store(q23,seq,earray_100),tail,s(index_99)),tail) = s(index_99),
inference(unit_resolution,[status(thm)],[635,24]) ).
tff(637,plain,
s(index_99) = select(store(store(q23,seq,earray_100),tail,s(index_99)),tail),
inference(symmetry,[status(thm)],[636]) ).
tff(638,plain,
( ( index_93 = select(q22,tail) )
<=> ( index_93 = select(q22,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(639,axiom,
index_93 = select(q22,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(640,plain,
index_93 = select(q22,tail),
inference(modus_ponens,[status(thm)],[639,638]) ).
tff(641,plain,
select(q22,tail) = index_93,
inference(symmetry,[status(thm)],[640]) ).
tff(642,plain,
( ( index_90 = s(index_87) )
<=> ( index_90 = s(index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(643,axiom,
index_90 = s(index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(644,plain,
index_90 = s(index_87),
inference(modus_ponens,[status(thm)],[643,642]) ).
tff(645,plain,
s(index_87) = index_90,
inference(symmetry,[status(thm)],[644]) ).
tff(646,plain,
( ( queue_89 = store(q21,seq,earray_88) )
<=> ( queue_89 = store(q21,seq,earray_88) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(647,axiom,
queue_89 = store(q21,seq,earray_88),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp262) ).
tff(648,plain,
queue_89 = store(q21,seq,earray_88),
inference(modus_ponens,[status(thm)],[647,646]) ).
tff(649,plain,
store(q21,seq,earray_88) = queue_89,
inference(symmetry,[status(thm)],[648]) ).
tff(650,plain,
store(store(q21,seq,earray_88),tail,s(index_87)) = store(queue_89,tail,index_90),
inference(monotonicity,[status(thm)],[649,645]) ).
tff(651,plain,
store(queue_89,tail,index_90) = store(store(q21,seq,earray_88),tail,s(index_87)),
inference(symmetry,[status(thm)],[650]) ).
tff(652,plain,
( ( queue_91 = store(queue_89,tail,index_90) )
<=> ( queue_91 = store(queue_89,tail,index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(653,axiom,
queue_91 = store(queue_89,tail,index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp263) ).
tff(654,plain,
queue_91 = store(queue_89,tail,index_90),
inference(modus_ponens,[status(thm)],[653,652]) ).
tff(655,plain,
( ( q22 = queue_91 )
<=> ( q22 = queue_91 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(656,axiom,
q22 = queue_91,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp281) ).
tff(657,plain,
q22 = queue_91,
inference(modus_ponens,[status(thm)],[656,655]) ).
tff(658,plain,
q22 = store(store(q21,seq,earray_88),tail,s(index_87)),
inference(transitivity,[status(thm)],[657,654,651]) ).
tff(659,plain,
select(q22,tail) = select(store(store(q21,seq,earray_88),tail,s(index_87)),tail),
inference(monotonicity,[status(thm)],[658]) ).
tff(660,plain,
select(store(store(q21,seq,earray_88),tail,s(index_87)),tail) = select(q22,tail),
inference(symmetry,[status(thm)],[659]) ).
tff(661,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q21,seq,earray_88),tail,s(index_87)),tail) = s(index_87) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(662,plain,
select(store(store(q21,seq,earray_88),tail,s(index_87)),tail) = s(index_87),
inference(unit_resolution,[status(thm)],[661,24]) ).
tff(663,plain,
s(index_87) = select(store(store(q21,seq,earray_88),tail,s(index_87)),tail),
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
( ( index_87 = select(q21,tail) )
<=> ( index_87 = select(q21,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(665,axiom,
index_87 = select(q21,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(666,plain,
index_87 = select(q21,tail),
inference(modus_ponens,[status(thm)],[665,664]) ).
tff(667,plain,
select(q21,tail) = index_87,
inference(symmetry,[status(thm)],[666]) ).
tff(668,plain,
s(select(q21,tail)) = s(index_87),
inference(monotonicity,[status(thm)],[667]) ).
tff(669,plain,
s(select(q21,tail)) = index_93,
inference(transitivity,[status(thm)],[668,663,660,641]) ).
tff(670,plain,
s(s(select(q21,tail))) = s(index_93),
inference(monotonicity,[status(thm)],[669]) ).
tff(671,plain,
s(index_93) = s(s(select(q21,tail))),
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q22,seq,earray_94),tail,s(index_93)),tail) = s(index_93) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(673,plain,
select(store(store(q22,seq,earray_94),tail,s(index_93)),tail) = s(index_93),
inference(unit_resolution,[status(thm)],[672,24]) ).
tff(674,plain,
( ( index_96 = s(index_93) )
<=> ( index_96 = s(index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(675,axiom,
index_96 = s(index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(676,plain,
index_96 = s(index_93),
inference(modus_ponens,[status(thm)],[675,674]) ).
tff(677,plain,
s(index_93) = index_96,
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
( ( queue_95 = store(q22,seq,earray_94) )
<=> ( queue_95 = store(q22,seq,earray_94) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(679,axiom,
queue_95 = store(q22,seq,earray_94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp264) ).
tff(680,plain,
queue_95 = store(q22,seq,earray_94),
inference(modus_ponens,[status(thm)],[679,678]) ).
tff(681,plain,
store(q22,seq,earray_94) = queue_95,
inference(symmetry,[status(thm)],[680]) ).
tff(682,plain,
store(store(q22,seq,earray_94),tail,s(index_93)) = store(queue_95,tail,index_96),
inference(monotonicity,[status(thm)],[681,677]) ).
tff(683,plain,
store(queue_95,tail,index_96) = store(store(q22,seq,earray_94),tail,s(index_93)),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
( ( queue_97 = store(queue_95,tail,index_96) )
<=> ( queue_97 = store(queue_95,tail,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(685,axiom,
queue_97 = store(queue_95,tail,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp265) ).
tff(686,plain,
queue_97 = store(queue_95,tail,index_96),
inference(modus_ponens,[status(thm)],[685,684]) ).
tff(687,plain,
( ( q23 = queue_97 )
<=> ( q23 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(688,axiom,
q23 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp282) ).
tff(689,plain,
q23 = queue_97,
inference(modus_ponens,[status(thm)],[688,687]) ).
tff(690,plain,
q23 = store(store(q22,seq,earray_94),tail,s(index_93)),
inference(transitivity,[status(thm)],[689,686,683]) ).
tff(691,plain,
select(q23,tail) = select(store(store(q22,seq,earray_94),tail,s(index_93)),tail),
inference(monotonicity,[status(thm)],[690]) ).
tff(692,plain,
( ( index_99 = select(q23,tail) )
<=> ( index_99 = select(q23,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(693,axiom,
index_99 = select(q23,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(694,plain,
index_99 = select(q23,tail),
inference(modus_ponens,[status(thm)],[693,692]) ).
tff(695,plain,
index_99 = s(s(select(q21,tail))),
inference(transitivity,[status(thm)],[694,691,673,671]) ).
tff(696,plain,
s(index_99) = s(s(s(select(q21,tail)))),
inference(monotonicity,[status(thm)],[695]) ).
tff(697,plain,
s(s(s(select(q21,tail)))) = s(index_99),
inference(symmetry,[status(thm)],[696]) ).
tff(698,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q21,tail)))) = select(q21,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(699,plain,
s(s(s(select(q21,tail)))) = select(q21,tail),
inference(unit_resolution,[status(thm)],[698,187]) ).
tff(700,plain,
select(q21,tail) = s(s(s(select(q21,tail)))),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
( ( index_84 = s(index_81) )
<=> ( index_84 = s(index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(702,axiom,
index_84 = s(index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(703,plain,
index_84 = s(index_81),
inference(modus_ponens,[status(thm)],[702,701]) ).
tff(704,plain,
s(index_81) = index_84,
inference(symmetry,[status(thm)],[703]) ).
tff(705,plain,
( ( queue_83 = store(q20,seq,earray_82) )
<=> ( queue_83 = store(q20,seq,earray_82) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(706,axiom,
queue_83 = store(q20,seq,earray_82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp260) ).
tff(707,plain,
queue_83 = store(q20,seq,earray_82),
inference(modus_ponens,[status(thm)],[706,705]) ).
tff(708,plain,
store(q20,seq,earray_82) = queue_83,
inference(symmetry,[status(thm)],[707]) ).
tff(709,plain,
store(store(q20,seq,earray_82),tail,s(index_81)) = store(queue_83,tail,index_84),
inference(monotonicity,[status(thm)],[708,704]) ).
tff(710,plain,
store(queue_83,tail,index_84) = store(store(q20,seq,earray_82),tail,s(index_81)),
inference(symmetry,[status(thm)],[709]) ).
tff(711,plain,
( ( queue_85 = store(queue_83,tail,index_84) )
<=> ( queue_85 = store(queue_83,tail,index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(712,axiom,
queue_85 = store(queue_83,tail,index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp261) ).
tff(713,plain,
queue_85 = store(queue_83,tail,index_84),
inference(modus_ponens,[status(thm)],[712,711]) ).
tff(714,plain,
( ( q21 = queue_85 )
<=> ( q21 = queue_85 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(715,axiom,
q21 = queue_85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp280) ).
tff(716,plain,
q21 = queue_85,
inference(modus_ponens,[status(thm)],[715,714]) ).
tff(717,plain,
q21 = store(store(q20,seq,earray_82),tail,s(index_81)),
inference(transitivity,[status(thm)],[716,713,710]) ).
tff(718,plain,
select(q21,tail) = select(store(store(q20,seq,earray_82),tail,s(index_81)),tail),
inference(monotonicity,[status(thm)],[717]) ).
tff(719,plain,
select(store(store(q20,seq,earray_82),tail,s(index_81)),tail) = select(q21,tail),
inference(symmetry,[status(thm)],[718]) ).
tff(720,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q20,seq,earray_82),tail,s(index_81)),tail) = s(index_81) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(721,plain,
select(store(store(q20,seq,earray_82),tail,s(index_81)),tail) = s(index_81),
inference(unit_resolution,[status(thm)],[720,24]) ).
tff(722,plain,
s(index_81) = select(store(store(q20,seq,earray_82),tail,s(index_81)),tail),
inference(symmetry,[status(thm)],[721]) ).
tff(723,plain,
( ( index_75 = select(q19,tail) )
<=> ( index_75 = select(q19,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(724,axiom,
index_75 = select(q19,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(725,plain,
index_75 = select(q19,tail),
inference(modus_ponens,[status(thm)],[724,723]) ).
tff(726,plain,
select(q19,tail) = index_75,
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(728,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(729,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[728,727]) ).
tff(730,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
( ( queue_65 = store(q18,seq,earray_64) )
<=> ( queue_65 = store(q18,seq,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(732,axiom,
queue_65 = store(q18,seq,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp253) ).
tff(733,plain,
queue_65 = store(q18,seq,earray_64),
inference(modus_ponens,[status(thm)],[732,731]) ).
tff(734,plain,
store(q18,seq,earray_64) = queue_65,
inference(symmetry,[status(thm)],[733]) ).
tff(735,plain,
store(store(q18,seq,earray_64),tail,s(index_63)) = store(queue_65,tail,index_66),
inference(monotonicity,[status(thm)],[734,730]) ).
tff(736,plain,
store(queue_65,tail,index_66) = store(store(q18,seq,earray_64),tail,s(index_63)),
inference(symmetry,[status(thm)],[735]) ).
tff(737,plain,
( ( queue_67 = store(queue_65,tail,index_66) )
<=> ( queue_67 = store(queue_65,tail,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(738,axiom,
queue_67 = store(queue_65,tail,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp254) ).
tff(739,plain,
queue_67 = store(queue_65,tail,index_66),
inference(modus_ponens,[status(thm)],[738,737]) ).
tff(740,plain,
( ( q19 = queue_67 )
<=> ( q19 = queue_67 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(741,axiom,
q19 = queue_67,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp277) ).
tff(742,plain,
q19 = queue_67,
inference(modus_ponens,[status(thm)],[741,740]) ).
tff(743,plain,
q19 = store(store(q18,seq,earray_64),tail,s(index_63)),
inference(transitivity,[status(thm)],[742,739,736]) ).
tff(744,plain,
select(q19,tail) = select(store(store(q18,seq,earray_64),tail,s(index_63)),tail),
inference(monotonicity,[status(thm)],[743]) ).
tff(745,plain,
select(store(store(q18,seq,earray_64),tail,s(index_63)),tail) = select(q19,tail),
inference(symmetry,[status(thm)],[744]) ).
tff(746,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q18,seq,earray_64),tail,s(index_63)),tail) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(747,plain,
select(store(store(q18,seq,earray_64),tail,s(index_63)),tail) = s(index_63),
inference(unit_resolution,[status(thm)],[746,24]) ).
tff(748,plain,
s(index_63) = select(store(store(q18,seq,earray_64),tail,s(index_63)),tail),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
( ( index_63 = select(q18,tail) )
<=> ( index_63 = select(q18,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(750,axiom,
index_63 = select(q18,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(751,plain,
index_63 = select(q18,tail),
inference(modus_ponens,[status(thm)],[750,749]) ).
tff(752,plain,
select(q18,tail) = index_63,
inference(symmetry,[status(thm)],[751]) ).
tff(753,plain,
s(select(q18,tail)) = s(index_63),
inference(monotonicity,[status(thm)],[752]) ).
tff(754,plain,
s(select(q18,tail)) = index_75,
inference(transitivity,[status(thm)],[753,748,745,726]) ).
tff(755,plain,
s(s(select(q18,tail))) = s(index_75),
inference(monotonicity,[status(thm)],[754]) ).
tff(756,plain,
s(index_75) = s(s(select(q18,tail))),
inference(symmetry,[status(thm)],[755]) ).
tff(757,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q19,seq,earray_76),tail,s(index_75)),tail) = s(index_75) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(758,plain,
select(store(store(q19,seq,earray_76),tail,s(index_75)),tail) = s(index_75),
inference(unit_resolution,[status(thm)],[757,24]) ).
tff(759,plain,
( ( index_78 = s(index_75) )
<=> ( index_78 = s(index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(760,axiom,
index_78 = s(index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(761,plain,
index_78 = s(index_75),
inference(modus_ponens,[status(thm)],[760,759]) ).
tff(762,plain,
s(index_75) = index_78,
inference(symmetry,[status(thm)],[761]) ).
tff(763,plain,
( ( queue_77 = store(q19,seq,earray_76) )
<=> ( queue_77 = store(q19,seq,earray_76) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(764,axiom,
queue_77 = store(q19,seq,earray_76),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp258) ).
tff(765,plain,
queue_77 = store(q19,seq,earray_76),
inference(modus_ponens,[status(thm)],[764,763]) ).
tff(766,plain,
store(q19,seq,earray_76) = queue_77,
inference(symmetry,[status(thm)],[765]) ).
tff(767,plain,
store(store(q19,seq,earray_76),tail,s(index_75)) = store(queue_77,tail,index_78),
inference(monotonicity,[status(thm)],[766,762]) ).
tff(768,plain,
store(queue_77,tail,index_78) = store(store(q19,seq,earray_76),tail,s(index_75)),
inference(symmetry,[status(thm)],[767]) ).
tff(769,plain,
( ( queue_79 = store(queue_77,tail,index_78) )
<=> ( queue_79 = store(queue_77,tail,index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(770,axiom,
queue_79 = store(queue_77,tail,index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp259) ).
tff(771,plain,
queue_79 = store(queue_77,tail,index_78),
inference(modus_ponens,[status(thm)],[770,769]) ).
tff(772,plain,
( ( q20 = queue_79 )
<=> ( q20 = queue_79 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(773,axiom,
q20 = queue_79,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp279) ).
tff(774,plain,
q20 = queue_79,
inference(modus_ponens,[status(thm)],[773,772]) ).
tff(775,plain,
q20 = store(store(q19,seq,earray_76),tail,s(index_75)),
inference(transitivity,[status(thm)],[774,771,768]) ).
tff(776,plain,
select(q20,tail) = select(store(store(q19,seq,earray_76),tail,s(index_75)),tail),
inference(monotonicity,[status(thm)],[775]) ).
tff(777,plain,
( ( index_81 = select(q20,tail) )
<=> ( index_81 = select(q20,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(778,axiom,
index_81 = select(q20,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(779,plain,
index_81 = select(q20,tail),
inference(modus_ponens,[status(thm)],[778,777]) ).
tff(780,plain,
index_81 = s(s(select(q18,tail))),
inference(transitivity,[status(thm)],[779,776,758,756]) ).
tff(781,plain,
s(index_81) = s(s(s(select(q18,tail)))),
inference(monotonicity,[status(thm)],[780]) ).
tff(782,plain,
s(s(s(select(q18,tail)))) = s(index_81),
inference(symmetry,[status(thm)],[781]) ).
tff(783,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q18,tail)))) = select(q18,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(784,plain,
s(s(s(select(q18,tail)))) = select(q18,tail),
inference(unit_resolution,[status(thm)],[783,187]) ).
tff(785,plain,
select(q18,tail) = s(s(s(select(q18,tail)))),
inference(symmetry,[status(thm)],[784]) ).
tff(786,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(787,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(788,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[787,786]) ).
tff(789,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[788]) ).
tff(790,plain,
( ( queue_59 = store(q17,seq,earray_58) )
<=> ( queue_59 = store(q17,seq,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(791,axiom,
queue_59 = store(q17,seq,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp251) ).
tff(792,plain,
queue_59 = store(q17,seq,earray_58),
inference(modus_ponens,[status(thm)],[791,790]) ).
tff(793,plain,
store(q17,seq,earray_58) = queue_59,
inference(symmetry,[status(thm)],[792]) ).
tff(794,plain,
store(store(q17,seq,earray_58),tail,s(index_57)) = store(queue_59,tail,index_60),
inference(monotonicity,[status(thm)],[793,789]) ).
tff(795,plain,
store(queue_59,tail,index_60) = store(store(q17,seq,earray_58),tail,s(index_57)),
inference(symmetry,[status(thm)],[794]) ).
tff(796,plain,
( ( queue_61 = store(queue_59,tail,index_60) )
<=> ( queue_61 = store(queue_59,tail,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(797,axiom,
queue_61 = store(queue_59,tail,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp252) ).
tff(798,plain,
queue_61 = store(queue_59,tail,index_60),
inference(modus_ponens,[status(thm)],[797,796]) ).
tff(799,plain,
( ( q18 = queue_61 )
<=> ( q18 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(800,axiom,
q18 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp276) ).
tff(801,plain,
q18 = queue_61,
inference(modus_ponens,[status(thm)],[800,799]) ).
tff(802,plain,
q18 = store(store(q17,seq,earray_58),tail,s(index_57)),
inference(transitivity,[status(thm)],[801,798,795]) ).
tff(803,plain,
select(q18,tail) = select(store(store(q17,seq,earray_58),tail,s(index_57)),tail),
inference(monotonicity,[status(thm)],[802]) ).
tff(804,plain,
select(store(store(q17,seq,earray_58),tail,s(index_57)),tail) = select(q18,tail),
inference(symmetry,[status(thm)],[803]) ).
tff(805,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q17,seq,earray_58),tail,s(index_57)),tail) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(806,plain,
select(store(store(q17,seq,earray_58),tail,s(index_57)),tail) = s(index_57),
inference(unit_resolution,[status(thm)],[805,24]) ).
tff(807,plain,
s(index_57) = select(store(store(q17,seq,earray_58),tail,s(index_57)),tail),
inference(symmetry,[status(thm)],[806]) ).
tff(808,plain,
( ( index_51 = select(q16,tail) )
<=> ( index_51 = select(q16,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(809,axiom,
index_51 = select(q16,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(810,plain,
index_51 = select(q16,tail),
inference(modus_ponens,[status(thm)],[809,808]) ).
tff(811,plain,
select(q16,tail) = index_51,
inference(symmetry,[status(thm)],[810]) ).
tff(812,plain,
( ( index_48 = s(index_45) )
<=> ( index_48 = s(index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(813,axiom,
index_48 = s(index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(814,plain,
index_48 = s(index_45),
inference(modus_ponens,[status(thm)],[813,812]) ).
tff(815,plain,
s(index_45) = index_48,
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
( ( queue_47 = store(q15,seq,earray_46) )
<=> ( queue_47 = store(q15,seq,earray_46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(817,axiom,
queue_47 = store(q15,seq,earray_46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp246) ).
tff(818,plain,
queue_47 = store(q15,seq,earray_46),
inference(modus_ponens,[status(thm)],[817,816]) ).
tff(819,plain,
store(q15,seq,earray_46) = queue_47,
inference(symmetry,[status(thm)],[818]) ).
tff(820,plain,
store(store(q15,seq,earray_46),tail,s(index_45)) = store(queue_47,tail,index_48),
inference(monotonicity,[status(thm)],[819,815]) ).
tff(821,plain,
store(queue_47,tail,index_48) = store(store(q15,seq,earray_46),tail,s(index_45)),
inference(symmetry,[status(thm)],[820]) ).
tff(822,plain,
( ( queue_49 = store(queue_47,tail,index_48) )
<=> ( queue_49 = store(queue_47,tail,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(823,axiom,
queue_49 = store(queue_47,tail,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp247) ).
tff(824,plain,
queue_49 = store(queue_47,tail,index_48),
inference(modus_ponens,[status(thm)],[823,822]) ).
tff(825,plain,
( ( q16 = queue_49 )
<=> ( q16 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(826,axiom,
q16 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp274) ).
tff(827,plain,
q16 = queue_49,
inference(modus_ponens,[status(thm)],[826,825]) ).
tff(828,plain,
q16 = store(store(q15,seq,earray_46),tail,s(index_45)),
inference(transitivity,[status(thm)],[827,824,821]) ).
tff(829,plain,
select(q16,tail) = select(store(store(q15,seq,earray_46),tail,s(index_45)),tail),
inference(monotonicity,[status(thm)],[828]) ).
tff(830,plain,
select(store(store(q15,seq,earray_46),tail,s(index_45)),tail) = select(q16,tail),
inference(symmetry,[status(thm)],[829]) ).
tff(831,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q15,seq,earray_46),tail,s(index_45)),tail) = s(index_45) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(832,plain,
select(store(store(q15,seq,earray_46),tail,s(index_45)),tail) = s(index_45),
inference(unit_resolution,[status(thm)],[831,24]) ).
tff(833,plain,
s(index_45) = select(store(store(q15,seq,earray_46),tail,s(index_45)),tail),
inference(symmetry,[status(thm)],[832]) ).
tff(834,plain,
( ( index_45 = select(q15,tail) )
<=> ( index_45 = select(q15,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(835,axiom,
index_45 = select(q15,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(836,plain,
index_45 = select(q15,tail),
inference(modus_ponens,[status(thm)],[835,834]) ).
tff(837,plain,
select(q15,tail) = index_45,
inference(symmetry,[status(thm)],[836]) ).
tff(838,plain,
s(select(q15,tail)) = s(index_45),
inference(monotonicity,[status(thm)],[837]) ).
tff(839,plain,
s(select(q15,tail)) = index_51,
inference(transitivity,[status(thm)],[838,833,830,811]) ).
tff(840,plain,
s(s(select(q15,tail))) = s(index_51),
inference(monotonicity,[status(thm)],[839]) ).
tff(841,plain,
s(index_51) = s(s(select(q15,tail))),
inference(symmetry,[status(thm)],[840]) ).
tff(842,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q16,seq,earray_52),tail,s(index_51)),tail) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(843,plain,
select(store(store(q16,seq,earray_52),tail,s(index_51)),tail) = s(index_51),
inference(unit_resolution,[status(thm)],[842,24]) ).
tff(844,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(845,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(846,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[845,844]) ).
tff(847,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[846]) ).
tff(848,plain,
( ( queue_53 = store(q16,seq,earray_52) )
<=> ( queue_53 = store(q16,seq,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(849,axiom,
queue_53 = store(q16,seq,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp249) ).
tff(850,plain,
queue_53 = store(q16,seq,earray_52),
inference(modus_ponens,[status(thm)],[849,848]) ).
tff(851,plain,
store(q16,seq,earray_52) = queue_53,
inference(symmetry,[status(thm)],[850]) ).
tff(852,plain,
store(store(q16,seq,earray_52),tail,s(index_51)) = store(queue_53,tail,index_54),
inference(monotonicity,[status(thm)],[851,847]) ).
tff(853,plain,
store(queue_53,tail,index_54) = store(store(q16,seq,earray_52),tail,s(index_51)),
inference(symmetry,[status(thm)],[852]) ).
tff(854,plain,
( ( queue_55 = store(queue_53,tail,index_54) )
<=> ( queue_55 = store(queue_53,tail,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(855,axiom,
queue_55 = store(queue_53,tail,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp250) ).
tff(856,plain,
queue_55 = store(queue_53,tail,index_54),
inference(modus_ponens,[status(thm)],[855,854]) ).
tff(857,plain,
( ( q17 = queue_55 )
<=> ( q17 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(858,axiom,
q17 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp275) ).
tff(859,plain,
q17 = queue_55,
inference(modus_ponens,[status(thm)],[858,857]) ).
tff(860,plain,
q17 = store(store(q16,seq,earray_52),tail,s(index_51)),
inference(transitivity,[status(thm)],[859,856,853]) ).
tff(861,plain,
select(q17,tail) = select(store(store(q16,seq,earray_52),tail,s(index_51)),tail),
inference(monotonicity,[status(thm)],[860]) ).
tff(862,plain,
( ( index_57 = select(q17,tail) )
<=> ( index_57 = select(q17,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(863,axiom,
index_57 = select(q17,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(864,plain,
index_57 = select(q17,tail),
inference(modus_ponens,[status(thm)],[863,862]) ).
tff(865,plain,
index_57 = s(s(select(q15,tail))),
inference(transitivity,[status(thm)],[864,861,843,841]) ).
tff(866,plain,
s(index_57) = s(s(s(select(q15,tail)))),
inference(monotonicity,[status(thm)],[865]) ).
tff(867,plain,
s(s(s(select(q15,tail)))) = s(index_57),
inference(symmetry,[status(thm)],[866]) ).
tff(868,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q15,tail)))) = select(q15,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(869,plain,
s(s(s(select(q15,tail)))) = select(q15,tail),
inference(unit_resolution,[status(thm)],[868,187]) ).
tff(870,plain,
select(q15,tail) = s(s(s(select(q15,tail)))),
inference(symmetry,[status(thm)],[869]) ).
tff(871,plain,
( ( index_42 = s(index_39) )
<=> ( index_42 = s(index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(872,axiom,
index_42 = s(index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(873,plain,
index_42 = s(index_39),
inference(modus_ponens,[status(thm)],[872,871]) ).
tff(874,plain,
s(index_39) = index_42,
inference(symmetry,[status(thm)],[873]) ).
tff(875,plain,
( ( queue_41 = store(q14,seq,earray_40) )
<=> ( queue_41 = store(q14,seq,earray_40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(876,axiom,
queue_41 = store(q14,seq,earray_40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(877,plain,
queue_41 = store(q14,seq,earray_40),
inference(modus_ponens,[status(thm)],[876,875]) ).
tff(878,plain,
store(q14,seq,earray_40) = queue_41,
inference(symmetry,[status(thm)],[877]) ).
tff(879,plain,
store(store(q14,seq,earray_40),tail,s(index_39)) = store(queue_41,tail,index_42),
inference(monotonicity,[status(thm)],[878,874]) ).
tff(880,plain,
store(queue_41,tail,index_42) = store(store(q14,seq,earray_40),tail,s(index_39)),
inference(symmetry,[status(thm)],[879]) ).
tff(881,plain,
( ( queue_43 = store(queue_41,tail,index_42) )
<=> ( queue_43 = store(queue_41,tail,index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(882,axiom,
queue_43 = store(queue_41,tail,index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(883,plain,
queue_43 = store(queue_41,tail,index_42),
inference(modus_ponens,[status(thm)],[882,881]) ).
tff(884,plain,
( ( q15 = queue_43 )
<=> ( q15 = queue_43 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(885,axiom,
q15 = queue_43,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp273) ).
tff(886,plain,
q15 = queue_43,
inference(modus_ponens,[status(thm)],[885,884]) ).
tff(887,plain,
q15 = store(store(q14,seq,earray_40),tail,s(index_39)),
inference(transitivity,[status(thm)],[886,883,880]) ).
tff(888,plain,
select(q15,tail) = select(store(store(q14,seq,earray_40),tail,s(index_39)),tail),
inference(monotonicity,[status(thm)],[887]) ).
tff(889,plain,
select(store(store(q14,seq,earray_40),tail,s(index_39)),tail) = select(q15,tail),
inference(symmetry,[status(thm)],[888]) ).
tff(890,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q14,seq,earray_40),tail,s(index_39)),tail) = s(index_39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(891,plain,
select(store(store(q14,seq,earray_40),tail,s(index_39)),tail) = s(index_39),
inference(unit_resolution,[status(thm)],[890,24]) ).
tff(892,plain,
s(index_39) = select(store(store(q14,seq,earray_40),tail,s(index_39)),tail),
inference(symmetry,[status(thm)],[891]) ).
tff(893,plain,
( ( index_33 = select(q13,tail) )
<=> ( index_33 = select(q13,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(894,axiom,
index_33 = select(q13,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(895,plain,
index_33 = select(q13,tail),
inference(modus_ponens,[status(thm)],[894,893]) ).
tff(896,plain,
select(q13,tail) = index_33,
inference(symmetry,[status(thm)],[895]) ).
tff(897,plain,
( ( q13 = queue_31 )
<=> ( q13 = queue_31 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(898,axiom,
q13 = queue_31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp271) ).
tff(899,plain,
q13 = queue_31,
inference(modus_ponens,[status(thm)],[898,897]) ).
tff(900,plain,
queue_31 = q13,
inference(symmetry,[status(thm)],[899]) ).
tff(901,plain,
( ( queue_31 = store(queue_29,tail,index_30) )
<=> ( queue_31 = store(queue_29,tail,index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(902,axiom,
queue_31 = store(queue_29,tail,index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(903,plain,
queue_31 = store(queue_29,tail,index_30),
inference(modus_ponens,[status(thm)],[902,901]) ).
tff(904,plain,
store(queue_29,tail,index_30) = queue_31,
inference(symmetry,[status(thm)],[903]) ).
tff(905,plain,
( ( index_30 = s(index_27) )
<=> ( index_30 = s(index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(906,axiom,
index_30 = s(index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(907,plain,
index_30 = s(index_27),
inference(modus_ponens,[status(thm)],[906,905]) ).
tff(908,plain,
s(index_27) = index_30,
inference(symmetry,[status(thm)],[907]) ).
tff(909,plain,
( ( queue_29 = store(q12,seq,earray_28) )
<=> ( queue_29 = store(q12,seq,earray_28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(910,axiom,
queue_29 = store(q12,seq,earray_28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(911,plain,
queue_29 = store(q12,seq,earray_28),
inference(modus_ponens,[status(thm)],[910,909]) ).
tff(912,plain,
store(q12,seq,earray_28) = queue_29,
inference(symmetry,[status(thm)],[911]) ).
tff(913,plain,
store(store(q12,seq,earray_28),tail,s(index_27)) = store(queue_29,tail,index_30),
inference(monotonicity,[status(thm)],[912,908]) ).
tff(914,plain,
store(store(q12,seq,earray_28),tail,s(index_27)) = q13,
inference(transitivity,[status(thm)],[913,904,900]) ).
tff(915,plain,
select(store(store(q12,seq,earray_28),tail,s(index_27)),tail) = select(q13,tail),
inference(monotonicity,[status(thm)],[914]) ).
tff(916,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q12,seq,earray_28),tail,s(index_27)),tail) = s(index_27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(917,plain,
select(store(store(q12,seq,earray_28),tail,s(index_27)),tail) = s(index_27),
inference(unit_resolution,[status(thm)],[916,24]) ).
tff(918,plain,
s(index_27) = select(store(store(q12,seq,earray_28),tail,s(index_27)),tail),
inference(symmetry,[status(thm)],[917]) ).
tff(919,plain,
( ( index_27 = select(q12,tail) )
<=> ( index_27 = select(q12,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(920,axiom,
index_27 = select(q12,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(921,plain,
index_27 = select(q12,tail),
inference(modus_ponens,[status(thm)],[920,919]) ).
tff(922,plain,
select(q12,tail) = index_27,
inference(symmetry,[status(thm)],[921]) ).
tff(923,plain,
s(select(q12,tail)) = s(index_27),
inference(monotonicity,[status(thm)],[922]) ).
tff(924,plain,
s(select(q12,tail)) = index_33,
inference(transitivity,[status(thm)],[923,918,915,896]) ).
tff(925,plain,
s(s(select(q12,tail))) = s(index_33),
inference(monotonicity,[status(thm)],[924]) ).
tff(926,plain,
s(index_33) = s(s(select(q12,tail))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q13,seq,earray_34),tail,s(index_33)),tail) = s(index_33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(928,plain,
select(store(store(q13,seq,earray_34),tail,s(index_33)),tail) = s(index_33),
inference(unit_resolution,[status(thm)],[927,24]) ).
tff(929,plain,
( ( q14 = queue_37 )
<=> ( q14 = queue_37 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(930,axiom,
q14 = queue_37,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp272) ).
tff(931,plain,
q14 = queue_37,
inference(modus_ponens,[status(thm)],[930,929]) ).
tff(932,plain,
queue_37 = q14,
inference(symmetry,[status(thm)],[931]) ).
tff(933,plain,
( ( queue_37 = store(queue_35,tail,index_36) )
<=> ( queue_37 = store(queue_35,tail,index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(934,axiom,
queue_37 = store(queue_35,tail,index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(935,plain,
queue_37 = store(queue_35,tail,index_36),
inference(modus_ponens,[status(thm)],[934,933]) ).
tff(936,plain,
store(queue_35,tail,index_36) = queue_37,
inference(symmetry,[status(thm)],[935]) ).
tff(937,plain,
( ( index_36 = s(index_33) )
<=> ( index_36 = s(index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(938,axiom,
index_36 = s(index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(939,plain,
index_36 = s(index_33),
inference(modus_ponens,[status(thm)],[938,937]) ).
tff(940,plain,
s(index_33) = index_36,
inference(symmetry,[status(thm)],[939]) ).
tff(941,plain,
( ( queue_35 = store(q13,seq,earray_34) )
<=> ( queue_35 = store(q13,seq,earray_34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(942,axiom,
queue_35 = store(q13,seq,earray_34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(943,plain,
queue_35 = store(q13,seq,earray_34),
inference(modus_ponens,[status(thm)],[942,941]) ).
tff(944,plain,
store(q13,seq,earray_34) = queue_35,
inference(symmetry,[status(thm)],[943]) ).
tff(945,plain,
store(store(q13,seq,earray_34),tail,s(index_33)) = store(queue_35,tail,index_36),
inference(monotonicity,[status(thm)],[944,940]) ).
tff(946,plain,
store(store(q13,seq,earray_34),tail,s(index_33)) = q14,
inference(transitivity,[status(thm)],[945,936,932]) ).
tff(947,plain,
select(store(store(q13,seq,earray_34),tail,s(index_33)),tail) = select(q14,tail),
inference(monotonicity,[status(thm)],[946]) ).
tff(948,plain,
select(q14,tail) = select(store(store(q13,seq,earray_34),tail,s(index_33)),tail),
inference(symmetry,[status(thm)],[947]) ).
tff(949,plain,
( ( index_39 = select(q14,tail) )
<=> ( index_39 = select(q14,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(950,axiom,
index_39 = select(q14,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(951,plain,
index_39 = select(q14,tail),
inference(modus_ponens,[status(thm)],[950,949]) ).
tff(952,plain,
index_39 = s(s(select(q12,tail))),
inference(transitivity,[status(thm)],[951,948,928,926]) ).
tff(953,plain,
s(index_39) = s(s(s(select(q12,tail)))),
inference(monotonicity,[status(thm)],[952]) ).
tff(954,plain,
s(s(s(select(q12,tail)))) = s(index_39),
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q12,tail)))) = select(q12,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(956,plain,
s(s(s(select(q12,tail)))) = select(q12,tail),
inference(unit_resolution,[status(thm)],[955,187]) ).
tff(957,plain,
select(q12,tail) = s(s(s(select(q12,tail)))),
inference(symmetry,[status(thm)],[956]) ).
tff(958,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(959,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(960,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[959,958]) ).
tff(961,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[960]) ).
tff(962,plain,
( ( queue_23 = store(q11,seq,earray_22) )
<=> ( queue_23 = store(q11,seq,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(963,axiom,
queue_23 = store(q11,seq,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(964,plain,
queue_23 = store(q11,seq,earray_22),
inference(modus_ponens,[status(thm)],[963,962]) ).
tff(965,plain,
store(q11,seq,earray_22) = queue_23,
inference(symmetry,[status(thm)],[964]) ).
tff(966,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = store(queue_23,tail,index_24),
inference(monotonicity,[status(thm)],[965,961]) ).
tff(967,plain,
store(queue_23,tail,index_24) = store(store(q11,seq,earray_22),tail,s(index_21)),
inference(symmetry,[status(thm)],[966]) ).
tff(968,plain,
( ( queue_25 = store(queue_23,tail,index_24) )
<=> ( queue_25 = store(queue_23,tail,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(969,axiom,
queue_25 = store(queue_23,tail,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(970,plain,
queue_25 = store(queue_23,tail,index_24),
inference(modus_ponens,[status(thm)],[969,968]) ).
tff(971,plain,
( ( q12 = queue_25 )
<=> ( q12 = queue_25 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(972,axiom,
q12 = queue_25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp270) ).
tff(973,plain,
q12 = queue_25,
inference(modus_ponens,[status(thm)],[972,971]) ).
tff(974,plain,
q12 = store(store(q11,seq,earray_22),tail,s(index_21)),
inference(transitivity,[status(thm)],[973,970,967]) ).
tff(975,plain,
select(q12,tail) = select(store(store(q11,seq,earray_22),tail,s(index_21)),tail),
inference(monotonicity,[status(thm)],[974]) ).
tff(976,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = select(q12,tail),
inference(symmetry,[status(thm)],[975]) ).
tff(977,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(978,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),tail) = s(index_21),
inference(unit_resolution,[status(thm)],[977,24]) ).
tff(979,plain,
s(index_21) = select(store(store(q11,seq,earray_22),tail,s(index_21)),tail),
inference(symmetry,[status(thm)],[978]) ).
tff(980,plain,
( ( index_15 = select(q10,tail) )
<=> ( index_15 = select(q10,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(981,axiom,
index_15 = select(q10,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(982,plain,
index_15 = select(q10,tail),
inference(modus_ponens,[status(thm)],[981,980]) ).
tff(983,plain,
select(q10,tail) = index_15,
inference(symmetry,[status(thm)],[982]) ).
tff(984,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(985,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp268) ).
tff(986,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[985,984]) ).
tff(987,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[986]) ).
tff(988,plain,
( ( queue_13 = store(queue_11,tail,index_12) )
<=> ( queue_13 = store(queue_11,tail,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(989,axiom,
queue_13 = store(queue_11,tail,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(990,plain,
queue_13 = store(queue_11,tail,index_12),
inference(modus_ponens,[status(thm)],[989,988]) ).
tff(991,plain,
store(queue_11,tail,index_12) = queue_13,
inference(symmetry,[status(thm)],[990]) ).
tff(992,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(993,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(994,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[993,992]) ).
tff(995,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[994]) ).
tff(996,plain,
( ( queue_11 = store(q9,seq,earray_10) )
<=> ( queue_11 = store(q9,seq,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(997,axiom,
queue_11 = store(q9,seq,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(998,plain,
queue_11 = store(q9,seq,earray_10),
inference(modus_ponens,[status(thm)],[997,996]) ).
tff(999,plain,
store(q9,seq,earray_10) = queue_11,
inference(symmetry,[status(thm)],[998]) ).
tff(1000,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = store(queue_11,tail,index_12),
inference(monotonicity,[status(thm)],[999,995]) ).
tff(1001,plain,
store(store(q9,seq,earray_10),tail,s(index_9)) = q10,
inference(transitivity,[status(thm)],[1000,991,987]) ).
tff(1002,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = select(q10,tail),
inference(monotonicity,[status(thm)],[1001]) ).
tff(1003,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(1004,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),tail) = s(index_9),
inference(unit_resolution,[status(thm)],[1003,24]) ).
tff(1005,plain,
s(index_9) = select(store(store(q9,seq,earray_10),tail,s(index_9)),tail),
inference(symmetry,[status(thm)],[1004]) ).
tff(1006,plain,
( ( index_9 = select(q9,tail) )
<=> ( index_9 = select(q9,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1007,axiom,
index_9 = select(q9,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(1008,plain,
index_9 = select(q9,tail),
inference(modus_ponens,[status(thm)],[1007,1006]) ).
tff(1009,plain,
select(q9,tail) = index_9,
inference(symmetry,[status(thm)],[1008]) ).
tff(1010,plain,
s(select(q9,tail)) = s(index_9),
inference(monotonicity,[status(thm)],[1009]) ).
tff(1011,plain,
s(select(q9,tail)) = index_15,
inference(transitivity,[status(thm)],[1010,1005,1002,983]) ).
tff(1012,plain,
s(s(select(q9,tail))) = s(index_15),
inference(monotonicity,[status(thm)],[1011]) ).
tff(1013,plain,
s(index_15) = s(s(select(q9,tail))),
inference(symmetry,[status(thm)],[1012]) ).
tff(1014,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(1015,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = s(index_15),
inference(unit_resolution,[status(thm)],[1014,24]) ).
tff(1016,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1017,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp269) ).
tff(1018,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[1017,1016]) ).
tff(1019,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[1018]) ).
tff(1020,plain,
( ( queue_19 = store(queue_17,tail,index_18) )
<=> ( queue_19 = store(queue_17,tail,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1021,axiom,
queue_19 = store(queue_17,tail,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(1022,plain,
queue_19 = store(queue_17,tail,index_18),
inference(modus_ponens,[status(thm)],[1021,1020]) ).
tff(1023,plain,
store(queue_17,tail,index_18) = queue_19,
inference(symmetry,[status(thm)],[1022]) ).
tff(1024,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1025,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(1026,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[1025,1024]) ).
tff(1027,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[1026]) ).
tff(1028,plain,
( ( queue_17 = store(q10,seq,earray_16) )
<=> ( queue_17 = store(q10,seq,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1029,axiom,
queue_17 = store(q10,seq,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(1030,plain,
queue_17 = store(q10,seq,earray_16),
inference(modus_ponens,[status(thm)],[1029,1028]) ).
tff(1031,plain,
store(q10,seq,earray_16) = queue_17,
inference(symmetry,[status(thm)],[1030]) ).
tff(1032,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = store(queue_17,tail,index_18),
inference(monotonicity,[status(thm)],[1031,1027]) ).
tff(1033,plain,
store(store(q10,seq,earray_16),tail,s(index_15)) = q11,
inference(transitivity,[status(thm)],[1032,1023,1019]) ).
tff(1034,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),tail) = select(q11,tail),
inference(monotonicity,[status(thm)],[1033]) ).
tff(1035,plain,
select(q11,tail) = select(store(store(q10,seq,earray_16),tail,s(index_15)),tail),
inference(symmetry,[status(thm)],[1034]) ).
tff(1036,plain,
( ( index_21 = select(q11,tail) )
<=> ( index_21 = select(q11,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1037,axiom,
index_21 = select(q11,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(1038,plain,
index_21 = select(q11,tail),
inference(modus_ponens,[status(thm)],[1037,1036]) ).
tff(1039,plain,
index_21 = s(s(select(q9,tail))),
inference(transitivity,[status(thm)],[1038,1035,1015,1013]) ).
tff(1040,plain,
s(index_21) = s(s(s(select(q9,tail)))),
inference(monotonicity,[status(thm)],[1039]) ).
tff(1041,plain,
s(s(s(select(q9,tail)))) = s(index_21),
inference(symmetry,[status(thm)],[1040]) ).
tff(1042,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q9,tail)))) = select(q9,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1043,plain,
s(s(s(select(q9,tail)))) = select(q9,tail),
inference(unit_resolution,[status(thm)],[1042,187]) ).
tff(1044,plain,
select(q9,tail) = s(s(s(select(q9,tail)))),
inference(symmetry,[status(thm)],[1043]) ).
tff(1045,plain,
( ( index_258 = s(index_255) )
<=> ( index_258 = s(index_255) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1046,axiom,
index_258 = s(index_255),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(1047,plain,
index_258 = s(index_255),
inference(modus_ponens,[status(thm)],[1046,1045]) ).
tff(1048,plain,
s(index_255) = index_258,
inference(symmetry,[status(thm)],[1047]) ).
tff(1049,plain,
( ( queue_257 = store(q8,seq,earray_256) )
<=> ( queue_257 = store(q8,seq,earray_256) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1050,axiom,
queue_257 = store(q8,seq,earray_256),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(1051,plain,
queue_257 = store(q8,seq,earray_256),
inference(modus_ponens,[status(thm)],[1050,1049]) ).
tff(1052,plain,
store(q8,seq,earray_256) = queue_257,
inference(symmetry,[status(thm)],[1051]) ).
tff(1053,plain,
store(store(q8,seq,earray_256),tail,s(index_255)) = store(queue_257,tail,index_258),
inference(monotonicity,[status(thm)],[1052,1048]) ).
tff(1054,plain,
store(queue_257,tail,index_258) = store(store(q8,seq,earray_256),tail,s(index_255)),
inference(symmetry,[status(thm)],[1053]) ).
tff(1055,plain,
( ( queue_259 = store(queue_257,tail,index_258) )
<=> ( queue_259 = store(queue_257,tail,index_258) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1056,axiom,
queue_259 = store(queue_257,tail,index_258),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(1057,plain,
queue_259 = store(queue_257,tail,index_258),
inference(modus_ponens,[status(thm)],[1056,1055]) ).
tff(1058,plain,
( ( q9 = queue_259 )
<=> ( q9 = queue_259 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1059,axiom,
q9 = queue_259,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp309) ).
tff(1060,plain,
q9 = queue_259,
inference(modus_ponens,[status(thm)],[1059,1058]) ).
tff(1061,plain,
q9 = store(store(q8,seq,earray_256),tail,s(index_255)),
inference(transitivity,[status(thm)],[1060,1057,1054]) ).
tff(1062,plain,
select(q9,tail) = select(store(store(q8,seq,earray_256),tail,s(index_255)),tail),
inference(monotonicity,[status(thm)],[1061]) ).
tff(1063,plain,
select(store(store(q8,seq,earray_256),tail,s(index_255)),tail) = select(q9,tail),
inference(symmetry,[status(thm)],[1062]) ).
tff(1064,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q8,seq,earray_256),tail,s(index_255)),tail) = s(index_255) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1065,plain,
select(store(store(q8,seq,earray_256),tail,s(index_255)),tail) = s(index_255),
inference(unit_resolution,[status(thm)],[1064,24]) ).
tff(1066,plain,
s(index_255) = select(store(store(q8,seq,earray_256),tail,s(index_255)),tail),
inference(symmetry,[status(thm)],[1065]) ).
tff(1067,plain,
( ( index_249 = select(q7,tail) )
<=> ( index_249 = select(q7,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1068,axiom,
index_249 = select(q7,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(1069,plain,
index_249 = select(q7,tail),
inference(modus_ponens,[status(thm)],[1068,1067]) ).
tff(1070,plain,
select(q7,tail) = index_249,
inference(symmetry,[status(thm)],[1069]) ).
tff(1071,plain,
( ( q7 = queue_247 )
<=> ( q7 = queue_247 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1072,axiom,
q7 = queue_247,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp307) ).
tff(1073,plain,
q7 = queue_247,
inference(modus_ponens,[status(thm)],[1072,1071]) ).
tff(1074,plain,
queue_247 = q7,
inference(symmetry,[status(thm)],[1073]) ).
tff(1075,plain,
( ( queue_247 = store(queue_245,tail,index_246) )
<=> ( queue_247 = store(queue_245,tail,index_246) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1076,axiom,
queue_247 = store(queue_245,tail,index_246),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(1077,plain,
queue_247 = store(queue_245,tail,index_246),
inference(modus_ponens,[status(thm)],[1076,1075]) ).
tff(1078,plain,
store(queue_245,tail,index_246) = queue_247,
inference(symmetry,[status(thm)],[1077]) ).
tff(1079,plain,
( ( index_246 = s(index_243) )
<=> ( index_246 = s(index_243) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1080,axiom,
index_246 = s(index_243),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(1081,plain,
index_246 = s(index_243),
inference(modus_ponens,[status(thm)],[1080,1079]) ).
tff(1082,plain,
s(index_243) = index_246,
inference(symmetry,[status(thm)],[1081]) ).
tff(1083,plain,
( ( queue_245 = store(q6,seq,earray_244) )
<=> ( queue_245 = store(q6,seq,earray_244) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1084,axiom,
queue_245 = store(q6,seq,earray_244),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(1085,plain,
queue_245 = store(q6,seq,earray_244),
inference(modus_ponens,[status(thm)],[1084,1083]) ).
tff(1086,plain,
store(q6,seq,earray_244) = queue_245,
inference(symmetry,[status(thm)],[1085]) ).
tff(1087,plain,
store(store(q6,seq,earray_244),tail,s(index_243)) = store(queue_245,tail,index_246),
inference(monotonicity,[status(thm)],[1086,1082]) ).
tff(1088,plain,
store(store(q6,seq,earray_244),tail,s(index_243)) = q7,
inference(transitivity,[status(thm)],[1087,1078,1074]) ).
tff(1089,plain,
select(store(store(q6,seq,earray_244),tail,s(index_243)),tail) = select(q7,tail),
inference(monotonicity,[status(thm)],[1088]) ).
tff(1090,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q6,seq,earray_244),tail,s(index_243)),tail) = s(index_243) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1091,plain,
select(store(store(q6,seq,earray_244),tail,s(index_243)),tail) = s(index_243),
inference(unit_resolution,[status(thm)],[1090,24]) ).
tff(1092,plain,
s(index_243) = select(store(store(q6,seq,earray_244),tail,s(index_243)),tail),
inference(symmetry,[status(thm)],[1091]) ).
tff(1093,plain,
( ( index_243 = select(q6,tail) )
<=> ( index_243 = select(q6,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1094,axiom,
index_243 = select(q6,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(1095,plain,
index_243 = select(q6,tail),
inference(modus_ponens,[status(thm)],[1094,1093]) ).
tff(1096,plain,
select(q6,tail) = index_243,
inference(symmetry,[status(thm)],[1095]) ).
tff(1097,plain,
s(select(q6,tail)) = s(index_243),
inference(monotonicity,[status(thm)],[1096]) ).
tff(1098,plain,
s(select(q6,tail)) = index_249,
inference(transitivity,[status(thm)],[1097,1092,1089,1070]) ).
tff(1099,plain,
s(s(select(q6,tail))) = s(index_249),
inference(monotonicity,[status(thm)],[1098]) ).
tff(1100,plain,
s(index_249) = s(s(select(q6,tail))),
inference(symmetry,[status(thm)],[1099]) ).
tff(1101,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q7,seq,earray_250),tail,s(index_249)),tail) = s(index_249) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1102,plain,
select(store(store(q7,seq,earray_250),tail,s(index_249)),tail) = s(index_249),
inference(unit_resolution,[status(thm)],[1101,24]) ).
tff(1103,plain,
( ( q8 = queue_253 )
<=> ( q8 = queue_253 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1104,axiom,
q8 = queue_253,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp308) ).
tff(1105,plain,
q8 = queue_253,
inference(modus_ponens,[status(thm)],[1104,1103]) ).
tff(1106,plain,
queue_253 = q8,
inference(symmetry,[status(thm)],[1105]) ).
tff(1107,plain,
( ( queue_253 = store(queue_251,tail,index_252) )
<=> ( queue_253 = store(queue_251,tail,index_252) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1108,axiom,
queue_253 = store(queue_251,tail,index_252),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(1109,plain,
queue_253 = store(queue_251,tail,index_252),
inference(modus_ponens,[status(thm)],[1108,1107]) ).
tff(1110,plain,
store(queue_251,tail,index_252) = queue_253,
inference(symmetry,[status(thm)],[1109]) ).
tff(1111,plain,
( ( index_252 = s(index_249) )
<=> ( index_252 = s(index_249) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1112,axiom,
index_252 = s(index_249),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(1113,plain,
index_252 = s(index_249),
inference(modus_ponens,[status(thm)],[1112,1111]) ).
tff(1114,plain,
s(index_249) = index_252,
inference(symmetry,[status(thm)],[1113]) ).
tff(1115,plain,
( ( queue_251 = store(q7,seq,earray_250) )
<=> ( queue_251 = store(q7,seq,earray_250) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1116,axiom,
queue_251 = store(q7,seq,earray_250),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(1117,plain,
queue_251 = store(q7,seq,earray_250),
inference(modus_ponens,[status(thm)],[1116,1115]) ).
tff(1118,plain,
store(q7,seq,earray_250) = queue_251,
inference(symmetry,[status(thm)],[1117]) ).
tff(1119,plain,
store(store(q7,seq,earray_250),tail,s(index_249)) = store(queue_251,tail,index_252),
inference(monotonicity,[status(thm)],[1118,1114]) ).
tff(1120,plain,
store(store(q7,seq,earray_250),tail,s(index_249)) = q8,
inference(transitivity,[status(thm)],[1119,1110,1106]) ).
tff(1121,plain,
select(store(store(q7,seq,earray_250),tail,s(index_249)),tail) = select(q8,tail),
inference(monotonicity,[status(thm)],[1120]) ).
tff(1122,plain,
select(q8,tail) = select(store(store(q7,seq,earray_250),tail,s(index_249)),tail),
inference(symmetry,[status(thm)],[1121]) ).
tff(1123,plain,
( ( index_255 = select(q8,tail) )
<=> ( index_255 = select(q8,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1124,axiom,
index_255 = select(q8,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(1125,plain,
index_255 = select(q8,tail),
inference(modus_ponens,[status(thm)],[1124,1123]) ).
tff(1126,plain,
index_255 = s(s(select(q6,tail))),
inference(transitivity,[status(thm)],[1125,1122,1102,1100]) ).
tff(1127,plain,
s(index_255) = s(s(s(select(q6,tail)))),
inference(monotonicity,[status(thm)],[1126]) ).
tff(1128,plain,
s(s(s(select(q6,tail)))) = s(index_255),
inference(symmetry,[status(thm)],[1127]) ).
tff(1129,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q6,tail)))) = select(q6,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1130,plain,
s(s(s(select(q6,tail)))) = select(q6,tail),
inference(unit_resolution,[status(thm)],[1129,187]) ).
tff(1131,plain,
select(q6,tail) = s(s(s(select(q6,tail)))),
inference(symmetry,[status(thm)],[1130]) ).
tff(1132,plain,
( ( index_240 = s(index_237) )
<=> ( index_240 = s(index_237) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1133,axiom,
index_240 = s(index_237),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(1134,plain,
index_240 = s(index_237),
inference(modus_ponens,[status(thm)],[1133,1132]) ).
tff(1135,plain,
s(index_237) = index_240,
inference(symmetry,[status(thm)],[1134]) ).
tff(1136,plain,
( ( queue_239 = store(q5,seq,earray_238) )
<=> ( queue_239 = store(q5,seq,earray_238) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1137,axiom,
queue_239 = store(q5,seq,earray_238),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(1138,plain,
queue_239 = store(q5,seq,earray_238),
inference(modus_ponens,[status(thm)],[1137,1136]) ).
tff(1139,plain,
store(q5,seq,earray_238) = queue_239,
inference(symmetry,[status(thm)],[1138]) ).
tff(1140,plain,
store(store(q5,seq,earray_238),tail,s(index_237)) = store(queue_239,tail,index_240),
inference(monotonicity,[status(thm)],[1139,1135]) ).
tff(1141,plain,
store(queue_239,tail,index_240) = store(store(q5,seq,earray_238),tail,s(index_237)),
inference(symmetry,[status(thm)],[1140]) ).
tff(1142,plain,
( ( queue_241 = store(queue_239,tail,index_240) )
<=> ( queue_241 = store(queue_239,tail,index_240) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1143,axiom,
queue_241 = store(queue_239,tail,index_240),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(1144,plain,
queue_241 = store(queue_239,tail,index_240),
inference(modus_ponens,[status(thm)],[1143,1142]) ).
tff(1145,plain,
( ( q6 = queue_241 )
<=> ( q6 = queue_241 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1146,axiom,
q6 = queue_241,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp306) ).
tff(1147,plain,
q6 = queue_241,
inference(modus_ponens,[status(thm)],[1146,1145]) ).
tff(1148,plain,
q6 = store(store(q5,seq,earray_238),tail,s(index_237)),
inference(transitivity,[status(thm)],[1147,1144,1141]) ).
tff(1149,plain,
select(q6,tail) = select(store(store(q5,seq,earray_238),tail,s(index_237)),tail),
inference(monotonicity,[status(thm)],[1148]) ).
tff(1150,plain,
select(store(store(q5,seq,earray_238),tail,s(index_237)),tail) = select(q6,tail),
inference(symmetry,[status(thm)],[1149]) ).
tff(1151,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q5,seq,earray_238),tail,s(index_237)),tail) = s(index_237) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1152,plain,
select(store(store(q5,seq,earray_238),tail,s(index_237)),tail) = s(index_237),
inference(unit_resolution,[status(thm)],[1151,24]) ).
tff(1153,plain,
s(index_237) = select(store(store(q5,seq,earray_238),tail,s(index_237)),tail),
inference(symmetry,[status(thm)],[1152]) ).
tff(1154,plain,
( ( index_231 = select(q4,tail) )
<=> ( index_231 = select(q4,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1155,axiom,
index_231 = select(q4,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(1156,plain,
index_231 = select(q4,tail),
inference(modus_ponens,[status(thm)],[1155,1154]) ).
tff(1157,plain,
select(q4,tail) = index_231,
inference(symmetry,[status(thm)],[1156]) ).
tff(1158,plain,
( ( q4 = queue_205 )
<=> ( q4 = queue_205 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1159,axiom,
q4 = queue_205,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp300) ).
tff(1160,plain,
q4 = queue_205,
inference(modus_ponens,[status(thm)],[1159,1158]) ).
tff(1161,plain,
queue_205 = q4,
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ( queue_205 = store(queue_203,tail,index_204) )
<=> ( queue_205 = store(queue_203,tail,index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1163,axiom,
queue_205 = store(queue_203,tail,index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(1164,plain,
queue_205 = store(queue_203,tail,index_204),
inference(modus_ponens,[status(thm)],[1163,1162]) ).
tff(1165,plain,
store(queue_203,tail,index_204) = queue_205,
inference(symmetry,[status(thm)],[1164]) ).
tff(1166,plain,
( ( index_204 = s(index_201) )
<=> ( index_204 = s(index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1167,axiom,
index_204 = s(index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(1168,plain,
index_204 = s(index_201),
inference(modus_ponens,[status(thm)],[1167,1166]) ).
tff(1169,plain,
s(index_201) = index_204,
inference(symmetry,[status(thm)],[1168]) ).
tff(1170,plain,
( ( queue_203 = store(q3,seq,earray_202) )
<=> ( queue_203 = store(q3,seq,earray_202) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1171,axiom,
queue_203 = store(q3,seq,earray_202),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(1172,plain,
queue_203 = store(q3,seq,earray_202),
inference(modus_ponens,[status(thm)],[1171,1170]) ).
tff(1173,plain,
store(q3,seq,earray_202) = queue_203,
inference(symmetry,[status(thm)],[1172]) ).
tff(1174,plain,
store(store(q3,seq,earray_202),tail,s(index_201)) = store(queue_203,tail,index_204),
inference(monotonicity,[status(thm)],[1173,1169]) ).
tff(1175,plain,
store(store(q3,seq,earray_202),tail,s(index_201)) = q4,
inference(transitivity,[status(thm)],[1174,1165,1161]) ).
tff(1176,plain,
select(store(store(q3,seq,earray_202),tail,s(index_201)),tail) = select(q4,tail),
inference(monotonicity,[status(thm)],[1175]) ).
tff(1177,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q3,seq,earray_202),tail,s(index_201)),tail) = s(index_201) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1178,plain,
select(store(store(q3,seq,earray_202),tail,s(index_201)),tail) = s(index_201),
inference(unit_resolution,[status(thm)],[1177,24]) ).
tff(1179,plain,
s(index_201) = select(store(store(q3,seq,earray_202),tail,s(index_201)),tail),
inference(symmetry,[status(thm)],[1178]) ).
tff(1180,plain,
( ( index_201 = select(q3,tail) )
<=> ( index_201 = select(q3,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1181,axiom,
index_201 = select(q3,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(1182,plain,
index_201 = select(q3,tail),
inference(modus_ponens,[status(thm)],[1181,1180]) ).
tff(1183,plain,
select(q3,tail) = index_201,
inference(symmetry,[status(thm)],[1182]) ).
tff(1184,plain,
s(select(q3,tail)) = s(index_201),
inference(monotonicity,[status(thm)],[1183]) ).
tff(1185,plain,
s(select(q3,tail)) = index_231,
inference(transitivity,[status(thm)],[1184,1179,1176,1157]) ).
tff(1186,plain,
s(s(select(q3,tail))) = s(index_231),
inference(monotonicity,[status(thm)],[1185]) ).
tff(1187,plain,
s(index_231) = s(s(select(q3,tail))),
inference(symmetry,[status(thm)],[1186]) ).
tff(1188,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q4,seq,earray_232),tail,s(index_231)),tail) = s(index_231) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1189,plain,
select(store(store(q4,seq,earray_232),tail,s(index_231)),tail) = s(index_231),
inference(unit_resolution,[status(thm)],[1188,24]) ).
tff(1190,plain,
( ( q5 = queue_235 )
<=> ( q5 = queue_235 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1191,axiom,
q5 = queue_235,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp305) ).
tff(1192,plain,
q5 = queue_235,
inference(modus_ponens,[status(thm)],[1191,1190]) ).
tff(1193,plain,
queue_235 = q5,
inference(symmetry,[status(thm)],[1192]) ).
tff(1194,plain,
( ( queue_235 = store(queue_233,tail,index_234) )
<=> ( queue_235 = store(queue_233,tail,index_234) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1195,axiom,
queue_235 = store(queue_233,tail,index_234),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(1196,plain,
queue_235 = store(queue_233,tail,index_234),
inference(modus_ponens,[status(thm)],[1195,1194]) ).
tff(1197,plain,
store(queue_233,tail,index_234) = queue_235,
inference(symmetry,[status(thm)],[1196]) ).
tff(1198,plain,
( ( index_234 = s(index_231) )
<=> ( index_234 = s(index_231) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1199,axiom,
index_234 = s(index_231),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(1200,plain,
index_234 = s(index_231),
inference(modus_ponens,[status(thm)],[1199,1198]) ).
tff(1201,plain,
s(index_231) = index_234,
inference(symmetry,[status(thm)],[1200]) ).
tff(1202,plain,
( ( queue_233 = store(q4,seq,earray_232) )
<=> ( queue_233 = store(q4,seq,earray_232) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1203,axiom,
queue_233 = store(q4,seq,earray_232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(1204,plain,
queue_233 = store(q4,seq,earray_232),
inference(modus_ponens,[status(thm)],[1203,1202]) ).
tff(1205,plain,
store(q4,seq,earray_232) = queue_233,
inference(symmetry,[status(thm)],[1204]) ).
tff(1206,plain,
store(store(q4,seq,earray_232),tail,s(index_231)) = store(queue_233,tail,index_234),
inference(monotonicity,[status(thm)],[1205,1201]) ).
tff(1207,plain,
store(store(q4,seq,earray_232),tail,s(index_231)) = q5,
inference(transitivity,[status(thm)],[1206,1197,1193]) ).
tff(1208,plain,
select(store(store(q4,seq,earray_232),tail,s(index_231)),tail) = select(q5,tail),
inference(monotonicity,[status(thm)],[1207]) ).
tff(1209,plain,
select(q5,tail) = select(store(store(q4,seq,earray_232),tail,s(index_231)),tail),
inference(symmetry,[status(thm)],[1208]) ).
tff(1210,plain,
( ( index_237 = select(q5,tail) )
<=> ( index_237 = select(q5,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1211,axiom,
index_237 = select(q5,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(1212,plain,
index_237 = select(q5,tail),
inference(modus_ponens,[status(thm)],[1211,1210]) ).
tff(1213,plain,
index_237 = s(s(select(q3,tail))),
inference(transitivity,[status(thm)],[1212,1209,1189,1187]) ).
tff(1214,plain,
s(index_237) = s(s(s(select(q3,tail)))),
inference(monotonicity,[status(thm)],[1213]) ).
tff(1215,plain,
s(s(s(select(q3,tail)))) = s(index_237),
inference(symmetry,[status(thm)],[1214]) ).
tff(1216,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q3,tail)))) = select(q3,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1217,plain,
s(s(s(select(q3,tail)))) = select(q3,tail),
inference(unit_resolution,[status(thm)],[1216,187]) ).
tff(1218,plain,
select(q3,tail) = s(s(s(select(q3,tail)))),
inference(symmetry,[status(thm)],[1217]) ).
tff(1219,plain,
( ( index_138 = s(index_135) )
<=> ( index_138 = s(index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1220,axiom,
index_138 = s(index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(1221,plain,
index_138 = s(index_135),
inference(modus_ponens,[status(thm)],[1220,1219]) ).
tff(1222,plain,
s(index_135) = index_138,
inference(symmetry,[status(thm)],[1221]) ).
tff(1223,plain,
( ( queue_137 = store(q2,seq,earray_136) )
<=> ( queue_137 = store(q2,seq,earray_136) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1224,axiom,
queue_137 = store(q2,seq,earray_136),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(1225,plain,
queue_137 = store(q2,seq,earray_136),
inference(modus_ponens,[status(thm)],[1224,1223]) ).
tff(1226,plain,
store(q2,seq,earray_136) = queue_137,
inference(symmetry,[status(thm)],[1225]) ).
tff(1227,plain,
store(store(q2,seq,earray_136),tail,s(index_135)) = store(queue_137,tail,index_138),
inference(monotonicity,[status(thm)],[1226,1222]) ).
tff(1228,plain,
store(queue_137,tail,index_138) = store(store(q2,seq,earray_136),tail,s(index_135)),
inference(symmetry,[status(thm)],[1227]) ).
tff(1229,plain,
( ( queue_139 = store(queue_137,tail,index_138) )
<=> ( queue_139 = store(queue_137,tail,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1230,axiom,
queue_139 = store(queue_137,tail,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(1231,plain,
queue_139 = store(queue_137,tail,index_138),
inference(modus_ponens,[status(thm)],[1230,1229]) ).
tff(1232,plain,
( ( q3 = queue_139 )
<=> ( q3 = queue_139 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1233,axiom,
q3 = queue_139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp289) ).
tff(1234,plain,
q3 = queue_139,
inference(modus_ponens,[status(thm)],[1233,1232]) ).
tff(1235,plain,
q3 = store(store(q2,seq,earray_136),tail,s(index_135)),
inference(transitivity,[status(thm)],[1234,1231,1228]) ).
tff(1236,plain,
select(q3,tail) = select(store(store(q2,seq,earray_136),tail,s(index_135)),tail),
inference(monotonicity,[status(thm)],[1235]) ).
tff(1237,plain,
select(store(store(q2,seq,earray_136),tail,s(index_135)),tail) = select(q3,tail),
inference(symmetry,[status(thm)],[1236]) ).
tff(1238,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q2,seq,earray_136),tail,s(index_135)),tail) = s(index_135) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1239,plain,
select(store(store(q2,seq,earray_136),tail,s(index_135)),tail) = s(index_135),
inference(unit_resolution,[status(thm)],[1238,24]) ).
tff(1240,plain,
s(index_135) = select(store(store(q2,seq,earray_136),tail,s(index_135)),tail),
inference(symmetry,[status(thm)],[1239]) ).
tff(1241,plain,
( ( index_69 = select(q1,tail) )
<=> ( index_69 = select(q1,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1242,axiom,
index_69 = select(q1,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(1243,plain,
index_69 = select(q1,tail),
inference(modus_ponens,[status(thm)],[1242,1241]) ).
tff(1244,plain,
select(q1,tail) = index_69,
inference(symmetry,[status(thm)],[1243]) ).
tff(1245,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1246,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp267) ).
tff(1247,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[1246,1245]) ).
tff(1248,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[1247]) ).
tff(1249,plain,
( ( queue_7 = store(queue_5,tail,index_6) )
<=> ( queue_7 = store(queue_5,tail,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1250,axiom,
queue_7 = store(queue_5,tail,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp255) ).
tff(1251,plain,
queue_7 = store(queue_5,tail,index_6),
inference(modus_ponens,[status(thm)],[1250,1249]) ).
tff(1252,plain,
store(queue_5,tail,index_6) = queue_7,
inference(symmetry,[status(thm)],[1251]) ).
tff(1253,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1254,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(1255,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[1254,1253]) ).
tff(1256,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[1255]) ).
tff(1257,plain,
( ( queue_5 = store(q0,seq,earray_4) )
<=> ( queue_5 = store(q0,seq,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1258,axiom,
queue_5 = store(q0,seq,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp248) ).
tff(1259,plain,
queue_5 = store(q0,seq,earray_4),
inference(modus_ponens,[status(thm)],[1258,1257]) ).
tff(1260,plain,
store(q0,seq,earray_4) = queue_5,
inference(symmetry,[status(thm)],[1259]) ).
tff(1261,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = store(queue_5,tail,index_6),
inference(monotonicity,[status(thm)],[1260,1256]) ).
tff(1262,plain,
store(store(q0,seq,earray_4),tail,s(index_3)) = q1,
inference(transitivity,[status(thm)],[1261,1252,1248]) ).
tff(1263,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = select(q1,tail),
inference(monotonicity,[status(thm)],[1262]) ).
tff(1264,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(1265,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),tail) = s(index_3),
inference(unit_resolution,[status(thm)],[1264,24]) ).
tff(1266,plain,
s(index_3) = select(store(store(q0,seq,earray_4),tail,s(index_3)),tail),
inference(symmetry,[status(thm)],[1265]) ).
tff(1267,plain,
( ( index_3 = select(q0,tail) )
<=> ( index_3 = select(q0,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1268,axiom,
index_3 = select(q0,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(1269,plain,
index_3 = select(q0,tail),
inference(modus_ponens,[status(thm)],[1268,1267]) ).
tff(1270,plain,
select(q0,tail) = index_3,
inference(symmetry,[status(thm)],[1269]) ).
tff(1271,plain,
s(select(q0,tail)) = s(index_3),
inference(monotonicity,[status(thm)],[1270]) ).
tff(1272,plain,
s(select(q0,tail)) = index_69,
inference(transitivity,[status(thm)],[1271,1266,1263,1244]) ).
tff(1273,plain,
s(s(select(q0,tail))) = s(index_69),
inference(monotonicity,[status(thm)],[1272]) ).
tff(1274,plain,
s(index_69) = s(s(select(q0,tail))),
inference(symmetry,[status(thm)],[1273]) ).
tff(1275,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(q1,seq,earray_70),tail,s(index_69)),tail) = s(index_69) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1276,plain,
select(store(store(q1,seq,earray_70),tail,s(index_69)),tail) = s(index_69),
inference(unit_resolution,[status(thm)],[1275,24]) ).
tff(1277,plain,
( ( q2 = queue_73 )
<=> ( q2 = queue_73 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1278,axiom,
q2 = queue_73,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp278) ).
tff(1279,plain,
q2 = queue_73,
inference(modus_ponens,[status(thm)],[1278,1277]) ).
tff(1280,plain,
queue_73 = q2,
inference(symmetry,[status(thm)],[1279]) ).
tff(1281,plain,
( ( queue_73 = store(queue_71,tail,index_72) )
<=> ( queue_73 = store(queue_71,tail,index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1282,axiom,
queue_73 = store(queue_71,tail,index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp257) ).
tff(1283,plain,
queue_73 = store(queue_71,tail,index_72),
inference(modus_ponens,[status(thm)],[1282,1281]) ).
tff(1284,plain,
store(queue_71,tail,index_72) = queue_73,
inference(symmetry,[status(thm)],[1283]) ).
tff(1285,plain,
( ( index_72 = s(index_69) )
<=> ( index_72 = s(index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1286,axiom,
index_72 = s(index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(1287,plain,
index_72 = s(index_69),
inference(modus_ponens,[status(thm)],[1286,1285]) ).
tff(1288,plain,
s(index_69) = index_72,
inference(symmetry,[status(thm)],[1287]) ).
tff(1289,plain,
( ( queue_71 = store(q1,seq,earray_70) )
<=> ( queue_71 = store(q1,seq,earray_70) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1290,axiom,
queue_71 = store(q1,seq,earray_70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp256) ).
tff(1291,plain,
queue_71 = store(q1,seq,earray_70),
inference(modus_ponens,[status(thm)],[1290,1289]) ).
tff(1292,plain,
store(q1,seq,earray_70) = queue_71,
inference(symmetry,[status(thm)],[1291]) ).
tff(1293,plain,
store(store(q1,seq,earray_70),tail,s(index_69)) = store(queue_71,tail,index_72),
inference(monotonicity,[status(thm)],[1292,1288]) ).
tff(1294,plain,
store(store(q1,seq,earray_70),tail,s(index_69)) = q2,
inference(transitivity,[status(thm)],[1293,1284,1280]) ).
tff(1295,plain,
select(store(store(q1,seq,earray_70),tail,s(index_69)),tail) = select(q2,tail),
inference(monotonicity,[status(thm)],[1294]) ).
tff(1296,plain,
select(q2,tail) = select(store(store(q1,seq,earray_70),tail,s(index_69)),tail),
inference(symmetry,[status(thm)],[1295]) ).
tff(1297,plain,
( ( index_135 = select(q2,tail) )
<=> ( index_135 = select(q2,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1298,axiom,
index_135 = select(q2,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(1299,plain,
index_135 = select(q2,tail),
inference(modus_ponens,[status(thm)],[1298,1297]) ).
tff(1300,plain,
index_135 = s(s(select(q0,tail))),
inference(transitivity,[status(thm)],[1299,1296,1276,1274]) ).
tff(1301,plain,
s(index_135) = s(s(s(select(q0,tail)))),
inference(monotonicity,[status(thm)],[1300]) ).
tff(1302,plain,
s(s(s(select(q0,tail)))) = s(index_135),
inference(symmetry,[status(thm)],[1301]) ).
tff(1303,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q0,tail)))) = select(q0,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1304,plain,
s(s(s(select(q0,tail)))) = select(q0,tail),
inference(unit_resolution,[status(thm)],[1303,187]) ).
tff(1305,plain,
select(q0,tail) = s(s(s(select(q0,tail)))),
inference(symmetry,[status(thm)],[1304]) ).
tff(1306,plain,
( ( index_0 = select(q,tail) )
<=> ( index_0 = select(q,tail) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1307,axiom,
index_0 = select(q,tail),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(1308,plain,
index_0 = select(q,tail),
inference(modus_ponens,[status(thm)],[1307,1306]) ).
tff(1309,plain,
select(q,tail) = index_0,
inference(symmetry,[status(thm)],[1308]) ).
tff(1310,plain,
store(q,head,select(q,tail)) = store(q,head,index_0),
inference(monotonicity,[status(thm)],[1309]) ).
tff(1311,plain,
store(q,head,index_0) = store(q,head,select(q,tail)),
inference(symmetry,[status(thm)],[1310]) ).
tff(1312,plain,
( ( queue_1 = store(q,head,index_0) )
<=> ( queue_1 = store(q,head,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1313,axiom,
queue_1 = store(q,head,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(1314,plain,
queue_1 = store(q,head,index_0),
inference(modus_ponens,[status(thm)],[1313,1312]) ).
tff(1315,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1316,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp266) ).
tff(1317,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[1316,1315]) ).
tff(1318,plain,
q0 = store(q,head,select(q,tail)),
inference(transitivity,[status(thm)],[1317,1314,1311]) ).
tff(1319,plain,
select(q0,tail) = select(store(q,head,select(q,tail)),tail),
inference(monotonicity,[status(thm)],[1318]) ).
tff(1320,plain,
select(store(q,head,select(q,tail)),tail) = select(q0,tail),
inference(symmetry,[status(thm)],[1319]) ).
tff(1321,plain,
( ( head != tail )
<=> ( head != tail ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1322,axiom,
head != tail,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_tail) ).
tff(1323,plain,
head != tail,
inference(modus_ponens,[status(thm)],[1322,1321]) ).
tff(1324,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(1325,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(1326,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)],[1325,1324]) ).
tff(1327,plain,
select(store(q,head,select(q,tail)),tail) = select(q,tail),
inference(unit_resolution,[status(thm)],[1326,89,1323]) ).
tff(1328,plain,
select(q,tail) = select(store(q,head,select(q,tail)),tail),
inference(symmetry,[status(thm)],[1327]) ).
tff(1329,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(1330,plain,
select(store(q,head,select(q,tail)),head) = select(q,tail),
inference(unit_resolution,[status(thm)],[1329,24]) ).
tff(1331,plain,
select(store(q,head,select(q,tail)),head) = select(store(q,head,index_0),head),
inference(monotonicity,[status(thm)],[1310]) ).
tff(1332,plain,
select(store(q,head,index_0),head) = select(store(q,head,select(q,tail)),head),
inference(symmetry,[status(thm)],[1331]) ).
tff(1333,plain,
( ( seq = head )
<=> ( head = seq ) ),
inference(commutativity,[status(thm)],[]) ).
tff(1334,plain,
( ( head = seq )
<=> ( seq = head ) ),
inference(symmetry,[status(thm)],[1333]) ).
tff(1335,plain,
( ( head != seq )
<=> ( seq != head ) ),
inference(monotonicity,[status(thm)],[1334]) ).
tff(1336,plain,
( ( head != seq )
<=> ( head != seq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1337,axiom,
head != seq,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',head_distinct_from_seq) ).
tff(1338,plain,
head != seq,
inference(modus_ponens,[status(thm)],[1337,1336]) ).
tff(1339,plain,
seq != head,
inference(modus_ponens,[status(thm)],[1338,1335]) ).
tff(1340,plain,
( ( ~ ! [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(1341,plain,
( ~ ! [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(1342,plain,
( ~ ! [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)],[1341,1340]) ).
tff(1343,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)],[1342,89,1339]) ).
tff(1344,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1345,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(1346,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[1345,1344]) ).
tff(1347,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[1346]) ).
tff(1348,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(1349,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)],[1348,24]) ).
tff(1350,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[1317]) ).
tff(1351,plain,
store(q,head,index_0) = queue_1,
inference(symmetry,[status(thm)],[1314]) ).
tff(1352,plain,
store(q,head,index_0) = q0,
inference(transitivity,[status(thm)],[1351,1350]) ).
tff(1353,plain,
store(store(q,head,index_0),seq,store(earray_2,index_3,e0)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[1352,1347]) ).
tff(1354,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)],[1353]) ).
tff(1355,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)],[1354]) ).
tff(1356,plain,
( ( ~ ! [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(1357,plain,
( ~ ! [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(1358,plain,
( ~ ! [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)],[1357,1356]) ).
tff(1359,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)],[1358,89,83]) ).
tff(1360,plain,
select(store(store(q0,seq,earray_4),tail,s(index_3)),seq) = select(q1,seq),
inference(monotonicity,[status(thm)],[1262]) ).
tff(1361,plain,
select(q1,seq) = select(store(store(q0,seq,earray_4),tail,s(index_3)),seq),
inference(symmetry,[status(thm)],[1360]) ).
tff(1362,plain,
select(q1,seq) = earray_4,
inference(transitivity,[status(thm)],[1361,1359,1355,1349,1347]) ).
tff(1363,plain,
store(store(q,head,index_0),seq,select(q1,seq)) = store(q0,seq,earray_4),
inference(monotonicity,[status(thm)],[1352,1362]) ).
tff(1364,plain,
select(store(store(q,head,index_0),seq,select(q1,seq)),head) = select(store(q0,seq,earray_4),head),
inference(monotonicity,[status(thm)],[1363]) ).
tff(1365,plain,
select(store(q0,seq,earray_4),head) = select(store(store(q,head,index_0),seq,select(q1,seq)),head),
inference(symmetry,[status(thm)],[1364]) ).
tff(1366,plain,
( ( tail = head )
<=> ( head = tail ) ),
inference(commutativity,[status(thm)],[]) ).
tff(1367,plain,
( ( head = tail )
<=> ( tail = head ) ),
inference(symmetry,[status(thm)],[1366]) ).
tff(1368,plain,
( ( head != tail )
<=> ( tail != head ) ),
inference(monotonicity,[status(thm)],[1367]) ).
tff(1369,plain,
tail != head,
inference(modus_ponens,[status(thm)],[1323,1368]) ).
tff(1370,plain,
( ( ~ ! [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,select(q13,tail)),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,select(q13,tail)),head) = select(store(q0,seq,earray_4),head) ) ) ),
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) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,select(q13,tail)),head) = select(store(q0,seq,earray_4),head) ) ),
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) ) )
| ( tail = head )
| ( select(store(store(q0,seq,earray_4),tail,select(q13,tail)),head) = select(store(q0,seq,earray_4),head) ) ),
inference(modus_ponens,[status(thm)],[1371,1370]) ).
tff(1373,plain,
select(store(store(q0,seq,earray_4),tail,select(q13,tail)),head) = select(store(q0,seq,earray_4),head),
inference(unit_resolution,[status(thm)],[1372,89,1369]) ).
tff(1374,plain,
select(q1,tail) = select(store(store(q0,seq,earray_4),tail,s(index_3)),tail),
inference(symmetry,[status(thm)],[1263]) ).
tff(1375,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q1,tail)))) = select(q1,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1376,plain,
s(s(s(select(q1,tail)))) = select(q1,tail),
inference(unit_resolution,[status(thm)],[1375,187]) ).
tff(1377,plain,
select(q2,tail) = index_135,
inference(symmetry,[status(thm)],[1299]) ).
tff(1378,plain,
s(index_69) = select(store(store(q1,seq,earray_70),tail,s(index_69)),tail),
inference(symmetry,[status(thm)],[1276]) ).
tff(1379,plain,
s(select(q1,tail)) = s(index_69),
inference(monotonicity,[status(thm)],[1244]) ).
tff(1380,plain,
s(select(q1,tail)) = index_135,
inference(transitivity,[status(thm)],[1379,1378,1295,1377]) ).
tff(1381,plain,
s(s(select(q1,tail))) = s(index_135),
inference(monotonicity,[status(thm)],[1380]) ).
tff(1382,plain,
s(s(select(q1,tail))) = index_201,
inference(transitivity,[status(thm)],[1381,1240,1237,1183]) ).
tff(1383,plain,
s(s(s(select(q1,tail)))) = s(index_201),
inference(monotonicity,[status(thm)],[1382]) ).
tff(1384,plain,
s(index_201) = s(s(s(select(q1,tail)))),
inference(symmetry,[status(thm)],[1383]) ).
tff(1385,plain,
select(q4,tail) = select(store(store(q3,seq,earray_202),tail,s(index_201)),tail),
inference(symmetry,[status(thm)],[1176]) ).
tff(1386,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q4,tail)))) = select(q4,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1387,plain,
s(s(s(select(q4,tail)))) = select(q4,tail),
inference(unit_resolution,[status(thm)],[1386,187]) ).
tff(1388,plain,
select(q5,tail) = index_237,
inference(symmetry,[status(thm)],[1212]) ).
tff(1389,plain,
s(index_231) = select(store(store(q4,seq,earray_232),tail,s(index_231)),tail),
inference(symmetry,[status(thm)],[1189]) ).
tff(1390,plain,
s(select(q4,tail)) = s(index_231),
inference(monotonicity,[status(thm)],[1157]) ).
tff(1391,plain,
s(select(q4,tail)) = index_237,
inference(transitivity,[status(thm)],[1390,1389,1208,1388]) ).
tff(1392,plain,
s(s(select(q4,tail))) = s(index_237),
inference(monotonicity,[status(thm)],[1391]) ).
tff(1393,plain,
s(s(select(q4,tail))) = index_243,
inference(transitivity,[status(thm)],[1392,1153,1150,1096]) ).
tff(1394,plain,
s(s(s(select(q4,tail)))) = s(index_243),
inference(monotonicity,[status(thm)],[1393]) ).
tff(1395,plain,
s(index_243) = s(s(s(select(q4,tail)))),
inference(symmetry,[status(thm)],[1394]) ).
tff(1396,plain,
select(q7,tail) = select(store(store(q6,seq,earray_244),tail,s(index_243)),tail),
inference(symmetry,[status(thm)],[1089]) ).
tff(1397,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q7,tail)))) = select(q7,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1398,plain,
s(s(s(select(q7,tail)))) = select(q7,tail),
inference(unit_resolution,[status(thm)],[1397,187]) ).
tff(1399,plain,
select(q8,tail) = index_255,
inference(symmetry,[status(thm)],[1125]) ).
tff(1400,plain,
s(index_249) = select(store(store(q7,seq,earray_250),tail,s(index_249)),tail),
inference(symmetry,[status(thm)],[1102]) ).
tff(1401,plain,
s(select(q7,tail)) = s(index_249),
inference(monotonicity,[status(thm)],[1070]) ).
tff(1402,plain,
s(select(q7,tail)) = index_255,
inference(transitivity,[status(thm)],[1401,1400,1121,1399]) ).
tff(1403,plain,
s(s(select(q7,tail))) = s(index_255),
inference(monotonicity,[status(thm)],[1402]) ).
tff(1404,plain,
s(s(select(q7,tail))) = index_9,
inference(transitivity,[status(thm)],[1403,1066,1063,1009]) ).
tff(1405,plain,
s(s(s(select(q7,tail)))) = s(index_9),
inference(monotonicity,[status(thm)],[1404]) ).
tff(1406,plain,
s(index_9) = s(s(s(select(q7,tail)))),
inference(symmetry,[status(thm)],[1405]) ).
tff(1407,plain,
select(q10,tail) = select(store(store(q9,seq,earray_10),tail,s(index_9)),tail),
inference(symmetry,[status(thm)],[1002]) ).
tff(1408,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q10,tail)))) = select(q10,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1409,plain,
s(s(s(select(q10,tail)))) = select(q10,tail),
inference(unit_resolution,[status(thm)],[1408,187]) ).
tff(1410,plain,
select(q11,tail) = index_21,
inference(symmetry,[status(thm)],[1038]) ).
tff(1411,plain,
s(index_15) = select(store(store(q10,seq,earray_16),tail,s(index_15)),tail),
inference(symmetry,[status(thm)],[1015]) ).
tff(1412,plain,
s(select(q10,tail)) = s(index_15),
inference(monotonicity,[status(thm)],[983]) ).
tff(1413,plain,
s(select(q10,tail)) = index_21,
inference(transitivity,[status(thm)],[1412,1411,1034,1410]) ).
tff(1414,plain,
s(s(select(q10,tail))) = s(index_21),
inference(monotonicity,[status(thm)],[1413]) ).
tff(1415,plain,
s(s(select(q10,tail))) = index_27,
inference(transitivity,[status(thm)],[1414,979,976,922]) ).
tff(1416,plain,
s(s(s(select(q10,tail)))) = s(index_27),
inference(monotonicity,[status(thm)],[1415]) ).
tff(1417,plain,
s(index_27) = s(s(s(select(q10,tail)))),
inference(symmetry,[status(thm)],[1416]) ).
tff(1418,plain,
select(q13,tail) = select(store(store(q12,seq,earray_28),tail,s(index_27)),tail),
inference(symmetry,[status(thm)],[915]) ).
tff(1419,plain,
select(q13,tail) = index_6,
inference(transitivity,[status(thm)],[1418,917,1417,1409,1407,1004,1406,1398,1396,1091,1395,1387,1385,1178,1384,1376,1374,1265,1256]) ).
tff(1420,plain,
store(store(q0,seq,earray_4),tail,select(q13,tail)) = store(queue_5,tail,index_6),
inference(monotonicity,[status(thm)],[1260,1419]) ).
tff(1421,plain,
select(store(store(q0,seq,earray_4),tail,select(q13,tail)),head) = select(store(queue_5,tail,index_6),head),
inference(monotonicity,[status(thm)],[1420]) ).
tff(1422,plain,
select(store(queue_5,tail,index_6),head) = select(store(store(q0,seq,earray_4),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[1421]) ).
tff(1423,plain,
( ( ~ ! [I: $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(1424,plain,
( ~ ! [I: $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(1425,plain,
( ~ ! [I: $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)],[1424,1423]) ).
tff(1426,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)],[1425,89,1339]) ).
tff(1427,plain,
( ( earray_70 = store(earray_68,index_69,e1) )
<=> ( earray_70 = store(earray_68,index_69,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1428,axiom,
earray_70 = store(earray_68,index_69,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(1429,plain,
earray_70 = store(earray_68,index_69,e1),
inference(modus_ponens,[status(thm)],[1428,1427]) ).
tff(1430,plain,
store(earray_68,index_69,e1) = earray_70,
inference(symmetry,[status(thm)],[1429]) ).
tff(1431,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_68,index_69,e1)),seq) = store(earray_68,index_69,e1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1432,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_68,index_69,e1)),seq) = store(earray_68,index_69,e1),
inference(unit_resolution,[status(thm)],[1431,24]) ).
tff(1433,plain,
store(queue_5,tail,index_6) = q1,
inference(transitivity,[status(thm)],[1252,1248]) ).
tff(1434,plain,
store(store(queue_5,tail,index_6),seq,store(earray_68,index_69,e1)) = store(q1,seq,earray_70),
inference(monotonicity,[status(thm)],[1433,1430]) ).
tff(1435,plain,
select(store(store(queue_5,tail,index_6),seq,store(earray_68,index_69,e1)),seq) = select(store(q1,seq,earray_70),seq),
inference(monotonicity,[status(thm)],[1434]) ).
tff(1436,plain,
select(store(q1,seq,earray_70),seq) = select(store(store(queue_5,tail,index_6),seq,store(earray_68,index_69,e1)),seq),
inference(symmetry,[status(thm)],[1435]) ).
tff(1437,plain,
( ( ~ ! [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_70),tail,s(index_69)),seq) = select(store(q1,seq,earray_70),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_70),tail,s(index_69)),seq) = select(store(q1,seq,earray_70),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1438,plain,
( ~ ! [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_70),tail,s(index_69)),seq) = select(store(q1,seq,earray_70),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1439,plain,
( ~ ! [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_70),tail,s(index_69)),seq) = select(store(q1,seq,earray_70),seq) ) ),
inference(modus_ponens,[status(thm)],[1438,1437]) ).
tff(1440,plain,
select(store(store(q1,seq,earray_70),tail,s(index_69)),seq) = select(store(q1,seq,earray_70),seq),
inference(unit_resolution,[status(thm)],[1439,89,83]) ).
tff(1441,plain,
select(store(store(q1,seq,earray_70),tail,s(index_69)),seq) = select(q2,seq),
inference(monotonicity,[status(thm)],[1294]) ).
tff(1442,plain,
select(q2,seq) = select(store(store(q1,seq,earray_70),tail,s(index_69)),seq),
inference(symmetry,[status(thm)],[1441]) ).
tff(1443,plain,
select(q2,seq) = earray_70,
inference(transitivity,[status(thm)],[1442,1440,1436,1432,1430]) ).
tff(1444,plain,
store(store(queue_5,tail,index_6),seq,select(q2,seq)) = store(q1,seq,earray_70),
inference(monotonicity,[status(thm)],[1433,1443]) ).
tff(1445,plain,
select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head) = select(store(q1,seq,earray_70),head),
inference(monotonicity,[status(thm)],[1444]) ).
tff(1446,plain,
select(store(q1,seq,earray_70),head) = select(store(store(queue_5,tail,index_6),seq,select(q2,seq)),head),
inference(symmetry,[status(thm)],[1445]) ).
tff(1447,plain,
( ( ~ ! [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_70),tail,select(q14,tail)),head) = select(store(q1,seq,earray_70),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_70),tail,select(q14,tail)),head) = select(store(q1,seq,earray_70),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1448,plain,
( ~ ! [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_70),tail,select(q14,tail)),head) = select(store(q1,seq,earray_70),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1449,plain,
( ~ ! [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_70),tail,select(q14,tail)),head) = select(store(q1,seq,earray_70),head) ) ),
inference(modus_ponens,[status(thm)],[1448,1447]) ).
tff(1450,plain,
select(store(store(q1,seq,earray_70),tail,select(q14,tail)),head) = select(store(q1,seq,earray_70),head),
inference(unit_resolution,[status(thm)],[1449,89,1369]) ).
tff(1451,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q2,tail)))) = select(q2,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1452,plain,
s(s(s(select(q2,tail)))) = select(q2,tail),
inference(unit_resolution,[status(thm)],[1451,187]) ).
tff(1453,plain,
s(select(q2,tail)) = s(index_135),
inference(monotonicity,[status(thm)],[1377]) ).
tff(1454,plain,
s(select(q2,tail)) = index_201,
inference(transitivity,[status(thm)],[1453,1240,1237,1183]) ).
tff(1455,plain,
s(s(select(q2,tail))) = s(index_201),
inference(monotonicity,[status(thm)],[1454]) ).
tff(1456,plain,
s(s(select(q2,tail))) = index_231,
inference(transitivity,[status(thm)],[1455,1179,1176,1157]) ).
tff(1457,plain,
s(s(s(select(q2,tail)))) = s(index_231),
inference(monotonicity,[status(thm)],[1456]) ).
tff(1458,plain,
s(index_231) = s(s(s(select(q2,tail)))),
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q5,tail)))) = select(q5,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1460,plain,
s(s(s(select(q5,tail)))) = select(q5,tail),
inference(unit_resolution,[status(thm)],[1459,187]) ).
tff(1461,plain,
s(select(q5,tail)) = s(index_237),
inference(monotonicity,[status(thm)],[1388]) ).
tff(1462,plain,
s(select(q5,tail)) = index_243,
inference(transitivity,[status(thm)],[1461,1153,1150,1096]) ).
tff(1463,plain,
s(s(select(q5,tail))) = s(index_243),
inference(monotonicity,[status(thm)],[1462]) ).
tff(1464,plain,
s(s(select(q5,tail))) = index_249,
inference(transitivity,[status(thm)],[1463,1092,1089,1070]) ).
tff(1465,plain,
s(s(s(select(q5,tail)))) = s(index_249),
inference(monotonicity,[status(thm)],[1464]) ).
tff(1466,plain,
s(index_249) = s(s(s(select(q5,tail)))),
inference(symmetry,[status(thm)],[1465]) ).
tff(1467,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q8,tail)))) = select(q8,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1468,plain,
s(s(s(select(q8,tail)))) = select(q8,tail),
inference(unit_resolution,[status(thm)],[1467,187]) ).
tff(1469,plain,
s(select(q8,tail)) = s(index_255),
inference(monotonicity,[status(thm)],[1399]) ).
tff(1470,plain,
s(select(q8,tail)) = index_9,
inference(transitivity,[status(thm)],[1469,1066,1063,1009]) ).
tff(1471,plain,
s(s(select(q8,tail))) = s(index_9),
inference(monotonicity,[status(thm)],[1470]) ).
tff(1472,plain,
s(s(select(q8,tail))) = index_15,
inference(transitivity,[status(thm)],[1471,1005,1002,983]) ).
tff(1473,plain,
s(s(s(select(q8,tail)))) = s(index_15),
inference(monotonicity,[status(thm)],[1472]) ).
tff(1474,plain,
s(index_15) = s(s(s(select(q8,tail)))),
inference(symmetry,[status(thm)],[1473]) ).
tff(1475,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q11,tail)))) = select(q11,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1476,plain,
s(s(s(select(q11,tail)))) = select(q11,tail),
inference(unit_resolution,[status(thm)],[1475,187]) ).
tff(1477,plain,
s(select(q11,tail)) = s(index_21),
inference(monotonicity,[status(thm)],[1410]) ).
tff(1478,plain,
s(select(q11,tail)) = index_27,
inference(transitivity,[status(thm)],[1477,979,976,922]) ).
tff(1479,plain,
s(s(select(q11,tail))) = s(index_27),
inference(monotonicity,[status(thm)],[1478]) ).
tff(1480,plain,
s(s(select(q11,tail))) = index_33,
inference(transitivity,[status(thm)],[1479,918,915,896]) ).
tff(1481,plain,
s(s(s(select(q11,tail)))) = s(index_33),
inference(monotonicity,[status(thm)],[1480]) ).
tff(1482,plain,
s(index_33) = s(s(s(select(q11,tail)))),
inference(symmetry,[status(thm)],[1481]) ).
tff(1483,plain,
select(q14,tail) = index_72,
inference(transitivity,[status(thm)],[948,928,1482,1476,1035,1015,1474,1468,1122,1102,1466,1460,1209,1189,1458,1452,1296,1276,1288]) ).
tff(1484,plain,
store(store(q1,seq,earray_70),tail,select(q14,tail)) = store(queue_71,tail,index_72),
inference(monotonicity,[status(thm)],[1292,1483]) ).
tff(1485,plain,
select(store(store(q1,seq,earray_70),tail,select(q14,tail)),head) = select(store(queue_71,tail,index_72),head),
inference(monotonicity,[status(thm)],[1484]) ).
tff(1486,plain,
select(store(queue_71,tail,index_72),head) = select(store(store(q1,seq,earray_70),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[1485]) ).
tff(1487,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head) = select(store(queue_71,tail,index_72),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_71,tail,index_72),seq,select(q3,seq)),head) = select(store(queue_71,tail,index_72),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1488,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head) = select(store(queue_71,tail,index_72),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1489,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head) = select(store(queue_71,tail,index_72),head) ) ),
inference(modus_ponens,[status(thm)],[1488,1487]) ).
tff(1490,plain,
select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head) = select(store(queue_71,tail,index_72),head),
inference(unit_resolution,[status(thm)],[1489,89,1339]) ).
tff(1491,plain,
( ( earray_136 = store(earray_134,index_135,e2) )
<=> ( earray_136 = store(earray_134,index_135,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1492,axiom,
earray_136 = store(earray_134,index_135,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(1493,plain,
earray_136 = store(earray_134,index_135,e2),
inference(modus_ponens,[status(thm)],[1492,1491]) ).
tff(1494,plain,
store(earray_134,index_135,e2) = earray_136,
inference(symmetry,[status(thm)],[1493]) ).
tff(1495,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_71,tail,index_72),seq,store(earray_134,index_135,e2)),seq) = store(earray_134,index_135,e2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1496,plain,
select(store(store(queue_71,tail,index_72),seq,store(earray_134,index_135,e2)),seq) = store(earray_134,index_135,e2),
inference(unit_resolution,[status(thm)],[1495,24]) ).
tff(1497,plain,
store(queue_71,tail,index_72) = q2,
inference(transitivity,[status(thm)],[1284,1280]) ).
tff(1498,plain,
store(store(queue_71,tail,index_72),seq,store(earray_134,index_135,e2)) = store(q2,seq,earray_136),
inference(monotonicity,[status(thm)],[1497,1494]) ).
tff(1499,plain,
select(store(store(queue_71,tail,index_72),seq,store(earray_134,index_135,e2)),seq) = select(store(q2,seq,earray_136),seq),
inference(monotonicity,[status(thm)],[1498]) ).
tff(1500,plain,
select(store(q2,seq,earray_136),seq) = select(store(store(queue_71,tail,index_72),seq,store(earray_134,index_135,e2)),seq),
inference(symmetry,[status(thm)],[1499]) ).
tff(1501,plain,
( ( ~ ! [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_136),tail,s(index_135)),seq) = select(store(q2,seq,earray_136),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_136),tail,s(index_135)),seq) = select(store(q2,seq,earray_136),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1502,plain,
( ~ ! [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_136),tail,s(index_135)),seq) = select(store(q2,seq,earray_136),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1503,plain,
( ~ ! [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_136),tail,s(index_135)),seq) = select(store(q2,seq,earray_136),seq) ) ),
inference(modus_ponens,[status(thm)],[1502,1501]) ).
tff(1504,plain,
select(store(store(q2,seq,earray_136),tail,s(index_135)),seq) = select(store(q2,seq,earray_136),seq),
inference(unit_resolution,[status(thm)],[1503,89,83]) ).
tff(1505,plain,
queue_139 = q3,
inference(symmetry,[status(thm)],[1234]) ).
tff(1506,plain,
store(queue_137,tail,index_138) = queue_139,
inference(symmetry,[status(thm)],[1231]) ).
tff(1507,plain,
store(store(q2,seq,earray_136),tail,s(index_135)) = q3,
inference(transitivity,[status(thm)],[1227,1506,1505]) ).
tff(1508,plain,
select(store(store(q2,seq,earray_136),tail,s(index_135)),seq) = select(q3,seq),
inference(monotonicity,[status(thm)],[1507]) ).
tff(1509,plain,
select(q3,seq) = select(store(store(q2,seq,earray_136),tail,s(index_135)),seq),
inference(symmetry,[status(thm)],[1508]) ).
tff(1510,plain,
select(q3,seq) = earray_136,
inference(transitivity,[status(thm)],[1509,1504,1500,1496,1494]) ).
tff(1511,plain,
store(store(queue_71,tail,index_72),seq,select(q3,seq)) = store(q2,seq,earray_136),
inference(monotonicity,[status(thm)],[1497,1510]) ).
tff(1512,plain,
select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head) = select(store(q2,seq,earray_136),head),
inference(monotonicity,[status(thm)],[1511]) ).
tff(1513,plain,
select(store(q2,seq,earray_136),head) = select(store(store(queue_71,tail,index_72),seq,select(q3,seq)),head),
inference(symmetry,[status(thm)],[1512]) ).
tff(1514,plain,
( ( ~ ! [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_136),tail,select(q12,tail)),head) = select(store(q2,seq,earray_136),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_136),tail,select(q12,tail)),head) = select(store(q2,seq,earray_136),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1515,plain,
( ~ ! [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_136),tail,select(q12,tail)),head) = select(store(q2,seq,earray_136),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1516,plain,
( ~ ! [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_136),tail,select(q12,tail)),head) = select(store(q2,seq,earray_136),head) ) ),
inference(modus_ponens,[status(thm)],[1515,1514]) ).
tff(1517,plain,
select(store(store(q2,seq,earray_136),tail,select(q12,tail)),head) = select(store(q2,seq,earray_136),head),
inference(unit_resolution,[status(thm)],[1516,89,1369]) ).
tff(1518,plain,
select(q12,tail) = index_138,
inference(transitivity,[status(thm)],[975,978,1040,1043,1062,1065,1127,1130,1149,1152,1214,1217,1236,1239,1222]) ).
tff(1519,plain,
store(store(q2,seq,earray_136),tail,select(q12,tail)) = store(queue_137,tail,index_138),
inference(monotonicity,[status(thm)],[1226,1518]) ).
tff(1520,plain,
select(store(store(q2,seq,earray_136),tail,select(q12,tail)),head) = select(store(queue_137,tail,index_138),head),
inference(monotonicity,[status(thm)],[1519]) ).
tff(1521,plain,
select(store(queue_137,tail,index_138),head) = select(store(store(q2,seq,earray_136),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[1520]) ).
tff(1522,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head) = select(store(queue_137,tail,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_137,tail,index_138),seq,select(q4,seq)),head) = select(store(queue_137,tail,index_138),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1523,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head) = select(store(queue_137,tail,index_138),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1524,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head) = select(store(queue_137,tail,index_138),head) ) ),
inference(modus_ponens,[status(thm)],[1523,1522]) ).
tff(1525,plain,
select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head) = select(store(queue_137,tail,index_138),head),
inference(unit_resolution,[status(thm)],[1524,89,1339]) ).
tff(1526,plain,
( ( earray_202 = store(earray_200,index_201,e3) )
<=> ( earray_202 = store(earray_200,index_201,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1527,axiom,
earray_202 = store(earray_200,index_201,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(1528,plain,
earray_202 = store(earray_200,index_201,e3),
inference(modus_ponens,[status(thm)],[1527,1526]) ).
tff(1529,plain,
store(earray_200,index_201,e3) = earray_202,
inference(symmetry,[status(thm)],[1528]) ).
tff(1530,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_137,tail,index_138),seq,store(earray_200,index_201,e3)),seq) = store(earray_200,index_201,e3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1531,plain,
select(store(store(queue_137,tail,index_138),seq,store(earray_200,index_201,e3)),seq) = store(earray_200,index_201,e3),
inference(unit_resolution,[status(thm)],[1530,24]) ).
tff(1532,plain,
store(queue_137,tail,index_138) = q3,
inference(transitivity,[status(thm)],[1506,1505]) ).
tff(1533,plain,
store(store(queue_137,tail,index_138),seq,store(earray_200,index_201,e3)) = store(q3,seq,earray_202),
inference(monotonicity,[status(thm)],[1532,1529]) ).
tff(1534,plain,
select(store(store(queue_137,tail,index_138),seq,store(earray_200,index_201,e3)),seq) = select(store(q3,seq,earray_202),seq),
inference(monotonicity,[status(thm)],[1533]) ).
tff(1535,plain,
select(store(q3,seq,earray_202),seq) = select(store(store(queue_137,tail,index_138),seq,store(earray_200,index_201,e3)),seq),
inference(symmetry,[status(thm)],[1534]) ).
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(q3,seq,earray_202),tail,s(index_201)),seq) = select(store(q3,seq,earray_202),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_202),tail,s(index_201)),seq) = select(store(q3,seq,earray_202),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1537,plain,
( ~ ! [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_202),tail,s(index_201)),seq) = select(store(q3,seq,earray_202),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1538,plain,
( ~ ! [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_202),tail,s(index_201)),seq) = select(store(q3,seq,earray_202),seq) ) ),
inference(modus_ponens,[status(thm)],[1537,1536]) ).
tff(1539,plain,
select(store(store(q3,seq,earray_202),tail,s(index_201)),seq) = select(store(q3,seq,earray_202),seq),
inference(unit_resolution,[status(thm)],[1538,89,83]) ).
tff(1540,plain,
select(store(store(q3,seq,earray_202),tail,s(index_201)),seq) = select(q4,seq),
inference(monotonicity,[status(thm)],[1175]) ).
tff(1541,plain,
select(q4,seq) = select(store(store(q3,seq,earray_202),tail,s(index_201)),seq),
inference(symmetry,[status(thm)],[1540]) ).
tff(1542,plain,
select(q4,seq) = earray_202,
inference(transitivity,[status(thm)],[1541,1539,1535,1531,1529]) ).
tff(1543,plain,
store(store(queue_137,tail,index_138),seq,select(q4,seq)) = store(q3,seq,earray_202),
inference(monotonicity,[status(thm)],[1532,1542]) ).
tff(1544,plain,
select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head) = select(store(q3,seq,earray_202),head),
inference(monotonicity,[status(thm)],[1543]) ).
tff(1545,plain,
select(store(q3,seq,earray_202),head) = select(store(store(queue_137,tail,index_138),seq,select(q4,seq)),head),
inference(symmetry,[status(thm)],[1544]) ).
tff(1546,plain,
( ( ~ ! [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_202),tail,select(q13,tail)),head) = select(store(q3,seq,earray_202),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_202),tail,select(q13,tail)),head) = select(store(q3,seq,earray_202),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1547,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_202),tail,select(q13,tail)),head) = select(store(q3,seq,earray_202),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1548,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q3,seq,earray_202),tail,select(q13,tail)),head) = select(store(q3,seq,earray_202),head) ) ),
inference(modus_ponens,[status(thm)],[1547,1546]) ).
tff(1549,plain,
select(store(store(q3,seq,earray_202),tail,select(q13,tail)),head) = select(store(q3,seq,earray_202),head),
inference(unit_resolution,[status(thm)],[1548,89,1369]) ).
tff(1550,plain,
select(q13,tail) = index_204,
inference(transitivity,[status(thm)],[1418,917,1417,1409,1407,1004,1406,1398,1396,1091,1395,1387,1385,1178,1169]) ).
tff(1551,plain,
store(store(q3,seq,earray_202),tail,select(q13,tail)) = store(queue_203,tail,index_204),
inference(monotonicity,[status(thm)],[1173,1550]) ).
tff(1552,plain,
select(store(store(q3,seq,earray_202),tail,select(q13,tail)),head) = select(store(queue_203,tail,index_204),head),
inference(monotonicity,[status(thm)],[1551]) ).
tff(1553,plain,
select(store(queue_203,tail,index_204),head) = select(store(store(q3,seq,earray_202),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[1552]) ).
tff(1554,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head) = select(store(queue_203,tail,index_204),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_203,tail,index_204),seq,select(q5,seq)),head) = select(store(queue_203,tail,index_204),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1555,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head) = select(store(queue_203,tail,index_204),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1556,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head) = select(store(queue_203,tail,index_204),head) ) ),
inference(modus_ponens,[status(thm)],[1555,1554]) ).
tff(1557,plain,
select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head) = select(store(queue_203,tail,index_204),head),
inference(unit_resolution,[status(thm)],[1556,89,1339]) ).
tff(1558,plain,
( ( earray_232 = store(earray_230,index_231,e4) )
<=> ( earray_232 = store(earray_230,index_231,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1559,axiom,
earray_232 = store(earray_230,index_231,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(1560,plain,
earray_232 = store(earray_230,index_231,e4),
inference(modus_ponens,[status(thm)],[1559,1558]) ).
tff(1561,plain,
store(earray_230,index_231,e4) = earray_232,
inference(symmetry,[status(thm)],[1560]) ).
tff(1562,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_203,tail,index_204),seq,store(earray_230,index_231,e4)),seq) = store(earray_230,index_231,e4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1563,plain,
select(store(store(queue_203,tail,index_204),seq,store(earray_230,index_231,e4)),seq) = store(earray_230,index_231,e4),
inference(unit_resolution,[status(thm)],[1562,24]) ).
tff(1564,plain,
store(queue_203,tail,index_204) = q4,
inference(transitivity,[status(thm)],[1165,1161]) ).
tff(1565,plain,
store(store(queue_203,tail,index_204),seq,store(earray_230,index_231,e4)) = store(q4,seq,earray_232),
inference(monotonicity,[status(thm)],[1564,1561]) ).
tff(1566,plain,
select(store(store(queue_203,tail,index_204),seq,store(earray_230,index_231,e4)),seq) = select(store(q4,seq,earray_232),seq),
inference(monotonicity,[status(thm)],[1565]) ).
tff(1567,plain,
select(store(q4,seq,earray_232),seq) = select(store(store(queue_203,tail,index_204),seq,store(earray_230,index_231,e4)),seq),
inference(symmetry,[status(thm)],[1566]) ).
tff(1568,plain,
( ( ~ ! [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_232),tail,s(index_231)),seq) = select(store(q4,seq,earray_232),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_232),tail,s(index_231)),seq) = select(store(q4,seq,earray_232),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1569,plain,
( ~ ! [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_232),tail,s(index_231)),seq) = select(store(q4,seq,earray_232),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1570,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q4,seq,earray_232),tail,s(index_231)),seq) = select(store(q4,seq,earray_232),seq) ) ),
inference(modus_ponens,[status(thm)],[1569,1568]) ).
tff(1571,plain,
select(store(store(q4,seq,earray_232),tail,s(index_231)),seq) = select(store(q4,seq,earray_232),seq),
inference(unit_resolution,[status(thm)],[1570,89,83]) ).
tff(1572,plain,
select(store(store(q4,seq,earray_232),tail,s(index_231)),seq) = select(q5,seq),
inference(monotonicity,[status(thm)],[1207]) ).
tff(1573,plain,
select(q5,seq) = select(store(store(q4,seq,earray_232),tail,s(index_231)),seq),
inference(symmetry,[status(thm)],[1572]) ).
tff(1574,plain,
select(q5,seq) = earray_232,
inference(transitivity,[status(thm)],[1573,1571,1567,1563,1561]) ).
tff(1575,plain,
store(store(queue_203,tail,index_204),seq,select(q5,seq)) = store(q4,seq,earray_232),
inference(monotonicity,[status(thm)],[1564,1574]) ).
tff(1576,plain,
select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head) = select(store(q4,seq,earray_232),head),
inference(monotonicity,[status(thm)],[1575]) ).
tff(1577,plain,
select(store(q4,seq,earray_232),head) = select(store(store(queue_203,tail,index_204),seq,select(q5,seq)),head),
inference(symmetry,[status(thm)],[1576]) ).
tff(1578,plain,
( ( ~ ! [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_232),tail,select(q14,tail)),head) = select(store(q4,seq,earray_232),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_232),tail,select(q14,tail)),head) = select(store(q4,seq,earray_232),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1579,plain,
( ~ ! [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_232),tail,select(q14,tail)),head) = select(store(q4,seq,earray_232),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1580,plain,
( ~ ! [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_232),tail,select(q14,tail)),head) = select(store(q4,seq,earray_232),head) ) ),
inference(modus_ponens,[status(thm)],[1579,1578]) ).
tff(1581,plain,
select(store(store(q4,seq,earray_232),tail,select(q14,tail)),head) = select(store(q4,seq,earray_232),head),
inference(unit_resolution,[status(thm)],[1580,89,1369]) ).
tff(1582,plain,
select(q14,tail) = index_234,
inference(transitivity,[status(thm)],[948,928,1482,1476,1035,1015,1474,1468,1122,1102,1466,1460,1209,1189,1201]) ).
tff(1583,plain,
store(store(q4,seq,earray_232),tail,select(q14,tail)) = store(queue_233,tail,index_234),
inference(monotonicity,[status(thm)],[1205,1582]) ).
tff(1584,plain,
select(store(store(q4,seq,earray_232),tail,select(q14,tail)),head) = select(store(queue_233,tail,index_234),head),
inference(monotonicity,[status(thm)],[1583]) ).
tff(1585,plain,
select(store(queue_233,tail,index_234),head) = select(store(store(q4,seq,earray_232),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[1584]) ).
tff(1586,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head) = select(store(queue_233,tail,index_234),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_233,tail,index_234),seq,select(q6,seq)),head) = select(store(queue_233,tail,index_234),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1587,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head) = select(store(queue_233,tail,index_234),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1588,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head) = select(store(queue_233,tail,index_234),head) ) ),
inference(modus_ponens,[status(thm)],[1587,1586]) ).
tff(1589,plain,
select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head) = select(store(queue_233,tail,index_234),head),
inference(unit_resolution,[status(thm)],[1588,89,1339]) ).
tff(1590,plain,
( ( earray_238 = store(earray_236,index_237,e5) )
<=> ( earray_238 = store(earray_236,index_237,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1591,axiom,
earray_238 = store(earray_236,index_237,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(1592,plain,
earray_238 = store(earray_236,index_237,e5),
inference(modus_ponens,[status(thm)],[1591,1590]) ).
tff(1593,plain,
store(earray_236,index_237,e5) = earray_238,
inference(symmetry,[status(thm)],[1592]) ).
tff(1594,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_233,tail,index_234),seq,store(earray_236,index_237,e5)),seq) = store(earray_236,index_237,e5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1595,plain,
select(store(store(queue_233,tail,index_234),seq,store(earray_236,index_237,e5)),seq) = store(earray_236,index_237,e5),
inference(unit_resolution,[status(thm)],[1594,24]) ).
tff(1596,plain,
store(queue_233,tail,index_234) = q5,
inference(transitivity,[status(thm)],[1197,1193]) ).
tff(1597,plain,
store(store(queue_233,tail,index_234),seq,store(earray_236,index_237,e5)) = store(q5,seq,earray_238),
inference(monotonicity,[status(thm)],[1596,1593]) ).
tff(1598,plain,
select(store(store(queue_233,tail,index_234),seq,store(earray_236,index_237,e5)),seq) = select(store(q5,seq,earray_238),seq),
inference(monotonicity,[status(thm)],[1597]) ).
tff(1599,plain,
select(store(q5,seq,earray_238),seq) = select(store(store(queue_233,tail,index_234),seq,store(earray_236,index_237,e5)),seq),
inference(symmetry,[status(thm)],[1598]) ).
tff(1600,plain,
( ( ~ ! [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_238),tail,s(index_237)),seq) = select(store(q5,seq,earray_238),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_238),tail,s(index_237)),seq) = select(store(q5,seq,earray_238),seq) ) ) ),
inference(rewrite,[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 = seq )
| ( select(store(store(q5,seq,earray_238),tail,s(index_237)),seq) = select(store(q5,seq,earray_238),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1602,plain,
( ~ ! [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_238),tail,s(index_237)),seq) = select(store(q5,seq,earray_238),seq) ) ),
inference(modus_ponens,[status(thm)],[1601,1600]) ).
tff(1603,plain,
select(store(store(q5,seq,earray_238),tail,s(index_237)),seq) = select(store(q5,seq,earray_238),seq),
inference(unit_resolution,[status(thm)],[1602,89,83]) ).
tff(1604,plain,
queue_241 = q6,
inference(symmetry,[status(thm)],[1147]) ).
tff(1605,plain,
store(queue_239,tail,index_240) = queue_241,
inference(symmetry,[status(thm)],[1144]) ).
tff(1606,plain,
store(store(q5,seq,earray_238),tail,s(index_237)) = q6,
inference(transitivity,[status(thm)],[1140,1605,1604]) ).
tff(1607,plain,
select(store(store(q5,seq,earray_238),tail,s(index_237)),seq) = select(q6,seq),
inference(monotonicity,[status(thm)],[1606]) ).
tff(1608,plain,
select(q6,seq) = select(store(store(q5,seq,earray_238),tail,s(index_237)),seq),
inference(symmetry,[status(thm)],[1607]) ).
tff(1609,plain,
select(q6,seq) = earray_238,
inference(transitivity,[status(thm)],[1608,1603,1599,1595,1593]) ).
tff(1610,plain,
store(store(queue_233,tail,index_234),seq,select(q6,seq)) = store(q5,seq,earray_238),
inference(monotonicity,[status(thm)],[1596,1609]) ).
tff(1611,plain,
select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head) = select(store(q5,seq,earray_238),head),
inference(monotonicity,[status(thm)],[1610]) ).
tff(1612,plain,
select(store(q5,seq,earray_238),head) = select(store(store(queue_233,tail,index_234),seq,select(q6,seq)),head),
inference(symmetry,[status(thm)],[1611]) ).
tff(1613,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head) = select(store(q5,seq,earray_238),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_238),tail,select(q12,tail)),head) = select(store(q5,seq,earray_238),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1614,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head) = select(store(q5,seq,earray_238),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1615,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head) = select(store(q5,seq,earray_238),head) ) ),
inference(modus_ponens,[status(thm)],[1614,1613]) ).
tff(1616,plain,
select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head) = select(store(q5,seq,earray_238),head),
inference(unit_resolution,[status(thm)],[1615,89,1369]) ).
tff(1617,plain,
select(q12,tail) = index_240,
inference(transitivity,[status(thm)],[975,978,1040,1043,1062,1065,1127,1130,1149,1152,1135]) ).
tff(1618,plain,
store(store(q5,seq,earray_238),tail,select(q12,tail)) = store(queue_239,tail,index_240),
inference(monotonicity,[status(thm)],[1139,1617]) ).
tff(1619,plain,
select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head) = select(store(queue_239,tail,index_240),head),
inference(monotonicity,[status(thm)],[1618]) ).
tff(1620,plain,
select(store(queue_239,tail,index_240),head) = select(store(store(q5,seq,earray_238),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[1619]) ).
tff(1621,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head) = select(store(queue_239,tail,index_240),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_239,tail,index_240),seq,select(q7,seq)),head) = select(store(queue_239,tail,index_240),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1622,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head) = select(store(queue_239,tail,index_240),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1623,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head) = select(store(queue_239,tail,index_240),head) ) ),
inference(modus_ponens,[status(thm)],[1622,1621]) ).
tff(1624,plain,
select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head) = select(store(queue_239,tail,index_240),head),
inference(unit_resolution,[status(thm)],[1623,89,1339]) ).
tff(1625,plain,
( ( earray_244 = store(earray_242,index_243,e6) )
<=> ( earray_244 = store(earray_242,index_243,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1626,axiom,
earray_244 = store(earray_242,index_243,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(1627,plain,
earray_244 = store(earray_242,index_243,e6),
inference(modus_ponens,[status(thm)],[1626,1625]) ).
tff(1628,plain,
store(earray_242,index_243,e6) = earray_244,
inference(symmetry,[status(thm)],[1627]) ).
tff(1629,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_239,tail,index_240),seq,store(earray_242,index_243,e6)),seq) = store(earray_242,index_243,e6) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1630,plain,
select(store(store(queue_239,tail,index_240),seq,store(earray_242,index_243,e6)),seq) = store(earray_242,index_243,e6),
inference(unit_resolution,[status(thm)],[1629,24]) ).
tff(1631,plain,
store(queue_239,tail,index_240) = q6,
inference(transitivity,[status(thm)],[1605,1604]) ).
tff(1632,plain,
store(store(queue_239,tail,index_240),seq,store(earray_242,index_243,e6)) = store(q6,seq,earray_244),
inference(monotonicity,[status(thm)],[1631,1628]) ).
tff(1633,plain,
select(store(store(queue_239,tail,index_240),seq,store(earray_242,index_243,e6)),seq) = select(store(q6,seq,earray_244),seq),
inference(monotonicity,[status(thm)],[1632]) ).
tff(1634,plain,
select(store(q6,seq,earray_244),seq) = select(store(store(queue_239,tail,index_240),seq,store(earray_242,index_243,e6)),seq),
inference(symmetry,[status(thm)],[1633]) ).
tff(1635,plain,
( ( ~ ! [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_244),tail,s(index_243)),seq) = select(store(q6,seq,earray_244),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_244),tail,s(index_243)),seq) = select(store(q6,seq,earray_244),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1636,plain,
( ~ ! [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_244),tail,s(index_243)),seq) = select(store(q6,seq,earray_244),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1637,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q6,seq,earray_244),tail,s(index_243)),seq) = select(store(q6,seq,earray_244),seq) ) ),
inference(modus_ponens,[status(thm)],[1636,1635]) ).
tff(1638,plain,
select(store(store(q6,seq,earray_244),tail,s(index_243)),seq) = select(store(q6,seq,earray_244),seq),
inference(unit_resolution,[status(thm)],[1637,89,83]) ).
tff(1639,plain,
select(store(store(q6,seq,earray_244),tail,s(index_243)),seq) = select(q7,seq),
inference(monotonicity,[status(thm)],[1088]) ).
tff(1640,plain,
select(q7,seq) = select(store(store(q6,seq,earray_244),tail,s(index_243)),seq),
inference(symmetry,[status(thm)],[1639]) ).
tff(1641,plain,
select(q7,seq) = earray_244,
inference(transitivity,[status(thm)],[1640,1638,1634,1630,1628]) ).
tff(1642,plain,
store(store(queue_239,tail,index_240),seq,select(q7,seq)) = store(q6,seq,earray_244),
inference(monotonicity,[status(thm)],[1631,1641]) ).
tff(1643,plain,
select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head) = select(store(q6,seq,earray_244),head),
inference(monotonicity,[status(thm)],[1642]) ).
tff(1644,plain,
select(store(q6,seq,earray_244),head) = select(store(store(queue_239,tail,index_240),seq,select(q7,seq)),head),
inference(symmetry,[status(thm)],[1643]) ).
tff(1645,plain,
( ( ~ ! [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_244),tail,select(q13,tail)),head) = select(store(q6,seq,earray_244),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_244),tail,select(q13,tail)),head) = select(store(q6,seq,earray_244),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1646,plain,
( ~ ! [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_244),tail,select(q13,tail)),head) = select(store(q6,seq,earray_244),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1647,plain,
( ~ ! [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_244),tail,select(q13,tail)),head) = select(store(q6,seq,earray_244),head) ) ),
inference(modus_ponens,[status(thm)],[1646,1645]) ).
tff(1648,plain,
select(store(store(q6,seq,earray_244),tail,select(q13,tail)),head) = select(store(q6,seq,earray_244),head),
inference(unit_resolution,[status(thm)],[1647,89,1369]) ).
tff(1649,plain,
select(q13,tail) = index_246,
inference(transitivity,[status(thm)],[1418,917,1417,1409,1407,1004,1406,1398,1396,1091,1082]) ).
tff(1650,plain,
store(store(q6,seq,earray_244),tail,select(q13,tail)) = store(queue_245,tail,index_246),
inference(monotonicity,[status(thm)],[1086,1649]) ).
tff(1651,plain,
select(store(store(q6,seq,earray_244),tail,select(q13,tail)),head) = select(store(queue_245,tail,index_246),head),
inference(monotonicity,[status(thm)],[1650]) ).
tff(1652,plain,
select(store(queue_245,tail,index_246),head) = select(store(store(q6,seq,earray_244),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[1651]) ).
tff(1653,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head) = select(store(queue_245,tail,index_246),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_245,tail,index_246),seq,select(q8,seq)),head) = select(store(queue_245,tail,index_246),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1654,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head) = select(store(queue_245,tail,index_246),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1655,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head) = select(store(queue_245,tail,index_246),head) ) ),
inference(modus_ponens,[status(thm)],[1654,1653]) ).
tff(1656,plain,
select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head) = select(store(queue_245,tail,index_246),head),
inference(unit_resolution,[status(thm)],[1655,89,1339]) ).
tff(1657,plain,
( ( earray_250 = store(earray_248,index_249,e7) )
<=> ( earray_250 = store(earray_248,index_249,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1658,axiom,
earray_250 = store(earray_248,index_249,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(1659,plain,
earray_250 = store(earray_248,index_249,e7),
inference(modus_ponens,[status(thm)],[1658,1657]) ).
tff(1660,plain,
store(earray_248,index_249,e7) = earray_250,
inference(symmetry,[status(thm)],[1659]) ).
tff(1661,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_245,tail,index_246),seq,store(earray_248,index_249,e7)),seq) = store(earray_248,index_249,e7) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1662,plain,
select(store(store(queue_245,tail,index_246),seq,store(earray_248,index_249,e7)),seq) = store(earray_248,index_249,e7),
inference(unit_resolution,[status(thm)],[1661,24]) ).
tff(1663,plain,
store(queue_245,tail,index_246) = q7,
inference(transitivity,[status(thm)],[1078,1074]) ).
tff(1664,plain,
store(store(queue_245,tail,index_246),seq,store(earray_248,index_249,e7)) = store(q7,seq,earray_250),
inference(monotonicity,[status(thm)],[1663,1660]) ).
tff(1665,plain,
select(store(store(queue_245,tail,index_246),seq,store(earray_248,index_249,e7)),seq) = select(store(q7,seq,earray_250),seq),
inference(monotonicity,[status(thm)],[1664]) ).
tff(1666,plain,
select(store(q7,seq,earray_250),seq) = select(store(store(queue_245,tail,index_246),seq,store(earray_248,index_249,e7)),seq),
inference(symmetry,[status(thm)],[1665]) ).
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(q7,seq,earray_250),tail,s(index_249)),seq) = select(store(q7,seq,earray_250),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_250),tail,s(index_249)),seq) = select(store(q7,seq,earray_250),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1668,plain,
( ~ ! [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_250),tail,s(index_249)),seq) = select(store(q7,seq,earray_250),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1669,plain,
( ~ ! [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_250),tail,s(index_249)),seq) = select(store(q7,seq,earray_250),seq) ) ),
inference(modus_ponens,[status(thm)],[1668,1667]) ).
tff(1670,plain,
select(store(store(q7,seq,earray_250),tail,s(index_249)),seq) = select(store(q7,seq,earray_250),seq),
inference(unit_resolution,[status(thm)],[1669,89,83]) ).
tff(1671,plain,
select(store(store(q7,seq,earray_250),tail,s(index_249)),seq) = select(q8,seq),
inference(monotonicity,[status(thm)],[1120]) ).
tff(1672,plain,
select(q8,seq) = select(store(store(q7,seq,earray_250),tail,s(index_249)),seq),
inference(symmetry,[status(thm)],[1671]) ).
tff(1673,plain,
select(q8,seq) = earray_250,
inference(transitivity,[status(thm)],[1672,1670,1666,1662,1660]) ).
tff(1674,plain,
store(store(queue_245,tail,index_246),seq,select(q8,seq)) = store(q7,seq,earray_250),
inference(monotonicity,[status(thm)],[1663,1673]) ).
tff(1675,plain,
select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head) = select(store(q7,seq,earray_250),head),
inference(monotonicity,[status(thm)],[1674]) ).
tff(1676,plain,
select(store(q7,seq,earray_250),head) = select(store(store(queue_245,tail,index_246),seq,select(q8,seq)),head),
inference(symmetry,[status(thm)],[1675]) ).
tff(1677,plain,
( ( ~ ! [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_250),tail,select(q14,tail)),head) = select(store(q7,seq,earray_250),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_250),tail,select(q14,tail)),head) = select(store(q7,seq,earray_250),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1678,plain,
( ~ ! [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_250),tail,select(q14,tail)),head) = select(store(q7,seq,earray_250),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1679,plain,
( ~ ! [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_250),tail,select(q14,tail)),head) = select(store(q7,seq,earray_250),head) ) ),
inference(modus_ponens,[status(thm)],[1678,1677]) ).
tff(1680,plain,
select(store(store(q7,seq,earray_250),tail,select(q14,tail)),head) = select(store(q7,seq,earray_250),head),
inference(unit_resolution,[status(thm)],[1679,89,1369]) ).
tff(1681,plain,
select(q14,tail) = index_252,
inference(transitivity,[status(thm)],[948,928,1482,1476,1035,1015,1474,1468,1122,1102,1114]) ).
tff(1682,plain,
store(store(q7,seq,earray_250),tail,select(q14,tail)) = store(queue_251,tail,index_252),
inference(monotonicity,[status(thm)],[1118,1681]) ).
tff(1683,plain,
select(store(store(q7,seq,earray_250),tail,select(q14,tail)),head) = select(store(queue_251,tail,index_252),head),
inference(monotonicity,[status(thm)],[1682]) ).
tff(1684,plain,
select(store(queue_251,tail,index_252),head) = select(store(store(q7,seq,earray_250),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[1683]) ).
tff(1685,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head) = select(store(queue_251,tail,index_252),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_251,tail,index_252),seq,select(q9,seq)),head) = select(store(queue_251,tail,index_252),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1686,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head) = select(store(queue_251,tail,index_252),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1687,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head) = select(store(queue_251,tail,index_252),head) ) ),
inference(modus_ponens,[status(thm)],[1686,1685]) ).
tff(1688,plain,
select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head) = select(store(queue_251,tail,index_252),head),
inference(unit_resolution,[status(thm)],[1687,89,1339]) ).
tff(1689,plain,
( ( earray_256 = store(earray_254,index_255,e8) )
<=> ( earray_256 = store(earray_254,index_255,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1690,axiom,
earray_256 = store(earray_254,index_255,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp58) ).
tff(1691,plain,
earray_256 = store(earray_254,index_255,e8),
inference(modus_ponens,[status(thm)],[1690,1689]) ).
tff(1692,plain,
store(earray_254,index_255,e8) = earray_256,
inference(symmetry,[status(thm)],[1691]) ).
tff(1693,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_251,tail,index_252),seq,store(earray_254,index_255,e8)),seq) = store(earray_254,index_255,e8) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1694,plain,
select(store(store(queue_251,tail,index_252),seq,store(earray_254,index_255,e8)),seq) = store(earray_254,index_255,e8),
inference(unit_resolution,[status(thm)],[1693,24]) ).
tff(1695,plain,
store(queue_251,tail,index_252) = q8,
inference(transitivity,[status(thm)],[1110,1106]) ).
tff(1696,plain,
store(store(queue_251,tail,index_252),seq,store(earray_254,index_255,e8)) = store(q8,seq,earray_256),
inference(monotonicity,[status(thm)],[1695,1692]) ).
tff(1697,plain,
select(store(store(queue_251,tail,index_252),seq,store(earray_254,index_255,e8)),seq) = select(store(q8,seq,earray_256),seq),
inference(monotonicity,[status(thm)],[1696]) ).
tff(1698,plain,
select(store(q8,seq,earray_256),seq) = select(store(store(queue_251,tail,index_252),seq,store(earray_254,index_255,e8)),seq),
inference(symmetry,[status(thm)],[1697]) ).
tff(1699,plain,
( ( ~ ! [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_256),tail,s(index_255)),seq) = select(store(q8,seq,earray_256),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_256),tail,s(index_255)),seq) = select(store(q8,seq,earray_256),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1700,plain,
( ~ ! [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_256),tail,s(index_255)),seq) = select(store(q8,seq,earray_256),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1701,plain,
( ~ ! [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_256),tail,s(index_255)),seq) = select(store(q8,seq,earray_256),seq) ) ),
inference(modus_ponens,[status(thm)],[1700,1699]) ).
tff(1702,plain,
select(store(store(q8,seq,earray_256),tail,s(index_255)),seq) = select(store(q8,seq,earray_256),seq),
inference(unit_resolution,[status(thm)],[1701,89,83]) ).
tff(1703,plain,
queue_259 = q9,
inference(symmetry,[status(thm)],[1060]) ).
tff(1704,plain,
store(queue_257,tail,index_258) = queue_259,
inference(symmetry,[status(thm)],[1057]) ).
tff(1705,plain,
store(store(q8,seq,earray_256),tail,s(index_255)) = q9,
inference(transitivity,[status(thm)],[1053,1704,1703]) ).
tff(1706,plain,
select(store(store(q8,seq,earray_256),tail,s(index_255)),seq) = select(q9,seq),
inference(monotonicity,[status(thm)],[1705]) ).
tff(1707,plain,
select(q9,seq) = select(store(store(q8,seq,earray_256),tail,s(index_255)),seq),
inference(symmetry,[status(thm)],[1706]) ).
tff(1708,plain,
select(q9,seq) = earray_256,
inference(transitivity,[status(thm)],[1707,1702,1698,1694,1692]) ).
tff(1709,plain,
store(store(queue_251,tail,index_252),seq,select(q9,seq)) = store(q8,seq,earray_256),
inference(monotonicity,[status(thm)],[1695,1708]) ).
tff(1710,plain,
select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head) = select(store(q8,seq,earray_256),head),
inference(monotonicity,[status(thm)],[1709]) ).
tff(1711,plain,
select(store(q8,seq,earray_256),head) = select(store(store(queue_251,tail,index_252),seq,select(q9,seq)),head),
inference(symmetry,[status(thm)],[1710]) ).
tff(1712,plain,
( ( ~ ! [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_256),tail,select(q12,tail)),head) = select(store(q8,seq,earray_256),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_256),tail,select(q12,tail)),head) = select(store(q8,seq,earray_256),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1713,plain,
( ~ ! [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_256),tail,select(q12,tail)),head) = select(store(q8,seq,earray_256),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1714,plain,
( ~ ! [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_256),tail,select(q12,tail)),head) = select(store(q8,seq,earray_256),head) ) ),
inference(modus_ponens,[status(thm)],[1713,1712]) ).
tff(1715,plain,
select(store(store(q8,seq,earray_256),tail,select(q12,tail)),head) = select(store(q8,seq,earray_256),head),
inference(unit_resolution,[status(thm)],[1714,89,1369]) ).
tff(1716,plain,
select(q12,tail) = index_258,
inference(transitivity,[status(thm)],[975,978,1040,1043,1062,1065,1048]) ).
tff(1717,plain,
store(store(q8,seq,earray_256),tail,select(q12,tail)) = store(queue_257,tail,index_258),
inference(monotonicity,[status(thm)],[1052,1716]) ).
tff(1718,plain,
select(store(store(q8,seq,earray_256),tail,select(q12,tail)),head) = select(store(queue_257,tail,index_258),head),
inference(monotonicity,[status(thm)],[1717]) ).
tff(1719,plain,
select(store(queue_257,tail,index_258),head) = select(store(store(q8,seq,earray_256),tail,select(q12,tail)),head),
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) ) )
| ( seq = head )
| ( select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head) = select(store(queue_257,tail,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_257,tail,index_258),seq,select(q10,seq)),head) = select(store(queue_257,tail,index_258),head) ) ) ),
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) ) )
| ( seq = head )
| ( select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head) = select(store(queue_257,tail,index_258),head) ) ),
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) ) )
| ( seq = head )
| ( select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head) = select(store(queue_257,tail,index_258),head) ) ),
inference(modus_ponens,[status(thm)],[1721,1720]) ).
tff(1723,plain,
select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head) = select(store(queue_257,tail,index_258),head),
inference(unit_resolution,[status(thm)],[1722,89,1339]) ).
tff(1724,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1725,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(1726,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[1725,1724]) ).
tff(1727,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[1726]) ).
tff(1728,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_257,tail,index_258),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1729,plain,
select(store(store(queue_257,tail,index_258),seq,store(earray_8,index_9,e9)),seq) = store(earray_8,index_9,e9),
inference(unit_resolution,[status(thm)],[1728,24]) ).
tff(1730,plain,
store(queue_257,tail,index_258) = q9,
inference(transitivity,[status(thm)],[1704,1703]) ).
tff(1731,plain,
store(store(queue_257,tail,index_258),seq,store(earray_8,index_9,e9)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[1730,1727]) ).
tff(1732,plain,
select(store(store(queue_257,tail,index_258),seq,store(earray_8,index_9,e9)),seq) = select(store(q9,seq,earray_10),seq),
inference(monotonicity,[status(thm)],[1731]) ).
tff(1733,plain,
select(store(q9,seq,earray_10),seq) = select(store(store(queue_257,tail,index_258),seq,store(earray_8,index_9,e9)),seq),
inference(symmetry,[status(thm)],[1732]) ).
tff(1734,plain,
( ( ~ ! [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(1735,plain,
( ~ ! [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(1736,plain,
( ~ ! [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)],[1735,1734]) ).
tff(1737,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)],[1736,89,83]) ).
tff(1738,plain,
select(store(store(q9,seq,earray_10),tail,s(index_9)),seq) = select(q10,seq),
inference(monotonicity,[status(thm)],[1001]) ).
tff(1739,plain,
select(q10,seq) = select(store(store(q9,seq,earray_10),tail,s(index_9)),seq),
inference(symmetry,[status(thm)],[1738]) ).
tff(1740,plain,
select(q10,seq) = earray_10,
inference(transitivity,[status(thm)],[1739,1737,1733,1729,1727]) ).
tff(1741,plain,
store(store(queue_257,tail,index_258),seq,select(q10,seq)) = store(q9,seq,earray_10),
inference(monotonicity,[status(thm)],[1730,1740]) ).
tff(1742,plain,
select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head) = select(store(q9,seq,earray_10),head),
inference(monotonicity,[status(thm)],[1741]) ).
tff(1743,plain,
select(store(q9,seq,earray_10),head) = select(store(store(queue_257,tail,index_258),seq,select(q10,seq)),head),
inference(symmetry,[status(thm)],[1742]) ).
tff(1744,plain,
( ( ~ ! [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,select(q13,tail)),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,select(q13,tail)),head) = select(store(q9,seq,earray_10),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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,select(q13,tail)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(quant_inst,[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,select(q13,tail)),head) = select(store(q9,seq,earray_10),head) ) ),
inference(modus_ponens,[status(thm)],[1745,1744]) ).
tff(1747,plain,
select(store(store(q9,seq,earray_10),tail,select(q13,tail)),head) = select(store(q9,seq,earray_10),head),
inference(unit_resolution,[status(thm)],[1746,89,1369]) ).
tff(1748,plain,
select(q13,tail) = index_12,
inference(transitivity,[status(thm)],[1418,917,1417,1409,1407,1004,995]) ).
tff(1749,plain,
store(store(q9,seq,earray_10),tail,select(q13,tail)) = store(queue_11,tail,index_12),
inference(monotonicity,[status(thm)],[999,1748]) ).
tff(1750,plain,
select(store(store(q9,seq,earray_10),tail,select(q13,tail)),head) = select(store(queue_11,tail,index_12),head),
inference(monotonicity,[status(thm)],[1749]) ).
tff(1751,plain,
select(store(queue_11,tail,index_12),head) = select(store(store(q9,seq,earray_10),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[1750]) ).
tff(1752,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_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(1753,plain,
( ~ ! [I: $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(1754,plain,
( ~ ! [I: $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)],[1753,1752]) ).
tff(1755,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)],[1754,89,1339]) ).
tff(1756,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1757,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(1758,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[1757,1756]) ).
tff(1759,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[1758]) ).
tff(1760,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(1761,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)],[1760,24]) ).
tff(1762,plain,
store(queue_11,tail,index_12) = q10,
inference(transitivity,[status(thm)],[991,987]) ).
tff(1763,plain,
store(store(queue_11,tail,index_12),seq,store(earray_14,index_15,e10)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[1762,1759]) ).
tff(1764,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)],[1763]) ).
tff(1765,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)],[1764]) ).
tff(1766,plain,
( ( ~ ! [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(1767,plain,
( ~ ! [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(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(q10,seq,earray_16),tail,s(index_15)),seq) = select(store(q10,seq,earray_16),seq) ) ),
inference(modus_ponens,[status(thm)],[1767,1766]) ).
tff(1769,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)],[1768,89,83]) ).
tff(1770,plain,
select(store(store(q10,seq,earray_16),tail,s(index_15)),seq) = select(q11,seq),
inference(monotonicity,[status(thm)],[1033]) ).
tff(1771,plain,
select(q11,seq) = select(store(store(q10,seq,earray_16),tail,s(index_15)),seq),
inference(symmetry,[status(thm)],[1770]) ).
tff(1772,plain,
select(q11,seq) = earray_16,
inference(transitivity,[status(thm)],[1771,1769,1765,1761,1759]) ).
tff(1773,plain,
store(store(queue_11,tail,index_12),seq,select(q11,seq)) = store(q10,seq,earray_16),
inference(monotonicity,[status(thm)],[1762,1772]) ).
tff(1774,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)],[1773]) ).
tff(1775,plain,
select(store(q10,seq,earray_16),head) = select(store(store(queue_11,tail,index_12),seq,select(q11,seq)),head),
inference(symmetry,[status(thm)],[1774]) ).
tff(1776,plain,
( ( ~ ! [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,select(q14,tail)),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,select(q14,tail)),head) = select(store(q10,seq,earray_16),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1777,plain,
( ~ ! [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,select(q14,tail)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1778,plain,
( ~ ! [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,select(q14,tail)),head) = select(store(q10,seq,earray_16),head) ) ),
inference(modus_ponens,[status(thm)],[1777,1776]) ).
tff(1779,plain,
select(store(store(q10,seq,earray_16),tail,select(q14,tail)),head) = select(store(q10,seq,earray_16),head),
inference(unit_resolution,[status(thm)],[1778,89,1369]) ).
tff(1780,plain,
select(q14,tail) = index_18,
inference(transitivity,[status(thm)],[948,928,1482,1476,1035,1015,1027]) ).
tff(1781,plain,
store(store(q10,seq,earray_16),tail,select(q14,tail)) = store(queue_17,tail,index_18),
inference(monotonicity,[status(thm)],[1031,1780]) ).
tff(1782,plain,
select(store(store(q10,seq,earray_16),tail,select(q14,tail)),head) = select(store(queue_17,tail,index_18),head),
inference(monotonicity,[status(thm)],[1781]) ).
tff(1783,plain,
select(store(queue_17,tail,index_18),head) = select(store(store(q10,seq,earray_16),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[1782]) ).
tff(1784,plain,
( ( ~ ! [I: $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(1785,plain,
( ~ ! [I: $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(1786,plain,
( ~ ! [I: $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)],[1785,1784]) ).
tff(1787,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)],[1786,89,1339]) ).
tff(1788,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1789,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(1790,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[1789,1788]) ).
tff(1791,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[1790]) ).
tff(1792,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(1793,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)],[1792,24]) ).
tff(1794,plain,
store(queue_17,tail,index_18) = q11,
inference(transitivity,[status(thm)],[1023,1019]) ).
tff(1795,plain,
store(store(queue_17,tail,index_18),seq,store(earray_20,index_21,e11)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[1794,1791]) ).
tff(1796,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)],[1795]) ).
tff(1797,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)],[1796]) ).
tff(1798,plain,
( ( ~ ! [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(1799,plain,
( ~ ! [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(1800,plain,
( ~ ! [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)],[1799,1798]) ).
tff(1801,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)],[1800,89,83]) ).
tff(1802,plain,
queue_25 = q12,
inference(symmetry,[status(thm)],[973]) ).
tff(1803,plain,
store(queue_23,tail,index_24) = queue_25,
inference(symmetry,[status(thm)],[970]) ).
tff(1804,plain,
store(store(q11,seq,earray_22),tail,s(index_21)) = q12,
inference(transitivity,[status(thm)],[966,1803,1802]) ).
tff(1805,plain,
select(store(store(q11,seq,earray_22),tail,s(index_21)),seq) = select(q12,seq),
inference(monotonicity,[status(thm)],[1804]) ).
tff(1806,plain,
select(q12,seq) = select(store(store(q11,seq,earray_22),tail,s(index_21)),seq),
inference(symmetry,[status(thm)],[1805]) ).
tff(1807,plain,
select(q12,seq) = earray_22,
inference(transitivity,[status(thm)],[1806,1801,1797,1793,1791]) ).
tff(1808,plain,
store(store(queue_17,tail,index_18),seq,select(q12,seq)) = store(q11,seq,earray_22),
inference(monotonicity,[status(thm)],[1794,1807]) ).
tff(1809,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)],[1808]) ).
tff(1810,plain,
select(store(q11,seq,earray_22),head) = select(store(store(queue_17,tail,index_18),seq,select(q12,seq)),head),
inference(symmetry,[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(q11,seq,earray_22),tail,select(q12,tail)),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,select(q12,tail)),head) = select(store(q11,seq,earray_22),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(q11,seq,earray_22),tail,select(q12,tail)),head) = select(store(q11,seq,earray_22),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(q11,seq,earray_22),tail,select(q12,tail)),head) = select(store(q11,seq,earray_22),head) ) ),
inference(modus_ponens,[status(thm)],[1812,1811]) ).
tff(1814,plain,
select(store(store(q11,seq,earray_22),tail,select(q12,tail)),head) = select(store(q11,seq,earray_22),head),
inference(unit_resolution,[status(thm)],[1813,89,1369]) ).
tff(1815,plain,
select(q12,tail) = index_24,
inference(transitivity,[status(thm)],[975,978,961]) ).
tff(1816,plain,
store(store(q11,seq,earray_22),tail,select(q12,tail)) = store(queue_23,tail,index_24),
inference(monotonicity,[status(thm)],[965,1815]) ).
tff(1817,plain,
select(store(store(q11,seq,earray_22),tail,select(q12,tail)),head) = select(store(queue_23,tail,index_24),head),
inference(monotonicity,[status(thm)],[1816]) ).
tff(1818,plain,
select(store(queue_23,tail,index_24),head) = select(store(store(q11,seq,earray_22),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[1817]) ).
tff(1819,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head) = select(store(queue_23,tail,index_24),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_23,tail,index_24),seq,select(q13,seq)),head) = select(store(queue_23,tail,index_24),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1820,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head) = select(store(queue_23,tail,index_24),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1821,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head) = select(store(queue_23,tail,index_24),head) ) ),
inference(modus_ponens,[status(thm)],[1820,1819]) ).
tff(1822,plain,
select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head) = select(store(queue_23,tail,index_24),head),
inference(unit_resolution,[status(thm)],[1821,89,1339]) ).
tff(1823,plain,
( ( earray_28 = store(earray_26,index_27,e12) )
<=> ( earray_28 = store(earray_26,index_27,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1824,axiom,
earray_28 = store(earray_26,index_27,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp61) ).
tff(1825,plain,
earray_28 = store(earray_26,index_27,e12),
inference(modus_ponens,[status(thm)],[1824,1823]) ).
tff(1826,plain,
store(earray_26,index_27,e12) = earray_28,
inference(symmetry,[status(thm)],[1825]) ).
tff(1827,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_23,tail,index_24),seq,store(earray_26,index_27,e12)),seq) = store(earray_26,index_27,e12) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1828,plain,
select(store(store(queue_23,tail,index_24),seq,store(earray_26,index_27,e12)),seq) = store(earray_26,index_27,e12),
inference(unit_resolution,[status(thm)],[1827,24]) ).
tff(1829,plain,
store(queue_23,tail,index_24) = q12,
inference(transitivity,[status(thm)],[1803,1802]) ).
tff(1830,plain,
store(store(queue_23,tail,index_24),seq,store(earray_26,index_27,e12)) = store(q12,seq,earray_28),
inference(monotonicity,[status(thm)],[1829,1826]) ).
tff(1831,plain,
select(store(store(queue_23,tail,index_24),seq,store(earray_26,index_27,e12)),seq) = select(store(q12,seq,earray_28),seq),
inference(monotonicity,[status(thm)],[1830]) ).
tff(1832,plain,
select(store(q12,seq,earray_28),seq) = select(store(store(queue_23,tail,index_24),seq,store(earray_26,index_27,e12)),seq),
inference(symmetry,[status(thm)],[1831]) ).
tff(1833,plain,
( ( ~ ! [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_28),tail,s(index_27)),seq) = select(store(q12,seq,earray_28),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_28),tail,s(index_27)),seq) = select(store(q12,seq,earray_28),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1834,plain,
( ~ ! [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_28),tail,s(index_27)),seq) = select(store(q12,seq,earray_28),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
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(q12,seq,earray_28),tail,s(index_27)),seq) = select(store(q12,seq,earray_28),seq) ) ),
inference(modus_ponens,[status(thm)],[1834,1833]) ).
tff(1836,plain,
select(store(store(q12,seq,earray_28),tail,s(index_27)),seq) = select(store(q12,seq,earray_28),seq),
inference(unit_resolution,[status(thm)],[1835,89,83]) ).
tff(1837,plain,
select(store(store(q12,seq,earray_28),tail,s(index_27)),seq) = select(q13,seq),
inference(monotonicity,[status(thm)],[914]) ).
tff(1838,plain,
select(q13,seq) = select(store(store(q12,seq,earray_28),tail,s(index_27)),seq),
inference(symmetry,[status(thm)],[1837]) ).
tff(1839,plain,
select(q13,seq) = earray_28,
inference(transitivity,[status(thm)],[1838,1836,1832,1828,1826]) ).
tff(1840,plain,
store(store(queue_23,tail,index_24),seq,select(q13,seq)) = store(q12,seq,earray_28),
inference(monotonicity,[status(thm)],[1829,1839]) ).
tff(1841,plain,
select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head) = select(store(q12,seq,earray_28),head),
inference(monotonicity,[status(thm)],[1840]) ).
tff(1842,plain,
select(store(q12,seq,earray_28),head) = select(store(store(queue_23,tail,index_24),seq,select(q13,seq)),head),
inference(symmetry,[status(thm)],[1841]) ).
tff(1843,plain,
( ( ~ ! [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_28),tail,select(q13,tail)),head) = select(store(q12,seq,earray_28),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_28),tail,select(q13,tail)),head) = select(store(q12,seq,earray_28),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1844,plain,
( ~ ! [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_28),tail,select(q13,tail)),head) = select(store(q12,seq,earray_28),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1845,plain,
( ~ ! [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_28),tail,select(q13,tail)),head) = select(store(q12,seq,earray_28),head) ) ),
inference(modus_ponens,[status(thm)],[1844,1843]) ).
tff(1846,plain,
select(store(store(q12,seq,earray_28),tail,select(q13,tail)),head) = select(store(q12,seq,earray_28),head),
inference(unit_resolution,[status(thm)],[1845,89,1369]) ).
tff(1847,plain,
select(q13,tail) = index_30,
inference(transitivity,[status(thm)],[1418,917,908]) ).
tff(1848,plain,
store(store(q12,seq,earray_28),tail,select(q13,tail)) = store(queue_29,tail,index_30),
inference(monotonicity,[status(thm)],[912,1847]) ).
tff(1849,plain,
select(store(store(q12,seq,earray_28),tail,select(q13,tail)),head) = select(store(queue_29,tail,index_30),head),
inference(monotonicity,[status(thm)],[1848]) ).
tff(1850,plain,
select(store(queue_29,tail,index_30),head) = select(store(store(q12,seq,earray_28),tail,select(q13,tail)),head),
inference(symmetry,[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_29,tail,index_30),seq,select(q14,seq)),head) = select(store(queue_29,tail,index_30),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_29,tail,index_30),seq,select(q14,seq)),head) = select(store(queue_29,tail,index_30),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_29,tail,index_30),seq,select(q14,seq)),head) = select(store(queue_29,tail,index_30),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_29,tail,index_30),seq,select(q14,seq)),head) = select(store(queue_29,tail,index_30),head) ) ),
inference(modus_ponens,[status(thm)],[1852,1851]) ).
tff(1854,plain,
select(store(store(queue_29,tail,index_30),seq,select(q14,seq)),head) = select(store(queue_29,tail,index_30),head),
inference(unit_resolution,[status(thm)],[1853,89,1339]) ).
tff(1855,plain,
( ( earray_34 = store(earray_32,index_33,e13) )
<=> ( earray_34 = store(earray_32,index_33,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1856,axiom,
earray_34 = store(earray_32,index_33,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(1857,plain,
earray_34 = store(earray_32,index_33,e13),
inference(modus_ponens,[status(thm)],[1856,1855]) ).
tff(1858,plain,
store(earray_32,index_33,e13) = earray_34,
inference(symmetry,[status(thm)],[1857]) ).
tff(1859,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_29,tail,index_30),seq,store(earray_32,index_33,e13)),seq) = store(earray_32,index_33,e13) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1860,plain,
select(store(store(queue_29,tail,index_30),seq,store(earray_32,index_33,e13)),seq) = store(earray_32,index_33,e13),
inference(unit_resolution,[status(thm)],[1859,24]) ).
tff(1861,plain,
store(queue_29,tail,index_30) = q13,
inference(transitivity,[status(thm)],[904,900]) ).
tff(1862,plain,
store(store(queue_29,tail,index_30),seq,store(earray_32,index_33,e13)) = store(q13,seq,earray_34),
inference(monotonicity,[status(thm)],[1861,1858]) ).
tff(1863,plain,
select(store(store(queue_29,tail,index_30),seq,store(earray_32,index_33,e13)),seq) = select(store(q13,seq,earray_34),seq),
inference(monotonicity,[status(thm)],[1862]) ).
tff(1864,plain,
select(store(q13,seq,earray_34),seq) = select(store(store(queue_29,tail,index_30),seq,store(earray_32,index_33,e13)),seq),
inference(symmetry,[status(thm)],[1863]) ).
tff(1865,plain,
( ( ~ ! [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_34),tail,s(index_33)),seq) = select(store(q13,seq,earray_34),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_34),tail,s(index_33)),seq) = select(store(q13,seq,earray_34),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1866,plain,
( ~ ! [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_34),tail,s(index_33)),seq) = select(store(q13,seq,earray_34),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1867,plain,
( ~ ! [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_34),tail,s(index_33)),seq) = select(store(q13,seq,earray_34),seq) ) ),
inference(modus_ponens,[status(thm)],[1866,1865]) ).
tff(1868,plain,
select(store(store(q13,seq,earray_34),tail,s(index_33)),seq) = select(store(q13,seq,earray_34),seq),
inference(unit_resolution,[status(thm)],[1867,89,83]) ).
tff(1869,plain,
select(store(store(q13,seq,earray_34),tail,s(index_33)),seq) = select(q14,seq),
inference(monotonicity,[status(thm)],[946]) ).
tff(1870,plain,
select(q14,seq) = select(store(store(q13,seq,earray_34),tail,s(index_33)),seq),
inference(symmetry,[status(thm)],[1869]) ).
tff(1871,plain,
select(q14,seq) = earray_34,
inference(transitivity,[status(thm)],[1870,1868,1864,1860,1858]) ).
tff(1872,plain,
store(store(queue_29,tail,index_30),seq,select(q14,seq)) = store(q13,seq,earray_34),
inference(monotonicity,[status(thm)],[1861,1871]) ).
tff(1873,plain,
select(store(store(queue_29,tail,index_30),seq,select(q14,seq)),head) = select(store(q13,seq,earray_34),head),
inference(monotonicity,[status(thm)],[1872]) ).
tff(1874,plain,
select(store(q13,seq,earray_34),head) = select(store(store(queue_29,tail,index_30),seq,select(q14,seq)),head),
inference(symmetry,[status(thm)],[1873]) ).
tff(1875,plain,
( ( ~ ! [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_34),tail,select(q14,tail)),head) = select(store(q13,seq,earray_34),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_34),tail,select(q14,tail)),head) = select(store(q13,seq,earray_34),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1876,plain,
( ~ ! [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_34),tail,select(q14,tail)),head) = select(store(q13,seq,earray_34),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1877,plain,
( ~ ! [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_34),tail,select(q14,tail)),head) = select(store(q13,seq,earray_34),head) ) ),
inference(modus_ponens,[status(thm)],[1876,1875]) ).
tff(1878,plain,
select(store(store(q13,seq,earray_34),tail,select(q14,tail)),head) = select(store(q13,seq,earray_34),head),
inference(unit_resolution,[status(thm)],[1877,89,1369]) ).
tff(1879,plain,
select(q14,tail) = index_36,
inference(transitivity,[status(thm)],[948,928,940]) ).
tff(1880,plain,
store(store(q13,seq,earray_34),tail,select(q14,tail)) = store(queue_35,tail,index_36),
inference(monotonicity,[status(thm)],[944,1879]) ).
tff(1881,plain,
select(store(store(q13,seq,earray_34),tail,select(q14,tail)),head) = select(store(queue_35,tail,index_36),head),
inference(monotonicity,[status(thm)],[1880]) ).
tff(1882,plain,
select(store(queue_35,tail,index_36),head) = select(store(store(q13,seq,earray_34),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[1881]) ).
tff(1883,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head) = select(store(queue_35,tail,index_36),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_35,tail,index_36),seq,select(q15,seq)),head) = select(store(queue_35,tail,index_36),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1884,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head) = select(store(queue_35,tail,index_36),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1885,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head) = select(store(queue_35,tail,index_36),head) ) ),
inference(modus_ponens,[status(thm)],[1884,1883]) ).
tff(1886,plain,
select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head) = select(store(queue_35,tail,index_36),head),
inference(unit_resolution,[status(thm)],[1885,89,1339]) ).
tff(1887,plain,
( ( earray_40 = store(earray_38,index_39,e14) )
<=> ( earray_40 = store(earray_38,index_39,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1888,axiom,
earray_40 = store(earray_38,index_39,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp66) ).
tff(1889,plain,
earray_40 = store(earray_38,index_39,e14),
inference(modus_ponens,[status(thm)],[1888,1887]) ).
tff(1890,plain,
store(earray_38,index_39,e14) = earray_40,
inference(symmetry,[status(thm)],[1889]) ).
tff(1891,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_35,tail,index_36),seq,store(earray_38,index_39,e14)),seq) = store(earray_38,index_39,e14) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1892,plain,
select(store(store(queue_35,tail,index_36),seq,store(earray_38,index_39,e14)),seq) = store(earray_38,index_39,e14),
inference(unit_resolution,[status(thm)],[1891,24]) ).
tff(1893,plain,
store(queue_35,tail,index_36) = q14,
inference(transitivity,[status(thm)],[936,932]) ).
tff(1894,plain,
store(store(queue_35,tail,index_36),seq,store(earray_38,index_39,e14)) = store(q14,seq,earray_40),
inference(monotonicity,[status(thm)],[1893,1890]) ).
tff(1895,plain,
select(store(store(queue_35,tail,index_36),seq,store(earray_38,index_39,e14)),seq) = select(store(q14,seq,earray_40),seq),
inference(monotonicity,[status(thm)],[1894]) ).
tff(1896,plain,
select(store(q14,seq,earray_40),seq) = select(store(store(queue_35,tail,index_36),seq,store(earray_38,index_39,e14)),seq),
inference(symmetry,[status(thm)],[1895]) ).
tff(1897,plain,
( ( ~ ! [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_40),tail,s(index_39)),seq) = select(store(q14,seq,earray_40),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_40),tail,s(index_39)),seq) = select(store(q14,seq,earray_40),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1898,plain,
( ~ ! [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_40),tail,s(index_39)),seq) = select(store(q14,seq,earray_40),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1899,plain,
( ~ ! [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_40),tail,s(index_39)),seq) = select(store(q14,seq,earray_40),seq) ) ),
inference(modus_ponens,[status(thm)],[1898,1897]) ).
tff(1900,plain,
select(store(store(q14,seq,earray_40),tail,s(index_39)),seq) = select(store(q14,seq,earray_40),seq),
inference(unit_resolution,[status(thm)],[1899,89,83]) ).
tff(1901,plain,
queue_43 = q15,
inference(symmetry,[status(thm)],[886]) ).
tff(1902,plain,
store(queue_41,tail,index_42) = queue_43,
inference(symmetry,[status(thm)],[883]) ).
tff(1903,plain,
store(store(q14,seq,earray_40),tail,s(index_39)) = q15,
inference(transitivity,[status(thm)],[879,1902,1901]) ).
tff(1904,plain,
select(store(store(q14,seq,earray_40),tail,s(index_39)),seq) = select(q15,seq),
inference(monotonicity,[status(thm)],[1903]) ).
tff(1905,plain,
select(q15,seq) = select(store(store(q14,seq,earray_40),tail,s(index_39)),seq),
inference(symmetry,[status(thm)],[1904]) ).
tff(1906,plain,
select(q15,seq) = earray_40,
inference(transitivity,[status(thm)],[1905,1900,1896,1892,1890]) ).
tff(1907,plain,
store(store(queue_35,tail,index_36),seq,select(q15,seq)) = store(q14,seq,earray_40),
inference(monotonicity,[status(thm)],[1893,1906]) ).
tff(1908,plain,
select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head) = select(store(q14,seq,earray_40),head),
inference(monotonicity,[status(thm)],[1907]) ).
tff(1909,plain,
select(store(q14,seq,earray_40),head) = select(store(store(queue_35,tail,index_36),seq,select(q15,seq)),head),
inference(symmetry,[status(thm)],[1908]) ).
tff(1910,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head) = select(store(q14,seq,earray_40),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_40),tail,select(q12,tail)),head) = select(store(q14,seq,earray_40),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1911,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head) = select(store(q14,seq,earray_40),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1912,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head) = select(store(q14,seq,earray_40),head) ) ),
inference(modus_ponens,[status(thm)],[1911,1910]) ).
tff(1913,plain,
select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head) = select(store(q14,seq,earray_40),head),
inference(unit_resolution,[status(thm)],[1912,89,1369]) ).
tff(1914,plain,
select(q12,tail) = index_42,
inference(transitivity,[status(thm)],[957,954,874]) ).
tff(1915,plain,
store(store(q14,seq,earray_40),tail,select(q12,tail)) = store(queue_41,tail,index_42),
inference(monotonicity,[status(thm)],[878,1914]) ).
tff(1916,plain,
select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head) = select(store(queue_41,tail,index_42),head),
inference(monotonicity,[status(thm)],[1915]) ).
tff(1917,plain,
select(store(queue_41,tail,index_42),head) = select(store(store(q14,seq,earray_40),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[1916]) ).
tff(1918,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head) = select(store(queue_41,tail,index_42),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_41,tail,index_42),seq,select(q16,seq)),head) = select(store(queue_41,tail,index_42),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1919,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head) = select(store(queue_41,tail,index_42),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1920,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head) = select(store(queue_41,tail,index_42),head) ) ),
inference(modus_ponens,[status(thm)],[1919,1918]) ).
tff(1921,plain,
select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head) = select(store(queue_41,tail,index_42),head),
inference(unit_resolution,[status(thm)],[1920,89,1339]) ).
tff(1922,plain,
( ( earray_46 = store(earray_44,index_45,e15) )
<=> ( earray_46 = store(earray_44,index_45,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1923,axiom,
earray_46 = store(earray_44,index_45,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(1924,plain,
earray_46 = store(earray_44,index_45,e15),
inference(modus_ponens,[status(thm)],[1923,1922]) ).
tff(1925,plain,
store(earray_44,index_45,e15) = earray_46,
inference(symmetry,[status(thm)],[1924]) ).
tff(1926,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_41,tail,index_42),seq,store(earray_44,index_45,e15)),seq) = store(earray_44,index_45,e15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1927,plain,
select(store(store(queue_41,tail,index_42),seq,store(earray_44,index_45,e15)),seq) = store(earray_44,index_45,e15),
inference(unit_resolution,[status(thm)],[1926,24]) ).
tff(1928,plain,
store(queue_41,tail,index_42) = q15,
inference(transitivity,[status(thm)],[1902,1901]) ).
tff(1929,plain,
store(store(queue_41,tail,index_42),seq,store(earray_44,index_45,e15)) = store(q15,seq,earray_46),
inference(monotonicity,[status(thm)],[1928,1925]) ).
tff(1930,plain,
select(store(store(queue_41,tail,index_42),seq,store(earray_44,index_45,e15)),seq) = select(store(q15,seq,earray_46),seq),
inference(monotonicity,[status(thm)],[1929]) ).
tff(1931,plain,
select(store(q15,seq,earray_46),seq) = select(store(store(queue_41,tail,index_42),seq,store(earray_44,index_45,e15)),seq),
inference(symmetry,[status(thm)],[1930]) ).
tff(1932,plain,
( ( ~ ! [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_46),tail,s(index_45)),seq) = select(store(q15,seq,earray_46),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_46),tail,s(index_45)),seq) = select(store(q15,seq,earray_46),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1933,plain,
( ~ ! [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_46),tail,s(index_45)),seq) = select(store(q15,seq,earray_46),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1934,plain,
( ~ ! [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_46),tail,s(index_45)),seq) = select(store(q15,seq,earray_46),seq) ) ),
inference(modus_ponens,[status(thm)],[1933,1932]) ).
tff(1935,plain,
select(store(store(q15,seq,earray_46),tail,s(index_45)),seq) = select(store(q15,seq,earray_46),seq),
inference(unit_resolution,[status(thm)],[1934,89,83]) ).
tff(1936,plain,
queue_49 = q16,
inference(symmetry,[status(thm)],[827]) ).
tff(1937,plain,
store(queue_47,tail,index_48) = queue_49,
inference(symmetry,[status(thm)],[824]) ).
tff(1938,plain,
store(store(q15,seq,earray_46),tail,s(index_45)) = q16,
inference(transitivity,[status(thm)],[820,1937,1936]) ).
tff(1939,plain,
select(store(store(q15,seq,earray_46),tail,s(index_45)),seq) = select(q16,seq),
inference(monotonicity,[status(thm)],[1938]) ).
tff(1940,plain,
select(q16,seq) = select(store(store(q15,seq,earray_46),tail,s(index_45)),seq),
inference(symmetry,[status(thm)],[1939]) ).
tff(1941,plain,
select(q16,seq) = earray_46,
inference(transitivity,[status(thm)],[1940,1935,1931,1927,1925]) ).
tff(1942,plain,
store(store(queue_41,tail,index_42),seq,select(q16,seq)) = store(q15,seq,earray_46),
inference(monotonicity,[status(thm)],[1928,1941]) ).
tff(1943,plain,
select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head) = select(store(q15,seq,earray_46),head),
inference(monotonicity,[status(thm)],[1942]) ).
tff(1944,plain,
select(store(q15,seq,earray_46),head) = select(store(store(queue_41,tail,index_42),seq,select(q16,seq)),head),
inference(symmetry,[status(thm)],[1943]) ).
tff(1945,plain,
( ( ~ ! [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_46),tail,select(q13,tail)),head) = select(store(q15,seq,earray_46),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_46),tail,select(q13,tail)),head) = select(store(q15,seq,earray_46),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1946,plain,
( ~ ! [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_46),tail,select(q13,tail)),head) = select(store(q15,seq,earray_46),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1947,plain,
( ~ ! [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_46),tail,select(q13,tail)),head) = select(store(q15,seq,earray_46),head) ) ),
inference(modus_ponens,[status(thm)],[1946,1945]) ).
tff(1948,plain,
select(store(store(q15,seq,earray_46),tail,select(q13,tail)),head) = select(store(q15,seq,earray_46),head),
inference(unit_resolution,[status(thm)],[1947,89,1369]) ).
tff(1949,plain,
select(q14,tail) = index_39,
inference(symmetry,[status(thm)],[951]) ).
tff(1950,plain,
s(index_33) = select(store(store(q13,seq,earray_34),tail,s(index_33)),tail),
inference(symmetry,[status(thm)],[928]) ).
tff(1951,plain,
s(select(q13,tail)) = s(index_33),
inference(monotonicity,[status(thm)],[896]) ).
tff(1952,plain,
s(select(q13,tail)) = index_39,
inference(transitivity,[status(thm)],[1951,1950,947,1949]) ).
tff(1953,plain,
s(s(select(q13,tail))) = s(index_39),
inference(monotonicity,[status(thm)],[1952]) ).
tff(1954,plain,
s(index_39) = s(s(select(q13,tail))),
inference(symmetry,[status(thm)],[1953]) ).
tff(1955,plain,
index_45 = s(s(select(q13,tail))),
inference(transitivity,[status(thm)],[836,888,891,1954]) ).
tff(1956,plain,
s(index_45) = s(s(s(select(q13,tail)))),
inference(monotonicity,[status(thm)],[1955]) ).
tff(1957,plain,
s(s(s(select(q13,tail)))) = s(index_45),
inference(symmetry,[status(thm)],[1956]) ).
tff(1958,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q13,tail)))) = select(q13,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1959,plain,
s(s(s(select(q13,tail)))) = select(q13,tail),
inference(unit_resolution,[status(thm)],[1958,187]) ).
tff(1960,plain,
select(q13,tail) = s(s(s(select(q13,tail)))),
inference(symmetry,[status(thm)],[1959]) ).
tff(1961,plain,
select(q13,tail) = index_48,
inference(transitivity,[status(thm)],[1960,1957,815]) ).
tff(1962,plain,
store(store(q15,seq,earray_46),tail,select(q13,tail)) = store(queue_47,tail,index_48),
inference(monotonicity,[status(thm)],[819,1961]) ).
tff(1963,plain,
select(store(store(q15,seq,earray_46),tail,select(q13,tail)),head) = select(store(queue_47,tail,index_48),head),
inference(monotonicity,[status(thm)],[1962]) ).
tff(1964,plain,
select(store(queue_47,tail,index_48),head) = select(store(store(q15,seq,earray_46),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[1963]) ).
tff(1965,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head) = select(store(queue_47,tail,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_47,tail,index_48),seq,select(q17,seq)),head) = select(store(queue_47,tail,index_48),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1966,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head) = select(store(queue_47,tail,index_48),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1967,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head) = select(store(queue_47,tail,index_48),head) ) ),
inference(modus_ponens,[status(thm)],[1966,1965]) ).
tff(1968,plain,
select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head) = select(store(queue_47,tail,index_48),head),
inference(unit_resolution,[status(thm)],[1967,89,1339]) ).
tff(1969,plain,
( ( earray_52 = store(earray_50,index_51,e16) )
<=> ( earray_52 = store(earray_50,index_51,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1970,axiom,
earray_52 = store(earray_50,index_51,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(1971,plain,
earray_52 = store(earray_50,index_51,e16),
inference(modus_ponens,[status(thm)],[1970,1969]) ).
tff(1972,plain,
store(earray_50,index_51,e16) = earray_52,
inference(symmetry,[status(thm)],[1971]) ).
tff(1973,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_47,tail,index_48),seq,store(earray_50,index_51,e16)),seq) = store(earray_50,index_51,e16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1974,plain,
select(store(store(queue_47,tail,index_48),seq,store(earray_50,index_51,e16)),seq) = store(earray_50,index_51,e16),
inference(unit_resolution,[status(thm)],[1973,24]) ).
tff(1975,plain,
store(queue_47,tail,index_48) = q16,
inference(transitivity,[status(thm)],[1937,1936]) ).
tff(1976,plain,
store(store(queue_47,tail,index_48),seq,store(earray_50,index_51,e16)) = store(q16,seq,earray_52),
inference(monotonicity,[status(thm)],[1975,1972]) ).
tff(1977,plain,
select(store(store(queue_47,tail,index_48),seq,store(earray_50,index_51,e16)),seq) = select(store(q16,seq,earray_52),seq),
inference(monotonicity,[status(thm)],[1976]) ).
tff(1978,plain,
select(store(q16,seq,earray_52),seq) = select(store(store(queue_47,tail,index_48),seq,store(earray_50,index_51,e16)),seq),
inference(symmetry,[status(thm)],[1977]) ).
tff(1979,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q16,seq,earray_52),tail,s(index_51)),seq) = select(store(q16,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(q16,seq,earray_52),tail,s(index_51)),seq) = select(store(q16,seq,earray_52),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1980,plain,
( ~ ! [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_52),tail,s(index_51)),seq) = select(store(q16,seq,earray_52),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1981,plain,
( ~ ! [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_52),tail,s(index_51)),seq) = select(store(q16,seq,earray_52),seq) ) ),
inference(modus_ponens,[status(thm)],[1980,1979]) ).
tff(1982,plain,
select(store(store(q16,seq,earray_52),tail,s(index_51)),seq) = select(store(q16,seq,earray_52),seq),
inference(unit_resolution,[status(thm)],[1981,89,83]) ).
tff(1983,plain,
queue_55 = q17,
inference(symmetry,[status(thm)],[859]) ).
tff(1984,plain,
store(queue_53,tail,index_54) = queue_55,
inference(symmetry,[status(thm)],[856]) ).
tff(1985,plain,
store(store(q16,seq,earray_52),tail,s(index_51)) = q17,
inference(transitivity,[status(thm)],[852,1984,1983]) ).
tff(1986,plain,
select(store(store(q16,seq,earray_52),tail,s(index_51)),seq) = select(q17,seq),
inference(monotonicity,[status(thm)],[1985]) ).
tff(1987,plain,
select(q17,seq) = select(store(store(q16,seq,earray_52),tail,s(index_51)),seq),
inference(symmetry,[status(thm)],[1986]) ).
tff(1988,plain,
select(q17,seq) = earray_52,
inference(transitivity,[status(thm)],[1987,1982,1978,1974,1972]) ).
tff(1989,plain,
store(store(queue_47,tail,index_48),seq,select(q17,seq)) = store(q16,seq,earray_52),
inference(monotonicity,[status(thm)],[1975,1988]) ).
tff(1990,plain,
select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head) = select(store(q16,seq,earray_52),head),
inference(monotonicity,[status(thm)],[1989]) ).
tff(1991,plain,
select(store(q16,seq,earray_52),head) = select(store(store(queue_47,tail,index_48),seq,select(q17,seq)),head),
inference(symmetry,[status(thm)],[1990]) ).
tff(1992,plain,
( ( ~ ! [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_52),tail,select(q14,tail)),head) = select(store(q16,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(q16,seq,earray_52),tail,select(q14,tail)),head) = select(store(q16,seq,earray_52),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1993,plain,
( ~ ! [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_52),tail,select(q14,tail)),head) = select(store(q16,seq,earray_52),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1994,plain,
( ~ ! [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_52),tail,select(q14,tail)),head) = select(store(q16,seq,earray_52),head) ) ),
inference(modus_ponens,[status(thm)],[1993,1992]) ).
tff(1995,plain,
select(store(store(q16,seq,earray_52),tail,select(q14,tail)),head) = select(store(q16,seq,earray_52),head),
inference(unit_resolution,[status(thm)],[1994,89,1369]) ).
tff(1996,plain,
s(select(q14,tail)) = s(index_39),
inference(monotonicity,[status(thm)],[1949]) ).
tff(1997,plain,
s(select(q14,tail)) = index_45,
inference(transitivity,[status(thm)],[1996,892,889,837]) ).
tff(1998,plain,
s(s(select(q14,tail))) = s(index_45),
inference(monotonicity,[status(thm)],[1997]) ).
tff(1999,plain,
s(index_45) = s(s(select(q14,tail))),
inference(symmetry,[status(thm)],[1998]) ).
tff(2000,plain,
index_51 = s(s(select(q14,tail))),
inference(transitivity,[status(thm)],[810,829,832,1999]) ).
tff(2001,plain,
s(index_51) = s(s(s(select(q14,tail)))),
inference(monotonicity,[status(thm)],[2000]) ).
tff(2002,plain,
s(s(s(select(q14,tail)))) = s(index_51),
inference(symmetry,[status(thm)],[2001]) ).
tff(2003,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q14,tail)))) = select(q14,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2004,plain,
s(s(s(select(q14,tail)))) = select(q14,tail),
inference(unit_resolution,[status(thm)],[2003,187]) ).
tff(2005,plain,
select(q14,tail) = s(s(s(select(q14,tail)))),
inference(symmetry,[status(thm)],[2004]) ).
tff(2006,plain,
select(q14,tail) = index_54,
inference(transitivity,[status(thm)],[2005,2002,847]) ).
tff(2007,plain,
store(store(q16,seq,earray_52),tail,select(q14,tail)) = store(queue_53,tail,index_54),
inference(monotonicity,[status(thm)],[851,2006]) ).
tff(2008,plain,
select(store(store(q16,seq,earray_52),tail,select(q14,tail)),head) = select(store(queue_53,tail,index_54),head),
inference(monotonicity,[status(thm)],[2007]) ).
tff(2009,plain,
select(store(queue_53,tail,index_54),head) = select(store(store(q16,seq,earray_52),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2008]) ).
tff(2010,plain,
( ( ~ ! [I: $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(q18,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(q18,seq)),head) = select(store(queue_53,tail,index_54),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2011,plain,
( ~ ! [I: $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(q18,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2012,plain,
( ~ ! [I: $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(q18,seq)),head) = select(store(queue_53,tail,index_54),head) ) ),
inference(modus_ponens,[status(thm)],[2011,2010]) ).
tff(2013,plain,
select(store(store(queue_53,tail,index_54),seq,select(q18,seq)),head) = select(store(queue_53,tail,index_54),head),
inference(unit_resolution,[status(thm)],[2012,89,1339]) ).
tff(2014,plain,
( ( earray_58 = store(earray_56,index_57,e17) )
<=> ( earray_58 = store(earray_56,index_57,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2015,axiom,
earray_58 = store(earray_56,index_57,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(2016,plain,
earray_58 = store(earray_56,index_57,e17),
inference(modus_ponens,[status(thm)],[2015,2014]) ).
tff(2017,plain,
store(earray_56,index_57,e17) = earray_58,
inference(symmetry,[status(thm)],[2016]) ).
tff(2018,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e17)),seq) = store(earray_56,index_57,e17) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2019,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e17)),seq) = store(earray_56,index_57,e17),
inference(unit_resolution,[status(thm)],[2018,24]) ).
tff(2020,plain,
store(queue_53,tail,index_54) = q17,
inference(transitivity,[status(thm)],[1984,1983]) ).
tff(2021,plain,
store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e17)) = store(q17,seq,earray_58),
inference(monotonicity,[status(thm)],[2020,2017]) ).
tff(2022,plain,
select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e17)),seq) = select(store(q17,seq,earray_58),seq),
inference(monotonicity,[status(thm)],[2021]) ).
tff(2023,plain,
select(store(q17,seq,earray_58),seq) = select(store(store(queue_53,tail,index_54),seq,store(earray_56,index_57,e17)),seq),
inference(symmetry,[status(thm)],[2022]) ).
tff(2024,plain,
( ( ~ ! [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_58),tail,s(index_57)),seq) = select(store(q17,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(q17,seq,earray_58),tail,s(index_57)),seq) = select(store(q17,seq,earray_58),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2025,plain,
( ~ ! [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_58),tail,s(index_57)),seq) = select(store(q17,seq,earray_58),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2026,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q17,seq,earray_58),tail,s(index_57)),seq) = select(store(q17,seq,earray_58),seq) ) ),
inference(modus_ponens,[status(thm)],[2025,2024]) ).
tff(2027,plain,
select(store(store(q17,seq,earray_58),tail,s(index_57)),seq) = select(store(q17,seq,earray_58),seq),
inference(unit_resolution,[status(thm)],[2026,89,83]) ).
tff(2028,plain,
queue_61 = q18,
inference(symmetry,[status(thm)],[801]) ).
tff(2029,plain,
store(queue_59,tail,index_60) = queue_61,
inference(symmetry,[status(thm)],[798]) ).
tff(2030,plain,
store(store(q17,seq,earray_58),tail,s(index_57)) = q18,
inference(transitivity,[status(thm)],[794,2029,2028]) ).
tff(2031,plain,
select(store(store(q17,seq,earray_58),tail,s(index_57)),seq) = select(q18,seq),
inference(monotonicity,[status(thm)],[2030]) ).
tff(2032,plain,
select(q18,seq) = select(store(store(q17,seq,earray_58),tail,s(index_57)),seq),
inference(symmetry,[status(thm)],[2031]) ).
tff(2033,plain,
select(q18,seq) = earray_58,
inference(transitivity,[status(thm)],[2032,2027,2023,2019,2017]) ).
tff(2034,plain,
store(store(queue_53,tail,index_54),seq,select(q18,seq)) = store(q17,seq,earray_58),
inference(monotonicity,[status(thm)],[2020,2033]) ).
tff(2035,plain,
select(store(store(queue_53,tail,index_54),seq,select(q18,seq)),head) = select(store(q17,seq,earray_58),head),
inference(monotonicity,[status(thm)],[2034]) ).
tff(2036,plain,
select(store(q17,seq,earray_58),head) = select(store(store(queue_53,tail,index_54),seq,select(q18,seq)),head),
inference(symmetry,[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(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(q17,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(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(q17,seq,earray_58),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(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(q17,seq,earray_58),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(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(q17,seq,earray_58),head) ) ),
inference(modus_ponens,[status(thm)],[2038,2037]) ).
tff(2040,plain,
select(store(store(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(q17,seq,earray_58),head),
inference(unit_resolution,[status(thm)],[2039,89,1369]) ).
tff(2041,plain,
select(q12,tail) = index_60,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,789]) ).
tff(2042,plain,
store(store(q17,seq,earray_58),tail,select(q12,tail)) = store(queue_59,tail,index_60),
inference(monotonicity,[status(thm)],[793,2041]) ).
tff(2043,plain,
select(store(store(q17,seq,earray_58),tail,select(q12,tail)),head) = select(store(queue_59,tail,index_60),head),
inference(monotonicity,[status(thm)],[2042]) ).
tff(2044,plain,
select(store(queue_59,tail,index_60),head) = select(store(store(q17,seq,earray_58),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2043]) ).
tff(2045,plain,
( ( ~ ! [I: $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(q19,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(q19,seq)),head) = select(store(queue_59,tail,index_60),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2046,plain,
( ~ ! [I: $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(q19,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2047,plain,
( ~ ! [I: $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(q19,seq)),head) = select(store(queue_59,tail,index_60),head) ) ),
inference(modus_ponens,[status(thm)],[2046,2045]) ).
tff(2048,plain,
select(store(store(queue_59,tail,index_60),seq,select(q19,seq)),head) = select(store(queue_59,tail,index_60),head),
inference(unit_resolution,[status(thm)],[2047,89,1339]) ).
tff(2049,plain,
( ( earray_64 = store(earray_62,index_63,e18) )
<=> ( earray_64 = store(earray_62,index_63,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2050,axiom,
earray_64 = store(earray_62,index_63,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(2051,plain,
earray_64 = store(earray_62,index_63,e18),
inference(modus_ponens,[status(thm)],[2050,2049]) ).
tff(2052,plain,
store(earray_62,index_63,e18) = earray_64,
inference(symmetry,[status(thm)],[2051]) ).
tff(2053,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,e18)),seq) = store(earray_62,index_63,e18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2054,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e18)),seq) = store(earray_62,index_63,e18),
inference(unit_resolution,[status(thm)],[2053,24]) ).
tff(2055,plain,
store(queue_59,tail,index_60) = q18,
inference(transitivity,[status(thm)],[2029,2028]) ).
tff(2056,plain,
store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e18)) = store(q18,seq,earray_64),
inference(monotonicity,[status(thm)],[2055,2052]) ).
tff(2057,plain,
select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e18)),seq) = select(store(q18,seq,earray_64),seq),
inference(monotonicity,[status(thm)],[2056]) ).
tff(2058,plain,
select(store(q18,seq,earray_64),seq) = select(store(store(queue_59,tail,index_60),seq,store(earray_62,index_63,e18)),seq),
inference(symmetry,[status(thm)],[2057]) ).
tff(2059,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_64),tail,s(index_63)),seq) = select(store(q18,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(q18,seq,earray_64),tail,s(index_63)),seq) = select(store(q18,seq,earray_64),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2060,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_64),tail,s(index_63)),seq) = select(store(q18,seq,earray_64),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q18,seq,earray_64),tail,s(index_63)),seq) = select(store(q18,seq,earray_64),seq) ) ),
inference(modus_ponens,[status(thm)],[2060,2059]) ).
tff(2062,plain,
select(store(store(q18,seq,earray_64),tail,s(index_63)),seq) = select(store(q18,seq,earray_64),seq),
inference(unit_resolution,[status(thm)],[2061,89,83]) ).
tff(2063,plain,
queue_67 = q19,
inference(symmetry,[status(thm)],[742]) ).
tff(2064,plain,
store(queue_65,tail,index_66) = queue_67,
inference(symmetry,[status(thm)],[739]) ).
tff(2065,plain,
store(store(q18,seq,earray_64),tail,s(index_63)) = q19,
inference(transitivity,[status(thm)],[735,2064,2063]) ).
tff(2066,plain,
select(store(store(q18,seq,earray_64),tail,s(index_63)),seq) = select(q19,seq),
inference(monotonicity,[status(thm)],[2065]) ).
tff(2067,plain,
select(q19,seq) = select(store(store(q18,seq,earray_64),tail,s(index_63)),seq),
inference(symmetry,[status(thm)],[2066]) ).
tff(2068,plain,
select(q19,seq) = earray_64,
inference(transitivity,[status(thm)],[2067,2062,2058,2054,2052]) ).
tff(2069,plain,
store(store(queue_59,tail,index_60),seq,select(q19,seq)) = store(q18,seq,earray_64),
inference(monotonicity,[status(thm)],[2055,2068]) ).
tff(2070,plain,
select(store(store(queue_59,tail,index_60),seq,select(q19,seq)),head) = select(store(q18,seq,earray_64),head),
inference(monotonicity,[status(thm)],[2069]) ).
tff(2071,plain,
select(store(q18,seq,earray_64),head) = select(store(store(queue_59,tail,index_60),seq,select(q19,seq)),head),
inference(symmetry,[status(thm)],[2070]) ).
tff(2072,plain,
( ( ~ ! [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_64),tail,select(q13,tail)),head) = select(store(q18,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(q18,seq,earray_64),tail,select(q13,tail)),head) = select(store(q18,seq,earray_64),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2073,plain,
( ~ ! [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_64),tail,select(q13,tail)),head) = select(store(q18,seq,earray_64),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2074,plain,
( ~ ! [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_64),tail,select(q13,tail)),head) = select(store(q18,seq,earray_64),head) ) ),
inference(modus_ponens,[status(thm)],[2073,2072]) ).
tff(2075,plain,
select(store(store(q18,seq,earray_64),tail,select(q13,tail)),head) = select(store(q18,seq,earray_64),head),
inference(unit_resolution,[status(thm)],[2074,89,1369]) ).
tff(2076,plain,
select(q17,tail) = index_57,
inference(symmetry,[status(thm)],[864]) ).
tff(2077,plain,
select(store(store(q16,seq,earray_52),tail,s(index_51)),tail) = select(q17,tail),
inference(symmetry,[status(thm)],[861]) ).
tff(2078,plain,
s(index_51) = select(store(store(q16,seq,earray_52),tail,s(index_51)),tail),
inference(symmetry,[status(thm)],[843]) ).
tff(2079,plain,
s(select(q16,tail)) = s(index_51),
inference(monotonicity,[status(thm)],[811]) ).
tff(2080,plain,
s(select(q16,tail)) = index_57,
inference(transitivity,[status(thm)],[2079,2078,2077,2076]) ).
tff(2081,plain,
s(s(select(q16,tail))) = s(index_57),
inference(monotonicity,[status(thm)],[2080]) ).
tff(2082,plain,
s(index_57) = s(s(select(q16,tail))),
inference(symmetry,[status(thm)],[2081]) ).
tff(2083,plain,
index_63 = s(s(select(q16,tail))),
inference(transitivity,[status(thm)],[751,803,806,2082]) ).
tff(2084,plain,
s(index_63) = s(s(s(select(q16,tail)))),
inference(monotonicity,[status(thm)],[2083]) ).
tff(2085,plain,
s(s(s(select(q16,tail)))) = s(index_63),
inference(symmetry,[status(thm)],[2084]) ).
tff(2086,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q16,tail)))) = select(q16,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2087,plain,
s(s(s(select(q16,tail)))) = select(q16,tail),
inference(unit_resolution,[status(thm)],[2086,187]) ).
tff(2088,plain,
select(q16,tail) = s(s(s(select(q16,tail)))),
inference(symmetry,[status(thm)],[2087]) ).
tff(2089,plain,
select(q13,tail) = index_66,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,730]) ).
tff(2090,plain,
store(store(q18,seq,earray_64),tail,select(q13,tail)) = store(queue_65,tail,index_66),
inference(monotonicity,[status(thm)],[734,2089]) ).
tff(2091,plain,
select(store(store(q18,seq,earray_64),tail,select(q13,tail)),head) = select(store(queue_65,tail,index_66),head),
inference(monotonicity,[status(thm)],[2090]) ).
tff(2092,plain,
select(store(queue_65,tail,index_66),head) = select(store(store(q18,seq,earray_64),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2091]) ).
tff(2093,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head) = select(store(queue_65,tail,index_66),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_65,tail,index_66),seq,select(q20,seq)),head) = select(store(queue_65,tail,index_66),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2094,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head) = select(store(queue_65,tail,index_66),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2095,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head) = select(store(queue_65,tail,index_66),head) ) ),
inference(modus_ponens,[status(thm)],[2094,2093]) ).
tff(2096,plain,
select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head) = select(store(queue_65,tail,index_66),head),
inference(unit_resolution,[status(thm)],[2095,89,1339]) ).
tff(2097,plain,
( ( earray_76 = store(earray_74,index_75,e19) )
<=> ( earray_76 = store(earray_74,index_75,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2098,axiom,
earray_76 = store(earray_74,index_75,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(2099,plain,
earray_76 = store(earray_74,index_75,e19),
inference(modus_ponens,[status(thm)],[2098,2097]) ).
tff(2100,plain,
store(earray_74,index_75,e19) = earray_76,
inference(symmetry,[status(thm)],[2099]) ).
tff(2101,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_65,tail,index_66),seq,store(earray_74,index_75,e19)),seq) = store(earray_74,index_75,e19) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2102,plain,
select(store(store(queue_65,tail,index_66),seq,store(earray_74,index_75,e19)),seq) = store(earray_74,index_75,e19),
inference(unit_resolution,[status(thm)],[2101,24]) ).
tff(2103,plain,
store(queue_65,tail,index_66) = q19,
inference(transitivity,[status(thm)],[2064,2063]) ).
tff(2104,plain,
store(store(queue_65,tail,index_66),seq,store(earray_74,index_75,e19)) = store(q19,seq,earray_76),
inference(monotonicity,[status(thm)],[2103,2100]) ).
tff(2105,plain,
select(store(store(queue_65,tail,index_66),seq,store(earray_74,index_75,e19)),seq) = select(store(q19,seq,earray_76),seq),
inference(monotonicity,[status(thm)],[2104]) ).
tff(2106,plain,
select(store(q19,seq,earray_76),seq) = select(store(store(queue_65,tail,index_66),seq,store(earray_74,index_75,e19)),seq),
inference(symmetry,[status(thm)],[2105]) ).
tff(2107,plain,
( ( ~ ! [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_76),tail,s(index_75)),seq) = select(store(q19,seq,earray_76),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_76),tail,s(index_75)),seq) = select(store(q19,seq,earray_76),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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(q19,seq,earray_76),tail,s(index_75)),seq) = select(store(q19,seq,earray_76),seq) ) ),
inference(quant_inst,[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(q19,seq,earray_76),tail,s(index_75)),seq) = select(store(q19,seq,earray_76),seq) ) ),
inference(modus_ponens,[status(thm)],[2108,2107]) ).
tff(2110,plain,
select(store(store(q19,seq,earray_76),tail,s(index_75)),seq) = select(store(q19,seq,earray_76),seq),
inference(unit_resolution,[status(thm)],[2109,89,83]) ).
tff(2111,plain,
queue_79 = q20,
inference(symmetry,[status(thm)],[774]) ).
tff(2112,plain,
store(queue_77,tail,index_78) = queue_79,
inference(symmetry,[status(thm)],[771]) ).
tff(2113,plain,
store(store(q19,seq,earray_76),tail,s(index_75)) = q20,
inference(transitivity,[status(thm)],[767,2112,2111]) ).
tff(2114,plain,
select(store(store(q19,seq,earray_76),tail,s(index_75)),seq) = select(q20,seq),
inference(monotonicity,[status(thm)],[2113]) ).
tff(2115,plain,
select(q20,seq) = select(store(store(q19,seq,earray_76),tail,s(index_75)),seq),
inference(symmetry,[status(thm)],[2114]) ).
tff(2116,plain,
select(q20,seq) = earray_76,
inference(transitivity,[status(thm)],[2115,2110,2106,2102,2100]) ).
tff(2117,plain,
store(store(queue_65,tail,index_66),seq,select(q20,seq)) = store(q19,seq,earray_76),
inference(monotonicity,[status(thm)],[2103,2116]) ).
tff(2118,plain,
select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head) = select(store(q19,seq,earray_76),head),
inference(monotonicity,[status(thm)],[2117]) ).
tff(2119,plain,
select(store(q19,seq,earray_76),head) = select(store(store(queue_65,tail,index_66),seq,select(q20,seq)),head),
inference(symmetry,[status(thm)],[2118]) ).
tff(2120,plain,
( ( ~ ! [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_76),tail,select(q14,tail)),head) = select(store(q19,seq,earray_76),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_76),tail,select(q14,tail)),head) = select(store(q19,seq,earray_76),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2121,plain,
( ~ ! [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_76),tail,select(q14,tail)),head) = select(store(q19,seq,earray_76),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2122,plain,
( ~ ! [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_76),tail,select(q14,tail)),head) = select(store(q19,seq,earray_76),head) ) ),
inference(modus_ponens,[status(thm)],[2121,2120]) ).
tff(2123,plain,
select(store(store(q19,seq,earray_76),tail,select(q14,tail)),head) = select(store(q19,seq,earray_76),head),
inference(unit_resolution,[status(thm)],[2122,89,1369]) ).
tff(2124,plain,
s(select(q17,tail)) = s(index_57),
inference(monotonicity,[status(thm)],[2076]) ).
tff(2125,plain,
s(select(q17,tail)) = index_63,
inference(transitivity,[status(thm)],[2124,807,804,752]) ).
tff(2126,plain,
s(s(select(q17,tail))) = s(index_63),
inference(monotonicity,[status(thm)],[2125]) ).
tff(2127,plain,
s(index_63) = s(s(select(q17,tail))),
inference(symmetry,[status(thm)],[2126]) ).
tff(2128,plain,
index_75 = s(s(select(q17,tail))),
inference(transitivity,[status(thm)],[725,744,747,2127]) ).
tff(2129,plain,
s(index_75) = s(s(s(select(q17,tail)))),
inference(monotonicity,[status(thm)],[2128]) ).
tff(2130,plain,
s(s(s(select(q17,tail)))) = s(index_75),
inference(symmetry,[status(thm)],[2129]) ).
tff(2131,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q17,tail)))) = select(q17,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2132,plain,
s(s(s(select(q17,tail)))) = select(q17,tail),
inference(unit_resolution,[status(thm)],[2131,187]) ).
tff(2133,plain,
select(q17,tail) = s(s(s(select(q17,tail)))),
inference(symmetry,[status(thm)],[2132]) ).
tff(2134,plain,
select(q14,tail) = index_78,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,762]) ).
tff(2135,plain,
store(store(q19,seq,earray_76),tail,select(q14,tail)) = store(queue_77,tail,index_78),
inference(monotonicity,[status(thm)],[766,2134]) ).
tff(2136,plain,
select(store(store(q19,seq,earray_76),tail,select(q14,tail)),head) = select(store(queue_77,tail,index_78),head),
inference(monotonicity,[status(thm)],[2135]) ).
tff(2137,plain,
select(store(queue_77,tail,index_78),head) = select(store(store(q19,seq,earray_76),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2136]) ).
tff(2138,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head) = select(store(queue_77,tail,index_78),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_77,tail,index_78),seq,select(q21,seq)),head) = select(store(queue_77,tail,index_78),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2139,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head) = select(store(queue_77,tail,index_78),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2140,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head) = select(store(queue_77,tail,index_78),head) ) ),
inference(modus_ponens,[status(thm)],[2139,2138]) ).
tff(2141,plain,
select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head) = select(store(queue_77,tail,index_78),head),
inference(unit_resolution,[status(thm)],[2140,89,1339]) ).
tff(2142,plain,
( ( earray_82 = store(earray_80,index_81,e20) )
<=> ( earray_82 = store(earray_80,index_81,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2143,axiom,
earray_82 = store(earray_80,index_81,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(2144,plain,
earray_82 = store(earray_80,index_81,e20),
inference(modus_ponens,[status(thm)],[2143,2142]) ).
tff(2145,plain,
store(earray_80,index_81,e20) = earray_82,
inference(symmetry,[status(thm)],[2144]) ).
tff(2146,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_77,tail,index_78),seq,store(earray_80,index_81,e20)),seq) = store(earray_80,index_81,e20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2147,plain,
select(store(store(queue_77,tail,index_78),seq,store(earray_80,index_81,e20)),seq) = store(earray_80,index_81,e20),
inference(unit_resolution,[status(thm)],[2146,24]) ).
tff(2148,plain,
store(queue_77,tail,index_78) = q20,
inference(transitivity,[status(thm)],[2112,2111]) ).
tff(2149,plain,
store(store(queue_77,tail,index_78),seq,store(earray_80,index_81,e20)) = store(q20,seq,earray_82),
inference(monotonicity,[status(thm)],[2148,2145]) ).
tff(2150,plain,
select(store(store(queue_77,tail,index_78),seq,store(earray_80,index_81,e20)),seq) = select(store(q20,seq,earray_82),seq),
inference(monotonicity,[status(thm)],[2149]) ).
tff(2151,plain,
select(store(q20,seq,earray_82),seq) = select(store(store(queue_77,tail,index_78),seq,store(earray_80,index_81,e20)),seq),
inference(symmetry,[status(thm)],[2150]) ).
tff(2152,plain,
( ( ~ ! [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_82),tail,s(index_81)),seq) = select(store(q20,seq,earray_82),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_82),tail,s(index_81)),seq) = select(store(q20,seq,earray_82),seq) ) ) ),
inference(rewrite,[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 = seq )
| ( select(store(store(q20,seq,earray_82),tail,s(index_81)),seq) = select(store(q20,seq,earray_82),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2154,plain,
( ~ ! [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_82),tail,s(index_81)),seq) = select(store(q20,seq,earray_82),seq) ) ),
inference(modus_ponens,[status(thm)],[2153,2152]) ).
tff(2155,plain,
select(store(store(q20,seq,earray_82),tail,s(index_81)),seq) = select(store(q20,seq,earray_82),seq),
inference(unit_resolution,[status(thm)],[2154,89,83]) ).
tff(2156,plain,
queue_85 = q21,
inference(symmetry,[status(thm)],[716]) ).
tff(2157,plain,
store(queue_83,tail,index_84) = queue_85,
inference(symmetry,[status(thm)],[713]) ).
tff(2158,plain,
store(store(q20,seq,earray_82),tail,s(index_81)) = q21,
inference(transitivity,[status(thm)],[709,2157,2156]) ).
tff(2159,plain,
select(store(store(q20,seq,earray_82),tail,s(index_81)),seq) = select(q21,seq),
inference(monotonicity,[status(thm)],[2158]) ).
tff(2160,plain,
select(q21,seq) = select(store(store(q20,seq,earray_82),tail,s(index_81)),seq),
inference(symmetry,[status(thm)],[2159]) ).
tff(2161,plain,
select(q21,seq) = earray_82,
inference(transitivity,[status(thm)],[2160,2155,2151,2147,2145]) ).
tff(2162,plain,
store(store(queue_77,tail,index_78),seq,select(q21,seq)) = store(q20,seq,earray_82),
inference(monotonicity,[status(thm)],[2148,2161]) ).
tff(2163,plain,
select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head) = select(store(q20,seq,earray_82),head),
inference(monotonicity,[status(thm)],[2162]) ).
tff(2164,plain,
select(store(q20,seq,earray_82),head) = select(store(store(queue_77,tail,index_78),seq,select(q21,seq)),head),
inference(symmetry,[status(thm)],[2163]) ).
tff(2165,plain,
( ( ~ ! [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_82),tail,select(q12,tail)),head) = select(store(q20,seq,earray_82),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_82),tail,select(q12,tail)),head) = select(store(q20,seq,earray_82),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2166,plain,
( ~ ! [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_82),tail,select(q12,tail)),head) = select(store(q20,seq,earray_82),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2167,plain,
( ~ ! [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_82),tail,select(q12,tail)),head) = select(store(q20,seq,earray_82),head) ) ),
inference(modus_ponens,[status(thm)],[2166,2165]) ).
tff(2168,plain,
select(store(store(q20,seq,earray_82),tail,select(q12,tail)),head) = select(store(q20,seq,earray_82),head),
inference(unit_resolution,[status(thm)],[2167,89,1369]) ).
tff(2169,plain,
select(q12,tail) = index_84,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,704]) ).
tff(2170,plain,
store(store(q20,seq,earray_82),tail,select(q12,tail)) = store(queue_83,tail,index_84),
inference(monotonicity,[status(thm)],[708,2169]) ).
tff(2171,plain,
select(store(store(q20,seq,earray_82),tail,select(q12,tail)),head) = select(store(queue_83,tail,index_84),head),
inference(monotonicity,[status(thm)],[2170]) ).
tff(2172,plain,
select(store(queue_83,tail,index_84),head) = select(store(store(q20,seq,earray_82),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2171]) ).
tff(2173,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head) = select(store(queue_83,tail,index_84),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_83,tail,index_84),seq,select(q22,seq)),head) = select(store(queue_83,tail,index_84),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2174,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head) = select(store(queue_83,tail,index_84),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2175,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head) = select(store(queue_83,tail,index_84),head) ) ),
inference(modus_ponens,[status(thm)],[2174,2173]) ).
tff(2176,plain,
select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head) = select(store(queue_83,tail,index_84),head),
inference(unit_resolution,[status(thm)],[2175,89,1339]) ).
tff(2177,plain,
( ( earray_88 = store(earray_86,index_87,e21) )
<=> ( earray_88 = store(earray_86,index_87,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2178,axiom,
earray_88 = store(earray_86,index_87,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp83) ).
tff(2179,plain,
earray_88 = store(earray_86,index_87,e21),
inference(modus_ponens,[status(thm)],[2178,2177]) ).
tff(2180,plain,
store(earray_86,index_87,e21) = earray_88,
inference(symmetry,[status(thm)],[2179]) ).
tff(2181,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_83,tail,index_84),seq,store(earray_86,index_87,e21)),seq) = store(earray_86,index_87,e21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2182,plain,
select(store(store(queue_83,tail,index_84),seq,store(earray_86,index_87,e21)),seq) = store(earray_86,index_87,e21),
inference(unit_resolution,[status(thm)],[2181,24]) ).
tff(2183,plain,
store(queue_83,tail,index_84) = q21,
inference(transitivity,[status(thm)],[2157,2156]) ).
tff(2184,plain,
store(store(queue_83,tail,index_84),seq,store(earray_86,index_87,e21)) = store(q21,seq,earray_88),
inference(monotonicity,[status(thm)],[2183,2180]) ).
tff(2185,plain,
select(store(store(queue_83,tail,index_84),seq,store(earray_86,index_87,e21)),seq) = select(store(q21,seq,earray_88),seq),
inference(monotonicity,[status(thm)],[2184]) ).
tff(2186,plain,
select(store(q21,seq,earray_88),seq) = select(store(store(queue_83,tail,index_84),seq,store(earray_86,index_87,e21)),seq),
inference(symmetry,[status(thm)],[2185]) ).
tff(2187,plain,
( ( ~ ! [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_88),tail,s(index_87)),seq) = select(store(q21,seq,earray_88),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_88),tail,s(index_87)),seq) = select(store(q21,seq,earray_88),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2188,plain,
( ~ ! [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_88),tail,s(index_87)),seq) = select(store(q21,seq,earray_88),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2189,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q21,seq,earray_88),tail,s(index_87)),seq) = select(store(q21,seq,earray_88),seq) ) ),
inference(modus_ponens,[status(thm)],[2188,2187]) ).
tff(2190,plain,
select(store(store(q21,seq,earray_88),tail,s(index_87)),seq) = select(store(q21,seq,earray_88),seq),
inference(unit_resolution,[status(thm)],[2189,89,83]) ).
tff(2191,plain,
queue_91 = q22,
inference(symmetry,[status(thm)],[657]) ).
tff(2192,plain,
store(queue_89,tail,index_90) = queue_91,
inference(symmetry,[status(thm)],[654]) ).
tff(2193,plain,
store(store(q21,seq,earray_88),tail,s(index_87)) = q22,
inference(transitivity,[status(thm)],[650,2192,2191]) ).
tff(2194,plain,
select(store(store(q21,seq,earray_88),tail,s(index_87)),seq) = select(q22,seq),
inference(monotonicity,[status(thm)],[2193]) ).
tff(2195,plain,
select(q22,seq) = select(store(store(q21,seq,earray_88),tail,s(index_87)),seq),
inference(symmetry,[status(thm)],[2194]) ).
tff(2196,plain,
select(q22,seq) = earray_88,
inference(transitivity,[status(thm)],[2195,2190,2186,2182,2180]) ).
tff(2197,plain,
store(store(queue_83,tail,index_84),seq,select(q22,seq)) = store(q21,seq,earray_88),
inference(monotonicity,[status(thm)],[2183,2196]) ).
tff(2198,plain,
select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head) = select(store(q21,seq,earray_88),head),
inference(monotonicity,[status(thm)],[2197]) ).
tff(2199,plain,
select(store(q21,seq,earray_88),head) = select(store(store(queue_83,tail,index_84),seq,select(q22,seq)),head),
inference(symmetry,[status(thm)],[2198]) ).
tff(2200,plain,
( ( ~ ! [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_88),tail,select(q13,tail)),head) = select(store(q21,seq,earray_88),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_88),tail,select(q13,tail)),head) = select(store(q21,seq,earray_88),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2201,plain,
( ~ ! [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_88),tail,select(q13,tail)),head) = select(store(q21,seq,earray_88),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2202,plain,
( ~ ! [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_88),tail,select(q13,tail)),head) = select(store(q21,seq,earray_88),head) ) ),
inference(modus_ponens,[status(thm)],[2201,2200]) ).
tff(2203,plain,
select(store(store(q21,seq,earray_88),tail,select(q13,tail)),head) = select(store(q21,seq,earray_88),head),
inference(unit_resolution,[status(thm)],[2202,89,1369]) ).
tff(2204,plain,
select(q20,tail) = index_81,
inference(symmetry,[status(thm)],[779]) ).
tff(2205,plain,
select(store(store(q19,seq,earray_76),tail,s(index_75)),tail) = select(q20,tail),
inference(symmetry,[status(thm)],[776]) ).
tff(2206,plain,
s(index_75) = select(store(store(q19,seq,earray_76),tail,s(index_75)),tail),
inference(symmetry,[status(thm)],[758]) ).
tff(2207,plain,
s(select(q19,tail)) = s(index_75),
inference(monotonicity,[status(thm)],[726]) ).
tff(2208,plain,
s(select(q19,tail)) = index_81,
inference(transitivity,[status(thm)],[2207,2206,2205,2204]) ).
tff(2209,plain,
s(s(select(q19,tail))) = s(index_81),
inference(monotonicity,[status(thm)],[2208]) ).
tff(2210,plain,
s(index_81) = s(s(select(q19,tail))),
inference(symmetry,[status(thm)],[2209]) ).
tff(2211,plain,
index_87 = s(s(select(q19,tail))),
inference(transitivity,[status(thm)],[666,718,721,2210]) ).
tff(2212,plain,
s(index_87) = s(s(s(select(q19,tail)))),
inference(monotonicity,[status(thm)],[2211]) ).
tff(2213,plain,
s(s(s(select(q19,tail)))) = s(index_87),
inference(symmetry,[status(thm)],[2212]) ).
tff(2214,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q19,tail)))) = select(q19,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2215,plain,
s(s(s(select(q19,tail)))) = select(q19,tail),
inference(unit_resolution,[status(thm)],[2214,187]) ).
tff(2216,plain,
select(q19,tail) = s(s(s(select(q19,tail)))),
inference(symmetry,[status(thm)],[2215]) ).
tff(2217,plain,
select(q13,tail) = index_90,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,645]) ).
tff(2218,plain,
store(store(q21,seq,earray_88),tail,select(q13,tail)) = store(queue_89,tail,index_90),
inference(monotonicity,[status(thm)],[649,2217]) ).
tff(2219,plain,
select(store(store(q21,seq,earray_88),tail,select(q13,tail)),head) = select(store(queue_89,tail,index_90),head),
inference(monotonicity,[status(thm)],[2218]) ).
tff(2220,plain,
select(store(queue_89,tail,index_90),head) = select(store(store(q21,seq,earray_88),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2219]) ).
tff(2221,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head) = select(store(queue_89,tail,index_90),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_89,tail,index_90),seq,select(q23,seq)),head) = select(store(queue_89,tail,index_90),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2222,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head) = select(store(queue_89,tail,index_90),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2223,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head) = select(store(queue_89,tail,index_90),head) ) ),
inference(modus_ponens,[status(thm)],[2222,2221]) ).
tff(2224,plain,
select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head) = select(store(queue_89,tail,index_90),head),
inference(unit_resolution,[status(thm)],[2223,89,1339]) ).
tff(2225,plain,
( ( earray_94 = store(earray_92,index_93,e22) )
<=> ( earray_94 = store(earray_92,index_93,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2226,axiom,
earray_94 = store(earray_92,index_93,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp85) ).
tff(2227,plain,
earray_94 = store(earray_92,index_93,e22),
inference(modus_ponens,[status(thm)],[2226,2225]) ).
tff(2228,plain,
store(earray_92,index_93,e22) = earray_94,
inference(symmetry,[status(thm)],[2227]) ).
tff(2229,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_89,tail,index_90),seq,store(earray_92,index_93,e22)),seq) = store(earray_92,index_93,e22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2230,plain,
select(store(store(queue_89,tail,index_90),seq,store(earray_92,index_93,e22)),seq) = store(earray_92,index_93,e22),
inference(unit_resolution,[status(thm)],[2229,24]) ).
tff(2231,plain,
store(queue_89,tail,index_90) = q22,
inference(transitivity,[status(thm)],[2192,2191]) ).
tff(2232,plain,
store(store(queue_89,tail,index_90),seq,store(earray_92,index_93,e22)) = store(q22,seq,earray_94),
inference(monotonicity,[status(thm)],[2231,2228]) ).
tff(2233,plain,
select(store(store(queue_89,tail,index_90),seq,store(earray_92,index_93,e22)),seq) = select(store(q22,seq,earray_94),seq),
inference(monotonicity,[status(thm)],[2232]) ).
tff(2234,plain,
select(store(q22,seq,earray_94),seq) = select(store(store(queue_89,tail,index_90),seq,store(earray_92,index_93,e22)),seq),
inference(symmetry,[status(thm)],[2233]) ).
tff(2235,plain,
( ( ~ ! [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_94),tail,s(index_93)),seq) = select(store(q22,seq,earray_94),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_94),tail,s(index_93)),seq) = select(store(q22,seq,earray_94),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2236,plain,
( ~ ! [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_94),tail,s(index_93)),seq) = select(store(q22,seq,earray_94),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2237,plain,
( ~ ! [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_94),tail,s(index_93)),seq) = select(store(q22,seq,earray_94),seq) ) ),
inference(modus_ponens,[status(thm)],[2236,2235]) ).
tff(2238,plain,
select(store(store(q22,seq,earray_94),tail,s(index_93)),seq) = select(store(q22,seq,earray_94),seq),
inference(unit_resolution,[status(thm)],[2237,89,83]) ).
tff(2239,plain,
queue_97 = q23,
inference(symmetry,[status(thm)],[689]) ).
tff(2240,plain,
store(queue_95,tail,index_96) = queue_97,
inference(symmetry,[status(thm)],[686]) ).
tff(2241,plain,
store(store(q22,seq,earray_94),tail,s(index_93)) = q23,
inference(transitivity,[status(thm)],[682,2240,2239]) ).
tff(2242,plain,
select(store(store(q22,seq,earray_94),tail,s(index_93)),seq) = select(q23,seq),
inference(monotonicity,[status(thm)],[2241]) ).
tff(2243,plain,
select(q23,seq) = select(store(store(q22,seq,earray_94),tail,s(index_93)),seq),
inference(symmetry,[status(thm)],[2242]) ).
tff(2244,plain,
select(q23,seq) = earray_94,
inference(transitivity,[status(thm)],[2243,2238,2234,2230,2228]) ).
tff(2245,plain,
store(store(queue_89,tail,index_90),seq,select(q23,seq)) = store(q22,seq,earray_94),
inference(monotonicity,[status(thm)],[2231,2244]) ).
tff(2246,plain,
select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head) = select(store(q22,seq,earray_94),head),
inference(monotonicity,[status(thm)],[2245]) ).
tff(2247,plain,
select(store(q22,seq,earray_94),head) = select(store(store(queue_89,tail,index_90),seq,select(q23,seq)),head),
inference(symmetry,[status(thm)],[2246]) ).
tff(2248,plain,
( ( ~ ! [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_94),tail,select(q14,tail)),head) = select(store(q22,seq,earray_94),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_94),tail,select(q14,tail)),head) = select(store(q22,seq,earray_94),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2249,plain,
( ~ ! [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_94),tail,select(q14,tail)),head) = select(store(q22,seq,earray_94),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2250,plain,
( ~ ! [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_94),tail,select(q14,tail)),head) = select(store(q22,seq,earray_94),head) ) ),
inference(modus_ponens,[status(thm)],[2249,2248]) ).
tff(2251,plain,
select(store(store(q22,seq,earray_94),tail,select(q14,tail)),head) = select(store(q22,seq,earray_94),head),
inference(unit_resolution,[status(thm)],[2250,89,1369]) ).
tff(2252,plain,
s(select(q20,tail)) = s(index_81),
inference(monotonicity,[status(thm)],[2204]) ).
tff(2253,plain,
s(select(q20,tail)) = index_87,
inference(transitivity,[status(thm)],[2252,722,719,667]) ).
tff(2254,plain,
s(s(select(q20,tail))) = s(index_87),
inference(monotonicity,[status(thm)],[2253]) ).
tff(2255,plain,
s(index_87) = s(s(select(q20,tail))),
inference(symmetry,[status(thm)],[2254]) ).
tff(2256,plain,
index_93 = s(s(select(q20,tail))),
inference(transitivity,[status(thm)],[640,659,662,2255]) ).
tff(2257,plain,
s(index_93) = s(s(s(select(q20,tail)))),
inference(monotonicity,[status(thm)],[2256]) ).
tff(2258,plain,
s(s(s(select(q20,tail)))) = s(index_93),
inference(symmetry,[status(thm)],[2257]) ).
tff(2259,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q20,tail)))) = select(q20,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2260,plain,
s(s(s(select(q20,tail)))) = select(q20,tail),
inference(unit_resolution,[status(thm)],[2259,187]) ).
tff(2261,plain,
select(q20,tail) = s(s(s(select(q20,tail)))),
inference(symmetry,[status(thm)],[2260]) ).
tff(2262,plain,
select(q14,tail) = index_96,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,677]) ).
tff(2263,plain,
store(store(q22,seq,earray_94),tail,select(q14,tail)) = store(queue_95,tail,index_96),
inference(monotonicity,[status(thm)],[681,2262]) ).
tff(2264,plain,
select(store(store(q22,seq,earray_94),tail,select(q14,tail)),head) = select(store(queue_95,tail,index_96),head),
inference(monotonicity,[status(thm)],[2263]) ).
tff(2265,plain,
select(store(queue_95,tail,index_96),head) = select(store(store(q22,seq,earray_94),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2264]) ).
tff(2266,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head) = select(store(queue_95,tail,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_95,tail,index_96),seq,select(q24,seq)),head) = select(store(queue_95,tail,index_96),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2267,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head) = select(store(queue_95,tail,index_96),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2268,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head) = select(store(queue_95,tail,index_96),head) ) ),
inference(modus_ponens,[status(thm)],[2267,2266]) ).
tff(2269,plain,
select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head) = select(store(queue_95,tail,index_96),head),
inference(unit_resolution,[status(thm)],[2268,89,1339]) ).
tff(2270,plain,
( ( earray_100 = store(earray_98,index_99,e23) )
<=> ( earray_100 = store(earray_98,index_99,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2271,axiom,
earray_100 = store(earray_98,index_99,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(2272,plain,
earray_100 = store(earray_98,index_99,e23),
inference(modus_ponens,[status(thm)],[2271,2270]) ).
tff(2273,plain,
store(earray_98,index_99,e23) = earray_100,
inference(symmetry,[status(thm)],[2272]) ).
tff(2274,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_95,tail,index_96),seq,store(earray_98,index_99,e23)),seq) = store(earray_98,index_99,e23) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2275,plain,
select(store(store(queue_95,tail,index_96),seq,store(earray_98,index_99,e23)),seq) = store(earray_98,index_99,e23),
inference(unit_resolution,[status(thm)],[2274,24]) ).
tff(2276,plain,
store(queue_95,tail,index_96) = q23,
inference(transitivity,[status(thm)],[2240,2239]) ).
tff(2277,plain,
store(store(queue_95,tail,index_96),seq,store(earray_98,index_99,e23)) = store(q23,seq,earray_100),
inference(monotonicity,[status(thm)],[2276,2273]) ).
tff(2278,plain,
select(store(store(queue_95,tail,index_96),seq,store(earray_98,index_99,e23)),seq) = select(store(q23,seq,earray_100),seq),
inference(monotonicity,[status(thm)],[2277]) ).
tff(2279,plain,
select(store(q23,seq,earray_100),seq) = select(store(store(queue_95,tail,index_96),seq,store(earray_98,index_99,e23)),seq),
inference(symmetry,[status(thm)],[2278]) ).
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(q23,seq,earray_100),tail,s(index_99)),seq) = select(store(q23,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(q23,seq,earray_100),tail,s(index_99)),seq) = select(store(q23,seq,earray_100),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2281,plain,
( ~ ! [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_100),tail,s(index_99)),seq) = select(store(q23,seq,earray_100),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2282,plain,
( ~ ! [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_100),tail,s(index_99)),seq) = select(store(q23,seq,earray_100),seq) ) ),
inference(modus_ponens,[status(thm)],[2281,2280]) ).
tff(2283,plain,
select(store(store(q23,seq,earray_100),tail,s(index_99)),seq) = select(store(q23,seq,earray_100),seq),
inference(unit_resolution,[status(thm)],[2282,89,83]) ).
tff(2284,plain,
queue_103 = q24,
inference(symmetry,[status(thm)],[631]) ).
tff(2285,plain,
store(queue_101,tail,index_102) = queue_103,
inference(symmetry,[status(thm)],[628]) ).
tff(2286,plain,
store(store(q23,seq,earray_100),tail,s(index_99)) = q24,
inference(transitivity,[status(thm)],[624,2285,2284]) ).
tff(2287,plain,
select(store(store(q23,seq,earray_100),tail,s(index_99)),seq) = select(q24,seq),
inference(monotonicity,[status(thm)],[2286]) ).
tff(2288,plain,
select(q24,seq) = select(store(store(q23,seq,earray_100),tail,s(index_99)),seq),
inference(symmetry,[status(thm)],[2287]) ).
tff(2289,plain,
select(q24,seq) = earray_100,
inference(transitivity,[status(thm)],[2288,2283,2279,2275,2273]) ).
tff(2290,plain,
store(store(queue_95,tail,index_96),seq,select(q24,seq)) = store(q23,seq,earray_100),
inference(monotonicity,[status(thm)],[2276,2289]) ).
tff(2291,plain,
select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head) = select(store(q23,seq,earray_100),head),
inference(monotonicity,[status(thm)],[2290]) ).
tff(2292,plain,
select(store(q23,seq,earray_100),head) = select(store(store(queue_95,tail,index_96),seq,select(q24,seq)),head),
inference(symmetry,[status(thm)],[2291]) ).
tff(2293,plain,
( ( ~ ! [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_100),tail,select(q12,tail)),head) = select(store(q23,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(q23,seq,earray_100),tail,select(q12,tail)),head) = select(store(q23,seq,earray_100),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2294,plain,
( ~ ! [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_100),tail,select(q12,tail)),head) = select(store(q23,seq,earray_100),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2295,plain,
( ~ ! [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_100),tail,select(q12,tail)),head) = select(store(q23,seq,earray_100),head) ) ),
inference(modus_ponens,[status(thm)],[2294,2293]) ).
tff(2296,plain,
select(store(store(q23,seq,earray_100),tail,select(q12,tail)),head) = select(store(q23,seq,earray_100),head),
inference(unit_resolution,[status(thm)],[2295,89,1369]) ).
tff(2297,plain,
select(q12,tail) = index_102,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,619]) ).
tff(2298,plain,
store(store(q23,seq,earray_100),tail,select(q12,tail)) = store(queue_101,tail,index_102),
inference(monotonicity,[status(thm)],[623,2297]) ).
tff(2299,plain,
select(store(store(q23,seq,earray_100),tail,select(q12,tail)),head) = select(store(queue_101,tail,index_102),head),
inference(monotonicity,[status(thm)],[2298]) ).
tff(2300,plain,
select(store(queue_101,tail,index_102),head) = select(store(store(q23,seq,earray_100),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2299]) ).
tff(2301,plain,
( ( ~ ! [I: $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(q25,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(q25,seq)),head) = select(store(queue_101,tail,index_102),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2302,plain,
( ~ ! [I: $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(q25,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2303,plain,
( ~ ! [I: $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(q25,seq)),head) = select(store(queue_101,tail,index_102),head) ) ),
inference(modus_ponens,[status(thm)],[2302,2301]) ).
tff(2304,plain,
select(store(store(queue_101,tail,index_102),seq,select(q25,seq)),head) = select(store(queue_101,tail,index_102),head),
inference(unit_resolution,[status(thm)],[2303,89,1339]) ).
tff(2305,plain,
( ( earray_106 = store(earray_104,index_105,e24) )
<=> ( earray_106 = store(earray_104,index_105,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2306,axiom,
earray_106 = store(earray_104,index_105,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(2307,plain,
earray_106 = store(earray_104,index_105,e24),
inference(modus_ponens,[status(thm)],[2306,2305]) ).
tff(2308,plain,
store(earray_104,index_105,e24) = earray_106,
inference(symmetry,[status(thm)],[2307]) ).
tff(2309,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,e24)),seq) = store(earray_104,index_105,e24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2310,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e24)),seq) = store(earray_104,index_105,e24),
inference(unit_resolution,[status(thm)],[2309,24]) ).
tff(2311,plain,
store(queue_101,tail,index_102) = q24,
inference(transitivity,[status(thm)],[2285,2284]) ).
tff(2312,plain,
store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e24)) = store(q24,seq,earray_106),
inference(monotonicity,[status(thm)],[2311,2308]) ).
tff(2313,plain,
select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e24)),seq) = select(store(q24,seq,earray_106),seq),
inference(monotonicity,[status(thm)],[2312]) ).
tff(2314,plain,
select(store(q24,seq,earray_106),seq) = select(store(store(queue_101,tail,index_102),seq,store(earray_104,index_105,e24)),seq),
inference(symmetry,[status(thm)],[2313]) ).
tff(2315,plain,
( ( ~ ! [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_106),tail,s(index_105)),seq) = select(store(q24,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(q24,seq,earray_106),tail,s(index_105)),seq) = select(store(q24,seq,earray_106),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2316,plain,
( ~ ! [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_106),tail,s(index_105)),seq) = select(store(q24,seq,earray_106),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2317,plain,
( ~ ! [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_106),tail,s(index_105)),seq) = select(store(q24,seq,earray_106),seq) ) ),
inference(modus_ponens,[status(thm)],[2316,2315]) ).
tff(2318,plain,
select(store(store(q24,seq,earray_106),tail,s(index_105)),seq) = select(store(q24,seq,earray_106),seq),
inference(unit_resolution,[status(thm)],[2317,89,83]) ).
tff(2319,plain,
queue_109 = q25,
inference(symmetry,[status(thm)],[572]) ).
tff(2320,plain,
store(queue_107,tail,index_108) = queue_109,
inference(symmetry,[status(thm)],[569]) ).
tff(2321,plain,
store(store(q24,seq,earray_106),tail,s(index_105)) = q25,
inference(transitivity,[status(thm)],[565,2320,2319]) ).
tff(2322,plain,
select(store(store(q24,seq,earray_106),tail,s(index_105)),seq) = select(q25,seq),
inference(monotonicity,[status(thm)],[2321]) ).
tff(2323,plain,
select(q25,seq) = select(store(store(q24,seq,earray_106),tail,s(index_105)),seq),
inference(symmetry,[status(thm)],[2322]) ).
tff(2324,plain,
select(q25,seq) = earray_106,
inference(transitivity,[status(thm)],[2323,2318,2314,2310,2308]) ).
tff(2325,plain,
store(store(queue_101,tail,index_102),seq,select(q25,seq)) = store(q24,seq,earray_106),
inference(monotonicity,[status(thm)],[2311,2324]) ).
tff(2326,plain,
select(store(store(queue_101,tail,index_102),seq,select(q25,seq)),head) = select(store(q24,seq,earray_106),head),
inference(monotonicity,[status(thm)],[2325]) ).
tff(2327,plain,
select(store(q24,seq,earray_106),head) = select(store(store(queue_101,tail,index_102),seq,select(q25,seq)),head),
inference(symmetry,[status(thm)],[2326]) ).
tff(2328,plain,
( ( ~ ! [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_106),tail,select(q13,tail)),head) = select(store(q24,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(q24,seq,earray_106),tail,select(q13,tail)),head) = select(store(q24,seq,earray_106),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2329,plain,
( ~ ! [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_106),tail,select(q13,tail)),head) = select(store(q24,seq,earray_106),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2330,plain,
( ~ ! [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_106),tail,select(q13,tail)),head) = select(store(q24,seq,earray_106),head) ) ),
inference(modus_ponens,[status(thm)],[2329,2328]) ).
tff(2331,plain,
select(store(store(q24,seq,earray_106),tail,select(q13,tail)),head) = select(store(q24,seq,earray_106),head),
inference(unit_resolution,[status(thm)],[2330,89,1369]) ).
tff(2332,plain,
select(q23,tail) = index_99,
inference(symmetry,[status(thm)],[694]) ).
tff(2333,plain,
select(store(store(q22,seq,earray_94),tail,s(index_93)),tail) = select(q23,tail),
inference(symmetry,[status(thm)],[691]) ).
tff(2334,plain,
s(index_93) = select(store(store(q22,seq,earray_94),tail,s(index_93)),tail),
inference(symmetry,[status(thm)],[673]) ).
tff(2335,plain,
s(select(q22,tail)) = s(index_93),
inference(monotonicity,[status(thm)],[641]) ).
tff(2336,plain,
s(select(q22,tail)) = index_99,
inference(transitivity,[status(thm)],[2335,2334,2333,2332]) ).
tff(2337,plain,
s(s(select(q22,tail))) = s(index_99),
inference(monotonicity,[status(thm)],[2336]) ).
tff(2338,plain,
s(index_99) = s(s(select(q22,tail))),
inference(symmetry,[status(thm)],[2337]) ).
tff(2339,plain,
index_105 = s(s(select(q22,tail))),
inference(transitivity,[status(thm)],[581,633,636,2338]) ).
tff(2340,plain,
s(index_105) = s(s(s(select(q22,tail)))),
inference(monotonicity,[status(thm)],[2339]) ).
tff(2341,plain,
s(s(s(select(q22,tail)))) = s(index_105),
inference(symmetry,[status(thm)],[2340]) ).
tff(2342,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q22,tail)))) = select(q22,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2343,plain,
s(s(s(select(q22,tail)))) = select(q22,tail),
inference(unit_resolution,[status(thm)],[2342,187]) ).
tff(2344,plain,
select(q22,tail) = s(s(s(select(q22,tail)))),
inference(symmetry,[status(thm)],[2343]) ).
tff(2345,plain,
select(q13,tail) = index_108,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,560]) ).
tff(2346,plain,
store(store(q24,seq,earray_106),tail,select(q13,tail)) = store(queue_107,tail,index_108),
inference(monotonicity,[status(thm)],[564,2345]) ).
tff(2347,plain,
select(store(store(q24,seq,earray_106),tail,select(q13,tail)),head) = select(store(queue_107,tail,index_108),head),
inference(monotonicity,[status(thm)],[2346]) ).
tff(2348,plain,
select(store(queue_107,tail,index_108),head) = select(store(store(q24,seq,earray_106),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2347]) ).
tff(2349,plain,
( ( ~ ! [I: $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(q26,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(q26,seq)),head) = select(store(queue_107,tail,index_108),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2350,plain,
( ~ ! [I: $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(q26,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2351,plain,
( ~ ! [I: $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(q26,seq)),head) = select(store(queue_107,tail,index_108),head) ) ),
inference(modus_ponens,[status(thm)],[2350,2349]) ).
tff(2352,plain,
select(store(store(queue_107,tail,index_108),seq,select(q26,seq)),head) = select(store(queue_107,tail,index_108),head),
inference(unit_resolution,[status(thm)],[2351,89,1339]) ).
tff(2353,plain,
( ( earray_112 = store(earray_110,index_111,e25) )
<=> ( earray_112 = store(earray_110,index_111,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2354,axiom,
earray_112 = store(earray_110,index_111,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(2355,plain,
earray_112 = store(earray_110,index_111,e25),
inference(modus_ponens,[status(thm)],[2354,2353]) ).
tff(2356,plain,
store(earray_110,index_111,e25) = earray_112,
inference(symmetry,[status(thm)],[2355]) ).
tff(2357,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,e25)),seq) = store(earray_110,index_111,e25) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2358,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e25)),seq) = store(earray_110,index_111,e25),
inference(unit_resolution,[status(thm)],[2357,24]) ).
tff(2359,plain,
store(queue_107,tail,index_108) = q25,
inference(transitivity,[status(thm)],[2320,2319]) ).
tff(2360,plain,
store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e25)) = store(q25,seq,earray_112),
inference(monotonicity,[status(thm)],[2359,2356]) ).
tff(2361,plain,
select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e25)),seq) = select(store(q25,seq,earray_112),seq),
inference(monotonicity,[status(thm)],[2360]) ).
tff(2362,plain,
select(store(q25,seq,earray_112),seq) = select(store(store(queue_107,tail,index_108),seq,store(earray_110,index_111,e25)),seq),
inference(symmetry,[status(thm)],[2361]) ).
tff(2363,plain,
( ( ~ ! [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_112),tail,s(index_111)),seq) = select(store(q25,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(q25,seq,earray_112),tail,s(index_111)),seq) = select(store(q25,seq,earray_112),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2364,plain,
( ~ ! [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_112),tail,s(index_111)),seq) = select(store(q25,seq,earray_112),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2365,plain,
( ~ ! [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_112),tail,s(index_111)),seq) = select(store(q25,seq,earray_112),seq) ) ),
inference(modus_ponens,[status(thm)],[2364,2363]) ).
tff(2366,plain,
select(store(store(q25,seq,earray_112),tail,s(index_111)),seq) = select(store(q25,seq,earray_112),seq),
inference(unit_resolution,[status(thm)],[2365,89,83]) ).
tff(2367,plain,
queue_115 = q26,
inference(symmetry,[status(thm)],[604]) ).
tff(2368,plain,
store(queue_113,tail,index_114) = queue_115,
inference(symmetry,[status(thm)],[601]) ).
tff(2369,plain,
store(store(q25,seq,earray_112),tail,s(index_111)) = q26,
inference(transitivity,[status(thm)],[597,2368,2367]) ).
tff(2370,plain,
select(store(store(q25,seq,earray_112),tail,s(index_111)),seq) = select(q26,seq),
inference(monotonicity,[status(thm)],[2369]) ).
tff(2371,plain,
select(q26,seq) = select(store(store(q25,seq,earray_112),tail,s(index_111)),seq),
inference(symmetry,[status(thm)],[2370]) ).
tff(2372,plain,
select(q26,seq) = earray_112,
inference(transitivity,[status(thm)],[2371,2366,2362,2358,2356]) ).
tff(2373,plain,
store(store(queue_107,tail,index_108),seq,select(q26,seq)) = store(q25,seq,earray_112),
inference(monotonicity,[status(thm)],[2359,2372]) ).
tff(2374,plain,
select(store(store(queue_107,tail,index_108),seq,select(q26,seq)),head) = select(store(q25,seq,earray_112),head),
inference(monotonicity,[status(thm)],[2373]) ).
tff(2375,plain,
select(store(q25,seq,earray_112),head) = select(store(store(queue_107,tail,index_108),seq,select(q26,seq)),head),
inference(symmetry,[status(thm)],[2374]) ).
tff(2376,plain,
( ( ~ ! [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_112),tail,select(q14,tail)),head) = select(store(q25,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(q25,seq,earray_112),tail,select(q14,tail)),head) = select(store(q25,seq,earray_112),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2377,plain,
( ~ ! [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_112),tail,select(q14,tail)),head) = select(store(q25,seq,earray_112),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2378,plain,
( ~ ! [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_112),tail,select(q14,tail)),head) = select(store(q25,seq,earray_112),head) ) ),
inference(modus_ponens,[status(thm)],[2377,2376]) ).
tff(2379,plain,
select(store(store(q25,seq,earray_112),tail,select(q14,tail)),head) = select(store(q25,seq,earray_112),head),
inference(unit_resolution,[status(thm)],[2378,89,1369]) ).
tff(2380,plain,
s(select(q23,tail)) = s(index_99),
inference(monotonicity,[status(thm)],[2332]) ).
tff(2381,plain,
s(select(q23,tail)) = index_105,
inference(transitivity,[status(thm)],[2380,637,634,582]) ).
tff(2382,plain,
s(s(select(q23,tail))) = s(index_105),
inference(monotonicity,[status(thm)],[2381]) ).
tff(2383,plain,
s(index_105) = s(s(select(q23,tail))),
inference(symmetry,[status(thm)],[2382]) ).
tff(2384,plain,
index_111 = s(s(select(q23,tail))),
inference(transitivity,[status(thm)],[555,574,577,2383]) ).
tff(2385,plain,
s(index_111) = s(s(s(select(q23,tail)))),
inference(monotonicity,[status(thm)],[2384]) ).
tff(2386,plain,
s(s(s(select(q23,tail)))) = s(index_111),
inference(symmetry,[status(thm)],[2385]) ).
tff(2387,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q23,tail)))) = select(q23,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2388,plain,
s(s(s(select(q23,tail)))) = select(q23,tail),
inference(unit_resolution,[status(thm)],[2387,187]) ).
tff(2389,plain,
select(q23,tail) = s(s(s(select(q23,tail)))),
inference(symmetry,[status(thm)],[2388]) ).
tff(2390,plain,
select(q14,tail) = index_114,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,592]) ).
tff(2391,plain,
store(store(q25,seq,earray_112),tail,select(q14,tail)) = store(queue_113,tail,index_114),
inference(monotonicity,[status(thm)],[596,2390]) ).
tff(2392,plain,
select(store(store(q25,seq,earray_112),tail,select(q14,tail)),head) = select(store(queue_113,tail,index_114),head),
inference(monotonicity,[status(thm)],[2391]) ).
tff(2393,plain,
select(store(queue_113,tail,index_114),head) = select(store(store(q25,seq,earray_112),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2392]) ).
tff(2394,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head) = select(store(queue_113,tail,index_114),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_113,tail,index_114),seq,select(q27,seq)),head) = select(store(queue_113,tail,index_114),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2395,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head) = select(store(queue_113,tail,index_114),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2396,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head) = select(store(queue_113,tail,index_114),head) ) ),
inference(modus_ponens,[status(thm)],[2395,2394]) ).
tff(2397,plain,
select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head) = select(store(queue_113,tail,index_114),head),
inference(unit_resolution,[status(thm)],[2396,89,1339]) ).
tff(2398,plain,
( ( earray_118 = store(earray_116,index_117,e26) )
<=> ( earray_118 = store(earray_116,index_117,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2399,axiom,
earray_118 = store(earray_116,index_117,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(2400,plain,
earray_118 = store(earray_116,index_117,e26),
inference(modus_ponens,[status(thm)],[2399,2398]) ).
tff(2401,plain,
store(earray_116,index_117,e26) = earray_118,
inference(symmetry,[status(thm)],[2400]) ).
tff(2402,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_113,tail,index_114),seq,store(earray_116,index_117,e26)),seq) = store(earray_116,index_117,e26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2403,plain,
select(store(store(queue_113,tail,index_114),seq,store(earray_116,index_117,e26)),seq) = store(earray_116,index_117,e26),
inference(unit_resolution,[status(thm)],[2402,24]) ).
tff(2404,plain,
store(queue_113,tail,index_114) = q26,
inference(transitivity,[status(thm)],[2368,2367]) ).
tff(2405,plain,
store(store(queue_113,tail,index_114),seq,store(earray_116,index_117,e26)) = store(q26,seq,earray_118),
inference(monotonicity,[status(thm)],[2404,2401]) ).
tff(2406,plain,
select(store(store(queue_113,tail,index_114),seq,store(earray_116,index_117,e26)),seq) = select(store(q26,seq,earray_118),seq),
inference(monotonicity,[status(thm)],[2405]) ).
tff(2407,plain,
select(store(q26,seq,earray_118),seq) = select(store(store(queue_113,tail,index_114),seq,store(earray_116,index_117,e26)),seq),
inference(symmetry,[status(thm)],[2406]) ).
tff(2408,plain,
( ( ~ ! [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_118),tail,s(index_117)),seq) = select(store(q26,seq,earray_118),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_118),tail,s(index_117)),seq) = select(store(q26,seq,earray_118),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2409,plain,
( ~ ! [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_118),tail,s(index_117)),seq) = select(store(q26,seq,earray_118),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2410,plain,
( ~ ! [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_118),tail,s(index_117)),seq) = select(store(q26,seq,earray_118),seq) ) ),
inference(modus_ponens,[status(thm)],[2409,2408]) ).
tff(2411,plain,
select(store(store(q26,seq,earray_118),tail,s(index_117)),seq) = select(store(q26,seq,earray_118),seq),
inference(unit_resolution,[status(thm)],[2410,89,83]) ).
tff(2412,plain,
queue_121 = q27,
inference(symmetry,[status(thm)],[546]) ).
tff(2413,plain,
store(queue_119,tail,index_120) = queue_121,
inference(symmetry,[status(thm)],[543]) ).
tff(2414,plain,
store(store(q26,seq,earray_118),tail,s(index_117)) = q27,
inference(transitivity,[status(thm)],[539,2413,2412]) ).
tff(2415,plain,
select(store(store(q26,seq,earray_118),tail,s(index_117)),seq) = select(q27,seq),
inference(monotonicity,[status(thm)],[2414]) ).
tff(2416,plain,
select(q27,seq) = select(store(store(q26,seq,earray_118),tail,s(index_117)),seq),
inference(symmetry,[status(thm)],[2415]) ).
tff(2417,plain,
select(q27,seq) = earray_118,
inference(transitivity,[status(thm)],[2416,2411,2407,2403,2401]) ).
tff(2418,plain,
store(store(queue_113,tail,index_114),seq,select(q27,seq)) = store(q26,seq,earray_118),
inference(monotonicity,[status(thm)],[2404,2417]) ).
tff(2419,plain,
select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head) = select(store(q26,seq,earray_118),head),
inference(monotonicity,[status(thm)],[2418]) ).
tff(2420,plain,
select(store(q26,seq,earray_118),head) = select(store(store(queue_113,tail,index_114),seq,select(q27,seq)),head),
inference(symmetry,[status(thm)],[2419]) ).
tff(2421,plain,
( ( ~ ! [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_118),tail,select(q12,tail)),head) = select(store(q26,seq,earray_118),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_118),tail,select(q12,tail)),head) = select(store(q26,seq,earray_118),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2422,plain,
( ~ ! [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_118),tail,select(q12,tail)),head) = select(store(q26,seq,earray_118),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2423,plain,
( ~ ! [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_118),tail,select(q12,tail)),head) = select(store(q26,seq,earray_118),head) ) ),
inference(modus_ponens,[status(thm)],[2422,2421]) ).
tff(2424,plain,
select(store(store(q26,seq,earray_118),tail,select(q12,tail)),head) = select(store(q26,seq,earray_118),head),
inference(unit_resolution,[status(thm)],[2423,89,1369]) ).
tff(2425,plain,
select(q12,tail) = index_120,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,534]) ).
tff(2426,plain,
store(store(q26,seq,earray_118),tail,select(q12,tail)) = store(queue_119,tail,index_120),
inference(monotonicity,[status(thm)],[538,2425]) ).
tff(2427,plain,
select(store(store(q26,seq,earray_118),tail,select(q12,tail)),head) = select(store(queue_119,tail,index_120),head),
inference(monotonicity,[status(thm)],[2426]) ).
tff(2428,plain,
select(store(queue_119,tail,index_120),head) = select(store(store(q26,seq,earray_118),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2427]) ).
tff(2429,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head) = select(store(queue_119,tail,index_120),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_119,tail,index_120),seq,select(q28,seq)),head) = select(store(queue_119,tail,index_120),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2430,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head) = select(store(queue_119,tail,index_120),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2431,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head) = select(store(queue_119,tail,index_120),head) ) ),
inference(modus_ponens,[status(thm)],[2430,2429]) ).
tff(2432,plain,
select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head) = select(store(queue_119,tail,index_120),head),
inference(unit_resolution,[status(thm)],[2431,89,1339]) ).
tff(2433,plain,
( ( earray_124 = store(earray_122,index_123,e27) )
<=> ( earray_124 = store(earray_122,index_123,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2434,axiom,
earray_124 = store(earray_122,index_123,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(2435,plain,
earray_124 = store(earray_122,index_123,e27),
inference(modus_ponens,[status(thm)],[2434,2433]) ).
tff(2436,plain,
store(earray_122,index_123,e27) = earray_124,
inference(symmetry,[status(thm)],[2435]) ).
tff(2437,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_119,tail,index_120),seq,store(earray_122,index_123,e27)),seq) = store(earray_122,index_123,e27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2438,plain,
select(store(store(queue_119,tail,index_120),seq,store(earray_122,index_123,e27)),seq) = store(earray_122,index_123,e27),
inference(unit_resolution,[status(thm)],[2437,24]) ).
tff(2439,plain,
store(queue_119,tail,index_120) = q27,
inference(transitivity,[status(thm)],[2413,2412]) ).
tff(2440,plain,
store(store(queue_119,tail,index_120),seq,store(earray_122,index_123,e27)) = store(q27,seq,earray_124),
inference(monotonicity,[status(thm)],[2439,2436]) ).
tff(2441,plain,
select(store(store(queue_119,tail,index_120),seq,store(earray_122,index_123,e27)),seq) = select(store(q27,seq,earray_124),seq),
inference(monotonicity,[status(thm)],[2440]) ).
tff(2442,plain,
select(store(q27,seq,earray_124),seq) = select(store(store(queue_119,tail,index_120),seq,store(earray_122,index_123,e27)),seq),
inference(symmetry,[status(thm)],[2441]) ).
tff(2443,plain,
( ( ~ ! [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_124),tail,s(index_123)),seq) = select(store(q27,seq,earray_124),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_124),tail,s(index_123)),seq) = select(store(q27,seq,earray_124),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2444,plain,
( ~ ! [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_124),tail,s(index_123)),seq) = select(store(q27,seq,earray_124),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2445,plain,
( ~ ! [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_124),tail,s(index_123)),seq) = select(store(q27,seq,earray_124),seq) ) ),
inference(modus_ponens,[status(thm)],[2444,2443]) ).
tff(2446,plain,
select(store(store(q27,seq,earray_124),tail,s(index_123)),seq) = select(store(q27,seq,earray_124),seq),
inference(unit_resolution,[status(thm)],[2445,89,83]) ).
tff(2447,plain,
queue_127 = q28,
inference(symmetry,[status(thm)],[487]) ).
tff(2448,plain,
store(queue_125,tail,index_126) = queue_127,
inference(symmetry,[status(thm)],[484]) ).
tff(2449,plain,
store(store(q27,seq,earray_124),tail,s(index_123)) = q28,
inference(transitivity,[status(thm)],[480,2448,2447]) ).
tff(2450,plain,
select(store(store(q27,seq,earray_124),tail,s(index_123)),seq) = select(q28,seq),
inference(monotonicity,[status(thm)],[2449]) ).
tff(2451,plain,
select(q28,seq) = select(store(store(q27,seq,earray_124),tail,s(index_123)),seq),
inference(symmetry,[status(thm)],[2450]) ).
tff(2452,plain,
select(q28,seq) = earray_124,
inference(transitivity,[status(thm)],[2451,2446,2442,2438,2436]) ).
tff(2453,plain,
store(store(queue_119,tail,index_120),seq,select(q28,seq)) = store(q27,seq,earray_124),
inference(monotonicity,[status(thm)],[2439,2452]) ).
tff(2454,plain,
select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head) = select(store(q27,seq,earray_124),head),
inference(monotonicity,[status(thm)],[2453]) ).
tff(2455,plain,
select(store(q27,seq,earray_124),head) = select(store(store(queue_119,tail,index_120),seq,select(q28,seq)),head),
inference(symmetry,[status(thm)],[2454]) ).
tff(2456,plain,
( ( ~ ! [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_124),tail,select(q13,tail)),head) = select(store(q27,seq,earray_124),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_124),tail,select(q13,tail)),head) = select(store(q27,seq,earray_124),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2457,plain,
( ~ ! [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_124),tail,select(q13,tail)),head) = select(store(q27,seq,earray_124),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2458,plain,
( ~ ! [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_124),tail,select(q13,tail)),head) = select(store(q27,seq,earray_124),head) ) ),
inference(modus_ponens,[status(thm)],[2457,2456]) ).
tff(2459,plain,
select(store(store(q27,seq,earray_124),tail,select(q13,tail)),head) = select(store(q27,seq,earray_124),head),
inference(unit_resolution,[status(thm)],[2458,89,1369]) ).
tff(2460,plain,
select(q26,tail) = index_117,
inference(symmetry,[status(thm)],[609]) ).
tff(2461,plain,
select(store(store(q25,seq,earray_112),tail,s(index_111)),tail) = select(q26,tail),
inference(symmetry,[status(thm)],[606]) ).
tff(2462,plain,
s(index_111) = select(store(store(q25,seq,earray_112),tail,s(index_111)),tail),
inference(symmetry,[status(thm)],[588]) ).
tff(2463,plain,
s(select(q25,tail)) = s(index_111),
inference(monotonicity,[status(thm)],[556]) ).
tff(2464,plain,
s(select(q25,tail)) = index_117,
inference(transitivity,[status(thm)],[2463,2462,2461,2460]) ).
tff(2465,plain,
s(s(select(q25,tail))) = s(index_117),
inference(monotonicity,[status(thm)],[2464]) ).
tff(2466,plain,
s(index_117) = s(s(select(q25,tail))),
inference(symmetry,[status(thm)],[2465]) ).
tff(2467,plain,
index_123 = s(s(select(q25,tail))),
inference(transitivity,[status(thm)],[496,548,551,2466]) ).
tff(2468,plain,
s(index_123) = s(s(s(select(q25,tail)))),
inference(monotonicity,[status(thm)],[2467]) ).
tff(2469,plain,
s(s(s(select(q25,tail)))) = s(index_123),
inference(symmetry,[status(thm)],[2468]) ).
tff(2470,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q25,tail)))) = select(q25,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2471,plain,
s(s(s(select(q25,tail)))) = select(q25,tail),
inference(unit_resolution,[status(thm)],[2470,187]) ).
tff(2472,plain,
select(q25,tail) = s(s(s(select(q25,tail)))),
inference(symmetry,[status(thm)],[2471]) ).
tff(2473,plain,
select(q13,tail) = index_126,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,578,575,2472,2469,475]) ).
tff(2474,plain,
store(store(q27,seq,earray_124),tail,select(q13,tail)) = store(queue_125,tail,index_126),
inference(monotonicity,[status(thm)],[479,2473]) ).
tff(2475,plain,
select(store(store(q27,seq,earray_124),tail,select(q13,tail)),head) = select(store(queue_125,tail,index_126),head),
inference(monotonicity,[status(thm)],[2474]) ).
tff(2476,plain,
select(store(queue_125,tail,index_126),head) = select(store(store(q27,seq,earray_124),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2475]) ).
tff(2477,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head) = select(store(queue_125,tail,index_126),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_125,tail,index_126),seq,select(q29,seq)),head) = select(store(queue_125,tail,index_126),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2478,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head) = select(store(queue_125,tail,index_126),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2479,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head) = select(store(queue_125,tail,index_126),head) ) ),
inference(modus_ponens,[status(thm)],[2478,2477]) ).
tff(2480,plain,
select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head) = select(store(queue_125,tail,index_126),head),
inference(unit_resolution,[status(thm)],[2479,89,1339]) ).
tff(2481,plain,
( ( earray_130 = store(earray_128,index_129,e28) )
<=> ( earray_130 = store(earray_128,index_129,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2482,axiom,
earray_130 = store(earray_128,index_129,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(2483,plain,
earray_130 = store(earray_128,index_129,e28),
inference(modus_ponens,[status(thm)],[2482,2481]) ).
tff(2484,plain,
store(earray_128,index_129,e28) = earray_130,
inference(symmetry,[status(thm)],[2483]) ).
tff(2485,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_125,tail,index_126),seq,store(earray_128,index_129,e28)),seq) = store(earray_128,index_129,e28) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2486,plain,
select(store(store(queue_125,tail,index_126),seq,store(earray_128,index_129,e28)),seq) = store(earray_128,index_129,e28),
inference(unit_resolution,[status(thm)],[2485,24]) ).
tff(2487,plain,
store(queue_125,tail,index_126) = q28,
inference(transitivity,[status(thm)],[2448,2447]) ).
tff(2488,plain,
store(store(queue_125,tail,index_126),seq,store(earray_128,index_129,e28)) = store(q28,seq,earray_130),
inference(monotonicity,[status(thm)],[2487,2484]) ).
tff(2489,plain,
select(store(store(queue_125,tail,index_126),seq,store(earray_128,index_129,e28)),seq) = select(store(q28,seq,earray_130),seq),
inference(monotonicity,[status(thm)],[2488]) ).
tff(2490,plain,
select(store(q28,seq,earray_130),seq) = select(store(store(queue_125,tail,index_126),seq,store(earray_128,index_129,e28)),seq),
inference(symmetry,[status(thm)],[2489]) ).
tff(2491,plain,
( ( ~ ! [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_130),tail,s(index_129)),seq) = select(store(q28,seq,earray_130),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_130),tail,s(index_129)),seq) = select(store(q28,seq,earray_130),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2492,plain,
( ~ ! [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_130),tail,s(index_129)),seq) = select(store(q28,seq,earray_130),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2493,plain,
( ~ ! [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_130),tail,s(index_129)),seq) = select(store(q28,seq,earray_130),seq) ) ),
inference(modus_ponens,[status(thm)],[2492,2491]) ).
tff(2494,plain,
select(store(store(q28,seq,earray_130),tail,s(index_129)),seq) = select(store(q28,seq,earray_130),seq),
inference(unit_resolution,[status(thm)],[2493,89,83]) ).
tff(2495,plain,
queue_133 = q29,
inference(symmetry,[status(thm)],[519]) ).
tff(2496,plain,
store(queue_131,tail,index_132) = queue_133,
inference(symmetry,[status(thm)],[516]) ).
tff(2497,plain,
store(store(q28,seq,earray_130),tail,s(index_129)) = q29,
inference(transitivity,[status(thm)],[512,2496,2495]) ).
tff(2498,plain,
select(store(store(q28,seq,earray_130),tail,s(index_129)),seq) = select(q29,seq),
inference(monotonicity,[status(thm)],[2497]) ).
tff(2499,plain,
select(q29,seq) = select(store(store(q28,seq,earray_130),tail,s(index_129)),seq),
inference(symmetry,[status(thm)],[2498]) ).
tff(2500,plain,
select(q29,seq) = earray_130,
inference(transitivity,[status(thm)],[2499,2494,2490,2486,2484]) ).
tff(2501,plain,
store(store(queue_125,tail,index_126),seq,select(q29,seq)) = store(q28,seq,earray_130),
inference(monotonicity,[status(thm)],[2487,2500]) ).
tff(2502,plain,
select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head) = select(store(q28,seq,earray_130),head),
inference(monotonicity,[status(thm)],[2501]) ).
tff(2503,plain,
select(store(q28,seq,earray_130),head) = select(store(store(queue_125,tail,index_126),seq,select(q29,seq)),head),
inference(symmetry,[status(thm)],[2502]) ).
tff(2504,plain,
( ( ~ ! [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_130),tail,select(q14,tail)),head) = select(store(q28,seq,earray_130),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_130),tail,select(q14,tail)),head) = select(store(q28,seq,earray_130),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2505,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q28,seq,earray_130),tail,select(q14,tail)),head) = select(store(q28,seq,earray_130),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2506,plain,
( ~ ! [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_130),tail,select(q14,tail)),head) = select(store(q28,seq,earray_130),head) ) ),
inference(modus_ponens,[status(thm)],[2505,2504]) ).
tff(2507,plain,
select(store(store(q28,seq,earray_130),tail,select(q14,tail)),head) = select(store(q28,seq,earray_130),head),
inference(unit_resolution,[status(thm)],[2506,89,1369]) ).
tff(2508,plain,
s(select(q26,tail)) = s(index_117),
inference(monotonicity,[status(thm)],[2460]) ).
tff(2509,plain,
s(select(q26,tail)) = index_123,
inference(transitivity,[status(thm)],[2508,552,549,497]) ).
tff(2510,plain,
s(s(select(q26,tail))) = s(index_123),
inference(monotonicity,[status(thm)],[2509]) ).
tff(2511,plain,
s(index_123) = s(s(select(q26,tail))),
inference(symmetry,[status(thm)],[2510]) ).
tff(2512,plain,
index_129 = s(s(select(q26,tail))),
inference(transitivity,[status(thm)],[470,489,492,2511]) ).
tff(2513,plain,
s(index_129) = s(s(s(select(q26,tail)))),
inference(monotonicity,[status(thm)],[2512]) ).
tff(2514,plain,
s(s(s(select(q26,tail)))) = s(index_129),
inference(symmetry,[status(thm)],[2513]) ).
tff(2515,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q26,tail)))) = select(q26,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2516,plain,
s(s(s(select(q26,tail)))) = select(q26,tail),
inference(unit_resolution,[status(thm)],[2515,187]) ).
tff(2517,plain,
select(q26,tail) = s(s(s(select(q26,tail)))),
inference(symmetry,[status(thm)],[2516]) ).
tff(2518,plain,
select(q14,tail) = index_132,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,2462,2461,2517,2514,507]) ).
tff(2519,plain,
store(store(q28,seq,earray_130),tail,select(q14,tail)) = store(queue_131,tail,index_132),
inference(monotonicity,[status(thm)],[511,2518]) ).
tff(2520,plain,
select(store(store(q28,seq,earray_130),tail,select(q14,tail)),head) = select(store(queue_131,tail,index_132),head),
inference(monotonicity,[status(thm)],[2519]) ).
tff(2521,plain,
select(store(queue_131,tail,index_132),head) = select(store(store(q28,seq,earray_130),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2520]) ).
tff(2522,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head) = select(store(queue_131,tail,index_132),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_131,tail,index_132),seq,select(q30,seq)),head) = select(store(queue_131,tail,index_132),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2523,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head) = select(store(queue_131,tail,index_132),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2524,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head) = select(store(queue_131,tail,index_132),head) ) ),
inference(modus_ponens,[status(thm)],[2523,2522]) ).
tff(2525,plain,
select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head) = select(store(queue_131,tail,index_132),head),
inference(unit_resolution,[status(thm)],[2524,89,1339]) ).
tff(2526,plain,
( ( earray_142 = store(earray_140,index_141,e29) )
<=> ( earray_142 = store(earray_140,index_141,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2527,axiom,
earray_142 = store(earray_140,index_141,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(2528,plain,
earray_142 = store(earray_140,index_141,e29),
inference(modus_ponens,[status(thm)],[2527,2526]) ).
tff(2529,plain,
store(earray_140,index_141,e29) = earray_142,
inference(symmetry,[status(thm)],[2528]) ).
tff(2530,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_131,tail,index_132),seq,store(earray_140,index_141,e29)),seq) = store(earray_140,index_141,e29) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2531,plain,
select(store(store(queue_131,tail,index_132),seq,store(earray_140,index_141,e29)),seq) = store(earray_140,index_141,e29),
inference(unit_resolution,[status(thm)],[2530,24]) ).
tff(2532,plain,
store(queue_131,tail,index_132) = q29,
inference(transitivity,[status(thm)],[2496,2495]) ).
tff(2533,plain,
store(store(queue_131,tail,index_132),seq,store(earray_140,index_141,e29)) = store(q29,seq,earray_142),
inference(monotonicity,[status(thm)],[2532,2529]) ).
tff(2534,plain,
select(store(store(queue_131,tail,index_132),seq,store(earray_140,index_141,e29)),seq) = select(store(q29,seq,earray_142),seq),
inference(monotonicity,[status(thm)],[2533]) ).
tff(2535,plain,
select(store(q29,seq,earray_142),seq) = select(store(store(queue_131,tail,index_132),seq,store(earray_140,index_141,e29)),seq),
inference(symmetry,[status(thm)],[2534]) ).
tff(2536,plain,
( ( ~ ! [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_142),tail,s(index_141)),seq) = select(store(q29,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(q29,seq,earray_142),tail,s(index_141)),seq) = select(store(q29,seq,earray_142),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2537,plain,
( ~ ! [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_142),tail,s(index_141)),seq) = select(store(q29,seq,earray_142),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2538,plain,
( ~ ! [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_142),tail,s(index_141)),seq) = select(store(q29,seq,earray_142),seq) ) ),
inference(modus_ponens,[status(thm)],[2537,2536]) ).
tff(2539,plain,
select(store(store(q29,seq,earray_142),tail,s(index_141)),seq) = select(store(q29,seq,earray_142),seq),
inference(unit_resolution,[status(thm)],[2538,89,83]) ).
tff(2540,plain,
queue_145 = q30,
inference(symmetry,[status(thm)],[461]) ).
tff(2541,plain,
store(queue_143,tail,index_144) = queue_145,
inference(symmetry,[status(thm)],[458]) ).
tff(2542,plain,
store(store(q29,seq,earray_142),tail,s(index_141)) = q30,
inference(transitivity,[status(thm)],[454,2541,2540]) ).
tff(2543,plain,
select(store(store(q29,seq,earray_142),tail,s(index_141)),seq) = select(q30,seq),
inference(monotonicity,[status(thm)],[2542]) ).
tff(2544,plain,
select(q30,seq) = select(store(store(q29,seq,earray_142),tail,s(index_141)),seq),
inference(symmetry,[status(thm)],[2543]) ).
tff(2545,plain,
select(q30,seq) = earray_142,
inference(transitivity,[status(thm)],[2544,2539,2535,2531,2529]) ).
tff(2546,plain,
store(store(queue_131,tail,index_132),seq,select(q30,seq)) = store(q29,seq,earray_142),
inference(monotonicity,[status(thm)],[2532,2545]) ).
tff(2547,plain,
select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head) = select(store(q29,seq,earray_142),head),
inference(monotonicity,[status(thm)],[2546]) ).
tff(2548,plain,
select(store(q29,seq,earray_142),head) = select(store(store(queue_131,tail,index_132),seq,select(q30,seq)),head),
inference(symmetry,[status(thm)],[2547]) ).
tff(2549,plain,
( ( ~ ! [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_142),tail,select(q12,tail)),head) = select(store(q29,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(q29,seq,earray_142),tail,select(q12,tail)),head) = select(store(q29,seq,earray_142),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2550,plain,
( ~ ! [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_142),tail,select(q12,tail)),head) = select(store(q29,seq,earray_142),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2551,plain,
( ~ ! [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_142),tail,select(q12,tail)),head) = select(store(q29,seq,earray_142),head) ) ),
inference(modus_ponens,[status(thm)],[2550,2549]) ).
tff(2552,plain,
select(store(store(q29,seq,earray_142),tail,select(q12,tail)),head) = select(store(q29,seq,earray_142),head),
inference(unit_resolution,[status(thm)],[2551,89,1369]) ).
tff(2553,plain,
select(q12,tail) = index_144,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,449]) ).
tff(2554,plain,
store(store(q29,seq,earray_142),tail,select(q12,tail)) = store(queue_143,tail,index_144),
inference(monotonicity,[status(thm)],[453,2553]) ).
tff(2555,plain,
select(store(store(q29,seq,earray_142),tail,select(q12,tail)),head) = select(store(queue_143,tail,index_144),head),
inference(monotonicity,[status(thm)],[2554]) ).
tff(2556,plain,
select(store(queue_143,tail,index_144),head) = select(store(store(q29,seq,earray_142),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2555]) ).
tff(2557,plain,
( ( ~ ! [I: $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(q31,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(q31,seq)),head) = select(store(queue_143,tail,index_144),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2558,plain,
( ~ ! [I: $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(q31,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2559,plain,
( ~ ! [I: $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(q31,seq)),head) = select(store(queue_143,tail,index_144),head) ) ),
inference(modus_ponens,[status(thm)],[2558,2557]) ).
tff(2560,plain,
select(store(store(queue_143,tail,index_144),seq,select(q31,seq)),head) = select(store(queue_143,tail,index_144),head),
inference(unit_resolution,[status(thm)],[2559,89,1339]) ).
tff(2561,plain,
( ( earray_148 = store(earray_146,index_147,e30) )
<=> ( earray_148 = store(earray_146,index_147,e30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2562,axiom,
earray_148 = store(earray_146,index_147,e30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(2563,plain,
earray_148 = store(earray_146,index_147,e30),
inference(modus_ponens,[status(thm)],[2562,2561]) ).
tff(2564,plain,
store(earray_146,index_147,e30) = earray_148,
inference(symmetry,[status(thm)],[2563]) ).
tff(2565,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,e30)),seq) = store(earray_146,index_147,e30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2566,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e30)),seq) = store(earray_146,index_147,e30),
inference(unit_resolution,[status(thm)],[2565,24]) ).
tff(2567,plain,
store(queue_143,tail,index_144) = q30,
inference(transitivity,[status(thm)],[2541,2540]) ).
tff(2568,plain,
store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e30)) = store(q30,seq,earray_148),
inference(monotonicity,[status(thm)],[2567,2564]) ).
tff(2569,plain,
select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e30)),seq) = select(store(q30,seq,earray_148),seq),
inference(monotonicity,[status(thm)],[2568]) ).
tff(2570,plain,
select(store(q30,seq,earray_148),seq) = select(store(store(queue_143,tail,index_144),seq,store(earray_146,index_147,e30)),seq),
inference(symmetry,[status(thm)],[2569]) ).
tff(2571,plain,
( ( ~ ! [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_148),tail,s(index_147)),seq) = select(store(q30,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(q30,seq,earray_148),tail,s(index_147)),seq) = select(store(q30,seq,earray_148),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2572,plain,
( ~ ! [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_148),tail,s(index_147)),seq) = select(store(q30,seq,earray_148),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2573,plain,
( ~ ! [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_148),tail,s(index_147)),seq) = select(store(q30,seq,earray_148),seq) ) ),
inference(modus_ponens,[status(thm)],[2572,2571]) ).
tff(2574,plain,
select(store(store(q30,seq,earray_148),tail,s(index_147)),seq) = select(store(q30,seq,earray_148),seq),
inference(unit_resolution,[status(thm)],[2573,89,83]) ).
tff(2575,plain,
queue_151 = q31,
inference(symmetry,[status(thm)],[402]) ).
tff(2576,plain,
store(queue_149,tail,index_150) = queue_151,
inference(symmetry,[status(thm)],[399]) ).
tff(2577,plain,
store(store(q30,seq,earray_148),tail,s(index_147)) = q31,
inference(transitivity,[status(thm)],[395,2576,2575]) ).
tff(2578,plain,
select(store(store(q30,seq,earray_148),tail,s(index_147)),seq) = select(q31,seq),
inference(monotonicity,[status(thm)],[2577]) ).
tff(2579,plain,
select(q31,seq) = select(store(store(q30,seq,earray_148),tail,s(index_147)),seq),
inference(symmetry,[status(thm)],[2578]) ).
tff(2580,plain,
select(q31,seq) = earray_148,
inference(transitivity,[status(thm)],[2579,2574,2570,2566,2564]) ).
tff(2581,plain,
store(store(queue_143,tail,index_144),seq,select(q31,seq)) = store(q30,seq,earray_148),
inference(monotonicity,[status(thm)],[2567,2580]) ).
tff(2582,plain,
select(store(store(queue_143,tail,index_144),seq,select(q31,seq)),head) = select(store(q30,seq,earray_148),head),
inference(monotonicity,[status(thm)],[2581]) ).
tff(2583,plain,
select(store(q30,seq,earray_148),head) = select(store(store(queue_143,tail,index_144),seq,select(q31,seq)),head),
inference(symmetry,[status(thm)],[2582]) ).
tff(2584,plain,
( ( ~ ! [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_148),tail,select(q13,tail)),head) = select(store(q30,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(q30,seq,earray_148),tail,select(q13,tail)),head) = select(store(q30,seq,earray_148),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2585,plain,
( ~ ! [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_148),tail,select(q13,tail)),head) = select(store(q30,seq,earray_148),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2586,plain,
( ~ ! [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_148),tail,select(q13,tail)),head) = select(store(q30,seq,earray_148),head) ) ),
inference(modus_ponens,[status(thm)],[2585,2584]) ).
tff(2587,plain,
select(store(store(q30,seq,earray_148),tail,select(q13,tail)),head) = select(store(q30,seq,earray_148),head),
inference(unit_resolution,[status(thm)],[2586,89,1369]) ).
tff(2588,plain,
select(q29,tail) = index_141,
inference(symmetry,[status(thm)],[524]) ).
tff(2589,plain,
select(store(store(q28,seq,earray_130),tail,s(index_129)),tail) = select(q29,tail),
inference(symmetry,[status(thm)],[521]) ).
tff(2590,plain,
s(index_129) = select(store(store(q28,seq,earray_130),tail,s(index_129)),tail),
inference(symmetry,[status(thm)],[503]) ).
tff(2591,plain,
s(select(q28,tail)) = s(index_129),
inference(monotonicity,[status(thm)],[471]) ).
tff(2592,plain,
s(select(q28,tail)) = index_141,
inference(transitivity,[status(thm)],[2591,2590,2589,2588]) ).
tff(2593,plain,
s(s(select(q28,tail))) = s(index_141),
inference(monotonicity,[status(thm)],[2592]) ).
tff(2594,plain,
s(index_141) = s(s(select(q28,tail))),
inference(symmetry,[status(thm)],[2593]) ).
tff(2595,plain,
index_147 = s(s(select(q28,tail))),
inference(transitivity,[status(thm)],[411,463,466,2594]) ).
tff(2596,plain,
s(index_147) = s(s(s(select(q28,tail)))),
inference(monotonicity,[status(thm)],[2595]) ).
tff(2597,plain,
s(s(s(select(q28,tail)))) = s(index_147),
inference(symmetry,[status(thm)],[2596]) ).
tff(2598,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q28,tail)))) = select(q28,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2599,plain,
s(s(s(select(q28,tail)))) = select(q28,tail),
inference(unit_resolution,[status(thm)],[2598,187]) ).
tff(2600,plain,
select(q28,tail) = s(s(s(select(q28,tail)))),
inference(symmetry,[status(thm)],[2599]) ).
tff(2601,plain,
select(q13,tail) = index_150,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,578,575,2472,2469,493,490,2600,2597,390]) ).
tff(2602,plain,
store(store(q30,seq,earray_148),tail,select(q13,tail)) = store(queue_149,tail,index_150),
inference(monotonicity,[status(thm)],[394,2601]) ).
tff(2603,plain,
select(store(store(q30,seq,earray_148),tail,select(q13,tail)),head) = select(store(queue_149,tail,index_150),head),
inference(monotonicity,[status(thm)],[2602]) ).
tff(2604,plain,
select(store(queue_149,tail,index_150),head) = select(store(store(q30,seq,earray_148),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2603]) ).
tff(2605,plain,
( ( ~ ! [I: $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(q32,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(q32,seq)),head) = select(store(queue_149,tail,index_150),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2606,plain,
( ~ ! [I: $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(q32,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2607,plain,
( ~ ! [I: $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(q32,seq)),head) = select(store(queue_149,tail,index_150),head) ) ),
inference(modus_ponens,[status(thm)],[2606,2605]) ).
tff(2608,plain,
select(store(store(queue_149,tail,index_150),seq,select(q32,seq)),head) = select(store(queue_149,tail,index_150),head),
inference(unit_resolution,[status(thm)],[2607,89,1339]) ).
tff(2609,plain,
( ( earray_154 = store(earray_152,index_153,e31) )
<=> ( earray_154 = store(earray_152,index_153,e31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2610,axiom,
earray_154 = store(earray_152,index_153,e31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(2611,plain,
earray_154 = store(earray_152,index_153,e31),
inference(modus_ponens,[status(thm)],[2610,2609]) ).
tff(2612,plain,
store(earray_152,index_153,e31) = earray_154,
inference(symmetry,[status(thm)],[2611]) ).
tff(2613,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_152,index_153,e31)),seq) = store(earray_152,index_153,e31) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2614,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_152,index_153,e31)),seq) = store(earray_152,index_153,e31),
inference(unit_resolution,[status(thm)],[2613,24]) ).
tff(2615,plain,
store(queue_149,tail,index_150) = q31,
inference(transitivity,[status(thm)],[2576,2575]) ).
tff(2616,plain,
store(store(queue_149,tail,index_150),seq,store(earray_152,index_153,e31)) = store(q31,seq,earray_154),
inference(monotonicity,[status(thm)],[2615,2612]) ).
tff(2617,plain,
select(store(store(queue_149,tail,index_150),seq,store(earray_152,index_153,e31)),seq) = select(store(q31,seq,earray_154),seq),
inference(monotonicity,[status(thm)],[2616]) ).
tff(2618,plain,
select(store(q31,seq,earray_154),seq) = select(store(store(queue_149,tail,index_150),seq,store(earray_152,index_153,e31)),seq),
inference(symmetry,[status(thm)],[2617]) ).
tff(2619,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_154),tail,s(index_153)),seq) = select(store(q31,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(q31,seq,earray_154),tail,s(index_153)),seq) = select(store(q31,seq,earray_154),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2620,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q31,seq,earray_154),tail,s(index_153)),seq) = select(store(q31,seq,earray_154),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2621,plain,
( ~ ! [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_154),tail,s(index_153)),seq) = select(store(q31,seq,earray_154),seq) ) ),
inference(modus_ponens,[status(thm)],[2620,2619]) ).
tff(2622,plain,
select(store(store(q31,seq,earray_154),tail,s(index_153)),seq) = select(store(q31,seq,earray_154),seq),
inference(unit_resolution,[status(thm)],[2621,89,83]) ).
tff(2623,plain,
queue_157 = q32,
inference(symmetry,[status(thm)],[434]) ).
tff(2624,plain,
store(queue_155,tail,index_156) = queue_157,
inference(symmetry,[status(thm)],[431]) ).
tff(2625,plain,
store(store(q31,seq,earray_154),tail,s(index_153)) = q32,
inference(transitivity,[status(thm)],[427,2624,2623]) ).
tff(2626,plain,
select(store(store(q31,seq,earray_154),tail,s(index_153)),seq) = select(q32,seq),
inference(monotonicity,[status(thm)],[2625]) ).
tff(2627,plain,
select(q32,seq) = select(store(store(q31,seq,earray_154),tail,s(index_153)),seq),
inference(symmetry,[status(thm)],[2626]) ).
tff(2628,plain,
select(q32,seq) = earray_154,
inference(transitivity,[status(thm)],[2627,2622,2618,2614,2612]) ).
tff(2629,plain,
store(store(queue_149,tail,index_150),seq,select(q32,seq)) = store(q31,seq,earray_154),
inference(monotonicity,[status(thm)],[2615,2628]) ).
tff(2630,plain,
select(store(store(queue_149,tail,index_150),seq,select(q32,seq)),head) = select(store(q31,seq,earray_154),head),
inference(monotonicity,[status(thm)],[2629]) ).
tff(2631,plain,
select(store(q31,seq,earray_154),head) = select(store(store(queue_149,tail,index_150),seq,select(q32,seq)),head),
inference(symmetry,[status(thm)],[2630]) ).
tff(2632,plain,
( ( ~ ! [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_154),tail,select(q14,tail)),head) = select(store(q31,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(q31,seq,earray_154),tail,select(q14,tail)),head) = select(store(q31,seq,earray_154),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2633,plain,
( ~ ! [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_154),tail,select(q14,tail)),head) = select(store(q31,seq,earray_154),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2634,plain,
( ~ ! [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_154),tail,select(q14,tail)),head) = select(store(q31,seq,earray_154),head) ) ),
inference(modus_ponens,[status(thm)],[2633,2632]) ).
tff(2635,plain,
select(store(store(q31,seq,earray_154),tail,select(q14,tail)),head) = select(store(q31,seq,earray_154),head),
inference(unit_resolution,[status(thm)],[2634,89,1369]) ).
tff(2636,plain,
s(select(q29,tail)) = s(index_141),
inference(monotonicity,[status(thm)],[2588]) ).
tff(2637,plain,
s(select(q29,tail)) = index_147,
inference(transitivity,[status(thm)],[2636,467,464,412]) ).
tff(2638,plain,
s(s(select(q29,tail))) = s(index_147),
inference(monotonicity,[status(thm)],[2637]) ).
tff(2639,plain,
s(index_147) = s(s(select(q29,tail))),
inference(symmetry,[status(thm)],[2638]) ).
tff(2640,plain,
index_153 = s(s(select(q29,tail))),
inference(transitivity,[status(thm)],[385,404,407,2639]) ).
tff(2641,plain,
s(index_153) = s(s(s(select(q29,tail)))),
inference(monotonicity,[status(thm)],[2640]) ).
tff(2642,plain,
s(s(s(select(q29,tail)))) = s(index_153),
inference(symmetry,[status(thm)],[2641]) ).
tff(2643,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q29,tail)))) = select(q29,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2644,plain,
s(s(s(select(q29,tail)))) = select(q29,tail),
inference(unit_resolution,[status(thm)],[2643,187]) ).
tff(2645,plain,
select(q29,tail) = s(s(s(select(q29,tail)))),
inference(symmetry,[status(thm)],[2644]) ).
tff(2646,plain,
select(q14,tail) = index_156,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,2462,2461,2517,2514,2590,2589,2645,2642,422]) ).
tff(2647,plain,
store(store(q31,seq,earray_154),tail,select(q14,tail)) = store(queue_155,tail,index_156),
inference(monotonicity,[status(thm)],[426,2646]) ).
tff(2648,plain,
select(store(store(q31,seq,earray_154),tail,select(q14,tail)),head) = select(store(queue_155,tail,index_156),head),
inference(monotonicity,[status(thm)],[2647]) ).
tff(2649,plain,
select(store(queue_155,tail,index_156),head) = select(store(store(q31,seq,earray_154),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2648]) ).
tff(2650,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head) = select(store(queue_155,tail,index_156),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_155,tail,index_156),seq,select(q33,seq)),head) = select(store(queue_155,tail,index_156),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2651,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head) = select(store(queue_155,tail,index_156),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2652,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head) = select(store(queue_155,tail,index_156),head) ) ),
inference(modus_ponens,[status(thm)],[2651,2650]) ).
tff(2653,plain,
select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head) = select(store(queue_155,tail,index_156),head),
inference(unit_resolution,[status(thm)],[2652,89,1339]) ).
tff(2654,plain,
( ( earray_160 = store(earray_158,index_159,e32) )
<=> ( earray_160 = store(earray_158,index_159,e32) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2655,axiom,
earray_160 = store(earray_158,index_159,e32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(2656,plain,
earray_160 = store(earray_158,index_159,e32),
inference(modus_ponens,[status(thm)],[2655,2654]) ).
tff(2657,plain,
store(earray_158,index_159,e32) = earray_160,
inference(symmetry,[status(thm)],[2656]) ).
tff(2658,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_155,tail,index_156),seq,store(earray_158,index_159,e32)),seq) = store(earray_158,index_159,e32) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2659,plain,
select(store(store(queue_155,tail,index_156),seq,store(earray_158,index_159,e32)),seq) = store(earray_158,index_159,e32),
inference(unit_resolution,[status(thm)],[2658,24]) ).
tff(2660,plain,
store(queue_155,tail,index_156) = q32,
inference(transitivity,[status(thm)],[2624,2623]) ).
tff(2661,plain,
store(store(queue_155,tail,index_156),seq,store(earray_158,index_159,e32)) = store(q32,seq,earray_160),
inference(monotonicity,[status(thm)],[2660,2657]) ).
tff(2662,plain,
select(store(store(queue_155,tail,index_156),seq,store(earray_158,index_159,e32)),seq) = select(store(q32,seq,earray_160),seq),
inference(monotonicity,[status(thm)],[2661]) ).
tff(2663,plain,
select(store(q32,seq,earray_160),seq) = select(store(store(queue_155,tail,index_156),seq,store(earray_158,index_159,e32)),seq),
inference(symmetry,[status(thm)],[2662]) ).
tff(2664,plain,
( ( ~ ! [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_160),tail,s(index_159)),seq) = select(store(q32,seq,earray_160),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_160),tail,s(index_159)),seq) = select(store(q32,seq,earray_160),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2665,plain,
( ~ ! [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_160),tail,s(index_159)),seq) = select(store(q32,seq,earray_160),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2666,plain,
( ~ ! [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_160),tail,s(index_159)),seq) = select(store(q32,seq,earray_160),seq) ) ),
inference(modus_ponens,[status(thm)],[2665,2664]) ).
tff(2667,plain,
select(store(store(q32,seq,earray_160),tail,s(index_159)),seq) = select(store(q32,seq,earray_160),seq),
inference(unit_resolution,[status(thm)],[2666,89,83]) ).
tff(2668,plain,
queue_163 = q33,
inference(symmetry,[status(thm)],[376]) ).
tff(2669,plain,
store(queue_161,tail,index_162) = queue_163,
inference(symmetry,[status(thm)],[373]) ).
tff(2670,plain,
store(store(q32,seq,earray_160),tail,s(index_159)) = q33,
inference(transitivity,[status(thm)],[369,2669,2668]) ).
tff(2671,plain,
select(store(store(q32,seq,earray_160),tail,s(index_159)),seq) = select(q33,seq),
inference(monotonicity,[status(thm)],[2670]) ).
tff(2672,plain,
select(q33,seq) = select(store(store(q32,seq,earray_160),tail,s(index_159)),seq),
inference(symmetry,[status(thm)],[2671]) ).
tff(2673,plain,
select(q33,seq) = earray_160,
inference(transitivity,[status(thm)],[2672,2667,2663,2659,2657]) ).
tff(2674,plain,
store(store(queue_155,tail,index_156),seq,select(q33,seq)) = store(q32,seq,earray_160),
inference(monotonicity,[status(thm)],[2660,2673]) ).
tff(2675,plain,
select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head) = select(store(q32,seq,earray_160),head),
inference(monotonicity,[status(thm)],[2674]) ).
tff(2676,plain,
select(store(q32,seq,earray_160),head) = select(store(store(queue_155,tail,index_156),seq,select(q33,seq)),head),
inference(symmetry,[status(thm)],[2675]) ).
tff(2677,plain,
( ( ~ ! [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_160),tail,select(q12,tail)),head) = select(store(q32,seq,earray_160),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_160),tail,select(q12,tail)),head) = select(store(q32,seq,earray_160),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2678,plain,
( ~ ! [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_160),tail,select(q12,tail)),head) = select(store(q32,seq,earray_160),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2679,plain,
( ~ ! [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_160),tail,select(q12,tail)),head) = select(store(q32,seq,earray_160),head) ) ),
inference(modus_ponens,[status(thm)],[2678,2677]) ).
tff(2680,plain,
select(store(store(q32,seq,earray_160),tail,select(q12,tail)),head) = select(store(q32,seq,earray_160),head),
inference(unit_resolution,[status(thm)],[2679,89,1369]) ).
tff(2681,plain,
select(q12,tail) = index_162,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,467,464,445,442,364]) ).
tff(2682,plain,
store(store(q32,seq,earray_160),tail,select(q12,tail)) = store(queue_161,tail,index_162),
inference(monotonicity,[status(thm)],[368,2681]) ).
tff(2683,plain,
select(store(store(q32,seq,earray_160),tail,select(q12,tail)),head) = select(store(queue_161,tail,index_162),head),
inference(monotonicity,[status(thm)],[2682]) ).
tff(2684,plain,
select(store(queue_161,tail,index_162),head) = select(store(store(q32,seq,earray_160),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2683]) ).
tff(2685,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head) = select(store(queue_161,tail,index_162),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_161,tail,index_162),seq,select(q34,seq)),head) = select(store(queue_161,tail,index_162),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2686,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head) = select(store(queue_161,tail,index_162),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2687,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head) = select(store(queue_161,tail,index_162),head) ) ),
inference(modus_ponens,[status(thm)],[2686,2685]) ).
tff(2688,plain,
select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head) = select(store(queue_161,tail,index_162),head),
inference(unit_resolution,[status(thm)],[2687,89,1339]) ).
tff(2689,plain,
( ( earray_166 = store(earray_164,index_165,e33) )
<=> ( earray_166 = store(earray_164,index_165,e33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2690,axiom,
earray_166 = store(earray_164,index_165,e33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(2691,plain,
earray_166 = store(earray_164,index_165,e33),
inference(modus_ponens,[status(thm)],[2690,2689]) ).
tff(2692,plain,
store(earray_164,index_165,e33) = earray_166,
inference(symmetry,[status(thm)],[2691]) ).
tff(2693,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_161,tail,index_162),seq,store(earray_164,index_165,e33)),seq) = store(earray_164,index_165,e33) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2694,plain,
select(store(store(queue_161,tail,index_162),seq,store(earray_164,index_165,e33)),seq) = store(earray_164,index_165,e33),
inference(unit_resolution,[status(thm)],[2693,24]) ).
tff(2695,plain,
store(queue_161,tail,index_162) = q33,
inference(transitivity,[status(thm)],[2669,2668]) ).
tff(2696,plain,
store(store(queue_161,tail,index_162),seq,store(earray_164,index_165,e33)) = store(q33,seq,earray_166),
inference(monotonicity,[status(thm)],[2695,2692]) ).
tff(2697,plain,
select(store(store(queue_161,tail,index_162),seq,store(earray_164,index_165,e33)),seq) = select(store(q33,seq,earray_166),seq),
inference(monotonicity,[status(thm)],[2696]) ).
tff(2698,plain,
select(store(q33,seq,earray_166),seq) = select(store(store(queue_161,tail,index_162),seq,store(earray_164,index_165,e33)),seq),
inference(symmetry,[status(thm)],[2697]) ).
tff(2699,plain,
( ( ~ ! [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_166),tail,s(index_165)),seq) = select(store(q33,seq,earray_166),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_166),tail,s(index_165)),seq) = select(store(q33,seq,earray_166),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2700,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q33,seq,earray_166),tail,s(index_165)),seq) = select(store(q33,seq,earray_166),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2701,plain,
( ~ ! [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_166),tail,s(index_165)),seq) = select(store(q33,seq,earray_166),seq) ) ),
inference(modus_ponens,[status(thm)],[2700,2699]) ).
tff(2702,plain,
select(store(store(q33,seq,earray_166),tail,s(index_165)),seq) = select(store(q33,seq,earray_166),seq),
inference(unit_resolution,[status(thm)],[2701,89,83]) ).
tff(2703,plain,
queue_169 = q34,
inference(symmetry,[status(thm)],[317]) ).
tff(2704,plain,
store(queue_167,tail,index_168) = queue_169,
inference(symmetry,[status(thm)],[314]) ).
tff(2705,plain,
store(store(q33,seq,earray_166),tail,s(index_165)) = q34,
inference(transitivity,[status(thm)],[310,2704,2703]) ).
tff(2706,plain,
select(store(store(q33,seq,earray_166),tail,s(index_165)),seq) = select(q34,seq),
inference(monotonicity,[status(thm)],[2705]) ).
tff(2707,plain,
select(q34,seq) = select(store(store(q33,seq,earray_166),tail,s(index_165)),seq),
inference(symmetry,[status(thm)],[2706]) ).
tff(2708,plain,
select(q34,seq) = earray_166,
inference(transitivity,[status(thm)],[2707,2702,2698,2694,2692]) ).
tff(2709,plain,
store(store(queue_161,tail,index_162),seq,select(q34,seq)) = store(q33,seq,earray_166),
inference(monotonicity,[status(thm)],[2695,2708]) ).
tff(2710,plain,
select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head) = select(store(q33,seq,earray_166),head),
inference(monotonicity,[status(thm)],[2709]) ).
tff(2711,plain,
select(store(q33,seq,earray_166),head) = select(store(store(queue_161,tail,index_162),seq,select(q34,seq)),head),
inference(symmetry,[status(thm)],[2710]) ).
tff(2712,plain,
( ( ~ ! [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_166),tail,select(q13,tail)),head) = select(store(q33,seq,earray_166),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_166),tail,select(q13,tail)),head) = select(store(q33,seq,earray_166),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2713,plain,
( ~ ! [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_166),tail,select(q13,tail)),head) = select(store(q33,seq,earray_166),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2714,plain,
( ~ ! [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_166),tail,select(q13,tail)),head) = select(store(q33,seq,earray_166),head) ) ),
inference(modus_ponens,[status(thm)],[2713,2712]) ).
tff(2715,plain,
select(store(store(q33,seq,earray_166),tail,select(q13,tail)),head) = select(store(q33,seq,earray_166),head),
inference(unit_resolution,[status(thm)],[2714,89,1369]) ).
tff(2716,plain,
select(q32,tail) = index_159,
inference(symmetry,[status(thm)],[439]) ).
tff(2717,plain,
select(store(store(q31,seq,earray_154),tail,s(index_153)),tail) = select(q32,tail),
inference(symmetry,[status(thm)],[436]) ).
tff(2718,plain,
s(index_153) = select(store(store(q31,seq,earray_154),tail,s(index_153)),tail),
inference(symmetry,[status(thm)],[418]) ).
tff(2719,plain,
s(select(q31,tail)) = s(index_153),
inference(monotonicity,[status(thm)],[386]) ).
tff(2720,plain,
s(select(q31,tail)) = index_159,
inference(transitivity,[status(thm)],[2719,2718,2717,2716]) ).
tff(2721,plain,
s(s(select(q31,tail))) = s(index_159),
inference(monotonicity,[status(thm)],[2720]) ).
tff(2722,plain,
s(index_159) = s(s(select(q31,tail))),
inference(symmetry,[status(thm)],[2721]) ).
tff(2723,plain,
index_165 = s(s(select(q31,tail))),
inference(transitivity,[status(thm)],[326,378,381,2722]) ).
tff(2724,plain,
s(index_165) = s(s(s(select(q31,tail)))),
inference(monotonicity,[status(thm)],[2723]) ).
tff(2725,plain,
s(s(s(select(q31,tail)))) = s(index_165),
inference(symmetry,[status(thm)],[2724]) ).
tff(2726,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q31,tail)))) = select(q31,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2727,plain,
s(s(s(select(q31,tail)))) = select(q31,tail),
inference(unit_resolution,[status(thm)],[2726,187]) ).
tff(2728,plain,
select(q31,tail) = s(s(s(select(q31,tail)))),
inference(symmetry,[status(thm)],[2727]) ).
tff(2729,plain,
select(q13,tail) = index_168,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,578,575,2472,2469,493,490,2600,2597,408,405,2728,2725,305]) ).
tff(2730,plain,
store(store(q33,seq,earray_166),tail,select(q13,tail)) = store(queue_167,tail,index_168),
inference(monotonicity,[status(thm)],[309,2729]) ).
tff(2731,plain,
select(store(store(q33,seq,earray_166),tail,select(q13,tail)),head) = select(store(queue_167,tail,index_168),head),
inference(monotonicity,[status(thm)],[2730]) ).
tff(2732,plain,
select(store(queue_167,tail,index_168),head) = select(store(store(q33,seq,earray_166),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2731]) ).
tff(2733,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head) = select(store(queue_167,tail,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_167,tail,index_168),seq,select(q35,seq)),head) = select(store(queue_167,tail,index_168),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2734,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head) = select(store(queue_167,tail,index_168),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2735,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head) = select(store(queue_167,tail,index_168),head) ) ),
inference(modus_ponens,[status(thm)],[2734,2733]) ).
tff(2736,plain,
select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head) = select(store(queue_167,tail,index_168),head),
inference(unit_resolution,[status(thm)],[2735,89,1339]) ).
tff(2737,plain,
( ( earray_172 = store(earray_170,index_171,e34) )
<=> ( earray_172 = store(earray_170,index_171,e34) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2738,axiom,
earray_172 = store(earray_170,index_171,e34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(2739,plain,
earray_172 = store(earray_170,index_171,e34),
inference(modus_ponens,[status(thm)],[2738,2737]) ).
tff(2740,plain,
store(earray_170,index_171,e34) = earray_172,
inference(symmetry,[status(thm)],[2739]) ).
tff(2741,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_167,tail,index_168),seq,store(earray_170,index_171,e34)),seq) = store(earray_170,index_171,e34) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2742,plain,
select(store(store(queue_167,tail,index_168),seq,store(earray_170,index_171,e34)),seq) = store(earray_170,index_171,e34),
inference(unit_resolution,[status(thm)],[2741,24]) ).
tff(2743,plain,
store(queue_167,tail,index_168) = q34,
inference(transitivity,[status(thm)],[2704,2703]) ).
tff(2744,plain,
store(store(queue_167,tail,index_168),seq,store(earray_170,index_171,e34)) = store(q34,seq,earray_172),
inference(monotonicity,[status(thm)],[2743,2740]) ).
tff(2745,plain,
select(store(store(queue_167,tail,index_168),seq,store(earray_170,index_171,e34)),seq) = select(store(q34,seq,earray_172),seq),
inference(monotonicity,[status(thm)],[2744]) ).
tff(2746,plain,
select(store(q34,seq,earray_172),seq) = select(store(store(queue_167,tail,index_168),seq,store(earray_170,index_171,e34)),seq),
inference(symmetry,[status(thm)],[2745]) ).
tff(2747,plain,
( ( ~ ! [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_172),tail,s(index_171)),seq) = select(store(q34,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(q34,seq,earray_172),tail,s(index_171)),seq) = select(store(q34,seq,earray_172),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2748,plain,
( ~ ! [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_172),tail,s(index_171)),seq) = select(store(q34,seq,earray_172),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2749,plain,
( ~ ! [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_172),tail,s(index_171)),seq) = select(store(q34,seq,earray_172),seq) ) ),
inference(modus_ponens,[status(thm)],[2748,2747]) ).
tff(2750,plain,
select(store(store(q34,seq,earray_172),tail,s(index_171)),seq) = select(store(q34,seq,earray_172),seq),
inference(unit_resolution,[status(thm)],[2749,89,83]) ).
tff(2751,plain,
queue_175 = q35,
inference(symmetry,[status(thm)],[349]) ).
tff(2752,plain,
store(queue_173,tail,index_174) = queue_175,
inference(symmetry,[status(thm)],[346]) ).
tff(2753,plain,
store(store(q34,seq,earray_172),tail,s(index_171)) = q35,
inference(transitivity,[status(thm)],[342,2752,2751]) ).
tff(2754,plain,
select(store(store(q34,seq,earray_172),tail,s(index_171)),seq) = select(q35,seq),
inference(monotonicity,[status(thm)],[2753]) ).
tff(2755,plain,
select(q35,seq) = select(store(store(q34,seq,earray_172),tail,s(index_171)),seq),
inference(symmetry,[status(thm)],[2754]) ).
tff(2756,plain,
select(q35,seq) = earray_172,
inference(transitivity,[status(thm)],[2755,2750,2746,2742,2740]) ).
tff(2757,plain,
store(store(queue_167,tail,index_168),seq,select(q35,seq)) = store(q34,seq,earray_172),
inference(monotonicity,[status(thm)],[2743,2756]) ).
tff(2758,plain,
select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head) = select(store(q34,seq,earray_172),head),
inference(monotonicity,[status(thm)],[2757]) ).
tff(2759,plain,
select(store(q34,seq,earray_172),head) = select(store(store(queue_167,tail,index_168),seq,select(q35,seq)),head),
inference(symmetry,[status(thm)],[2758]) ).
tff(2760,plain,
( ( ~ ! [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_172),tail,select(q14,tail)),head) = select(store(q34,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(q34,seq,earray_172),tail,select(q14,tail)),head) = select(store(q34,seq,earray_172),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2761,plain,
( ~ ! [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_172),tail,select(q14,tail)),head) = select(store(q34,seq,earray_172),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2762,plain,
( ~ ! [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_172),tail,select(q14,tail)),head) = select(store(q34,seq,earray_172),head) ) ),
inference(modus_ponens,[status(thm)],[2761,2760]) ).
tff(2763,plain,
select(store(store(q34,seq,earray_172),tail,select(q14,tail)),head) = select(store(q34,seq,earray_172),head),
inference(unit_resolution,[status(thm)],[2762,89,1369]) ).
tff(2764,plain,
s(select(q32,tail)) = s(index_159),
inference(monotonicity,[status(thm)],[2716]) ).
tff(2765,plain,
s(select(q32,tail)) = index_165,
inference(transitivity,[status(thm)],[2764,382,379,327]) ).
tff(2766,plain,
s(s(select(q32,tail))) = s(index_165),
inference(monotonicity,[status(thm)],[2765]) ).
tff(2767,plain,
s(index_165) = s(s(select(q32,tail))),
inference(symmetry,[status(thm)],[2766]) ).
tff(2768,plain,
index_171 = s(s(select(q32,tail))),
inference(transitivity,[status(thm)],[300,319,322,2767]) ).
tff(2769,plain,
s(index_171) = s(s(s(select(q32,tail)))),
inference(monotonicity,[status(thm)],[2768]) ).
tff(2770,plain,
s(s(s(select(q32,tail)))) = s(index_171),
inference(symmetry,[status(thm)],[2769]) ).
tff(2771,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q32,tail)))) = select(q32,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2772,plain,
s(s(s(select(q32,tail)))) = select(q32,tail),
inference(unit_resolution,[status(thm)],[2771,187]) ).
tff(2773,plain,
select(q32,tail) = s(s(s(select(q32,tail)))),
inference(symmetry,[status(thm)],[2772]) ).
tff(2774,plain,
select(q14,tail) = index_174,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,2462,2461,2517,2514,2590,2589,2645,2642,2718,2717,2773,2770,337]) ).
tff(2775,plain,
store(store(q34,seq,earray_172),tail,select(q14,tail)) = store(queue_173,tail,index_174),
inference(monotonicity,[status(thm)],[341,2774]) ).
tff(2776,plain,
select(store(store(q34,seq,earray_172),tail,select(q14,tail)),head) = select(store(queue_173,tail,index_174),head),
inference(monotonicity,[status(thm)],[2775]) ).
tff(2777,plain,
select(store(queue_173,tail,index_174),head) = select(store(store(q34,seq,earray_172),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2776]) ).
tff(2778,plain,
( ( ~ ! [I: $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(q36,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(q36,seq)),head) = select(store(queue_173,tail,index_174),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2779,plain,
( ~ ! [I: $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(q36,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2780,plain,
( ~ ! [I: $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(q36,seq)),head) = select(store(queue_173,tail,index_174),head) ) ),
inference(modus_ponens,[status(thm)],[2779,2778]) ).
tff(2781,plain,
select(store(store(queue_173,tail,index_174),seq,select(q36,seq)),head) = select(store(queue_173,tail,index_174),head),
inference(unit_resolution,[status(thm)],[2780,89,1339]) ).
tff(2782,plain,
( ( earray_178 = store(earray_176,index_177,e35) )
<=> ( earray_178 = store(earray_176,index_177,e35) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2783,axiom,
earray_178 = store(earray_176,index_177,e35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(2784,plain,
earray_178 = store(earray_176,index_177,e35),
inference(modus_ponens,[status(thm)],[2783,2782]) ).
tff(2785,plain,
store(earray_176,index_177,e35) = earray_178,
inference(symmetry,[status(thm)],[2784]) ).
tff(2786,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,e35)),seq) = store(earray_176,index_177,e35) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2787,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e35)),seq) = store(earray_176,index_177,e35),
inference(unit_resolution,[status(thm)],[2786,24]) ).
tff(2788,plain,
store(queue_173,tail,index_174) = q35,
inference(transitivity,[status(thm)],[2752,2751]) ).
tff(2789,plain,
store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e35)) = store(q35,seq,earray_178),
inference(monotonicity,[status(thm)],[2788,2785]) ).
tff(2790,plain,
select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e35)),seq) = select(store(q35,seq,earray_178),seq),
inference(monotonicity,[status(thm)],[2789]) ).
tff(2791,plain,
select(store(q35,seq,earray_178),seq) = select(store(store(queue_173,tail,index_174),seq,store(earray_176,index_177,e35)),seq),
inference(symmetry,[status(thm)],[2790]) ).
tff(2792,plain,
( ( ~ ! [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_178),tail,s(index_177)),seq) = select(store(q35,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(q35,seq,earray_178),tail,s(index_177)),seq) = select(store(q35,seq,earray_178),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2793,plain,
( ~ ! [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_178),tail,s(index_177)),seq) = select(store(q35,seq,earray_178),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2794,plain,
( ~ ! [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_178),tail,s(index_177)),seq) = select(store(q35,seq,earray_178),seq) ) ),
inference(modus_ponens,[status(thm)],[2793,2792]) ).
tff(2795,plain,
select(store(store(q35,seq,earray_178),tail,s(index_177)),seq) = select(store(q35,seq,earray_178),seq),
inference(unit_resolution,[status(thm)],[2794,89,83]) ).
tff(2796,plain,
queue_181 = q36,
inference(symmetry,[status(thm)],[291]) ).
tff(2797,plain,
store(queue_179,tail,index_180) = queue_181,
inference(symmetry,[status(thm)],[288]) ).
tff(2798,plain,
store(store(q35,seq,earray_178),tail,s(index_177)) = q36,
inference(transitivity,[status(thm)],[284,2797,2796]) ).
tff(2799,plain,
select(store(store(q35,seq,earray_178),tail,s(index_177)),seq) = select(q36,seq),
inference(monotonicity,[status(thm)],[2798]) ).
tff(2800,plain,
select(q36,seq) = select(store(store(q35,seq,earray_178),tail,s(index_177)),seq),
inference(symmetry,[status(thm)],[2799]) ).
tff(2801,plain,
select(q36,seq) = earray_178,
inference(transitivity,[status(thm)],[2800,2795,2791,2787,2785]) ).
tff(2802,plain,
store(store(queue_173,tail,index_174),seq,select(q36,seq)) = store(q35,seq,earray_178),
inference(monotonicity,[status(thm)],[2788,2801]) ).
tff(2803,plain,
select(store(store(queue_173,tail,index_174),seq,select(q36,seq)),head) = select(store(q35,seq,earray_178),head),
inference(monotonicity,[status(thm)],[2802]) ).
tff(2804,plain,
select(store(q35,seq,earray_178),head) = select(store(store(queue_173,tail,index_174),seq,select(q36,seq)),head),
inference(symmetry,[status(thm)],[2803]) ).
tff(2805,plain,
( ( ~ ! [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_178),tail,select(q12,tail)),head) = select(store(q35,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(q35,seq,earray_178),tail,select(q12,tail)),head) = select(store(q35,seq,earray_178),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2806,plain,
( ~ ! [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_178),tail,select(q12,tail)),head) = select(store(q35,seq,earray_178),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2807,plain,
( ~ ! [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_178),tail,select(q12,tail)),head) = select(store(q35,seq,earray_178),head) ) ),
inference(modus_ponens,[status(thm)],[2806,2805]) ).
tff(2808,plain,
select(store(store(q35,seq,earray_178),tail,select(q12,tail)),head) = select(store(q35,seq,earray_178),head),
inference(unit_resolution,[status(thm)],[2807,89,1369]) ).
tff(2809,plain,
select(q12,tail) = index_180,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,467,464,445,442,382,379,360,357,279]) ).
tff(2810,plain,
store(store(q35,seq,earray_178),tail,select(q12,tail)) = store(queue_179,tail,index_180),
inference(monotonicity,[status(thm)],[283,2809]) ).
tff(2811,plain,
select(store(store(q35,seq,earray_178),tail,select(q12,tail)),head) = select(store(queue_179,tail,index_180),head),
inference(monotonicity,[status(thm)],[2810]) ).
tff(2812,plain,
select(store(queue_179,tail,index_180),head) = select(store(store(q35,seq,earray_178),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2811]) ).
tff(2813,plain,
( ( ~ ! [I: $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(q37,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(q37,seq)),head) = select(store(queue_179,tail,index_180),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2814,plain,
( ~ ! [I: $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(q37,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2815,plain,
( ~ ! [I: $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(q37,seq)),head) = select(store(queue_179,tail,index_180),head) ) ),
inference(modus_ponens,[status(thm)],[2814,2813]) ).
tff(2816,plain,
select(store(store(queue_179,tail,index_180),seq,select(q37,seq)),head) = select(store(queue_179,tail,index_180),head),
inference(unit_resolution,[status(thm)],[2815,89,1339]) ).
tff(2817,plain,
( ( earray_184 = store(earray_182,index_183,e36) )
<=> ( earray_184 = store(earray_182,index_183,e36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2818,axiom,
earray_184 = store(earray_182,index_183,e36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(2819,plain,
earray_184 = store(earray_182,index_183,e36),
inference(modus_ponens,[status(thm)],[2818,2817]) ).
tff(2820,plain,
store(earray_182,index_183,e36) = earray_184,
inference(symmetry,[status(thm)],[2819]) ).
tff(2821,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,e36)),seq) = store(earray_182,index_183,e36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2822,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e36)),seq) = store(earray_182,index_183,e36),
inference(unit_resolution,[status(thm)],[2821,24]) ).
tff(2823,plain,
store(queue_179,tail,index_180) = q36,
inference(transitivity,[status(thm)],[2797,2796]) ).
tff(2824,plain,
store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e36)) = store(q36,seq,earray_184),
inference(monotonicity,[status(thm)],[2823,2820]) ).
tff(2825,plain,
select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e36)),seq) = select(store(q36,seq,earray_184),seq),
inference(monotonicity,[status(thm)],[2824]) ).
tff(2826,plain,
select(store(q36,seq,earray_184),seq) = select(store(store(queue_179,tail,index_180),seq,store(earray_182,index_183,e36)),seq),
inference(symmetry,[status(thm)],[2825]) ).
tff(2827,plain,
( ( ~ ! [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_184),tail,s(index_183)),seq) = select(store(q36,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(q36,seq,earray_184),tail,s(index_183)),seq) = select(store(q36,seq,earray_184),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2828,plain,
( ~ ! [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_184),tail,s(index_183)),seq) = select(store(q36,seq,earray_184),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2829,plain,
( ~ ! [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_184),tail,s(index_183)),seq) = select(store(q36,seq,earray_184),seq) ) ),
inference(modus_ponens,[status(thm)],[2828,2827]) ).
tff(2830,plain,
select(store(store(q36,seq,earray_184),tail,s(index_183)),seq) = select(store(q36,seq,earray_184),seq),
inference(unit_resolution,[status(thm)],[2829,89,83]) ).
tff(2831,plain,
queue_187 = q37,
inference(symmetry,[status(thm)],[232]) ).
tff(2832,plain,
store(queue_185,tail,index_186) = queue_187,
inference(symmetry,[status(thm)],[229]) ).
tff(2833,plain,
store(store(q36,seq,earray_184),tail,s(index_183)) = q37,
inference(transitivity,[status(thm)],[225,2832,2831]) ).
tff(2834,plain,
select(store(store(q36,seq,earray_184),tail,s(index_183)),seq) = select(q37,seq),
inference(monotonicity,[status(thm)],[2833]) ).
tff(2835,plain,
select(q37,seq) = select(store(store(q36,seq,earray_184),tail,s(index_183)),seq),
inference(symmetry,[status(thm)],[2834]) ).
tff(2836,plain,
select(q37,seq) = earray_184,
inference(transitivity,[status(thm)],[2835,2830,2826,2822,2820]) ).
tff(2837,plain,
store(store(queue_179,tail,index_180),seq,select(q37,seq)) = store(q36,seq,earray_184),
inference(monotonicity,[status(thm)],[2823,2836]) ).
tff(2838,plain,
select(store(store(queue_179,tail,index_180),seq,select(q37,seq)),head) = select(store(q36,seq,earray_184),head),
inference(monotonicity,[status(thm)],[2837]) ).
tff(2839,plain,
select(store(q36,seq,earray_184),head) = select(store(store(queue_179,tail,index_180),seq,select(q37,seq)),head),
inference(symmetry,[status(thm)],[2838]) ).
tff(2840,plain,
( ( ~ ! [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_184),tail,select(q13,tail)),head) = select(store(q36,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(q36,seq,earray_184),tail,select(q13,tail)),head) = select(store(q36,seq,earray_184),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2841,plain,
( ~ ! [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_184),tail,select(q13,tail)),head) = select(store(q36,seq,earray_184),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2842,plain,
( ~ ! [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_184),tail,select(q13,tail)),head) = select(store(q36,seq,earray_184),head) ) ),
inference(modus_ponens,[status(thm)],[2841,2840]) ).
tff(2843,plain,
select(store(store(q36,seq,earray_184),tail,select(q13,tail)),head) = select(store(q36,seq,earray_184),head),
inference(unit_resolution,[status(thm)],[2842,89,1369]) ).
tff(2844,plain,
select(q35,tail) = index_177,
inference(symmetry,[status(thm)],[354]) ).
tff(2845,plain,
select(store(store(q34,seq,earray_172),tail,s(index_171)),tail) = select(q35,tail),
inference(symmetry,[status(thm)],[351]) ).
tff(2846,plain,
s(index_171) = select(store(store(q34,seq,earray_172),tail,s(index_171)),tail),
inference(symmetry,[status(thm)],[333]) ).
tff(2847,plain,
s(select(q34,tail)) = s(index_171),
inference(monotonicity,[status(thm)],[301]) ).
tff(2848,plain,
s(select(q34,tail)) = index_177,
inference(transitivity,[status(thm)],[2847,2846,2845,2844]) ).
tff(2849,plain,
s(s(select(q34,tail))) = s(index_177),
inference(monotonicity,[status(thm)],[2848]) ).
tff(2850,plain,
s(index_177) = s(s(select(q34,tail))),
inference(symmetry,[status(thm)],[2849]) ).
tff(2851,plain,
index_183 = s(s(select(q34,tail))),
inference(transitivity,[status(thm)],[241,293,296,2850]) ).
tff(2852,plain,
s(index_183) = s(s(s(select(q34,tail)))),
inference(monotonicity,[status(thm)],[2851]) ).
tff(2853,plain,
s(s(s(select(q34,tail)))) = s(index_183),
inference(symmetry,[status(thm)],[2852]) ).
tff(2854,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q34,tail)))) = select(q34,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2855,plain,
s(s(s(select(q34,tail)))) = select(q34,tail),
inference(unit_resolution,[status(thm)],[2854,187]) ).
tff(2856,plain,
select(q34,tail) = s(s(s(select(q34,tail)))),
inference(symmetry,[status(thm)],[2855]) ).
tff(2857,plain,
select(q13,tail) = index_186,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,578,575,2472,2469,493,490,2600,2597,408,405,2728,2725,323,320,2856,2853,220]) ).
tff(2858,plain,
store(store(q36,seq,earray_184),tail,select(q13,tail)) = store(queue_185,tail,index_186),
inference(monotonicity,[status(thm)],[224,2857]) ).
tff(2859,plain,
select(store(store(q36,seq,earray_184),tail,select(q13,tail)),head) = select(store(queue_185,tail,index_186),head),
inference(monotonicity,[status(thm)],[2858]) ).
tff(2860,plain,
select(store(queue_185,tail,index_186),head) = select(store(store(q36,seq,earray_184),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2859]) ).
tff(2861,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head) = select(store(queue_185,tail,index_186),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_185,tail,index_186),seq,select(q38,seq)),head) = select(store(queue_185,tail,index_186),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2862,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head) = select(store(queue_185,tail,index_186),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2863,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head) = select(store(queue_185,tail,index_186),head) ) ),
inference(modus_ponens,[status(thm)],[2862,2861]) ).
tff(2864,plain,
select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head) = select(store(queue_185,tail,index_186),head),
inference(unit_resolution,[status(thm)],[2863,89,1339]) ).
tff(2865,plain,
( ( earray_190 = store(earray_188,index_189,e37) )
<=> ( earray_190 = store(earray_188,index_189,e37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2866,axiom,
earray_190 = store(earray_188,index_189,e37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp33) ).
tff(2867,plain,
earray_190 = store(earray_188,index_189,e37),
inference(modus_ponens,[status(thm)],[2866,2865]) ).
tff(2868,plain,
store(earray_188,index_189,e37) = earray_190,
inference(symmetry,[status(thm)],[2867]) ).
tff(2869,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_185,tail,index_186),seq,store(earray_188,index_189,e37)),seq) = store(earray_188,index_189,e37) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2870,plain,
select(store(store(queue_185,tail,index_186),seq,store(earray_188,index_189,e37)),seq) = store(earray_188,index_189,e37),
inference(unit_resolution,[status(thm)],[2869,24]) ).
tff(2871,plain,
store(queue_185,tail,index_186) = q37,
inference(transitivity,[status(thm)],[2832,2831]) ).
tff(2872,plain,
store(store(queue_185,tail,index_186),seq,store(earray_188,index_189,e37)) = store(q37,seq,earray_190),
inference(monotonicity,[status(thm)],[2871,2868]) ).
tff(2873,plain,
select(store(store(queue_185,tail,index_186),seq,store(earray_188,index_189,e37)),seq) = select(store(q37,seq,earray_190),seq),
inference(monotonicity,[status(thm)],[2872]) ).
tff(2874,plain,
select(store(q37,seq,earray_190),seq) = select(store(store(queue_185,tail,index_186),seq,store(earray_188,index_189,e37)),seq),
inference(symmetry,[status(thm)],[2873]) ).
tff(2875,plain,
( ( ~ ! [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_190),tail,s(index_189)),seq) = select(store(q37,seq,earray_190),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_190),tail,s(index_189)),seq) = select(store(q37,seq,earray_190),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2876,plain,
( ~ ! [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_190),tail,s(index_189)),seq) = select(store(q37,seq,earray_190),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2877,plain,
( ~ ! [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_190),tail,s(index_189)),seq) = select(store(q37,seq,earray_190),seq) ) ),
inference(modus_ponens,[status(thm)],[2876,2875]) ).
tff(2878,plain,
select(store(store(q37,seq,earray_190),tail,s(index_189)),seq) = select(store(q37,seq,earray_190),seq),
inference(unit_resolution,[status(thm)],[2877,89,83]) ).
tff(2879,plain,
queue_193 = q38,
inference(symmetry,[status(thm)],[264]) ).
tff(2880,plain,
store(queue_191,tail,index_192) = queue_193,
inference(symmetry,[status(thm)],[261]) ).
tff(2881,plain,
store(store(q37,seq,earray_190),tail,s(index_189)) = q38,
inference(transitivity,[status(thm)],[257,2880,2879]) ).
tff(2882,plain,
select(store(store(q37,seq,earray_190),tail,s(index_189)),seq) = select(q38,seq),
inference(monotonicity,[status(thm)],[2881]) ).
tff(2883,plain,
select(q38,seq) = select(store(store(q37,seq,earray_190),tail,s(index_189)),seq),
inference(symmetry,[status(thm)],[2882]) ).
tff(2884,plain,
select(q38,seq) = earray_190,
inference(transitivity,[status(thm)],[2883,2878,2874,2870,2868]) ).
tff(2885,plain,
store(store(queue_185,tail,index_186),seq,select(q38,seq)) = store(q37,seq,earray_190),
inference(monotonicity,[status(thm)],[2871,2884]) ).
tff(2886,plain,
select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head) = select(store(q37,seq,earray_190),head),
inference(monotonicity,[status(thm)],[2885]) ).
tff(2887,plain,
select(store(q37,seq,earray_190),head) = select(store(store(queue_185,tail,index_186),seq,select(q38,seq)),head),
inference(symmetry,[status(thm)],[2886]) ).
tff(2888,plain,
( ( ~ ! [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_190),tail,select(q14,tail)),head) = select(store(q37,seq,earray_190),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_190),tail,select(q14,tail)),head) = select(store(q37,seq,earray_190),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2889,plain,
( ~ ! [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_190),tail,select(q14,tail)),head) = select(store(q37,seq,earray_190),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2890,plain,
( ~ ! [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_190),tail,select(q14,tail)),head) = select(store(q37,seq,earray_190),head) ) ),
inference(modus_ponens,[status(thm)],[2889,2888]) ).
tff(2891,plain,
select(store(store(q37,seq,earray_190),tail,select(q14,tail)),head) = select(store(q37,seq,earray_190),head),
inference(unit_resolution,[status(thm)],[2890,89,1369]) ).
tff(2892,plain,
s(select(q35,tail)) = s(index_177),
inference(monotonicity,[status(thm)],[2844]) ).
tff(2893,plain,
s(select(q35,tail)) = index_183,
inference(transitivity,[status(thm)],[2892,297,294,242]) ).
tff(2894,plain,
s(s(select(q35,tail))) = s(index_183),
inference(monotonicity,[status(thm)],[2893]) ).
tff(2895,plain,
s(index_183) = s(s(select(q35,tail))),
inference(symmetry,[status(thm)],[2894]) ).
tff(2896,plain,
index_189 = s(s(select(q35,tail))),
inference(transitivity,[status(thm)],[215,234,237,2895]) ).
tff(2897,plain,
s(index_189) = s(s(s(select(q35,tail)))),
inference(monotonicity,[status(thm)],[2896]) ).
tff(2898,plain,
s(s(s(select(q35,tail)))) = s(index_189),
inference(symmetry,[status(thm)],[2897]) ).
tff(2899,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q35,tail)))) = select(q35,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2900,plain,
s(s(s(select(q35,tail)))) = select(q35,tail),
inference(unit_resolution,[status(thm)],[2899,187]) ).
tff(2901,plain,
select(q35,tail) = s(s(s(select(q35,tail)))),
inference(symmetry,[status(thm)],[2900]) ).
tff(2902,plain,
select(q14,tail) = index_192,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,2462,2461,2517,2514,2590,2589,2645,2642,2718,2717,2773,2770,2846,2845,2901,2898,252]) ).
tff(2903,plain,
store(store(q37,seq,earray_190),tail,select(q14,tail)) = store(queue_191,tail,index_192),
inference(monotonicity,[status(thm)],[256,2902]) ).
tff(2904,plain,
select(store(store(q37,seq,earray_190),tail,select(q14,tail)),head) = select(store(queue_191,tail,index_192),head),
inference(monotonicity,[status(thm)],[2903]) ).
tff(2905,plain,
select(store(queue_191,tail,index_192),head) = select(store(store(q37,seq,earray_190),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[2904]) ).
tff(2906,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head) = select(store(queue_191,tail,index_192),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_191,tail,index_192),seq,select(q39,seq)),head) = select(store(queue_191,tail,index_192),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2907,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head) = select(store(queue_191,tail,index_192),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2908,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head) = select(store(queue_191,tail,index_192),head) ) ),
inference(modus_ponens,[status(thm)],[2907,2906]) ).
tff(2909,plain,
select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head) = select(store(queue_191,tail,index_192),head),
inference(unit_resolution,[status(thm)],[2908,89,1339]) ).
tff(2910,plain,
( ( earray_196 = store(earray_194,index_195,e38) )
<=> ( earray_196 = store(earray_194,index_195,e38) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2911,axiom,
earray_196 = store(earray_194,index_195,e38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(2912,plain,
earray_196 = store(earray_194,index_195,e38),
inference(modus_ponens,[status(thm)],[2911,2910]) ).
tff(2913,plain,
store(earray_194,index_195,e38) = earray_196,
inference(symmetry,[status(thm)],[2912]) ).
tff(2914,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_191,tail,index_192),seq,store(earray_194,index_195,e38)),seq) = store(earray_194,index_195,e38) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2915,plain,
select(store(store(queue_191,tail,index_192),seq,store(earray_194,index_195,e38)),seq) = store(earray_194,index_195,e38),
inference(unit_resolution,[status(thm)],[2914,24]) ).
tff(2916,plain,
store(queue_191,tail,index_192) = q38,
inference(transitivity,[status(thm)],[2880,2879]) ).
tff(2917,plain,
store(store(queue_191,tail,index_192),seq,store(earray_194,index_195,e38)) = store(q38,seq,earray_196),
inference(monotonicity,[status(thm)],[2916,2913]) ).
tff(2918,plain,
select(store(store(queue_191,tail,index_192),seq,store(earray_194,index_195,e38)),seq) = select(store(q38,seq,earray_196),seq),
inference(monotonicity,[status(thm)],[2917]) ).
tff(2919,plain,
select(store(q38,seq,earray_196),seq) = select(store(store(queue_191,tail,index_192),seq,store(earray_194,index_195,e38)),seq),
inference(symmetry,[status(thm)],[2918]) ).
tff(2920,plain,
( ( ~ ! [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_196),tail,s(index_195)),seq) = select(store(q38,seq,earray_196),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_196),tail,s(index_195)),seq) = select(store(q38,seq,earray_196),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2921,plain,
( ~ ! [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_196),tail,s(index_195)),seq) = select(store(q38,seq,earray_196),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2922,plain,
( ~ ! [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_196),tail,s(index_195)),seq) = select(store(q38,seq,earray_196),seq) ) ),
inference(modus_ponens,[status(thm)],[2921,2920]) ).
tff(2923,plain,
select(store(store(q38,seq,earray_196),tail,s(index_195)),seq) = select(store(q38,seq,earray_196),seq),
inference(unit_resolution,[status(thm)],[2922,89,83]) ).
tff(2924,plain,
queue_199 = q39,
inference(symmetry,[status(thm)],[206]) ).
tff(2925,plain,
store(queue_197,tail,index_198) = queue_199,
inference(symmetry,[status(thm)],[203]) ).
tff(2926,plain,
store(store(q38,seq,earray_196),tail,s(index_195)) = q39,
inference(transitivity,[status(thm)],[199,2925,2924]) ).
tff(2927,plain,
select(store(store(q38,seq,earray_196),tail,s(index_195)),seq) = select(q39,seq),
inference(monotonicity,[status(thm)],[2926]) ).
tff(2928,plain,
select(q39,seq) = select(store(store(q38,seq,earray_196),tail,s(index_195)),seq),
inference(symmetry,[status(thm)],[2927]) ).
tff(2929,plain,
select(q39,seq) = earray_196,
inference(transitivity,[status(thm)],[2928,2923,2919,2915,2913]) ).
tff(2930,plain,
store(store(queue_191,tail,index_192),seq,select(q39,seq)) = store(q38,seq,earray_196),
inference(monotonicity,[status(thm)],[2916,2929]) ).
tff(2931,plain,
select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head) = select(store(q38,seq,earray_196),head),
inference(monotonicity,[status(thm)],[2930]) ).
tff(2932,plain,
select(store(q38,seq,earray_196),head) = select(store(store(queue_191,tail,index_192),seq,select(q39,seq)),head),
inference(symmetry,[status(thm)],[2931]) ).
tff(2933,plain,
( ( ~ ! [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_196),tail,select(q12,tail)),head) = select(store(q38,seq,earray_196),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_196),tail,select(q12,tail)),head) = select(store(q38,seq,earray_196),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2934,plain,
( ~ ! [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_196),tail,select(q12,tail)),head) = select(store(q38,seq,earray_196),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2935,plain,
( ~ ! [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_196),tail,select(q12,tail)),head) = select(store(q38,seq,earray_196),head) ) ),
inference(modus_ponens,[status(thm)],[2934,2933]) ).
tff(2936,plain,
select(store(store(q38,seq,earray_196),tail,select(q12,tail)),head) = select(store(q38,seq,earray_196),head),
inference(unit_resolution,[status(thm)],[2935,89,1369]) ).
tff(2937,plain,
select(q12,tail) = index_198,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,467,464,445,442,382,379,360,357,297,294,275,272,194]) ).
tff(2938,plain,
store(store(q38,seq,earray_196),tail,select(q12,tail)) = store(queue_197,tail,index_198),
inference(monotonicity,[status(thm)],[198,2937]) ).
tff(2939,plain,
select(store(store(q38,seq,earray_196),tail,select(q12,tail)),head) = select(store(queue_197,tail,index_198),head),
inference(monotonicity,[status(thm)],[2938]) ).
tff(2940,plain,
select(store(queue_197,tail,index_198),head) = select(store(store(q38,seq,earray_196),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[2939]) ).
tff(2941,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head) = select(store(queue_197,tail,index_198),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_197,tail,index_198),seq,select(q40,seq)),head) = select(store(queue_197,tail,index_198),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2942,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head) = select(store(queue_197,tail,index_198),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2943,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head) = select(store(queue_197,tail,index_198),head) ) ),
inference(modus_ponens,[status(thm)],[2942,2941]) ).
tff(2944,plain,
select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head) = select(store(queue_197,tail,index_198),head),
inference(unit_resolution,[status(thm)],[2943,89,1339]) ).
tff(2945,plain,
( ( earray_208 = store(earray_206,index_207,e39) )
<=> ( earray_208 = store(earray_206,index_207,e39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2946,axiom,
earray_208 = store(earray_206,index_207,e39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(2947,plain,
earray_208 = store(earray_206,index_207,e39),
inference(modus_ponens,[status(thm)],[2946,2945]) ).
tff(2948,plain,
store(earray_206,index_207,e39) = earray_208,
inference(symmetry,[status(thm)],[2947]) ).
tff(2949,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_197,tail,index_198),seq,store(earray_206,index_207,e39)),seq) = store(earray_206,index_207,e39) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2950,plain,
select(store(store(queue_197,tail,index_198),seq,store(earray_206,index_207,e39)),seq) = store(earray_206,index_207,e39),
inference(unit_resolution,[status(thm)],[2949,24]) ).
tff(2951,plain,
store(queue_197,tail,index_198) = q39,
inference(transitivity,[status(thm)],[2925,2924]) ).
tff(2952,plain,
store(store(queue_197,tail,index_198),seq,store(earray_206,index_207,e39)) = store(q39,seq,earray_208),
inference(monotonicity,[status(thm)],[2951,2948]) ).
tff(2953,plain,
select(store(store(queue_197,tail,index_198),seq,store(earray_206,index_207,e39)),seq) = select(store(q39,seq,earray_208),seq),
inference(monotonicity,[status(thm)],[2952]) ).
tff(2954,plain,
select(store(q39,seq,earray_208),seq) = select(store(store(queue_197,tail,index_198),seq,store(earray_206,index_207,e39)),seq),
inference(symmetry,[status(thm)],[2953]) ).
tff(2955,plain,
( ( ~ ! [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_208),tail,s(index_207)),seq) = select(store(q39,seq,earray_208),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_208),tail,s(index_207)),seq) = select(store(q39,seq,earray_208),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2956,plain,
( ~ ! [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_208),tail,s(index_207)),seq) = select(store(q39,seq,earray_208),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2957,plain,
( ~ ! [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_208),tail,s(index_207)),seq) = select(store(q39,seq,earray_208),seq) ) ),
inference(modus_ponens,[status(thm)],[2956,2955]) ).
tff(2958,plain,
select(store(store(q39,seq,earray_208),tail,s(index_207)),seq) = select(store(q39,seq,earray_208),seq),
inference(unit_resolution,[status(thm)],[2957,89,83]) ).
tff(2959,plain,
queue_211 = q40,
inference(symmetry,[status(thm)],[140]) ).
tff(2960,plain,
store(queue_209,tail,index_210) = queue_211,
inference(symmetry,[status(thm)],[137]) ).
tff(2961,plain,
store(store(q39,seq,earray_208),tail,s(index_207)) = q40,
inference(transitivity,[status(thm)],[133,2960,2959]) ).
tff(2962,plain,
select(store(store(q39,seq,earray_208),tail,s(index_207)),seq) = select(q40,seq),
inference(monotonicity,[status(thm)],[2961]) ).
tff(2963,plain,
select(q40,seq) = select(store(store(q39,seq,earray_208),tail,s(index_207)),seq),
inference(symmetry,[status(thm)],[2962]) ).
tff(2964,plain,
select(q40,seq) = earray_208,
inference(transitivity,[status(thm)],[2963,2958,2954,2950,2948]) ).
tff(2965,plain,
store(store(queue_197,tail,index_198),seq,select(q40,seq)) = store(q39,seq,earray_208),
inference(monotonicity,[status(thm)],[2951,2964]) ).
tff(2966,plain,
select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head) = select(store(q39,seq,earray_208),head),
inference(monotonicity,[status(thm)],[2965]) ).
tff(2967,plain,
select(store(q39,seq,earray_208),head) = select(store(store(queue_197,tail,index_198),seq,select(q40,seq)),head),
inference(symmetry,[status(thm)],[2966]) ).
tff(2968,plain,
( ( ~ ! [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_208),tail,select(q13,tail)),head) = select(store(q39,seq,earray_208),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_208),tail,select(q13,tail)),head) = select(store(q39,seq,earray_208),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2969,plain,
( ~ ! [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_208),tail,select(q13,tail)),head) = select(store(q39,seq,earray_208),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2970,plain,
( ~ ! [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_208),tail,select(q13,tail)),head) = select(store(q39,seq,earray_208),head) ) ),
inference(modus_ponens,[status(thm)],[2969,2968]) ).
tff(2971,plain,
select(store(store(q39,seq,earray_208),tail,select(q13,tail)),head) = select(store(q39,seq,earray_208),head),
inference(unit_resolution,[status(thm)],[2970,89,1369]) ).
tff(2972,plain,
select(q38,tail) = index_195,
inference(symmetry,[status(thm)],[269]) ).
tff(2973,plain,
select(store(store(q37,seq,earray_190),tail,s(index_189)),tail) = select(q38,tail),
inference(symmetry,[status(thm)],[266]) ).
tff(2974,plain,
s(index_189) = select(store(store(q37,seq,earray_190),tail,s(index_189)),tail),
inference(symmetry,[status(thm)],[248]) ).
tff(2975,plain,
s(select(q37,tail)) = s(index_189),
inference(monotonicity,[status(thm)],[216]) ).
tff(2976,plain,
s(select(q37,tail)) = index_195,
inference(transitivity,[status(thm)],[2975,2974,2973,2972]) ).
tff(2977,plain,
s(s(select(q37,tail))) = s(index_195),
inference(monotonicity,[status(thm)],[2976]) ).
tff(2978,plain,
s(index_195) = s(s(select(q37,tail))),
inference(symmetry,[status(thm)],[2977]) ).
tff(2979,plain,
index_207 = s(s(select(q37,tail))),
inference(transitivity,[status(thm)],[149,208,211,2978]) ).
tff(2980,plain,
s(index_207) = s(s(s(select(q37,tail)))),
inference(monotonicity,[status(thm)],[2979]) ).
tff(2981,plain,
s(s(s(select(q37,tail)))) = s(index_207),
inference(symmetry,[status(thm)],[2980]) ).
tff(2982,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q37,tail)))) = select(q37,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2983,plain,
s(s(s(select(q37,tail)))) = select(q37,tail),
inference(unit_resolution,[status(thm)],[2982,187]) ).
tff(2984,plain,
select(q37,tail) = s(s(s(select(q37,tail)))),
inference(symmetry,[status(thm)],[2983]) ).
tff(2985,plain,
select(q13,tail) = index_210,
inference(transitivity,[status(thm)],[1960,1957,833,830,2088,2085,748,745,2216,2213,663,660,2344,2341,578,575,2472,2469,493,490,2600,2597,408,405,2728,2725,323,320,2856,2853,238,235,2984,2981,128]) ).
tff(2986,plain,
store(store(q39,seq,earray_208),tail,select(q13,tail)) = store(queue_209,tail,index_210),
inference(monotonicity,[status(thm)],[132,2985]) ).
tff(2987,plain,
select(store(store(q39,seq,earray_208),tail,select(q13,tail)),head) = select(store(queue_209,tail,index_210),head),
inference(monotonicity,[status(thm)],[2986]) ).
tff(2988,plain,
select(store(queue_209,tail,index_210),head) = select(store(store(q39,seq,earray_208),tail,select(q13,tail)),head),
inference(symmetry,[status(thm)],[2987]) ).
tff(2989,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head) = select(store(queue_209,tail,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_209,tail,index_210),seq,select(q41,seq)),head) = select(store(queue_209,tail,index_210),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2990,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head) = select(store(queue_209,tail,index_210),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2991,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( seq = head )
| ( select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head) = select(store(queue_209,tail,index_210),head) ) ),
inference(modus_ponens,[status(thm)],[2990,2989]) ).
tff(2992,plain,
select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head) = select(store(queue_209,tail,index_210),head),
inference(unit_resolution,[status(thm)],[2991,89,1339]) ).
tff(2993,plain,
( ( earray_214 = store(earray_212,index_213,e40) )
<=> ( earray_214 = store(earray_212,index_213,e40) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2994,axiom,
earray_214 = store(earray_212,index_213,e40),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp43) ).
tff(2995,plain,
earray_214 = store(earray_212,index_213,e40),
inference(modus_ponens,[status(thm)],[2994,2993]) ).
tff(2996,plain,
store(earray_212,index_213,e40) = earray_214,
inference(symmetry,[status(thm)],[2995]) ).
tff(2997,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(queue_209,tail,index_210),seq,store(earray_212,index_213,e40)),seq) = store(earray_212,index_213,e40) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2998,plain,
select(store(store(queue_209,tail,index_210),seq,store(earray_212,index_213,e40)),seq) = store(earray_212,index_213,e40),
inference(unit_resolution,[status(thm)],[2997,24]) ).
tff(2999,plain,
store(queue_209,tail,index_210) = q40,
inference(transitivity,[status(thm)],[2960,2959]) ).
tff(3000,plain,
store(store(queue_209,tail,index_210),seq,store(earray_212,index_213,e40)) = store(q40,seq,earray_214),
inference(monotonicity,[status(thm)],[2999,2996]) ).
tff(3001,plain,
select(store(store(queue_209,tail,index_210),seq,store(earray_212,index_213,e40)),seq) = select(store(q40,seq,earray_214),seq),
inference(monotonicity,[status(thm)],[3000]) ).
tff(3002,plain,
select(store(q40,seq,earray_214),seq) = select(store(store(queue_209,tail,index_210),seq,store(earray_212,index_213,e40)),seq),
inference(symmetry,[status(thm)],[3001]) ).
tff(3003,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_214),tail,s(index_213)),seq) = select(store(q40,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(q40,seq,earray_214),tail,s(index_213)),seq) = select(store(q40,seq,earray_214),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3004,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_214),tail,s(index_213)),seq) = select(store(q40,seq,earray_214),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3005,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q40,seq,earray_214),tail,s(index_213)),seq) = select(store(q40,seq,earray_214),seq) ) ),
inference(modus_ponens,[status(thm)],[3004,3003]) ).
tff(3006,plain,
select(store(store(q40,seq,earray_214),tail,s(index_213)),seq) = select(store(q40,seq,earray_214),seq),
inference(unit_resolution,[status(thm)],[3005,89,83]) ).
tff(3007,plain,
queue_217 = q41,
inference(symmetry,[status(thm)],[172]) ).
tff(3008,plain,
store(queue_215,tail,index_216) = queue_217,
inference(symmetry,[status(thm)],[169]) ).
tff(3009,plain,
store(store(q40,seq,earray_214),tail,s(index_213)) = q41,
inference(transitivity,[status(thm)],[165,3008,3007]) ).
tff(3010,plain,
select(store(store(q40,seq,earray_214),tail,s(index_213)),seq) = select(q41,seq),
inference(monotonicity,[status(thm)],[3009]) ).
tff(3011,plain,
select(q41,seq) = select(store(store(q40,seq,earray_214),tail,s(index_213)),seq),
inference(symmetry,[status(thm)],[3010]) ).
tff(3012,plain,
select(q41,seq) = earray_214,
inference(transitivity,[status(thm)],[3011,3006,3002,2998,2996]) ).
tff(3013,plain,
store(store(queue_209,tail,index_210),seq,select(q41,seq)) = store(q40,seq,earray_214),
inference(monotonicity,[status(thm)],[2999,3012]) ).
tff(3014,plain,
select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head) = select(store(q40,seq,earray_214),head),
inference(monotonicity,[status(thm)],[3013]) ).
tff(3015,plain,
select(store(q40,seq,earray_214),head) = select(store(store(queue_209,tail,index_210),seq,select(q41,seq)),head),
inference(symmetry,[status(thm)],[3014]) ).
tff(3016,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(q40,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(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(q40,seq,earray_214),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3017,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(q40,seq,earray_214),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3018,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(q40,seq,earray_214),head) ) ),
inference(modus_ponens,[status(thm)],[3017,3016]) ).
tff(3019,plain,
select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(q40,seq,earray_214),head),
inference(unit_resolution,[status(thm)],[3018,89,1369]) ).
tff(3020,plain,
s(select(q38,tail)) = s(index_195),
inference(monotonicity,[status(thm)],[2972]) ).
tff(3021,plain,
s(select(q38,tail)) = index_207,
inference(transitivity,[status(thm)],[3020,212,209,150]) ).
tff(3022,plain,
s(s(select(q38,tail))) = s(index_207),
inference(monotonicity,[status(thm)],[3021]) ).
tff(3023,plain,
s(index_207) = s(s(select(q38,tail))),
inference(symmetry,[status(thm)],[3022]) ).
tff(3024,plain,
index_213 = s(s(select(q38,tail))),
inference(transitivity,[status(thm)],[123,142,145,3023]) ).
tff(3025,plain,
s(index_213) = s(s(s(select(q38,tail)))),
inference(monotonicity,[status(thm)],[3024]) ).
tff(3026,plain,
s(s(s(select(q38,tail)))) = s(index_213),
inference(symmetry,[status(thm)],[3025]) ).
tff(3027,plain,
( ~ ! [X: $i] : ( s(s(s(X))) = X )
| ( s(s(s(select(q38,tail)))) = select(q38,tail) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3028,plain,
s(s(s(select(q38,tail)))) = select(q38,tail),
inference(unit_resolution,[status(thm)],[3027,187]) ).
tff(3029,plain,
select(q38,tail) = s(s(s(select(q38,tail)))),
inference(symmetry,[status(thm)],[3028]) ).
tff(3030,plain,
select(q14,tail) = index_216,
inference(transitivity,[status(thm)],[2005,2002,2078,2077,2133,2130,2206,2205,2261,2258,2334,2333,2389,2386,2462,2461,2517,2514,2590,2589,2645,2642,2718,2717,2773,2770,2846,2845,2901,2898,2974,2973,3029,3026,160]) ).
tff(3031,plain,
store(store(q40,seq,earray_214),tail,select(q14,tail)) = store(queue_215,tail,index_216),
inference(monotonicity,[status(thm)],[164,3030]) ).
tff(3032,plain,
select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head) = select(store(queue_215,tail,index_216),head),
inference(monotonicity,[status(thm)],[3031]) ).
tff(3033,plain,
select(store(queue_215,tail,index_216),head) = select(store(store(q40,seq,earray_214),tail,select(q14,tail)),head),
inference(symmetry,[status(thm)],[3032]) ).
tff(3034,plain,
( ( ~ ! [I: $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(q42,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(q42,seq)),head) = select(store(queue_215,tail,index_216),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3035,plain,
( ~ ! [I: $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(q42,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3036,plain,
( ~ ! [I: $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(q42,seq)),head) = select(store(queue_215,tail,index_216),head) ) ),
inference(modus_ponens,[status(thm)],[3035,3034]) ).
tff(3037,plain,
select(store(store(queue_215,tail,index_216),seq,select(q42,seq)),head) = select(store(queue_215,tail,index_216),head),
inference(unit_resolution,[status(thm)],[3036,89,1339]) ).
tff(3038,plain,
( ( earray_220 = store(earray_218,index_219,e41) )
<=> ( earray_220 = store(earray_218,index_219,e41) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3039,axiom,
earray_220 = store(earray_218,index_219,e41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(3040,plain,
earray_220 = store(earray_218,index_219,e41),
inference(modus_ponens,[status(thm)],[3039,3038]) ).
tff(3041,plain,
store(earray_218,index_219,e41) = earray_220,
inference(symmetry,[status(thm)],[3040]) ).
tff(3042,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,e41)),seq) = store(earray_218,index_219,e41) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3043,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e41)),seq) = store(earray_218,index_219,e41),
inference(unit_resolution,[status(thm)],[3042,24]) ).
tff(3044,plain,
store(queue_215,tail,index_216) = q41,
inference(transitivity,[status(thm)],[3008,3007]) ).
tff(3045,plain,
store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e41)) = store(q41,seq,earray_220),
inference(monotonicity,[status(thm)],[3044,3041]) ).
tff(3046,plain,
select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e41)),seq) = select(store(q41,seq,earray_220),seq),
inference(monotonicity,[status(thm)],[3045]) ).
tff(3047,plain,
select(store(q41,seq,earray_220),seq) = select(store(store(queue_215,tail,index_216),seq,store(earray_218,index_219,e41)),seq),
inference(symmetry,[status(thm)],[3046]) ).
tff(3048,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_220),tail,s(index_219)),seq) = select(store(q41,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(q41,seq,earray_220),tail,s(index_219)),seq) = select(store(q41,seq,earray_220),seq) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3049,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_220),tail,s(index_219)),seq) = select(store(q41,seq,earray_220),seq) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3050,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = seq )
| ( select(store(store(q41,seq,earray_220),tail,s(index_219)),seq) = select(store(q41,seq,earray_220),seq) ) ),
inference(modus_ponens,[status(thm)],[3049,3048]) ).
tff(3051,plain,
select(store(store(q41,seq,earray_220),tail,s(index_219)),seq) = select(store(q41,seq,earray_220),seq),
inference(unit_resolution,[status(thm)],[3050,89,83]) ).
tff(3052,plain,
store(store(q41,seq,earray_220),tail,s(index_219)) = q42,
inference(transitivity,[status(thm)],[113,76,72]) ).
tff(3053,plain,
select(store(store(q41,seq,earray_220),tail,s(index_219)),seq) = select(q42,seq),
inference(monotonicity,[status(thm)],[3052]) ).
tff(3054,plain,
select(q42,seq) = select(store(store(q41,seq,earray_220),tail,s(index_219)),seq),
inference(symmetry,[status(thm)],[3053]) ).
tff(3055,plain,
select(q42,seq) = earray_220,
inference(transitivity,[status(thm)],[3054,3051,3047,3043,3041]) ).
tff(3056,plain,
store(store(queue_215,tail,index_216),seq,select(q42,seq)) = store(q41,seq,earray_220),
inference(monotonicity,[status(thm)],[3044,3055]) ).
tff(3057,plain,
select(store(store(queue_215,tail,index_216),seq,select(q42,seq)),head) = select(store(q41,seq,earray_220),head),
inference(monotonicity,[status(thm)],[3056]) ).
tff(3058,plain,
select(store(q41,seq,earray_220),head) = select(store(store(queue_215,tail,index_216),seq,select(q42,seq)),head),
inference(symmetry,[status(thm)],[3057]) ).
tff(3059,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(q41,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(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(q41,seq,earray_220),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3060,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(q41,seq,earray_220),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3061,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(q41,seq,earray_220),head) ) ),
inference(modus_ponens,[status(thm)],[3060,3059]) ).
tff(3062,plain,
select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(q41,seq,earray_220),head),
inference(unit_resolution,[status(thm)],[3061,89,1369]) ).
tff(3063,plain,
select(q12,tail) = index_222,
inference(transitivity,[status(thm)],[957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,467,464,445,442,382,379,360,357,297,294,275,272,212,209,190,180,108]) ).
tff(3064,plain,
store(store(q41,seq,earray_220),tail,select(q12,tail)) = store(queue_221,tail,index_222),
inference(monotonicity,[status(thm)],[112,3063]) ).
tff(3065,plain,
select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head) = select(store(queue_221,tail,index_222),head),
inference(monotonicity,[status(thm)],[3064]) ).
tff(3066,plain,
select(store(queue_221,tail,index_222),head) = select(store(store(q41,seq,earray_220),tail,select(q12,tail)),head),
inference(symmetry,[status(thm)],[3065]) ).
tff(3067,plain,
( ( ~ ! [I: $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(q43,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(q43,seq)),head) = select(store(queue_221,tail,index_222),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3068,plain,
( ~ ! [I: $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(q43,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3069,plain,
( ~ ! [I: $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(q43,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(modus_ponens,[status(thm)],[3068,3067]) ).
tff(3070,plain,
( ( seq = head )
| ( select(store(store(queue_221,tail,index_222),seq,select(q43,seq)),head) = select(store(queue_221,tail,index_222),head) ) ),
inference(unit_resolution,[status(thm)],[3069,89]) ).
tff(3071,plain,
select(store(store(queue_221,tail,index_222),seq,select(q43,seq)),head) = select(store(queue_221,tail,index_222),head),
inference(unit_resolution,[status(thm)],[3070,1339]) ).
tff(3072,plain,
select(q43,seq) = earray_226,
inference(transitivity,[status(thm)],[98,93,80,64,68]) ).
tff(3073,plain,
store(store(queue_221,tail,index_222),seq,select(q43,seq)) = store(q42,seq,earray_226),
inference(monotonicity,[status(thm)],[77,3072]) ).
tff(3074,plain,
select(store(store(queue_221,tail,index_222),seq,select(q43,seq)),head) = select(store(q42,seq,earray_226),head),
inference(monotonicity,[status(thm)],[3073]) ).
tff(3075,plain,
select(store(q42,seq,earray_226),head) = select(store(store(queue_221,tail,index_222),seq,select(q43,seq)),head),
inference(symmetry,[status(thm)],[3074]) ).
tff(3076,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,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(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,seq,earray_226),head) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3077,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,seq,earray_226),head) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(3078,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( tail = head )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,seq,earray_226),head) ) ),
inference(modus_ponens,[status(thm)],[3077,3076]) ).
tff(3079,plain,
( ( tail = head )
| ( select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,seq,earray_226),head) ) ),
inference(unit_resolution,[status(thm)],[3078,89]) ).
tff(3080,plain,
select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(store(q42,seq,earray_226),head),
inference(unit_resolution,[status(thm)],[3079,1369]) ).
tff(3081,plain,
select(store(store(q42,seq,earray_226),tail,s(index_225)),head) = select(q43,head),
inference(monotonicity,[status(thm)],[96]) ).
tff(3082,plain,
select(q43,head) = select(store(store(q42,seq,earray_226),tail,s(index_225)),head),
inference(symmetry,[status(thm)],[3081]) ).
tff(3083,plain,
( ( index_261 = select(q43,head) )
<=> ( index_261 = select(q43,head) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3084,axiom,
index_261 = select(q43,head),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(3085,plain,
index_261 = select(q43,head),
inference(modus_ponens,[status(thm)],[3084,3083]) ).
tff(3086,plain,
index_261 = select(q42,tail),
inference(transitivity,[status(thm)],[3085,3082,3080,3075,3071,3066,3062,3058,3037,3033,3019,3015,2992,2988,2971,2967,2944,2940,2936,2932,2909,2905,2891,2887,2864,2860,2843,2839,2816,2812,2808,2804,2781,2777,2763,2759,2736,2732,2715,2711,2688,2684,2680,2676,2653,2649,2635,2631,2608,2604,2587,2583,2560,2556,2552,2548,2525,2521,2507,2503,2480,2476,2459,2455,2432,2428,2424,2420,2397,2393,2379,2375,2352,2348,2331,2327,2304,2300,2296,2292,2269,2265,2251,2247,2224,2220,2203,2199,2176,2172,2168,2164,2141,2137,2123,2119,2096,2092,2075,2071,2048,2044,2040,2036,2013,2009,1995,1991,1968,1964,1948,1944,1921,1917,1913,1909,1886,1882,1878,1874,1854,1850,1846,1842,1822,1818,1814,1810,1787,1783,1779,1775,1755,1751,1747,1743,1723,1719,1715,1711,1688,1684,1680,1676,1656,1652,1648,1644,1624,1620,1616,1612,1589,1585,1581,1577,1557,1553,1549,1545,1525,1521,1517,1513,1490,1486,1450,1446,1426,1422,1373,1365,1343,1332,1330,1328,1320,1305,1302,1240,1237,1218,1215,1153,1150,1131,1128,1066,1063,1044,1041,979,976,957,954,892,889,870,867,807,804,785,782,722,719,700,697,637,634,615,612,552,549,530,527,467,464,445,442,382,379,360,357,297,294,275,272,212,209,190,180,120,117]) ).
tff(3087,plain,
select(earray_260,index_261) = select(store(select(q42,seq),select(q42,tail),e42),select(q42,tail)),
inference(monotonicity,[status(thm)],[102,3086]) ).
tff(3088,plain,
( ( elem_262 = select(earray_260,index_261) )
<=> ( elem_262 = select(earray_260,index_261) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3089,axiom,
elem_262 = select(earray_260,index_261),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(3090,plain,
elem_262 = select(earray_260,index_261),
inference(modus_ponens,[status(thm)],[3089,3088]) ).
tff(3091,plain,
elem_262 = elem_265,
inference(transitivity,[status(thm)],[3090,3087,104,4]) ).
tff(3092,plain,
( ( elem_262 != elem_265 )
<=> ( elem_262 != elem_265 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3093,axiom,
elem_262 != elem_265,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(3094,plain,
elem_262 != elem_265,
inference(modus_ponens,[status(thm)],[3093,3092]) ).
tff(3095,plain,
$false,
inference(unit_resolution,[status(thm)],[3094,3091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV571-1.043 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Fri Jun 20 10:25:02 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
% 0.54/0.72 % E exiting
%------------------------------------------------------------------------------