%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:35:12 PM UTC 2026
% Result : Unsatisfiable 8.27s 1.75s
% Output : CNFRefutation 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 137 ( 137 unt; 0 def)
% Number of atoms : 237 ( 136 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 355 ( 0 sgn 355 !; 0 ?; 339 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tcf(c_57,plain,
! [X0: $i] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
inference(cnf_transformation,[],[f8]) ).
tcf(c_77,plain,
! [X0: $i] : mult(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_57,c_59]) ).
tcf(c_79,plain,
! [X0: $i] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(superposition,[status(thm)],[c_77,c_59]) ).
tcf(c_80,plain,
! [X0: $i] : mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_58,c_60]) ).
tcf(c_81,plain,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(demodulation,[status(thm)],[c_64,c_60]) ).
tcf(c_82,plain,
mult(rd(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(demodulation,[status(thm)],[c_81,c_60]) ).
tcf(c_85,plain,
! [X0: $i] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(superposition,[status(thm)],[c_77,c_60]) ).
tcf(c_87,plain,
! [X0: $i] : mult(rd(X0,X0),ld(rd(X0,X0),X0)) = ld(rd(X0,X0),X0),
inference(superposition,[status(thm)],[c_80,c_59]) ).
tcf(c_92,plain,
! [X0: $i] : ld(X0,mult(X0,ld(X0,X0))) = rd(X0,X0),
inference(superposition,[status(thm)],[c_80,c_63]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] : mult(rd(rd(X0,X0),X1),X1) = ld(X0,mult(X0,ld(X1,X1))),
inference(superposition,[status(thm)],[c_63,c_60]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,mult(X0,X1)),ld(X1,X1)) = ld(ld(X0,X2),mult(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_77,c_61]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,mult(X0,rd(X1,X1))),X1) = ld(ld(X0,X2),mult(ld(X0,X2),X1)),
inference(superposition,[status(thm)],[c_80,c_61]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : ld(mult(ld(X0,mult(X0,X1)),X2),mult(mult(ld(X0,mult(X0,X1)),X2),mult(X3,X4))) = mult(ld(ld(X0,X5),mult(ld(X0,X5),X3)),X4),
inference(superposition,[status(thm)],[c_61,c_61]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(superposition,[status(thm)],[c_61,c_59]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,rd(mult(ld(X0,X0),X1),X1)) = rd(mult(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[c_77,c_62]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X0),rd(mult(X0,X1),X1)) = rd(mult(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[status(thm)],[c_80,c_62]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rd(mult(mult(X0,X1),mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(superposition,[status(thm)],[c_60,c_62]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(superposition,[status(thm)],[c_62,c_60]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : rd(mult(mult(X0,X1),mult(X2,rd(mult(X3,X4),X4))),mult(X2,rd(mult(X3,X4),X4))) = mult(X0,rd(mult(X1,rd(X5,X4)),rd(X5,X4))),
inference(superposition,[status(thm)],[c_62,c_62]) ).
tcf(c_117,plain,
! [X0: $i] : ld(X0,X0) = rd(X0,X0),
inference(demodulation,[status(thm)],[c_92,c_59,c_79]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),X1),X1) = ld(X0,mult(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[c_94,c_117]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] : mult(rd(ld(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(demodulation,[status(thm)],[c_119,c_59]) ).
tcf(c_122,plain,
! [X0: $i] : mult(ld(X0,X0),ld(ld(X0,X0),X0)) = ld(ld(X0,X0),X0),
inference(demodulation,[status(thm)],[c_87,c_117]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[c_115,c_60]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X0),rd(mult(X0,X1),X1)) = rd(mult(X0,rd(X2,X1)),rd(X2,X1)),
inference(demodulation,[status(thm)],[c_107,c_117]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),mult(rd(X0,X2),X2)),
inference(demodulation,[status(thm)],[c_124,c_60]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(demodulation,[status(thm)],[c_106,c_60]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(demodulation,[status(thm)],[c_104,c_59]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,mult(X0,ld(X1,X1))),X1) = ld(ld(X0,X2),mult(ld(X0,X2),X1)),
inference(demodulation,[status(thm)],[c_101,c_117]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,ld(X1,X1))),X1) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(demodulation,[status(thm)],[c_128,c_59]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] : mult(mult(X0,ld(X0,X1)),ld(X1,X1)) = mult(ld(X0,X2),ld(ld(X0,X2),X1)),
inference(demodulation,[status(thm)],[c_100,c_59]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(mult(X0,X1),mult(rd(X2,X3),X3)),mult(rd(X2,X3),X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(demodulation,[status(thm)],[c_112,c_60]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : mult(rd(mult(X0,X1),mult(X2,mult(rd(X3,X4),X4))),mult(X2,mult(rd(X3,X4),X4))) = mult(X0,mult(rd(X1,rd(X5,X4)),rd(X5,X4))),
inference(demodulation,[status(thm)],[c_116,c_60]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(X0,mult(rd(X1,rd(X2,X3)),rd(X2,X3))) = iPr_def_10(X0,X1,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_136]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : mult(rd(mult(X0,X1),mult(X2,mult(rd(X3,X4),X4))),mult(X2,mult(rd(X3,X4),X4))) = iPr_def_10(X0,X1,X4),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_136]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : mult(mult(mult(X0,ld(X0,X1)),X2),ld(mult(mult(X0,ld(X0,X1)),X2),mult(X3,X4))) = mult(mult(ld(X0,X5),ld(ld(X0,X5),X3)),X4),
inference(demodulation,[status(thm)],[c_103,c_59]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(mult(ld(X0,X1),ld(ld(X0,X1),X2)),X3) = iPr_def_11(X0,X2,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_139]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : mult(mult(mult(X0,ld(X0,X1)),X2),ld(mult(mult(X0,ld(X0,X1)),X2),mult(X3,X4))) = iPr_def_11(X0,X3,X4),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_139]) ).
tcf(c_147,plain,
! [X0: $i] : mult(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_80,c_117]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(ld(rd(X1,X2),rd(X1,X2)),rd(X1,X2))) = iPr_def_10(X0,rd(X1,X2),X2),
inference(superposition,[status(thm)],[c_117,c_137]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(rd(X1,ld(X2,X2)),ld(X2,X2))) = iPr_def_10(X0,X1,X2),
inference(superposition,[status(thm)],[c_117,c_137]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i] : mult(ld(ld(X0,X0),X0),X1) = iPr_def_11(X0,X0,X1),
inference(superposition,[status(thm)],[c_122,c_140]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : mult(rd(mult(X0,X1),mult(X2,rd(mult(X3,X4),X4))),mult(X2,rd(mult(X3,X4),X4))) = mult(X0,mult(rd(X1,rd(X5,X4)),rd(X5,X4))),
inference(superposition,[status(thm)],[c_62,c_123]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(ld(X0,X0),mult(rd(X0,X1),X1)),
inference(superposition,[status(thm)],[c_117,c_125]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : mult(rd(X0,rd(X1,X0)),rd(X1,X0)) = mult(ld(X0,X0),mult(ld(X0,X0),X0)),
inference(superposition,[status(thm)],[c_117,c_125]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(X0,rd(X1,rd(X2,X3))),rd(X1,rd(X2,X3))) = iPr_def_10(ld(X0,X0),X0,X3),
inference(superposition,[status(thm)],[c_125,c_137]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(superposition,[status(thm)],[c_120,c_126]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),mult(rd(X0,X1),X1)) = mult(X0,mult(rd(ld(X0,X0),X1),X1)),
inference(superposition,[status(thm)],[c_126,c_125]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,rd(X3,X2)),rd(X3,X2)),
inference(superposition,[status(thm)],[c_126,c_126]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(rd(X0,rd(X1,rd(X2,X3))),rd(X1,rd(X2,X3))) = iPr_def_10(X0,ld(X0,X0),X3),
inference(superposition,[status(thm)],[c_126,c_137]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : mult(mult(ld(X0,mult(X0,X1)),X2),ld(mult(ld(X0,mult(X0,X1)),X2),mult(X3,X4))) = mult(mult(ld(X0,X5),ld(ld(X0,X5),X3)),X4),
inference(superposition,[status(thm)],[c_61,c_127]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : mult(ld(ld(X0,X0),X1),ld(ld(ld(X0,X0),X1),X0)) = mult(ld(X0,X0),X0),
inference(superposition,[status(thm)],[c_77,c_129]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X3)) = iPr_def_11(X0,ld(X3,X3),X3),
inference(superposition,[status(thm)],[c_129,c_140]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_77,c_130]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] : mult(ld(ld(X0,X0),X1),ld(ld(ld(X0,X0),X1),X0)) = mult(ld(ld(X0,X0),X0),ld(X0,X0)),
inference(superposition,[status(thm)],[c_122,c_130]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(ld(X0,X3),ld(ld(X0,X3),X2)),
inference(superposition,[status(thm)],[c_130,c_130]) ).
tcf(c_493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : mult(ld(ld(X0,X1),X2),ld(ld(ld(X0,X1),X2),X3)) = iPr_def_11(X0,X3,ld(X3,X3)),
inference(superposition,[status(thm)],[c_130,c_140]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i,X2: $i] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = iPr_def_12(X0,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_492]) ).
tcf(c_509,plain,
! [X0: $i] : mult(ld(X0,X0),X0) = iPr_def_12(ld(X0,X0),X0),
inference(demodulation,[status(thm)],[c_439,c_507]) ).
tcf(c_510,plain,
! [X0: $i] : iPr_def_12(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_509,c_147]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = iPr_def_13(X0,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_403]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i] : mult(ld(X0,X0),mult(rd(X0,X1),X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(demodulation,[status(thm)],[c_394,c_120]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X0,ld(X0,ld(X1,X1)))) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_381,c_511]) ).
tcf(c_516,plain,
! [X0: $i] : mult(ld(X0,X0),mult(ld(X0,X0),X0)) = iPr_def_13(X0,X0),
inference(demodulation,[status(thm)],[c_350,c_511]) ).
tcf(c_517,plain,
! [X0: $i] : iPr_def_13(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_516,c_147]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,ld(X1,X1)) = iPr_def_12(ld(X0,X2),X1),
inference(demodulation,[status(thm)],[c_493,c_507]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,ld(X1,X1),X1) = iPr_def_12(ld(X0,X2),X1),
inference(demodulation,[status(thm)],[c_458,c_507]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,ld(X0,X0),X1) = iPr_def_13(X0,rd(X2,X1)),
inference(demodulation,[status(thm)],[c_404,c_511]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(ld(X0,X0),X0,X1) = iPr_def_13(X0,rd(X2,X1)),
inference(demodulation,[status(thm)],[c_367,c_511]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,rd(X1,X2),X2) = mult(X0,rd(X1,X2)),
inference(demodulation,[status(thm)],[c_272,c_147]) ).
tcf(c_532,plain,
! [X0: $i] : iPr_def_11(X0,X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_474,c_293,c_507,c_510]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : mult(mult(ld(X0,mult(X0,X1)),X2),ld(mult(ld(X0,mult(X0,X1)),X2),mult(X3,X4))) = mult(iPr_def_12(X0,X3),X4),
inference(demodulation,[status(thm)],[c_412,c_507]) ).
tcf(c_666,plain,
! [X0: $i,X1: $i,X2: $i] : mult(iPr_def_12(X0,X1),X2) = iPr_def_11(X0,X1,X2),
inference(demodulation,[status(thm)],[c_665,c_59,c_141]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : mult(rd(mult(X0,X1),mult(X2,rd(mult(X3,X4),X4))),mult(X2,rd(mult(X3,X4),X4))) = mult(X0,iPr_def_13(X1,X4)),
inference(demodulation,[status(thm)],[c_325,c_511]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,iPr_def_13(X1,X2)) = iPr_def_10(X0,X1,X2),
inference(demodulation,[status(thm)],[c_713,c_60,c_138]) ).
tcf(c_741,plain,
! [X0: $i] : mult(ld(X0,X0),mult(rd(X0,X0),X0)) = rd(X0,ld(X0,X0)),
inference(demodulation,[status(thm)],[c_85,c_340]) ).
tcf(c_742,plain,
! [X0: $i] : rd(X0,ld(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_741,c_513,c_514,c_517]) ).
tcf(c_743,plain,
! [X0: $i] : ld(ld(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_122,c_470]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(rd(X1,X2),X2)) = iPr_def_13(mult(X0,X1),X2),
inference(demodulation,[status(thm)],[c_123,c_511]) ).
tcf(c_1439,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,rd(mult(X1,ld(X2,X2)),ld(X2,X2))) = rd(mult(mult(X0,X1),X2),X2),
inference(superposition,[status(thm)],[c_742,c_62]) ).
tcf(c_1478,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,X1,X1) = mult(X0,X1),
inference(superposition,[status(thm)],[c_517,c_714]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i] : iPr_def_11(ld(X0,X0),X1,ld(X1,X1)) = iPr_def_12(X0,X1),
inference(superposition,[status(thm)],[c_743,c_519]) ).
tcf(c_1528,plain,
! [X0: $i,X1: $i] : iPr_def_12(ld(X0,X1),X0) = X0,
inference(superposition,[status(thm)],[c_519,c_532]) ).
tcf(c_1576,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,ld(X1,X1),X1) = mult(X0,ld(X1,X1)),
inference(superposition,[status(thm)],[c_117,c_531]) ).
tcf(c_1627,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),X2),X2) = iPr_def_10(X0,X1,X2),
inference(demodulation,[status(thm)],[c_1439,c_60,c_278]) ).
tcf(c_1739,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = iPr_def_12(ld(X0,X0),X1),
inference(superposition,[status(thm)],[c_743,c_507]) ).
tcf(c_1915,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(ld(ld(X0,X0),X1),X2) = iPr_def_12(X0,X2),
inference(superposition,[status(thm)],[c_1525,c_519]) ).
tcf(c_1957,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X0)) = iPr_def_13(X0,rd(X1,X0)),
inference(superposition,[status(thm)],[c_1576,c_523]) ).
tcf(c_1987,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = iPr_def_10(X0,X1,X1),
inference(superposition,[status(thm)],[c_60,c_1627]) ).
tcf(c_1991,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,ld(X0,X0),X1) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_77,c_1627]) ).
tcf(c_1997,plain,
! [X0: $i,X1: $i] : iPr_def_10(ld(X0,X0),X0,X1) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_147,c_1627]) ).
tcf(c_2010,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,rd(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_1957,c_77]) ).
tcf(c_2013,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_1987,c_1478]) ).
tcf(c_2101,plain,
! [X0: $i,X1: $i] : ld(X0,mult(X0,X1)) = iPr_def_12(ld(X0,X0),X1),
inference(demodulation,[status(thm)],[c_59,c_1739]) ).
tcf(c_2114,plain,
iPr_def_10(x6,ld(x6,x6),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(demodulation,[status(thm)],[c_82,c_1991]) ).
tcf(c_3722,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(rd(X1,X0),X0)) = X0,
inference(superposition,[status(thm)],[c_60,c_2010]) ).
tcf(c_3874,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(mult(rd(X1,X0),X0),X0)) = X0,
inference(superposition,[status(thm)],[c_60,c_3722]) ).
tcf(c_3946,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(mult(X0,X1),mult(ld(X2,X2),X2)),mult(ld(X2,X2),X2)) = mult(X0,mult(rd(X1,X2),X2)),
inference(superposition,[status(thm)],[c_117,c_131]) ).
tcf(c_4139,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_3874,c_2013]) ).
tcf(c_4192,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(mult(X0,X1),X2) = iPr_def_10(X0,X1,X2),
inference(demodulation,[status(thm)],[c_3946,c_147,c_751,c_1627]) ).
tcf(c_4311,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_11(X1,X2,X0)) = X0,
inference(superposition,[status(thm)],[c_666,c_4139]) ).
tcf(c_4427,plain,
! [X0: $i,X1: $i] : iPr_def_10(ld(X0,X0),X0,X1) = iPr_def_13(X0,X1),
inference(superposition,[status(thm)],[c_147,c_4192]) ).
tcf(c_4487,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(iPr_def_12(ld(ld(X0,X0),ld(X0,X0)),X1),X2) = iPr_def_12(X0,X2),
inference(superposition,[status(thm)],[c_2101,c_1915]) ).
tcf(c_4597,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(iPr_def_12(X0,X1),X2) = iPr_def_12(X0,X2),
inference(demodulation,[status(thm)],[c_4487,c_1915]) ).
tcf(c_4627,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,rd(X1,X2)) = iPr_def_13(X0,X2),
inference(demodulation,[status(thm)],[c_525,c_4427]) ).
tcf(c_4633,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,ld(X0,X0),X1) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_523,c_4627]) ).
tcf(c_4638,plain,
mult(rd(x6,x8),x8) != iPr_def_13(x6,ld(x7,x8)),
inference(demodulation,[status(thm)],[c_2114,c_4633]) ).
tcf(c_5044,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_12(ld(X1,X2),X0)) = X0,
inference(superposition,[status(thm)],[c_521,c_4311]) ).
tcf(c_5186,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(ld(X0,X1),X2) = iPr_def_12(X0,X2),
inference(superposition,[status(thm)],[c_1528,c_4597]) ).
tcf(c_5207,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,iPr_def_12(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_5044,c_5186]) ).
tcf(c_5246,plain,
! [X0: $i,X1: $i] : mult(X0,ld(X0,X1)) = iPr_def_12(X0,X1),
inference(demodulation,[status(thm)],[c_1739,c_5186]) ).
tcf(c_5323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_13(X0,mult(X1,rd(mult(X2,X3),X3))) = iPr_def_13(X0,rd(X4,X3)),
inference(superposition,[status(thm)],[c_62,c_4627]) ).
tcf(c_5369,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,X1,iPr_def_12(X2,X1)) = mult(X0,X1),
inference(superposition,[status(thm)],[c_5207,c_714]) ).
tcf(c_5398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(X0,iPr_def_10(X1,X2,X3)) = iPr_def_13(X0,X3),
inference(demodulation,[status(thm)],[c_5323,c_60,c_751,c_4192,c_4627]) ).
tcf(c_6500,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,mult(X1,X2)) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_1478,c_5398]) ).
tcf(c_6503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(X0,mult(X1,X2)) = iPr_def_13(X0,iPr_def_12(X3,X2)),
inference(superposition,[status(thm)],[c_5369,c_5398]) ).
tcf(c_6547,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_12(X1,X2)) = iPr_def_13(X0,X2),
inference(demodulation,[status(thm)],[c_6503,c_6500]) ).
tcf(c_7028,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,ld(X1,X2)) = iPr_def_13(X0,iPr_def_12(X1,X2)),
inference(superposition,[status(thm)],[c_5246,c_6500]) ).
tcf(c_7232,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,ld(X1,X2)) = iPr_def_13(X0,X2),
inference(demodulation,[status(thm)],[c_7028,c_6547]) ).
tcf(c_7322,plain,
mult(rd(x6,x8),x8) != iPr_def_13(x6,x8),
inference(demodulation,[status(thm)],[c_4638,c_7232]) ).
tcf(c_9748,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = iPr_def_13(X0,X1),
inference(superposition,[status(thm)],[c_1997,c_4427]) ).
tcf(c_10053,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_7322,c_9748]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP685-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 15:42:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running UEQ theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 8.27/1.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.27/1.75 % SZS status Started for theBenchmark.p
% 8.27/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 8.27/1.75
% 8.27/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.27/1.75
% 8.27/1.75 % ------ iProver source info
% 8.27/1.75
% 8.27/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 8.27/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.27/1.75 % git: non_committed_changes: false
% 8.27/1.75
% 8.27/1.75 % ------ Parsing...% successful
% 8.27/1.75
% 8.27/1.75
% 8.27/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.27/1.75 % ------ Proving...
% 8.27/1.75 % ------ Problem Properties
% 8.27/1.75
% 8.27/1.75 %
% 8.27/1.75 % clauses 8
% 8.27/1.75 % conjectures 1
% 8.27/1.75 % EPR 0
% 8.27/1.75 % Horn 8
% 8.27/1.75 % unary 8
% 8.27/1.75 % binary 0
% 8.27/1.75 % lits 8
% 8.27/1.75 % lits eq 8
% 8.27/1.75 % fd_pure 0
% 8.27/1.75 % fd_pseudo 0
% 8.27/1.75 % fd_cond 0
% 8.27/1.75 % fd_pseudo_cond 0
% 8.27/1.75 % AC symbols 0
% 8.27/1.75
% 8.27/1.75 % ------ Input Options Time Limit: Unbounded
% 8.27/1.75
% 8.27/1.75
% 8.27/1.75 % ------
% 8.27/1.75 % Current options:
% 8.27/1.75 % ------
% 8.27/1.75
% 8.27/1.75
% 8.27/1.75 %
% 8.27/1.75
% 8.27/1.75 % ------ Proving...
% 8.27/1.75 %
% 8.27/1.75
% 8.27/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 8.27/1.75
% 8.27/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.27/1.75
% 8.27/1.75
%------------------------------------------------------------------------------