%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 4.00s 1.17s
% Output : CNFRefutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 119 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 151 !; 0 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
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',c06) ).
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',c07) ).
fof(f8,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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_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(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
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_80,plain,
! [X0: $i] : mult(rd(X0,X0),X0) = X0,
inference(demodulation,[status(thm)],[c_58,c_60]) ).
tcf(c_81,plain,
rd(mult(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference(demodulation,[status(thm)],[c_64,c_60]) ).
tcf(c_82,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
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_86,plain,
! [X0: $i] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_80,c_60]) ).
tcf(c_91,plain,
! [X0: $i] : rd(mult(rd(X0,X0),X0),X0) = ld(X0,X0),
inference(superposition,[status(thm)],[c_77,c_63]) ).
tcf(c_107,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_108,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_115,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_116,plain,
! [X0: $i] : mult(rd(rd(X0,X0),X0),X0) = ld(X0,X0),
inference(demodulation,[status(thm)],[c_91,c_60]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(rd(X0,X0),mult(rd(X0,X2),X2)),
inference(demodulation,[status(thm)],[c_108,c_60]) ).
tcf(c_120,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_107,c_60]) ).
tcf(c_129,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_115,c_60]) ).
tcf(c_130,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_129]) ).
tcf(c_229,plain,
! [X0: $i] : ld(X0,X0) = rd(X0,X0),
inference(superposition,[status(thm)],[c_116,c_86]) ).
tcf(c_274,plain,
! [X0: $i] : mult(rd(X0,rd(X0,X0)),rd(X0,X0)) = rd(X0,rd(X0,X0)),
inference(demodulation,[status(thm)],[c_85,c_229]) ).
tcf(c_276,plain,
! [X0: $i] : mult(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_77,c_229]) ).
tcf(c_280,plain,
! [X0: $i] : rd(X0,rd(X0,X0)) = X0,
inference(demodulation,[status(thm)],[c_274,c_80,c_119]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,rd(mult(X1,rd(X2,X2)),rd(X2,X2))) = rd(mult(mult(X0,X1),X2),X2),
inference(superposition,[status(thm)],[c_280,c_62]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] : mult(X0,mult(X1,rd(X1,X1))) = iPr_def_10(X0,X1,X1),
inference(superposition,[status(thm)],[c_280,c_130]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i,X2: $i] : mult(X0,mult(rd(X1,X2),X2)) = iPr_def_10(X0,X1,rd(X2,X2)),
inference(superposition,[status(thm)],[c_280,c_130]) ).
tcf(c_518,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(rd(X0,X0),X0,X3),
inference(superposition,[status(thm)],[c_119,c_130]) ).
tcf(c_557,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_120,c_120]) ).
tcf(c_558,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_120,c_130]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,X1,X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_414,c_276]) ).
tcf(c_639,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_557]) ).
tcf(c_653,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_381,c_60,c_130]) ).
tcf(c_660,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_558,c_639]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,rd(X0,X0),X1) = iPr_def_13(X0,rd(X2,X1)),
inference(demodulation,[status(thm)],[c_660,c_229]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(rd(X0,X0),X0,X1) = iPr_def_13(X0,rd(X2,X1)),
inference(demodulation,[status(thm)],[c_518,c_639]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = iPr_def_10(rd(X0,X0),X0,rd(X2,X2)),
inference(demodulation,[status(thm)],[c_119,c_420]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] : iPr_def_10(rd(X0,X0),X0,rd(X1,X1)) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_902,c_639]) ).
tcf(c_1721,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_653]) ).
tcf(c_1724,plain,
! [X0: $i,X1: $i] : iPr_def_10(rd(X0,X0),X0,X1) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_80,c_653]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,rd(X0,X0),X1) = mult(rd(X0,X1),X1),
inference(superposition,[status(thm)],[c_276,c_653]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X0),X0) = iPr_def_13(X0,rd(X1,X0)),
inference(superposition,[status(thm)],[c_664,c_625]) ).
tcf(c_1784,plain,
! [X0: $i,X1: $i] : iPr_def_10(rd(X0,X0),X0,X1) = iPr_def_10(X0,rd(X0,X0),X1),
inference(superposition,[status(thm)],[c_664,c_661]) ).
tcf(c_1812,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,rd(X1,rd(X2,X2))) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_903,c_664]) ).
tcf(c_1817,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,rd(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_1780,c_80]) ).
tcf(c_1821,plain,
! [X0: $i,X1: $i] : mult(mult(rd(X0,X1),X1),X1) = mult(X0,X1),
inference(demodulation,[status(thm)],[c_1721,c_625]) ).
tcf(c_1851,plain,
iPr_def_10(rd(a,a),a,mult(b,c)) != mult(rd(a,c),c),
inference(demodulation,[status(thm)],[c_82,c_1724]) ).
tcf(c_1852,plain,
iPr_def_10(a,rd(a,a),mult(b,c)) != mult(rd(a,c),c),
inference(demodulation,[status(thm)],[c_1851,c_1784]) ).
tcf(c_3111,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(rd(X1,X0),X0)) = X0,
inference(superposition,[status(thm)],[c_60,c_1817]) ).
tcf(c_3230,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,mult(rd(X1,rd(X2,X2)),rd(X2,X2))) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_60,c_1812]) ).
tcf(c_3289,plain,
! [X0: $i,X1: $i,X2: $i] : mult(rd(X0,X1),X1) = iPr_def_13(X0,rd(X2,X1)),
inference(superposition,[status(thm)],[c_1730,c_661]) ).
tcf(c_3397,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_13(X1,X2)) = iPr_def_13(X0,X2),
inference(demodulation,[status(thm)],[c_3230,c_639]) ).
tcf(c_3783,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(mult(rd(X1,X0),X0),X0)) = X0,
inference(superposition,[status(thm)],[c_60,c_3111]) ).
tcf(c_3813,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,rd(X1,X2)) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_1817,c_3397]) ).
tcf(c_3816,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,mult(rd(X1,X2),X2)) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_3111,c_3397]) ).
tcf(c_3872,plain,
! [X0: $i] : iPr_def_13(a,rd(X0,mult(b,c))) != mult(rd(a,c),c),
inference(superposition,[status(thm)],[c_661,c_1852]) ).
tcf(c_4008,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,mult(rd(X1,X2),X2)) = mult(rd(X0,X2),X2),
inference(superposition,[status(thm)],[c_60,c_3289]) ).
tcf(c_4045,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,mult(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_3783,c_1821]) ).
tcf(c_4053,plain,
! [X0: $i,X1: $i] : mult(rd(X0,X1),X1) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_4008,c_3816]) ).
tcf(c_4077,plain,
iPr_def_13(a,mult(b,c)) != iPr_def_13(a,c),
inference(demodulation,[status(thm)],[c_3872,c_3813,c_4053]) ).
tcf(c_4784,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,mult(X1,X2)) = iPr_def_13(X0,X2),
inference(superposition,[status(thm)],[c_4045,c_3397]) ).
tcf(c_5106,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_4077,c_4784]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.34 % Computer : n017.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 15:37:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.37 Running UEQ theorem proving
% 0.13/0.37 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
% 0.13/0.38
% 0.13/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.38
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 4.00/1.17 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.00/1.17 % SZS status Started for theBenchmark.p
% 4.00/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.00/1.17
% 4.00/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.00/1.17
% 4.00/1.17 % ------ iProver source info
% 4.00/1.17
% 4.00/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 4.00/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.00/1.17 % git: non_committed_changes: false
% 4.00/1.17
% 4.00/1.17 % ------ Parsing...% successful
% 4.00/1.17
% 4.00/1.17
% 4.00/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.00/1.17 % ------ Proving...
% 4.00/1.17 % ------ Problem Properties
% 4.00/1.17
% 4.00/1.17 %
% 4.00/1.17 % clauses 8
% 4.00/1.17 % conjectures 1
% 4.00/1.17 % EPR 0
% 4.00/1.17 % Horn 8
% 4.00/1.17 % unary 8
% 4.00/1.17 % binary 0
% 4.00/1.17 % lits 8
% 4.00/1.17 % lits eq 8
% 4.00/1.17 % fd_pure 0
% 4.00/1.17 % fd_pseudo 0
% 4.00/1.17 % fd_cond 0
% 4.00/1.17 % fd_pseudo_cond 0
% 4.00/1.17 % AC symbols 0
% 4.00/1.17
% 4.00/1.17 % ------ Input Options Time Limit: Unbounded
% 4.00/1.17
% 4.00/1.17
% 4.00/1.17 % ------
% 4.00/1.17 % Current options:
% 4.00/1.17 % ------
% 4.00/1.17
% 4.00/1.17
% 4.00/1.17 %
% 4.00/1.17
% 4.00/1.17 % ------ Proving...
% 4.00/1.17 %
% 4.00/1.17
% 4.00/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 4.00/1.17
% 4.00/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.00/1.17
% 4.00/1.17
%------------------------------------------------------------------------------