%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 01:29:52 PM UTC 2026
% Result : Unsatisfiable 1.77s 1.19s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 85 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
fof(f9,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f10,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutator) ).
fof(f12,plain,
identity != commutator(commutator(a,b),b),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
identity != multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))),
inference(definition_unfolding,[],[f12,f8,f8]) ).
tcf(c_57,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_62,plain,
! [X0: $i] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_63,negated_conjecture,
multiply(multiply(a,multiply(b,multiply(inverse(a),inverse(b)))),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))) != identity,
inference(cnf_transformation,[],[f13]) ).
tcf(c_83,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(b),multiply(b,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))))) != identity,
inference(demodulation,[status(thm)],[c_63,c_59]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_61,c_59]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_58,c_59]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_59,c_61]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,multiply(X1,X2)),X3) = multiply(multiply(X0,X1),multiply(X2,X3)),
inference(superposition,[status(thm)],[c_59,c_59]) ).
tcf(c_149,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(identity,multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b)))))) != identity,
inference(demodulation,[status(thm)],[c_83,c_142]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_139,c_57]) ).
tcf(c_162,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_61,c_158]) ).
tcf(c_163,plain,
! [X0: $i] : multiply(inverse(X0),inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_62,c_158]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[status(thm)],[c_158,c_59]) ).
tcf(c_173,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_162,c_60]) ).
tcf(c_174,plain,
! [X0: $i] : multiply(inverse(X0),inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_163,c_60]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_173,c_158]) ).
tcf(c_190,plain,
! [X0: $i] : multiply(X0,X0) = inverse(X0),
inference(superposition,[status(thm)],[c_174,c_158]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[c_190,c_59]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_190,c_59]) ).
tcf(c_230,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,multiply(inverse(a),inverse(b))))),inverse(b))))) != identity,
inference(demodulation,[status(thm)],[c_149,c_57]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_145,c_180]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),multiply(X0,multiply(X1,X2))) = multiply(inverse(multiply(X0,X1)),X2),
inference(superposition,[status(thm)],[c_59,c_200]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(X1,X0)),X2)) = multiply(inverse(X1),X2),
inference(superposition,[status(thm)],[c_169,c_180]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_248,c_60]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = inverse(multiply(X1,X2)),
inference(superposition,[status(thm)],[c_59,c_428]) ).
tcf(c_443,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_428,c_180]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_428,c_428]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(light_normalisation,[status(thm)],[c_447,c_173]) ).
tcf(c_454,plain,
multiply(a,multiply(b,multiply(inverse(a),multiply(inverse(multiply(a,multiply(b,inverse(multiply(b,a))))),inverse(b))))) != identity,
inference(demodulation,[status(thm)],[c_230,c_443]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_158,c_453]) ).
tcf(c_505,plain,
multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(multiply(b,a)),a))))))) != identity,
inference(demodulation,[status(thm)],[c_454,c_59,c_148,c_443]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X1,multiply(X0,X1))) = multiply(X0,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[c_201,c_200]) ).
tcf(c_919,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(X0),X1)),X2) = inverse(multiply(inverse(multiply(X0,X2)),X1)),
inference(superposition,[status(thm)],[c_342,c_453]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,X1)),X2)) = multiply(multiply(inverse(X2),X0),X1),
inference(light_normalisation,[status(thm)],[c_919,c_470]) ).
tcf(c_2176,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X0,multiply(X1,X2)))) = multiply(inverse(multiply(X0,X1)),X2),
inference(demodulation,[status(thm)],[c_289,c_59]) ).
tcf(c_2236,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),X2)),X0) = inverse(multiply(X1,multiply(X0,multiply(X1,X2)))),
inference(superposition,[status(thm)],[c_2176,c_453]) ).
tcf(c_2279,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(X0),X1),X2),X1) = inverse(multiply(X2,multiply(X1,multiply(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_2236,c_942]) ).
tcf(c_2298,plain,
multiply(a,multiply(b,multiply(multiply(multiply(inverse(multiply(inverse(multiply(b,a)),a)),a),b),a))) != identity,
inference(demodulation,[status(thm)],[c_505,c_2279]) ).
tcf(c_2299,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2298,c_61,c_59,c_428,c_436,c_470,c_677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n019.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 13:11:50 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running UEQ theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 1.77/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.77/1.19 % SZS status Started for theBenchmark.p
% 1.77/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.19
% 1.77/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.77/1.19
% 1.77/1.19 % ------ iProver source info
% 1.77/1.19
% 1.77/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 1.77/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.77/1.19 % git: non_committed_changes: false
% 1.77/1.19
% 1.77/1.19 % ------ Parsing...% successful
% 1.77/1.19
% 1.77/1.19
% 1.77/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.77/1.19
% 1.77/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.77/1.19
% 1.77/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.77/1.19
% 1.77/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.77/1.19 % ------ Proving...
% 1.77/1.19 % ------ Problem Properties
% 1.77/1.19
% 1.77/1.19 %
% 1.77/1.19 % clauses 7
% 1.77/1.19 % conjectures 0
% 1.77/1.19 % EPR 0
% 1.77/1.19 % Horn 7
% 1.77/1.19 % unary 7
% 1.77/1.19 % binary 0
% 1.77/1.20 % lits 7
% 1.77/1.20 % lits eq 7
% 1.77/1.20 % fd_pure 0
% 1.77/1.20 % fd_pseudo 0
% 1.77/1.20 % fd_cond 0
% 1.77/1.20 % fd_pseudo_cond 0
% 1.77/1.20 % AC symbols 0
% 1.77/1.20
% 1.77/1.20 % ------ Input Options Time Limit: Unbounded
% 1.77/1.20
% 1.77/1.20
% 1.77/1.20 % ------
% 1.77/1.20 % Current options:
% 1.77/1.20 % ------
% 1.77/1.20
% 1.77/1.20
% 1.77/1.20 %
% 1.77/1.20
% 1.77/1.20 % ------ Proving...
% 1.77/1.20 %
% 1.77/1.20
% 1.77/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.20
% 1.77/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.77/1.20
% 1.77/1.20
%------------------------------------------------------------------------------