%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 4.01s 1.34s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 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 : 79 ( 0 sgn 79 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : commutator(X0,X1) = multiply(X0,multiply(X1,multiply(inverse(X0),inverse(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
commutator(commutator(a,b),b) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutator) ).
fof(f9,plain,
identity != commutator(commutator(a,b),b),
inference(reorient_equations,[],[f8]) ).
fof(f10,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,[],[f9,f5,f5]) ).
tcf(c_55,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_58,plain,
! [X0: $i] : multiply(X0,multiply(X0,X0)) = identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_59,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,[],[f10]) ).
tcf(c_74,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_59,c_57]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(multiply(X0,X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_58,c_57]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_56,c_57]) ).
tcf(c_123,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_57,c_57]) ).
tcf(c_124,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_74,c_119]) ).
tcf(c_130,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_124,c_55]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_119,c_55]) ).
tcf(c_132,plain,
! [X0: $i] : multiply(inverse(X0),identity) = multiply(X0,X0),
inference(superposition,[status(thm)],[c_58,c_131]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_57,c_131]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,multiply(X0,X1))) = X1,
inference(demodulation,[status(thm)],[c_117,c_55,c_57]) ).
tcf(c_159,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_58,c_156]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X0,X1)) = multiply(inverse(X0),X1),
inference(superposition,[status(thm)],[c_156,c_131]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_156,c_167]) ).
tcf(c_212,plain,
! [X0: $i] : multiply(X0,X0) = inverse(X0),
inference(demodulation,[status(thm)],[c_132,c_159]) ).
tcf(c_217,plain,
! [X0: $i] : multiply(inverse(X0),inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_212,c_131]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,multiply(X0,X1))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_212,c_57]) ).
tcf(c_223,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_217,c_212]) ).
tcf(c_225,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_223,c_56]) ).
tcf(c_272,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_57,c_167]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,identity)) = inverse(X1),
inference(superposition,[status(thm)],[c_225,c_135]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(light_normalisation,[status(thm)],[c_388,c_159]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_131,c_400]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_172,c_400]) ).
tcf(c_490,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_130,c_472]) ).
tcf(c_498,plain,
multiply(a,multiply(b,inverse(multiply(b,multiply(a,multiply(b,multiply(inverse(multiply(b,a)),a))))))) != identity,
inference(demodulation,[status(thm)],[c_490,c_57,c_123,c_472]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_472,c_172]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(X1,multiply(X2,X0)))) = inverse(multiply(X1,X2)),
inference(superposition,[status(thm)],[c_57,c_513]) ).
tcf(c_562,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(X1,X0)),X2)) = multiply(inverse(X1),X2),
inference(superposition,[status(thm)],[c_513,c_57]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X1,multiply(X0,X1))) = multiply(X0,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[c_219,c_167]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,X1)),X2)) = multiply(inverse(multiply(inverse(X0),X2)),X1),
inference(superposition,[status(thm)],[c_562,c_400]) ).
tcf(c_2491,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_272,c_57]) ).
tcf(c_2551,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_2491,c_400]) ).
tcf(c_2594,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(inverse(X0),X1)),X2),X0) = inverse(multiply(X2,multiply(X0,multiply(X2,X1)))),
inference(light_normalisation,[status(thm)],[c_2551,c_1127]) ).
tcf(c_2595,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,multiply(X1,multiply(X0,X2)))) = multiply(multiply(multiply(inverse(X2),X1),X0),X1),
inference(light_normalisation,[status(thm)],[c_2594,c_475]) ).
tcf(c_2613,plain,
multiply(a,multiply(b,multiply(multiply(multiply(inverse(multiply(inverse(multiply(b,a)),a)),a),b),a))) != identity,
inference(demodulation,[status(thm)],[c_498,c_2595]) ).
tcf(c_2614,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2613,c_57,c_225,c_475,c_513,c_549,c_721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.21/0.46 % Computer : n001.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Wed Sep 23 13:16:50 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.51 Running UEQ theorem proving
% 0.24/0.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.53 % Detected problem language: tptp
% 0.24/0.54 % Proving...
% 4.01/1.34 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.01/1.34 % SZS status Started for theBenchmark.p
% 4.01/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 4.01/1.34
% 4.01/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.01/1.34
% 4.01/1.34 % ------ iProver source info
% 4.01/1.34
% 4.01/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 4.01/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.01/1.34 % git: non_committed_changes: false
% 4.01/1.34
% 4.01/1.34 % ------ Parsing...% successful
% 4.01/1.34
% 4.01/1.34
% 4.01/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.01/1.34
% 4.01/1.34 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.01/1.34
% 4.01/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.01/1.34
% 4.01/1.34 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.01/1.34 % ------ Proving...
% 4.01/1.34 % ------ Problem Properties
% 4.01/1.34
% 4.01/1.34 %
% 4.01/1.34 % clauses 5
% 4.01/1.34 % conjectures 0
% 4.01/1.34 % EPR 0
% 4.01/1.34 % Horn 5
% 4.01/1.34 % unary 5
% 4.01/1.34 % binary 0
% 4.01/1.34 % lits 5
% 4.01/1.34 % lits eq 5
% 4.01/1.34 % fd_pure 0
% 4.01/1.34 % fd_pseudo 0
% 4.01/1.34 % fd_cond 0
% 4.01/1.34 % fd_pseudo_cond 0
% 4.01/1.34 % AC symbols 0
% 4.01/1.34
% 4.01/1.34 % ------ Input Options Time Limit: Unbounded
% 4.01/1.34
% 4.01/1.34
% 4.01/1.34 % ------
% 4.01/1.34 % Current options:
% 4.01/1.34 % ------
% 4.01/1.34
% 4.01/1.34
% 4.01/1.34 %
% 4.01/1.34
% 4.01/1.34 % ------ Proving...
% 4.01/1.34 %
% 4.01/1.34
% 4.01/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 4.01/1.34
% 4.01/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/1.34
% 4.01/1.34
%------------------------------------------------------------------------------