%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP013-1 : 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 : n004.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 01:29:54 PM UTC 2026
% Result : Unsatisfiable 2.78s 11.33s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 29 unt; 1 def)
% Number of atoms : 55 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f9,axiom,
! [X0] : product(X0,X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',squareness) ).
fof(f10,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f11,axiom,
product(inverse(a),inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_a_times_inverse_b_is_d) ).
fof(f12,axiom,
! [X2,X0,X1] :
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverses_have_property) ).
fof(f13,negated_conjecture,
~ product(c,d,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_times_d_is_identity) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i] : product(X0,X0,identity),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
product(a,b,c),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
product(inverse(a),inverse(b),d),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,negated_conjecture,
~ product(c,d,identity),
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,plain,
! [X0: $i] : multiply(X0,X0) = identity,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_81,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_82,plain,
multiply(inverse(a),inverse(b)) = d,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = X1 )
| ( multiply(inverse(X0),inverse(X1)) != X2 ) ),
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_85,plain,
multiply(c,d) != identity,
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_87,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_65]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),inverse(X1))) = X1,
inference(unflattening,[status(thm)],[c_83]) ).
tcf(c_181,definition,
iPr_def_10 = multiply(c,d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_182,plain,
iPr_def_10 != identity,
inference(demodulation,[status(thm)],[c_85,c_181]) ).
tcf(c_239,plain,
! [X0: $i] : multiply(X0,identity) = inverse(X0),
inference(superposition,[status(thm)],[c_89,c_147]) ).
tcf(c_243,plain,
! [X0: $i] : inverse(X0) = X0,
inference(light_normalisation,[status(thm)],[c_239,c_87]) ).
tcf(c_248,plain,
multiply(a,inverse(b)) = d,
inference(demodulation,[status(thm)],[c_82,c_243]) ).
tcf(c_268,plain,
c = d,
inference(demodulation,[status(thm)],[c_248,c_81,c_243]) ).
tcf(c_271,plain,
multiply(c,c) = iPr_def_10,
inference(demodulation,[status(thm)],[c_181,c_268]) ).
tcf(c_273,plain,
identity = iPr_def_10,
inference(demodulation,[status(thm)],[c_271,c_80]) ).
tcf(c_277,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_182,c_273]) ).
tcf(c_278,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.40 % Computer : n004.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Wed Sep 23 13:13:51 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.44 Running first-order theorem proving
% 0.11/10.44 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.46
% 0.11/10.46 % ======== iProver multi-core TPTP/SMT =========
% 0.11/10.46
% 0.11/10.46 % Detected problem language: tptp
% 0.11/10.47 % Proving...
% 2.78/11.33 % SZS status Started for theBenchmark.p
% 2.78/11.33 % SZS status Unsatisfiable for theBenchmark.p
% 2.78/11.33
% 2.78/11.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.78/11.33
% 2.78/11.33 % ------ iProver source info
% 2.78/11.33
% 2.78/11.33 % git: date: 2026-07-19 20:42:38 +0200
% 2.78/11.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.78/11.33 % git: non_committed_changes: false
% 2.78/11.33
% 2.78/11.33 % ------ Parsing...% successful
% 2.78/11.33
% 2.78/11.33
% 2.78/11.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.78/11.33
% 2.78/11.33 % ------ Preprocessing... sup_sim: 5 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.78/11.33
% 2.78/11.33 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.78/11.33 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.78/11.33
% 2.78/11.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.78/11.33 % ------ Proving...
% 2.78/11.33 % ------ Problem Properties
% 2.78/11.33
% 2.78/11.33 %
% 2.78/11.33 % clauses 11
% 2.78/11.33 % conjectures 0
% 2.78/11.33 % EPR 1
% 2.78/11.33 % Horn 11
% 2.78/11.33 % unary 11
% 2.78/11.33 % binary 0
% 2.78/11.33 % lits 11
% 2.78/11.33 % lits eq 11
% 2.78/11.33 % fd_pure 0
% 2.78/11.33 % fd_pseudo 0
% 2.78/11.33 % fd_cond 0
% 2.78/11.33 % fd_pseudo_cond 0
% 2.78/11.33 % AC symbols 0
% 2.78/11.33
% 2.78/11.33 % ------ Schedule UEQ
% 2.78/11.33
% 2.78/11.33 % ------ Option_UEQ Time Limit: 10.
% 2.78/11.33
% 2.78/11.33
% 2.78/11.33 % ------
% 2.78/11.33 % Current options:
% 2.78/11.33 % ------
% 2.78/11.33
% 2.78/11.33
% 2.78/11.33 %
% 2.78/11.33
% 2.78/11.33 % ------ Proving...
% 2.78/11.33 %
% 2.78/11.33
% 2.78/11.33 % SZS status Unsatisfiable for theBenchmark.p
% 2.78/11.33
% 2.78/11.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.78/11.33
% 2.78/11.33
%------------------------------------------------------------------------------