%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP012-1 : 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 : n014.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 01:29:53 PM UTC 2026
% Result : Unsatisfiable 3.45s 1.29s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 46 unt; 1 def)
% Number of atoms : 121 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 41 ( 0 sgn 41 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
fof(f3,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
fof(f4,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
fof(f9,axiom,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
fof(f10,axiom,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
fof(f11,negated_conjecture,
~ product(c,d,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_multiply_d_is_identity) ).
tcf(c_60,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
product(a,b,c),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
product(inverse(b),inverse(a),d),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
~ product(c,d,identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_76,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_77,plain,
multiply(inverse(b),inverse(a)) = d,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_78,plain,
multiply(c,d) != identity,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_80,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_81,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_82,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_63]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_88]) ).
tcf(c_161,definition,
iPr_def_10 = multiply(c,d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_162,plain,
iPr_def_10 != identity,
inference(demodulation,[status(thm)],[c_78,c_161]) ).
tcf(c_213,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(superposition,[status(thm)],[c_76,c_134]) ).
tcf(c_214,plain,
! [X0: $i] : multiply(inverse(b),multiply(inverse(a),X0)) = multiply(d,X0),
inference(superposition,[status(thm)],[c_77,c_134]) ).
tcf(c_215,plain,
! [X0: $i] : multiply(c,multiply(d,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_161,c_134]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_81,c_134]) ).
tcf(c_226,plain,
multiply(iPr_def_10,inverse(d)) = multiply(c,identity),
inference(superposition,[status(thm)],[c_82,c_215]) ).
tcf(c_229,plain,
multiply(iPr_def_10,inverse(d)) = c,
inference(demodulation,[status(thm)],[c_226,c_80]) ).
tcf(c_233,plain,
multiply(c,inverse(b)) = multiply(a,identity),
inference(superposition,[status(thm)],[c_82,c_213]) ).
tcf(c_236,plain,
multiply(c,inverse(b)) = a,
inference(demodulation,[status(thm)],[c_233,c_80]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_218,c_79]) ).
tcf(c_253,plain,
multiply(inverse(iPr_def_10),c) = inverse(d),
inference(superposition,[status(thm)],[c_229,c_240]) ).
tcf(c_275,plain,
multiply(inverse(b),identity) = multiply(d,a),
inference(superposition,[status(thm)],[c_81,c_214]) ).
tcf(c_282,plain,
multiply(d,a) = inverse(b),
inference(demodulation,[status(thm)],[c_275,c_80]) ).
tcf(c_285,plain,
multiply(c,inverse(b)) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_282,c_215]) ).
tcf(c_286,plain,
multiply(iPr_def_10,a) = a,
inference(light_normalisation,[status(thm)],[c_285,c_236]) ).
tcf(c_288,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(a,X0)) = multiply(a,X0),
inference(superposition,[status(thm)],[c_286,c_134]) ).
tcf(c_290,plain,
multiply(iPr_def_10,c) = c,
inference(superposition,[status(thm)],[c_76,c_288]) ).
tcf(c_296,plain,
multiply(inverse(iPr_def_10),c) = c,
inference(superposition,[status(thm)],[c_290,c_240]) ).
tcf(c_298,plain,
inverse(d) = c,
inference(demodulation,[status(thm)],[c_253,c_296]) ).
tcf(c_302,plain,
multiply(c,d) = identity,
inference(superposition,[status(thm)],[c_298,c_81]) ).
tcf(c_303,plain,
identity = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_302,c_161]) ).
tcf(c_310,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_162,c_303]) ).
tcf(c_311,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:13:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 0.14/0.39
% 0.14/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.39
% 0.14/0.39 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 3.45/1.29 % SZS status Started for theBenchmark.p
% 3.45/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.45/1.29
% 3.45/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.45/1.29
% 3.45/1.29 % ------ iProver source info
% 3.45/1.29
% 3.45/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.45/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.45/1.29 % git: non_committed_changes: false
% 3.45/1.29
% 3.45/1.29 % ------ Parsing...% successful
% 3.45/1.29
% 3.45/1.29
% 3.45/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.45/1.29
% 3.45/1.29 % ------ Preprocessing... sup_sim: 4 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 %
% 3.45/1.29
% 3.45/1.29 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.45/1.29 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.45/1.29
% 3.45/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.45/1.29 % ------ Proving...
% 3.45/1.29 % ------ Problem Properties
% 3.45/1.29
% 3.45/1.29 %
% 3.45/1.29 % clauses 9
% 3.45/1.29 % conjectures 0
% 3.45/1.29 % EPR 1
% 3.45/1.29 % Horn 9
% 3.45/1.29 % unary 9
% 3.45/1.29 % binary 0
% 3.45/1.29 % lits 9
% 3.45/1.29 % lits eq 9
% 3.45/1.29 % fd_pure 0
% 3.45/1.29 % fd_pseudo 0
% 3.45/1.29 % fd_cond 0
% 3.45/1.29 % fd_pseudo_cond 0
% 3.45/1.29 % AC symbols 0
% 3.45/1.29
% 3.45/1.29 % ------ Schedule UEQ
% 3.45/1.29
% 3.45/1.29 % ------ Option_UEQ Time Limit: 10.
% 3.45/1.29
% 3.45/1.29
% 3.45/1.29 % ------
% 3.45/1.29 % Current options:
% 3.45/1.29 % ------
% 3.45/1.29
% 3.45/1.29
% 3.45/1.29 %
% 3.45/1.29
% 3.45/1.29 % ------ Proving...
% 3.45/1.29 %
% 3.45/1.29
% 3.45/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 3.45/1.29
% 3.45/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.45/1.29
% 3.45/1.29
%------------------------------------------------------------------------------