%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP010-1 : 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 : n013.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 2.09s 1.28s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 26 unt; 1 def)
% Number of atoms : 64 ( 19 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 23 :)
% 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(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,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_identity) ).
fof(f10,negated_conjecture,
~ product(b,a,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_multiply_a_is_identity) ).
tcf(c_59,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,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_67,plain,
product(a,b,identity),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,negated_conjecture,
~ product(b,a,identity),
inference(cnf_transformation,[],[f10]) ).
tcf(c_74,plain,
multiply(a,b) = identity,
inference(well_definedness,[status(thm)],[c_67]) ).
tcf(c_75,plain,
multiply(b,a) != identity,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_76,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_59]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_60]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_85,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_66]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_85]) ).
tcf(c_152,definition,
iPr_def_10 = multiply(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_153,plain,
iPr_def_10 != identity,
inference(demodulation,[status(thm)],[c_75,c_152]) ).
tcf(c_196,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_74,c_129]) ).
tcf(c_206,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_196,c_76]) ).
tcf(c_216,plain,
multiply(a,identity) = inverse(b),
inference(superposition,[status(thm)],[c_79,c_206]) ).
tcf(c_224,plain,
inverse(b) = a,
inference(demodulation,[status(thm)],[c_216,c_77]) ).
tcf(c_225,plain,
multiply(b,a) = identity,
inference(superposition,[status(thm)],[c_224,c_79]) ).
tcf(c_227,plain,
identity = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_225,c_152]) ).
tcf(c_234,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_153,c_227]) ).
tcf(c_235,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:12:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.09/1.28 % SZS status Started for theBenchmark.p
% 2.09/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.28
% 2.09/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.09/1.28
% 2.09/1.28 % ------ iProver source info
% 2.09/1.28
% 2.09/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.09/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.09/1.28 % git: non_committed_changes: false
% 2.09/1.28
% 2.09/1.28 % ------ Parsing...% successful
% 2.09/1.28
% 2.09/1.28
% 2.09/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.09/1.28
% 2.09/1.28 % ------ 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 %
% 2.09/1.28
% 2.09/1.28 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.09/1.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.09/1.28
% 2.09/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.09/1.28 % ------ Proving...
% 2.09/1.28 % ------ Problem Properties
% 2.09/1.28
% 2.09/1.28 %
% 2.09/1.28 % clauses 8
% 2.09/1.28 % conjectures 0
% 2.09/1.28 % EPR 1
% 2.09/1.28 % Horn 8
% 2.09/1.28 % unary 8
% 2.09/1.28 % binary 0
% 2.09/1.28 % lits 8
% 2.09/1.28 % lits eq 8
% 2.09/1.28 % fd_pure 0
% 2.09/1.28 % fd_pseudo 0
% 2.09/1.28 % fd_cond 0
% 2.09/1.28 % fd_pseudo_cond 0
% 2.09/1.28 % AC symbols 0
% 2.09/1.28
% 2.09/1.28 % ------ Schedule UEQ
% 2.09/1.28
% 2.09/1.28 % ------ Option_UEQ Time Limit: 10.
% 2.09/1.28
% 2.09/1.28
% 2.09/1.28 % ------
% 2.09/1.28 % Current options:
% 2.09/1.28 % ------
% 2.09/1.28
% 2.09/1.28
% 2.09/1.28 %
% 2.09/1.28
% 2.09/1.28 % ------ Proving...
% 2.09/1.28 %
% 2.09/1.28
% 2.09/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.28
% 2.09/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.09/1.28
% 2.09/1.28
%------------------------------------------------------------------------------