%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP001-5 : 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 : n003.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 01:29:51 PM UTC 2026
% Result : Unsatisfiable 2.24s 1.20s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 17 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : product(X0,identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f3,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f5,axiom,
! [X0] : product(X0,X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_element) ).
fof(f6,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f7,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tcf(c_56,plain,
! [X0: $i] : product(X0,X0,identity),
inference(cnf_transformation,[],[f5]) ).
tcf(c_57,plain,
product(a,b,c),
inference(cnf_transformation,[],[f6]) ).
tcf(c_58,negated_conjecture,
~ product(b,a,c),
inference(cnf_transformation,[],[f7]) ).
tcf(c_59,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,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,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,X2)
| ~ product(identity,X3,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_61,c_59]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(c,X2,X1)
| ~ product(b,X2,X0)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[c_61,c_57]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(identity,X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_62,c_60]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X3,X2)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_62,c_59]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_62,c_56]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,identity)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[c_65,c_56]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(b,a,c)
| ~ product(b,X0,X2)
| ~ product(X2,X1,c)
| ~ product(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(X0,X1,a)
| ~ product(X2,X1,c)
| ~ product(b,X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_107,c_58,c_107]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ product(b,X0,X2)
| ~ product(X2,X1,c)
| ~ product(X0,X1,a) ),
inference(renaming,[status(thm)],[c_109]) ).
tcf(c_116,plain,
! [X0: $i] :
( product(c,X0,c)
| ~ product(b,X0,b) ),
inference(resolution,[status(thm)],[c_67,c_57]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( product(identity,X0,X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[c_84,c_59]) ).
tcf(c_172,plain,
! [X0: $i] :
( ~ product(b,b,identity)
| ~ product(b,X0,a)
| ~ product(identity,X0,c) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_177,plain,
! [X0: $i] :
( product(a,c,X0)
| ~ product(identity,b,X0) ),
inference(resolution,[status(thm)],[c_86,c_57]) ).
tcf(c_186,plain,
product(c,identity,c),
inference(resolution,[status(thm)],[c_116,c_59]) ).
tcf(c_193,plain,
! [X0: $i] :
( product(identity,c,X0)
| ~ product(c,identity,X0) ),
inference(resolution,[status(thm)],[c_186,c_84]) ).
tcf(c_203,plain,
product(identity,c,c),
inference(resolution,[status(thm)],[c_186,c_119]) ).
tcf(c_211,plain,
! [X0: $i] :
( product(identity,X0,c)
| ~ product(identity,c,X0) ),
inference(resolution,[status(thm)],[c_203,c_85]) ).
tcf(c_219,plain,
product(c,c,identity),
inference(resolution,[status(thm)],[c_203,c_92]) ).
tcf(c_228,plain,
! [X0: $i] :
( product(c,X0,identity)
| ~ product(identity,c,X0) ),
inference(resolution,[status(thm)],[c_219,c_85]) ).
tcf(c_306,plain,
product(b,b,identity),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_318,plain,
product(a,c,b),
inference(resolution,[status(thm)],[c_177,c_60]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,X2,X1)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[c_318,c_62]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(b,X2,X1)
| ~ product(c,X2,X0)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[c_318,c_61]) ).
tcf(c_591,plain,
! [X0: $i] :
( product(a,X0,b)
| ~ product(c,identity,X0) ),
inference(resolution,[status(thm)],[c_324,c_59]) ).
tcf(c_607,plain,
! [X0: $i] :
( product(b,X0,a)
| ~ product(c,X0,identity) ),
inference(resolution,[status(thm)],[c_326,c_59]) ).
tcf(c_652,plain,
! [X0: $i] : ~ product(c,identity,X0),
inference(global_subsumption_just,[status(thm)],[c_591,c_172,c_193,c_211,c_228,c_306,c_607]) ).
tcf(c_655,plain,
$false,
inference(resolution,[status(thm)],[c_652,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.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 13:12:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running EPR theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 2.24/1.20 % SZS status Started for theBenchmark.p
% 2.24/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.24/1.20
% 2.24/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.24/1.20
% 2.24/1.20 % ------ iProver source info
% 2.24/1.20
% 2.24/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.24/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.24/1.20 % git: non_committed_changes: false
% 2.24/1.20
% 2.24/1.20 % ------ Parsing...% successful
% 2.24/1.20
% 2.24/1.20
% 2.24/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_horn
% 2.24/1.20 %
% 2.24/1.20
% 2.24/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 2.24/1.20
% 2.24/1.20 % ------ Preprocessing...% ------ preprocesses with Option_epr_horn
% 2.24/1.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.24/1.20 % ------ Proving...
% 2.24/1.20 % ------ Problem Properties
% 2.24/1.20
% 2.24/1.20 %
% 2.24/1.20 % clauses 7
% 2.24/1.20 % conjectures 1
% 2.24/1.20 % EPR 7
% 2.24/1.20 % Horn 7
% 2.24/1.20 % unary 5
% 2.24/1.20 % binary 0
% 2.24/1.20 % lits 13
% 2.24/1.20 % lits eq 0
% 2.24/1.20 % fd_pure 0
% 2.24/1.20 % fd_pseudo 0
% 2.24/1.20 % fd_cond 0
% 2.24/1.20 % fd_pseudo_cond 0
% 2.24/1.20 % AC symbols 0
% 2.24/1.20
% 2.24/1.20 % ------ Schedule EPR Horn non eq is on
% 2.24/1.20
% 2.24/1.20 % ------ no equalities: superposition off
% 2.24/1.20
% 2.24/1.20 % ------ Option_epr_horn Time Limit: Unbounded
% 2.24/1.20
% 2.24/1.20
% 2.24/1.20 % ------
% 2.24/1.20 % Current options:
% 2.24/1.20 % ------
% 2.24/1.20
% 2.24/1.20
% 2.24/1.20 %
% 2.24/1.20
% 2.24/1.20 % ------ Proving...
% 2.24/1.20 %
% 2.24/1.20
% 2.24/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.24/1.20
% 2.24/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.24/1.20
% 2.24/1.20
%------------------------------------------------------------------------------