%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP004-1 : 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 : n019.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 0.92s 1.29s
% Output : CNFRefutation 0.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 40 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 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 : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(inverse(X0),X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f2,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_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/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f5,negated_conjecture,
! [X0] : ~ product(a,X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_right_inverse) ).
tcf(c_54,plain,
! [X0: $i] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_56,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_57,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_58,negated_conjecture,
! [X0: $i] : ~ product(a,X0,identity),
inference(cnf_transformation,[],[f5]) ).
tcf(c_84,negated_conjecture,
! [X0: $i] : ~ product(a,X0,identity),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(a,X1,identity)
| ~ product(X3,X2,identity)
| ~ product(X3,X0,a)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_91,plain,
product(identity,a,a),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X4,a)
| ~ product(X2,X3,a)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,a)
| ~ product(identity,a,a)
| ~ product(X1,a,X2)
| ~ product(X0,X1,identity) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_117,plain,
! [X0: $i] :
( product(X0,identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(X0,inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_118,plain,
product(inverse(a),a,identity),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_178,plain,
( product(inverse(inverse(a)),identity,a)
| ~ product(identity,a,a)
| ~ product(inverse(a),a,identity)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_179,plain,
product(inverse(inverse(a)),inverse(a),identity),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( product(a,X1,identity)
| ~ product(identity,X1,X0)
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),X0,identity) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_415,plain,
product(identity,inverse(a),inverse(a)),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_472,plain,
! [X0: $i] :
( product(a,X0,identity)
| ~ product(identity,X0,inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_402]) ).
tcf(c_886,plain,
( product(a,inverse(a),identity)
| ~ product(identity,inverse(a),inverse(a))
| ~ product(inverse(inverse(a)),identity,a)
| ~ product(inverse(inverse(a)),inverse(a),identity) ),
inference(instantiation,[status(thm)],[c_472]) ).
tcf(c_1702,plain,
~ product(a,inverse(a),identity),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_1703,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1702,c_886,c_415,c_179,c_178,c_118,c_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:12:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 0.92/1.29 % SZS status Started for theBenchmark.p
% 0.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.92/1.29
% 0.92/1.29 % ------ iProver source info
% 0.92/1.29
% 0.92/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.92/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.92/1.29 % git: non_committed_changes: false
% 0.92/1.29
% 0.92/1.29 % ------ Parsing...% successful
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.92/1.29
% 0.92/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 % ------ Problem Properties
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29 % clauses 5
% 0.92/1.29 % conjectures 1
% 0.92/1.29 % EPR 4
% 0.92/1.29 % Horn 5
% 0.92/1.29 % unary 3
% 0.92/1.29 % binary 0
% 0.92/1.29 % lits 11
% 0.92/1.29 % lits eq 0
% 0.92/1.29 % fd_pure 0
% 0.92/1.29 % fd_pseudo 0
% 0.92/1.29 % fd_cond 0
% 0.92/1.29 % fd_pseudo_cond 0
% 0.92/1.29 % AC symbols 0
% 0.92/1.29
% 0.92/1.29 % ------ Schedule dynamic 5 is on
% 0.92/1.29
% 0.92/1.29 % ------ no equalities: superposition off
% 0.92/1.29
% 0.92/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 % ------
% 0.92/1.29 % Current options:
% 0.92/1.29 % ------
% 0.92/1.29
% 0.92/1.29
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % ------ Proving...
% 0.92/1.29 %
% 0.92/1.29
% 0.92/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 0.92/1.29
% 0.92/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.92/1.29
% 0.92/1.29
%------------------------------------------------------------------------------