%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP008-1 : 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 : 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 01:29:53 PM UTC 2026
% Result : Unsatisfiable 2.22s 1.28s
% Output : CNFRefutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 44 ( 11 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 26 ( 11 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 12 ( 0 sgn 12 !; 0 ?; 8 :)
% 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(f10,axiom,
! [X0] :
( q(X0)
| product(X0,j(X0),h(X0))
| product(j(X0),X0,h(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning3) ).
fof(f11,axiom,
! [X0] :
( q(X0)
| ~ product(X0,j(X0),h(X0))
| ~ product(j(X0),X0,h(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown_meaning4) ).
fof(f12,negated_conjecture,
~ q(identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_is_q) ).
tcf(c_61,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i] : product(X0,identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_70,plain,
! [X0: $i] :
( q(X0)
| product(X0,j(X0),h(X0))
| product(j(X0),X0,h(X0)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] :
( q(X0)
| ~ product(X0,j(X0),h(X0))
| ~ product(j(X0),X0,h(X0)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
~ q(identity),
inference(cnf_transformation,[],[f12]) ).
tcf(c_82,plain,
! [X0: $i] :
( q(X0)
| ( multiply(X0,j(X0)) = h(X0) )
| ( multiply(j(X0),X0) = h(X0) ) ),
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_83,plain,
! [X0: $i] :
( q(X0)
| ( multiply(X0,j(X0)) != h(X0) )
| ( multiply(j(X0),X0) != h(X0) ) ),
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_61]) ).
tcf(c_85,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(well_definedness,[status(thm)],[c_62]) ).
tcf(c_321,negated_conjecture,
~ q(identity),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_457,plain,
( ( multiply(identity,j(identity)) = h(identity) )
| ( multiply(j(identity),identity) = h(identity) ) ),
inference(superposition,[status(thm)],[c_82,c_321]) ).
tcf(c_463,plain,
j(identity) = h(identity),
inference(demodulation,[status(thm)],[c_457,c_84,c_85]) ).
tcf(c_470,plain,
( q(identity)
| ( j(identity) != h(identity) )
| ( multiply(identity,j(identity)) != h(identity) ) ),
inference(superposition,[status(thm)],[c_85,c_83]) ).
tcf(c_471,plain,
q(identity),
inference(ground_joinability,[status(thm)],[c_470,c_84,c_463]) ).
tcf(c_472,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_471,c_321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 13:14:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.22/1.28 % SZS status Started for theBenchmark.p
% 2.22/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.22/1.28
% 2.22/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.22/1.28
% 2.22/1.28 % ------ iProver source info
% 2.22/1.28
% 2.22/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.22/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.22/1.28 % git: non_committed_changes: false
% 2.22/1.28
% 2.22/1.28 % ------ Parsing...% successful
% 2.22/1.28
% 2.22/1.28
% 2.22/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.22/1.28
% 2.22/1.28 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.22/1.28
% 2.22/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.22/1.28
% 2.22/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.22/1.28 % ------ Proving...
% 2.22/1.28 % ------ Problem Properties
% 2.22/1.28
% 2.22/1.28 %
% 2.22/1.28 % clauses 9
% 2.22/1.28 % conjectures 1
% 2.22/1.28 % EPR 1
% 2.22/1.28 % Horn 8
% 2.22/1.28 % unary 6
% 2.22/1.28 % binary 1
% 2.22/1.28 % lits 14
% 2.22/1.28 % lits eq 10
% 2.22/1.28 % fd_pure 0
% 2.22/1.28 % fd_pseudo 0
% 2.22/1.28 % fd_cond 0
% 2.22/1.28 % fd_pseudo_cond 0
% 2.22/1.28 % AC symbols 0
% 2.22/1.28
% 2.22/1.28 % ------ Schedule dynamic 5 is on
% 2.22/1.28
% 2.22/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.22/1.28
% 2.22/1.28
% 2.22/1.28 % ------
% 2.22/1.28 % Current options:
% 2.22/1.28 % ------
% 2.22/1.28
% 2.22/1.28
% 2.22/1.28 %
% 2.22/1.28
% 2.22/1.28 % ------ Proving...
% 2.22/1.28 %
% 2.22/1.28
% 2.22/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.22/1.28
% 2.22/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.22/1.28
% 2.22/1.28
%------------------------------------------------------------------------------