%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP043-2 : 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 : n009.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 01:30:01 PM UTC 2026
% Result : Unsatisfiable 2.21s 1.25s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 46 ( 24 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,axiom,
equalish(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_equals_c) ).
fof(f10,negated_conjecture,
~ equalish(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity) ).
tcf(c_59,plain,
! [X0: $i] : product(identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X0,X1,X3)
| ~ equalish(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
equalish(a,b),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
equalish(b,c),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,negated_conjecture,
~ equalish(a,c),
inference(cnf_transformation,[],[f10]) ).
tcf(c_69,plain,
product(identity,a,a),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,b)
| ~ equalish(a,b)
| ~ product(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,c)
| ~ equalish(b,c)
| ~ product(X0,X1,b) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(identity,X0,X1)
| ~ product(identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_171,plain,
( product(identity,a,b)
| ~ equalish(a,b)
| ~ product(identity,a,a) ),
inference(instantiation,[status(thm)],[c_158]) ).
tcf(c_187,plain,
( equalish(a,c)
| ~ product(identity,a,c)
| ~ product(identity,a,a) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_201,plain,
! [X0: $i] :
( product(identity,X0,c)
| ~ equalish(b,c)
| ~ product(identity,X0,b) ),
inference(instantiation,[status(thm)],[c_159]) ).
tcf(c_202,plain,
( product(identity,a,c)
| ~ equalish(b,c)
| ~ product(identity,a,b) ),
inference(instantiation,[status(thm)],[c_201]) ).
tcf(c_203,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_202,c_187,c_171,c_69,c_68,c_66,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP043-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 13:22:43 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.38 Running first-order theorem proving
% 0.08/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.39
% 0.08/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.39
% 0.11/0.39 % Detected problem language: tptp
% 0.11/0.40 % Proving...
% 2.21/1.25 % SZS status Started for theBenchmark.p
% 2.21/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.21/1.25
% 2.21/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.21/1.25
% 2.21/1.25 % ------ iProver source info
% 2.21/1.25
% 2.21/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.21/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.21/1.25 % git: non_committed_changes: false
% 2.21/1.25
% 2.21/1.25 % ------ Parsing...% successful
% 2.21/1.25
% 2.21/1.25
% 2.21/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.21/1.25
% 2.21/1.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.21/1.25
% 2.21/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.21/1.25 % ------ Proving...
% 2.21/1.25 % ------ Problem Properties
% 2.21/1.25
% 2.21/1.25 %
% 2.21/1.25 % clauses 10
% 2.21/1.25 % conjectures 1
% 2.21/1.25 % EPR 8
% 2.21/1.25 % Horn 10
% 2.21/1.25 % unary 6
% 2.21/1.25 % binary 0
% 2.21/1.25 % lits 20
% 2.21/1.25 % lits eq 0
% 2.21/1.25 % fd_pure 0
% 2.21/1.25 % fd_pseudo 0
% 2.21/1.25 % fd_cond 0
% 2.21/1.25 % fd_pseudo_cond 0
% 2.21/1.25 % AC symbols 0
% 2.21/1.25
% 2.21/1.25 % ------ Schedule dynamic 5 is on
% 2.21/1.25
% 2.21/1.25 % ------ no equalities: superposition off
% 2.21/1.25
% 2.21/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.21/1.25
% 2.21/1.25
% 2.21/1.25 % ------
% 2.21/1.25 % Current options:
% 2.21/1.25 % ------
% 2.21/1.25
% 2.21/1.25
% 2.21/1.25 %
% 2.21/1.25
% 2.21/1.25 % ------ Proving...
% 2.21/1.25 %
% 2.21/1.25
% 2.21/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.21/1.25
% 2.21/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.21/1.25
% 2.21/1.25
%------------------------------------------------------------------------------