%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT010-1 : 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 : n001.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 01:01:09 PM UTC 2026
% Result : Unsatisfiable 2.03s 1.29s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 80 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 88 ( 45 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
fof(f4,axiom,
! [X2,X3,X0,X1,X4] :
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
fof(f16,axiom,
! [X0,X1] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',identity2) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
fof(f19,axiom,
defined(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ba_defined) ).
fof(f20,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ba_equals_codomain_of_b) ).
tcf(c_69,plain,
defined(b,a),
inference(cnf_transformation,[],[f19]) ).
tcf(c_70,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
inference(cnf_transformation,[],[f20]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_78,plain,
! [X0: $i] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_80,plain,
! [X0: $i] : identity_map(codomain(X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,X2)
| ~ defined(X2,X1)
| ( codomain(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_80]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( product(X0,codomain(X1),X0)
| ~ defined(X0,codomain(X1)) ),
inference(unflattening,[status(thm)],[c_265]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ( codomain(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_84]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( product(codomain(X0),X1,X1)
| ~ defined(codomain(X0),X1) ),
inference(unflattening,[status(thm)],[c_286]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_78,c_72]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ defined(X0,codomain(X1))
| ~ product(X0,codomain(X1),X2) ),
inference(superposition,[status(thm)],[c_266,c_76]) ).
tcf(c_947,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_78,c_73]) ).
tcf(c_1359,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ product(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_947,c_75,c_947]) ).
tcf(c_1365,plain,
! [X0: $i,X1: $i] :
( defined(codomain(X0),compose(X0,X1))
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_77,c_1359]) ).
tcf(c_1921,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ product(X0,codomain(X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_774,c_75]) ).
tcf(c_1931,plain,
! [X0: $i,X1: $i] :
( ( codomain(X0) = codomain(X1) )
| ~ defined(codomain(X0),codomain(X1)) ),
inference(superposition,[status(thm)],[c_287,c_1921]) ).
tcf(c_2230,plain,
! [X0: $i,X1: $i] :
( ( codomain(X0) = codomain(X1) )
| ~ defined(codomain(X0),X1) ),
inference(superposition,[status(thm)],[c_738,c_1931]) ).
tcf(c_2312,plain,
! [X0: $i,X1: $i] :
( ( codomain(compose(X0,X1)) = codomain(X0) )
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_1365,c_2230]) ).
tcf(c_2564,plain,
codomain(compose(b,a)) = codomain(b),
inference(superposition,[status(thm)],[c_69,c_2312]) ).
tcf(c_2582,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2564,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : 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 : n001.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 : Fri Sep 25 07:00:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.03/1.29 % SZS status Started for theBenchmark.p
% 2.03/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.29
% 2.03/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.03/1.29
% 2.03/1.29 % ------ iProver source info
% 2.03/1.29
% 2.03/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.03/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.03/1.29 % git: non_committed_changes: false
% 2.03/1.29
% 2.03/1.29 % ------ Parsing...% successful
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.03/1.29
% 2.03/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.03/1.29 % ------ Proving...
% 2.03/1.29 % ------ Problem Properties
% 2.03/1.29
% 2.03/1.29 %
% 2.03/1.29 % clauses 16
% 2.03/1.29 % conjectures 1
% 2.03/1.29 % EPR 9
% 2.03/1.29 % Horn 16
% 2.03/1.29 % unary 4
% 2.03/1.29 % binary 4
% 2.03/1.29 % lits 40
% 2.03/1.29 % lits eq 2
% 2.03/1.29 % fd_pure 0
% 2.03/1.29 % fd_pseudo 0
% 2.03/1.29 % fd_cond 0
% 2.03/1.29 % fd_pseudo_cond 1
% 2.03/1.29 % AC symbols 0
% 2.03/1.29
% 2.03/1.29 % ------ Schedule dynamic 5 is on
% 2.03/1.29
% 2.03/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 % ------
% 2.03/1.29 % Current options:
% 2.03/1.29 % ------
% 2.03/1.29
% 2.03/1.29
% 2.03/1.29 %
% 2.03/1.29
% 2.03/1.29 % ------ Proving...
% 2.03/1.29 %
% 2.03/1.29
% 2.03/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.03/1.29
% 2.03/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.03/1.29
% 2.03/1.29
%------------------------------------------------------------------------------