%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT018-1 : 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 : n002.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 01:01:11 PM UTC 2026
% Result : Unsatisfiable 1.43s 1.28s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 24 unt; 1 def)
% Number of atoms : 114 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 103 ( 53 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
fof(f2,axiom,
! [X2,X0,X1] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom3) ).
fof(f9,axiom,
! [X2,X0,X1] :
( defined(X0,X2)
| ~ identity_map(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
fof(f10,axiom,
! [X0] : identity_map(domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
fof(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
fof(f12,axiom,
! [X0] : defined(X0,domain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
fof(f14,axiom,
! [X0] : product(X0,domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_codomain) ).
fof(f19,axiom,
defined(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f20,axiom,
defined(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f21,negated_conjecture,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
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,X3: $i] :
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X0,X2)
| ~ identity_map(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,plain,
! [X0: $i] : identity_map(domain(X0)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i] : identity_map(codomain(X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
! [X0: $i] : defined(X0,domain(X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_83,plain,
! [X0: $i] : product(X0,domain(X0),X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_84,plain,
! [X0: $i] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_88,plain,
defined(a,b),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
defined(b,c),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
~ defined(a,compose(b,c)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,plain,
product(codomain(b),b,b),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_352,definition,
iPr_def_10 = compose(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_353,negated_conjecture,
~ defined(a,iPr_def_10),
inference(demodulation,[status(thm)],[c_90,c_352]) ).
tcf(c_646,plain,
( product(b,c,iPr_def_10)
| ~ defined(b,c) ),
inference(superposition,[status(thm)],[c_352,c_70]) ).
tcf(c_648,plain,
product(b,c,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_646,c_89]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i] :
( defined(domain(X0),X1)
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_83,c_72]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_75]) ).
tcf(c_709,plain,
! [X0: $i] :
( defined(X0,b)
| ~ defined(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_648,c_75]) ).
tcf(c_728,plain,
! [X0: $i] :
( defined(domain(X0),b)
| ~ defined(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_671,c_709]) ).
tcf(c_772,plain,
! [X0: $i] :
( defined(a,X0)
| ~ identity_map(b)
| ~ defined(b,X0) ),
inference(superposition,[status(thm)],[c_88,c_78]) ).
tcf(c_774,plain,
! [X0: $i,X1: $i] :
( defined(X0,X1)
| ~ identity_map(domain(X0))
| ~ defined(domain(X0),X1) ),
inference(superposition,[status(thm)],[c_81,c_78]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( defined(X0,X1)
| ~ defined(domain(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_774,c_79]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_84,c_73]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i] :
( defined(a,X0)
| ~ defined(a,b)
| ~ product(X0,X1,b) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_980,plain,
! [X0: $i,X1: $i] :
( defined(X0,codomain(X1))
| ~ defined(domain(X0),X1) ),
inference(superposition,[status(thm)],[c_706,c_797]) ).
tcf(c_1373,plain,
! [X0: $i] :
( defined(X0,codomain(b))
| ~ defined(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_728,c_980]) ).
tcf(c_1649,plain,
( defined(a,codomain(b))
| ~ identity_map(b)
| ~ defined(b,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1373,c_772]) ).
tcf(c_2090,plain,
! [X0: $i,X1: $i] :
( defined(a,codomain(X0))
| ~ defined(a,b)
| ~ product(codomain(X0),X1,b) ),
inference(instantiation,[status(thm)],[c_938]) ).
tcf(c_2092,plain,
( defined(a,codomain(b))
| ~ defined(a,b)
| ~ product(codomain(b),b,b) ),
inference(instantiation,[status(thm)],[c_2090]) ).
tcf(c_3538,plain,
defined(a,codomain(b)),
inference(global_subsumption_just,[status(thm)],[c_1649,c_88,c_95,c_2092]) ).
tcf(c_3540,plain,
! [X0: $i] :
( defined(a,X0)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),X0) ),
inference(superposition,[status(thm)],[c_3538,c_78]) ).
tcf(c_3541,plain,
! [X0: $i] :
( defined(a,X0)
| ~ defined(codomain(b),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3540,c_80]) ).
tcf(c_4034,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ product(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_867,c_71,c_867]) ).
tcf(c_4045,plain,
defined(codomain(b),iPr_def_10),
inference(superposition,[status(thm)],[c_648,c_4034]) ).
tcf(c_4116,plain,
defined(a,iPr_def_10),
inference(superposition,[status(thm)],[c_4045,c_3541]) ).
tcf(c_4117,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4116,c_353]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 07:00:05 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.39 Running first-order theorem proving
% 0.15/0.39 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
% 0.15/0.41
% 0.15/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.41
% 0.15/0.41 % Detected problem language: tptp
% 0.15/0.42 % Proving...
% 1.43/1.28 % SZS status Started for theBenchmark.p
% 1.43/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.28
% 1.43/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.43/1.28
% 1.43/1.28 % ------ iProver source info
% 1.43/1.28
% 1.43/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.43/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.43/1.28 % git: non_committed_changes: false
% 1.43/1.28
% 1.43/1.28 % ------ Parsing...% successful
% 1.43/1.28
% 1.43/1.28
% 1.43/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.43/1.28
% 1.43/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.43/1.28
% 1.43/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.43/1.28
% 1.43/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.43/1.28 % ------ Proving...
% 1.43/1.28 % ------ Problem Properties
% 1.43/1.28
% 1.43/1.28 %
% 1.43/1.28 % clauses 22
% 1.43/1.28 % conjectures 1
% 1.43/1.28 % EPR 14
% 1.43/1.28 % Horn 22
% 1.43/1.28 % unary 10
% 1.43/1.28 % binary 2
% 1.43/1.28 % lits 49
% 1.43/1.28 % lits eq 2
% 1.43/1.28 % fd_pure 0
% 1.43/1.28 % fd_pseudo 0
% 1.43/1.28 % fd_cond 0
% 1.43/1.28 % fd_pseudo_cond 1
% 1.43/1.28 % AC symbols 0
% 1.43/1.28
% 1.43/1.28 % ------ Schedule dynamic 5 is on
% 1.43/1.28
% 1.43/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.43/1.28
% 1.43/1.28
% 1.43/1.28 % ------
% 1.43/1.28 % Current options:
% 1.43/1.28 % ------
% 1.43/1.28
% 1.43/1.28
% 1.43/1.28 %
% 1.43/1.28
% 1.43/1.28 % ------ Proving...
% 1.43/1.28 %
% 1.43/1.28
% 1.43/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.28
% 1.43/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.43/1.28
% 1.43/1.28
%------------------------------------------------------------------------------