%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT006-1 : 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 : n007.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 01:01:07 PM UTC 2026
% Result : Unsatisfiable 3.58s 1.27s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 16 unt; 1 def)
% Number of atoms : 87 ( 10 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 64 ( 34 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
! [X0] : identity_map(codomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',codomain_is_an_identity_map) ).
fof(f15,axiom,
! [X0] : product(codomain(X0),X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
fof(f19,axiom,
defined(h,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_defined) ).
fof(f20,axiom,
identity_map(h),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_is_the_identity_map) ).
fof(f21,negated_conjecture,
codomain(a) != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_is_h) ).
fof(f22,plain,
h != codomain(a),
inference(reorient_equations,[],[f21]) ).
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_80,plain,
! [X0: $i] : identity_map(codomain(X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_84,plain,
! [X0: $i] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_87,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_88,plain,
defined(h,a),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
identity_map(h),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,negated_conjecture,
codomain(a) != h,
inference(cnf_transformation,[],[f22]) ).
tcf(c_387,definition,
iPr_def_10 = codomain(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_388,negated_conjecture,
iPr_def_10 != h,
inference(demodulation,[status(thm)],[c_90,c_387]) ).
tcf(c_670,plain,
identity_map(iPr_def_10),
inference(superposition,[status(thm)],[c_387,c_80]) ).
tcf(c_671,plain,
product(iPr_def_10,a,a),
inference(superposition,[status(thm)],[c_387,c_84]) ).
tcf(c_733,plain,
! [X0: $i] :
( defined(X0,iPr_def_10)
| ~ defined(X0,a) ),
inference(superposition,[status(thm)],[c_671,c_75]) ).
tcf(c_745,plain,
( defined(h,iPr_def_10)
| ~ defined(h,a) ),
inference(instantiation,[status(thm)],[c_733]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_10 = h )
| ~ product(X0,X1,iPr_def_10)
| ~ product(X0,X1,h) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_2273,plain,
! [X0: $i] :
( product(X0,iPr_def_10,iPr_def_10)
| ~ identity_map(X0)
| ~ defined(X0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_2274,plain,
! [X0: $i] :
( ( iPr_def_10 = h )
| ~ product(X0,iPr_def_10,iPr_def_10)
| ~ product(X0,iPr_def_10,h) ),
inference(instantiation,[status(thm)],[c_887]) ).
tcf(c_2275,plain,
( product(h,iPr_def_10,iPr_def_10)
| ~ identity_map(h)
| ~ defined(h,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_2273]) ).
tcf(c_2276,plain,
( ( iPr_def_10 = h )
| ~ product(h,iPr_def_10,iPr_def_10)
| ~ product(h,iPr_def_10,h) ),
inference(instantiation,[status(thm)],[c_2274]) ).
tcf(c_2870,plain,
( product(h,iPr_def_10,h)
| ~ identity_map(iPr_def_10)
| ~ defined(h,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_2871,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2870,c_2276,c_2275,c_745,c_670,c_388,c_88,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 06:50:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 3.58/1.27 % SZS status Started for theBenchmark.p
% 3.58/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.58/1.27
% 3.58/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.58/1.27
% 3.58/1.27 % ------ iProver source info
% 3.58/1.27
% 3.58/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.58/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.58/1.27 % git: non_committed_changes: false
% 3.58/1.27
% 3.58/1.27 % ------ Parsing...% successful
% 3.58/1.27
% 3.58/1.27
% 3.58/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.58/1.27
% 3.58/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.58/1.27
% 3.58/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.58/1.27
% 3.58/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.58/1.27 % ------ Proving...
% 3.58/1.27 % ------ Problem Properties
% 3.58/1.27
% 3.58/1.27 %
% 3.58/1.27 % clauses 22
% 3.58/1.27 % conjectures 1
% 3.58/1.27 % EPR 14
% 3.58/1.27 % Horn 22
% 3.58/1.27 % unary 10
% 3.58/1.27 % binary 2
% 3.58/1.27 % lits 49
% 3.58/1.27 % lits eq 3
% 3.58/1.27 % fd_pure 0
% 3.58/1.27 % fd_pseudo 0
% 3.58/1.27 % fd_cond 0
% 3.58/1.27 % fd_pseudo_cond 1
% 3.58/1.27 % AC symbols 0
% 3.58/1.27
% 3.58/1.27 % ------ Schedule dynamic 5 is on
% 3.58/1.27
% 3.58/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.58/1.27
% 3.58/1.27
% 3.58/1.27 % ------
% 3.58/1.27 % Current options:
% 3.58/1.27 % ------
% 3.58/1.27
% 3.58/1.27
% 3.58/1.27 %
% 3.58/1.27
% 3.58/1.27 % ------ Proving...
% 3.58/1.27 %
% 3.58/1.27
% 3.58/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 3.58/1.27
% 3.58/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.58/1.27
% 3.58/1.27
%------------------------------------------------------------------------------