%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT001-1 : 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 : n018.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 01:01:01 PM UTC 2026
% Result : Unsatisfiable 15.22s 3.27s
% Output : CNFRefutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 54 ( 18 unt; 0 def)
% Number of atoms : 133 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 160 ( 81 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?; 62 :)
% 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(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(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).
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(f7,axiom,
! [X2,X3,X0,X1,X4] :
( defined(X4,X1)
| ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom5) ).
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(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(f19,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_equals_c) ).
fof(f20,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ product(c,X2,X1)
| ~ product(c,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product) ).
fof(f21,axiom,
product(b,h,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bh_equals_d) ).
fof(f22,axiom,
product(b,g,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bg_equals_d) ).
fof(f23,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( defined(X3,X2)
| ~ defined(X4,X1)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X5,X2,X4)
| ~ product(X5,X0,X3)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_77,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,X3: $i,X4: $i] :
( defined(X2,X3)
| ~ defined(X0,X4)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X2,X1)
| ~ identity_map(X0)
| ~ defined(X2,X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_82,plain,
! [X0: $i] : identity_map(codomain(X0)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_86,plain,
! [X0: $i] : product(codomain(X0),X0,X0),
inference(cnf_transformation,[],[f15]) ).
tcf(c_90,plain,
product(a,b,c),
inference(cnf_transformation,[],[f19]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ product(c,X2,X1)
| ~ product(c,X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,plain,
product(b,h,d),
inference(cnf_transformation,[],[f21]) ).
tcf(c_93,plain,
product(b,g,d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_94,negated_conjecture,
h != g,
inference(cnf_transformation,[],[f23]) ).
tcf(c_95,plain,
identity_map(codomain(b)),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_570,plain,
! [X0: $i] :
( ( h = g )
| ~ product(c,g,X0)
| ~ product(c,h,X0) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_582,plain,
( ( h = g )
| ~ product(c,g,compose(c,g))
| ~ product(c,h,compose(c,g)) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_601,plain,
( product(c,g,compose(c,g))
| ~ defined(c,g) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(c,X4,X2)
| ~ product(X0,X3,c)
| ~ product(X3,X4,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(a,X1,X2)
| ~ product(a,b,c)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(c,X2,X1)
| ~ product(a,b,c)
| ~ product(b,X2,X0)
| ~ product(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_671]) ).
tcf(c_818,plain,
defined(b,h),
inference(superposition,[status(thm)],[c_92,c_73]) ).
tcf(c_959,plain,
! [X0: $i,X1: $i] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_86,c_77]) ).
tcf(c_1455,plain,
! [X0: $i] :
( product(c,h,X0)
| ~ product(b,h,d)
| ~ product(a,b,c)
| ~ product(a,d,X0) ),
inference(instantiation,[status(thm)],[c_801]) ).
tcf(c_3566,plain,
defined(a,b),
inference(superposition,[status(thm)],[c_90,c_73]) ).
tcf(c_3634,plain,
! [X0: $i,X1: $i] :
( defined(X0,d)
| ~ defined(X1,h)
| ~ product(X0,b,X1) ),
inference(superposition,[status(thm)],[c_92,c_75]) ).
tcf(c_3650,plain,
( defined(codomain(b),d)
| ~ defined(b,h) ),
inference(superposition,[status(thm)],[c_86,c_3634]) ).
tcf(c_3671,plain,
defined(codomain(b),d),
inference(global_subsumption_just,[status(thm)],[c_3650,c_818,c_3650]) ).
tcf(c_3673,plain,
! [X0: $i] :
( defined(X0,d)
| ~ identity_map(codomain(b))
| ~ defined(X0,codomain(b)) ),
inference(superposition,[status(thm)],[c_3671,c_80]) ).
tcf(c_3683,plain,
! [X0: $i,X1: $i] :
( defined(c,X0)
| ~ defined(a,X1)
| ~ product(b,X0,X1) ),
inference(superposition,[status(thm)],[c_90,c_78]) ).
tcf(c_5064,plain,
! [X0: $i] :
( defined(X0,d)
| ~ defined(X0,codomain(b)) ),
inference(global_subsumption_just,[status(thm)],[c_3673,c_95,c_3673]) ).
tcf(c_5068,plain,
! [X0: $i] :
( defined(X0,d)
| ~ defined(X0,b) ),
inference(superposition,[status(thm)],[c_959,c_5064]) ).
tcf(c_5340,plain,
( defined(c,g)
| ~ defined(a,d) ),
inference(superposition,[status(thm)],[c_93,c_3683]) ).
tcf(c_5752,plain,
defined(a,d),
inference(superposition,[status(thm)],[c_3566,c_5068]) ).
tcf(c_11757,plain,
! [X0: $i] :
( product(a,X0,compose(c,g))
| ~ product(a,b,c)
| ~ product(b,g,X0)
| ~ product(c,g,compose(c,g)) ),
inference(instantiation,[status(thm)],[c_752]) ).
tcf(c_61459,plain,
( product(a,d,compose(c,g))
| ~ product(b,g,d)
| ~ product(a,b,c)
| ~ product(c,g,compose(c,g)) ),
inference(instantiation,[status(thm)],[c_11757]) ).
tcf(c_68204,plain,
( product(c,h,compose(c,g))
| ~ product(b,h,d)
| ~ product(a,b,c)
| ~ product(a,d,compose(c,g)) ),
inference(instantiation,[status(thm)],[c_1455]) ).
tcf(c_68206,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_68204,c_61459,c_5752,c_5340,c_601,c_582,c_94,c_90,c_92,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 06:51:20 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 15.22/3.27 % SZS status Started for theBenchmark.p
% 15.22/3.27 % SZS status Unsatisfiable for theBenchmark.p
% 15.22/3.27
% 15.22/3.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.22/3.27
% 15.22/3.27 % ------ iProver source info
% 15.22/3.27
% 15.22/3.27 % git: date: 2026-07-19 20:42:38 +0200
% 15.22/3.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.22/3.27 % git: non_committed_changes: false
% 15.22/3.27
% 15.22/3.27 % ------ Parsing...% successful
% 15.22/3.27
% 15.22/3.27
% 15.22/3.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.22/3.27
% 15.22/3.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 15.22/3.27
% 15.22/3.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.22/3.27
% 15.22/3.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.22/3.27 % ------ Proving...
% 15.22/3.27 % ------ Problem Properties
% 15.22/3.27
% 15.22/3.27 %
% 15.22/3.27 % clauses 23
% 15.22/3.27 % conjectures 1
% 15.22/3.27 % EPR 16
% 15.22/3.27 % Horn 23
% 15.22/3.27 % unary 10
% 15.22/3.27 % binary 2
% 15.22/3.27 % lits 52
% 15.22/3.27 % lits eq 3
% 15.22/3.27 % fd_pure 0
% 15.22/3.27 % fd_pseudo 0
% 15.22/3.27 % fd_cond 0
% 15.22/3.27 % fd_pseudo_cond 2
% 15.22/3.27 % AC symbols 0
% 15.22/3.27
% 15.22/3.27 % ------ Input Options Time Limit: Unbounded
% 15.22/3.27
% 15.22/3.27
% 15.22/3.27 % ------
% 15.22/3.27 % Current options:
% 15.22/3.27 % ------
% 15.22/3.27
% 15.22/3.27
% 15.22/3.27 %
% 15.22/3.27
% 15.22/3.27 % ------ Proving...
% 15.22/3.27 %
% 15.22/3.27
% 15.22/3.27 % SZS status Unsatisfiable for theBenchmark.p
% 15.22/3.27
% 15.22/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.22/3.27
% 15.22/3.27
%------------------------------------------------------------------------------