%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : CAT003-1 : 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 01:01:03 PM UTC 2026
% Result : Unsatisfiable 6.39s 1.76s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 19 unt; 0 def)
% Number of atoms : 108 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 125 ( 65 ~; 60 |; 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 : 93 ( 0 sgn 93 !; 0 ?; 60 :)
% 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(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(X2,c,X1)
| ~ product(X0,c,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product) ).
fof(f21,axiom,
product(h,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_equals_d) ).
fof(f22,axiom,
product(g,a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ga_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(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,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(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,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(X4,X1)
| ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,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_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(X2,c,X1)
| ~ product(X0,c,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,plain,
product(h,a,d),
inference(cnf_transformation,[],[f21]) ).
tcf(c_93,plain,
product(g,a,d),
inference(cnf_transformation,[],[f22]) ).
tcf(c_94,negated_conjecture,
h != g,
inference(cnf_transformation,[],[f23]) ).
tcf(c_661,plain,
defined(g,a),
inference(superposition,[status(thm)],[c_93,c_73]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i] :
( defined(X0,codomain(X1))
| ~ defined(X0,X1) ),
inference(superposition,[status(thm)],[c_86,c_77]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_86,c_75]) ).
tcf(c_811,plain,
! [X0: $i] :
( ( h = g )
| ~ product(g,c,X0)
| ~ product(h,c,X0) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_957,plain,
! [X0: $i,X1: $i] :
( defined(X1,b)
| ~ defined(X0,c)
| ~ product(X0,a,X1) ),
inference(superposition,[status(thm)],[c_90,c_78]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X2,X1)
| ~ identity_map(codomain(X0))
| ~ defined(X2,X0)
| ~ defined(codomain(X0),X1) ),
inference(superposition,[status(thm)],[c_734,c_80]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(X2,X1)
| ~ defined(X2,X0)
| ~ defined(codomain(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1046,c_82]) ).
tcf(c_1113,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(g,X1,X2)
| ~ product(g,a,d)
| ~ product(d,X0,X2)
| ~ product(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_1164,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(h,X1,X2)
| ~ product(d,X0,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_92,c_76]) ).
tcf(c_1855,plain,
! [X0: $i] :
( product(g,c,X0)
| ~ product(g,a,d)
| ~ product(a,b,c)
| ~ product(d,b,X0) ),
inference(instantiation,[status(thm)],[c_1113]) ).
tcf(c_2740,plain,
! [X0: $i] :
( product(h,c,X0)
| ~ product(d,b,X0) ),
inference(superposition,[status(thm)],[c_90,c_1164]) ).
tcf(c_2774,plain,
! [X0: $i] : ~ product(d,b,X0),
inference(global_subsumption_just,[status(thm)],[c_2740,c_93,c_90,c_94,c_811,c_1855,c_2740]) ).
tcf(c_2777,plain,
~ defined(d,b),
inference(superposition,[status(thm)],[c_72,c_2774]) ).
tcf(c_5640,plain,
( defined(d,b)
| ~ defined(g,c) ),
inference(superposition,[status(thm)],[c_93,c_957]) ).
tcf(c_5650,plain,
~ defined(g,c),
inference(forward_subsumption_resolution,[status(thm)],[c_5640,c_2777]) ).
tcf(c_11048,plain,
! [X0: $i,X1: $i,X2: $i] :
( defined(codomain(X0),X2)
| ~ product(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_778,c_73,c_778]) ).
tcf(c_11054,plain,
defined(codomain(a),c),
inference(superposition,[status(thm)],[c_90,c_11048]) ).
tcf(c_11272,plain,
! [X0: $i] :
( defined(X0,c)
| ~ defined(X0,a) ),
inference(superposition,[status(thm)],[c_11054,c_1053]) ).
tcf(c_11605,plain,
defined(g,c),
inference(superposition,[status(thm)],[c_661,c_11272]) ).
tcf(c_11617,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11605,c_5650]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Fri Sep 25 06:53:35 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 6.39/1.76 % SZS status Started for theBenchmark.p
% 6.39/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 6.39/1.76
% 6.39/1.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.39/1.76
% 6.39/1.76 % ------ iProver source info
% 6.39/1.76
% 6.39/1.76 % git: date: 2026-07-19 20:42:38 +0200
% 6.39/1.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.39/1.76 % git: non_committed_changes: false
% 6.39/1.76
% 6.39/1.76 % ------ Parsing...% successful
% 6.39/1.76
% 6.39/1.76
% 6.39/1.76 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.39/1.76
% 6.39/1.76 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.39/1.76
% 6.39/1.76 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.39/1.76
% 6.39/1.76 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.39/1.76 % ------ Proving...
% 6.39/1.76 % ------ Problem Properties
% 6.39/1.76
% 6.39/1.76 %
% 6.39/1.76 % clauses 23
% 6.39/1.76 % conjectures 1
% 6.39/1.76 % EPR 16
% 6.39/1.76 % Horn 23
% 6.39/1.76 % unary 10
% 6.39/1.76 % binary 2
% 6.39/1.76 % lits 52
% 6.39/1.76 % lits eq 3
% 6.39/1.76 % fd_pure 0
% 6.39/1.76 % fd_pseudo 0
% 6.39/1.76 % fd_cond 0
% 6.39/1.76 % fd_pseudo_cond 2
% 6.39/1.76 % AC symbols 0
% 6.39/1.76
% 6.39/1.76 % ------ Schedule dynamic 5 is on
% 6.39/1.76
% 6.39/1.76 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.39/1.76
% 6.39/1.76
% 6.39/1.76 % ------
% 6.39/1.76 % Current options:
% 6.39/1.76 % ------
% 6.39/1.76
% 6.39/1.76
% 6.39/1.76 %
% 6.39/1.76
% 6.39/1.76 % ------ Proving...
% 6.39/1.76 %
% 6.39/1.76
% 6.39/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 6.39/1.76
% 6.39/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.39/1.77
% 6.39/1.77
%------------------------------------------------------------------------------