%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 02:47:16 PM UTC 2026
% Result : Unsatisfiable 4.14s 1.28s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 15 unt; 1 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f78,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subset_relation) ).
fof(f79,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',identity_relation) ).
fof(f80,plain,
identity_relation = intersection(inverse(subset_relation),subset_relation),
inference(reorient_equations,[],[f79]) ).
fof(f122,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_alternate_defn1_1) ).
fof(f165,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f78,f39]) ).
fof(f166,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f80,f39]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_221,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(cnf_transformation,[],[f165]) ).
tcf(c_222,plain,
intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) = identity_relation,
inference(cnf_transformation,[],[f166]) ).
tcf(c_255,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_2974,definition,
iPr_def_10 = cross_product(universal_class,universal_class),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2975,negated_conjecture,
~ subclass(identity_relation,iPr_def_10),
inference(demodulation,[status(thm)],[c_255,c_2974]) ).
tcf(c_3890,plain,
! [X0: $i] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) ),
inference(superposition,[status(thm)],[c_222,c_181]) ).
tcf(c_3902,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),subset_relation) ),
inference(superposition,[status(thm)],[c_163,c_3890]) ).
tcf(c_4236,plain,
intersection(iPr_def_10,intersection(iPr_def_10,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) = subset_relation,
inference(light_normalisation,[status(thm)],[c_221,c_2974]) ).
tcf(c_4238,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,subset_relation) ),
inference(superposition,[status(thm)],[c_4236,c_180]) ).
tcf(c_4344,plain,
! [X0: $i] :
( subclass(identity_relation,X0)
| member(not_subclass_element(identity_relation,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3902,c_4238]) ).
tcf(c_4559,plain,
subclass(identity_relation,iPr_def_10),
inference(superposition,[status(thm)],[c_4344,c_164]) ).
tcf(c_4561,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4559,c_2975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:02:10 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.14/1.28 % SZS status Started for theBenchmark.p
% 4.14/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.14/1.28
% 4.14/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.14/1.28
% 4.14/1.28 % ------ iProver source info
% 4.14/1.28
% 4.14/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.14/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.14/1.28 % git: non_committed_changes: false
% 4.14/1.28
% 4.14/1.28 % ------ Parsing...% successful
% 4.14/1.28
% 4.14/1.28
% 4.14/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.14/1.28
% 4.14/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 4.14/1.28
% 4.14/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.14/1.28
% 4.14/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.14/1.28 % ------ Proving...
% 4.14/1.28 % ------ Problem Properties
% 4.14/1.28
% 4.14/1.28 %
% 4.14/1.28 % clauses 83
% 4.14/1.28 % conjectures 1
% 4.14/1.28 % EPR 13
% 4.14/1.28 % Horn 75
% 4.14/1.28 % unary 22
% 4.14/1.28 % binary 40
% 4.14/1.28 % lits 171
% 4.14/1.28 % lits eq 26
% 4.14/1.28 % fd_pure 0
% 4.14/1.28 % fd_pseudo 0
% 4.14/1.28 % fd_cond 3
% 4.14/1.28 % fd_pseudo_cond 7
% 4.14/1.28 % AC symbols 0
% 4.14/1.28
% 4.14/1.28 % ------ Schedule dynamic 5 is on
% 4.14/1.28
% 4.14/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.14/1.28
% 4.14/1.28
% 4.14/1.28 % ------
% 4.14/1.28 % Current options:
% 4.14/1.28 % ------
% 4.14/1.28
% 4.14/1.28
% 4.14/1.28 %
% 4.14/1.28
% 4.14/1.28 % ------ Proving...
% 4.14/1.28 %
% 4.14/1.28
% 4.14/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.14/1.28
% 4.14/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.28
% 4.14/1.28
%------------------------------------------------------------------------------