%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 02:23:18 PM UTC 2026
% Result : Unsatisfiable 15.13s 3.25s
% Output : CNFRefutation 15.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 89 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 86 ( 43 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',symmetrization) ).
fof(f126,axiom,
! [X0,X1] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),union(identity_relation,symmetrization_of(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',connected2) ).
fof(f176,negated_conjecture,
subclass(cross_product(y,y),identity_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_connect_class_property4_1) ).
fof(f177,negated_conjecture,
~ connected(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_connect_class_property4_2) ).
fof(f191,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f247,plain,
! [X0,X1] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(X1),complement(domain_of(flip(cross_product(X1,universal_class)))))))))) ),
inference(definition_unfolding,[],[f126,f26,f191]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_212,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(X1),complement(domain_of(flip(cross_product(X1,universal_class)))))))))) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_344,negated_conjecture,
subclass(cross_product(y,y),identity_relation),
inference(cnf_transformation,[],[f176]) ).
tcf(c_345,negated_conjecture,
~ connected(x,y),
inference(cnf_transformation,[],[f177]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(X1),complement(domain_of(flip(cross_product(X1,universal_class)))))))))) ),
inference(prop_impl_just,[status(thm)],[c_305]) ).
tcf(c_1675,plain,
! [X0: $i,X1: $i] :
( ~ subclass(cross_product(X0,X0),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(X1),complement(domain_of(flip(cross_product(X1,universal_class))))))))))
| ( X1 != x )
| ( X0 != y ) ),
inference(resolution_lifted,[status(thm)],[c_345,c_650]) ).
tcf(c_1676,plain,
~ subclass(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(unflattening,[status(thm)],[c_1675]) ).
tcf(c_4868,plain,
( subclass(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))))
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_4869,plain,
( subclass(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))))
| member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),cross_product(y,y)) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_4900,plain,
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))
| member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))))
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),universal_class) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_5212,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),X1)
| ~ subclass(X0,X1)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),X0) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_5220,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),X0)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_227]) ).
tcf(c_6391,plain,
! [X0: $i] :
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),X0)
| ~ subclass(cross_product(y,y),X0)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),cross_product(y,y)) ),
inference(instantiation,[status(thm)],[c_5212]) ).
tcf(c_6392,plain,
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),universal_class)
| ~ subclass(cross_product(y,y),universal_class)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),cross_product(y,y)) ),
inference(instantiation,[status(thm)],[c_6391]) ).
tcf(c_6565,plain,
! [X0: $i] :
( member(X0,identity_relation)
| ~ member(X0,cross_product(y,y)) ),
inference(superposition,[status(thm)],[c_344,c_209]) ).
tcf(c_6573,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_212,c_209]) ).
tcf(c_7095,plain,
! [X0: $i] :
( subclass(cross_product(y,y),X0)
| member(not_subclass_element(cross_product(y,y),X0),identity_relation) ),
inference(superposition,[status(thm)],[c_210,c_6565]) ).
tcf(c_7099,plain,
! [X0: $i] :
( subclass(cross_product(y,y),X0)
| member(not_subclass_element(cross_product(y,y),X0),universal_class) ),
inference(superposition,[status(thm)],[c_7095,c_6573]) ).
tcf(c_7153,plain,
subclass(cross_product(y,y),universal_class),
inference(superposition,[status(thm)],[c_7099,c_211]) ).
tcf(c_8186,plain,
! [X0: $i] :
( ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),X0)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(X0)) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_8209,plain,
! [X0: $i,X1: $i] :
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(X0))
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(complement(X0),X1)) ),
inference(instantiation,[status(thm)],[c_5220]) ).
tcf(c_10749,plain,
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(identity_relation))
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))) ),
inference(instantiation,[status(thm)],[c_8209]) ).
tcf(c_13801,plain,
( ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),complement(identity_relation)) ),
inference(instantiation,[status(thm)],[c_8186]) ).
tcf(c_19442,plain,
( member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),complement(intersection(complement(identity_relation),complement(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),cross_product(y,y)) ),
inference(instantiation,[status(thm)],[c_6391]) ).
tcf(c_19445,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19442,c_13801,c_10749,c_7153,c_6392,c_4900,c_4868,c_4869,c_1676,c_344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM049-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 02:46:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 15.13/3.25 % SZS status Started for theBenchmark.p
% 15.13/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 15.13/3.25
% 15.13/3.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.13/3.25
% 15.13/3.25 % ------ iProver source info
% 15.13/3.25
% 15.13/3.25 % git: date: 2026-07-19 20:42:38 +0200
% 15.13/3.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.13/3.25 % git: non_committed_changes: false
% 15.13/3.25
% 15.13/3.25 % ------ Parsing...% successful
% 15.13/3.25
% 15.13/3.25
% 15.13/3.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.13/3.25
% 15.13/3.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 15.13/3.25
% 15.13/3.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.13/3.25
% 15.13/3.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.13/3.25 % ------ Proving...
% 15.13/3.25 % ------ Problem Properties
% 15.13/3.25
% 15.13/3.25 %
% 15.13/3.25 % clauses 116
% 15.13/3.25 % conjectures 2
% 15.13/3.25 % EPR 15
% 15.13/3.25 % Horn 104
% 15.13/3.25 % unary 27
% 15.13/3.25 % binary 58
% 15.13/3.25 % lits 250
% 15.13/3.25 % lits eq 39
% 15.13/3.25 % fd_pure 0
% 15.13/3.25 % fd_pseudo 0
% 15.13/3.25 % fd_cond 5
% 15.13/3.25 % fd_pseudo_cond 10
% 15.13/3.25 % AC symbols 0
% 15.13/3.25
% 15.13/3.25 % ------ Input Options Time Limit: Unbounded
% 15.13/3.25
% 15.13/3.25
% 15.13/3.25 % ------
% 15.13/3.25 % Current options:
% 15.13/3.25 % ------
% 15.13/3.25
% 15.13/3.25
% 15.13/3.25 %
% 15.13/3.25
% 15.13/3.25 % ------ Proving...
% 15.13/3.25 %
% 15.13/3.25
% 15.13/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 15.13/3.25
% 15.13/3.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.13/3.25
% 15.13/3.25
%------------------------------------------------------------------------------