%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM045-1 : 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 : n010.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 02:23:17 PM UTC 2026
% Result : Unsatisfiable 50.72s 12.93s
% Output : CNFRefutation 50.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 13 unt; 0 def)
% Number of atoms : 115 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 114 ( 54 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 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; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 44 :)
% 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(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction1) ).
fof(f67,axiom,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
fof(f124,axiom,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(restrict(X0,X1,X1),complement(identity_relation)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
fof(f176,negated_conjecture,
restrict(intersection(x,identity_relation),y,y) = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property7_1) ).
fof(f177,plain,
null_class = restrict(intersection(x,identity_relation),y,y),
inference(reorient_equations,[],[f176]) ).
fof(f178,negated_conjecture,
~ irreflexive(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property7_2) ).
fof(f246,plain,
! [X0,X1] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(definition_unfolding,[],[f124,f28]) ).
fof(f269,plain,
null_class = intersection(intersection(x,identity_relation),cross_product(y,y)),
inference(definition_unfolding,[],[f177,f28]) ).
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_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
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_261,plain,
! [X0: $i] :
( member(regular(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_344,negated_conjecture,
intersection(intersection(x,identity_relation),cross_product(y,y)) = null_class,
inference(cnf_transformation,[],[f269]) ).
tcf(c_345,negated_conjecture,
~ irreflexive(x,y),
inference(cnf_transformation,[],[f178]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] :
( ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| irreflexive(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_303]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( irreflexive(X0,X1)
| ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation)) ),
inference(renaming,[status(thm)],[c_458]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i] :
( ~ subclass(intersection(X0,cross_product(X1,X1)),complement(identity_relation))
| ( X1 != y )
| ( X0 != x ) ),
inference(resolution_lifted,[status(thm)],[c_345,c_459]) ).
tcf(c_1365,plain,
~ subclass(intersection(x,cross_product(y,y)),complement(identity_relation)),
inference(unflattening,[status(thm)],[c_1364]) ).
tcf(c_5407,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_210,c_228]) ).
tcf(c_5426,plain,
( subclass(intersection(x,cross_product(y,y)),complement(identity_relation))
| member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_5467,plain,
! [X0: $i] :
( ( complement(X0) = null_class )
| ~ member(regular(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_261,c_230]) ).
tcf(c_5516,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_212,c_209]) ).
tcf(c_5566,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),X0)
| ~ subclass(intersection(x,cross_product(y,y)),X0)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_5567,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class)
| ~ subclass(intersection(x,cross_product(y,y)),universal_class)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))) ),
inference(instantiation,[status(thm)],[c_5566]) ).
tcf(c_5571,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),intersection(x,cross_product(y,y))) ),
inference(instantiation,[status(thm)],[c_227]) ).
tcf(c_5584,plain,
! [X0: $i] :
( member(regular(X0),universal_class)
| ( X0 = null_class ) ),
inference(superposition,[status(thm)],[c_261,c_5516]) ).
tcf(c_6623,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,cross_product(y,y))
| ~ member(X0,intersection(x,identity_relation)) ),
inference(superposition,[status(thm)],[c_344,c_229]) ).
tcf(c_6654,plain,
complement(universal_class) = null_class,
inference(superposition,[status(thm)],[c_5584,c_5467]) ).
tcf(c_6747,plain,
! [X0: $i] :
( member(X0,null_class)
| ~ member(X0,identity_relation)
| ~ member(X0,x)
| ~ member(X0,cross_product(y,y)) ),
inference(superposition,[status(thm)],[c_229,c_6623]) ).
tcf(c_6864,plain,
subclass(intersection(x,cross_product(y,y)),universal_class),
inference(instantiation,[status(thm)],[c_212]) ).
tcf(c_6882,plain,
! [X0: $i] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(superposition,[status(thm)],[c_6654,c_230]) ).
tcf(c_7549,plain,
! [X0: $i,X1: $i] :
( subclass(intersection(X0,cross_product(y,y)),X1)
| member(not_subclass_element(intersection(X0,cross_product(y,y)),X1),null_class)
| ~ member(not_subclass_element(intersection(X0,cross_product(y,y)),X1),identity_relation)
| ~ member(not_subclass_element(intersection(X0,cross_product(y,y)),X1),x) ),
inference(superposition,[status(thm)],[c_5407,c_6747]) ).
tcf(c_12255,plain,
( subclass(intersection(x,cross_product(y,y)),complement(identity_relation))
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),complement(identity_relation)) ),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_89349,plain,
! [X0: $i] :
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),X0)
| member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),complement(X0))
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_89377,plain,
( ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class) ),
inference(instantiation,[status(thm)],[c_6882]) ).
tcf(c_89565,plain,
( subclass(intersection(x,cross_product(y,y)),complement(identity_relation))
| member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),null_class)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation)
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),x) ),
inference(instantiation,[status(thm)],[c_7549]) ).
tcf(c_100595,plain,
( member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),identity_relation)
| member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),complement(identity_relation))
| ~ member(not_subclass_element(intersection(x,cross_product(y,y)),complement(identity_relation)),universal_class) ),
inference(instantiation,[status(thm)],[c_89349]) ).
tcf(c_100596,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_100595,c_89565,c_89377,c_12255,c_6864,c_5571,c_5567,c_5426,c_1365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM045-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 02:45:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 50.72/12.93 % SZS status Started for theBenchmark.p
% 50.72/12.93 % SZS status Unsatisfiable for theBenchmark.p
% 50.72/12.93
% 50.72/12.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.72/12.93
% 50.72/12.93 % ------ iProver source info
% 50.72/12.93
% 50.72/12.93 % git: date: 2026-07-19 20:42:38 +0200
% 50.72/12.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.72/12.93 % git: non_committed_changes: false
% 50.72/12.93
% 50.72/12.93 % ------ Parsing...% successful
% 50.72/12.93
% 50.72/12.93
% 50.72/12.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.72/12.93
% 50.72/12.93 % ------ 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: 4 0s sf_e pe_s pe_e %
% 50.72/12.93
% 50.72/12.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.72/12.93
% 50.72/12.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 50.72/12.93 % ------ Proving...
% 50.72/12.93 % ------ Problem Properties
% 50.72/12.93
% 50.72/12.93 %
% 50.72/12.93 % clauses 116
% 50.72/12.93 % conjectures 1
% 50.72/12.93 % EPR 14
% 50.72/12.93 % Horn 104
% 50.72/12.93 % unary 27
% 50.72/12.93 % binary 58
% 50.72/12.93 % lits 250
% 50.72/12.93 % lits eq 40
% 50.72/12.93 % fd_pure 0
% 50.72/12.93 % fd_pseudo 0
% 50.72/12.93 % fd_cond 5
% 50.72/12.93 % fd_pseudo_cond 10
% 50.72/12.93 % AC symbols 0
% 50.72/12.93
% 50.72/12.93 % ------ Input Options Time Limit: Unbounded
% 50.72/12.93
% 50.72/12.93
% 50.72/12.93 % ------
% 50.72/12.93 % Current options:
% 50.72/12.93 % ------
% 50.72/12.93
% 50.72/12.93
% 50.72/12.93 %
% 50.72/12.93
% 50.72/12.93 % ------ Proving...
% 50.72/12.93 %
% 50.72/12.93
% 50.72/12.93 % SZS status Unsatisfiable for theBenchmark.p
% 50.72/12.93
% 50.72/12.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.72/12.93
% 50.72/12.93
%------------------------------------------------------------------------------