%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM159-1 : 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 : n009.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 02:23:26 PM UTC 2026
% Result : Unsatisfiable 63.35s 10.35s
% Output : CNFRefutation 63.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 47 ( 23 unt; 0 def)
% Number of atoms : 79 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 27 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 42 :)
% 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(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(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(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(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',image) ).
fof(f154,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',kind_1_ordinals) ).
fof(f176,negated_conjecture,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_to_kind_1_ordinal_1) ).
fof(f178,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f181,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f178,f28]) ).
fof(f259,plain,
kind_1_ordinals = complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f154,f26,f12,f181]) ).
fof(f267,plain,
~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))),kind_1_ordinals),
inference(definition_unfolding,[],[f176,f181]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_211,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_227,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] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_324,plain,
complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))) = kind_1_ordinals,
inference(cnf_transformation,[],[f259]) ).
tcf(c_343,negated_conjecture,
~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))),kind_1_ordinals),
inference(cnf_transformation,[],[f267]) ).
tcf(c_10437,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_211,c_208]) ).
tcf(c_10507,plain,
! [X0: $i,X1: $i] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_209,c_229]) ).
tcf(c_10511,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class) ),
inference(superposition,[status(thm)],[c_230,c_210]) ).
tcf(c_10665,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_209,c_10437]) ).
tcf(c_11222,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ),
inference(superposition,[status(thm)],[c_230,c_10507]) ).
tcf(c_11238,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(X1))
| member(not_subclass_element(X0,complement(X1)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10511,c_10665]) ).
tcf(c_11254,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,complement(intersection(X1,X2)))
| member(not_subclass_element(X0,complement(intersection(X1,X2))),X2) ),
inference(superposition,[status(thm)],[c_11238,c_227]) ).
tcf(c_11256,plain,
! [X0: $i,X1: $i] :
( subclass(X0,complement(complement(X1)))
| ~ member(not_subclass_element(X0,complement(complement(X1))),X1) ),
inference(superposition,[status(thm)],[c_11238,c_229]) ).
tcf(c_83195,plain,
! [X0: $i,X1: $i] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11222,c_10665]) ).
tcf(c_83213,plain,
! [X0: $i] : subclass(complement(complement(X0)),X0),
inference(superposition,[status(thm)],[c_83195,c_210]) ).
tcf(c_84889,plain,
! [X0: $i,X1: $i] : subclass(complement(X0),complement(intersection(X1,X0))),
inference(superposition,[status(thm)],[c_11254,c_10507]) ).
tcf(c_85218,plain,
subclass(complement(complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))))),kind_1_ordinals),
inference(superposition,[status(thm)],[c_324,c_84889]) ).
tcf(c_90866,plain,
! [X0: $i] : subclass(X0,complement(complement(X0))),
inference(superposition,[status(thm)],[c_209,c_11256]) ).
tcf(c_91025,plain,
! [X0: $i] :
( ( complement(complement(X0)) = X0 )
| ~ subclass(complement(complement(X0)),X0) ),
inference(superposition,[status(thm)],[c_90866,c_214]) ).
tcf(c_91029,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_91025,c_83213]) ).
tcf(c_91201,plain,
subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))),kind_1_ordinals),
inference(superposition,[status(thm)],[c_91029,c_85218]) ).
tcf(c_91231,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_91201,c_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM159-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 03:04:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 63.35/10.35 % SZS status Started for theBenchmark.p
% 63.35/10.35 % SZS status Unsatisfiable for theBenchmark.p
% 63.35/10.35
% 63.35/10.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 63.35/10.35
% 63.35/10.35 % ------ iProver source info
% 63.35/10.35
% 63.35/10.35 % git: date: 2026-07-19 20:42:38 +0200
% 63.35/10.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 63.35/10.35 % git: non_committed_changes: false
% 63.35/10.35
% 63.35/10.35 % ------ Parsing...% successful
% 63.35/10.35
% 63.35/10.35
% 63.35/10.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 63.35/10.35
% 63.35/10.35 % ------ 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 %
% 63.35/10.35
% 63.35/10.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 63.35/10.35
% 63.35/10.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 63.35/10.35 % ------ Proving...
% 63.35/10.35 % ------ Problem Properties
% 63.35/10.35
% 63.35/10.35 %
% 63.35/10.35 % clauses 115
% 63.35/10.35 % conjectures 1
% 63.35/10.35 % EPR 14
% 63.35/10.35 % Horn 103
% 63.35/10.35 % unary 26
% 63.35/10.35 % binary 58
% 63.35/10.35 % lits 249
% 63.35/10.35 % lits eq 39
% 63.35/10.35 % fd_pure 0
% 63.35/10.35 % fd_pseudo 0
% 63.35/10.35 % fd_cond 5
% 63.35/10.35 % fd_pseudo_cond 10
% 63.35/10.35 % AC symbols 0
% 63.35/10.35
% 63.35/10.35 % ------ Input Options Time Limit: Unbounded
% 63.35/10.35
% 63.35/10.35
% 63.35/10.35 % ------
% 63.35/10.35 % Current options:
% 63.35/10.35 % ------
% 63.35/10.35
% 63.35/10.35
% 63.35/10.35 %
% 63.35/10.35
% 63.35/10.35 % ------ Proving...
% 63.35/10.35 %
% 63.35/10.35
% 63.35/10.35 % SZS status Unsatisfiable for theBenchmark.p
% 63.35/10.35
% 63.35/10.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 63.35/10.36
% 63.35/10.36
%------------------------------------------------------------------------------