%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU323+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 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 02:51:43 PM UTC 2026
% Result : Theorem 230.90s 50.15s
% Output : Proof 230.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 45
% Syntax : Number of formulae : 241 ( 97 unt; 0 def)
% Number of atoms : 825 ( 158 equ)
% Maximal formula atoms : 49 ( 3 avg)
% Number of connectives : 1020 ( 436 ~; 260 |; 264 &)
% ( 10 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 18 con; 0-4 aty)
% Number of variables : 421 ( 23 sgn 268 !; 40 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f425,lemma,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ( closed_subset(B,A)
<=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f425_nnf,plain,
! [A] :
( ! [B] :
( ( ( ~ open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(nnf_transformation,[status(thm)],[f425]) ).
fof(f425_sk,plain,
! [A,B] :
( ( ( ~ open_subset(subset_complement(the_carrier(A),B),A)
| closed_subset(B,A) )
& ( open_subset(subset_complement(the_carrier(A),B),A)
| ~ closed_subset(B,A) ) )
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(skolemisation,[status(esa)],[f425_nnf]) ).
cnf(c2159,plain,
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(esa)],[f425_sk]) ).
cnf(t172,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,ifeq(closed_subset(X2,X1),true,open_subset(subset_complement(the_carrier(X1),X2),X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2159]) ).
cnf(t337,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,ifeq(closed_subset(X2,X1),true,open_subset(subset_complement(the_carrier(X1),X2),X1),true),true),true) = true,
inference(orient,[status(thm)],[t172]) ).
fof(f160,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f160_nnf,plain,
! [A,B] :
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(nnf_transformation,[status(thm)],[f160]) ).
fof(f160_sk,plain,
! [A,B] :
( element(topstr_closure(A,B),powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(skolemisation,[status(esa)],[f160_nnf]) ).
cnf(c552,plain,
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(esa)],[f160_sk]) ).
cnf(t164,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,element(topstr_closure(X1,X2),powerset(the_carrier(X1))),true),true) = true,
inference(equality_encoding,[status(esa)],[c552]) ).
cnf(t346,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,element(topstr_closure(X1,X2),powerset(the_carrier(X1))),true),true) = true,
inference(orient,[status(thm)],[t164]) ).
fof(f147,axiom,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f147_nnf,plain,
! [A,B] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f147]) ).
fof(f147_sk,plain,
! [B,A] :
( element(subset_complement(A,B),powerset(A))
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f147_nnf]) ).
cnf(c539,plain,
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f147_sk]) ).
cnf(t118,plain,
ifeq(element(X1,powerset(X2)),true,element(subset_complement(X2,X1),powerset(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c539]) ).
cnf(t286,plain,
ifeq(element(X1,powerset(X2)),true,element(subset_complement(X2,X1),powerset(X2)),true) = true,
inference(orient,[status(thm)],[t118]) ).
fof(f482,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f482_neg,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
inference(negated_conjecture,[status(cth)],[f482]) ).
fof(f482_nnf,plain,
? [A] :
( ? [B] :
( ~ open_subset(interior(A,B),A)
& element(B,powerset(the_carrier(A))) )
& top_str(A)
& topological_space(A) ),
inference(nnf_transformation,[status(thm)],[f482_neg]) ).
fof(f482_sk,plain,
( ~ open_subset(interior(sk342,sk343),sk342)
& element(sk343,powerset(the_carrier(sk342)))
& top_str(sk342)
& topological_space(sk342) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk342,sk343])],[f482_nnf]) ).
cnf(c2261,plain,
element(sk343,powerset(the_carrier(sk342))),
inference(cnf_transformation,[status(esa)],[f482_sk]) ).
cnf(t41,plain,
element(sk343,powerset(the_carrier(sk342))) = true,
inference(equality_encoding,[status(esa)],[c2261]) ).
cnf(t589,plain,
element(sk343,powerset(the_carrier(sk342))) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t595,plain,
true = ifeq(true,true,element(subset_complement(the_carrier(sk342),sk343),powerset(the_carrier(sk342))),true),
inference(cp,[status(thm)],[t286,t589]) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t184,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t42]) ).
cnf(t126691,plain,
true = element(subset_complement(the_carrier(sk342),sk343),powerset(the_carrier(sk342))),
inference(step,[status(thm)],[t595,t184]) ).
cnf(t2858,plain,
element(subset_complement(the_carrier(sk342),sk343),powerset(the_carrier(sk342))) = true,
inference(orient,[status(thm)],[t126691]) ).
cnf(t2873,plain,
true = ifeq(top_str(sk342),true,ifeq(true,true,element(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),powerset(the_carrier(sk342))),true),true),
inference(cp,[status(thm)],[t346,t2858]) ).
cnf(c2260,plain,
top_str(sk342),
inference(cnf_transformation,[status(esa)],[f482_sk]) ).
cnf(t8,plain,
top_str(sk342) = true,
inference(equality_encoding,[status(esa)],[c2260]) ).
cnf(t914,plain,
top_str(sk342) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t128069,plain,
true = ifeq(true,true,ifeq(true,true,element(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),powerset(the_carrier(sk342))),true),true),
inference(step,[status(thm)],[t2873,t914]) ).
cnf(t128070,plain,
true = ifeq(true,true,element(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),powerset(the_carrier(sk342))),true),
inference(step,[status(thm)],[t128069,t184]) ).
cnf(t128071,plain,
true = element(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),powerset(the_carrier(sk342))),
inference(step,[status(thm)],[t128070,t184]) ).
cnf(t125523,plain,
element(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),powerset(the_carrier(sk342))) = true,
inference(orient,[status(thm)],[t128071]) ).
cnf(t125551,plain,
true = ifeq(top_str(sk342),true,ifeq(true,true,ifeq(closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true,open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),true),true),true),
inference(cp,[status(thm)],[t337,t125523]) ).
cnf(t128072,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true,open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),true),true),true),
inference(step,[status(thm)],[t125551,t914]) ).
cnf(t128073,plain,
true = ifeq(true,true,ifeq(closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true,open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),true),true),
inference(step,[status(thm)],[t128072,t184]) ).
cnf(t128074,plain,
true = ifeq(closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true,open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),true),
inference(step,[status(thm)],[t128073,t184]) ).
fof(f215,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> closed_subset(topstr_closure(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f215_nnf,plain,
! [A,B] :
( closed_subset(topstr_closure(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(nnf_transformation,[status(thm)],[f215]) ).
fof(f215_sk,plain,
! [A,B] :
( closed_subset(topstr_closure(A,B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(skolemisation,[status(esa)],[f215_nnf]) ).
cnf(c643,plain,
( closed_subset(topstr_closure(X0,X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[status(esa)],[f215_sk]) ).
cnf(t169,plain,
ifeq(topological_space(X1),true,ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,closed_subset(topstr_closure(X1,X2),X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c643]) ).
cnf(t358,plain,
ifeq(topological_space(X1),true,ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,closed_subset(topstr_closure(X1,X2),X1),true),true),true) = true,
inference(orient,[status(thm)],[t169]) ).
cnf(t2880,plain,
true = ifeq(topological_space(sk342),true,ifeq(top_str(sk342),true,ifeq(true,true,closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true),true),true),
inference(cp,[status(thm)],[t358,t2858]) ).
cnf(c2259,plain,
topological_space(sk342),
inference(cnf_transformation,[status(esa)],[f482_sk]) ).
cnf(t9,plain,
topological_space(sk342) = true,
inference(equality_encoding,[status(esa)],[c2259]) ).
cnf(t959,plain,
topological_space(sk342) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t126728,plain,
true = ifeq(true,true,ifeq(top_str(sk342),true,ifeq(true,true,closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true),true),true),
inference(step,[status(thm)],[t2880,t959]) ).
cnf(t126729,plain,
true = ifeq(top_str(sk342),true,ifeq(true,true,closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true),true),
inference(step,[status(thm)],[t126728,t184]) ).
cnf(t126730,plain,
true = ifeq(true,true,ifeq(true,true,closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true),true),
inference(step,[status(thm)],[t126729,t914]) ).
cnf(t126731,plain,
true = ifeq(true,true,closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),true),
inference(step,[status(thm)],[t126730,t184]) ).
cnf(t126732,plain,
true = closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342),
inference(step,[status(thm)],[t126731,t184]) ).
cnf(t3400,plain,
closed_subset(topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)),sk342) = true,
inference(orient,[status(thm)],[t126732]) ).
cnf(t128075,plain,
true = ifeq(true,true,open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),true),
inference(step,[status(thm)],[t128074,t3400]) ).
cnf(t128076,plain,
true = open_subset(subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))),sk342),
inference(step,[status(thm)],[t128075,t184]) ).
fof(f64,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f64_nnf,plain,
! [A] :
( ! [B] :
( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [A,B] :
( interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c244,plain,
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t180,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,interior(X1,X2),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))),
inference(equality_encoding,[status(esa)],[c244]) ).
cnf(t997,plain,
ifeq(top_str(X1),true,ifeq(element(X2,powerset(the_carrier(X1))),true,interior(X1,X2),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))),subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))),
inference(orient,[status(thm)],[t180]) ).
cnf(t1001,plain,
subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))) = ifeq(top_str(sk342),true,ifeq(true,true,interior(sk342,sk343),subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)))),subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)))),
inference(cp,[status(thm)],[t997,t589]) ).
cnf(t127926,plain,
subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))) = ifeq(true,true,ifeq(true,true,interior(sk342,sk343),subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)))),subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)))),
inference(step,[status(thm)],[t1001,t914]) ).
cnf(t127927,plain,
subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))) = ifeq(true,true,interior(sk342,sk343),subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343)))),
inference(step,[status(thm)],[t127926,t184]) ).
cnf(t127928,plain,
subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))) = interior(sk342,sk343),
inference(step,[status(thm)],[t127927,t184]) ).
cnf(t101929,plain,
subset_complement(the_carrier(sk342),topstr_closure(sk342,subset_complement(the_carrier(sk342),sk343))) = interior(sk342,sk343),
inference(orient,[status(thm)],[t127928]) ).
cnf(t128077,plain,
true = open_subset(interior(sk342,sk343),sk342),
inference(step,[status(thm)],[t128076,t101929]) ).
cnf(c2262,plain,
~ open_subset(interior(sk342,sk343),sk342),
inference(cnf_transformation,[status(esa)],[f482_sk]) ).
cnf(t43,plain,
open_subset(interior(sk342,sk343),sk342) = false,
inference(equality_encoding,[status(esa)],[c2262]) ).
cnf(t1192,plain,
open_subset(interior(sk342,sk343),sk342) = false,
inference(orient,[status(thm)],[t43]) ).
cnf(t128078,plain,
true = false,
inference(step,[status(thm)],[t128077,t1192]) ).
cnf(t125575,plain,
false = true,
inference(orient,[status(thm)],[t128078]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f45,axiom,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> ! [C] :
( element(C,powerset(the_carrier(A)))
=> ( C = topstr_closure(A,B)
<=> ! [D] :
( in(D,the_carrier(A))
=> ( in(D,C)
<=> ! [E] :
( element(E,powerset(the_carrier(A)))
=> ~ ( disjoint(B,E)
& in(D,E)
& open_subset(E,A) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(f45_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( ( ( ! [E] :
( ~ disjoint(B,E)
| ~ in(D,E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) )
& ~ in(D,C) )
| ( ? [E] :
( disjoint(B,E)
& in(D,E)
& open_subset(E,A)
& element(E,powerset(the_carrier(A))) )
& in(D,C) ) )
& in(D,the_carrier(A)) )
| C = topstr_closure(A,B) )
& ( ! [D] :
( ( ( ? [E] :
( disjoint(B,E)
& in(D,E)
& open_subset(E,A)
& element(E,powerset(the_carrier(A))) )
| in(D,C) )
& ( ! [E] :
( ~ disjoint(B,E)
| ~ in(D,E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ in(D,the_carrier(A)) )
| C != topstr_closure(A,B) ) )
| ~ element(C,powerset(the_carrier(A))) )
| ~ element(B,powerset(the_carrier(A))) )
| ~ top_str(A) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [A,B,C,D,E] :
( ( ( ( ( ( ( ~ disjoint(B,E)
| ~ in(sk11(A,B,C),E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) )
& ~ in(sk11(A,B,C),C) )
| ( disjoint(B,sk12(A,B,C))
& in(sk11(A,B,C),sk12(A,B,C))
& open_subset(sk12(A,B,C),A)
& element(sk12(A,B,C),powerset(the_carrier(A)))
& in(sk11(A,B,C),C) ) )
& in(sk11(A,B,C),the_carrier(A)) )
| C = topstr_closure(A,B) )
& ( ( ( ( disjoint(B,sk10(A,B,C,D))
& in(D,sk10(A,B,C,D))
& open_subset(sk10(A,B,C,D),A)
& element(sk10(A,B,C,D),powerset(the_carrier(A))) )
| in(D,C) )
& ( ~ disjoint(B,E)
| ~ in(D,E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A)))
| ~ in(D,C) ) )
| ~ in(D,the_carrier(A))
| C != topstr_closure(A,B) ) )
| ~ element(C,powerset(the_carrier(A)))
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12])],[f45_nnf]) ).
cnf(c129,plain,
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,X2)
| ~ in(X3,the_carrier(X0))
| X2 != topstr_closure(X0,X1)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f65,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = fiber(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(ordered_pair(D,B),A)
& D != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_wellord1) ).
fof(f65_nnf,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( in(ordered_pair(D,B),A)
& D != B
& ~ in(D,C) )
| ( ( ~ in(ordered_pair(D,B),A)
| D = B )
& in(D,C) ) )
| C = fiber(A,B) )
& ( ! [D] :
( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,C,B,D] :
( ( ( ( in(ordered_pair(sk37(A,B,C),B),A)
& sk37(A,B,C) != B
& ~ in(sk37(A,B,C),C) )
| ( ( ~ in(ordered_pair(sk37(A,B,C),B),A)
| sk37(A,B,C) = B )
& in(sk37(A,B,C),C) )
| C = fiber(A,B) )
& ( ( ( ~ in(ordered_pair(D,B),A)
| D = B
| in(D,C) )
& ( ( in(ordered_pair(D,B),A)
& D != B )
| ~ in(D,C) ) )
| C != fiber(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk37])],[f65_nnf]) ).
cnf(c245,plain,
( X3 != X1
| ~ in(X3,X2)
| X2 != fiber(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
fof(f67,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f67_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B] :
( ( in(sk40(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk40])],[f67_nnf]) ).
cnf(c263,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
fof(f94,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f94_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( ~ in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f94]) ).
fof(f94_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk73(A,B,C),B)
& in(sk73(A,B,C),A)
& ~ in(sk73(A,B,C),C) )
| ( ( in(sk73(A,B,C),B)
| ~ in(sk73(A,B,C),A) )
& in(sk73(A,B,C),C) )
| C = set_difference(A,B) )
& ( ( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk73])],[f94_nnf]) ).
cnf(c395,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
fof(f115,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f115_nnf,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [A,B] :
( ( A = B
| ~ subset(A,B)
| proper_subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c504,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
fof(f196,axiom,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(f196_nnf,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c598,plain,
~ empty(singleton(X0)),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
fof(f197,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f197_nnf,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c600,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
fof(f199,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f199_nnf,plain,
! [A] : ~ empty(succ(A)),
inference(nnf_transformation,[status(thm)],[f199]) ).
fof(f199_sk,plain,
! [A] : ~ empty(succ(A)),
inference(skolemisation,[status(esa)],[f199_nnf]) ).
cnf(c606,plain,
~ empty(succ(X0)),
inference(cnf_transformation,[status(esa)],[f199_sk]) ).
fof(f200,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal2) ).
fof(f200_nnf,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(nnf_transformation,[status(thm)],[f200]) ).
fof(f200_sk,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(skolemisation,[status(esa)],[f200_nnf]) ).
cnf(c610,plain,
~ empty(omega),
inference(cnf_transformation,[status(esa)],[f200_sk]) ).
fof(f204,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f204_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f204]) ).
fof(f204_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f204_nnf]) ).
cnf(c619,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f204_sk]) ).
fof(f206,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f206_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f206]) ).
fof(f206_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f206_nnf]) ).
cnf(c621,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f206_sk]) ).
fof(f210,axiom,
! [A] :
( ( natural(A)
& ordinal(A) )
=> ( natural(succ(A))
& ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_arytm_3) ).
fof(f210_nnf,plain,
! [A] :
( ( natural(succ(A))
& ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ natural(A)
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f210]) ).
fof(f210_sk,plain,
! [A] :
( ( natural(succ(A))
& ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ natural(A)
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f210_nnf]) ).
cnf(c626,plain,
( ~ empty(succ(X0))
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f210_sk]) ).
fof(f214,axiom,
! [A] : ~ empty(singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f214_nnf,plain,
! [A] : ~ empty(singleton(A)),
inference(nnf_transformation,[status(thm)],[f214]) ).
fof(f214_sk,plain,
! [A] : ~ empty(singleton(A)),
inference(skolemisation,[status(esa)],[f214_nnf]) ).
cnf(c642,plain,
~ empty(singleton(X0)),
inference(cnf_transformation,[status(esa)],[f214_sk]) ).
fof(f228,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_ordinal1) ).
fof(f228_nnf,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f228]) ).
fof(f228_sk,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f228_nnf]) ).
cnf(c679,plain,
( ~ empty(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f228_sk]) ).
fof(f230,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f230_nnf,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f230]) ).
fof(f230_sk,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f230_nnf]) ).
cnf(c684,plain,
~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f230_sk]) ).
fof(f255,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f255_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f255]) ).
fof(f255_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f255_nnf]) ).
cnf(c729,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f255_sk]) ).
fof(f257,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f257_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f257]) ).
fof(f257_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f257_nnf]) ).
cnf(c733,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f257_sk]) ).
fof(f259,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f259_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f259]) ).
fof(f259_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f259_nnf]) ).
cnf(c735,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f259_sk]) ).
fof(f276,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f276_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f276]) ).
fof(f276_sk,plain,
( natural(sk117)
& ordinal(sk117)
& epsilon_connected(sk117)
& epsilon_transitive(sk117)
& ~ empty(sk117) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk117])],[f276_nnf]) ).
cnf(c774,plain,
~ empty(sk117),
inference(cnf_transformation,[status(esa)],[f276_sk]) ).
fof(f277,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f277_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f277]) ).
fof(f277_sk,plain,
( finite(sk118)
& ~ empty(sk118) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk118])],[f277_nnf]) ).
cnf(c779,plain,
~ empty(sk118),
inference(cnf_transformation,[status(esa)],[f277_sk]) ).
fof(f280,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(f280_nnf,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f280]) ).
fof(f280_sk,plain,
( v5_membered(sk121)
& v4_membered(sk121)
& v3_membered(sk121)
& v2_membered(sk121)
& v1_membered(sk121)
& ~ empty(sk121) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk121])],[f280_nnf]) ).
cnf(c787,plain,
~ empty(sk121),
inference(cnf_transformation,[status(esa)],[f280_sk]) ).
fof(f292,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f292_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f292]) ).
fof(f292_sk,plain,
( relation(sk133)
& ~ empty(sk133) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk133])],[f292_nnf]) ).
cnf(c834,plain,
~ empty(sk133),
inference(cnf_transformation,[status(esa)],[f292_sk]) ).
fof(f294,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f294_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f294]) ).
fof(f294_sk,plain,
~ empty(sk135),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk135])],[f294_nnf]) ).
cnf(c838,plain,
~ empty(sk135),
inference(cnf_transformation,[status(esa)],[f294_sk]) ).
fof(f297,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f297_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f297]) ).
fof(f297_sk,plain,
( ordinal(sk138)
& epsilon_connected(sk138)
& epsilon_transitive(sk138)
& ~ empty(sk138) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk138])],[f297_nnf]) ).
cnf(c845,plain,
~ empty(sk138),
inference(cnf_transformation,[status(esa)],[f297_sk]) ).
fof(f299,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f299_nnf,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f299]) ).
fof(f299_sk,plain,
( ~ empty_carrier(sk140)
& one_sorted_str(sk140) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk140])],[f299_nnf]) ).
cnf(c852,plain,
~ empty_carrier(sk140),
inference(cnf_transformation,[status(esa)],[f299_sk]) ).
fof(f321,lemma,
( ( ! [D] :
( ordinal(D)
=> ( ( ! [K] :
( ordinal(K)
=> ( in(K,D)
=> ( in(K,omega)
=> ! [L] :
( element(L,powerset(powerset(K)))
=> ~ ( ! [M] :
~ ( ! [N] :
( ( subset(M,N)
& in(N,L) )
=> N = M )
& in(M,L) )
& L != empty_set ) ) ) ) )
& being_limit_ordinal(D) )
=> ( ( in(D,omega)
=> ! [O] :
( element(O,powerset(powerset(D)))
=> ~ ( ! [P] :
~ ( ! [Q] :
( ( subset(P,Q)
& in(Q,O) )
=> Q = P )
& in(P,O) )
& O != empty_set ) ) )
| D = empty_set ) ) )
& ! [D] :
( ordinal(D)
=> ( ( in(D,omega)
=> ! [E] :
( element(E,powerset(powerset(D)))
=> ~ ( ! [F] :
~ ( ! [G] :
( ( subset(F,G)
& in(G,E) )
=> G = F )
& in(F,E) )
& E != empty_set ) ) )
=> ( in(succ(D),omega)
=> ! [H] :
( element(H,powerset(powerset(succ(D))))
=> ~ ( ! [I] :
~ ( ! [J] :
( ( subset(I,J)
& in(J,H) )
=> J = I )
& in(I,H) )
& H != empty_set ) ) ) ) )
& ( in(empty_set,omega)
=> ! [A] :
( element(A,powerset(powerset(empty_set)))
=> ~ ( ! [B] :
~ ( ! [C] :
( ( subset(B,C)
& in(C,A) )
=> C = B )
& in(B,A) )
& A != empty_set ) ) ) )
=> ! [D] :
( ordinal(D)
=> ( in(D,omega)
=> ! [R] :
( element(R,powerset(powerset(D)))
=> ~ ( ! [S] :
~ ( ! [T] :
( ( subset(S,T)
& in(T,R) )
=> T = S )
& in(S,R) )
& R != empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
fof(f321_nnf,plain,
( ! [D] :
( ! [R] :
( ? [S] :
( ! [T] :
( T = S
| ~ subset(S,T)
| ~ in(T,R) )
& in(S,R) )
| R = empty_set
| ~ element(R,powerset(powerset(D))) )
| ~ in(D,omega)
| ~ ordinal(D) )
| ? [D] :
( ? [O] :
( ! [P] :
( ? [Q] :
( Q != P
& subset(P,Q)
& in(Q,O) )
| ~ in(P,O) )
& O != empty_set
& element(O,powerset(powerset(D))) )
& in(D,omega)
& D != empty_set
& ! [K] :
( ! [L] :
( ? [M] :
( ! [N] :
( N = M
| ~ subset(M,N)
| ~ in(N,L) )
& in(M,L) )
| L = empty_set
| ~ element(L,powerset(powerset(K))) )
| ~ in(K,omega)
| ~ in(K,D)
| ~ ordinal(K) )
& being_limit_ordinal(D)
& ordinal(D) )
| ? [D] :
( ? [H] :
( ! [I] :
( ? [J] :
( J != I
& subset(I,J)
& in(J,H) )
| ~ in(I,H) )
& H != empty_set
& element(H,powerset(powerset(succ(D)))) )
& in(succ(D),omega)
& ( ! [E] :
( ? [F] :
( ! [G] :
( G = F
| ~ subset(F,G)
| ~ in(G,E) )
& in(F,E) )
| E = empty_set
| ~ element(E,powerset(powerset(D))) )
| ~ in(D,omega) )
& ordinal(D) )
| ( ? [A] :
( ! [B] :
( ? [C] :
( C != B
& subset(B,C)
& in(C,A) )
| ~ in(B,A) )
& A != empty_set
& element(A,powerset(powerset(empty_set))) )
& in(empty_set,omega) ) ),
inference(nnf_transformation,[status(thm)],[f321]) ).
fof(f321_sk,plain,
! [B,E,G,I,K,L,N,P,D,R,T] :
( ( ( T = sk167(D,R)
| ~ subset(sk167(D,R),T)
| ~ in(T,R) )
& in(sk167(D,R),R) )
| R = empty_set
| ~ element(R,powerset(powerset(D)))
| ~ in(D,omega)
| ~ ordinal(D)
| ( ( ( sk166(P) != P
& subset(P,sk166(P))
& in(sk166(P),sk165) )
| ~ in(P,sk165) )
& sk165 != empty_set
& element(sk165,powerset(powerset(sk163)))
& in(sk163,omega)
& sk163 != empty_set
& ( ( ( N = sk164(K,L)
| ~ subset(sk164(K,L),N)
| ~ in(N,L) )
& in(sk164(K,L),L) )
| L = empty_set
| ~ element(L,powerset(powerset(K)))
| ~ in(K,omega)
| ~ in(K,sk163)
| ~ ordinal(K) )
& being_limit_ordinal(sk163)
& ordinal(sk163) )
| ( ( ( sk162(I) != I
& subset(I,sk162(I))
& in(sk162(I),sk161) )
| ~ in(I,sk161) )
& sk161 != empty_set
& element(sk161,powerset(powerset(succ(sk159))))
& in(succ(sk159),omega)
& ( ( ( G = sk160(E)
| ~ subset(sk160(E),G)
| ~ in(G,E) )
& in(sk160(E),E) )
| E = empty_set
| ~ element(E,powerset(powerset(sk159)))
| ~ in(sk159,omega) )
& ordinal(sk159) )
| ( ( ( sk158(B) != B
& subset(B,sk158(B))
& in(sk158(B),sk157) )
| ~ in(B,sk157) )
& sk157 != empty_set
& element(sk157,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk157,sk158,sk159,sk160,sk161,sk162,sk163,sk164,sk165,sk166,sk167])],[f321_nnf]) ).
cnf(c996,plain,
( sk158(X1) != X1
| ~ def1(X1) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1001,plain,
( sk157 != empty_set
| ~ def3(X1) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1010,plain,
( ~ subset(sk160(X4),X6)
| ~ in(X6,X4)
| ~ def6(X6,X4) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1032,plain,
( sk162(X8) != X8
| ~ def13(X8) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1037,plain,
( sk161 != empty_set
| ~ def15(X8) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1055,plain,
( ~ subset(sk164(X10,X11),X13)
| ~ in(X13,X11)
| ~ def21(X13,X11,X10) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1086,plain,
( sk166(X15) != X15
| ~ def31(X15) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1091,plain,
( sk165 != empty_set
| ~ def33(X15) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1100,plain,
( sk163 != empty_set
| ~ def36(X15) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
cnf(c1112,plain,
( ~ subset(sk167(X3,X17),X19)
| ~ in(X19,X17)
| ~ def40(X19,X17,X3) ),
inference(cnf_transformation,[status(esa),new_symbols(definition,[def0,def1,def2,def3,def4,def5,def6,def7,def8,def9,def10,def11,def12,def13,def14,def15,def16,def17,def18,def19,def20,def21,def22,def23,def24,def25,def26,def27,def28,def29,def30,def31,def32,def33,def34,def35,def36,def37,def38,def39,def40,def41,def42,def43,def44,def45,def46,def47])],[f321_sk]) ).
fof(f451,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f451_nnf,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f451]) ).
fof(f451_sk,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f451_nnf]) ).
cnf(c2206,plain,
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f451_sk]) ).
fof(f454,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f454_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f454]) ).
fof(f454_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk335(A,B),B)
& in(sk335(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk335])],[f454_nnf]) ).
cnf(c2212,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f454_sk]) ).
fof(f458,lemma,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f458_nnf,plain,
! [A] :
( ( ( ~ being_limit_ordinal(A)
| ! [B] :
( A != succ(B)
| ~ ordinal(B) ) )
& ( ? [B] :
( A = succ(B)
& ordinal(B) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f458]) ).
fof(f458_sk,plain,
! [A,B] :
( ( ( ~ being_limit_ordinal(A)
| A != succ(B)
| ~ ordinal(B) )
& ( ( A = succ(sk337(A))
& ordinal(sk337(A)) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk337])],[f458_nnf]) ).
cnf(c2221,plain,
( ~ being_limit_ordinal(X0)
| X0 != succ(X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f458_sk]) ).
fof(f480,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f480_nnf,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f480]) ).
fof(f480_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk341(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk341])],[f480_nnf]) ).
cnf(c2257,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f480_sk]) ).
fof(f486,lemma,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f486_nnf,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f486]) ).
fof(f486_sk,plain,
! [C,A,B] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(skolemisation,[status(esa)],[f486_nnf]) ).
cnf(c2284,plain,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f486_sk]) ).
fof(f491,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f491_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f491]) ).
fof(f491_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f491_nnf]) ).
cnf(c2291,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f491_sk]) ).
fof(f495,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f495_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f495]) ).
fof(f495_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f495_nnf]) ).
cnf(c2297,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f495_sk]) ).
fof(f500,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f500_nnf,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(nnf_transformation,[status(thm)],[f500]) ).
fof(f500_sk,plain,
! [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) = A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) != A ) ),
inference(skolemisation,[status(esa)],[f500_nnf]) ).
cnf(c2304,plain,
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[status(esa)],[f500_sk]) ).
fof(f511,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f511_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f511]) ).
fof(f511_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f511_nnf]) ).
cnf(c2322,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f511_sk]) ).
fof(f513,axiom,
! [A,B] :
~ ( ! [C] :
~ ( ! [D] :
~ ( in(D,C)
& in(D,B) )
& in(C,B) )
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
fof(f513_nnf,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f513]) ).
fof(f513_sk,plain,
! [A,B,D] :
( ( ( ~ in(D,sk349(A,B))
| ~ in(D,B) )
& in(sk349(A,B),B) )
| ~ in(A,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk349])],[f513_nnf]) ).
cnf(c2326,plain,
( ~ in(X3,sk349(X0,X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f513_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c129,c245,c263,c395,c504,c598,c600,c606,c610,c619,c621,c626,c642,c679,c684,c729,c733,c735,c774,c779,c787,c834,c838,c845,c852,c996,c1001,c1010,c1032,c1037,c1055,c1086,c1091,c1100,c1112,c2206,c2212,c2221,c2257,c2262,c2284,c2291,c2297,c2304,c2322,c2326]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t125575]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU323+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/20.39 % Computer : n008.cluster.edu
% 0.10/20.39 % Model : x86_64 x86_64
% 0.10/20.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.39 % Memory : 8046.5625MB
% 0.10/20.39 % OS : Linux 6.8.0-71-generic
% 0.10/20.39 % CPULimit : 300
% 0.10/20.39 % WCLimit : 300
% 0.10/20.39 % DateTime : Thu Sep 24 13:43:01 UTC 2026
% 0.10/20.40 % CPUTime :
% 0.10/20.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 230.90/50.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 230.90/50.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------