%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU373+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 : n017.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 02:51:53 PM UTC 2026
% Result : Theorem 107.74s 14.63s
% Output : Proof 107.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 69
% Syntax : Number of formulae : 340 ( 119 unt; 0 def)
% Number of atoms : 1494 ( 190 equ)
% Maximal formula atoms : 49 ( 4 avg)
% Number of connectives : 1739 ( 585 ~; 313 |; 766 &)
% ( 14 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-3 aty)
% Number of functors : 68 ( 68 usr; 30 con; 0-4 aty)
% Number of variables : 524 ( 31 sgn 327 !; 66 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f79,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( rel_str(B)
=> ( subrelstr(B,A)
<=> ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
fof(f79_nnf,plain,
! [A] :
( ! [B] :
( ( ( ~ subset(the_InternalRel(B),the_InternalRel(A))
| ~ subset(the_carrier(B),the_carrier(A))
| subrelstr(B,A) )
& ( ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) )
| ~ subrelstr(B,A) ) )
| ~ rel_str(B) )
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f79]) ).
fof(f79_sk,plain,
! [A,B] :
( ( ( ~ subset(the_InternalRel(B),the_InternalRel(A))
| ~ subset(the_carrier(B),the_carrier(A))
| subrelstr(B,A) )
& ( ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) )
| ~ subrelstr(B,A) ) )
| ~ rel_str(B)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f79_nnf]) ).
cnf(c260,plain,
( subset(the_carrier(X1),the_carrier(X0))
| ~ subrelstr(X1,X0)
| ~ rel_str(X1)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f79_sk]) ).
cnf(t209,plain,
ifeq(rel_str(X1),true,ifeq(rel_str(X2),true,ifeq(subrelstr(X2,X1),true,subset(the_carrier(X2),the_carrier(X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c260]) ).
cnf(t381,plain,
ifeq(rel_str(X1),true,ifeq(rel_str(X2),true,ifeq(subrelstr(X2,X1),true,subset(the_carrier(X2),the_carrier(X1)),true),true),true) = true,
inference(orient,[status(thm)],[t209]) ).
fof(f178,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( net_str(C,A)
=> ( subnetstr(C,A,B)
<=> ( the_mapping(A,C) = relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
& subrelstr(C,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
fof(f178_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( the_mapping(A,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
| ~ subrelstr(C,B)
| subnetstr(C,A,B) )
& ( ( the_mapping(A,C) = relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
& subrelstr(C,B) )
| ~ subnetstr(C,A,B) ) )
| ~ net_str(C,A) )
| ~ net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [A,B,C] :
( ( ( the_mapping(A,C) != relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
| ~ subrelstr(C,B)
| subnetstr(C,A,B) )
& ( ( the_mapping(A,C) = relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
& subrelstr(C,B) )
| ~ subnetstr(C,A,B) ) )
| ~ net_str(C,A)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c733,plain,
( subrelstr(X2,X1)
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X2,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(t219,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,ifeq(net_str(X3,X1),true,ifeq(subnetstr(X3,X1,X2),true,subrelstr(X3,X2),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c733]) ).
cnf(t405,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,ifeq(net_str(X3,X1),true,ifeq(subnetstr(X3,X1,X2),true,subrelstr(X3,X2),true),true),true),true) = true,
inference(orient,[status(thm)],[t219]) ).
fof(f594,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> subset(the_carrier(C),the_carrier(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_yellow_6) ).
fof(f594_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> subset(the_carrier(C),the_carrier(B)) ) ) ),
inference(negated_conjecture,[status(cth)],[f594]) ).
fof(f594_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ subset(the_carrier(C),the_carrier(B))
& subnetstr(C,A,B) )
& net_str(B,A) )
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f594_neg]) ).
fof(f594_sk,plain,
( ~ subset(the_carrier(sk477),the_carrier(sk476))
& subnetstr(sk477,sk475,sk476)
& net_str(sk476,sk475)
& one_sorted_str(sk475) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk475,sk476,sk477])],[f594_nnf]) ).
cnf(c3310,plain,
subnetstr(sk477,sk475,sk476),
inference(cnf_transformation,[status(esa)],[f594_sk]) ).
cnf(t66,plain,
subnetstr(sk477,sk475,sk476) = true,
inference(equality_encoding,[status(esa)],[c3310]) ).
cnf(t752,plain,
subnetstr(sk477,sk475,sk476) = true,
inference(orient,[status(thm)],[t66]) ).
cnf(t754,plain,
true = ifeq(one_sorted_str(sk475),true,ifeq(net_str(sk476,sk475),true,ifeq(net_str(sk477,sk475),true,ifeq(true,true,subrelstr(sk477,sk476),true),true),true),true),
inference(cp,[status(thm)],[t405,t752]) ).
cnf(c3308,plain,
one_sorted_str(sk475),
inference(cnf_transformation,[status(esa)],[f594_sk]) ).
cnf(t6,plain,
one_sorted_str(sk475) = true,
inference(equality_encoding,[status(esa)],[c3308]) ).
cnf(t712,plain,
one_sorted_str(sk475) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t4898,plain,
true = ifeq(true,true,ifeq(net_str(sk476,sk475),true,ifeq(net_str(sk477,sk475),true,ifeq(true,true,subrelstr(sk477,sk476),true),true),true),true),
inference(step,[status(thm)],[t754,t712]) ).
cnf(t67,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t224,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t67]) ).
cnf(t4899,plain,
true = ifeq(net_str(sk476,sk475),true,ifeq(net_str(sk477,sk475),true,ifeq(true,true,subrelstr(sk477,sk476),true),true),true),
inference(step,[status(thm)],[t4898,t224]) ).
cnf(c3309,plain,
net_str(sk476,sk475),
inference(cnf_transformation,[status(esa)],[f594_sk]) ).
cnf(t32,plain,
net_str(sk476,sk475) = true,
inference(equality_encoding,[status(esa)],[c3309]) ).
cnf(t742,plain,
net_str(sk476,sk475) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t4900,plain,
true = ifeq(true,true,ifeq(net_str(sk477,sk475),true,ifeq(true,true,subrelstr(sk477,sk476),true),true),true),
inference(step,[status(thm)],[t4899,t742]) ).
cnf(t4901,plain,
true = ifeq(net_str(sk477,sk475),true,ifeq(true,true,subrelstr(sk477,sk476),true),true),
inference(step,[status(thm)],[t4900,t224]) ).
fof(f275,axiom,
! [A,B] :
( ( net_str(B,A)
& one_sorted_str(A) )
=> ! [C] :
( subnetstr(C,A,B)
=> net_str(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
fof(f275_nnf,plain,
! [A,B] :
( ! [C] :
( net_str(C,A)
| ~ subnetstr(C,A,B) )
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f275]) ).
fof(f275_sk,plain,
! [A,B,C] :
( net_str(C,A)
| ~ subnetstr(C,A,B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f275_nnf]) ).
cnf(c864,plain,
( net_str(X2,X0)
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f275_sk]) ).
cnf(t207,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,ifeq(subnetstr(X3,X1,X2),true,net_str(X3,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c864]) ).
cnf(t406,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,ifeq(subnetstr(X3,X1,X2),true,net_str(X3,X1),true),true),true) = true,
inference(orient,[status(thm)],[t207]) ).
cnf(t753,plain,
true = ifeq(one_sorted_str(sk475),true,ifeq(net_str(sk476,sk475),true,ifeq(true,true,net_str(sk477,sk475),true),true),true),
inference(cp,[status(thm)],[t406,t752]) ).
cnf(t4602,plain,
true = ifeq(true,true,ifeq(net_str(sk476,sk475),true,ifeq(true,true,net_str(sk477,sk475),true),true),true),
inference(step,[status(thm)],[t753,t712]) ).
cnf(t4603,plain,
true = ifeq(net_str(sk476,sk475),true,ifeq(true,true,net_str(sk477,sk475),true),true),
inference(step,[status(thm)],[t4602,t224]) ).
cnf(t4604,plain,
true = ifeq(true,true,ifeq(true,true,net_str(sk477,sk475),true),true),
inference(step,[status(thm)],[t4603,t742]) ).
cnf(t4605,plain,
true = ifeq(true,true,net_str(sk477,sk475),true),
inference(step,[status(thm)],[t4604,t224]) ).
cnf(t4606,plain,
true = net_str(sk477,sk475),
inference(step,[status(thm)],[t4605,t224]) ).
cnf(t1006,plain,
net_str(sk477,sk475) = true,
inference(orient,[status(thm)],[t4606]) ).
cnf(t4902,plain,
true = ifeq(true,true,ifeq(true,true,subrelstr(sk477,sk476),true),true),
inference(step,[status(thm)],[t4901,t1006]) ).
cnf(t4903,plain,
true = ifeq(true,true,subrelstr(sk477,sk476),true),
inference(step,[status(thm)],[t4902,t224]) ).
cnf(t4904,plain,
true = subrelstr(sk477,sk476),
inference(step,[status(thm)],[t4903,t224]) ).
cnf(t4527,plain,
subrelstr(sk477,sk476) = true,
inference(orient,[status(thm)],[t4904]) ).
cnf(t4530,plain,
true = ifeq(rel_str(sk476),true,ifeq(rel_str(sk477),true,ifeq(true,true,subset(the_carrier(sk477),the_carrier(sk476)),true),true),true),
inference(cp,[status(thm)],[t381,t4527]) ).
fof(f268,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f268_nnf,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f268]) ).
fof(f268_sk,plain,
! [A,B] :
( rel_str(B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(skolemisation,[status(esa)],[f268_nnf]) ).
cnf(c856,plain,
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(esa)],[f268_sk]) ).
cnf(t155,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,rel_str(X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c856]) ).
cnf(t407,plain,
ifeq(one_sorted_str(X1),true,ifeq(net_str(X2,X1),true,rel_str(X2),true),true) = true,
inference(orient,[status(thm)],[t155]) ).
cnf(t743,plain,
true = ifeq(one_sorted_str(sk475),true,ifeq(true,true,rel_str(sk476),true),true),
inference(cp,[status(thm)],[t407,t742]) ).
cnf(t4597,plain,
true = ifeq(true,true,ifeq(true,true,rel_str(sk476),true),true),
inference(step,[status(thm)],[t743,t712]) ).
cnf(t4598,plain,
true = ifeq(true,true,rel_str(sk476),true),
inference(step,[status(thm)],[t4597,t224]) ).
cnf(t4599,plain,
true = rel_str(sk476),
inference(step,[status(thm)],[t4598,t224]) ).
cnf(t978,plain,
rel_str(sk476) = true,
inference(orient,[status(thm)],[t4599]) ).
cnf(t4905,plain,
true = ifeq(true,true,ifeq(rel_str(sk477),true,ifeq(true,true,subset(the_carrier(sk477),the_carrier(sk476)),true),true),true),
inference(step,[status(thm)],[t4530,t978]) ).
cnf(t4906,plain,
true = ifeq(rel_str(sk477),true,ifeq(true,true,subset(the_carrier(sk477),the_carrier(sk476)),true),true),
inference(step,[status(thm)],[t4905,t224]) ).
cnf(t1007,plain,
true = ifeq(one_sorted_str(sk475),true,ifeq(true,true,rel_str(sk477),true),true),
inference(cp,[status(thm)],[t407,t1006]) ).
cnf(t4607,plain,
true = ifeq(true,true,ifeq(true,true,rel_str(sk477),true),true),
inference(step,[status(thm)],[t1007,t712]) ).
cnf(t4608,plain,
true = ifeq(true,true,rel_str(sk477),true),
inference(step,[status(thm)],[t4607,t224]) ).
cnf(t4609,plain,
true = rel_str(sk477),
inference(step,[status(thm)],[t4608,t224]) ).
cnf(t1013,plain,
rel_str(sk477) = true,
inference(orient,[status(thm)],[t4609]) ).
cnf(t4907,plain,
true = ifeq(true,true,ifeq(true,true,subset(the_carrier(sk477),the_carrier(sk476)),true),true),
inference(step,[status(thm)],[t4906,t1013]) ).
cnf(t4908,plain,
true = ifeq(true,true,subset(the_carrier(sk477),the_carrier(sk476)),true),
inference(step,[status(thm)],[t4907,t224]) ).
cnf(t4909,plain,
true = subset(the_carrier(sk477),the_carrier(sk476)),
inference(step,[status(thm)],[t4908,t224]) ).
cnf(c3311,plain,
~ subset(the_carrier(sk477),the_carrier(sk476)),
inference(cnf_transformation,[status(esa)],[f594_sk]) ).
cnf(t69,plain,
subset(the_carrier(sk477),the_carrier(sk476)) = false,
inference(equality_encoding,[status(esa)],[c3311]) ).
cnf(t812,plain,
subset(the_carrier(sk477),the_carrier(sk476)) = false,
inference(orient,[status(thm)],[t69]) ).
cnf(t4910,plain,
true = false,
inference(step,[status(thm)],[t4909,t812]) ).
cnf(t4531,plain,
false = true,
inference(orient,[status(thm)],[t4910]) ).
fof(f2,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f2_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f3,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f3_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f20,axiom,
! [A] :
( rel_str(A)
=> ( with_suprema_relstr(A)
=> ~ empty_carrier(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
fof(f20_nnf,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_suprema_relstr(A)
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_suprema_relstr(A)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c54,plain,
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f34,axiom,
! [A] :
( rel_str(A)
=> ( with_infima_relstr(A)
=> ~ empty_carrier(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
fof(f34_nnf,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_infima_relstr(A)
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [A] :
( ~ empty_carrier(A)
| ~ with_infima_relstr(A)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c90,plain,
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
fof(f77,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(f77_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)],[f77]) ).
fof(f77_sk,plain,
! [A,B,C,D,E] :
( ( ( ( ( ( ( ~ disjoint(B,E)
| ~ in(sk18(A,B,C),E)
| ~ open_subset(E,A)
| ~ element(E,powerset(the_carrier(A))) )
& ~ in(sk18(A,B,C),C) )
| ( disjoint(B,sk19(A,B,C))
& in(sk18(A,B,C),sk19(A,B,C))
& open_subset(sk19(A,B,C),A)
& element(sk19(A,B,C),powerset(the_carrier(A)))
& in(sk18(A,B,C),C) ) )
& in(sk18(A,B,C),the_carrier(A)) )
| C = topstr_closure(A,B) )
& ( ( ( ( disjoint(B,sk17(A,B,C,D))
& in(D,sk17(A,B,C,D))
& open_subset(sk17(A,B,C,D),A)
& element(sk17(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,[sk17,sk18,sk19])],[f77_nnf]) ).
cnf(c235,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)],[f77_sk]) ).
fof(f107,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(f107_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)],[f107]) ).
fof(f107_sk,plain,
! [A,C,B,D] :
( ( ( ( in(ordered_pair(sk53(A,B,C),B),A)
& sk53(A,B,C) != B
& ~ in(sk53(A,B,C),C) )
| ( ( ~ in(ordered_pair(sk53(A,B,C),B),A)
| sk53(A,B,C) = B )
& in(sk53(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,[sk53])],[f107_nnf]) ).
cnf(c390,plain,
( X3 != X1
| ~ in(X3,X2)
| X2 != fiber(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f107_sk]) ).
fof(f109,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f109_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [A,B] :
( ( in(sk56(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk56])],[f109_nnf]) ).
cnf(c408,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
fof(f114,axiom,
! [A] :
( centered(A)
<=> ( ! [B] :
~ ( set_meet(B) = empty_set
& finite(B)
& subset(B,A)
& B != empty_set )
& A != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_compts_1) ).
fof(f114_nnf,plain,
! [A] :
( ( ? [B] :
( set_meet(B) = empty_set
& finite(B)
& subset(B,A)
& B != empty_set )
| A = empty_set
| centered(A) )
& ( ( ! [B] :
( set_meet(B) != empty_set
| ~ finite(B)
| ~ subset(B,A)
| B = empty_set )
& A != empty_set )
| ~ centered(A) ) ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [A,B] :
( ( ( set_meet(sk59(A)) = empty_set
& finite(sk59(A))
& subset(sk59(A),A)
& sk59(A) != empty_set )
| A = empty_set
| centered(A) )
& ( ( ( set_meet(B) != empty_set
| ~ finite(B)
| ~ subset(B,A)
| B = empty_set )
& A != empty_set )
| ~ centered(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk59])],[f114_nnf]) ).
cnf(c423,plain,
( X0 != empty_set
| ~ centered(X0) ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
fof(f123,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f123_nnf,plain,
! [A,B] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(nnf_transformation,[status(thm)],[f123]) ).
fof(f123_sk,plain,
! [B,A] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(skolemisation,[status(esa)],[f123_nnf]) ).
cnf(c457,plain,
( X1 != union(X0)
| ~ proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f123_sk]) ).
fof(f147,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(f147_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)],[f147]) ).
fof(f147_sk,plain,
! [C,A,B,D] :
( ( ( ~ in(sk94(A,B,C),B)
& in(sk94(A,B,C),A)
& ~ in(sk94(A,B,C),C) )
| ( ( in(sk94(A,B,C),B)
| ~ in(sk94(A,B,C),A) )
& in(sk94(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,[sk94])],[f147_nnf]) ).
cnf(c571,plain,
( ~ in(X3,X1)
| ~ in(X3,X2)
| X2 != set_difference(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f147_sk]) ).
fof(f176,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f176_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)],[f176]) ).
fof(f176_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)],[f176_nnf]) ).
cnf(c713,plain,
( X0 != X1
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f176_sk]) ).
fof(f305,axiom,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finset_1) ).
fof(f305_nnf,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(nnf_transformation,[status(thm)],[f305]) ).
fof(f305_sk,plain,
! [A] :
( finite(singleton(A))
& ~ empty(singleton(A)) ),
inference(skolemisation,[status(esa)],[f305_nnf]) ).
cnf(c905,plain,
~ empty(singleton(X0)),
inference(cnf_transformation,[status(esa)],[f305_sk]) ).
fof(f306,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(f306_nnf,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f306]) ).
fof(f306_sk,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(skolemisation,[status(esa)],[f306_nnf]) ).
cnf(c907,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f306_sk]) ).
fof(f308,axiom,
! [A] :
( complete_latt_str(boole_lattice(A))
& boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).
fof(f308_nnf,plain,
! [A] :
( complete_latt_str(boole_lattice(A))
& boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(nnf_transformation,[status(thm)],[f308]) ).
fof(f308_sk,plain,
! [A] :
( complete_latt_str(boole_lattice(A))
& boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(skolemisation,[status(esa)],[f308_nnf]) ).
cnf(c913,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f308_sk]) ).
fof(f309,axiom,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(f309_nnf,plain,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(nnf_transformation,[status(thm)],[f309]) ).
fof(f309_sk,plain,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(skolemisation,[status(esa)],[f309_nnf]) ).
cnf(c930,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f309_sk]) ).
fof(f311,axiom,
! [A] : ~ empty(succ(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal1) ).
fof(f311_nnf,plain,
! [A] : ~ empty(succ(A)),
inference(nnf_transformation,[status(thm)],[f311]) ).
fof(f311_sk,plain,
! [A] : ~ empty(succ(A)),
inference(skolemisation,[status(esa)],[f311_nnf]) ).
cnf(c934,plain,
~ empty(succ(X0)),
inference(cnf_transformation,[status(esa)],[f311_sk]) ).
fof(f312,axiom,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_ordinal2) ).
fof(f312_nnf,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(nnf_transformation,[status(thm)],[f312]) ).
fof(f312_sk,plain,
( ~ empty(omega)
& ordinal(omega)
& epsilon_connected(omega)
& epsilon_transitive(omega) ),
inference(skolemisation,[status(esa)],[f312_nnf]) ).
cnf(c938,plain,
~ empty(omega),
inference(cnf_transformation,[status(esa)],[f312_sk]) ).
fof(f316,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f316_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f316]) ).
fof(f316_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f316_nnf]) ).
cnf(c947,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f316_sk]) ).
fof(f318,axiom,
! [A,B] :
( relation_of2(B,singleton(A),singleton(A))
=> ( trivial_carrier(rel_str_of(singleton(A),B))
& strict_rel_str(rel_str_of(singleton(A),B))
& ~ empty_carrier(rel_str_of(singleton(A),B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_yellow_0) ).
fof(f318_nnf,plain,
! [A,B] :
( ( trivial_carrier(rel_str_of(singleton(A),B))
& strict_rel_str(rel_str_of(singleton(A),B))
& ~ empty_carrier(rel_str_of(singleton(A),B)) )
| ~ relation_of2(B,singleton(A),singleton(A)) ),
inference(nnf_transformation,[status(thm)],[f318]) ).
fof(f318_sk,plain,
! [B,A] :
( ( trivial_carrier(rel_str_of(singleton(A),B))
& strict_rel_str(rel_str_of(singleton(A),B))
& ~ empty_carrier(rel_str_of(singleton(A),B)) )
| ~ relation_of2(B,singleton(A),singleton(A)) ),
inference(skolemisation,[status(esa)],[f318_nnf]) ).
cnf(c949,plain,
( ~ empty_carrier(rel_str_of(singleton(X0),X1))
| ~ relation_of2(X1,singleton(X0),singleton(X0)) ),
inference(cnf_transformation,[status(esa)],[f318_sk]) ).
fof(f320,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f320_nnf,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f320]) ).
fof(f320_sk,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f320_nnf]) ).
cnf(c959,plain,
~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f320_sk]) ).
fof(f324,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(f324_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)],[f324]) ).
fof(f324_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)],[f324_nnf]) ).
cnf(c964,plain,
( ~ empty(succ(X0))
| ~ natural(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f324_sk]) ).
fof(f325,axiom,
! [A,B] :
( finite(unordered_pair(A,B))
& ~ empty(unordered_pair(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finset_1) ).
fof(f325_nnf,plain,
! [A,B] :
( finite(unordered_pair(A,B))
& ~ empty(unordered_pair(A,B)) ),
inference(nnf_transformation,[status(thm)],[f325]) ).
fof(f325_sk,plain,
! [A,B] :
( finite(unordered_pair(A,B))
& ~ empty(unordered_pair(A,B)) ),
inference(skolemisation,[status(esa)],[f325_nnf]) ).
cnf(c969,plain,
~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f325_sk]) ).
fof(f328,axiom,
! [A] :
( lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_lattice3) ).
fof(f328_nnf,plain,
! [A] :
( lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(nnf_transformation,[status(thm)],[f328]) ).
fof(f328_sk,plain,
! [A] :
( lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(skolemisation,[status(esa)],[f328_nnf]) ).
cnf(c978,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f328_sk]) ).
fof(f334,axiom,
! [A] : ~ empty(singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f334_nnf,plain,
! [A] : ~ empty(singleton(A)),
inference(nnf_transformation,[status(thm)],[f334]) ).
fof(f334_sk,plain,
! [A] : ~ empty(singleton(A)),
inference(skolemisation,[status(esa)],[f334_nnf]) ).
cnf(c1008,plain,
~ empty(singleton(X0)),
inference(cnf_transformation,[status(esa)],[f334_sk]) ).
fof(f350,axiom,
! [A] :
( boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_lattice3) ).
fof(f350_nnf,plain,
! [A] :
( boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(nnf_transformation,[status(thm)],[f350]) ).
fof(f350_sk,plain,
! [A] :
( boolean_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& lattice(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& join_commutative(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
inference(skolemisation,[status(esa)],[f350_nnf]) ).
cnf(c1058,plain,
~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f350_sk]) ).
fof(f353,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(f353_nnf,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f353]) ).
fof(f353_sk,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f353_nnf]) ).
cnf(c1080,plain,
( ~ empty(succ(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f353_sk]) ).
fof(f355,axiom,
! [A,B] : ~ empty(unordered_pair(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f355_nnf,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(nnf_transformation,[status(thm)],[f355]) ).
fof(f355_sk,plain,
! [A,B] : ~ empty(unordered_pair(A,B)),
inference(skolemisation,[status(esa)],[f355_nnf]) ).
cnf(c1085,plain,
~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f355_sk]) ).
fof(f379,axiom,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_yellow_1) ).
fof(f379_nnf,plain,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(nnf_transformation,[status(thm)],[f379]) ).
fof(f379_sk,plain,
! [A] :
( antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(skolemisation,[status(esa)],[f379_nnf]) ).
cnf(c1163,plain,
~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[status(esa)],[f379_sk]) ).
fof(f381,axiom,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_yellow_1) ).
fof(f381_nnf,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(nnf_transformation,[status(thm)],[f381]) ).
fof(f381_sk,plain,
! [A] :
( complete_relstr(boole_POSet(A))
& with_infima_relstr(boole_POSet(A))
& with_suprema_relstr(boole_POSet(A))
& bounded_relstr(boole_POSet(A))
& upper_bounded_relstr(boole_POSet(A))
& lower_bounded_relstr(boole_POSet(A))
& antisymmetric_relstr(boole_POSet(A))
& transitive_relstr(boole_POSet(A))
& reflexive_relstr(boole_POSet(A))
& strict_rel_str(boole_POSet(A))
& ~ empty_carrier(boole_POSet(A)) ),
inference(skolemisation,[status(esa)],[f381_nnf]) ).
cnf(c1170,plain,
~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[status(esa)],[f381_sk]) ).
fof(f396,axiom,
! [A,B] : ~ proper_subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f396_nnf,plain,
! [A,B] : ~ proper_subset(A,A),
inference(nnf_transformation,[status(thm)],[f396]) ).
fof(f396_sk,plain,
! [A] : ~ proper_subset(A,A),
inference(skolemisation,[status(esa)],[f396_nnf]) ).
cnf(c1209,plain,
~ proper_subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f396_sk]) ).
fof(f398,lemma,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f398_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f398]) ).
fof(f398_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f398_nnf]) ).
cnf(c1213,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f398_sk]) ).
fof(f400,lemma,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f400_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f400]) ).
fof(f400_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f400_nnf]) ).
cnf(c1215,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f400_sk]) ).
fof(f417,axiom,
? [A] :
( upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& modular_lattstr(A)
& distributive_lattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc10_lattices) ).
fof(f417_nnf,plain,
? [A] :
( upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& modular_lattstr(A)
& distributive_lattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f417]) ).
fof(f417_sk,plain,
( upper_bounded_semilattstr(sk159)
& lower_bounded_semilattstr(sk159)
& modular_lattstr(sk159)
& distributive_lattstr(sk159)
& lattice(sk159)
& join_absorbing(sk159)
& meet_absorbing(sk159)
& meet_associative(sk159)
& meet_commutative(sk159)
& join_associative(sk159)
& join_commutative(sk159)
& strict_latt_str(sk159)
& ~ empty_carrier(sk159)
& latt_str(sk159) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk159])],[f417_nnf]) ).
cnf(c1255,plain,
~ empty_carrier(sk159),
inference(cnf_transformation,[status(esa)],[f417_sk]) ).
fof(f418,axiom,
? [A] :
( bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc11_lattices) ).
fof(f418_nnf,plain,
? [A] :
( bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f418]) ).
fof(f418_sk,plain,
( bounded_lattstr(sk160)
& upper_bounded_semilattstr(sk160)
& lower_bounded_semilattstr(sk160)
& lattice(sk160)
& join_absorbing(sk160)
& meet_absorbing(sk160)
& meet_associative(sk160)
& meet_commutative(sk160)
& join_associative(sk160)
& join_commutative(sk160)
& strict_latt_str(sk160)
& ~ empty_carrier(sk160)
& latt_str(sk160) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk160])],[f418_nnf]) ).
cnf(c1269,plain,
~ empty_carrier(sk160),
inference(cnf_transformation,[status(esa)],[f418_sk]) ).
fof(f419,axiom,
? [A] :
( complemented_lattstr(A)
& bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc12_lattices) ).
fof(f419_nnf,plain,
? [A] :
( complemented_lattstr(A)
& bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f419]) ).
fof(f419_sk,plain,
( complemented_lattstr(sk161)
& bounded_lattstr(sk161)
& upper_bounded_semilattstr(sk161)
& lower_bounded_semilattstr(sk161)
& lattice(sk161)
& join_absorbing(sk161)
& meet_absorbing(sk161)
& meet_associative(sk161)
& meet_commutative(sk161)
& join_associative(sk161)
& join_commutative(sk161)
& strict_latt_str(sk161)
& ~ empty_carrier(sk161)
& latt_str(sk161) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk161])],[f419_nnf]) ).
cnf(c1282,plain,
~ empty_carrier(sk161),
inference(cnf_transformation,[status(esa)],[f419_sk]) ).
fof(f420,axiom,
? [A] :
( boolean_lattstr(A)
& complemented_lattstr(A)
& bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& distributive_lattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_lattices) ).
fof(f420_nnf,plain,
? [A] :
( boolean_lattstr(A)
& complemented_lattstr(A)
& bounded_lattstr(A)
& upper_bounded_semilattstr(A)
& lower_bounded_semilattstr(A)
& distributive_lattstr(A)
& lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f420]) ).
fof(f420_sk,plain,
( boolean_lattstr(sk162)
& complemented_lattstr(sk162)
& bounded_lattstr(sk162)
& upper_bounded_semilattstr(sk162)
& lower_bounded_semilattstr(sk162)
& distributive_lattstr(sk162)
& lattice(sk162)
& join_absorbing(sk162)
& meet_absorbing(sk162)
& meet_associative(sk162)
& meet_commutative(sk162)
& join_associative(sk162)
& join_commutative(sk162)
& strict_latt_str(sk162)
& ~ empty_carrier(sk162)
& latt_str(sk162) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk162])],[f420_nnf]) ).
cnf(c1296,plain,
~ empty_carrier(sk162),
inference(cnf_transformation,[status(esa)],[f420_sk]) ).
fof(f421,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(f421_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f421]) ).
fof(f421_sk,plain,
( natural(sk163)
& ordinal(sk163)
& epsilon_connected(sk163)
& epsilon_transitive(sk163)
& ~ empty(sk163) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk163])],[f421_nnf]) ).
cnf(c1311,plain,
~ empty(sk163),
inference(cnf_transformation,[status(esa)],[f421_sk]) ).
fof(f422,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f422_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f422]) ).
fof(f422_sk,plain,
( finite(sk164)
& ~ empty(sk164) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk164])],[f422_nnf]) ).
cnf(c1316,plain,
~ empty(sk164),
inference(cnf_transformation,[status(esa)],[f422_sk]) ).
fof(f425,axiom,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_lattice3) ).
fof(f425_nnf,plain,
? [A] :
( complete_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f425]) ).
fof(f425_sk,plain,
( complete_relstr(sk167)
& antisymmetric_relstr(sk167)
& transitive_relstr(sk167)
& reflexive_relstr(sk167)
& strict_rel_str(sk167)
& ~ empty_carrier(sk167)
& rel_str(sk167) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk167])],[f425_nnf]) ).
cnf(c1325,plain,
~ empty_carrier(sk167),
inference(cnf_transformation,[status(esa)],[f425_sk]) ).
fof(f426,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(f426_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)],[f426]) ).
fof(f426_sk,plain,
( v5_membered(sk168)
& v4_membered(sk168)
& v3_membered(sk168)
& v2_membered(sk168)
& v1_membered(sk168)
& ~ empty(sk168) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk168])],[f426_nnf]) ).
cnf(c1331,plain,
~ empty(sk168),
inference(cnf_transformation,[status(esa)],[f426_sk]) ).
fof(f436,axiom,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_yellow_0) ).
fof(f436_nnf,plain,
? [A] :
( trivial_carrier(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f436]) ).
fof(f436_sk,plain,
( trivial_carrier(sk178)
& complete_relstr(sk178)
& with_infima_relstr(sk178)
& with_suprema_relstr(sk178)
& antisymmetric_relstr(sk178)
& transitive_relstr(sk178)
& reflexive_relstr(sk178)
& strict_rel_str(sk178)
& ~ empty_carrier(sk178)
& rel_str(sk178) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk178])],[f436_nnf]) ).
cnf(c1361,plain,
~ empty_carrier(sk178),
inference(cnf_transformation,[status(esa)],[f436_sk]) ).
fof(f440,axiom,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_lattice3) ).
fof(f440_nnf,plain,
? [A] :
( complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f440]) ).
fof(f440_sk,plain,
( complete_relstr(sk182)
& with_infima_relstr(sk182)
& with_suprema_relstr(sk182)
& antisymmetric_relstr(sk182)
& transitive_relstr(sk182)
& reflexive_relstr(sk182)
& strict_rel_str(sk182)
& ~ empty_carrier(sk182)
& rel_str(sk182) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk182])],[f440_nnf]) ).
cnf(c1391,plain,
~ empty_carrier(sk182),
inference(cnf_transformation,[status(esa)],[f440_sk]) ).
fof(f441,axiom,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_orders_2) ).
fof(f441_nnf,plain,
? [A] :
( antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& strict_rel_str(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f441]) ).
fof(f441_sk,plain,
( antisymmetric_relstr(sk183)
& transitive_relstr(sk183)
& reflexive_relstr(sk183)
& strict_rel_str(sk183)
& ~ empty_carrier(sk183)
& rel_str(sk183) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk183])],[f441_nnf]) ).
cnf(c1400,plain,
~ empty_carrier(sk183),
inference(cnf_transformation,[status(esa)],[f441_sk]) ).
fof(f444,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f444_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f444]) ).
fof(f444_sk,plain,
( relation(sk186)
& ~ empty(sk186) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk186])],[f444_nnf]) ).
cnf(c1415,plain,
~ empty(sk186),
inference(cnf_transformation,[status(esa)],[f444_sk]) ).
fof(f446,axiom,
! [A] :
? [B] :
( ~ proper_element(B,powerset(A))
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_tex_2) ).
fof(f446_nnf,plain,
! [A] :
? [B] :
( ~ proper_element(B,powerset(A))
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f446]) ).
fof(f446_sk,plain,
! [A] :
( ~ proper_element(sk188(A),powerset(A))
& element(sk188(A),powerset(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk188])],[f446_nnf]) ).
cnf(c1420,plain,
~ proper_element(sk188(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f446_sk]) ).
fof(f448,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f448_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f448]) ).
fof(f448_sk,plain,
~ empty(sk190),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk190])],[f448_nnf]) ).
cnf(c1424,plain,
~ empty(sk190),
inference(cnf_transformation,[status(esa)],[f448_sk]) ).
fof(f449,axiom,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_yellow_0) ).
fof(f449_nnf,plain,
? [A] :
( bounded_relstr(A)
& upper_bounded_relstr(A)
& lower_bounded_relstr(A)
& complete_relstr(A)
& with_infima_relstr(A)
& with_suprema_relstr(A)
& antisymmetric_relstr(A)
& transitive_relstr(A)
& reflexive_relstr(A)
& ~ empty_carrier(A)
& rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f449]) ).
fof(f449_sk,plain,
( bounded_relstr(sk191)
& upper_bounded_relstr(sk191)
& lower_bounded_relstr(sk191)
& complete_relstr(sk191)
& with_infima_relstr(sk191)
& with_suprema_relstr(sk191)
& antisymmetric_relstr(sk191)
& transitive_relstr(sk191)
& reflexive_relstr(sk191)
& ~ empty_carrier(sk191)
& rel_str(sk191) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk191])],[f449_nnf]) ).
cnf(c1426,plain,
~ empty_carrier(sk191),
inference(cnf_transformation,[status(esa)],[f449_sk]) ).
fof(f453,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f453_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f453]) ).
fof(f453_sk,plain,
( ordinal(sk195)
& epsilon_connected(sk195)
& epsilon_transitive(sk195)
& ~ empty(sk195) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk195])],[f453_nnf]) ).
cnf(c1444,plain,
~ empty(sk195),
inference(cnf_transformation,[status(esa)],[f453_sk]) ).
fof(f456,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f456_nnf,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(nnf_transformation,[status(thm)],[f456]) ).
fof(f456_sk,plain,
( ~ empty_carrier(sk198)
& one_sorted_str(sk198) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk198])],[f456_nnf]) ).
cnf(c1458,plain,
~ empty_carrier(sk198),
inference(cnf_transformation,[status(esa)],[f456_sk]) ).
fof(f460,axiom,
? [A] :
( strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_lattices) ).
fof(f460_nnf,plain,
? [A] :
( strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f460]) ).
fof(f460_sk,plain,
( strict_latt_str(sk202)
& ~ empty_carrier(sk202)
& latt_str(sk202) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk202])],[f460_nnf]) ).
cnf(c1468,plain,
~ empty_carrier(sk202),
inference(cnf_transformation,[status(esa)],[f460_sk]) ).
fof(f463,axiom,
? [A] :
( lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_lattices) ).
fof(f463_nnf,plain,
? [A] :
( lattice(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& strict_latt_str(A)
& ~ empty_carrier(A)
& latt_str(A) ),
inference(nnf_transformation,[status(thm)],[f463]) ).
fof(f463_sk,plain,
( lattice(sk205)
& join_absorbing(sk205)
& meet_absorbing(sk205)
& meet_associative(sk205)
& meet_commutative(sk205)
& join_associative(sk205)
& join_commutative(sk205)
& strict_latt_str(sk205)
& ~ empty_carrier(sk205)
& latt_str(sk205) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk205])],[f463_nnf]) ).
cnf(c1476,plain,
~ empty_carrier(sk205),
inference(cnf_transformation,[status(esa)],[f463_sk]) ).
fof(f500,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(f500_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)],[f500]) ).
fof(f500_sk,plain,
! [B,E,G,I,K,L,N,P,D,R,T] :
( ( ( T = sk239(D,R)
| ~ subset(sk239(D,R),T)
| ~ in(T,R) )
& in(sk239(D,R),R) )
| R = empty_set
| ~ element(R,powerset(powerset(D)))
| ~ in(D,omega)
| ~ ordinal(D)
| ( ( ( sk238(P) != P
& subset(P,sk238(P))
& in(sk238(P),sk237) )
| ~ in(P,sk237) )
& sk237 != empty_set
& element(sk237,powerset(powerset(sk235)))
& in(sk235,omega)
& sk235 != empty_set
& ( ( ( N = sk236(K,L)
| ~ subset(sk236(K,L),N)
| ~ in(N,L) )
& in(sk236(K,L),L) )
| L = empty_set
| ~ element(L,powerset(powerset(K)))
| ~ in(K,omega)
| ~ in(K,sk235)
| ~ ordinal(K) )
& being_limit_ordinal(sk235)
& ordinal(sk235) )
| ( ( ( sk234(I) != I
& subset(I,sk234(I))
& in(sk234(I),sk233) )
| ~ in(I,sk233) )
& sk233 != empty_set
& element(sk233,powerset(powerset(succ(sk231))))
& in(succ(sk231),omega)
& ( ( ( G = sk232(E)
| ~ subset(sk232(E),G)
| ~ in(G,E) )
& in(sk232(E),E) )
| E = empty_set
| ~ element(E,powerset(powerset(sk231)))
| ~ in(sk231,omega) )
& ordinal(sk231) )
| ( ( ( sk230(B) != B
& subset(B,sk230(B))
& in(sk230(B),sk229) )
| ~ in(B,sk229) )
& sk229 != empty_set
& element(sk229,powerset(powerset(empty_set)))
& in(empty_set,omega) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk229,sk230,sk231,sk232,sk233,sk234,sk235,sk236,sk237,sk238,sk239])],[f500_nnf]) ).
cnf(c1719,plain,
( sk230(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])],[f500_sk]) ).
cnf(c1724,plain,
( sk229 != 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])],[f500_sk]) ).
cnf(c1733,plain,
( ~ subset(sk232(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])],[f500_sk]) ).
cnf(c1755,plain,
( sk234(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])],[f500_sk]) ).
cnf(c1760,plain,
( sk233 != 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])],[f500_sk]) ).
cnf(c1778,plain,
( ~ subset(sk236(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])],[f500_sk]) ).
cnf(c1809,plain,
( sk238(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])],[f500_sk]) ).
cnf(c1814,plain,
( sk237 != 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])],[f500_sk]) ).
cnf(c1823,plain,
( sk235 != 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])],[f500_sk]) ).
cnf(c1835,plain,
( ~ subset(sk239(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])],[f500_sk]) ).
fof(f668,lemma,
! [A,B,C] :
~ ( in(C,A)
& in(B,C)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_ordinal1) ).
fof(f668_nnf,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f668]) ).
fof(f668_sk,plain,
! [A,B,C] :
( ~ in(C,A)
| ~ in(B,C)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f668_nnf]) ).
cnf(c3454,plain,
( ~ in(X2,X0)
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f668_sk]) ).
fof(f671,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(f671_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)],[f671]) ).
fof(f671_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,B)
| ~ in(C,A) )
& ( ( in(sk493(A,B),B)
& in(sk493(A,B),A) )
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk493])],[f671_nnf]) ).
cnf(c3460,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[status(esa)],[f671_sk]) ).
fof(f675,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(f675_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)],[f675]) ).
fof(f675_sk,plain,
! [A,B] :
( ( ( ~ being_limit_ordinal(A)
| A != succ(B)
| ~ ordinal(B) )
& ( ( A = succ(sk495(A))
& ordinal(sk495(A)) )
| being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk495])],[f675_nnf]) ).
cnf(c3469,plain,
( ~ being_limit_ordinal(X0)
| X0 != succ(X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f675_sk]) ).
fof(f699,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(f699_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)],[f699]) ).
fof(f699_sk,plain,
! [A,B,C] :
( ( ~ disjoint(A,B)
| ~ in(C,set_intersection2(A,B)) )
& ( in(sk499(A,B),set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk499])],[f699_nnf]) ).
cnf(c3508,plain,
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f699_sk]) ).
fof(f707,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(f707_nnf,plain,
! [A,B,C] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f707]) ).
fof(f707_sk,plain,
! [C,A,B] :
( ~ in(B,C)
| ~ in(B,subset_complement(A,C))
| ~ element(C,powerset(A)) ),
inference(skolemisation,[status(esa)],[f707_nnf]) ).
cnf(c3538,plain,
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f707_sk]) ).
fof(f714,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f714_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f714]) ).
fof(f714_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f714_nnf]) ).
cnf(c3548,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f714_sk]) ).
fof(f715,lemma,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f715_nnf,plain,
! [A,B] :
( ( ( B = A
| proper_element(B,powerset(A)) )
& ( B != A
| ~ proper_element(B,powerset(A)) ) )
| ~ element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f715]) ).
fof(f715_sk,plain,
! [B,A] :
( ( ( B = A
| proper_element(B,powerset(A)) )
& ( B != A
| ~ proper_element(B,powerset(A)) ) )
| ~ element(B,powerset(A)) ),
inference(skolemisation,[status(esa)],[f715_nnf]) ).
cnf(c3549,plain,
( X1 != X0
| ~ proper_element(X1,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[status(esa)],[f715_sk]) ).
fof(f720,lemma,
! [A,B] :
~ ( proper_subset(B,A)
& subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f720_nnf,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f720]) ).
fof(f720_sk,plain,
! [A,B] :
( ~ proper_subset(B,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f720_nnf]) ).
cnf(c3557,plain,
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f720_sk]) ).
fof(f727,lemma,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f727_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)],[f727]) ).
fof(f727_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)],[f727_nnf]) ).
cnf(c3566,plain,
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[status(esa)],[f727_sk]) ).
fof(f740,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f740_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f740]) ).
fof(f740_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f740_nnf]) ).
cnf(c3589,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f740_sk]) ).
fof(f743,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(f743_nnf,plain,
! [A,B] :
( ? [C] :
( ! [D] :
( ~ in(D,C)
| ~ in(D,B) )
& in(C,B) )
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f743]) ).
fof(f743_sk,plain,
! [A,B,D] :
( ( ( ~ in(D,sk506(A,B))
| ~ in(D,B) )
& in(sk506(A,B),B) )
| ~ in(A,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk506])],[f743_nnf]) ).
cnf(c3595,plain,
( ~ in(X3,sk506(X0,X1))
| ~ in(X3,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f743_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2,c3,c54,c90,c235,c390,c408,c423,c457,c571,c713,c905,c907,c913,c930,c934,c938,c947,c949,c959,c964,c969,c978,c1008,c1058,c1080,c1085,c1163,c1170,c1209,c1213,c1215,c1255,c1269,c1282,c1296,c1311,c1316,c1325,c1331,c1361,c1391,c1400,c1415,c1420,c1424,c1426,c1444,c1458,c1468,c1476,c1719,c1724,c1733,c1755,c1760,c1778,c1809,c1814,c1823,c1835,c3311,c3454,c3460,c3469,c3508,c3538,c3548,c3549,c3557,c3566,c3589,c3595]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4531]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU373+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:48:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 107.74/14.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 107.74/14.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------