TSTP Solution File: SET655+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:34:57 EDT 2023
% Result : Theorem 8.38s 1.44s
% Output : CNFRefutation 8.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 110 ( 14 unt; 0 def)
% Number of atoms : 417 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 525 ( 218 ~; 218 |; 40 &)
% ( 12 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 235 (; 227 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( ( subset(B,C)
& subset(D,E) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,D))
=> ( ( subset(B,C)
& subset(D,E) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,D))
=> ( ( subset(B,C)
& subset(D,E) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ~ subset(B,C)
| ~ subset(D,E)
| subset(cross_product(B,D),cross_product(C,E)) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( subset(B,C)
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ subset(B,C)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ( ilf_type(sk0_1(C,B),set_type)
& member(sk0_1(C,B),B)
& ~ member(sk0_1(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f41,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f42,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) )
& ( ilf_type(C,subset_type(B))
| ~ ilf_type(C,member_type(power_set(B))) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f48,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(B,B) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( member(B,power_set(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f51,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ? [D] :
( ilf_type(D,set_type)
& member(D,B)
& ~ member(D,C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ( ~ member(B,power_set(C))
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| member(D,C) ) )
& ( member(B,power_set(C))
| ( ilf_type(sk0_3(C,B),set_type)
& member(sk0_3(C,B),B)
& ~ member(sk0_3(C,B),C) ) ) ) ) ),
inference(skolemization,[status(esa)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| member(sk0_3(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ member(sk0_3(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f57,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f60,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f61,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( empty(C)
| ~ ilf_type(C,set_type)
| ( ( ~ ilf_type(B,member_type(C))
| member(B,C) )
& ( ilf_type(B,member_type(C))
| ~ member(B,C) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f67,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( empty(B)
<=> ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f68,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ? [C] :
( ilf_type(C,set_type)
& member(C,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ( ~ empty(B)
| ! [C] :
( ~ ilf_type(C,set_type)
| ~ member(C,B) ) )
& ( empty(B)
| ( ilf_type(sk0_5(B),set_type)
& member(sk0_5(B),B) ) ) ) ),
inference(skolemization,[status(esa)],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f88,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f89,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ilf_type(F,relation_type(B,D))
& subset(B,C)
& subset(D,E)
& ~ ilf_type(F,relation_type(C,E)) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f90,plain,
( ilf_type(sk0_9,set_type)
& ilf_type(sk0_10,set_type)
& ilf_type(sk0_11,set_type)
& ilf_type(sk0_12,set_type)
& ilf_type(sk0_13,relation_type(sk0_9,sk0_11))
& subset(sk0_9,sk0_10)
& subset(sk0_11,sk0_12)
& ~ ilf_type(sk0_13,relation_type(sk0_10,sk0_12)) ),
inference(skolemization,[status(esa)],[f89]) ).
fof(f95,plain,
ilf_type(sk0_13,relation_type(sk0_9,sk0_11)),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f96,plain,
subset(sk0_9,sk0_10),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f97,plain,
subset(sk0_11,sk0_12),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f98,plain,
~ ilf_type(sk0_13,relation_type(sk0_10,sk0_12)),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f99,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f70]) ).
fof(f100,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X1,member_type(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f88]) ).
fof(f113,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f62,f88]) ).
fof(f114,plain,
! [X0,X1] :
( empty(X0)
| ~ ilf_type(X1,member_type(X0))
| member(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f88]) ).
fof(f115,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f58,f88]) ).
fof(f116,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| ~ member(sk0_3(X0,X1),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f88]) ).
fof(f117,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sk0_3(X1,X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f88]) ).
fof(f118,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,power_set(X0))
| member(sk0_3(X0,X1),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f88]) ).
fof(f119,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sk0_3(X1,X0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f88]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f88]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f88]) ).
fof(f122,plain,
! [X0] : subset(X0,X0),
inference(backward_subsumption_resolution,[status(thm)],[f49,f88]) ).
fof(f124,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f88]) ).
fof(f125,plain,
! [X0,X1] :
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f88]) ).
fof(f126,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f88]) ).
fof(f127,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f88]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f88]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f88]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ilf_type(X1,subset_type(cross_product(X2,X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[f28,f88]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f88]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ilf_type(X1,relation_type(X2,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f27,f88]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f88]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X3,X0)
| ~ subset(X1,X2)
| subset(cross_product(X3,X1),cross_product(X0,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f25,f88]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cross_product(X2,X0),cross_product(X3,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f88]) ).
fof(f147,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f114,f115]) ).
fof(f151,plain,
! [X0,X1,X2] :
( member(X0,power_set(X1))
| ~ subset(X0,X2)
| ~ ilf_type(sk0_3(X1,X0),set_type)
| member(sk0_3(X1,X0),X2) ),
inference(resolution,[status(thm)],[f119,f133]) ).
fof(f152,plain,
! [X0,X1,X2] :
( member(X0,power_set(X1))
| ~ subset(X0,X2)
| member(sk0_3(X1,X0),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f88]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2))))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f125,f139]) ).
fof(f162,plain,
~ ilf_type(sk0_13,member_type(power_set(cross_product(sk0_10,sk0_12)))),
inference(resolution,[status(thm)],[f161,f98]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ subset(power_set(X1),X2)
| ~ ilf_type(X0,set_type)
| member(X0,X2) ),
inference(resolution,[status(thm)],[f147,f133]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ subset(power_set(X1),X2)
| member(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f88]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[status(thm)],[f121,f88]) ).
fof(f172,plain,
( spl0_0
<=> ilf_type(power_set(cross_product(sk0_10,sk0_12)),set_type) ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( ~ ilf_type(power_set(cross_product(sk0_10,sk0_12)),set_type)
| spl0_0 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( spl0_1
<=> member(sk0_13,power_set(cross_product(sk0_10,sk0_12))) ),
introduced(split_symbol_definition) ).
fof(f177,plain,
( ~ member(sk0_13,power_set(cross_product(sk0_10,sk0_12)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( ~ ilf_type(power_set(cross_product(sk0_10,sk0_12)),set_type)
| ~ member(sk0_13,power_set(cross_product(sk0_10,sk0_12))) ),
inference(resolution,[status(thm)],[f162,f100]) ).
fof(f179,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f178,f172,f175]) ).
fof(f180,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f88]) ).
fof(f181,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| ~ member(sk0_3(X1,X2),X0)
| member(X2,power_set(X1)) ),
inference(resolution,[status(thm)],[f170,f117]) ).
fof(f291,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f152,f117]) ).
fof(f292,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f291]) ).
fof(f295,plain,
! [X0,X1,X2,X3] :
( member(cross_product(X0,X1),power_set(cross_product(X2,X3)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X2)
| ~ subset(X1,X3) ),
inference(resolution,[status(thm)],[f292,f141]) ).
fof(f296,plain,
! [X0,X1,X2,X3] :
( member(cross_product(X0,X1),power_set(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X2)
| ~ subset(X1,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f295,f88]) ).
fof(f390,plain,
! [X0,X1,X2] :
( ~ subset(power_set(X0),X1)
| member(X2,X1)
| ~ ilf_type(X2,subset_type(X0)) ),
inference(resolution,[status(thm)],[f166,f127]) ).
fof(f396,plain,
! [X0,X1,X2,X3] :
( ~ subset(power_set(cross_product(X0,X1)),X2)
| member(X3,X2)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f390,f137]) ).
fof(f402,plain,
! [X0,X1,X2] :
( member(X0,power_set(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f396,f122]) ).
fof(f411,plain,
member(sk0_13,power_set(cross_product(sk0_9,sk0_11))),
inference(resolution,[status(thm)],[f402,f95]) ).
fof(f445,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,power_set(X1))
| member(X2,power_set(X1))
| ~ member(X3,power_set(X0))
| ~ member(sk0_3(X1,X2),X3) ),
inference(resolution,[status(thm)],[f197,f170]) ).
fof(f1721,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| member(X2,power_set(X1))
| ~ member(X2,power_set(X0))
| member(X2,power_set(X1)) ),
inference(resolution,[status(thm)],[f445,f119]) ).
fof(f1722,plain,
! [X0,X1,X2] :
( ~ member(X0,power_set(X1))
| member(X2,power_set(X1))
| ~ member(X2,power_set(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f1721]) ).
fof(f2052,plain,
! [X0] :
( ~ member(cross_product(sk0_9,sk0_11),power_set(X0))
| member(sk0_13,power_set(X0)) ),
inference(resolution,[status(thm)],[f1722,f411]) ).
fof(f2110,plain,
! [X0,X1] :
( member(sk0_13,power_set(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ subset(sk0_9,X0)
| ~ subset(sk0_11,X1) ),
inference(resolution,[status(thm)],[f2052,f296]) ).
fof(f2111,plain,
! [X0,X1] :
( member(sk0_13,power_set(cross_product(X0,X1)))
| ~ subset(sk0_9,X0)
| ~ subset(sk0_11,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2110,f88]) ).
fof(f3146,plain,
! [X0] :
( member(sk0_13,power_set(cross_product(X0,sk0_12)))
| ~ subset(sk0_9,X0) ),
inference(resolution,[status(thm)],[f2111,f97]) ).
fof(f3152,plain,
member(sk0_13,power_set(cross_product(sk0_10,sk0_12))),
inference(resolution,[status(thm)],[f3146,f96]) ).
fof(f3153,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f3152,f177]) ).
fof(f3154,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f3153]) ).
fof(f3155,plain,
$false,
inference(sat_refutation,[status(thm)],[f179,f181,f3154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n009.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 10:10:46 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 8.38/1.44 % Refutation found
% 8.38/1.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.38/1.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.38/1.47 % Elapsed time: 1.168640 seconds
% 8.38/1.47 % CPU time: 8.600038 seconds
% 8.38/1.47 % Memory used: 93.996 MB
%------------------------------------------------------------------------------