%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET655+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:43:44 PM UTC 2026
% Result : Theorem 25.68s 3.80s
% Output : Proof 25.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 106 ( 17 unt; 0 def)
% Number of atoms : 409 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 506 ( 203 ~; 220 |; 41 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 214 ( 2 sgn 79 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f18_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c35,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f1,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(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( subset(cross_product(B,D),cross_product(C,E))
| ~ subset(D,E)
| ~ subset(B,C)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D,E] :
( subset(cross_product(B,D),cross_product(C,E))
| ~ subset(D,E)
| ~ subset(B,C)
| ~ ilf_type(E,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p261,plain,
( subset(cross_product(X3,X1),cross_product(X0,X2))
| ~ subset(X1,X2)
| ~ subset(X3,X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c1]) ).
cnf(p385,plain,
( subset(cross_product(X2,X0),cross_product(X3,X1))
| ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p261,c35]) ).
cnf(p513,plain,
( subset(cross_product(X1,X3),cross_product(X2,X0))
| ~ subset(X3,X0)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p385,c35]) ).
cnf(p632,plain,
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p513,c35]) ).
fof(f19,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(D,E)
& subset(B,C) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_17) ).
fof(f19_neg,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(D,E)
& subset(B,C) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ ilf_type(F,relation_type(C,E))
& subset(D,E)
& subset(B,C)
& ilf_type(F,relation_type(B,D)) )
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ ilf_type(sk13,relation_type(sk10,sk12))
& subset(sk11,sk12)
& subset(sk9,sk10)
& ilf_type(sk13,relation_type(sk9,sk11))
& ilf_type(sk12,set_type)
& ilf_type(sk11,set_type)
& ilf_type(sk10,set_type)
& ilf_type(sk9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12,sk13])],[f19_nnf]) ).
cnf(c41,plain,
subset(sk9,sk10),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p820,plain,
( subset(cross_product(sk9,X0),cross_product(sk10,X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p632,c41]) ).
cnf(c42,plain,
subset(sk11,sk12),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p830,plain,
subset(cross_product(sk9,sk11),cross_product(sk10,sk12)),
inference(resolution,[status(thm)],[p820,c42]) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',p10) ).
fof(f9_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk3(B,C),C)
& member(sk3(B,C),B)
& ilf_type(sk3(B,C),set_type) )
| member(B,power_set(C)) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f9_nnf]) ).
cnf(c14,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p274,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c14]) ).
cnf(p427,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p274,c35]) ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D,E] :
( ( ( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p263,plain,
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c3]) ).
cnf(p411,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p263,c35]) ).
cnf(c40,plain,
ilf_type(sk13,relation_type(sk9,sk11)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p413,plain,
ilf_type(sk13,subset_type(cross_product(sk9,sk11))),
inference(resolution,[status(thm)],[p411,c40]) ).
fof(f6,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/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f6_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c10,plain,
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p270,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c10]) ).
cnf(p350,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p270,c35]) ).
cnf(p421,plain,
ilf_type(sk13,member_type(power_set(cross_product(sk9,sk11)))),
inference(resolution,[status(thm)],[p413,p350]) ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f11_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B,C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c20,plain,
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p278,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c35,c20]) ).
cnf(p404,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p278,c35]) ).
cnf(p422,plain,
( member(sk13,power_set(cross_product(sk9,sk11)))
| empty(power_set(cross_product(sk9,sk11))) ),
inference(resolution,[status(thm)],[p421,p404]) ).
cnf(p532,plain,
( empty(power_set(cross_product(sk9,sk11)))
| member(X0,cross_product(sk9,sk11))
| ~ member(X0,sk13)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p427,p422]) ).
cnf(p594,plain,
( empty(power_set(cross_product(sk9,sk11)))
| member(X0,cross_product(sk9,sk11))
| ~ member(X0,sk13) ),
inference(resolution,[status(thm)],[p532,c35]) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f4_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk1(B,C),C)
& member(sk1(B,C),B)
& ilf_type(sk1(B,C),set_type) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c7,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p268,plain,
( member(sk1(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c7]) ).
cnf(p328,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p268,c35]) ).
cnf(p596,plain,
( subset(sk13,X0)
| empty(power_set(cross_product(sk9,sk11)))
| member(sk1(sk13,X0),cross_product(sk9,sk11)) ),
inference(resolution,[status(thm)],[p594,p328]) ).
cnf(c8,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p269,plain,
( ~ member(sk1(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c8]) ).
cnf(p338,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p269,c35]) ).
cnf(p603,plain,
( subset(sk13,cross_product(sk9,sk11))
| subset(sk13,cross_product(sk9,sk11))
| empty(power_set(cross_product(sk9,sk11))) ),
inference(resolution,[status(thm)],[p596,p338]) ).
cnf(p605,plain,
( subset(sk13,cross_product(sk9,sk11))
| empty(power_set(cross_product(sk9,sk11))) ),
inference(factoring,[status(thm)],[p603]) ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f10_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c18,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p277,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c35,c18]) ).
cnf(p607,plain,
subset(sk13,cross_product(sk9,sk11)),
inference(resolution,[status(thm)],[p605,p277]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p259,plain,
( subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c0]) ).
cnf(p373,plain,
( subset(X1,X0)
| ~ subset(X2,X0)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p259,c35]) ).
cnf(p505,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p373,c35]) ).
cnf(p608,plain,
( subset(sk13,X0)
| ~ subset(cross_product(sk9,sk11),X0) ),
inference(resolution,[status(thm)],[p607,p505]) ).
cnf(p841,plain,
subset(sk13,cross_product(sk10,sk12)),
inference(resolution,[status(thm)],[p830,p608]) ).
cnf(c5,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p267,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c5]) ).
cnf(p419,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p267,c35]) ).
cnf(p846,plain,
( member(X0,cross_product(sk10,sk12))
| ~ member(X0,sk13)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p841,p419]) ).
cnf(p1129,plain,
( member(X0,cross_product(sk10,sk12))
| ~ member(X0,sk13) ),
inference(resolution,[status(thm)],[p846,c35]) ).
cnf(c16,plain,
( member(sk3(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p275,plain,
( member(sk3(X1,X0),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c16]) ).
cnf(p379,plain,
( member(sk3(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p275,c35]) ).
cnf(p1132,plain,
( member(sk13,power_set(X0))
| member(sk3(sk13,X0),cross_product(sk10,sk12)) ),
inference(resolution,[status(thm)],[p1129,p379]) ).
cnf(c17,plain,
( ~ member(sk3(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p276,plain,
( ~ member(sk3(X1,X0),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c17]) ).
cnf(p390,plain,
( ~ member(sk3(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p276,c35]) ).
cnf(p1141,plain,
( member(sk13,power_set(cross_product(sk10,sk12)))
| member(sk13,power_set(cross_product(sk10,sk12))) ),
inference(resolution,[status(thm)],[p1132,p390]) ).
cnf(p1564,plain,
member(sk13,power_set(cross_product(sk10,sk12))),
inference(factoring,[status(thm)],[p1141]) ).
cnf(c21,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p279,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c35,c21]) ).
cnf(p435,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p279,c35]) ).
cnf(p1565,plain,
( ilf_type(sk13,member_type(power_set(cross_product(sk10,sk12))))
| empty(power_set(cross_product(sk10,sk12))) ),
inference(resolution,[status(thm)],[p1564,p435]) ).
cnf(c11,plain,
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p271,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c11]) ).
cnf(p367,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p271,c35]) ).
cnf(p1787,plain,
( ilf_type(sk13,subset_type(cross_product(sk10,sk12)))
| empty(power_set(cross_product(sk10,sk12))) ),
inference(resolution,[status(thm)],[p1565,p367]) ).
cnf(c2,plain,
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p262,plain,
( ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c35,c2]) ).
cnf(p397,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p262,c35]) ).
cnf(p1788,plain,
( ilf_type(sk13,relation_type(sk10,sk12))
| empty(power_set(cross_product(sk10,sk12))) ),
inference(resolution,[status(thm)],[p1787,p397]) ).
cnf(p1790,plain,
ilf_type(sk13,relation_type(sk10,sk12)),
inference(resolution,[status(thm)],[p1788,p277]) ).
cnf(c43,plain,
~ ilf_type(sk13,relation_type(sk10,sk12)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p1791,plain,
$false,
inference(resolution,[status(thm)],[p1790,c43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET655+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n001.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 11:40:37 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.68/3.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.68/3.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------