%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET649+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 : n010.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 02:43:43 PM UTC 2026
% Result : Theorem 28.02s 4.52s
% Output : Proof 28.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 18 unt; 0 def)
% Number of atoms : 342 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 418 ( 169 ~; 172 |; 37 &)
% ( 4 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 178 ( 2 sgn 81 !; 5 ?)
% 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(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c2,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)],[f2_sk]) ).
fof(f25,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f25_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c48,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p67,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)],[c2,c48]) ).
cnf(p246,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)],[p67,c48]) ).
cnf(p733,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)],[p246,c48]) ).
cnf(p2588,plain,
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p733,c48]) ).
fof(f26,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_11) ).
fof(f26_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ~ ilf_type(D,relation_type(B,C))
& subset(range_of(D),C)
& subset(domain_of(D),B)
& ilf_type(D,binary_relation_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
( ~ ilf_type(sk14,relation_type(sk12,sk13))
& subset(range_of(sk14),sk13)
& subset(domain_of(sk14),sk12)
& ilf_type(sk14,binary_relation_type)
& ilf_type(sk13,set_type)
& ilf_type(sk12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f26_nnf]) ).
cnf(c52,plain,
subset(domain_of(sk14),sk12),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p2589,plain,
( subset(cross_product(domain_of(sk14),X0),cross_product(sk12,X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p2588,c52]) ).
fof(f16,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f16_nnf,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c27,plain,
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p58,plain,
subset(X0,X0),
inference(resolution,[status(thm)],[c27,c48]) ).
cnf(p2857,plain,
subset(cross_product(domain_of(sk14),X0),cross_product(sk12,X0)),
inference(resolution,[status(thm)],[p2589,p58]) ).
cnf(p2591,plain,
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p2588,p58]) ).
cnf(c53,plain,
subset(range_of(sk14),sk13),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p2668,plain,
subset(cross_product(X0,range_of(sk14)),cross_product(X0,sk13)),
inference(resolution,[status(thm)],[p2591,c53]) ).
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(p55,plain,
( subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c0,c48]) ).
cnf(p198,plain,
( subset(X1,X0)
| ~ subset(X2,X0)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p55,c48]) ).
cnf(p317,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p198,c48]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( subset(B,cross_product(domain_of(B),range_of(B)))
| ~ ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] :
( subset(B,cross_product(domain_of(B),range_of(B)))
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c51,plain,
ilf_type(sk14,binary_relation_type),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p57,plain,
subset(sk14,cross_product(domain_of(sk14),range_of(sk14))),
inference(resolution,[status(thm)],[c1,c51]) ).
cnf(p321,plain,
( subset(sk14,X0)
| ~ subset(cross_product(domain_of(sk14),range_of(sk14)),X0) ),
inference(resolution,[status(thm)],[p317,p57]) ).
cnf(p2788,plain,
subset(sk14,cross_product(domain_of(sk14),sk13)),
inference(resolution,[status(thm)],[p2668,p321]) ).
cnf(p2803,plain,
( subset(sk14,X0)
| ~ subset(cross_product(domain_of(sk14),sk13),X0) ),
inference(resolution,[status(thm)],[p2788,p317]) ).
cnf(p2960,plain,
subset(sk14,cross_product(sk12,sk13)),
inference(resolution,[status(thm)],[p2857,p2803]) ).
fof(f11,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',p12) ).
fof(f11_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)],[f11]) ).
fof(f11_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk4(B,C),C)
& member(sk4(B,C),B)
& ilf_type(sk4(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,[sk4])],[f11_nnf]) ).
cnf(c18,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)],[f11_sk]) ).
cnf(p105,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c18,c48]) ).
cnf(p314,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p105,c48]) ).
cnf(p2963,plain,
( member(X0,cross_product(sk12,sk13))
| ~ member(X0,sk14)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p2960,p314]) ).
cnf(p3706,plain,
( member(X0,cross_product(sk12,sk13))
| ~ member(X0,sk14) ),
inference(resolution,[status(thm)],[p2963,c48]) ).
fof(f19,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',p20) ).
fof(f19_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)],[f19]) ).
fof(f19_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk9(B,C),C)
& member(sk9(B,C),B)
& ilf_type(sk9(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,[sk9])],[f19_nnf]) ).
cnf(c37,plain,
( member(sk9(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p173,plain,
( member(sk9(X1,X0),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c37,c48]) ).
cnf(p174,plain,
( member(sk9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p173,c48]) ).
cnf(p3713,plain,
( member(sk14,power_set(X0))
| member(sk9(sk14,X0),cross_product(sk12,sk13)) ),
inference(resolution,[status(thm)],[p3706,p174]) ).
cnf(c38,plain,
( ~ member(sk9(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p176,plain,
( ~ member(sk9(X1,X0),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c38,c48]) ).
cnf(p181,plain,
( ~ member(sk9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p176,c48]) ).
cnf(p3776,plain,
( member(sk14,power_set(cross_product(sk12,sk13)))
| member(sk14,power_set(cross_product(sk12,sk13))) ),
inference(resolution,[status(thm)],[p3713,p181]) ).
cnf(p4170,plain,
member(sk14,power_set(cross_product(sk12,sk13))),
inference(factoring,[status(thm)],[p3776]) ).
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_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)],[f21_nnf]) ).
cnf(c42,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)],[f21_sk]) ).
cnf(p191,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c42,c48]) ).
cnf(p197,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p191,c48]) ).
cnf(p4171,plain,
( ilf_type(sk14,member_type(power_set(cross_product(sk12,sk13))))
| empty(power_set(cross_product(sk12,sk13))) ),
inference(resolution,[status(thm)],[p4170,p197]) ).
fof(f14,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',p15) ).
fof(f14_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)],[f14]) ).
fof(f14_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)],[f14_nnf]) ).
cnf(c25,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)],[f14_sk]) ).
cnf(p129,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c25,c48]) ).
cnf(p130,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p129,c48]) ).
cnf(p4218,plain,
( ilf_type(sk14,subset_type(cross_product(sk12,sk13)))
| empty(power_set(cross_product(sk12,sk13))) ),
inference(resolution,[status(thm)],[p4171,p130]) ).
fof(f3,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',p4) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c3,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)],[f3_sk]) ).
cnf(p69,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)],[c3,c48]) ).
cnf(p91,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p69,c48]) ).
cnf(p4219,plain,
( ilf_type(sk14,relation_type(sk12,sk13))
| empty(power_set(cross_product(sk12,sk13))) ),
inference(resolution,[status(thm)],[p4218,p91]) ).
fof(f20,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',p21) ).
fof(f20_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c39,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p59,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c39,c48]) ).
cnf(p4232,plain,
ilf_type(sk14,relation_type(sk12,sk13)),
inference(resolution,[status(thm)],[p4219,p59]) ).
cnf(c54,plain,
~ ilf_type(sk14,relation_type(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p4233,plain,
$false,
inference(resolution,[status(thm)],[p4232,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:34:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.02/4.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.02/4.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------