%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET668+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 02:43:46 PM UTC 2026
% Result : Theorem 26.22s 4.02s
% Output : Proof 26.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 99 ( 15 unt; 0 def)
% Number of atoms : 371 ( 29 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 463 ( 191 ~; 196 |; 34 &)
% ( 4 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 198 ( 2 sgn 87 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) )
| ~ subset(identity_relation_of(D),E)
| ~ ilf_type(E,relation_type(B,C)) )
| ~ 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(D,range(B,C,E))
& subset(D,domain(B,C,E)) )
| ~ subset(identity_relation_of(D),E)
| ~ ilf_type(E,relation_type(B,C))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( subset(X2,range(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f31,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p32) ).
fof(f31_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c59,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p80,plain,
( subset(X1,range(X3,X0,X2))
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c2,c59]) ).
cnf(p324,plain,
( subset(X0,range(X2,X3,X1))
| ~ subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p80,c59]) ).
cnf(p775,plain,
( subset(X3,range(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p324,c59]) ).
fof(f32,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_31) ).
fof(f32_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( ~ subset(C,range(C,B,D))
| C != domain(C,B,D) )
& subset(identity_relation_of(C),D)
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( ( ~ subset(sk13,range(sk13,sk12,sk14))
| sk13 != domain(sk13,sk12,sk14) )
& subset(identity_relation_of(sk13),sk14)
& ilf_type(sk14,relation_type(sk13,sk12))
& ilf_type(sk13,set_type)
& ilf_type(sk12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f32_nnf]) ).
cnf(c62,plain,
ilf_type(sk14,relation_type(sk13,sk12)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p4245,plain,
( subset(X0,range_of(sk14))
| ~ subset(identity_relation_of(X0),sk14) ),
inference(resolution,[status(thm)],[p775,c62]) ).
cnf(c63,plain,
subset(identity_relation_of(sk13),sk14),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p4260,plain,
subset(sk13,range_of(sk14)),
inference(resolution,[status(thm)],[p4245,c63]) ).
cnf(c1,plain,
( subset(X2,domain(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p71,plain,
( subset(X1,domain(X3,X0,X2))
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c1,c59]) ).
cnf(p307,plain,
( subset(X0,domain(X2,X3,X1))
| ~ subset(identity_relation_of(X0),X1)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p71,c59]) ).
cnf(p720,plain,
( subset(X3,domain(X1,X2,X0))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p307,c59]) ).
cnf(p3876,plain,
( subset(X0,domain_of(sk14))
| ~ subset(identity_relation_of(X0),sk14) ),
inference(resolution,[status(thm)],[p720,c62]) ).
cnf(p3891,plain,
subset(sk13,domain_of(sk14)),
inference(resolution,[status(thm)],[p3876,c63]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ( subset(C,B)
& subset(B,C) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( B = C
| ~ subset(C,B)
| ~ subset(B,C)
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( B = C
| ~ subset(C,B)
| ~ subset(B,C)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p66,plain,
( X1 = X0
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c59,c0]) ).
cnf(p144,plain,
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p66,c59]) ).
cnf(p3892,plain,
( sk13 = domain_of(sk14)
| ~ subset(domain_of(sk14),sk13) ),
inference(resolution,[status(thm)],[p3891,p144]) ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p29) ).
fof(f28_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [B,C,D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c56,plain,
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p280,plain,
( ilf_type(domain(X2,X0,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c56,c59]) ).
cnf(p651,plain,
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p280,c59]) ).
cnf(p3527,plain,
ilf_type(domain_of(sk14),subset_type(sk13)),
inference(resolution,[status(thm)],[p651,c62]) ).
fof(f15,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',p16) ).
fof(f15_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)],[f15]) ).
fof(f15_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)],[f15_nnf]) ).
cnf(c30,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)],[f15_sk]) ).
cnf(p182,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c30,c59]) ).
cnf(p219,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p182,c59]) ).
cnf(p3542,plain,
ilf_type(domain_of(sk14),member_type(power_set(sk13))),
inference(resolution,[status(thm)],[p3527,p219]) ).
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(c41,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(p225,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c41,c59]) ).
cnf(p252,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p225,c59]) ).
cnf(p3543,plain,
( member(domain_of(sk14),power_set(sk13))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3542,p252]) ).
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(sk6(B,C),C)
& member(sk6(B,C),B)
& ilf_type(sk6(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,[sk6])],[f19_nnf]) ).
cnf(c35,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)],[f19_sk]) ).
cnf(p195,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,c59]) ).
cnf(p466,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p195,c59]) ).
cnf(p3544,plain,
( member(X0,sk13)
| ~ member(X0,domain_of(sk14))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3543,p466]) ).
cnf(p3573,plain,
( member(X0,sk13)
| ~ member(X0,domain_of(sk14))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3544,c59]) ).
fof(f6,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',p7) ).
fof(f6_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)],[f6]) ).
fof(f6_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])],[f6_nnf]) ).
cnf(c12,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p140,plain,
( member(sk1(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c12,c59]) ).
cnf(p142,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p140,c59]) ).
cnf(p3576,plain,
( subset(domain_of(sk14),X0)
| member(sk1(domain_of(sk14),X0),sk13)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3573,p142]) ).
cnf(c13,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p147,plain,
( ~ member(sk1(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c13,c59]) ).
cnf(p149,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p147,c59]) ).
cnf(p3595,plain,
( subset(domain_of(sk14),sk13)
| subset(domain_of(sk14),sk13)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3576,p149]) ).
cnf(p3597,plain,
( subset(domain_of(sk14),sk13)
| empty(power_set(sk13)) ),
inference(factoring,[status(thm)],[p3595]) ).
cnf(p3907,plain,
( empty(power_set(sk13))
| sk13 = domain_of(sk14) ),
inference(resolution,[status(thm)],[p3892,p3597]) ).
fof(f29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f29_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [B,C,D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c57,plain,
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p284,plain,
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c57,c59]) ).
cnf(p663,plain,
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p284,c59]) ).
cnf(p3547,plain,
range(sk13,sk12,sk14) = range_of(sk14),
inference(resolution,[status(thm)],[p663,c62]) ).
fof(f27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
fof(f27_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [B,C,D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c55,plain,
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p265,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c55,c59]) ).
cnf(p380,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p265,c59]) ).
cnf(p383,plain,
domain(sk13,sk12,sk14) = domain_of(sk14),
inference(resolution,[status(thm)],[p380,c62]) ).
cnf(c64,plain,
( ~ subset(sk13,range(sk13,sk12,sk14))
| sk13 != domain(sk13,sk12,sk14) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p384,plain,
( ~ subset(sk13,range(sk13,sk12,sk14))
| sk13 != domain_of(sk14) ),
inference(demodulation,[status(thm)],[p383,c64]) ).
cnf(p3548,plain,
( ~ subset(sk13,range_of(sk14))
| sk13 != domain_of(sk14) ),
inference(demodulation,[status(thm)],[p3547,p384]) ).
cnf(p3910,plain,
( ~ subset(sk13,range_of(sk14))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3907,p3548]) ).
cnf(p4264,plain,
empty(power_set(sk13)),
inference(resolution,[status(thm)],[p4260,p3910]) ).
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(p75,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c39,c59]) ).
cnf(p4265,plain,
$false,
inference(resolution,[status(thm)],[p4264,p75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET668+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.58 % Computer : n010.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 11:37:01 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.22/4.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.22/4.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------