%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 30.95s 4.47s
% Output : Proof 30.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 100 ( 16 unt; 0 def)
% Number of atoms : 373 ( 31 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 465 ( 192 ~; 197 |; 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/sandbox2/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/sandbox2/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(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_32) ).
fof(f32_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( C != range(B,C,D)
| ~ subset(C,domain(B,C,D)) )
& subset(identity_relation_of(C),D)
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( ( sk13 != range(sk12,sk13,sk14)
| ~ subset(sk13,domain(sk12,sk13,sk14)) )
& subset(identity_relation_of(sk13),sk14)
& ilf_type(sk14,relation_type(sk12,sk13))
& 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(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p4163,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(p4180,plain,
subset(sk13,range_of(sk14)),
inference(resolution,[status(thm)],[p4163,c63]) ).
fof(f30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f30_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(range(B,C,D),subset_type(C))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B,C,D] :
( ilf_type(range(B,C,D),subset_type(C))
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c58,plain,
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p298,plain,
( ilf_type(range(X2,X0,X1),subset_type(X0))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c58,c59]) ).
cnf(p715,plain,
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p298,c59]) ).
cnf(p3857,plain,
ilf_type(range_of(sk14),subset_type(sk13)),
inference(resolution,[status(thm)],[p715,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/sandbox2/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(p3872,plain,
ilf_type(range_of(sk14),member_type(power_set(sk13))),
inference(resolution,[status(thm)],[p3857,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/sandbox2/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(p3873,plain,
( member(range_of(sk14),power_set(sk13))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3872,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/sandbox2/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(p3874,plain,
( member(X0,sk13)
| ~ member(X0,range_of(sk14))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3873,p466]) ).
cnf(p4002,plain,
( member(X0,sk13)
| ~ member(X0,range_of(sk14))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p3874,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/sandbox2/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(p4005,plain,
( subset(range_of(sk14),X0)
| member(sk1(range_of(sk14),X0),sk13)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p4002,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(p4039,plain,
( subset(range_of(sk14),sk13)
| subset(range_of(sk14),sk13)
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p4005,p149]) ).
cnf(p4043,plain,
( subset(range_of(sk14),sk13)
| empty(power_set(sk13)) ),
inference(factoring,[status(thm)],[p4039]) ).
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/sandbox2/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(p4044,plain,
( range_of(sk14) = sk13
| ~ subset(sk13,range_of(sk14))
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p4043,p144]) ).
cnf(p4184,plain,
( range_of(sk14) = sk13
| empty(power_set(sk13)) ),
inference(resolution,[status(thm)],[p4180,p4044]) ).
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(p3877,plain,
( subset(X0,domain_of(sk14))
| ~ subset(identity_relation_of(X0),sk14) ),
inference(resolution,[status(thm)],[p720,c62]) ).
cnf(p3892,plain,
subset(sk13,domain_of(sk14)),
inference(resolution,[status(thm)],[p3877,c63]) ).
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/sandbox2/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(sk12,sk13,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/sandbox2/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(sk12,sk13,sk14) = domain_of(sk14),
inference(resolution,[status(thm)],[p380,c62]) ).
cnf(c64,plain,
( sk13 != range(sk12,sk13,sk14)
| ~ subset(sk13,domain(sk12,sk13,sk14)) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p384,plain,
( sk13 != range(sk12,sk13,sk14)
| ~ subset(sk13,domain_of(sk14)) ),
inference(demodulation,[status(thm)],[p383,c64]) ).
cnf(p3548,plain,
( sk13 != range_of(sk14)
| ~ subset(sk13,domain_of(sk14)) ),
inference(demodulation,[status(thm)],[p3547,p384]) ).
cnf(p3896,plain,
sk13 != range_of(sk14),
inference(resolution,[status(thm)],[p3892,p3548]) ).
cnf(p4185,plain,
( sk13 != sk13
| empty(power_set(sk13)) ),
inference(superposition,[status(thm)],[p4184,p3896]) ).
cnf(p4216,plain,
empty(power_set(sk13)),
inference(equality_resolution,[status(thm)],[p4185]) ).
fof(f20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox2/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(p4217,plain,
$false,
inference(resolution,[status(thm)],[p4216,p75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET669+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 11:37:18 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.95/4.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.95/4.47 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------