%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET680+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 : n016.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 02:43:47 PM UTC 2026
% Result : Theorem 24.38s 3.56s
% Output : Proof 24.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 107 ( 18 unt; 0 def)
% Number of atoms : 408 ( 7 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 504 ( 203 ~; 203 |; 54 &)
% ( 7 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-3 aty)
% Number of variables : 205 ( 9 sgn 96 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk7(B,C),C)
& member(sk7(B,C),B)
& ilf_type(sk7(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,[sk7])],[f21_nnf]) ).
cnf(c39,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)],[f21_sk]) ).
fof(f30,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(f30_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c57,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p186,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)],[c39,c57]) ).
cnf(p487,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p186,c57]) ).
fof(f29,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/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f29_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)],[f29]) ).
fof(f29_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)],[f29_nnf]) ).
cnf(c56,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)],[f29_sk]) ).
cnf(p273,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)],[c56,c57]) ).
cnf(p442,plain,
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p273,c57]) ).
fof(f31,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_47) ).
fof(f31_neg,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
<=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( ( ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,member_type(C)) )
& ~ member(E,domain(B,C,D)) )
| ( ! [F] :
( ~ member(ordered_pair(E,F),D)
| ~ ilf_type(F,member_type(C)) )
& member(E,domain(B,C,D)) ) )
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
! [F] :
( ( ( member(ordered_pair(sk14,sk15),sk13)
& ilf_type(sk15,member_type(sk12))
& ~ member(sk14,domain(sk11,sk12,sk13)) )
| ( ( ~ member(ordered_pair(sk14,F),sk13)
| ~ ilf_type(F,member_type(sk12)) )
& member(sk14,domain(sk11,sk12,sk13)) ) )
& ilf_type(sk14,member_type(sk11))
& ilf_type(sk13,relation_type(sk11,sk12))
& ilf_type(sk12,set_type)
& ~ empty(sk12)
& ilf_type(sk11,set_type)
& ~ empty(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14,sk15])],[f31_nnf]) ).
cnf(c62,plain,
ilf_type(sk13,relation_type(sk11,sk12)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p443,plain,
ilf_type(range_of(sk13),subset_type(sk12)),
inference(resolution,[status(thm)],[p442,c62]) ).
fof(f18,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',p19) ).
fof(f18_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)],[f18]) ).
fof(f18_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)],[f18_nnf]) ).
cnf(c29,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)],[f18_sk]) ).
cnf(p135,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c29,c57]) ).
cnf(p136,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p135,c57]) ).
cnf(p455,plain,
ilf_type(range_of(sk13),member_type(power_set(sk12))),
inference(resolution,[status(thm)],[p443,p136]) ).
fof(f7,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',p8) ).
fof(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c13,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)],[f7_sk]) ).
cnf(p117,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c13,c57]) ).
cnf(p130,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p117,c57]) ).
cnf(p456,plain,
( member(range_of(sk13),power_set(sk12))
| empty(power_set(sk12)) ),
inference(resolution,[status(thm)],[p455,p130]) ).
cnf(p566,plain,
( empty(power_set(sk12))
| member(X0,sk12)
| ~ member(X0,range_of(sk13))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p487,p456]) ).
cnf(p669,plain,
( empty(power_set(sk12))
| member(X0,sk12)
| ~ member(X0,range_of(sk13)) ),
inference(resolution,[status(thm)],[p566,c57]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(C,range_of(D))
& member(B,domain_of(D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(C,range_of(D))
& member(B,domain_of(D)) )
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( member(C,range_of(D))
& member(B,domain_of(D)) )
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c4,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p76,plain,
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c4,c57]) ).
cnf(p284,plain,
( member(X2,range_of(X0))
| ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p76,c57]) ).
fof(f25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f25_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [B,C,D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c52,plain,
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p188,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c52,c57]) ).
cnf(p189,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p188,c57]) ).
fof(f5,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',p6) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c11,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)],[f5_sk]) ).
cnf(p111,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)],[c11,c57]) ).
cnf(p176,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p111,c57]) ).
cnf(p177,plain,
ilf_type(sk13,subset_type(cross_product(sk11,sk12))),
inference(resolution,[status(thm)],[p176,c62]) ).
cnf(p194,plain,
relation_like(sk13),
inference(resolution,[status(thm)],[p189,p177]) ).
fof(f16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f16_nnf,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c27,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p108,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c27]) ).
cnf(p109,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p108,c57]) ).
cnf(p196,plain,
ilf_type(sk13,binary_relation_type),
inference(resolution,[status(thm)],[p194,p109]) ).
cnf(p300,plain,
( member(X1,range_of(sk13))
| ~ member(ordered_pair(X0,X1),sk13) ),
inference(resolution,[status(thm)],[p284,p196]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type) )
| member(B,domain_of(C)) )
& ( ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ( ~ member(ordered_pair(B,D),C)
| ~ ilf_type(D,set_type)
| member(B,domain_of(C)) )
& ( ( member(ordered_pair(B,sk0(B,C)),C)
& ilf_type(sk0(B,C),set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(ordered_pair(X0,X2),X1)
| ~ ilf_type(X2,set_type)
| member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p73,plain,
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type)
| member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[c2,c57]) ).
cnf(p277,plain,
( ~ member(ordered_pair(X0,X1),sk13)
| ~ ilf_type(X1,set_type)
| member(X0,domain_of(sk13)) ),
inference(resolution,[status(thm)],[p73,p196]) ).
cnf(p290,plain,
( ~ member(ordered_pair(X0,X1),sk13)
| member(X0,domain_of(sk13)) ),
inference(resolution,[status(thm)],[p277,c57]) ).
fof(f26,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',p27) ).
fof(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c53,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)],[f26_sk]) ).
cnf(p244,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c53,c57]) ).
cnf(p256,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p244,c57]) ).
cnf(p257,plain,
domain(sk11,sk12,sk13) = domain_of(sk13),
inference(resolution,[status(thm)],[p256,c62]) ).
cnf(c66,plain,
( member(ordered_pair(sk14,sk15),sk13)
| member(sk14,domain(sk11,sk12,sk13)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p259,plain,
( member(ordered_pair(sk14,sk15),sk13)
| member(sk14,domain_of(sk13)) ),
inference(demodulation,[status(thm)],[p257,c66]) ).
cnf(p291,plain,
( member(sk14,domain_of(sk13))
| member(sk14,domain_of(sk13)) ),
inference(resolution,[status(thm)],[p290,p259]) ).
cnf(p292,plain,
member(sk14,domain_of(sk13)),
inference(factoring,[status(thm)],[p291]) ).
cnf(c1,plain,
( member(ordered_pair(X0,sk0(X0,X1)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p70,plain,
( member(ordered_pair(X1,sk0(X1,X0)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[c1,c57]) ).
cnf(p197,plain,
( member(ordered_pair(X0,sk0(X0,sk13)),sk13)
| ~ member(X0,domain_of(sk13)) ),
inference(resolution,[status(thm)],[p196,p70]) ).
cnf(p294,plain,
member(ordered_pair(sk14,sk0(sk14,sk13)),sk13),
inference(resolution,[status(thm)],[p292,p197]) ).
cnf(p315,plain,
member(sk0(sk14,sk13),range_of(sk13)),
inference(resolution,[status(thm)],[p300,p294]) ).
cnf(p674,plain,
( empty(power_set(sk12))
| member(sk0(sk14,sk13),sk12) ),
inference(resolution,[status(thm)],[p669,p315]) ).
cnf(c14,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)],[f7_sk]) ).
cnf(p129,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c14,c57]) ).
cnf(p146,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p129,c57]) ).
cnf(p684,plain,
( ilf_type(sk0(sk14,sk13),member_type(sk12))
| empty(sk12)
| empty(power_set(sk12)) ),
inference(resolution,[status(thm)],[p674,p146]) ).
cnf(c67,plain,
( ~ member(sk14,domain(sk11,sk12,sk13))
| ~ member(ordered_pair(sk14,X4),sk13)
| ~ ilf_type(X4,member_type(sk12)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p260,plain,
( ~ member(sk14,domain_of(sk13))
| ~ member(ordered_pair(sk14,X0),sk13)
| ~ ilf_type(X0,member_type(sk12)) ),
inference(demodulation,[status(thm)],[p257,c67]) ).
cnf(p690,plain,
( ~ member(sk14,domain_of(sk13))
| ~ member(ordered_pair(sk14,sk0(sk14,sk13)),sk13)
| empty(sk12)
| empty(power_set(sk12)) ),
inference(resolution,[status(thm)],[p684,p260]) ).
cnf(p2140,plain,
( ~ member(sk14,domain_of(sk13))
| empty(sk12)
| empty(power_set(sk12)) ),
inference(resolution,[status(thm)],[p690,p294]) ).
cnf(p2141,plain,
( empty(sk12)
| empty(power_set(sk12)) ),
inference(resolution,[status(thm)],[p2140,p292]) ).
fof(f22,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',p23) ).
fof(f22_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c43,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p71,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c43,c57]) ).
cnf(p2144,plain,
empty(sk12),
inference(resolution,[status(thm)],[p2141,p71]) ).
cnf(c60,plain,
~ empty(sk12),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p2145,plain,
$false,
inference(resolution,[status(thm)],[p2144,c60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET680+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 : n016.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 11:43:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.38/3.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.38/3.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------