%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET682+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 : n004.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 02:43:48 PM UTC 2026
% Result : Theorem 24.83s 4.01s
% Output : Proof 24.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 101 ( 21 unt; 0 def)
% Number of atoms : 362 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 438 ( 177 ~; 173 |; 45 &)
% ( 4 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 187 ( 5 sgn 94 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,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',p23) ).
fof(f22_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)],[f22]) ).
fof(f22_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)],[f22_nnf]) ).
cnf(c39,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)],[f22_sk]) ).
fof(f23,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f23_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c40,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p249,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)],[c39,c40]) ).
cnf(p370,plain,
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p249,c40]) ).
fof(f24,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(F,range(B,C,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_49) ).
fof(f24_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(F,range(B,C,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ! [F] :
( ~ member(F,range(B,C,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)],[f24_neg]) ).
fof(f24_sk,plain,
! [F] :
( ( ~ member(F,range(sk10,sk11,sk12))
| ~ ilf_type(F,member_type(sk11)) )
& member(sk13,domain(sk10,sk11,sk12))
& ilf_type(sk13,member_type(sk10))
& ilf_type(sk12,relation_type(sk10,sk11))
& ilf_type(sk11,set_type)
& ~ empty(sk11)
& ilf_type(sk10,set_type)
& ~ empty(sk10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11,sk12,sk13])],[f24_nnf]) ).
cnf(c45,plain,
ilf_type(sk12,relation_type(sk10,sk11)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p506,plain,
ilf_type(range_of(sk12),subset_type(sk11)),
inference(resolution,[status(thm)],[p370,c45]) ).
fof(f11,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',p12) ).
fof(f11_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)],[f11]) ).
fof(f11_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)],[f11_nnf]) ).
cnf(c18,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)],[f11_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)],[c18,c40]) ).
cnf(p142,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p129,c40]) ).
cnf(p509,plain,
ilf_type(range_of(sk12),member_type(power_set(sk11))),
inference(resolution,[status(thm)],[p506,p142]) ).
fof(f3,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',p4) ).
fof(f3_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)],[f3]) ).
fof(f3_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)],[f3_nnf]) ).
cnf(c5,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)],[f3_sk]) ).
cnf(p102,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c40,c5]) ).
cnf(p185,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p102,c40]) ).
cnf(p510,plain,
( member(range_of(sk12),power_set(sk11))
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p509,p185]) ).
fof(f13,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',p14) ).
fof(f13_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)],[f13]) ).
fof(f13_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])],[f13_nnf]) ).
cnf(c21,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)],[f13_sk]) ).
cnf(p154,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)],[c21,c40]) ).
cnf(p282,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p154,c40]) ).
cnf(p511,plain,
( member(X0,sk11)
| ~ member(X0,range_of(sk12))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p510,p282]) ).
cnf(p536,plain,
( member(X0,sk11)
| ~ member(X0,range_of(sk12))
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p511,c40]) ).
fof(f19,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',p20) ).
fof(f19_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)],[f19]) ).
fof(f19_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)],[f19_nnf]) ).
cnf(c36,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)],[f19_sk]) ).
cnf(p223,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c36,c40]) ).
cnf(p361,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p223,c40]) ).
cnf(p485,plain,
domain(sk10,sk11,sk12) = domain_of(sk12),
inference(resolution,[status(thm)],[p361,c45]) ).
cnf(c47,plain,
member(sk13,domain(sk10,sk11,sk12)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p486,plain,
member(sk13,domain_of(sk12)),
inference(demodulation,[status(thm)],[p485,c47]) ).
fof(f17,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/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f17_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)],[f17]) ).
fof(f17_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)],[f17_nnf]) ).
cnf(c34,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)],[f17_sk]) ).
cnf(p208,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c34,c40]) ).
cnf(p212,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p208,c40]) ).
fof(f1,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/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f1_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)],[f1]) ).
fof(f1_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)],[f1_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)],[f1_sk]) ).
cnf(c42,plain,
ilf_type(sk10,set_type),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p62,plain,
( ilf_type(X1,subset_type(cross_product(sk10,X0)))
| ~ ilf_type(X1,relation_type(sk10,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c3,c42]) ).
cnf(c44,plain,
ilf_type(sk11,set_type),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p91,plain,
( ilf_type(X0,subset_type(cross_product(sk10,sk11)))
| ~ ilf_type(X0,relation_type(sk10,sk11)) ),
inference(resolution,[status(thm)],[p62,c44]) ).
cnf(p95,plain,
ilf_type(sk12,subset_type(cross_product(sk10,sk11))),
inference(resolution,[status(thm)],[p91,c45]) ).
cnf(p215,plain,
relation_like(sk12),
inference(resolution,[status(thm)],[p212,p95]) ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c16,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)],[f9_sk]) ).
cnf(p122,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c16]) ).
cnf(p125,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p122,c40]) ).
cnf(p224,plain,
ilf_type(sk12,binary_relation_type),
inference(resolution,[status(thm)],[p215,p125]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
=> ? [D] :
( member(D,range_of(C))
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ? [D] :
( member(D,range_of(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] :
( ( member(sk0(B,C),range_of(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(c1,plain,
( member(sk0(X0,X1),range_of(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(p98,plain,
( member(sk0(X1,X0),range_of(X0))
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[c40,c1]) ).
cnf(p225,plain,
( member(sk0(X0,sk12),range_of(sk12))
| ~ member(X0,domain_of(sk12)) ),
inference(resolution,[status(thm)],[p224,p98]) ).
cnf(p490,plain,
member(sk0(sk13,sk12),range_of(sk12)),
inference(resolution,[status(thm)],[p486,p225]) ).
cnf(p545,plain,
( member(sk0(sk13,sk12),sk11)
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p536,p490]) ).
cnf(c6,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)],[f3_sk]) ).
cnf(p103,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c40,c6]) ).
cnf(p274,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p103,c40]) ).
cnf(p550,plain,
( ilf_type(sk0(sk13,sk12),member_type(sk11))
| empty(sk11)
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p545,p274]) ).
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_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)],[f21_nnf]) ).
cnf(c38,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)],[f21_sk]) ).
cnf(p239,plain,
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c38,c40]) ).
cnf(p367,plain,
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p239,c40]) ).
cnf(p498,plain,
range(sk10,sk11,sk12) = range_of(sk12),
inference(resolution,[status(thm)],[p367,c45]) ).
cnf(c48,plain,
( ~ member(X4,range(sk10,sk11,sk12))
| ~ ilf_type(X4,member_type(sk11)) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p499,plain,
( ~ member(X0,range_of(sk12))
| ~ ilf_type(X0,member_type(sk11)) ),
inference(demodulation,[status(thm)],[p498,c48]) ).
cnf(p557,plain,
( ~ member(sk0(sk13,sk12),range_of(sk12))
| empty(sk11)
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p550,p499]) ).
cnf(p558,plain,
( empty(sk11)
| empty(power_set(sk11)) ),
inference(resolution,[status(thm)],[p557,p490]) ).
fof(f14,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',p15) ).
fof(f14_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c25,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p109,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c25,c40]) ).
cnf(p559,plain,
empty(sk11),
inference(resolution,[status(thm)],[p558,p109]) ).
cnf(c43,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p560,plain,
$false,
inference(resolution,[status(thm)],[p559,c43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n004.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 11:39:05 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.83/4.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.83/4.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------