%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET674+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 : n017.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 82.23s 11.14s
% Output : Proof 82.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 201 ( 21 unt; 0 def)
% Number of atoms : 763 ( 61 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 953 ( 391 ~; 426 |; 67 &)
% ( 10 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-4 aty)
% Number of variables : 430 ( 9 sgn 170 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,inverse2(D,B))
<=> ? [E] :
( member(E,B)
& member(ordered_pair(C,E),D)
& ilf_type(E,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f4_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( ! [E] :
( ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| ~ ilf_type(E,set_type) )
| member(C,inverse2(D,B)) )
& ( ? [E] :
( member(E,B)
& member(ordered_pair(C,E),D)
& ilf_type(E,set_type) )
| ~ member(C,inverse2(D,B)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C,D,E] :
( ( ( ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| ~ ilf_type(E,set_type)
| member(C,inverse2(D,B)) )
& ( ( member(sk3(B,C,D),B)
& member(ordered_pair(C,sk3(B,C,D)),D)
& ilf_type(sk3(B,C,D),set_type) )
| ~ member(C,inverse2(D,B)) ) )
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f4_nnf]) ).
cnf(c15,plain,
( ~ member(X3,X0)
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X3,set_type)
| member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f39,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p40) ).
fof(f39_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c82,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p133,plain,
( ~ member(X3,X2)
| ~ member(ordered_pair(X0,X3),X1)
| ~ ilf_type(X3,set_type)
| member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c15,c82]) ).
cnf(p420,plain,
( ~ member(X3,X2)
| ~ member(ordered_pair(X1,X3),X0)
| ~ ilf_type(X3,set_type)
| member(X1,inverse2(X0,X2))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p133,c82]) ).
fof(f7,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',p8) ).
fof(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c24,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)],[f7_sk]) ).
cnf(p189,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)],[c24,c82]) ).
cnf(p192,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p189,c82]) ).
fof(f40,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( inverse4(B,C,D,C) = domain(B,C,D)
& image4(B,C,D,B) = range(B,C,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_38) ).
fof(f40_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( inverse4(B,C,D,C) = domain(B,C,D)
& image4(B,C,D,B) = range(B,C,D) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f40_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( inverse4(B,C,D,C) != domain(B,C,D)
| image4(B,C,D,B) != range(B,C,D) )
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f40_neg]) ).
fof(f40_sk,plain,
( ( inverse4(sk16,sk17,sk18,sk17) != domain(sk16,sk17,sk18)
| image4(sk16,sk17,sk18,sk16) != range(sk16,sk17,sk18) )
& ilf_type(sk18,relation_type(sk16,sk17))
& ilf_type(sk17,set_type)
& ilf_type(sk16,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18])],[f40_nnf]) ).
cnf(c85,plain,
ilf_type(sk18,relation_type(sk16,sk17)),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p194,plain,
ilf_type(sk18,subset_type(cross_product(sk16,sk17))),
inference(resolution,[status(thm)],[p192,c85]) ).
fof(f28,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',p29) ).
fof(f28_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)],[f28]) ).
fof(f28_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)],[f28_nnf]) ).
cnf(c69,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)],[f28_sk]) ).
cnf(p141,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c69,c82]) ).
cnf(p143,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p141,c82]) ).
cnf(p196,plain,
relation_like(sk18),
inference(resolution,[status(thm)],[p194,p143]) ).
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/sandbox2/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(c37,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(p103,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c37]) ).
cnf(p104,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p103,c82]) ).
cnf(p198,plain,
ilf_type(sk18,binary_relation_type),
inference(resolution,[status(thm)],[p196,p104]) ).
cnf(p1195,plain,
( ~ member(X2,X1)
| ~ member(ordered_pair(X0,X2),sk18)
| ~ ilf_type(X2,set_type)
| member(X0,inverse2(sk18,X1)) ),
inference(resolution,[status(thm)],[p420,p198]) ).
cnf(p1454,plain,
( ~ member(X2,X1)
| ~ member(ordered_pair(X0,X2),sk18)
| member(X0,inverse2(sk18,X1)) ),
inference(resolution,[status(thm)],[p1195,c82]) ).
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/sandbox2/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(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(p88,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,c82]) ).
cnf(p199,plain,
( member(ordered_pair(X0,sk0(X0,sk18)),sk18)
| ~ member(X0,domain_of(sk18)) ),
inference(resolution,[status(thm)],[p198,p88]) ).
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk9(B,C),C)
& member(sk9(B,C),B)
& ilf_type(sk9(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,[sk9])],[f21_nnf]) ).
cnf(c51,plain,
( member(sk9(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p134,plain,
( member(sk9(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c51,c82]) ).
cnf(p135,plain,
( member(sk9(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p134,c82]) ).
cnf(p206,plain,
( subset(domain_of(sk18),X0)
| member(ordered_pair(sk9(domain_of(sk18),X0),sk0(sk9(domain_of(sk18),X0),sk18)),sk18) ),
inference(resolution,[status(thm)],[p199,p135]) ).
cnf(p1459,plain,
( subset(domain_of(sk18),X0)
| ~ member(sk0(sk9(domain_of(sk18),X0),sk18),X1)
| member(sk9(domain_of(sk18),X0),inverse2(sk18,X1)) ),
inference(resolution,[status(thm)],[p1454,p206]) ).
fof(f34,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',p35) ).
fof(f34_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)],[f34]) ).
fof(f34_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)],[f34_nnf]) ).
cnf(c77,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)],[f34_sk]) ).
cnf(p314,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)],[c77,c82]) ).
cnf(p763,plain,
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p314,c82]) ).
cnf(p3973,plain,
ilf_type(range_of(sk18),subset_type(sk17)),
inference(resolution,[status(thm)],[p763,c85]) ).
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/sandbox2/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(c39,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(p150,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c39,c82]) ).
cnf(p151,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p150,c82]) ).
cnf(p3981,plain,
ilf_type(range_of(sk18),member_type(power_set(sk17))),
inference(resolution,[status(thm)],[p3973,p151]) ).
fof(f25,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',p26) ).
fof(f25_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)],[f25]) ).
fof(f25_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)],[f25_nnf]) ).
cnf(c60,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)],[f25_sk]) ).
cnf(p250,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c60,c82]) ).
cnf(p251,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p250,c82]) ).
cnf(p3982,plain,
( member(range_of(sk18),power_set(sk17))
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p3981,p251]) ).
fof(f23,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',p24) ).
fof(f23_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)],[f23]) ).
fof(f23_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk10(B,C),C)
& member(sk10(B,C),B)
& ilf_type(sk10(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,[sk10])],[f23_nnf]) ).
cnf(c54,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)],[f23_sk]) ).
cnf(p243,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)],[c54,c82]) ).
cnf(p634,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p243,c82]) ).
cnf(p3983,plain,
( member(X0,sk17)
| ~ member(X0,range_of(sk18))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p3982,p634]) ).
cnf(p4142,plain,
( member(X0,sk17)
| ~ member(X0,range_of(sk18))
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p3983,c82]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,range_of(C))
<=> ? [D] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type) )
| member(B,range_of(C)) )
& ( ? [D] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) )
| ~ member(B,range_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type)
| member(B,range_of(C)) )
& ( ( member(ordered_pair(sk1(B,C),B),C)
& ilf_type(sk1(B,C),set_type) )
| ~ member(B,range_of(C)) ) )
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X2,set_type)
| member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p98,plain,
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[c5,c82]) ).
cnf(p360,plain,
( ~ member(ordered_pair(X1,X0),sk18)
| ~ ilf_type(X1,set_type)
| member(X0,range_of(sk18)) ),
inference(resolution,[status(thm)],[p98,p198]) ).
cnf(p364,plain,
( ~ member(ordered_pair(X1,X0),sk18)
| member(X0,range_of(sk18)) ),
inference(resolution,[status(thm)],[p360,c82]) ).
cnf(p367,plain,
( subset(domain_of(sk18),X0)
| member(sk0(sk9(domain_of(sk18),X0),sk18),range_of(sk18)) ),
inference(resolution,[status(thm)],[p364,p206]) ).
cnf(p4151,plain,
( subset(domain_of(sk18),X0)
| member(sk0(sk9(domain_of(sk18),X0),sk18),sk17)
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p4142,p367]) ).
cnf(p11124,plain,
( subset(domain_of(sk18),X0)
| empty(power_set(sk17))
| subset(domain_of(sk18),X0)
| member(sk9(domain_of(sk18),X0),inverse2(sk18,sk17)) ),
inference(resolution,[status(thm)],[p1459,p4151]) ).
cnf(p19176,plain,
( empty(power_set(sk17))
| subset(domain_of(sk18),X0)
| member(sk9(domain_of(sk18),X0),inverse2(sk18,sk17)) ),
inference(factoring,[status(thm)],[p11124]) ).
cnf(c52,plain,
( ~ member(sk9(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p138,plain,
( ~ member(sk9(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c52,c82]) ).
cnf(p139,plain,
( ~ member(sk9(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p138,c82]) ).
cnf(p19177,plain,
( subset(domain_of(sk18),inverse2(sk18,sk17))
| empty(power_set(sk17))
| subset(domain_of(sk18),inverse2(sk18,sk17)) ),
inference(resolution,[status(thm)],[p19176,p139]) ).
cnf(p19182,plain,
( empty(power_set(sk17))
| subset(domain_of(sk18),inverse2(sk18,sk17)) ),
inference(factoring,[status(thm)],[p19177]) ).
cnf(c13,plain,
( member(ordered_pair(X1,sk3(X0,X1,X2)),X2)
| ~ member(X1,inverse2(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p124,plain,
( member(ordered_pair(X0,sk3(X2,X0,X1)),X1)
| ~ member(X0,inverse2(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c13,c82]) ).
cnf(p410,plain,
( member(ordered_pair(X1,sk3(X2,X1,X0)),X0)
| ~ member(X1,inverse2(X0,X2))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p124,c82]) ).
cnf(p1095,plain,
( member(ordered_pair(X0,sk3(X1,X0,sk18)),sk18)
| ~ member(X0,inverse2(sk18,X1)) ),
inference(resolution,[status(thm)],[p410,p198]) ).
cnf(p1101,plain,
( subset(inverse2(sk18,X0),X1)
| member(ordered_pair(sk9(inverse2(sk18,X0),X1),sk3(X0,sk9(inverse2(sk18,X0),X1),sk18)),sk18) ),
inference(resolution,[status(thm)],[p1095,p135]) ).
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(p91,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,c82]) ).
cnf(p226,plain,
( ~ member(ordered_pair(X0,X1),sk18)
| ~ ilf_type(X1,set_type)
| member(X0,domain_of(sk18)) ),
inference(resolution,[status(thm)],[p91,p198]) ).
cnf(p228,plain,
( ~ member(ordered_pair(X0,X1),sk18)
| member(X0,domain_of(sk18)) ),
inference(resolution,[status(thm)],[p226,c82]) ).
cnf(p8040,plain,
( member(sk9(inverse2(sk18,X0),X1),domain_of(sk18))
| subset(inverse2(sk18,X0),X1) ),
inference(resolution,[status(thm)],[p1101,p228]) ).
cnf(p8047,plain,
( subset(inverse2(sk18,X0),domain_of(sk18))
| subset(inverse2(sk18,X0),domain_of(sk18)) ),
inference(resolution,[status(thm)],[p8040,p139]) ).
cnf(p8051,plain,
subset(inverse2(sk18,X0),domain_of(sk18)),
inference(factoring,[status(thm)],[p8047]) ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(C,B)
& subset(B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f9_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,C] :
( ( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c28,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p193,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X1 = X0
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c28,c82]) ).
cnf(p221,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[p193,c82]) ).
cnf(p8052,plain,
( ~ subset(domain_of(sk18),inverse2(sk18,X0))
| inverse2(sk18,X0) = domain_of(sk18) ),
inference(resolution,[status(thm)],[p8051,p221]) ).
cnf(p19185,plain,
( inverse2(sk18,sk17) = domain_of(sk18)
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p19182,p8052]) ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,image(D,B))
<=> ? [E] :
( member(E,B)
& member(ordered_pair(E,C),D)
& ilf_type(E,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( ! [E] :
( ~ member(E,B)
| ~ member(ordered_pair(E,C),D)
| ~ ilf_type(E,set_type) )
| member(C,image(D,B)) )
& ( ? [E] :
( member(E,B)
& member(ordered_pair(E,C),D)
& ilf_type(E,set_type) )
| ~ member(C,image(D,B)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D,E] :
( ( ( ~ member(E,B)
| ~ member(ordered_pair(E,C),D)
| ~ ilf_type(E,set_type)
| member(C,image(D,B)) )
& ( ( member(sk2(B,C,D),B)
& member(ordered_pair(sk2(B,C,D),C),D)
& ilf_type(sk2(B,C,D),set_type) )
| ~ member(C,image(D,B)) ) )
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f3_nnf]) ).
cnf(c11,plain,
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type)
| member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p115,plain,
( ~ member(X3,X2)
| ~ member(ordered_pair(X3,X0),X1)
| ~ ilf_type(X3,set_type)
| member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c11,c82]) ).
cnf(p401,plain,
( ~ member(X3,X2)
| ~ member(ordered_pair(X3,X1),X0)
| ~ ilf_type(X3,set_type)
| member(X1,image(X0,X2))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p115,c82]) ).
cnf(p1050,plain,
( ~ member(X2,X1)
| ~ member(ordered_pair(X2,X0),sk18)
| ~ ilf_type(X2,set_type)
| member(X0,image(sk18,X1)) ),
inference(resolution,[status(thm)],[p401,p198]) ).
cnf(p1312,plain,
( ~ member(X2,X1)
| ~ member(ordered_pair(X2,X0),sk18)
| member(X0,image(sk18,X1)) ),
inference(resolution,[status(thm)],[p1050,c82]) ).
cnf(c4,plain,
( member(ordered_pair(sk1(X0,X1),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p95,plain,
( member(ordered_pair(sk1(X1,X0),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[c4,c82]) ).
cnf(p200,plain,
( member(ordered_pair(sk1(X0,sk18),X0),sk18)
| ~ member(X0,range_of(sk18)) ),
inference(resolution,[status(thm)],[p198,p95]) ).
cnf(p210,plain,
( subset(range_of(sk18),X0)
| member(ordered_pair(sk1(sk9(range_of(sk18),X0),sk18),sk9(range_of(sk18),X0)),sk18) ),
inference(resolution,[status(thm)],[p200,p135]) ).
cnf(p1319,plain,
( subset(range_of(sk18),X0)
| ~ member(sk1(sk9(range_of(sk18),X0),sk18),X1)
| member(sk9(range_of(sk18),X0),image(sk18,X1)) ),
inference(resolution,[status(thm)],[p1312,p210]) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f32_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)],[f32]) ).
fof(f32_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)],[f32_nnf]) ).
cnf(c75,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)],[f32_sk]) ).
cnf(p306,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)],[c75,c82]) ).
cnf(p753,plain,
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p306,c82]) ).
cnf(p3921,plain,
ilf_type(domain_of(sk18),subset_type(sk16)),
inference(resolution,[status(thm)],[p753,c85]) ).
cnf(p3929,plain,
ilf_type(domain_of(sk18),member_type(power_set(sk16))),
inference(resolution,[status(thm)],[p3921,p151]) ).
cnf(p3930,plain,
( member(domain_of(sk18),power_set(sk16))
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p3929,p251]) ).
cnf(p3931,plain,
( member(X0,sk16)
| ~ member(X0,domain_of(sk18))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p3930,p634]) ).
cnf(p3986,plain,
( member(X0,sk16)
| ~ member(X0,domain_of(sk18))
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p3931,c82]) ).
cnf(p231,plain,
( subset(range_of(sk18),X0)
| member(sk1(sk9(range_of(sk18),X0),sk18),domain_of(sk18)) ),
inference(resolution,[status(thm)],[p228,p210]) ).
cnf(p3993,plain,
( subset(range_of(sk18),X0)
| member(sk1(sk9(range_of(sk18),X0),sk18),sk16)
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p3986,p231]) ).
cnf(p9693,plain,
( subset(range_of(sk18),X0)
| empty(power_set(sk16))
| subset(range_of(sk18),X0)
| member(sk9(range_of(sk18),X0),image(sk18,sk16)) ),
inference(resolution,[status(thm)],[p1319,p3993]) ).
cnf(p16350,plain,
( empty(power_set(sk16))
| subset(range_of(sk18),X0)
| member(sk9(range_of(sk18),X0),image(sk18,sk16)) ),
inference(factoring,[status(thm)],[p9693]) ).
cnf(p16351,plain,
( subset(range_of(sk18),image(sk18,sk16))
| empty(power_set(sk16))
| subset(range_of(sk18),image(sk18,sk16)) ),
inference(resolution,[status(thm)],[p16350,p139]) ).
cnf(p16356,plain,
( empty(power_set(sk16))
| subset(range_of(sk18),image(sk18,sk16)) ),
inference(factoring,[status(thm)],[p16351]) ).
cnf(c9,plain,
( member(ordered_pair(sk2(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p102,plain,
( member(ordered_pair(sk2(X2,X0,X1),X0),X1)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c9,c82]) ).
cnf(p379,plain,
( member(ordered_pair(sk2(X2,X1,X0),X1),X0)
| ~ member(X1,image(X0,X2))
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p102,c82]) ).
cnf(p966,plain,
( member(ordered_pair(sk2(X1,X0,sk18),X0),sk18)
| ~ member(X0,image(sk18,X1)) ),
inference(resolution,[status(thm)],[p379,p198]) ).
cnf(p972,plain,
( subset(image(sk18,X0),X1)
| member(ordered_pair(sk2(X0,sk9(image(sk18,X0),X1),sk18),sk9(image(sk18,X0),X1)),sk18) ),
inference(resolution,[status(thm)],[p966,p135]) ).
cnf(p3913,plain,
( member(sk9(image(sk18,X0),X1),range_of(sk18))
| subset(image(sk18,X0),X1) ),
inference(resolution,[status(thm)],[p972,p364]) ).
cnf(p3918,plain,
( subset(image(sk18,X0),range_of(sk18))
| subset(image(sk18,X0),range_of(sk18)) ),
inference(resolution,[status(thm)],[p3913,p139]) ).
cnf(p3932,plain,
subset(image(sk18,X0),range_of(sk18)),
inference(factoring,[status(thm)],[p3918]) ).
cnf(p3935,plain,
( ~ subset(range_of(sk18),image(sk18,X0))
| image(sk18,X0) = range_of(sk18) ),
inference(resolution,[status(thm)],[p3932,p221]) ).
cnf(p16364,plain,
( image(sk18,sk16) = range_of(sk18)
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p16356,p3935]) ).
fof(f37,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38) ).
fof(f37_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( inverse4(B,C,D,E) = inverse2(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [B,C,D,E] :
( inverse4(B,C,D,E) = inverse2(D,E)
| ~ ilf_type(E,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c80,plain,
( inverse4(X0,X1,X2,X3) = inverse2(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p343,plain,
( inverse4(X2,X0,X1,X3) = inverse2(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c80,c82]) ).
cnf(p876,plain,
( inverse4(X1,X2,X0,X3) = inverse2(X0,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p343,c82]) ).
cnf(p4865,plain,
( inverse4(sk16,sk17,sk18,X0) = inverse2(sk18,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p876,c85]) ).
cnf(p4874,plain,
inverse4(sk16,sk17,sk18,X0) = inverse2(sk18,X0),
inference(resolution,[status(thm)],[p4865,c82]) ).
fof(f35,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> image4(B,C,D,E) = image(D,E) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p36) ).
fof(f35_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( image4(B,C,D,E) = image(D,E)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [B,C,D,E] :
( image4(B,C,D,E) = image(D,E)
| ~ ilf_type(E,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c78,plain,
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p324,plain,
( image4(X2,X0,X1,X3) = image(X1,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c78,c82]) ).
cnf(p806,plain,
( image4(X1,X2,X0,X3) = image(X0,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p324,c82]) ).
cnf(p4471,plain,
( image4(sk16,sk17,sk18,X0) = image(sk18,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p806,c85]) ).
cnf(p4479,plain,
image4(sk16,sk17,sk18,X0) = image(sk18,X0),
inference(resolution,[status(thm)],[p4471,c82]) ).
fof(f33,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',p34) ).
fof(f33_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)],[f33]) ).
fof(f33_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)],[f33_nnf]) ).
cnf(c76,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)],[f33_sk]) ).
cnf(p308,plain,
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c76,c82]) ).
cnf(p758,plain,
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p308,c82]) ).
cnf(p3959,plain,
range(sk16,sk17,sk18) = range_of(sk18),
inference(resolution,[status(thm)],[p758,c85]) ).
fof(f31,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',p32) ).
fof(f31_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)],[f31]) ).
fof(f31_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)],[f31_nnf]) ).
cnf(c74,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)],[f31_sk]) ).
cnf(p304,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c74,c82]) ).
cnf(p748,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p304,c82]) ).
cnf(p3902,plain,
domain(sk16,sk17,sk18) = domain_of(sk18),
inference(resolution,[status(thm)],[p748,c85]) ).
cnf(c86,plain,
( inverse4(sk16,sk17,sk18,sk17) != domain(sk16,sk17,sk18)
| image4(sk16,sk17,sk18,sk16) != range(sk16,sk17,sk18) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p3903,plain,
( inverse4(sk16,sk17,sk18,sk17) != domain_of(sk18)
| image4(sk16,sk17,sk18,sk16) != range(sk16,sk17,sk18) ),
inference(demodulation,[status(thm)],[p3902,c86]) ).
cnf(p3960,plain,
( inverse4(sk16,sk17,sk18,sk17) != domain_of(sk18)
| image4(sk16,sk17,sk18,sk16) != range_of(sk18) ),
inference(demodulation,[status(thm)],[p3959,p3903]) ).
cnf(p4480,plain,
( inverse4(sk16,sk17,sk18,sk17) != domain_of(sk18)
| image(sk18,sk16) != range_of(sk18) ),
inference(demodulation,[status(thm)],[p4479,p3960]) ).
cnf(p4875,plain,
( inverse2(sk18,sk17) != domain_of(sk18)
| image(sk18,sk16) != range_of(sk18) ),
inference(demodulation,[status(thm)],[p4874,p4480]) ).
cnf(p16436,plain,
( inverse2(sk18,sk17) != domain_of(sk18)
| empty(power_set(sk16)) ),
inference(resolution,[status(thm)],[p16364,p4875]) ).
cnf(p19567,plain,
( empty(power_set(sk16))
| empty(power_set(sk17)) ),
inference(resolution,[status(thm)],[p19185,p16436]) ).
fof(f24,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',p25) ).
fof(f24_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c58,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p89,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c58,c82]) ).
cnf(p19603,plain,
empty(power_set(sk16)),
inference(resolution,[status(thm)],[p19567,p89]) ).
cnf(p19604,plain,
$false,
inference(resolution,[status(thm)],[p19603,p89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET674+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:33:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 82.23/11.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 82.23/11.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------