%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 02:10:27 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 170 ( 16 unt; 25 def)
% Number of atoms : 624 ( 27 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 770 ( 316 ~; 312 |; 64 &)
% ( 35 <=>; 42 =>; 0 <=; 1 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 26 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 239 ( 222 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,set_type)
=> ( F = ordered_pair(D,E)
<=> F = unordered_pair(unordered_pair(D,E),singleton(D)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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/sandbox2/benchmark/theBenchmark.p') ).
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,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') ).
fof(f24,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') ).
fof(f25,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') ).
fof(f26,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)
=> ilf_type(image4(B,C,D,E),subset_type(C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ( ilf_type(D,set_type)
& ~ empty(D) )
=> ! [E] :
( ilf_type(E,relation_type(D,B))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,image4(D,B,E,C))
<=> ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ( ilf_type(D,set_type)
& ~ empty(D) )
=> ! [E] :
( ilf_type(E,relation_type(D,B))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,image4(D,B,E,C))
<=> ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(C,image(D,B))
<=> ? [E] :
( member(E,B)
& member(ordered_pair(E,C),D)
& ilf_type(E,set_type) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f31,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)],[f30]) ).
fof(f32,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(sK0_skl(D,C,B),B)
& member(ordered_pair(sK0_skl(D,C,B),C),D)
& ilf_type(sK0_skl(D,C,B),set_type) )
| ~ member(C,image(D,B)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(D,C,B))],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( member(ordered_pair(sK0_skl(X2,X1,X0),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(thm)],[f32]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,X1,X0),X0)
| ~ 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(thm)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ 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(thm)],[f32]) ).
fof(f37,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( member(E,C)
& member(D,B) )
| ~ member(ordered_pair(D,E),F)
| ~ ilf_type(F,relation_type(B,C)) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f40,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( F = ordered_pair(D,E)
<=> F = unordered_pair(unordered_pair(D,E),singleton(D)) )
| ~ ilf_type(F,set_type) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ! [F] :
( ( ( F != unordered_pair(unordered_pair(D,E),singleton(D))
| F = ordered_pair(D,E) )
& ( F = unordered_pair(unordered_pair(D,E),singleton(D))
| F != ordered_pair(D,E) ) )
| ~ ilf_type(F,set_type) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( ! [D] :
( ! [E] :
( ! [F] :
( ( ( F != unordered_pair(unordered_pair(D,E),singleton(D))
| F = ordered_pair(D,E) )
& ( F = unordered_pair(unordered_pair(D,E),singleton(D))
| F != ordered_pair(D,E) ) )
| ~ ilf_type(F,set_type) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ! [C] : ~ ilf_type(C,set_type)
| ! [B] : ~ ilf_type(B,set_type) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4] :
( X4 = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 != ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( X4 != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 = ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,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(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( 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(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ 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(thm)],[f54]) ).
fof(f76,plain,
! [B] :
( ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f77,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)],[f76]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f119,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(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f120,plain,
! [X0,X1,X2] :
( 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(thm)],[f119]) ).
fof(f121,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(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( 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(thm)],[f121]) ).
fof(f123,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ilf_type(image4(B,C,D,E),subset_type(C))
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ilf_type(image4(X0,X1,X2,X3),subset_type(X1))
| ~ 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(thm)],[f123]) ).
fof(f125,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f126,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ( member(F,image4(D,B,E,C))
<~> ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) ) )
& ilf_type(F,member_type(B)) )
& ilf_type(E,relation_type(D,B)) )
& ilf_type(D,set_type)
& ~ empty(D) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f127,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ( ! [G] :
( ~ member(G,C)
| ~ member(ordered_pair(G,F),E)
| ~ ilf_type(G,member_type(D)) )
| ~ member(F,image4(D,B,E,C)) )
& ( ? [G] :
( member(G,C)
& member(ordered_pair(G,F),E)
& ilf_type(G,member_type(D)) )
| member(F,image4(D,B,E,C)) )
& ilf_type(F,member_type(B)) )
& ilf_type(E,relation_type(D,B)) )
& ilf_type(D,set_type)
& ~ empty(D) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
( ( ! [G] :
( ~ member(G,sK12_skl)
| ~ member(ordered_pair(G,sK15_skl),sK14_skl)
| ~ ilf_type(G,member_type(sK13_skl)) )
| ~ member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) )
& ( ( member(sK16_skl,sK12_skl)
& member(ordered_pair(sK16_skl,sK15_skl),sK14_skl)
& ilf_type(sK16_skl,member_type(sK13_skl)) )
| member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) )
& ilf_type(sK15_skl,member_type(sK11_skl))
& ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))
& ilf_type(sK13_skl,set_type)
& ~ empty(sK13_skl)
& ilf_type(sK12_skl,set_type)
& ~ empty(sK12_skl)
& ilf_type(sK11_skl,set_type)
& ~ empty(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK11_skl),skolemize(C,sK12_skl),skolemize(D,sK13_skl),skolemize(E,sK14_skl),skolemize(F,sK15_skl),skolemize(G,sK16_skl)],[f127]) ).
fof(f129,plain,
~ empty(sK11_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f133,plain,
~ empty(sK13_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f135,plain,
ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f136,plain,
ilf_type(sK15_skl,member_type(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f138,plain,
( member(ordered_pair(sK16_skl,sK15_skl),sK14_skl)
| member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f139,plain,
( member(sK16_skl,sK12_skl)
| member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f140,plain,
! [X0] :
( ~ member(X0,sK12_skl)
| ~ member(ordered_pair(X0,sK15_skl),sK14_skl)
| ~ ilf_type(X0,member_type(sK13_skl))
| ~ member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f141,definition,
! [X0] :
( sQ0_spl
<=> ~ ilf_type(X0,set_type) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f142,plain,
! [X0] :
( ~ sQ0_spl
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
! [X2,X3,X4] :
( sQ1_spl
<=> ( X4 = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 != ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f141,f144]) ).
fof(f148,definition,
! [X2,X3,X4] :
( sQ2_spl
<=> ( X4 != unordered_pair(unordered_pair(X2,X3),singleton(X2))
| X4 = ordered_pair(X2,X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f141,f148]) ).
fof(f152,definition,
( sQ3_spl
<=> member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ3_spl
| member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( sQ3_spl
| ~ member(sK15_skl,image4(sK13_skl,sK11_skl,sK14_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f159,definition,
( sQ5_spl
<=> member(ordered_pair(sK16_skl,sK15_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ5_spl
| member(ordered_pair(sK16_skl,sK15_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f138,f152,f159]) ).
fof(f163,definition,
( sQ6_spl
<=> member(sK16_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ6_spl
| member(sK16_skl,sK12_skl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ6_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f139,f152,f163]) ).
fof(f167,definition,
! [X0] :
( sQ7_spl
<=> ( ~ member(X0,sK12_skl)
| ~ member(ordered_pair(X0,sK15_skl),sK14_skl)
| ~ ilf_type(X0,member_type(sK13_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f168,plain,
! [X0] :
( ~ sQ7_spl
| ~ member(X0,sK12_skl)
| ~ member(ordered_pair(X0,sK15_skl),sK14_skl)
| ~ ilf_type(X0,member_type(sK13_skl)) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f140,f152,f167]) ).
fof(f171,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f80]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4] :
( member(X1,X4)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,relation_type(X4,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f125]) ).
fof(f174,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f125]) ).
fof(f175,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f125]) ).
fof(f176,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f179,plain,
! [X0,X1,X2] :
( member(ordered_pair(sK0_skl(X1,X0,X2),X0),X1)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f125]) ).
fof(f180,plain,
! [X0,X1,X2] :
( member(sK0_skl(X1,X0,X2),X2)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f125]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ 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(forward_subsumption_resolution,[status(thm)],[f36,f125]) ).
fof(f182,plain,
! [X0,X1,X2] :
( ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f125]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f125]) ).
fof(f184,plain,
( ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl)))
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f135,f183]) ).
fof(f185,definition,
( sQ8_spl
<=> ilf_type(sK11_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ8_spl
| ~ ilf_type(sK11_skl,set_type) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ9_spl
<=> ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ9_spl
| ilf_type(sK14_skl,subset_type(cross_product(sK13_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f184,f185,f188]) ).
fof(f192,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f187,f125]) ).
fof(f193,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( member(sK15_skl,sK11_skl)
| ~ ilf_type(sK11_skl,set_type)
| empty(sK11_skl) ),
inference(resolution,[status(thm)],[f136,f174]) ).
fof(f195,definition,
( sQ10_spl
<=> empty(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ10_spl
| empty(sK11_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ11_spl
<=> member(sK15_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ11_spl
| ~ sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f194,f195,f185,f198]) ).
fof(f202,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f129]) ).
fof(f203,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( ~ sQ9_spl
| ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f189,f182]) ).
fof(f205,definition,
( sQ12_spl
<=> ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ9_spl
| sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f204,f185,f205,f188]) ).
fof(f209,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f125]) ).
fof(f210,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f209,f125]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( 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(forward_subsumption_resolution,[status(thm)],[f122,f125]) ).
fof(f213,plain,
! [X0,X1,X2,X3] :
( image4(X2,X0,X1,X3) = image(X1,X3)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f212,f125]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( image4(X1,X2,X0,X3) = image(X0,X3)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f125]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ilf_type(image4(X2,X0,X1,X3),subset_type(X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f125]) ).
fof(f242,plain,
! [X0] : image4(sK13_skl,sK11_skl,sK14_skl,X0) = image(sK14_skl,X0),
inference(resolution,[status(thm)],[f214,f135]) ).
fof(f253,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f125]) ).
fof(f261,plain,
( ~ sQ3_spl
| member(sK15_skl,image(sK14_skl,sK12_skl)) ),
inference(backward_demodulation,[status(thm)],[f242,f153]) ).
fof(f262,plain,
! [X0] :
( ilf_type(image(sK14_skl,X0),subset_type(sK11_skl))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14_skl,relation_type(sK13_skl,sK11_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(paramodulation,[status(thm)],[f242,f215]) ).
fof(f263,definition,
! [X0] :
( sQ13_spl
<=> ( ilf_type(image(sK14_skl,X0),subset_type(sK11_skl))
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ13_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f262,f185,f205,f263]) ).
fof(f268,plain,
( ~ sQ3_spl
| member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl)
| ~ ilf_type(sK14_skl,binary_relation_type)
| ~ ilf_type(sK15_skl,set_type) ),
inference(resolution,[status(thm)],[f261,f180]) ).
fof(f269,plain,
( ~ sQ3_spl
| member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl)
| ~ ilf_type(sK14_skl,binary_relation_type)
| ~ ilf_type(sK15_skl,set_type) ),
inference(resolution,[status(thm)],[f261,f179]) ).
fof(f270,definition,
( sQ14_spl
<=> ilf_type(sK15_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ14_spl
| ~ ilf_type(sK15_skl,set_type) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ15_spl
<=> ilf_type(sK14_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ15_spl
| ~ ilf_type(sK14_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,definition,
( sQ16_spl
<=> member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( ~ sQ3_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f268,f270,f273,f276,f152]) ).
fof(f280,definition,
( sQ17_spl
<=> member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ17_spl
| member(ordered_pair(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK15_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( ~ sQ3_spl
| sQ17_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f269,f270,f273,f280,f152]) ).
fof(f285,definition,
( sQ18_spl
<=> empty(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ18_spl
| empty(sK13_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ19_spl
<=> ilf_type(sK13_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ19_spl
| ~ ilf_type(sK13_skl,set_type) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f295,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f125]) ).
fof(f296,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f297,plain,
( sQ15_spl
| ~ relation_like(sK14_skl) ),
inference(resolution,[status(thm)],[f275,f253]) ).
fof(f396,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f125]) ).
fof(f397,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f396,f125]) ).
fof(f400,plain,
! [X0,X1] :
( sQ15_spl
| ~ ilf_type(sK14_skl,subset_type(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f397,f297]) ).
fof(f406,plain,
( ~ sQ9_spl
| sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f400]) ).
fof(f408,plain,
( ~ sQ9_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f413,plain,
( ~ sQ7_spl
| ~ sQ17_spl
| ~ member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK12_skl)
| ~ ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl)) ),
inference(resolution,[status(thm)],[f281,f168]) ).
fof(f416,plain,
! [X0,X1] :
( ~ sQ17_spl
| member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),X1)
| ~ ilf_type(sK14_skl,relation_type(X1,X0))
| ~ ilf_type(sK15_skl,set_type)
| ~ ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f281,f172]) ).
fof(f417,definition,
( sQ21_spl
<=> ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ21_spl
| ~ ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),member_type(sK13_skl)) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( ~ sQ7_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f413,f417,f276,f280,f167]) ).
fof(f424,definition,
( sQ23_spl
<=> ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),set_type) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( sQ23_spl
| ~ ilf_type(sK0_skl(sK14_skl,sK15_skl,sK12_skl),set_type) ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f432,definition,
! [X0,X1] :
( sQ25_spl
<=> ( member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),X1)
| ~ ilf_type(sK14_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f433,plain,
! [X0,X1] :
( ~ sQ25_spl
| member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),X1)
| ~ ilf_type(sK14_skl,relation_type(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ23_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f416,f432,f424,f270,f280]) ).
fof(f436,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f125]) ).
fof(f437,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( ~ sQ25_spl
| member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),X0)
| ~ ilf_type(sK14_skl,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f125]) ).
fof(f454,plain,
( sQ21_spl
| ~ member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK13_skl)
| empty(sK13_skl) ),
inference(resolution,[status(thm)],[f419,f210]) ).
fof(f455,definition,
( sQ26_spl
<=> member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ26_spl
| ~ member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ21_spl
| ~ sQ26_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f454,f285,f455,f417]) ).
fof(f459,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f286,f133]) ).
fof(f460,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f478,plain,
( ~ sQ25_spl
| member(sK0_skl(sK14_skl,sK15_skl,sK12_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f438,f135]) ).
fof(f479,plain,
( ~ sQ25_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f457]) ).
fof(f480,plain,
( ~ sQ25_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f481,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f125]) ).
fof(f482,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ3_spl
| ~ member(sK15_skl,image(sK14_skl,sK12_skl)) ),
inference(forward_demodulation,[status(thm)],[f242,f154]) ).
fof(f484,plain,
! [X0] :
( ~ sQ5_spl
| ~ member(sK16_skl,X0)
| ~ ilf_type(sK16_skl,set_type)
| member(sK15_skl,image(sK14_skl,X0))
| ~ ilf_type(sK14_skl,binary_relation_type)
| ~ ilf_type(sK15_skl,set_type) ),
inference(resolution,[status(thm)],[f160,f181]) ).
fof(f487,definition,
! [X0] :
( sQ27_spl
<=> ( ~ member(sK16_skl,X0)
| member(sK15_skl,image(sK14_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f488,plain,
! [X0] :
( ~ sQ27_spl
| ~ member(sK16_skl,X0)
| member(sK15_skl,image(sK14_skl,X0)) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,definition,
( sQ28_spl
<=> ilf_type(sK16_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ28_spl
| ~ ilf_type(sK16_skl,set_type) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( ~ sQ5_spl
| ~ sQ28_spl
| sQ27_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f484,f270,f273,f487,f490,f159]) ).
fof(f499,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f125]) ).
fof(f500,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f504,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ member(sK16_skl,sK12_skl) ),
inference(resolution,[status(thm)],[f488,f483]) ).
fof(f507,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f164]) ).
fof(f508,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f151,f162,f166,f170,f176,f191,f193,f201,f203,f208,f266,f279,f283,f296,f408,f420,f435,f437,f458,f460,f480,f482,f493,f500,f508]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET685+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:33:25 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.047648 seconds
% 0.11/0.42 % CPU time: 0.155941 seconds
% 0.11/0.42 % Total memory used: 30.724 MB
% 0.11/0.42 % Net memory used: 30.604 MB
%------------------------------------------------------------------------------