%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET673+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:10:25 PM UTC 2026
% Result : Theorem 4.92s 1.08s
% Output : CNFRefutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 103 ( 14 unt; 0 def)
% Number of atoms : 442 ( 20 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 594 ( 255 ~; 249 |; 38 &)
% ( 10 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 203 ( 196 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( B = C
<=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(D,E),B)
<=> member(ordered_pair(D,E),C) ) ) ) ) ) ),
file('/export/starexec/sandbox/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,binary_relation_type)
=> ( member(ordered_pair(C,D),restrict(B,E))
<=> ( member(ordered_pair(C,D),E)
& member(D,B) ) ) ) ) ) ),
file('/export/starexec/sandbox/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,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ilf_type(restrict(B,C),binary_relation_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> restrict4(B,C,D,E) = restrict(D,E) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(C,D)
=> restrict4(B,C,D,E) = E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(C,D)
=> restrict4(B,C,D,E) = E ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ( B = C
<=> ! [D] :
( ! [E] :
( ( member(ordered_pair(D,E),B)
<=> member(ordered_pair(D,E),C) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ? [E] :
( ( member(ordered_pair(D,E),C)
| member(ordered_pair(D,E),B) )
& ( ~ member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B) )
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
| B = C )
& ( ! [D] :
( ! [E] :
( ( ( ~ member(ordered_pair(D,E),C)
| member(ordered_pair(D,E),B) )
& ( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B) ) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| B != C ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [B] :
( ! [C] :
( ( ( ( ( member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),C)
| member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),B) )
& ( ~ member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),C)
| ~ member(ordered_pair(sK0_skl(C,B),sK1_skl(C,B)),B) )
& ilf_type(sK1_skl(C,B),set_type)
& ilf_type(sK0_skl(C,B),set_type) )
| B = C )
& ( ! [D] :
( ! [E] :
( ( ( ~ member(ordered_pair(D,E),C)
| member(ordered_pair(D,E),B) )
& ( member(ordered_pair(D,E),C)
| ~ member(ordered_pair(D,E),B) ) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| B != C ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(C,B)),skolemize(E,sK1_skl(C,B))],[f31]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X1)
| ~ member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = X1
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f38,plain,
! [X0,X1] :
( member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X1)
| member(ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0)),X0)
| X0 = X1
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f39,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( member(ordered_pair(C,D),restrict(B,E))
<=> ( member(ordered_pair(C,D),E)
& member(D,B) ) )
| ~ ilf_type(E,binary_relation_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( ( ~ member(ordered_pair(C,D),E)
| ~ member(D,B)
| member(ordered_pair(C,D),restrict(B,E)) )
& ( ( member(ordered_pair(C,D),E)
& member(D,B) )
| ~ member(ordered_pair(C,D),restrict(B,E)) ) )
| ~ ilf_type(E,binary_relation_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X1,X2),X3)
| ~ member(X2,X0)
| member(ordered_pair(X1,X2),restrict(X0,X3))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,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)],[f3]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( member(X3,X1)
| ~ 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)],[f44]) ).
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)],[f4]) ).
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] :
( ( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3_skl(C,B),C)
& member(sK3_skl(C,B),B)
& ilf_type(sK3_skl(C,B),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(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(D,sK3_skl(C,B))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f64,plain,
! [B] :
( ! [C] :
( ilf_type(restrict(B,C),binary_relation_type)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f65,plain,
! [X0,X1] :
( ilf_type(restrict(X0,X1),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,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)],[f10]) ).
fof(f67,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)],[f66]) ).
fof(f70,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)],[f67]) ).
fof(f112,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)],[f22]) ).
fof(f113,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)],[f112]) ).
fof(f122,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( restrict4(B,C,D,E) = restrict(D,E)
| ~ ilf_type(E,relation_type(B,C)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( restrict4(X0,X1,X2,X3) = restrict(X2,X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f126,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f127,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( restrict4(B,C,D,E) != E
& subset(C,D)
& ilf_type(E,relation_type(B,C)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f128,plain,
( restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl) != sK15_skl
& subset(sK13_skl,sK14_skl)
& ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl))
& ilf_type(sK14_skl,set_type)
& ilf_type(sK13_skl,set_type)
& ilf_type(sK12_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl,sK15_skl]),skolemize(B,sK12_skl),skolemize(C,sK13_skl),skolemize(D,sK14_skl),skolemize(E,sK15_skl)],[f127]) ).
fof(f132,plain,
ilf_type(sK15_skl,relation_type(sK12_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f133,plain,
subset(sK13_skl,sK14_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f134,plain,
restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl) != sK15_skl,
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f135,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( restrict4(X0,X1,X3,X2) = restrict(X3,X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f123,f126]) ).
fof(f142,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f113,f126]) ).
fof(f156,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f135,f126]) ).
fof(f158,plain,
! [X0,X1] :
( ilf_type(restrict(X1,X0),binary_relation_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f126]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f126]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f49,f126]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X1)
| ~ member(ordered_pair(X2,X4),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f46,f126]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X1,X3),X2)
| ~ member(X3,X0)
| member(ordered_pair(X1,X3),restrict(X0,X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f126]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X1,X3),X2)
| ~ member(ordered_pair(X1,X3),restrict(X0,X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f126]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( restrict4(X2,X0,X3,X1) = restrict(X3,X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f126]) ).
fof(f174,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f126]) ).
fof(f185,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f126]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f126]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X0)
| ~ member(ordered_pair(X1,X4),X2)
| ~ ilf_type(X2,relation_type(X3,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f126]) ).
fof(f191,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X0,X2),X1)
| ~ member(X2,X3)
| member(ordered_pair(X0,X2),restrict(X3,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f126]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),X1)
| ~ member(ordered_pair(X0,X2),restrict(X3,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f126]) ).
fof(f198,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl),binary_relation_type) ),
inference(resolution,[status(thm)],[f37,f134]) ).
fof(f203,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl),binary_relation_type) ),
inference(resolution,[status(thm)],[f38,f134]) ).
fof(f229,plain,
! [X0] :
( restrict4(sK12_skl,sK13_skl,X0,sK15_skl) = restrict(X0,sK15_skl)
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f172,f132]) ).
fof(f231,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl),binary_relation_type) ),
inference(backward_demodulation,[status(thm)],[f238,f198]) ).
fof(f235,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl),binary_relation_type) ),
inference(backward_demodulation,[status(thm)],[f238,f203]) ).
fof(f238,plain,
! [X0] : restrict4(sK12_skl,sK13_skl,X0,sK15_skl) = restrict(X0,sK15_skl),
inference(forward_subsumption_resolution,[status(thm)],[f229,f126]) ).
fof(f239,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f231]) ).
fof(f240,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f239]) ).
fof(f241,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f240]) ).
fof(f242,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f241]) ).
fof(f243,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f242]) ).
fof(f244,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f158]) ).
fof(f251,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f235]) ).
fof(f252,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f251]) ).
fof(f253,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f252]) ).
fof(f254,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict4(sK12_skl,sK13_skl,sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f253]) ).
fof(f255,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(restrict(sK14_skl,sK15_skl),binary_relation_type) ),
inference(forward_demodulation,[status(thm)],[f238,f254]) ).
fof(f256,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl))
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f158]) ).
fof(f545,plain,
( ~ relation_like(sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),restrict(sK14_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f256,f156]) ).
fof(f569,plain,
! [X0] :
( member(X0,sK14_skl)
| ~ member(X0,sK13_skl)
| ~ ilf_type(sK14_skl,set_type) ),
inference(resolution,[status(thm)],[f185,f133]) ).
fof(f607,plain,
! [X0] :
( member(X0,sK14_skl)
| ~ member(X0,sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f126]) ).
fof(f686,plain,
ilf_type(sK15_skl,subset_type(cross_product(sK12_skl,sK13_skl))),
inference(resolution,[status(thm)],[f187,f132]) ).
fof(f699,plain,
! [X0,X1] :
( member(X1,sK13_skl)
| ~ member(ordered_pair(X0,X1),sK15_skl)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13_skl,set_type) ),
inference(resolution,[status(thm)],[f189,f132]) ).
fof(f733,plain,
! [X0,X1] :
( member(X1,sK13_skl)
| ~ member(ordered_pair(X0,X1),sK15_skl)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f126]) ).
fof(f913,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK14_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),set_type) ),
inference(resolution,[status(thm)],[f191,f244]) ).
fof(f972,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK14_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f913]) ).
fof(f973,plain,
( ~ member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK14_skl)
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f126]) ).
fof(f1053,plain,
! [X0,X1,X2,X3] :
( ~ relation_like(X3)
| member(ordered_pair(X0,X1),X3)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f192,f156]) ).
fof(f1054,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),set_type) ),
inference(resolution,[status(thm)],[f192,f256]) ).
fof(f1089,plain,
( ~ relation_like(sK15_skl)
| member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f545,f1093]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] :
( ~ relation_like(X3)
| member(ordered_pair(X0,X1),X3)
| ~ member(ordered_pair(X0,X1),restrict(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1053,f126]) ).
fof(f1094,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type)
| ~ ilf_type(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f1054]) ).
fof(f1095,plain,
( ~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK14_skl)
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f973,f1102]) ).
fof(f1102,plain,
( member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f1094,f126]) ).
fof(f1258,plain,
relation_like(sK15_skl),
inference(resolution,[status(thm)],[f686,f174]) ).
fof(f1265,plain,
member(ordered_pair(sK0_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl),
inference(backward_subsumption_resolution,[status(thm)],[f1089,f1258]) ).
fof(f1277,plain,
ilf_type(sK15_skl,binary_relation_type),
inference(resolution,[status(thm)],[f1258,f156]) ).
fof(f1304,plain,
~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK14_skl),
inference(backward_subsumption_resolution,[status(thm)],[f1095,f1277]) ).
fof(f1335,plain,
~ member(sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl)),sK13_skl),
inference(resolution,[status(thm)],[f1304,f607]) ).
fof(f1481,plain,
! [X0] :
( ~ member(ordered_pair(X0,sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f733,f1335]) ).
fof(f1506,plain,
! [X0] : ~ member(ordered_pair(X0,sK1_skl(sK15_skl,restrict(sK14_skl,sK15_skl))),sK15_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1481,f126]) ).
fof(f1507,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1265,f1506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET673+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:34:46 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 4.92/1.08 % Refutation found
% 4.92/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.92/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.92/1.12 % Elapsed time: 0.768390 seconds
% 4.92/1.12 % CPU time: 5.763285 seconds
% 4.92/1.12 % Total memory used: 180.078 MB
% 4.92/1.12 % Net memory used: 167.573 MB
%------------------------------------------------------------------------------