%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET661+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 02:10:23 PM UTC 2026
% Result : Theorem 0.15s 0.59s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 151 ( 22 unt; 0 def)
% Number of atoms : 491 ( 55 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 595 ( 255 ~; 252 |; 37 &)
% ( 12 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 264 ( 254 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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') ).
fof(f2,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') ).
fof(f4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),inverse(D))
<=> member(ordered_pair(C,B),D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f8,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') ).
fof(f14,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(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') ).
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') ).
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') ).
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') ).
fof(f35,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> inverse3(B,C,D) = inverse(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(inverse3(B,C,D),relation_type(C,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( range(C,B,inverse3(B,C,D)) = domain(B,C,D)
& domain(C,B,inverse3(B,C,D)) = range(B,C,D) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( range(C,B,inverse3(B,C,D)) = domain(B,C,D)
& domain(C,B,inverse3(B,C,D)) = range(B,C,D) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,plain,
! [B] :
( ! [C] :
( ( member(B,domain_of(C))
<=> ? [D] :
( member(ordered_pair(B,D),C)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f41,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)],[f40]) ).
fof(f42,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_skl(C,B)),C)
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,domain_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( member(ordered_pair(X0,sK0_skl(X1,X0)),X1)
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ 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(thm)],[f42]) ).
fof(f46,plain,
! [B] :
( ! [C] :
( ( member(B,range_of(C))
<=> ? [D] :
( member(ordered_pair(D,B),C)
& ilf_type(D,set_type) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f47,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)],[f46]) ).
fof(f48,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,B),C)
| ~ ilf_type(D,set_type) )
| member(B,range_of(C)) )
& ( ( member(ordered_pair(sK1_skl(C,B),B),C)
& ilf_type(sK1_skl(C,B),set_type) )
| ~ member(B,range_of(C)) ) )
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( member(ordered_pair(sK1_skl(X1,X0),X0),X1)
| ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ 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(thm)],[f48]) ).
fof(f55,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(ordered_pair(B,C),inverse(D))
<=> member(ordered_pair(C,B),D) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f56,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( ( ~ member(ordered_pair(C,B),D)
| member(ordered_pair(B,C),inverse(D)) )
& ( member(ordered_pair(C,B),D)
| ~ member(ordered_pair(B,C),inverse(D)) ) )
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( member(ordered_pair(X1,X0),X2)
| ~ member(ordered_pair(X0,X1),inverse(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X1,X0),X2)
| member(ordered_pair(X0,X1),inverse(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f65,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)],[f6]) ).
fof(f67,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)],[f65]) ).
fof(f71,plain,
! [B] :
( ! [C] :
( ( B = C
<=> ( subset(C,B)
& subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f72,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)],[f71]) ).
fof(f75,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f86,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)],[f14]) ).
fof(f87,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)],[f86]) ).
fof(f90,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)],[f87]) ).
fof(f112,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)],[f21]) ).
fof(f113,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)],[f112]) ).
fof(f114,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK7_skl(C,B),C)
& member(sK7_skl(C,B),B)
& ilf_type(sK7_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,[sK7_skl]),skolemize(D,sK7_skl(C,B))],[f113]) ).
fof(f117,plain,
! [X0,X1] :
( member(sK7_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
! [X0,X1] :
( ~ member(sK7_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f147,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)],[f28]) ).
fof(f148,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)],[f147]) ).
fof(f157,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(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f158,plain,
! [X0,X1,X2] :
( 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(thm)],[f157]) ).
fof(f161,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(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f162,plain,
! [X0,X1,X2] :
( 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(thm)],[f161]) ).
fof(f165,plain,
! [B] :
( ! [C] :
( ! [D] :
( inverse3(B,C,D) = inverse(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f166,plain,
! [X0,X1,X2] :
( inverse3(X0,X1,X2) = inverse(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f167,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(inverse3(B,C,D),relation_type(C,B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f168,plain,
! [X0,X1,X2] :
( ilf_type(inverse3(X0,X1,X2),relation_type(X1,X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f170,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( range(C,B,inverse3(B,C,D)) != domain(B,C,D)
| domain(C,B,inverse3(B,C,D)) != range(B,C,D) )
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f171,plain,
( ( range(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != domain(sK14_skl,sK15_skl,sK16_skl)
| domain(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != range(sK14_skl,sK15_skl,sK16_skl) )
& ilf_type(sK16_skl,relation_type(sK14_skl,sK15_skl))
& ilf_type(sK15_skl,set_type)
& ilf_type(sK14_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK14_skl),skolemize(C,sK15_skl),skolemize(D,sK16_skl)],[f170]) ).
fof(f174,plain,
ilf_type(sK16_skl,relation_type(sK14_skl,sK15_skl)),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
( range(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != domain(sK14_skl,sK15_skl,sK16_skl)
| domain(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != range(sK14_skl,sK15_skl,sK16_skl) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f180,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f90]) ).
fof(f181,plain,
! [X0,X1,X2] :
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f169]) ).
fof(f182,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f181,f169]) ).
fof(f183,plain,
domain(sK14_skl,sK15_skl,sK16_skl) = domain_of(sK16_skl),
inference(resolution,[status(thm)],[f182,f174]) ).
fof(f184,plain,
! [X0,X1,X2] :
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f162,f169]) ).
fof(f185,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f184,f169]) ).
fof(f191,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK0_skl(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f169]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type)
| member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f169]) ).
fof(f195,plain,
! [X0,X1] :
( member(sK7_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f169]) ).
fof(f212,plain,
( range(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != domain_of(sK16_skl)
| domain(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != range(sK14_skl,sK15_skl,sK16_skl) ),
inference(forward_demodulation,[status(thm)],[f183,f175]) ).
fof(f213,plain,
range(sK14_skl,sK15_skl,sK16_skl) = range_of(sK16_skl),
inference(resolution,[status(thm)],[f185,f174]) ).
fof(f214,plain,
( range(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != domain_of(sK16_skl)
| domain(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != range_of(sK16_skl) ),
inference(backward_demodulation,[status(thm)],[f213,f212]) ).
fof(f218,plain,
! [X0,X1,X2] :
( inverse3(X2,X0,X1) = inverse(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f169]) ).
fof(f219,plain,
! [X0,X1,X2] :
( inverse3(X1,X2,X0) = inverse(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f218,f169]) ).
fof(f220,plain,
inverse3(sK14_skl,sK15_skl,sK16_skl) = inverse(sK16_skl),
inference(resolution,[status(thm)],[f219,f174]) ).
fof(f221,plain,
( range(sK15_skl,sK14_skl,inverse(sK16_skl)) != domain_of(sK16_skl)
| domain(sK15_skl,sK14_skl,inverse3(sK14_skl,sK15_skl,sK16_skl)) != range_of(sK16_skl) ),
inference(backward_demodulation,[status(thm)],[f220,f214]) ).
fof(f222,plain,
( range(sK15_skl,sK14_skl,inverse(sK16_skl)) != domain_of(sK16_skl)
| domain(sK15_skl,sK14_skl,inverse(sK16_skl)) != range_of(sK16_skl) ),
inference(forward_demodulation,[status(thm)],[f220,f221]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ilf_type(inverse3(X2,X0,X1),relation_type(X0,X2))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f169]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ilf_type(inverse3(X1,X2,X0),relation_type(X2,X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f223,f169]) ).
fof(f225,plain,
ilf_type(inverse3(sK14_skl,sK15_skl,sK16_skl),relation_type(sK15_skl,sK14_skl)),
inference(resolution,[status(thm)],[f224,f174]) ).
fof(f226,plain,
ilf_type(inverse(sK16_skl),relation_type(sK15_skl,sK14_skl)),
inference(forward_demodulation,[status(thm)],[f220,f225]) ).
fof(f229,plain,
range(sK15_skl,sK14_skl,inverse(sK16_skl)) = range_of(inverse(sK16_skl)),
inference(resolution,[status(thm)],[f226,f185]) ).
fof(f230,plain,
domain(sK15_skl,sK14_skl,inverse(sK16_skl)) = domain_of(inverse(sK16_skl)),
inference(resolution,[status(thm)],[f226,f182]) ).
fof(f236,plain,
( range_of(inverse(sK16_skl)) != domain_of(sK16_skl)
| domain(sK15_skl,sK14_skl,inverse(sK16_skl)) != range_of(sK16_skl) ),
inference(backward_demodulation,[status(thm)],[f229,f222]) ).
fof(f264,plain,
( range_of(inverse(sK16_skl)) != domain_of(sK16_skl)
| domain_of(inverse(sK16_skl)) != range_of(sK16_skl) ),
inference(forward_demodulation,[status(thm)],[f230,f236]) ).
fof(f339,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f169]) ).
fof(f343,plain,
! [X0,X1] :
( member(ordered_pair(sK1_skl(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f169]) ).
fof(f344,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| member(X1,range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f169]) ).
fof(f532,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X1 = X0
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f169]) ).
fof(f533,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f532,f169]) ).
fof(f534,plain,
! [X0,X1] :
( ~ member(sK7_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f169]) ).
fof(f535,plain,
! [X0,X1] :
( ~ member(sK7_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f534,f169]) ).
fof(f538,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)],[f148,f169]) ).
fof(f539,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f538,f169]) ).
fof(f547,plain,
! [X0,X1,X2] :
( member(ordered_pair(X0,X2),X1)
| ~ member(ordered_pair(X2,X0),inverse(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f169]) ).
fof(f798,plain,
! [X0,X1,X2] :
( ~ member(ordered_pair(X0,X2),X1)
| member(ordered_pair(X2,X0),inverse(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f169]) ).
fof(f802,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)],[f67,f169]) ).
fof(f803,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f802,f169]) ).
fof(f1026,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f803,f539]) ).
fof(f1046,plain,
relation_like(inverse(sK16_skl)),
inference(resolution,[status(thm)],[f1026,f226]) ).
fof(f1047,plain,
relation_like(sK16_skl),
inference(resolution,[status(thm)],[f1026,f174]) ).
fof(f1048,plain,
ilf_type(sK16_skl,binary_relation_type),
inference(resolution,[status(thm)],[f1047,f339]) ).
fof(f1053,plain,
ilf_type(inverse(sK16_skl),binary_relation_type),
inference(resolution,[status(thm)],[f1046,f339]) ).
fof(f1054,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16_skl)
| ~ ilf_type(X1,set_type)
| member(X0,range_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1048,f344]) ).
fof(f1055,plain,
! [X0] :
( member(ordered_pair(sK1_skl(sK16_skl,X0),X0),sK16_skl)
| ~ member(X0,range_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1048,f343]) ).
fof(f1057,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK16_skl)
| ~ ilf_type(X1,set_type)
| member(X0,domain_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1048,f192]) ).
fof(f1058,plain,
! [X0] :
( member(ordered_pair(X0,sK0_skl(sK16_skl,X0)),sK16_skl)
| ~ member(X0,domain_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1048,f191]) ).
fof(f1059,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16_skl)
| member(X0,range_of(sK16_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1054,f169]) ).
fof(f1060,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK16_skl)
| member(X0,domain_of(sK16_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f169]) ).
fof(f1069,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),inverse(sK16_skl))
| ~ ilf_type(X1,set_type)
| member(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1053,f344]) ).
fof(f1070,plain,
! [X0] :
( member(ordered_pair(sK1_skl(inverse(sK16_skl),X0),X0),inverse(sK16_skl))
| ~ member(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1053,f343]) ).
fof(f1072,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),inverse(sK16_skl))
| ~ ilf_type(X1,set_type)
| member(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1053,f192]) ).
fof(f1073,plain,
! [X0] :
( member(ordered_pair(X0,sK0_skl(inverse(sK16_skl),X0)),inverse(sK16_skl))
| ~ member(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1053,f191]) ).
fof(f1074,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),inverse(sK16_skl))
| member(X0,range_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1069,f169]) ).
fof(f1075,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),inverse(sK16_skl))
| member(X0,domain_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1072,f169]) ).
fof(f1131,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ ilf_type(X0,set_type)
| member(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1074,f798]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| member(X0,range_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1131,f169]) ).
fof(f1133,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ ilf_type(X1,set_type)
| member(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1075,f798]) ).
fof(f1134,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| member(X0,domain_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1133,f169]) ).
fof(f1155,plain,
! [X0] :
( member(ordered_pair(X0,sK1_skl(inverse(sK16_skl),X0)),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ member(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1070,f547]) ).
fof(f1156,plain,
! [X0] :
( member(ordered_pair(X0,sK1_skl(inverse(sK16_skl),X0)),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ member(X0,range_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1155,f169]) ).
fof(f1159,plain,
! [X0] :
( member(ordered_pair(sK0_skl(inverse(sK16_skl),X0),X0),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ ilf_type(sK0_skl(inverse(sK16_skl),X0),set_type)
| ~ member(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1073,f547]) ).
fof(f1160,plain,
! [X0] :
( member(ordered_pair(sK0_skl(inverse(sK16_skl),X0),X0),sK16_skl)
| ~ ilf_type(sK16_skl,binary_relation_type)
| ~ member(X0,domain_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1159,f169]) ).
fof(f1173,plain,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),sK16_skl)
| member(X0,range_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1132,f1048]) ).
fof(f1174,plain,
! [X0,X1] :
( subset(X0,range_of(inverse(sK16_skl)))
| ~ member(ordered_pair(sK7_skl(range_of(inverse(sK16_skl)),X0),X1),sK16_skl) ),
inference(resolution,[status(thm)],[f1173,f535]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ member(ordered_pair(X1,X0),sK16_skl)
| member(X0,domain_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1134,f1048]) ).
fof(f1176,plain,
! [X0,X1] :
( subset(X1,domain_of(inverse(sK16_skl)))
| ~ member(ordered_pair(X0,sK7_skl(domain_of(inverse(sK16_skl)),X1)),sK16_skl) ),
inference(resolution,[status(thm)],[f1175,f535]) ).
fof(f1186,plain,
! [X0] :
( ~ member(sK7_skl(range_of(inverse(sK16_skl)),X0),domain_of(sK16_skl))
| subset(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1174,f1058]) ).
fof(f1187,plain,
( subset(domain_of(sK16_skl),range_of(inverse(sK16_skl)))
| ~ ilf_type(range_of(inverse(sK16_skl)),set_type)
| subset(domain_of(sK16_skl),range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1186,f195]) ).
fof(f1188,plain,
( ~ ilf_type(range_of(inverse(sK16_skl)),set_type)
| subset(domain_of(sK16_skl),range_of(inverse(sK16_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f1187]) ).
fof(f1189,plain,
subset(domain_of(sK16_skl),range_of(inverse(sK16_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f1188,f169]) ).
fof(f1190,plain,
( ~ subset(range_of(inverse(sK16_skl)),domain_of(sK16_skl))
| range_of(inverse(sK16_skl)) = domain_of(sK16_skl) ),
inference(resolution,[status(thm)],[f1189,f533]) ).
fof(f1191,plain,
! [X0] :
( ~ member(sK7_skl(domain_of(inverse(sK16_skl)),X0),range_of(sK16_skl))
| subset(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1176,f1055]) ).
fof(f1192,plain,
( subset(range_of(sK16_skl),domain_of(inverse(sK16_skl)))
| ~ ilf_type(domain_of(inverse(sK16_skl)),set_type)
| subset(range_of(sK16_skl),domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1191,f195]) ).
fof(f1193,plain,
( ~ ilf_type(domain_of(inverse(sK16_skl)),set_type)
| subset(range_of(sK16_skl),domain_of(inverse(sK16_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f1192]) ).
fof(f1194,plain,
subset(range_of(sK16_skl),domain_of(inverse(sK16_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f1193,f169]) ).
fof(f1195,plain,
( ~ subset(domain_of(inverse(sK16_skl)),range_of(sK16_skl))
| domain_of(inverse(sK16_skl)) = range_of(sK16_skl) ),
inference(resolution,[status(thm)],[f1194,f533]) ).
fof(f1218,plain,
! [X0] :
( member(ordered_pair(X0,sK1_skl(inverse(sK16_skl),X0)),sK16_skl)
| ~ member(X0,range_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1156,f1048]) ).
fof(f1220,plain,
! [X0] :
( member(X0,domain_of(sK16_skl))
| ~ member(X0,range_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1218,f1060]) ).
fof(f1233,plain,
! [X0] :
( subset(range_of(inverse(sK16_skl)),X0)
| ~ ilf_type(X0,set_type)
| member(sK7_skl(X0,range_of(inverse(sK16_skl))),domain_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1220,f195]) ).
fof(f1238,plain,
! [X0] :
( subset(range_of(inverse(sK16_skl)),X0)
| member(sK7_skl(X0,range_of(inverse(sK16_skl))),domain_of(sK16_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1233,f169]) ).
fof(f1244,plain,
( subset(range_of(inverse(sK16_skl)),domain_of(sK16_skl))
| subset(range_of(inverse(sK16_skl)),domain_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1238,f535]) ).
fof(f1246,plain,
subset(range_of(inverse(sK16_skl)),domain_of(sK16_skl)),
inference(duplicate_literals_removal,[status(thm)],[f1244]) ).
fof(f1247,plain,
! [X0] :
( member(ordered_pair(sK0_skl(inverse(sK16_skl),X0),X0),sK16_skl)
| ~ member(X0,domain_of(inverse(sK16_skl))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1160,f1048]) ).
fof(f1250,plain,
! [X0] :
( member(X0,range_of(sK16_skl))
| ~ member(X0,domain_of(inverse(sK16_skl))) ),
inference(resolution,[status(thm)],[f1247,f1059]) ).
fof(f1259,plain,
range_of(inverse(sK16_skl)) = domain_of(sK16_skl),
inference(backward_subsumption_resolution,[status(thm)],[f1190,f1246]) ).
fof(f1283,plain,
( domain_of(sK16_skl) != domain_of(sK16_skl)
| domain_of(inverse(sK16_skl)) != range_of(sK16_skl) ),
inference(backward_demodulation,[status(thm)],[f1259,f264]) ).
fof(f1300,plain,
domain_of(inverse(sK16_skl)) != range_of(sK16_skl),
inference(trivial_equality_resolution,[status(thm)],[f1283]) ).
fof(f1301,plain,
~ subset(domain_of(inverse(sK16_skl)),range_of(sK16_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f1195,f1300]) ).
fof(f1361,plain,
! [X0] :
( subset(domain_of(inverse(sK16_skl)),X0)
| ~ ilf_type(X0,set_type)
| member(sK7_skl(X0,domain_of(inverse(sK16_skl))),range_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1250,f195]) ).
fof(f1366,plain,
! [X0] :
( subset(domain_of(inverse(sK16_skl)),X0)
| member(sK7_skl(X0,domain_of(inverse(sK16_skl))),range_of(sK16_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1361,f169]) ).
fof(f1380,plain,
( subset(domain_of(inverse(sK16_skl)),range_of(sK16_skl))
| subset(domain_of(inverse(sK16_skl)),range_of(sK16_skl)) ),
inference(resolution,[status(thm)],[f1366,f535]) ).
fof(f1382,plain,
subset(domain_of(inverse(sK16_skl)),range_of(sK16_skl)),
inference(duplicate_literals_removal,[status(thm)],[f1380]) ).
fof(f1383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1382,f1301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET661+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:32:09 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.59 % Refutation found
% 0.15/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.31/0.61 % Elapsed time: 0.247573 seconds
% 1.31/0.61 % CPU time: 1.582957 seconds
% 1.31/0.61 % Total memory used: 116.861 MB
% 1.31/0.61 % Net memory used: 114.701 MB
%------------------------------------------------------------------------------