%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET996+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:11:07 PM UTC 2026
% Result : Theorem 54.71s 7.36s
% Output : CNFRefutation 54.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 32 unt; 0 def)
% Number of atoms : 340 ( 89 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 370 ( 145 ~; 151 |; 57 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 204 ( 188 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B,C] :
( element(C,A)
=> ? [D] :
( ! [E] :
( in(E,B)
=> apply(D,E) = C )
& relation_dom(D) = B
& function(D)
& relation(D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A,B] :
~ ( ! [C] :
( ( function(C)
& relation(C) )
=> ~ ( subset(relation_rng(C),A)
& B = relation_dom(C) ) )
& ~ ( B != empty_set
& A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A,B] :
~ ( ! [C] :
( ( function(C)
& relation(C) )
=> ~ ( subset(relation_rng(C),A)
& B = relation_dom(C) ) )
& ~ ( B != empty_set
& A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f29,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f43,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f45,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK2_skl(B,A) = apply(A,sK3_skl(B,A))
& in(sK3_skl(B,A),relation_dom(A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( sK2_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK1_skl(C,B,A))
& in(sK1_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK1_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),relation_dom(X0))
| in(sK2_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f61,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f73,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f76,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f81,plain,
( relation(sK6_skl)
& empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f16]) ).
fof(f82,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f101,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f102,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [A,B,C] :
( ? [D] :
( ! [E] :
( apply(D,E) = C
| ~ in(E,B) )
& relation_dom(D) = B
& function(D)
& relation(D) )
| ~ element(C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f104,plain,
! [C] :
( ! [B] :
? [D] :
( ! [E] :
( apply(D,E) = C
| ~ in(E,B) )
& relation_dom(D) = B
& function(D)
& relation(D) )
| ! [A] : ~ element(C,A) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f105,plain,
! [C] :
( ! [B] :
( ! [E] :
( apply(sK13_skl(B,C),E) = C
| ~ in(E,B) )
& relation_dom(sK13_skl(B,C)) = B
& function(sK13_skl(B,C))
& relation(sK13_skl(B,C)) )
| ! [A] : ~ element(C,A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(D,sK13_skl(B,C))],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( relation(sK13_skl(X2,X0))
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0,X1,X2] :
( function(sK13_skl(X2,X0))
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f108,plain,
! [X0,X1,X2] :
( relation_dom(sK13_skl(X2,X0)) = X2
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( apply(sK13_skl(X3,X0),X2) = X0
| ~ in(X2,X3)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f110,plain,
? [A,B] :
( ! [C] :
( ~ subset(relation_rng(C),A)
| B != relation_dom(C)
| ~ function(C)
| ~ relation(C) )
& ( B = empty_set
| A != empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f111,plain,
( ! [C] :
( ~ subset(relation_rng(C),sK14_skl)
| sK15_skl != relation_dom(C)
| ~ function(C)
| ~ relation(C) )
& ( sK15_skl = empty_set
| sK14_skl != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(A,sK14_skl),skolemize(B,sK15_skl)],[f110]) ).
fof(f112,plain,
( sK15_skl = empty_set
| sK14_skl != empty_set ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( ~ subset(relation_rng(X0),sK14_skl)
| sK15_skl != relation_dom(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f118,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f119,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f120,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f129,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f130,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f132,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f137,plain,
! [X0,X1] :
( in(sK1_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f138,plain,
! [X0,X1] :
( X1 = apply(X0,sK1_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f140,plain,
function(empty_set),
inference(resolution,[status(thm)],[f61,f39]) ).
fof(f145,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| in(sK1_skl(sK0_skl(X1,relation_rng(X0)),relation_rng(X0),X0),relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f137,f47]) ).
fof(f146,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| sK0_skl(X1,relation_rng(X0)) = apply(X0,sK1_skl(sK0_skl(X1,relation_rng(X0)),relation_rng(X0),X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f138,f47]) ).
fof(f150,plain,
empty(relation_dom(empty_set)),
inference(resolution,[status(thm)],[f73,f61]) ).
fof(f152,plain,
empty(relation_rng(empty_set)),
inference(resolution,[status(thm)],[f76,f61]) ).
fof(f159,plain,
function(sK6_skl),
inference(resolution,[status(thm)],[f82,f39]) ).
fof(f161,plain,
! [X0] :
( in(sK3_skl(X0,empty_set),relation_dom(empty_set))
| in(sK2_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set)
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f57,f140]) ).
fof(f163,plain,
! [X0] :
( in(sK3_skl(X0,empty_set),relation_dom(empty_set))
| in(sK2_skl(X0,empty_set),X0)
| X0 = relation_rng(empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f62]) ).
fof(f168,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f130,f82]) ).
fof(f176,plain,
! [X0] :
( X0 = sK6_skl
| ~ empty(X0) ),
inference(backward_demodulation,[status(thm)],[f168,f130]) ).
fof(f177,plain,
! [X0] : subset(sK6_skl,X0),
inference(backward_demodulation,[status(thm)],[f168,f118]) ).
fof(f182,plain,
( sK15_skl = sK6_skl
| sK14_skl != empty_set ),
inference(backward_demodulation,[status(thm)],[f168,f112]) ).
fof(f183,plain,
( sK15_skl = sK6_skl
| sK14_skl != sK6_skl ),
inference(forward_demodulation,[status(thm)],[f168,f182]) ).
fof(f201,plain,
empty(relation_dom(sK6_skl)),
inference(forward_demodulation,[status(thm)],[f168,f150]) ).
fof(f203,plain,
relation_dom(sK6_skl) = sK6_skl,
inference(resolution,[status(thm)],[f201,f176]) ).
fof(f213,plain,
empty(relation_rng(sK6_skl)),
inference(forward_demodulation,[status(thm)],[f168,f152]) ).
fof(f215,plain,
relation_rng(sK6_skl) = sK6_skl,
inference(resolution,[status(thm)],[f213,f176]) ).
fof(f254,plain,
( ~ subset(relation_rng(sK6_skl),sK14_skl)
| sK15_skl != sK6_skl
| ~ function(sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f203,f113]) ).
fof(f256,plain,
( ~ subset(relation_rng(sK6_skl),sK14_skl)
| sK15_skl != sK6_skl
| ~ function(sK6_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f83]) ).
fof(f262,plain,
! [X0] : element(X0,powerset(X0)),
inference(resolution,[status(thm)],[f122,f102]) ).
fof(f272,plain,
( ~ subset(relation_rng(sK6_skl),sK14_skl)
| sK15_skl != sK6_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f256,f159]) ).
fof(f276,plain,
( ~ subset(sK6_skl,sK14_skl)
| sK15_skl != sK6_skl ),
inference(backward_demodulation,[status(thm)],[f215,f272]) ).
fof(f282,plain,
sK15_skl != sK6_skl,
inference(forward_subsumption_resolution,[status(thm)],[f276,f177]) ).
fof(f297,plain,
sK14_skl != sK6_skl,
inference(backward_subsumption_resolution,[status(thm)],[f183,f282]) ).
fof(f351,plain,
! [X0,X1,X2] :
( apply(sK13_skl(X1,X2),X0) = X2
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f262,f109]) ).
fof(f352,plain,
! [X0,X1] : relation_dom(sK13_skl(X0,X1)) = X0,
inference(resolution,[status(thm)],[f262,f108]) ).
fof(f353,plain,
! [X0,X1] : function(sK13_skl(X0,X1)),
inference(resolution,[status(thm)],[f262,f107]) ).
fof(f354,plain,
! [X0,X1] : relation(sK13_skl(X0,X1)),
inference(resolution,[status(thm)],[f262,f106]) ).
fof(f377,plain,
! [X0,X1,X2] :
( subset(relation_rng(sK13_skl(X0,X1)),X2)
| sK0_skl(X2,relation_rng(sK13_skl(X0,X1))) = apply(sK13_skl(X0,X1),sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)))
| ~ relation(sK13_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f353,f146]) ).
fof(f378,plain,
! [X0,X1,X2] :
( subset(relation_rng(sK13_skl(X0,X1)),X2)
| in(sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)),relation_dom(sK13_skl(X0,X1)))
| ~ relation(sK13_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f353,f145]) ).
fof(f410,plain,
! [X0] :
( ~ subset(relation_rng(sK13_skl(sK15_skl,X0)),sK14_skl)
| ~ function(sK13_skl(sK15_skl,X0))
| ~ relation(sK13_skl(sK15_skl,X0)) ),
inference(resolution,[status(thm)],[f352,f113]) ).
fof(f414,plain,
! [X0] :
( ~ subset(relation_rng(sK13_skl(sK15_skl,X0)),sK14_skl)
| ~ function(sK13_skl(sK15_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f354]) ).
fof(f419,plain,
! [X0] :
( in(sK3_skl(X0,empty_set),relation_dom(empty_set))
| in(sK2_skl(X0,empty_set),X0)
| X0 = relation_rng(sK6_skl) ),
inference(forward_demodulation,[status(thm)],[f168,f163]) ).
fof(f420,plain,
! [X0] :
( in(sK3_skl(X0,empty_set),relation_dom(empty_set))
| in(sK2_skl(X0,empty_set),X0)
| X0 = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f215,f419]) ).
fof(f421,plain,
! [X0] :
( in(sK3_skl(X0,empty_set),relation_dom(empty_set))
| in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f168,f420]) ).
fof(f422,plain,
! [X0] :
( in(sK3_skl(X0,sK6_skl),relation_dom(empty_set))
| in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f168,f421]) ).
fof(f423,plain,
! [X0] :
( in(sK3_skl(X0,sK6_skl),relation_dom(sK6_skl))
| in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f168,f422]) ).
fof(f424,plain,
! [X0] :
( in(sK3_skl(X0,sK6_skl),sK6_skl)
| in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f203,f423]) ).
fof(f439,plain,
! [X0] :
( ~ empty(sK6_skl)
| in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(resolution,[status(thm)],[f424,f133]) ).
fof(f442,plain,
! [X0] :
( in(sK2_skl(X0,sK6_skl),X0)
| X0 = sK6_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f439,f82]) ).
fof(f510,plain,
! [X0] : ~ subset(relation_rng(sK13_skl(sK15_skl,X0)),sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f414,f353]) ).
fof(f1863,plain,
! [X0,X1,X2] :
( subset(relation_rng(sK13_skl(X1,X2)),X0)
| sK0_skl(X0,relation_rng(sK13_skl(X1,X2))) = apply(sK13_skl(X1,X2),sK1_skl(sK0_skl(X0,relation_rng(sK13_skl(X1,X2))),relation_rng(sK13_skl(X1,X2)),sK13_skl(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f354]) ).
fof(f1864,plain,
! [X0] : sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0))) = apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0))),relation_rng(sK13_skl(sK15_skl,X0)),sK13_skl(sK15_skl,X0))),
inference(resolution,[status(thm)],[f1863,f510]) ).
fof(f1877,plain,
! [X0,X1,X2] :
( subset(relation_rng(sK13_skl(X0,X1)),X2)
| in(sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1)),X0)
| ~ relation(sK13_skl(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f352,f378]) ).
fof(f1878,plain,
! [X0,X1,X2] :
( subset(relation_rng(sK13_skl(X1,X2)),X0)
| in(sK1_skl(sK0_skl(X0,relation_rng(sK13_skl(X1,X2))),relation_rng(sK13_skl(X1,X2)),sK13_skl(X1,X2)),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1877,f354]) ).
fof(f1896,plain,
! [X0,X1,X2,X3] :
( apply(sK13_skl(X0,X3),sK1_skl(sK0_skl(X2,relation_rng(sK13_skl(X0,X1))),relation_rng(sK13_skl(X0,X1)),sK13_skl(X0,X1))) = X3
| subset(relation_rng(sK13_skl(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f1878,f351]) ).
fof(f26160,plain,
! [X0,X1] : apply(sK13_skl(sK15_skl,X0),sK1_skl(sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X1))),relation_rng(sK13_skl(sK15_skl,X1)),sK13_skl(sK15_skl,X1))) = X0,
inference(resolution,[status(thm)],[f1896,f510]) ).
fof(f26325,plain,
! [X0] : sK0_skl(sK14_skl,relation_rng(sK13_skl(sK15_skl,X0))) = X0,
inference(backward_demodulation,[status(thm)],[f26160,f1864]) ).
fof(f26346,plain,
! [X0] :
( ~ in(X0,sK14_skl)
| subset(relation_rng(sK13_skl(sK15_skl,X0)),sK14_skl) ),
inference(paramodulation,[status(thm)],[f26325,f48]) ).
fof(f26360,plain,
! [X0] : ~ in(X0,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f26346,f510]) ).
fof(f26427,plain,
sK14_skl = sK6_skl,
inference(resolution,[status(thm)],[f26360,f442]) ).
fof(f26448,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f26427,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET996+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:49:03 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 54.71/7.36 % Refutation found
% 54.71/7.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 54.71/7.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.84/7.43 % Elapsed time: 7.039921 seconds
% 27.84/7.43 % CPU time: 55.568557 seconds
% 27.84/7.43 % Total memory used: 437.936 MB
% 27.84/7.43 % Net memory used: 380.704 MB
%------------------------------------------------------------------------------