%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU046+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 : n014.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 02:19:08 PM UTC 2026
% Result : Theorem 0.12s 5.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 111 ( 20 unt; 9 def)
% Number of atoms : 342 ( 23 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 375 ( 144 ~; 145 |; 58 &)
% ( 17 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 9 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 165 ( 151 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
& subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f50,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f58,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f65,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f69,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f70,plain,
! [B] :
( ( ! [A] : function(relation_rng_restriction(A,B))
& ! [A] : relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f72,plain,
! [X0,X1] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f83,plain,
( function(sK2_skl)
& relation(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(A,sK2_skl)],[f17]) ).
fof(f84,plain,
relation(sK2_skl),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f102,plain,
! [A] :
( empty(sK8_skl(A))
& element(sK8_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f23]) ).
fof(f103,plain,
! [X0] : element(sK8_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0] : empty(sK8_skl(X0)),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f107,plain,
( one_to_one(sK10_skl)
& function(sK10_skl)
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f25]) ).
fof(f108,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f116,plain,
! [A,B] :
( subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f117,plain,
! [B] :
( ! [A] : subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( subset(relation_rng(relation_rng_restriction(X1,X0)),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f122,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f133,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f134,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f136,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f139,definition,
! [A,C,D] :
( sP0_prd(D,C,A)
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f140,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> sP0_prd(D,C,A) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(formula_renaming,[status(thm)],[f138,f139]) ).
fof(f141,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK13_skl(A,C,B)) != apply(C,sK13_skl(A,C,B))
& in(sK13_skl(A,C,B),relation_dom(B)) )
| ( ( sP0_prd(sK12_skl(A,C,B),C,A)
| in(sK12_skl(A,C,B),relation_dom(B)) )
& ( ~ sP0_prd(sK12_skl(A,C,B),C,A)
| ~ in(sK12_skl(A,C,B),relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(D,sK12_skl(A,C,B)),skolemize(D,sK13_skl(A,C,B))],[f142]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X3,X1,X2)
| ~ in(X3,relation_dom(X0))
| X0 != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f151,plain,
? [A,B] :
( ( ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) )
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f152,plain,
? [B] :
( ( ? [A] : ~ subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B))
| ? [A] : ~ subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f153,plain,
( ( ~ subset(relation_rng(relation_rng_restriction(sK16_skl,sK14_skl)),relation_rng(sK14_skl))
| ~ subset(relation_dom(relation_rng_restriction(sK15_skl,sK14_skl)),relation_dom(sK14_skl)) )
& function(sK14_skl)
& relation(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK14_skl),skolemize(A,sK15_skl),skolemize(A,sK16_skl)],[f152]) ).
fof(f154,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f155,plain,
function(sK14_skl),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f156,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK16_skl,sK14_skl)),relation_rng(sK14_skl))
| ~ subset(relation_dom(relation_rng_restriction(sK15_skl,sK14_skl)),relation_dom(sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f160,plain,
! [A,C,D] :
( ( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| sP0_prd(D,C,A) )
& ( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ sP0_prd(D,C,A) ) ),
inference(NNF_transformation,[status(thm)],[f139]) ).
fof(f161,plain,
( ! [A,C,D] :
( ~ in(apply(C,D),A)
| ~ in(D,relation_dom(C))
| sP0_prd(D,C,A) )
& ! [A,C,D] :
( ( in(apply(C,D),A)
& in(D,relation_dom(C)) )
| ~ sP0_prd(D,C,A) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0,X1,X2] :
( in(X0,relation_dom(X1))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f165,definition,
( sQ0_spl
<=> subset(relation_dom(relation_rng_restriction(sK15_skl,sK14_skl)),relation_dom(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ0_spl
| ~ subset(relation_dom(relation_rng_restriction(sK15_skl,sK14_skl)),relation_dom(sK14_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ1_spl
<=> subset(relation_rng(relation_rng_restriction(sK16_skl,sK14_skl)),relation_rng(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ1_spl
| ~ subset(relation_rng(relation_rng_restriction(sK16_skl,sK14_skl)),relation_rng(sK14_skl)) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f165,f168]) ).
fof(f172,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f144]) ).
fof(f249,plain,
( sQ0_spl
| in(sK0_skl(relation_dom(sK14_skl),relation_dom(relation_rng_restriction(sK15_skl,sK14_skl))),relation_dom(relation_rng_restriction(sK15_skl,sK14_skl))) ),
inference(resolution,[status(thm)],[f55,f167]) ).
fof(f296,plain,
! [X0] : sK8_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f134,f104]) ).
fof(f362,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f296,f103]) ).
fof(f388,plain,
( sQ1_spl
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f170,f118]) ).
fof(f390,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f154]) ).
fof(f391,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f137,f62]) ).
fof(f393,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f392,f54]) ).
fof(f418,plain,
! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f122,f362]) ).
fof(f422,plain,
! [X0] : in(empty_set,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f418,f65]) ).
fof(f496,plain,
! [X0,X1,X2] :
( sP0_prd(X2,X1,X0)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f59]) ).
fof(f573,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X2,X1))
| in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f162,f496]) ).
fof(f574,plain,
! [X0,X1,X2] :
( ~ in(X0,relation_dom(relation_rng_restriction(X2,X1)))
| ~ function(X1)
| ~ relation(X1)
| in(X0,relation_dom(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f72]) ).
fof(f711,plain,
( sQ0_spl
| ~ function(sK14_skl)
| ~ relation(sK14_skl)
| in(sK0_skl(relation_dom(sK14_skl),relation_dom(relation_rng_restriction(sK15_skl,sK14_skl))),relation_dom(sK14_skl)) ),
inference(resolution,[status(thm)],[f574,f249]) ).
fof(f713,definition,
( sQ35_spl
<=> in(sK0_skl(relation_dom(sK14_skl),relation_dom(relation_rng_restriction(sK15_skl,sK14_skl))),relation_dom(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( ~ sQ35_spl
| in(sK0_skl(relation_dom(sK14_skl),relation_dom(relation_rng_restriction(sK15_skl,sK14_skl))),relation_dom(sK14_skl)) ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f716,definition,
( sQ36_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f718,plain,
( sQ36_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f716]) ).
fof(f719,definition,
( sQ37_spl
<=> function(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( sQ37_spl
| ~ function(sK14_skl) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( sQ0_spl
| ~ sQ37_spl
| ~ sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f711,f713,f716,f719,f165]) ).
fof(f723,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f155]) ).
fof(f724,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f723]) ).
fof(f766,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f718,f154]) ).
fof(f767,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f766]) ).
fof(f829,definition,
( sQ43_spl
<=> subset(powerset(empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( ~ sQ43_spl
| subset(powerset(empty_set),empty_set) ),
inference(component_clause,[status(thm)],[f829]) ).
fof(f845,plain,
! [X0] :
( ~ sQ43_spl
| ~ in(X0,powerset(empty_set)) ),
inference(resolution,[status(thm)],[f830,f393]) ).
fof(f849,plain,
( ~ sQ43_spl
| $false ),
inference(resolution,[status(thm)],[f845,f422]) ).
fof(f854,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f849]) ).
fof(f939,definition,
( sQ50_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f941,plain,
( sQ50_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f939]) ).
fof(f950,definition,
( sQ53_spl
<=> relation(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( sQ53_spl
| ~ relation(sK2_skl) ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f1025,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f952,f84]) ).
fof(f1026,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f1025]) ).
fof(f1027,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f941,f108]) ).
fof(f1028,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f1027]) ).
fof(f1412,plain,
( ~ sQ35_spl
| subset(relation_dom(relation_rng_restriction(sK15_skl,sK14_skl)),relation_dom(sK14_skl)) ),
inference(resolution,[status(thm)],[f714,f56]) ).
fof(f1425,plain,
( ~ sQ35_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1412,f167]) ).
fof(f1426,plain,
( ~ sQ35_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1425]) ).
fof(f1427,plain,
$false,
inference(sat_refutation,[status(thm)],[f171,f391,f722,f724,f767,f854,f1026,f1028,f1426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU046+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 05:47:56 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.12/5.46 % Refutation found
% 0.12/5.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.47 % Elapsed time: 0.102139 seconds
% 0.12/5.47 % CPU time: 0.607829 seconds
% 0.12/5.47 % Total memory used: 93.485 MB
% 0.12/5.47 % Net memory used: 92.250 MB
%------------------------------------------------------------------------------