%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:20:02 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 139 ( 20 unt; 15 def)
% Number of atoms : 393 ( 103 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 416 ( 162 ~; 171 |; 47 &)
% ( 22 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 15 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 136 ( 127 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( B = empty_set
=> ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set ) )
& ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [A] :
( empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ( subset(B,C)
=> ( ( relation_of2_as_subset(D,A,C)
& quasi_total(D,A,C)
& function(D) )
| ( A != empty_set
& B = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f67,plain,
! [A,B,C] :
( ( ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set
| B != empty_set )
& ( ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) )
| ( A != empty_set
& B = empty_set ) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f68,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( A != empty_set
& B = empty_set ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f69,plain,
! [A,B,C] :
( ( ( ( quasi_total(C,A,B)
<=> C = empty_set )
| A = empty_set
| B != empty_set )
& ( ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) )
| sP0_prd(B,A) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(formula_renaming,[status(thm)],[f67,f68]) ).
fof(f70,plain,
! [A,B,C] :
( ( ( ( ( C != empty_set
| quasi_total(C,A,B) )
& ( C = empty_set
| ~ quasi_total(C,A,B) ) )
| A = empty_set
| B != empty_set )
& ( ( ( A != relation_dom_as_subset(A,B,C)
| quasi_total(C,A,B) )
& ( A = relation_dom_as_subset(A,B,C)
| ~ quasi_total(C,A,B) ) )
| sP0_prd(B,A) ) )
| ~ relation_of2_as_subset(C,A,B) ),
inference(NNF_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( X1 = relation_dom_as_subset(X1,X2,X0)
| ~ quasi_total(X0,X1,X2)
| sP0_prd(X2,X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( X1 != relation_dom_as_subset(X1,X2,X0)
| quasi_total(X0,X1,X2)
| sP0_prd(X2,X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f88,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f96,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f97,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f107,plain,
( empty(sK5_skl)
& one_to_one(sK5_skl)
& function(sK5_skl)
& relation(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f27]) ).
fof(f111,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f148,plain,
! [A,B,C] :
( relation_dom_as_subset(A,B,C) = relation_dom(C)
| ~ relation_of2(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f149,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f151,plain,
( ! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ! [A,B,C] :
( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f152,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,B)
| ~ subset(A,B)
| ~ relation_of2_as_subset(D,C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f157,plain,
! [A,C,D] :
( ! [B] :
( relation_of2_as_subset(D,C,B)
| ~ subset(A,B) )
| ~ relation_of2_as_subset(D,C,A) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X0,X1,X3)
| ~ subset(X2,X3)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f167,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f168,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f175,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f176,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f183,plain,
? [A,B,C,D] :
( ( ~ relation_of2_as_subset(D,A,C)
| ~ quasi_total(D,A,C)
| ~ function(D) )
& ( A = empty_set
| B != empty_set )
& subset(B,C)
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f184,plain,
? [A,B,D] :
( ? [C] :
( ( ~ relation_of2_as_subset(D,A,C)
| ~ quasi_total(D,A,C)
| ~ function(D) )
& ( A = empty_set
| B != empty_set )
& subset(B,C) )
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f185,plain,
( ( ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl)
| ~ quasi_total(sK19_skl,sK17_skl,sK20_skl)
| ~ function(sK19_skl) )
& ( sK17_skl = empty_set
| sK18_skl != empty_set )
& subset(sK18_skl,sK20_skl)
& relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl)
& quasi_total(sK19_skl,sK17_skl,sK18_skl)
& function(sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl,sK20_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl),skolemize(D,sK19_skl),skolemize(C,sK20_skl)],[f184]) ).
fof(f186,plain,
function(sK19_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
quasi_total(sK19_skl,sK17_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f188,plain,
relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f189,plain,
subset(sK18_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f190,plain,
( sK17_skl = empty_set
| sK18_skl != empty_set ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f191,plain,
( ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl)
| ~ quasi_total(sK19_skl,sK17_skl,sK20_skl)
| ~ function(sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f192,plain,
! [A,B] :
( ( A = empty_set
| B != empty_set
| sP0_prd(B,A) )
& ( ( A != empty_set
& B = empty_set )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f193,plain,
( ! [A,B] :
( A = empty_set
| B != empty_set
| sP0_prd(B,A) )
& ! [A,B] :
( ( A != empty_set
& B = empty_set )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f194,plain,
! [X0,X1] :
( X0 = empty_set
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f195,plain,
! [X0,X1] :
( X1 != empty_set
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f197,definition,
( sQ0_spl
<=> sK18_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ0_spl
| sK18_skl != empty_set ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
( sQ1_spl
<=> sK17_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ1_spl
| sK17_skl = empty_set ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f190,f197,f200]) ).
fof(f204,definition,
( sQ2_spl
<=> function(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ2_spl
| ~ function(sK19_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ3_spl
<=> quasi_total(sK19_skl,sK17_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ3_spl
| ~ quasi_total(sK19_skl,sK17_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ4_spl
<=> relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ4_spl
| relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f212,plain,
( sQ4_spl
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f191,f204,f207,f210]) ).
fof(f216,plain,
! [X0] : ~ sP0_prd(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f195]) ).
fof(f219,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f111,f176]) ).
fof(f224,plain,
! [X0] :
( X0 = sK5_skl
| ~ empty(X0) ),
inference(backward_demodulation,[status(thm)],[f219,f176]) ).
fof(f226,plain,
( sQ0_spl
| sK18_skl != sK5_skl ),
inference(backward_demodulation,[status(thm)],[f219,f199]) ).
fof(f235,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f219,f168]) ).
fof(f236,plain,
! [X0] :
( X0 = sK5_skl
| ~ subset(X0,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f219,f235]) ).
fof(f239,plain,
! [X0] :
( sQ4_spl
| ~ subset(X0,sK20_skl)
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,X0) ),
inference(resolution,[status(thm)],[f158,f212]) ).
fof(f253,plain,
( sQ4_spl
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f239,f189]) ).
fof(f255,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f188]) ).
fof(f256,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f186]) ).
fof(f258,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f269,plain,
! [X0] : ~ sP0_prd(X0,sK5_skl),
inference(forward_demodulation,[status(thm)],[f219,f216]) ).
fof(f270,plain,
! [X0,X1] :
( sK5_skl != relation_dom_as_subset(sK5_skl,X1,X0)
| quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK5_skl,X1) ),
inference(resolution,[status(thm)],[f269,f72]) ).
fof(f271,plain,
! [X0,X1] :
( sK5_skl = relation_dom_as_subset(sK5_skl,X1,X0)
| ~ quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK5_skl,X1) ),
inference(resolution,[status(thm)],[f269,f71]) ).
fof(f297,plain,
! [X0,X1] :
( X0 = sK5_skl
| ~ sP0_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f219,f194]) ).
fof(f298,plain,
! [X0,X1,X2] :
( X2 != relation_dom_as_subset(X2,X0,X1)
| quasi_total(X1,X2,X0)
| ~ relation_of2_as_subset(X1,X2,X0)
| X0 = sK5_skl ),
inference(resolution,[status(thm)],[f297,f72]) ).
fof(f299,plain,
! [X0,X1,X2] :
( X2 = relation_dom_as_subset(X2,X0,X1)
| ~ quasi_total(X1,X2,X0)
| ~ relation_of2_as_subset(X1,X2,X0)
| X0 = sK5_skl ),
inference(resolution,[status(thm)],[f297,f71]) ).
fof(f300,plain,
empty(relation_dom(sK5_skl)),
inference(resolution,[status(thm)],[f97,f111]) ).
fof(f303,plain,
relation_dom(sK5_skl) = sK5_skl,
inference(resolution,[status(thm)],[f300,f224]) ).
fof(f304,definition,
( sQ10_spl
<=> empty(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ10_spl
| ~ empty(sK5_skl) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ11_spl
<=> relation(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( relation(sK5_skl)
| ~ empty(sK5_skl) ),
inference(paramodulation,[status(thm)],[f303,f98]) ).
fof(f315,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f314,f304,f307]) ).
fof(f316,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f111]) ).
fof(f317,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f327,plain,
( sQ3_spl
| sK17_skl != relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl)
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl)
| sK20_skl = sK5_skl ),
inference(resolution,[status(thm)],[f298,f209]) ).
fof(f330,definition,
( sQ13_spl
<=> sK20_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ13_spl
| sK20_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ14_spl
<=> sK17_skl = relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ14_spl
| sK17_skl != relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f327,f330,f210,f333,f207]) ).
fof(f343,plain,
( ~ sQ13_spl
| subset(sK18_skl,sK5_skl) ),
inference(backward_demodulation,[status(thm)],[f331,f189]) ).
fof(f356,plain,
( sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl)
| ~ quasi_total(sK19_skl,sK17_skl,sK18_skl)
| sK18_skl = sK5_skl ),
inference(resolution,[status(thm)],[f299,f188]) ).
fof(f359,definition,
( sQ18_spl
<=> sK18_skl = sK5_skl ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( ~ sQ18_spl
| sK18_skl = sK5_skl ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,definition,
( sQ19_spl
<=> quasi_total(sK19_skl,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ19_spl
| ~ quasi_total(sK19_skl,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ20_spl
<=> sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ20_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( sQ20_spl
| ~ sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f356,f359,f362,f365]) ).
fof(f377,plain,
( ~ sQ13_spl
| sK18_skl = sK5_skl ),
inference(resolution,[status(thm)],[f343,f236]) ).
fof(f378,plain,
( ~ sQ13_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f226]) ).
fof(f379,plain,
( ~ sQ13_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( ~ sQ1_spl
| sK17_skl = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f219,f201]) ).
fof(f389,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl = relation_dom_as_subset(sK17_skl,X1,X0)
| ~ quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK5_skl,X1) ),
inference(backward_demodulation,[status(thm)],[f380,f271]) ).
fof(f391,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl != relation_dom_as_subset(sK17_skl,X1,X0)
| quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK5_skl,X1) ),
inference(backward_demodulation,[status(thm)],[f380,f270]) ).
fof(f409,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl = relation_dom_as_subset(sK17_skl,X1,X0)
| ~ quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f389]) ).
fof(f410,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl = relation_dom_as_subset(sK17_skl,X1,X0)
| ~ quasi_total(X0,sK17_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f409]) ).
fof(f411,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,X1,X0)
| ~ quasi_total(X0,sK17_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f410]) ).
fof(f416,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl != relation_dom_as_subset(sK17_skl,X1,X0)
| quasi_total(X0,sK5_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f391]) ).
fof(f417,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK5_skl != relation_dom_as_subset(sK17_skl,X1,X0)
| quasi_total(X0,sK17_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f416]) ).
fof(f418,plain,
! [X0,X1] :
( ~ sQ1_spl
| sK17_skl != relation_dom_as_subset(sK17_skl,X1,X0)
| quasi_total(X0,sK17_skl,X1)
| ~ relation_of2_as_subset(X0,sK17_skl,X1) ),
inference(forward_demodulation,[status(thm)],[f380,f417]) ).
fof(f487,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[f152,f149]) ).
fof(f555,definition,
( sQ29_spl
<=> relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( sQ29_spl
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f713,definition,
( sQ44_spl
<=> empty(powerset(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( ~ sQ44_spl
| empty(powerset(sK17_skl)) ),
inference(component_clause,[status(thm)],[f713]) ).
fof(f722,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f88]) ).
fof(f723,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f735,plain,
( ~ sQ1_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl)
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f411,f187]) ).
fof(f745,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f735,f555,f365,f200]) ).
fof(f746,plain,
( sQ3_spl
| ~ sQ1_spl
| sK17_skl != relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl)
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK20_skl) ),
inference(resolution,[status(thm)],[f418,f209]) ).
fof(f750,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f746,f210,f333,f200,f207]) ).
fof(f946,plain,
( ~ sQ4_spl
| relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl) = relation_dom(sK19_skl) ),
inference(resolution,[status(thm)],[f487,f211]) ).
fof(f947,plain,
relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) = relation_dom(sK19_skl),
inference(resolution,[status(thm)],[f487,f188]) ).
fof(f951,plain,
( ~ sQ20_spl
| sK17_skl = relation_dom(sK19_skl) ),
inference(forward_demodulation,[status(thm)],[f366,f947]) ).
fof(f970,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f188]) ).
fof(f971,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f1134,plain,
( ~ sQ18_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f226]) ).
fof(f1135,plain,
( ~ sQ18_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1134]) ).
fof(f1246,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| relation_dom_as_subset(sK17_skl,sK20_skl,sK19_skl) = sK17_skl ),
inference(forward_demodulation,[status(thm)],[f951,f946]) ).
fof(f1247,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1246,f335]) ).
fof(f1248,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1247]) ).
fof(f1249,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f187]) ).
fof(f1250,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f1249]) ).
fof(f1251,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f213,f256,f258,f315,f317,f336,f368,f379,f723,f745,f750,f971,f1135,f1248,f1250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 06:12:40 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.50 % Refutation found
% 0.19/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.53 % Elapsed time: 0.075026 seconds
% 0.19/0.53 % CPU time: 0.306114 seconds
% 0.19/0.53 % Total memory used: 69.843 MB
% 0.19/0.53 % Net memory used: 69.579 MB
%------------------------------------------------------------------------------