%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 42
% Syntax : Number of formulae : 190 ( 36 unt; 23 def)
% Number of atoms : 478 ( 79 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 449 ( 161 ~; 174 |; 63 &)
% ( 30 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 23 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 150 ( 135 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ! [A,B,C,D] :
( ( relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) )
=> ! [E] :
( ( function(E)
& relation(E) )
=> ( in(C,A)
=> ( apply(relation_composition(D,E),C) = apply(E,apply(D,C))
| B = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f50,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
! [C] :
( relation(C)
| ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f71,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(f72,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( A != empty_set
& B = empty_set ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f73,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)],[f71,f72]) ).
fof(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f83,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f84,plain,
! [X0,X1,X2] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f94,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f106,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f107,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f109,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f114,plain,
( function(sK3_skl)
& relation(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f30]) ).
fof(f115,plain,
relation(sK3_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
function(sK3_skl),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f144,plain,
( relation(sK11_skl)
& ~ empty(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f38]) ).
fof(f146,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f152,plain,
( one_to_one(sK14_skl)
& function(sK14_skl)
& relation(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(A,sK14_skl)],[f41]) ).
fof(f153,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
function(sK14_skl),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f156,plain,
( relation_empty_yielding(sK15_skl)
& relation(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(A,sK15_skl)],[f42]) ).
fof(f157,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f159,plain,
( function(sK16_skl)
& relation_empty_yielding(sK16_skl)
& relation(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f43]) ).
fof(f160,plain,
relation(sK16_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
function(sK16_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,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)],[f44]) ).
fof(f164,plain,
! [X0,X1,X2] :
( relation_dom_as_subset(X1,X2,X0) = relation_dom(X0)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,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)],[f45]) ).
fof(f166,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)],[f165]) ).
fof(f167,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f166]) ).
fof(f171,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f172,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
? [A,B,C,D] :
( ? [E] :
( apply(relation_composition(D,E),C) != apply(E,apply(D,C))
& B != empty_set
& in(C,A)
& function(E)
& relation(E) )
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f174,plain,
? [A,B,D] :
( ? [E] :
( ? [C] :
( apply(relation_composition(D,E),C) != apply(E,apply(D,C))
& B != empty_set
& in(C,A) )
& function(E)
& relation(E) )
& relation_of2_as_subset(D,A,B)
& quasi_total(D,A,B)
& function(D) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f175,plain,
( apply(relation_composition(sK19_skl,sK20_skl),sK21_skl) != apply(sK20_skl,apply(sK19_skl,sK21_skl))
& sK18_skl != empty_set
& in(sK21_skl,sK17_skl)
& function(sK20_skl)
& relation(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,sK21_skl]),skolemize(A,sK17_skl),skolemize(B,sK18_skl),skolemize(D,sK19_skl),skolemize(E,sK20_skl),skolemize(C,sK21_skl)],[f174]) ).
fof(f176,plain,
function(sK19_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
quasi_total(sK19_skl,sK17_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f178,plain,
relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f179,plain,
relation(sK20_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f180,plain,
function(sK20_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f181,plain,
in(sK21_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f182,plain,
sK18_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f183,plain,
apply(relation_composition(sK19_skl,sK20_skl),sK21_skl) != apply(sK20_skl,apply(sK19_skl,sK21_skl)),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f184,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f185,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B)) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f184]) ).
fof(f186,plain,
! [X0,X1,X2] :
( apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f188,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f199,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f200,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f201,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f202,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f203,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f207,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)],[f72]) ).
fof(f208,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)],[f207]) ).
fof(f209,plain,
! [X0,X1] :
( X0 = empty_set
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f216,definition,
( sQ1_spl
<=> sK18_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ1_spl
| sK18_skl = empty_set ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f240,plain,
! [X0] :
( relation_dom(X0) = empty_set
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f109,f200]) ).
fof(f278,plain,
~ empty(sK17_skl),
inference(resolution,[status(thm)],[f181,f203]) ).
fof(f338,definition,
( sQ9_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ9_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f347,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f94]) ).
fof(f348,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,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)],[f167,f164]) ).
fof(f352,plain,
! [X0,X1,X2] :
( empty(relation_dom(X0))
| ~ element(X2,relation_dom(X0))
| apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f188]) ).
fof(f373,plain,
( empty(relation_dom(sK19_skl))
| ~ element(sK21_skl,relation_dom(sK19_skl))
| ~ function(sK20_skl)
| ~ relation(sK20_skl)
| ~ function(sK19_skl)
| ~ relation(sK19_skl) ),
inference(resolution,[status(thm)],[f352,f183]) ).
fof(f374,definition,
( sQ13_spl
<=> relation(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ13_spl
| ~ relation(sK19_skl) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f377,definition,
( sQ14_spl
<=> function(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( sQ14_spl
| ~ function(sK19_skl) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,definition,
( sQ15_spl
<=> relation(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ15_spl
| ~ relation(sK20_skl) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,definition,
( sQ16_spl
<=> function(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ16_spl
| ~ function(sK20_skl) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ17_spl
<=> element(sK21_skl,relation_dom(sK19_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( sQ17_spl
| ~ element(sK21_skl,relation_dom(sK19_skl)) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,definition,
( sQ18_spl
<=> empty(relation_dom(sK19_skl)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ18_spl
| empty(relation_dom(sK19_skl)) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( sQ18_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f373,f374,f377,f380,f383,f386,f389]) ).
fof(f406,plain,
( ~ sQ18_spl
| ~ relation(sK19_skl)
| empty(sK19_skl) ),
inference(resolution,[status(thm)],[f390,f107]) ).
fof(f416,definition,
( sQ19_spl
<=> empty(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ19_spl
| empty(sK19_skl) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f406,f416,f374,f389]) ).
fof(f420,plain,
! [X0,X1] :
( sQ13_spl
| ~ element(sK19_skl,powerset(cartesian_product2(X0,X1))) ),
inference(resolution,[status(thm)],[f376,f66]) ).
fof(f423,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 = empty_set ),
inference(resolution,[status(thm)],[f209,f75]) ).
fof(f445,plain,
! [X0,X1] :
( sQ13_spl
| ~ relation_of2_as_subset(sK19_skl,X0,X1) ),
inference(resolution,[status(thm)],[f420,f84]) ).
fof(f457,plain,
( sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f178,f445]) ).
fof(f459,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f465,plain,
( ~ sQ19_spl
| relation_dom(sK19_skl) = empty_set ),
inference(resolution,[status(thm)],[f417,f240]) ).
fof(f468,plain,
( ~ sQ19_spl
| sK19_skl = empty_set ),
inference(resolution,[status(thm)],[f417,f200]) ).
fof(f525,plain,
( ~ sQ19_spl
| relation_of2_as_subset(empty_set,sK17_skl,sK18_skl) ),
inference(backward_demodulation,[status(thm)],[f468,f178]) ).
fof(f527,plain,
( ~ sQ19_spl
| quasi_total(empty_set,sK17_skl,sK18_skl) ),
inference(backward_demodulation,[status(thm)],[f468,f177]) ).
fof(f543,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f180]) ).
fof(f544,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f382,f179]) ).
fof(f546,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f554,plain,
( ~ sQ19_spl
| relation_dom_as_subset(sK17_skl,sK18_skl,empty_set) = relation_dom(empty_set) ),
inference(resolution,[status(thm)],[f349,f525]) ).
fof(f562,plain,
( ~ sQ19_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,empty_set)
| ~ quasi_total(empty_set,sK17_skl,sK18_skl)
| sK18_skl = empty_set ),
inference(resolution,[status(thm)],[f423,f525]) ).
fof(f565,definition,
( sQ25_spl
<=> quasi_total(empty_set,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ25_spl
| ~ quasi_total(empty_set,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,definition,
( sQ26_spl
<=> sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( ~ sQ26_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,empty_set) ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ19_spl
| sQ26_spl
| ~ sQ25_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f562,f216,f565,f568,f416]) ).
fof(f572,plain,
( sQ25_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f527]) ).
fof(f573,plain,
( sQ25_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f572]) ).
fof(f581,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f182]) ).
fof(f582,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f594,plain,
( ~ sQ19_spl
| relation_dom(empty_set) = empty_set ),
inference(forward_demodulation,[status(thm)],[f468,f465]) ).
fof(f620,plain,
( ~ sQ19_spl
| relation_dom_as_subset(sK17_skl,sK18_skl,empty_set) = empty_set ),
inference(forward_demodulation,[status(thm)],[f594,f554]) ).
fof(f641,plain,
( ~ sQ26_spl
| ~ sQ19_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f643,f278]) ).
fof(f643,plain,
( ~ sQ26_spl
| ~ sQ19_spl
| sK17_skl = empty_set ),
inference(forward_demodulation,[status(thm)],[f620,f569]) ).
fof(f645,plain,
( ~ sQ26_spl
| ~ sQ19_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f641,f338,f416,f568]) ).
fof(f652,plain,
( sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl)
| ~ quasi_total(sK19_skl,sK17_skl,sK18_skl)
| sK18_skl = empty_set ),
inference(resolution,[status(thm)],[f178,f423]) ).
fof(f653,plain,
relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) = relation_dom(sK19_skl),
inference(resolution,[status(thm)],[f178,f349]) ).
fof(f654,definition,
( sQ30_spl
<=> quasi_total(sK19_skl,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( sQ30_spl
| ~ quasi_total(sK19_skl,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,definition,
( sQ31_spl
<=> sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ31_spl
| sK17_skl = relation_dom_as_subset(sK17_skl,sK18_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f661,plain,
( sQ31_spl
| ~ sQ30_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f652,f216,f654,f657]) ).
fof(f708,definition,
( sQ32_spl
<=> relation(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( sQ32_spl
| ~ relation(sK16_skl) ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f712,definition,
( sQ33_spl
<=> function(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ33_spl
| ~ function(sK16_skl) ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f737,definition,
( sQ36_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ36_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f837,definition,
( sQ43_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( sQ43_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f837]) ).
fof(f841,definition,
( sQ44_spl
<=> function(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( sQ44_spl
| ~ function(sK14_skl) ),
inference(component_clause,[status(thm)],[f841]) ).
fof(f865,definition,
( sQ47_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f867,plain,
( sQ47_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f929,definition,
( sQ56_spl
<=> relation(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f931,plain,
( sQ56_spl
| ~ relation(sK3_skl) ),
inference(component_clause,[status(thm)],[f929]) ).
fof(f933,definition,
( sQ57_spl
<=> function(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ57_spl
| ~ function(sK3_skl) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f989,definition,
( sQ61_spl
<=> relation_of2(sK19_skl,sK17_skl,sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( sQ61_spl
| ~ relation_of2(sK19_skl,sK17_skl,sK18_skl) ),
inference(component_clause,[status(thm)],[f989]) ).
fof(f996,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f177]) ).
fof(f997,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f1015,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f176]) ).
fof(f1016,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f1015]) ).
fof(f1054,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f160]) ).
fof(f1055,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1056,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f162]) ).
fof(f1057,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1056]) ).
fof(f1078,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f739,f157]) ).
fof(f1079,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1078]) ).
fof(f1138,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f839,f153]) ).
fof(f1139,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f1138]) ).
fof(f1140,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f843,f154]) ).
fof(f1141,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f1140]) ).
fof(f1171,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f867,f146]) ).
fof(f1172,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f1171]) ).
fof(f1194,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f931,f115]) ).
fof(f1195,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f1194]) ).
fof(f1196,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f935,f116]) ).
fof(f1197,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f1196]) ).
fof(f1209,plain,
( sQ61_spl
| ~ relation_of2_as_subset(sK19_skl,sK17_skl,sK18_skl) ),
inference(resolution,[status(thm)],[f991,f167]) ).
fof(f1210,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1209,f178]) ).
fof(f1211,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f1210]) ).
fof(f1212,plain,
( ~ sQ31_spl
| sK17_skl = relation_dom(sK19_skl) ),
inference(backward_demodulation,[status(thm)],[f658,f653]) ).
fof(f1240,plain,
( sQ17_spl
| ~ sQ31_spl
| ~ element(sK21_skl,sK17_skl) ),
inference(forward_demodulation,[status(thm)],[f1212,f388]) ).
fof(f1242,plain,
( sQ17_spl
| ~ sQ31_spl
| ~ in(sK21_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f1240,f172]) ).
fof(f1243,plain,
( sQ17_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f181]) ).
fof(f1244,plain,
( sQ17_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1243]) ).
fof(f1245,plain,
$false,
inference(sat_refutation,[status(thm)],[f348,f392,f419,f459,f544,f546,f571,f573,f582,f645,f661,f997,f1016,f1055,f1057,f1079,f1139,f1141,f1172,f1195,f1197,f1211,f1244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU292+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:08:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.51 % Elapsed time: 0.139930 seconds
% 0.14/0.51 % CPU time: 0.541477 seconds
% 0.14/0.51 % Total memory used: 88.197 MB
% 0.14/0.51 % Net memory used: 87.759 MB
%------------------------------------------------------------------------------