%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU072+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 : n012.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 02:19:11 PM UTC 2026
% Result : Theorem 0.03s 0.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 189 ( 31 unt; 22 def)
% Number of atoms : 541 ( 107 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 600 ( 248 ~; 248 |; 54 &)
% ( 32 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 32 ( 30 usr; 23 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 147 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> relation(A) ),
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(f6,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
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(f11,axiom,
! [A] : ~ empty(singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f33,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f43,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f45,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f47,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f52,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(f53,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)],[f52]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK1_skl(B,A) = apply(A,sK2_skl(B,A))
& in(sK2_skl(B,A),relation_dom(A)) )
| in(sK1_skl(B,A),B) )
& ( ! [D] :
( sK1_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK1_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,sK0_skl(C,B,A))
& in(sK0_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,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f54]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f62,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f63,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [A] :
( ( ( ( sK3_skl(A) != sK4_skl(A)
& apply(A,sK3_skl(A)) = apply(A,sK4_skl(A))
& in(sK4_skl(A),relation_dom(A))
& in(sK3_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl(A)),skolemize(C,sK4_skl(A))],[f63]) ).
fof(f66,plain,
! [X0] :
( in(sK3_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
! [X0] :
( in(sK4_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [X0] :
( apply(X0,sK3_skl(X0)) = apply(X0,sK4_skl(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f69,plain,
! [X0] :
( sK3_skl(X0) != sK4_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f72,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f75,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f77,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f84,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f85,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f87,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f88,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,plain,
( function(sK6_skl)
& relation(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f17]) ).
fof(f92,plain,
function(sK6_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f121,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f122,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [A,B] :
( relation_image(B,singleton(A)) = singleton(apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f124,plain,
! [B] :
( ! [A] :
( relation_image(B,singleton(A)) = singleton(apply(B,A))
| ~ in(A,relation_dom(B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( relation_image(X0,singleton(X1)) = singleton(apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [A,B] :
( ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f127,plain,
! [A,B] :
( ( ( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
! [B] :
( ( ! [A] :
( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ! [A] :
( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( relation_inverse_image(X0,singleton(X1)) != empty_set
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
? [A] :
( ~ one_to_one(A)
& ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f132,plain,
( ~ one_to_one(sK16_skl)
& ! [B] : subset(relation_inverse_image(sK16_skl,relation_image(sK16_skl,B)),B)
& function(sK16_skl)
& relation(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f131]) ).
fof(f133,plain,
relation(sK16_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
function(sK16_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
! [X0] : subset(relation_inverse_image(sK16_skl,relation_image(sK16_skl,X0)),X0),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f136,plain,
~ one_to_one(sK16_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f139,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f140,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f34]) ).
fof(f142,plain,
( ! [A,B] :
( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ! [A,B] :
( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f147,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f146]) ).
fof(f149,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f156,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f157,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f159,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f168,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f174,plain,
! [X0] :
( relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(X0))) = singleton(X0)
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(X0))) = empty_set ),
inference(resolution,[status(thm)],[f143,f135]) ).
fof(f179,definition,
! [X0] :
( sQ1_spl
<=> empty_set = singleton(X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f180,plain,
! [X0] :
( ~ sQ1_spl
| empty_set = singleton(X0) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f186,plain,
function(empty_set),
inference(resolution,[status(thm)],[f72,f45]) ).
fof(f262,definition,
( sQ16_spl
<=> relation(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ16_spl
| ~ relation(sK16_skl) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f269,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f133]) ).
fof(f270,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f412,plain,
( in(sK3_skl(sK16_skl),relation_dom(sK16_skl))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f66,f136]) ).
fof(f413,definition,
( sQ31_spl
<=> function(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( sQ31_spl
| ~ function(sK16_skl) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,definition,
( sQ32_spl
<=> in(sK3_skl(sK16_skl),relation_dom(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ32_spl
| in(sK3_skl(sK16_skl),relation_dom(sK16_skl)) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( sQ32_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f412,f262,f413,f416]) ).
fof(f420,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f134]) ).
fof(f421,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f422,plain,
( in(sK4_skl(sK16_skl),relation_dom(sK16_skl))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f67,f136]) ).
fof(f423,definition,
( sQ33_spl
<=> in(sK4_skl(sK16_skl),relation_dom(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( ~ sQ33_spl
| in(sK4_skl(sK16_skl),relation_dom(sK16_skl)) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( sQ33_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f422,f262,f413,f423]) ).
fof(f429,plain,
( ~ sQ32_spl
| relation_image(sK16_skl,singleton(sK3_skl(sK16_skl))) = singleton(apply(sK16_skl,sK3_skl(sK16_skl)))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f417,f125]) ).
fof(f439,definition,
( sQ36_spl
<=> relation_image(sK16_skl,singleton(sK3_skl(sK16_skl))) = singleton(apply(sK16_skl,sK3_skl(sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ36_spl
| relation_image(sK16_skl,singleton(sK3_skl(sK16_skl))) = singleton(apply(sK16_skl,sK3_skl(sK16_skl))) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ32_spl
| sQ36_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f429,f262,f413,f439,f416]) ).
fof(f444,plain,
( ~ sQ33_spl
| in(apply(sK16_skl,sK4_skl(sK16_skl)),relation_rng(sK16_skl))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f424,f168]) ).
fof(f445,plain,
( ~ sQ33_spl
| relation_image(sK16_skl,singleton(sK4_skl(sK16_skl))) = singleton(apply(sK16_skl,sK4_skl(sK16_skl)))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f424,f125]) ).
fof(f451,definition,
( sQ38_spl
<=> in(apply(sK16_skl,sK4_skl(sK16_skl)),relation_rng(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ38_spl
| in(apply(sK16_skl,sK4_skl(sK16_skl)),relation_rng(sK16_skl)) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( ~ sQ33_spl
| sQ38_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f444,f262,f413,f451,f423]) ).
fof(f455,definition,
( sQ39_spl
<=> relation_image(sK16_skl,singleton(sK4_skl(sK16_skl))) = singleton(apply(sK16_skl,sK4_skl(sK16_skl))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ39_spl
| relation_image(sK16_skl,singleton(sK4_skl(sK16_skl))) = singleton(apply(sK16_skl,sK4_skl(sK16_skl))) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( ~ sQ33_spl
| sQ39_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f445,f262,f413,f455,f423]) ).
fof(f492,plain,
( ~ sQ38_spl
| relation_inverse_image(sK16_skl,singleton(apply(sK16_skl,sK4_skl(sK16_skl)))) != empty_set
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f452,f129]) ).
fof(f502,definition,
( sQ46_spl
<=> relation_inverse_image(sK16_skl,singleton(apply(sK16_skl,sK4_skl(sK16_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( sQ46_spl
| relation_inverse_image(sK16_skl,singleton(apply(sK16_skl,sK4_skl(sK16_skl)))) != empty_set ),
inference(component_clause,[status(thm)],[f502]) ).
fof(f505,plain,
( ~ sQ38_spl
| ~ sQ46_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f492,f262,f502,f451]) ).
fof(f515,plain,
( ~ sQ1_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f180,f77]) ).
fof(f535,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f72]) ).
fof(f536,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f549,plain,
empty(relation_dom(empty_set)),
inference(resolution,[status(thm)],[f85,f72]) ).
fof(f552,plain,
relation_dom(empty_set) = empty_set,
inference(resolution,[status(thm)],[f549,f157]) ).
fof(f556,definition,
( sQ47_spl
<=> function(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ47_spl
| ~ function(relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f556]) ).
fof(f582,plain,
( sQ47_spl
| ~ function(empty_set) ),
inference(forward_demodulation,[status(thm)],[f552,f558]) ).
fof(f583,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f186]) ).
fof(f584,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f589,definition,
( sQ52_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ52_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f593,plain,
empty(relation_rng(empty_set)),
inference(resolution,[status(thm)],[f88,f72]) ).
fof(f599,plain,
relation(relation_rng(empty_set)),
inference(resolution,[status(thm)],[f593,f47]) ).
fof(f600,plain,
function(relation_rng(empty_set)),
inference(resolution,[status(thm)],[f593,f45]) ).
fof(f601,definition,
( sQ53_spl
<=> function(relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f603,plain,
( sQ53_spl
| ~ function(relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f608,plain,
( apply(sK16_skl,sK3_skl(sK16_skl)) = apply(sK16_skl,sK4_skl(sK16_skl))
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f68,f136]) ).
fof(f609,definition,
( sQ55_spl
<=> apply(sK16_skl,sK3_skl(sK16_skl)) = apply(sK16_skl,sK4_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( ~ sQ55_spl
| apply(sK16_skl,sK3_skl(sK16_skl)) = apply(sK16_skl,sK4_skl(sK16_skl)) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( sQ55_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f608,f262,f413,f609]) ).
fof(f613,plain,
( sK3_skl(sK16_skl) != sK4_skl(sK16_skl)
| ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f69,f136]) ).
fof(f614,definition,
( sQ56_spl
<=> sK3_skl(sK16_skl) = sK4_skl(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ56_spl
| sK3_skl(sK16_skl) != sK4_skl(sK16_skl) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,plain,
( ~ sQ56_spl
| ~ sQ31_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f613,f262,f413,f614]) ).
fof(f639,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f600]) ).
fof(f640,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f639]) ).
fof(f655,definition,
( sQ59_spl
<=> relation(relation_rng(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( sQ59_spl
| ~ relation(relation_rng(empty_set)) ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f666,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f657,f599]) ).
fof(f667,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f735,plain,
( sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK3_skl(sK16_skl)))) != empty_set ),
inference(backward_demodulation,[status(thm)],[f736,f504]) ).
fof(f736,plain,
( ~ sQ36_spl
| ~ sQ55_spl
| relation_image(sK16_skl,singleton(sK3_skl(sK16_skl))) = singleton(apply(sK16_skl,sK4_skl(sK16_skl))) ),
inference(forward_demodulation,[status(thm)],[f610,f440]) ).
fof(f804,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f72]) ).
fof(f805,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f804]) ).
fof(f854,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| empty(powerset(X1))
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f149,f140]) ).
fof(f855,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f854,f75]) ).
fof(f867,plain,
! [X0,X1] :
( ~ in(powerset(X1),X0)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[f855,f43]) ).
fof(f874,plain,
! [X0,X1] :
( ~ subset(powerset(X1),X0)
| ~ subset(powerset(X0),X1) ),
inference(resolution,[status(thm)],[f867,f855]) ).
fof(f884,plain,
! [X0] : ~ subset(powerset(powerset(X0)),X0),
inference(resolution,[status(thm)],[f874,f122]) ).
fof(f939,definition,
( sQ90_spl
<=> relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK3_skl(sK16_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f940,plain,
( ~ sQ90_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK3_skl(sK16_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f939]) ).
fof(f943,plain,
( ~ sQ90_spl
| sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f940,f735]) ).
fof(f944,plain,
( ~ sQ90_spl
| sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f943]) ).
fof(f1013,definition,
( sQ96_spl
<=> empty(powerset(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
( ~ sQ96_spl
| empty(powerset(empty_set)) ),
inference(component_clause,[status(thm)],[f1013]) ).
fof(f1018,plain,
( ~ sQ96_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1014,f75]) ).
fof(f1019,plain,
~ sQ96_spl,
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1032,definition,
( sQ98_spl
<=> powerset(empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( ~ sQ98_spl
| powerset(empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f1032]) ).
fof(f1049,plain,
( ~ sQ98_spl
| ~ subset(powerset(empty_set),empty_set) ),
inference(paramodulation,[status(thm)],[f1033,f884]) ).
fof(f1068,plain,
( ~ sQ98_spl
| ~ subset(empty_set,empty_set) ),
inference(forward_demodulation,[status(thm)],[f1033,f1049]) ).
fof(f1069,plain,
( ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1068,f122]) ).
fof(f1070,plain,
~ sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1069]) ).
fof(f1090,plain,
( sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl
| ~ sQ39_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) != empty_set ),
inference(backward_demodulation,[status(thm)],[f1096,f735]) ).
fof(f1096,plain,
( ~ sQ39_spl
| ~ sQ36_spl
| ~ sQ55_spl
| relation_image(sK16_skl,singleton(sK4_skl(sK16_skl))) = relation_image(sK16_skl,singleton(sK3_skl(sK16_skl))) ),
inference(forward_demodulation,[status(thm)],[f736,f456]) ).
fof(f1099,plain,
( ~ sQ39_spl
| ~ sQ36_spl
| ~ sQ55_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = singleton(sK3_skl(sK16_skl))
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK3_skl(sK16_skl)))) = empty_set ),
inference(paramodulation,[status(thm)],[f1096,f174]) ).
fof(f1101,definition,
( sQ101_spl
<=> relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = singleton(sK3_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1102,plain,
( ~ sQ101_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = singleton(sK3_skl(sK16_skl)) ),
inference(component_clause,[status(thm)],[f1101]) ).
fof(f1105,definition,
( sQ102_spl
<=> relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1106,plain,
( ~ sQ102_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = empty_set ),
inference(component_clause,[status(thm)],[f1105]) ).
fof(f1109,plain,
( ~ sQ39_spl
| ~ sQ36_spl
| ~ sQ55_spl
| sQ101_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1099,f939,f1101,f609,f439,f455]) ).
fof(f1177,plain,
( ~ sQ102_spl
| sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1106,f1090]) ).
fof(f1178,plain,
( ~ sQ102_spl
| sQ46_spl
| ~ sQ36_spl
| ~ sQ55_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f1177]) ).
fof(f1304,plain,
( ~ sQ101_spl
| relation_inverse_image(sK16_skl,relation_image(sK16_skl,singleton(sK4_skl(sK16_skl)))) = empty_set
| singleton(sK4_skl(sK16_skl)) = singleton(sK3_skl(sK16_skl)) ),
inference(paramodulation,[status(thm)],[f174,f1102]) ).
fof(f1309,definition,
( sQ124_spl
<=> singleton(sK4_skl(sK16_skl)) = singleton(sK3_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1310,plain,
( ~ sQ124_spl
| singleton(sK4_skl(sK16_skl)) = singleton(sK3_skl(sK16_skl)) ),
inference(component_clause,[status(thm)],[f1309]) ).
fof(f1312,plain,
( ~ sQ101_spl
| sQ102_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1304,f1309,f1105,f1101]) ).
fof(f1336,plain,
! [X0] :
( ~ sQ124_spl
| X0 = sK3_skl(sK16_skl)
| ~ subset(singleton(X0),singleton(sK4_skl(sK16_skl))) ),
inference(paramodulation,[status(thm)],[f1310,f159]) ).
fof(f1457,definition,
( sQ139_spl
<=> function(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( sQ139_spl
| ~ function(sK6_skl) ),
inference(component_clause,[status(thm)],[f1457]) ).
fof(f1479,plain,
( sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1459,f92]) ).
fof(f1480,plain,
sQ139_spl,
inference(contradiction_clause,[status(thm)],[f1479]) ).
fof(f1585,plain,
( ~ sQ124_spl
| sK4_skl(sK16_skl) = sK3_skl(sK16_skl) ),
inference(resolution,[status(thm)],[f1336,f122]) ).
fof(f1588,plain,
( ~ sQ124_spl
| sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1585,f616]) ).
fof(f1589,plain,
( ~ sQ124_spl
| sQ56_spl ),
inference(contradiction_clause,[status(thm)],[f1588]) ).
fof(f1590,plain,
$false,
inference(sat_refutation,[status(thm)],[f270,f419,f421,f426,f442,f454,f458,f505,f536,f584,f612,f617,f640,f667,f805,f944,f1019,f1070,f1109,f1178,f1312,f1480,f1589]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 05:49:01 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.33 % Refutation found
% 0.03/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.36 % Elapsed time: 0.061539 seconds
% 0.07/0.36 % CPU time: 0.232985 seconds
% 0.07/0.36 % Total memory used: 87.452 MB
% 0.07/0.36 % Net memory used: 87.038 MB
%------------------------------------------------------------------------------