%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU234+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 : n006.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 02:19:49 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 179 ( 35 unt; 24 def)
% Number of atoms : 455 ( 21 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 418 ( 142 ~; 152 |; 84 &)
% ( 28 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 25 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 99 ( 87 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A] :
( ! [B] :
( in(B,A)
=> ( subset(B,A)
& ordinal(B) ) )
=> ordinal(A) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f41,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f49,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f55,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f61,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( subset(B,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
! [A] :
( ( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(NNF_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
( ! [A] :
( ? [B] :
( ~ subset(B,A)
& in(B,A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(miniscoping,[status(thm)],[f63]) ).
fof(f65,plain,
( ! [A] :
( ( ~ subset(sK0_skl(A),A)
& in(sK0_skl(A),A) )
| epsilon_transitive(A) )
& ! [A] :
( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f64]) ).
fof(f67,plain,
! [X0] :
( in(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f68,plain,
! [X0] :
( ~ subset(sK0_skl(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f70,plain,
! [A] :
( ( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(NNF_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
( ! [A] :
( ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f72,plain,
( ! [A] :
( ( ~ in(sK2_skl(A),sK1_skl(A))
& sK1_skl(A) != sK2_skl(A)
& ~ in(sK1_skl(A),sK2_skl(A))
& in(sK2_skl(A),A)
& in(sK1_skl(A),A) )
| epsilon_connected(A) )
& ! [A] :
( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(B,sK1_skl(A)),skolemize(C,sK2_skl(A))],[f71]) ).
fof(f74,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
! [X0] :
( in(sK2_skl(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f76,plain,
! [X0] :
( ~ in(sK1_skl(X0),sK2_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f77,plain,
! [X0] :
( sK1_skl(X0) != sK2_skl(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f78,plain,
! [X0] :
( ~ in(sK2_skl(X0),sK1_skl(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f86,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f92,plain,
function(empty_set),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f95,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f97,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f103,plain,
( ordinal(sK5_skl)
& epsilon_connected(sK5_skl)
& epsilon_transitive(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f20]) ).
fof(f104,plain,
epsilon_transitive(sK5_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
epsilon_connected(sK5_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f107,plain,
( relation(sK6_skl)
& empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f21]) ).
fof(f108,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
( function(sK8_skl)
& empty(sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f23]) ).
fof(f114,plain,
empty(sK8_skl),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
function(sK8_skl),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f116,plain,
( ordinal(sK9_skl)
& epsilon_connected(sK9_skl)
& epsilon_transitive(sK9_skl)
& empty(sK9_skl)
& one_to_one(sK9_skl)
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f24]) ).
fof(f118,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
empty(sK9_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f121,plain,
epsilon_transitive(sK9_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f122,plain,
epsilon_connected(sK9_skl),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f133,plain,
( ordinal(sK13_skl)
& epsilon_connected(sK13_skl)
& epsilon_transitive(sK13_skl)
& ~ empty(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f28]) ).
fof(f135,plain,
epsilon_transitive(sK13_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
epsilon_connected(sK13_skl),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f149,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f150,plain,
! [X0,X1] :
( in(X1,X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f153,plain,
? [A] :
( ~ ordinal(A)
& ! [B] :
( ( subset(B,A)
& ordinal(B) )
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f154,plain,
( ~ ordinal(sK16_skl)
& ! [B] :
( ( subset(B,sK16_skl)
& ordinal(B) )
| ~ in(B,sK16_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(A,sK16_skl)],[f153]) ).
fof(f155,plain,
! [X0] :
( ordinal(X0)
| ~ in(X0,sK16_skl) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
! [X0] :
( subset(X0,sK16_skl)
| ~ in(X0,sK16_skl) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
~ ordinal(sK16_skl),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f170,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f171,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
epsilon_connected(empty_set),
inference(resolution,[status(thm)],[f49,f97]) ).
fof(f180,plain,
! [X0,X1] :
( ~ empty(X0)
| X0 = X1
| in(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f150,f172]) ).
fof(f182,definition,
( sQ0_spl
<=> ordinal(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ0_spl
| ordinal(sK16_skl) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f193,plain,
! [X0,X1] :
( ~ empty(X1)
| X1 = X0
| in(X1,X0)
| ~ ordinal(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f61]) ).
fof(f197,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ empty(X1)
| X1 = X0
| ~ ordinal(X0) ),
inference(resolution,[status(thm)],[f193,f172]) ).
fof(f207,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ empty(X0)
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f61]) ).
fof(f210,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f86,f207]) ).
fof(f218,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f108,f210]) ).
fof(f220,plain,
! [X0] :
( ~ empty(X0)
| X0 = sK6_skl ),
inference(resolution,[status(thm)],[f108,f207]) ).
fof(f230,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f51]) ).
fof(f232,plain,
( one_to_one(empty_set)
| ~ empty(empty_set) ),
inference(resolution,[status(thm)],[f230,f92]) ).
fof(f240,definition,
( sQ7_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ7_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ8_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f232,f240,f243]) ).
fof(f247,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f86]) ).
fof(f248,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f249,plain,
epsilon_transitive(sK6_skl),
inference(backward_demodulation,[status(thm)],[f218,f95]) ).
fof(f251,plain,
function(sK6_skl),
inference(backward_demodulation,[status(thm)],[f218,f92]) ).
fof(f256,plain,
epsilon_connected(sK6_skl),
inference(backward_demodulation,[status(thm)],[f218,f176]) ).
fof(f260,plain,
( one_to_one(sK6_skl)
| ~ empty(sK6_skl) ),
inference(resolution,[status(thm)],[f251,f230]) ).
fof(f261,definition,
( sQ9_spl
<=> empty(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ9_spl
| ~ empty(sK6_skl) ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,definition,
( sQ10_spl
<=> one_to_one(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f260,f261,f264]) ).
fof(f268,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f108]) ).
fof(f269,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f282,plain,
sK8_skl = sK6_skl,
inference(resolution,[status(thm)],[f114,f220]) ).
fof(f290,plain,
( one_to_one(sK8_skl)
| ~ empty(sK8_skl) ),
inference(resolution,[status(thm)],[f115,f230]) ).
fof(f291,definition,
( sQ11_spl
<=> empty(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ11_spl
| ~ empty(sK8_skl) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
( sQ12_spl
<=> one_to_one(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f290,f291,f294]) ).
fof(f298,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f114]) ).
fof(f299,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f300,plain,
( one_to_one(sK9_skl)
| ~ empty(sK9_skl) ),
inference(resolution,[status(thm)],[f118,f230]) ).
fof(f301,definition,
( sQ13_spl
<=> empty(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ13_spl
| ~ empty(sK9_skl) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ14_spl
<=> one_to_one(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f300,f301,f304]) ).
fof(f326,plain,
( ordinal(sK13_skl)
| ~ epsilon_connected(sK13_skl) ),
inference(resolution,[status(thm)],[f57,f135]) ).
fof(f327,plain,
( ordinal(sK9_skl)
| ~ epsilon_connected(sK9_skl) ),
inference(resolution,[status(thm)],[f57,f121]) ).
fof(f328,plain,
( ordinal(sK6_skl)
| ~ epsilon_connected(sK6_skl) ),
inference(resolution,[status(thm)],[f57,f249]) ).
fof(f329,plain,
( ordinal(sK5_skl)
| ~ epsilon_connected(sK5_skl) ),
inference(resolution,[status(thm)],[f57,f104]) ).
fof(f330,definition,
( sQ17_spl
<=> epsilon_connected(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ17_spl
| ~ epsilon_connected(sK13_skl) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ18_spl
<=> ordinal(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f326,f330,f333]) ).
fof(f337,definition,
( sQ19_spl
<=> epsilon_connected(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ19_spl
| ~ epsilon_connected(sK9_skl) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
( sQ20_spl
<=> ordinal(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f327,f337,f340]) ).
fof(f344,definition,
( sQ21_spl
<=> epsilon_connected(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ21_spl
| ~ epsilon_connected(sK6_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ22_spl
<=> ordinal(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f328,f344,f347]) ).
fof(f351,definition,
( sQ23_spl
<=> epsilon_connected(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ23_spl
| ~ epsilon_connected(sK5_skl) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,definition,
( sQ24_spl
<=> ordinal(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f329,f351,f354]) ).
fof(f358,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f105]) ).
fof(f359,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f256]) ).
fof(f361,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f122]) ).
fof(f363,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f372,plain,
epsilon_connected(sK8_skl),
inference(backward_demodulation,[status(thm)],[f282,f256]) ).
fof(f377,plain,
epsilon_transitive(sK8_skl),
inference(backward_demodulation,[status(thm)],[f282,f249]) ).
fof(f384,plain,
( ordinal(sK8_skl)
| ~ epsilon_connected(sK8_skl) ),
inference(resolution,[status(thm)],[f377,f57]) ).
fof(f385,definition,
( sQ25_spl
<=> epsilon_connected(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( sQ25_spl
| ~ epsilon_connected(sK8_skl) ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,definition,
( sQ26_spl
<=> ordinal(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f384,f385,f388]) ).
fof(f392,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f372]) ).
fof(f393,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f425,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f120]) ).
fof(f426,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f427,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f136]) ).
fof(f428,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( subset(sK0_skl(sK16_skl),sK16_skl)
| epsilon_transitive(sK16_skl) ),
inference(resolution,[status(thm)],[f67,f156]) ).
fof(f434,definition,
( sQ29_spl
<=> epsilon_transitive(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ29_spl
| epsilon_transitive(sK16_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ30_spl
<=> subset(sK0_skl(sK16_skl),sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ30_spl
| subset(sK0_skl(sK16_skl),sK16_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f429,f434,f437]) ).
fof(f452,plain,
( ~ sQ29_spl
| ordinal(sK16_skl)
| ~ epsilon_connected(sK16_skl) ),
inference(resolution,[status(thm)],[f435,f57]) ).
fof(f453,definition,
( sQ32_spl
<=> epsilon_connected(sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ29_spl
| sQ0_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f452,f453,f182,f434]) ).
fof(f457,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f157]) ).
fof(f458,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f480,plain,
( ordinal(sK1_skl(sK16_skl))
| epsilon_connected(sK16_skl) ),
inference(resolution,[status(thm)],[f74,f155]) ).
fof(f492,definition,
( sQ34_spl
<=> ordinal(sK1_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ34_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f480,f453,f492]) ).
fof(f506,plain,
( ordinal(sK2_skl(sK16_skl))
| epsilon_connected(sK16_skl) ),
inference(resolution,[status(thm)],[f75,f155]) ).
fof(f518,definition,
( sQ37_spl
<=> ordinal(sK2_skl(sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ37_spl
| ordinal(sK2_skl(sK16_skl)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,plain,
( sQ37_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f506,f453,f518]) ).
fof(f539,plain,
! [X0] :
( sK2_skl(X0) = sK1_skl(X0)
| in(sK2_skl(X0),sK1_skl(X0))
| ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(resolution,[status(thm)],[f76,f150]) ).
fof(f541,plain,
! [X0] :
( in(sK2_skl(X0),sK1_skl(X0))
| ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f77]) ).
fof(f570,plain,
! [X0] :
( ~ ordinal(sK1_skl(X0))
| ~ ordinal(sK2_skl(X0))
| epsilon_connected(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f78]) ).
fof(f571,plain,
( ~ sQ37_spl
| ~ ordinal(sK1_skl(sK16_skl))
| epsilon_connected(sK16_skl) ),
inference(resolution,[status(thm)],[f570,f519]) ).
fof(f572,plain,
( ~ sQ37_spl
| ~ sQ34_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f571,f453,f492,f518]) ).
fof(f580,plain,
( ~ sQ30_spl
| epsilon_transitive(sK16_skl) ),
inference(resolution,[status(thm)],[f438,f68]) ).
fof(f581,plain,
( ~ sQ30_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f580,f434,f437]) ).
fof(f582,plain,
$false,
inference(sat_refutation,[status(thm)],[f246,f248,f267,f269,f297,f299,f307,f336,f343,f350,f357,f359,f361,f363,f391,f393,f426,f428,f440,f456,f458,f495,f521,f572,f581]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:00:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.049972 seconds
% 0.12/0.41 % CPU time: 0.167409 seconds
% 0.12/0.41 % Total memory used: 78.382 MB
% 0.12/0.41 % Net memory used: 78.259 MB
%------------------------------------------------------------------------------