%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:40:47 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 26
% Syntax : Number of formulae : 109 ( 10 unt; 17 def)
% Number of atoms : 404 ( 101 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 502 ( 207 ~; 192 |; 55 &)
% ( 25 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 18 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 109 ( 87 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != X
| app(cons(X1,nil),X2) != W ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,Y) = U
& app(Y,Z) = V
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,cons(X1,nil)) != X
| app(cons(X1,nil),X2) != W ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,Y) = U
& app(Y,Z) = V
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& app(cons(X1,nil),X2) = W
& ssList(X2) )
& ssItem(X1) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ! [Z] :
( app(Z,Y) != U
| app(Y,Z) != V
| ~ ssList(Z) )
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK49_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ! [Y] :
( ! [Z] :
( app(Z,Y) != sK47_skl
| app(Y,Z) != sK48_skl
| ~ ssList(Z) )
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X1,sK51_skl),skolemize(X2,sK52_skl)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
! [X0,X1] :
( app(X1,X0) != sK47_skl
| app(X0,X1) != sK48_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f429,f432]) ).
fof(f436,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f439,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f425,f436,f439]) ).
fof(f443,definition,
( sQ4_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f426,f443,f439]) ).
fof(f447,definition,
( sQ5_spl
<=> app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f427,f447,f439]) ).
fof(f451,definition,
( sQ6_spl
<=> app(sK52_skl,cons(sK51_skl,nil)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f428,f451,f439]) ).
fof(f458,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f489,plain,
! [X0] :
( ~ sQ0_spl
| app(sK49_skl,X0) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f430,f249]) ).
fof(f508,plain,
( sQ3_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f441,f220]) ).
fof(f510,definition,
( sQ10_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ10_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,plain,
( sQ3_spl
| sQ1_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f508,f510,f513,f432,f439]) ).
fof(f521,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f223]) ).
fof(f522,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f420]) ).
fof(f524,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
! [X0,X1] :
( app(X1,X0) != sK47_skl
| app(X0,X1) != sK50_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f526,plain,
! [X0,X1] :
( app(X1,X0) != sK49_skl
| app(X0,X1) != sK50_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f525]) ).
fof(f527,plain,
! [X0] :
( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK49_skl)
| app(cons(X0,sK3_skl(X0,sK49_skl)),sK2_skl(X0,sK49_skl)) != sK50_skl
| ~ ssList(sK2_skl(X0,sK49_skl))
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl))) ),
inference(resolution,[status(thm)],[f526,f111]) ).
fof(f528,definition,
! [X0] :
( sQ13_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| app(cons(X0,sK3_skl(X0,sK49_skl)),sK2_skl(X0,sK49_skl)) != sK50_skl
| ~ ssList(sK2_skl(X0,sK49_skl))
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f531,definition,
( sQ14_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ14_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,plain,
( ~ sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f527,f528,f531]) ).
fof(f544,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ1_spl
| app(X1,X0) != sK50_skl
| app(X0,X1) != sK50_skl
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f547,f526]) ).
fof(f547,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f433,f430]) ).
fof(f582,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| app(sK50_skl,X0) = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f547,f489]) ).
fof(f592,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ ssList(sK50_skl)
| app(sK50_skl,sK50_skl) != sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f544,f582]) ).
fof(f594,definition,
( sQ22_spl
<=> app(sK50_skl,sK50_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ22_spl
| app(sK50_skl,sK50_skl) != sK50_skl ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f592,f510,f594,f432,f429]) ).
fof(f599,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ22_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f596,f582]) ).
fof(f601,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sQ22_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f599,f510,f594,f432,f429]) ).
fof(f609,definition,
( sQ24_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( sQ24_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f615,plain,
( ~ sQ5_spl
| app(sK52_skl,cons(sK51_skl,nil)) != sK50_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f526,f448]) ).
fof(f616,plain,
( ~ ssList(sK49_skl)
| app(sK49_skl,nil) != sK50_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f526,f249]) ).
fof(f617,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| app(sK5_skl(X0,sK49_skl),X0) != sK50_skl
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f526,f123]) ).
fof(f618,plain,
( ~ ssList(sK49_skl)
| app(nil,sK49_skl) != sK50_skl
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f526,f389]) ).
fof(f621,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ24_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f615,f443,f609,f451,f447]) ).
fof(f622,definition,
( sQ25_spl
<=> app(sK49_skl,nil) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( ~ sQ25_spl
| ~ sQ11_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f616,f531,f513,f622]) ).
fof(f626,definition,
! [X0] :
( sQ26_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| app(sK5_skl(X0,sK49_skl),X0) != sK50_skl
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ14_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f617,f626,f531]) ).
fof(f630,definition,
( sQ27_spl
<=> app(nil,sK49_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( ~ sQ27_spl
| ~ sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f618,f513,f531,f630]) ).
fof(f642,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f419]) ).
fof(f643,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f645,plain,
( sQ24_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f611]) ).
fof(f646,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f458]) ).
fof(f647,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f645,f513,f436,f609]) ).
fof(f648,definition,
! [X0] :
( sQ30_spl
<=> ( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( sQ30_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f646,f513,f648]) ).
fof(f652,plain,
$false,
inference(sat_refutation,[status(thm)],[f435,f442,f446,f450,f454,f516,f522,f524,f534,f597,f601,f621,f625,f629,f633,f643,f647,f651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 08:15:36 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.57 % Elapsed time: 0.107175 seconds
% 0.27/0.57 % CPU time: 0.162750 seconds
% 0.27/0.57 % Total memory used: 24.784 MB
% 0.27/0.57 % Net memory used: 24.734 MB
%------------------------------------------------------------------------------