%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC384+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 : n004.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 02:41:01 PM UTC 2026
% Result : Theorem 0.24s 0.80s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 104 ( 11 unt; 14 def)
% Number of atoms : 434 ( 71 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 522 ( 192 ~; 187 |; 101 &)
% ( 21 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 13 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 152 ( 115 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& 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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& singletonP(U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| ~ neq(V,nil)
| 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)
=> ( ( segmentP(V,U)
& singletonP(U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f219,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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ singletonP(U) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ singletonP(U) )
& ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ~ segmentP(sK48_skl,sK47_skl)
| ~ singletonP(sK47_skl) )
& ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) )
& neq(sK48_skl,nil)
& 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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( ~ segmentP(sK48_skl,sK47_skl)
| ~ singletonP(sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,definition,
! [Y,Z,X2] :
( sP1_prd(X2,Z,Y)
<=> ( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f430,plain,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
inference(formula_renaming,[status(thm)],[f416,f429]) ).
fof(f431,plain,
! [W,X,Y] :
( ( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f431]) ).
fof(f433,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ( lt(sK55_skl(X1,Z,Y,X,W),Y)
& memberP(X1,sK55_skl(X1,Z,Y,X,W))
& ssItem(sK55_skl(X1,Z,Y,X,W)) )
| ~ sP1_prd(sK54_skl(X1,Z,Y,X,W),Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(sK53_skl(Y,X,W),X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,sK52_skl(Y,X,W),Y)
& app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W)) = X
& cons(Y,nil) = W
& ssList(sK53_skl(Y,X,W))
& ssList(sK52_skl(Y,X,W))
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f438,plain,
! [X0,X1,X2] :
( app(app(sK52_skl(X0,X1,X2),X2),sK53_skl(X0,X1,X2)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f450,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f450,f453]) ).
fof(f461,definition,
( sQ3_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f464,definition,
( sQ4_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ4_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f461,f464]) ).
fof(f471,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f474,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f483,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f484,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f483]) ).
fof(f507,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f451]) ).
fof(f508,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f507]) ).
fof(f509,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f508,f434]) ).
fof(f516,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f437,f508]) ).
fof(f517,plain,
( ~ sQ0_spl
| ~ ssItem(sK51_skl)
| singletonP(sK47_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f516,f471]) ).
fof(f519,definition,
( sQ5_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ5_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ6_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ6_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f517,f519,f461,f522,f450]) ).
fof(f529,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f533,plain,
( ~ sQ1_spl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f423,f454]) ).
fof(f563,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f223]) ).
fof(f564,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f565,plain,
( ~ sQ0_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f524]) ).
fof(f566,plain,
( ~ sQ0_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f598,plain,
( ~ sQ1_spl
| neq(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f533,f425]) ).
fof(f599,plain,
( ~ sQ1_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f598,f484]) ).
fof(f600,plain,
( ~ sQ1_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f599,f529,f453]) ).
fof(f609,plain,
( sQ5_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f521,f222]) ).
fof(f610,plain,
( sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f609,f529,f522,f519]) ).
fof(f613,definition,
( sQ16_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ16_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f624,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f419]) ).
fof(f625,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f643,plain,
( ~ sQ0_spl
| app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)) = sK48_skl ),
inference(resolution,[status(thm)],[f508,f438]) ).
fof(f707,definition,
( sQ26_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f709,plain,
( sQ26_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f707]) ).
fof(f722,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f709,f420]) ).
fof(f723,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f722]) ).
fof(f1215,plain,
( ~ sQ0_spl
| ~ ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl))
| ~ ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl))
| segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f643,f474]) ).
fof(f1218,definition,
( sQ71_spl
<=> segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1219,plain,
( ~ sQ71_spl
| segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl) ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1221,definition,
( sQ72_spl
<=> ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1223,plain,
( sQ72_spl
| ~ ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1221]) ).
fof(f1224,definition,
( sQ73_spl
<=> ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1226,plain,
( sQ73_spl
| ~ ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1224]) ).
fof(f1227,plain,
( ~ sQ0_spl
| ~ sQ73_spl
| ~ sQ72_spl
| sQ71_spl
| ~ sQ16_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1215,f707,f613,f1218,f1221,f1224,f450]) ).
fof(f1236,plain,
( sQ73_spl
| ~ sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f1226,f436]) ).
fof(f1237,plain,
( sQ73_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1236,f508]) ).
fof(f1238,plain,
( sQ73_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1237]) ).
fof(f1239,plain,
( ~ sQ71_spl
| ~ sQ0_spl
| segmentP(sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f643,f1219]) ).
fof(f1240,plain,
( ~ sQ71_spl
| ~ sQ0_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1239,f466]) ).
fof(f1241,plain,
( ~ sQ71_spl
| ~ sQ0_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1240]) ).
fof(f1253,plain,
( sQ72_spl
| ~ sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f1223,f435]) ).
fof(f1254,plain,
( sQ72_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1253,f508]) ).
fof(f1255,plain,
( sQ72_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1254]) ).
fof(f1256,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f467,f525,f564,f566,f600,f610,f625,f723,f1227,f1238,f1241,f1255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC384+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n004.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 08:20:21 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.24/0.80 % Refutation found
% 0.24/0.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.85 % Elapsed time: 0.367995 seconds
% 0.24/0.85 % CPU time: 2.221478 seconds
% 0.24/0.85 % Total memory used: 131.127 MB
% 0.24/0.85 % Net memory used: 129.353 MB
%------------------------------------------------------------------------------