%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC219+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:40:26 PM UTC 2026
% Result : Theorem 45.34s 26.53s
% Output : CNFRefutation 45.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 47
% Syntax : Number of formulae : 218 ( 39 unt; 31 def)
% Number of atoms : 769 ( 109 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 956 ( 405 ~; 403 |; 92 &)
% ( 33 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 31 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 167 ( 140 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(X2,Y)
| ~ leq(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(X2,Y)
| ~ leq(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
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(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
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(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
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(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f330,plain,
cyclefreeP(nil),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f333,plain,
totalorderP(nil),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f336,plain,
strictorderP(nil),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f359,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f362,plain,
equalelemsP(nil),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
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] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ? [X2] :
( ~ leq(X2,Y)
& leq(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ? [X2] :
( ~ leq(X2,Y)
& leq(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ leq(sK51_skl(X1,Z,Y),Y)
& leq(Y,sK51_skl(X1,Z,Y))
& memberP(X1,sK51_skl(X1,Z,Y))
& memberP(Z,sK51_skl(X1,Z,Y))
& ssItem(sK51_skl(X1,Z,Y)) )
| app(app(Z,cons(Y,nil)),X1) != sK47_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != sK47_skl
& 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(X2,sK51_skl(X1,Z,Y)),skolemize(X3,sK52_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,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0,X1,X2] :
( ssItem(sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [X0,X1,X2] :
( memberP(X1,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
! [W,X,X3] :
( ( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f434,plain,
( ! [W,X,X3] :
( ? [X4] :
( leq(X4,X3)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
( ! [W,X,X3] :
( ( leq(sK53_skl(X3,X,W),X3)
& memberP(X,sK53_skl(X3,X,W))
& X3 != sK53_skl(X3,X,W)
& ssItem(sK53_skl(X3,X,W)) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X4,X3)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(X4,sK53_skl(X3,X,W))],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f444,definition,
( sQ0_spl
<=> sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f451,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f444,f451]) ).
fof(f498,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f510,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f223]) ).
fof(f511,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f517,plain,
! [X0,X1] :
( memberP(X0,sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil)))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f123,f427]) ).
fof(f518,plain,
! [X0,X1] :
( ssItem(sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil)))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f123,f426]) ).
fof(f520,definition,
( sQ11_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ11_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
! [X0,X1] :
( sQ12_spl
<=> ( memberP(X0,sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f524,plain,
! [X0,X1] :
( ~ sQ12_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil))) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f517,f520,f523]) ).
fof(f527,definition,
! [X0,X1] :
( sQ13_spl
<=> ( ssItem(sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f528,plain,
! [X0,X1] :
( ~ sQ13_spl
| ssItem(sK51_skl(sK5_skl(app(X0,cons(X1,nil)),sK47_skl),X0,X1))
| ~ ssList(sK5_skl(app(X0,cons(X1,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ frontsegP(sK47_skl,app(X0,cons(X1,nil)))
| ~ ssList(app(X0,cons(X1,nil))) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f518,f520,f527]) ).
fof(f531,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f419]) ).
fof(f532,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f539,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(equality_resolution,[status(thm)],[f124]) ).
fof(f545,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f245]) ).
fof(f546,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f547,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f546]) ).
fof(f548,plain,
( ~ sQ0_spl
| ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f547,f436]) ).
fof(f653,plain,
( ~ sQ0_spl
| cons(sK52_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f437,f547]) ).
fof(f678,definition,
( sQ25_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f680,plain,
( sQ25_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f719,plain,
( sQ25_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f680,f548]) ).
fof(f720,plain,
( sQ25_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f719]) ).
fof(f725,plain,
( ~ sQ2_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f452,f424]) ).
fof(f726,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f725,f425]) ).
fof(f727,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f726]) ).
fof(f802,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f123]) ).
fof(f810,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f802]) ).
fof(f811,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f810,f122]) ).
fof(f974,definition,
( sQ56_spl
<=> cyclefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( sQ56_spl
| ~ cyclefreeP(nil) ),
inference(component_clause,[status(thm)],[f974]) ).
fof(f1060,definition,
! [X1] :
( sQ70_spl
<=> ( ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1061,plain,
! [X0] :
( ~ sQ70_spl
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1060]) ).
fof(f1068,definition,
( sQ72_spl
<=> totalorderP(nil) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1070,plain,
( sQ72_spl
| ~ totalorderP(nil) ),
inference(component_clause,[status(thm)],[f1068]) ).
fof(f1088,plain,
! [X0] :
( ~ sQ70_spl
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1061]) ).
fof(f1121,plain,
( ~ sQ70_spl
| nil != nil ),
inference(resolution,[status(thm)],[f1088,f223]) ).
fof(f1124,plain,
( ~ sQ70_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1121]) ).
fof(f1125,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f1124]) ).
fof(f1181,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(sK52_skl)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ),
inference(paramodulation,[status(thm)],[f653,f524]) ).
fof(f1192,definition,
! [X0] :
( sQ86_spl
<=> ( memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1193,plain,
! [X0] :
( ~ sQ86_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f1192]) ).
fof(f1195,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ25_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1181,f1192,f678,f523,f444]) ).
fof(f1196,plain,
! [X0] :
( ~ sQ86_spl
| ~ sQ0_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1193]) ).
fof(f1197,plain,
! [X0] :
( ~ sQ86_spl
| ~ sQ0_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,sK47_skl))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1196]) ).
fof(f1198,plain,
! [X0] :
( ~ sQ86_spl
| ~ sQ0_spl
| memberP(X0,sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,sK47_skl),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,sK47_skl))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1197]) ).
fof(f1286,definition,
( sQ92_spl
<=> strictorderP(nil) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1288,plain,
( sQ92_spl
| ~ strictorderP(nil) ),
inference(component_clause,[status(thm)],[f1286]) ).
fof(f1301,plain,
( sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1288,f336]) ).
fof(f1302,plain,
sQ92_spl,
inference(contradiction_clause,[status(thm)],[f1301]) ).
fof(f1315,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ13_spl
| ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ ssItem(sK52_skl)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ),
inference(paramodulation,[status(thm)],[f653,f528]) ).
fof(f1316,definition,
! [X0] :
( sQ98_spl
<=> ( ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1317,plain,
! [X0] :
( ~ sQ98_spl
| ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f1316]) ).
fof(f1319,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ25_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1315,f1316,f678,f527,f444]) ).
fof(f1320,plain,
! [X0] :
( ~ sQ98_spl
| ~ sQ0_spl
| ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,cons(sK52_skl,nil)))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1317]) ).
fof(f1321,plain,
! [X0] :
( ~ sQ98_spl
| ~ sQ0_spl
| ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,cons(sK52_skl,nil)),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,sK47_skl))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1320]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ98_spl
| ~ sQ0_spl
| ssItem(sK51_skl(sK5_skl(app(X0,sK47_skl),sK47_skl),X0,sK52_skl))
| ~ ssList(sK5_skl(app(X0,sK47_skl),sK47_skl))
| ~ ssList(X0)
| ~ frontsegP(sK47_skl,app(X0,sK47_skl))
| ~ ssList(app(X0,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f1321]) ).
fof(f1493,definition,
( sQ113_spl
<=> totalorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1495,plain,
( sQ113_spl
| ~ totalorderedP(nil) ),
inference(component_clause,[status(thm)],[f1493]) ).
fof(f1508,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1495,f339]) ).
fof(f1509,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f1508]) ).
fof(f1551,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f976,f330]) ).
fof(f1552,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f1551]) ).
fof(f1619,definition,
( sQ131_spl
<=> strictorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1621,plain,
( sQ131_spl
| ~ strictorderedP(nil) ),
inference(component_clause,[status(thm)],[f1619]) ).
fof(f1623,plain,
( sQ131_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1621,f349]) ).
fof(f1624,plain,
sQ131_spl,
inference(contradiction_clause,[status(thm)],[f1623]) ).
fof(f1687,definition,
( sQ136_spl
<=> duplicatefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1689,plain,
( sQ136_spl
| ~ duplicatefreeP(nil) ),
inference(component_clause,[status(thm)],[f1687]) ).
fof(f1702,plain,
( sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1689,f359]) ).
fof(f1703,plain,
sQ136_spl,
inference(contradiction_clause,[status(thm)],[f1702]) ).
fof(f1811,definition,
( sQ147_spl
<=> equalelemsP(nil) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1813,plain,
( sQ147_spl
| ~ equalelemsP(nil) ),
inference(component_clause,[status(thm)],[f1811]) ).
fof(f1828,plain,
( sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1813,f362]) ).
fof(f1829,plain,
sQ147_spl,
inference(contradiction_clause,[status(thm)],[f1828]) ).
fof(f2250,definition,
( sQ206_spl
<=> ssList(app(nil,cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2251,plain,
( ~ sQ206_spl
| ssList(app(nil,cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f2250]) ).
fof(f2252,plain,
( sQ206_spl
| ~ ssList(app(nil,cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f2250]) ).
fof(f2257,plain,
( sQ206_spl
| ~ sQ0_spl
| ~ ssList(app(nil,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f2252]) ).
fof(f2258,plain,
( sQ206_spl
| ~ sQ0_spl
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2257,f245]) ).
fof(f2259,plain,
( sQ206_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2258,f498,f520,f444,f2250]) ).
fof(f2260,plain,
( ~ sQ206_spl
| ~ sQ0_spl
| ssList(app(nil,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f653,f2251]) ).
fof(f2661,definition,
( sQ255_spl
<=> ssList(app(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2663,plain,
( sQ255_spl
| ~ ssList(app(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2661]) ).
fof(f2665,plain,
( sQ255_spl
| ~ sQ206_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2663,f2260]) ).
fof(f2666,plain,
( sQ255_spl
| ~ sQ206_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f2665]) ).
fof(f2871,definition,
( sQ272_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2872,plain,
( ~ sQ272_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f2871]) ).
fof(f3737,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1070,f333]) ).
fof(f3738,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f3737]) ).
fof(f3844,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f811,f245]) ).
fof(f4020,plain,
! [X0,X1] :
( sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3844,f545]) ).
fof(f4392,definition,
! [X0] :
( sQ374_spl
<=> ( X0 = sK52_skl
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f4393,plain,
! [X0] :
( ~ sQ374_spl
| X0 = sK52_skl
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f4392]) ).
fof(f4599,plain,
( ~ sQ374_spl
| sK0_skl = sK52_skl ),
inference(resolution,[status(thm)],[f4393,f103]) ).
fof(f4600,plain,
( ~ sQ374_spl
| sK1_skl = sK52_skl ),
inference(resolution,[status(thm)],[f4393,f104]) ).
fof(f4631,plain,
( ~ sQ374_spl
| sK1_skl = sK0_skl ),
inference(forward_demodulation,[status(thm)],[f4599,f4600]) ).
fof(f4632,plain,
( ~ sQ374_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4631,f105]) ).
fof(f4633,plain,
~ sQ374_spl,
inference(contradiction_clause,[status(thm)],[f4632]) ).
fof(f4912,definition,
( sQ393_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f4914,plain,
( sQ393_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f4912]) ).
fof(f4918,plain,
( sQ393_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4914,f420]) ).
fof(f4919,plain,
sQ393_spl,
inference(contradiction_clause,[status(thm)],[f4918]) ).
fof(f5447,definition,
( sQ426_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f5449,plain,
( sQ426_spl
| sK48_skl != sK48_skl ),
inference(component_clause,[status(thm)],[f5447]) ).
fof(f6050,definition,
( sQ484_spl
<=> sK47_skl = app(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f6051,plain,
( ~ sQ484_spl
| sK47_skl = app(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f6050]) ).
fof(f6052,plain,
( sQ484_spl
| sK47_skl != app(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f6050]) ).
fof(f6054,definition,
( sQ485_spl
<=> sK47_skl = app(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f6055,plain,
( ~ sQ485_spl
| sK47_skl = app(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f6054]) ).
fof(f6056,plain,
( sQ485_spl
| sK47_skl != app(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f6054]) ).
fof(f6219,plain,
( ~ sQ484_spl
| sK5_skl(sK47_skl,sK47_skl) = nil
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f6051,f4020]) ).
fof(f6224,plain,
( ~ sQ484_spl
| ~ ssList(nil)
| frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f6051,f545]) ).
fof(f6291,definition,
( sQ510_spl
<=> sK5_skl(sK47_skl,sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f6292,plain,
( ~ sQ510_spl
| sK5_skl(sK47_skl,sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f6291]) ).
fof(f6294,plain,
( ~ sQ484_spl
| sQ510_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f6219,f498,f520,f6291,f6050]) ).
fof(f6299,plain,
( ~ sQ484_spl
| ~ sQ8_spl
| sQ272_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6224,f520,f2871,f498,f6050]) ).
fof(f6460,plain,
( sQ485_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6056,f249]) ).
fof(f6461,plain,
( sQ485_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6460,f520,f6054]) ).
fof(f6710,plain,
( sQ484_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6052,f389]) ).
fof(f6711,plain,
( sQ484_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6710,f520,f6050]) ).
fof(f19854,plain,
( sQ426_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5449]) ).
fof(f19855,plain,
sQ426_spl,
inference(contradiction_clause,[status(thm)],[f19854]) ).
fof(f22907,definition,
( sQ2626_spl
<=> ssItem(sK51_skl(sK5_skl(app(nil,sK47_skl),sK47_skl),nil,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2626_spl])],[split_symbol_definition]) ).
fof(f22909,plain,
( sQ2626_spl
| ~ ssItem(sK51_skl(sK5_skl(app(nil,sK47_skl),sK47_skl),nil,sK52_skl)) ),
inference(component_clause,[status(thm)],[f22907]) ).
fof(f22912,plain,
( sQ2626_spl
| ~ sQ485_spl
| ~ ssItem(sK51_skl(sK5_skl(sK47_skl,sK47_skl),nil,sK52_skl)) ),
inference(forward_demodulation,[status(thm)],[f6055,f22909]) ).
fof(f22913,plain,
( sQ2626_spl
| ~ sQ485_spl
| ~ sQ510_spl
| ~ ssItem(sK51_skl(nil,nil,sK52_skl)) ),
inference(forward_demodulation,[status(thm)],[f6292,f22912]) ).
fof(f23196,plain,
( ~ sQ86_spl
| ~ sQ0_spl
| ~ ssItem(sK51_skl(sK5_skl(app(nil,sK47_skl),sK47_skl),nil,sK52_skl))
| ~ ssList(sK5_skl(app(nil,sK47_skl),sK47_skl))
| ~ ssList(nil)
| ~ frontsegP(sK47_skl,app(nil,sK47_skl))
| ~ ssList(app(nil,sK47_skl)) ),
inference(resolution,[status(thm)],[f1198,f279]) ).
fof(f23216,definition,
( sQ2650_spl
<=> frontsegP(sK47_skl,app(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2650_spl])],[split_symbol_definition]) ).
fof(f23218,plain,
( sQ2650_spl
| ~ frontsegP(sK47_skl,app(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f23216]) ).
fof(f23219,definition,
( sQ2651_spl
<=> ssList(sK5_skl(app(nil,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2651_spl])],[split_symbol_definition]) ).
fof(f23221,plain,
( sQ2651_spl
| ~ ssList(sK5_skl(app(nil,sK47_skl),sK47_skl)) ),
inference(component_clause,[status(thm)],[f23219]) ).
fof(f23222,plain,
( ~ sQ86_spl
| ~ sQ0_spl
| ~ sQ2626_spl
| ~ sQ2651_spl
| ~ sQ8_spl
| ~ sQ2650_spl
| ~ sQ255_spl ),
inference(split_clause,[status(thm)],[f23196,f2661,f23216,f498,f23219,f22907,f444,f1192]) ).
fof(f23227,plain,
( sQ2651_spl
| ~ sQ485_spl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f6055,f23221]) ).
fof(f23228,plain,
( sQ2651_spl
| ~ sQ485_spl
| ~ sQ510_spl
| ~ ssList(nil) ),
inference(forward_demodulation,[status(thm)],[f6292,f23227]) ).
fof(f23229,plain,
( sQ2651_spl
| ~ sQ485_spl
| ~ sQ510_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23228,f223]) ).
fof(f23230,plain,
( sQ2651_spl
| ~ sQ485_spl
| ~ sQ510_spl ),
inference(contradiction_clause,[status(thm)],[f23229]) ).
fof(f23231,plain,
( sQ2650_spl
| ~ sQ485_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f6055,f23218]) ).
fof(f23232,plain,
( sQ2650_spl
| ~ sQ485_spl
| ~ sQ272_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23231,f2872]) ).
fof(f23233,plain,
( sQ2650_spl
| ~ sQ485_spl
| ~ sQ272_spl ),
inference(contradiction_clause,[status(thm)],[f23232]) ).
fof(f28027,plain,
( ~ sQ485_spl
| ~ sQ98_spl
| ~ sQ0_spl
| ssItem(sK51_skl(sK5_skl(sK47_skl,sK47_skl),nil,sK52_skl))
| ~ ssList(sK5_skl(app(nil,sK47_skl),sK47_skl))
| ~ ssList(nil)
| ~ frontsegP(sK47_skl,app(nil,sK47_skl))
| ~ ssList(app(nil,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f6055,f1322]) ).
fof(f28028,definition,
( sQ2980_spl
<=> ssItem(sK51_skl(sK5_skl(sK47_skl,sK47_skl),nil,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2980_spl])],[split_symbol_definition]) ).
fof(f28029,plain,
( ~ sQ2980_spl
| ssItem(sK51_skl(sK5_skl(sK47_skl,sK47_skl),nil,sK52_skl)) ),
inference(component_clause,[status(thm)],[f28028]) ).
fof(f28031,plain,
( ~ sQ485_spl
| ~ sQ98_spl
| ~ sQ0_spl
| sQ2980_spl
| ~ sQ2651_spl
| ~ sQ8_spl
| ~ sQ2650_spl
| ~ sQ255_spl ),
inference(split_clause,[status(thm)],[f28027,f2661,f23216,f498,f23219,f28028,f444,f1316,f6054]) ).
fof(f28032,plain,
( ~ sQ2980_spl
| ~ sQ510_spl
| ssItem(sK51_skl(nil,nil,sK52_skl)) ),
inference(forward_demodulation,[status(thm)],[f6292,f28029]) ).
fof(f28033,plain,
( ~ sQ2980_spl
| ~ sQ510_spl
| sQ2626_spl
| ~ sQ485_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28032,f22913]) ).
fof(f28034,plain,
( ~ sQ2980_spl
| ~ sQ510_spl
| sQ2626_spl
| ~ sQ485_spl ),
inference(contradiction_clause,[status(thm)],[f28033]) ).
fof(f28035,plain,
$false,
inference(sat_refutation,[status(thm)],[f454,f511,f526,f530,f532,f720,f727,f1125,f1195,f1302,f1319,f1509,f1552,f1624,f1703,f1829,f2259,f2666,f3738,f4633,f4919,f6294,f6299,f6461,f6711,f19855,f23222,f23230,f23233,f28031,f28034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC219+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/20.77 % Computer : n012.cluster.edu
% 0.08/20.77 % Model : x86_64 x86_64
% 0.08/20.77 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/20.77 % Memory : 8046.5625MB
% 0.08/20.77 % OS : Linux 6.8.0-71-generic
% 0.08/20.77 % CPULimit : 300
% 0.08/20.77 % WCLimit : 300
% 0.08/20.77 % DateTime : Mon Sep 21 08:05:30 UTC 2026
% 0.08/20.77 % CPUTime :
% 0.08/20.78 % Drodi V4.1.1
% 45.34/26.53 % Refutation found
% 45.34/26.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 45.34/26.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 45.34/26.57 % Elapsed time: 5.796777 seconds
% 45.34/26.57 % CPU time: 45.891210 seconds
% 45.34/26.57 % Total memory used: 385.515 MB
% 45.34/26.57 % Net memory used: 353.423 MB
%------------------------------------------------------------------------------