%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC152+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 : n017.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 02:40:10 PM UTC 2026
% Result : Theorem 0.14s 0.97s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 202 ( 20 unt; 34 def)
% Number of atoms : 798 ( 93 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 991 ( 395 ~; 408 |; 121 &)
% ( 40 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 34 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-3 aty)
% Number of variables : 180 ( 137 !; 43 ?)
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
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(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X5] :
( ? [X6] :
( leq(X5,X6)
& memberP(X,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X,X5)
| cons(X5,nil) != W
| ~ ssItem(X5) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( leq(Y,Z)
& ! [X4] :
( ( leq(X4,Z)
& leq(Y,X4) )
| ~ memberP(X2,X4)
| ~ ssItem(X4) ) )
| ~ leq(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != U
| ~ ssList(X3) ) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X5] :
( ? [X6] :
( leq(X5,X6)
& memberP(X,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X,X5)
| cons(X5,nil) != W
| ~ ssItem(X5) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( leq(Y,Z)
& ! [X4] :
( ( leq(X4,Z)
& leq(Y,X4) )
| ~ memberP(X2,X4)
| ~ ssItem(X4) ) )
| ~ leq(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != U
| ~ ssList(X3) ) ) ) ) )
| U != W
| V != X
| ~ ssList(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(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
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(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(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X5] :
( ! [X6] :
( ~ leq(X5,X6)
| ~ memberP(X,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X,X5)
& cons(X5,nil) = W
& ssItem(X5) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ leq(Y,Z)
| ? [X4] :
( ( ~ leq(X4,Z)
| ~ leq(Y,X4) )
& memberP(X2,X4)
& ssItem(X4) ) )
& leq(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = U
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,X5] :
( sP0_prd(X5,X,W)
<=> ( ! [X6] :
( ~ leq(X5,X6)
| ~ memberP(X,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X,X5)
& cons(X5,nil) = W
& ssItem(X5) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X5] : sP0_prd(X5,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ~ leq(Y,Z)
| ? [X4] :
( ( ~ leq(X4,Z)
| ~ leq(Y,X4) )
& memberP(X2,X4)
& ssItem(X4) ) )
& leq(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = U
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X5] : sP0_prd(X5,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ~ leq(Y,Z)
| ? [X4] :
( ( ~ leq(X4,Z)
| ~ leq(Y,X4) )
& memberP(X2,X4)
& ssItem(X4) ) )
& leq(Z,Y)
& ? [X3] :
( app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = U
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK57_skl,sK50_skl,sK49_skl) )
& ( ~ leq(sK51_skl,sK52_skl)
| ( ( ~ leq(sK56_skl,sK52_skl)
| ~ leq(sK51_skl,sK56_skl) )
& memberP(sK54_skl,sK56_skl)
& ssItem(sK56_skl) ) )
& leq(sK52_skl,sK51_skl)
& app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl) = sK47_skl
& ssList(sK55_skl)
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_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,sK53_skl,sK54_skl,sK55_skl,sK56_skl,sK57_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl),skolemize(X4,sK56_skl),skolemize(X5,sK57_skl)],[f418]) ).
fof(f420,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
ssList(sK55_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f432,plain,
leq(sK52_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f433,plain,
( ~ leq(sK51_skl,sK52_skl)
| ssItem(sK56_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f434,plain,
( ~ leq(sK51_skl,sK52_skl)
| memberP(sK54_skl,sK56_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f435,plain,
( ~ leq(sK51_skl,sK52_skl)
| ~ leq(sK56_skl,sK52_skl)
| ~ leq(sK51_skl,sK56_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f437,plain,
( nil = sK49_skl
| sP0_prd(sK57_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f438,plain,
! [W,X,X5] :
( ( ? [X6] :
( leq(X5,X6)
& memberP(X,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X,X5)
| cons(X5,nil) != W
| ~ ssItem(X5)
| sP0_prd(X5,X,W) )
& ( ( ! [X6] :
( ~ leq(X5,X6)
| ~ memberP(X,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X,X5)
& cons(X5,nil) = W
& ssItem(X5) )
| ~ sP0_prd(X5,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f439,plain,
( ! [W,X,X5] :
( ? [X6] :
( leq(X5,X6)
& memberP(X,X6)
& X5 != X6
& ssItem(X6) )
| ~ memberP(X,X5)
| cons(X5,nil) != W
| ~ ssItem(X5)
| sP0_prd(X5,X,W) )
& ! [W,X,X5] :
( ( ! [X6] :
( ~ leq(X5,X6)
| ~ memberP(X,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X,X5)
& cons(X5,nil) = W
& ssItem(X5) )
| ~ sP0_prd(X5,X,W) ) ),
inference(miniscoping,[status(thm)],[f438]) ).
fof(f440,plain,
( ! [W,X,X5] :
( ( leq(X5,sK58_skl(X5,X,W))
& memberP(X,sK58_skl(X5,X,W))
& X5 != sK58_skl(X5,X,W)
& ssItem(sK58_skl(X5,X,W)) )
| ~ memberP(X,X5)
| cons(X5,nil) != W
| ~ ssItem(X5)
| sP0_prd(X5,X,W) )
& ! [W,X,X5] :
( ( ! [X6] :
( ~ leq(X5,X6)
| ~ memberP(X,X6)
| X5 = X6
| ~ ssItem(X6) )
& memberP(X,X5)
& cons(X5,nil) = W
& ssItem(X5) )
| ~ sP0_prd(X5,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl]),skolemize(X6,sK58_skl(X5,X,W))],[f439]) ).
fof(f441,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f442,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f449,definition,
( sQ0_spl
<=> ssItem(sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f452,definition,
( sQ1_spl
<=> leq(sK51_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ1_spl
| ~ leq(sK51_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f449,f452]) ).
fof(f456,definition,
( sQ2_spl
<=> memberP(sK54_skl,sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ2_spl
| memberP(sK54_skl,sK56_skl) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f434,f456,f452]) ).
fof(f460,definition,
( sQ3_spl
<=> leq(sK51_skl,sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ3_spl
| ~ leq(sK51_skl,sK56_skl) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,definition,
( sQ4_spl
<=> leq(sK56_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ4_spl
| ~ leq(sK56_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f435,f460,f463,f452]) ).
fof(f467,definition,
( sQ5_spl
<=> sP0_prd(sK57_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ5_spl
| sP0_prd(sK57_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f474,definition,
( sQ7_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( ~ sQ7_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( sQ7_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f437,f467,f474]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f516,plain,
( ~ sQ5_spl
| sP0_prd(sK57_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f468]) ).
fof(f517,plain,
( ~ sQ5_spl
| sP0_prd(sK57_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f516]) ).
fof(f519,plain,
( ~ sQ5_spl
| ssItem(sK57_skl) ),
inference(resolution,[status(thm)],[f517,f441]) ).
fof(f520,plain,
( ~ sQ5_spl
| cons(sK57_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f442,f517]) ).
fof(f523,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ9_spl
<=> ssItem(sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( sQ9_spl
| ~ ssItem(sK57_skl) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f537,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f223]) ).
fof(f538,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ sQ7_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f475]) ).
fof(f542,definition,
( sQ12_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( sQ12_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ13_spl
<=> ssList(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( sQ13_spl
| ~ ssList(sK55_skl) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f551,definition,
( sQ14_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( sQ14_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f554,definition,
( sQ15_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( sQ15_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f554]) ).
fof(f557,definition,
( sQ16_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( ~ sQ16_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f561,plain,
! [X0] :
( ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK55_skl)
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f431,f271]) ).
fof(f562,definition,
! [X0] :
( sQ17_spl
<=> ( ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f563,plain,
! [X0] :
( ~ sQ17_spl
| ~ memberP(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f561,f562,f542,f545]) ).
fof(f566,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f430]) ).
fof(f567,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f590,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f427]) ).
fof(f591,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f426]) ).
fof(f593,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f714,plain,
( ~ sQ7_spl
| nil = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f540,f425]) ).
fof(f882,plain,
( sQ12_spl
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(resolution,[status(thm)],[f544,f245]) ).
fof(f883,definition,
( sQ60_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f885,plain,
( sQ60_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f886,definition,
( sQ61_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f888,plain,
( sQ61_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f889,plain,
( sQ12_spl
| ~ sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f882,f883,f886,f542]) ).
fof(f890,plain,
( sQ60_spl
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f885,f245]) ).
fof(f891,definition,
( sQ62_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f893,plain,
( sQ62_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f891]) ).
fof(f894,definition,
( sQ63_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( sQ63_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f894]) ).
fof(f897,plain,
( sQ60_spl
| ~ sQ63_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f890,f891,f894,f883]) ).
fof(f898,plain,
( sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f896,f429]) ).
fof(f899,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f898]) ).
fof(f900,plain,
( sQ61_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f888,f222]) ).
fof(f901,plain,
( sQ61_spl
| ~ sQ15_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f900,f523,f554,f886]) ).
fof(f907,plain,
( sQ62_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f893,f245]) ).
fof(f908,definition,
( sQ64_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( sQ64_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f911,definition,
( sQ65_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( sQ65_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f914,plain,
( sQ62_spl
| ~ sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f907,f908,f911,f891]) ).
fof(f915,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f910,f428]) ).
fof(f916,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f915]) ).
fof(f917,plain,
( sQ65_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f913,f222]) ).
fof(f918,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f917,f523,f551,f911]) ).
fof(f1102,plain,
( ~ sQ5_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f528]) ).
fof(f1103,plain,
( ~ sQ5_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1102]) ).
fof(f1112,plain,
! [X0] :
( ~ sQ5_spl
| memberP(nil,X0)
| X0 = sK57_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK57_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f520,f275]) ).
fof(f1154,definition,
! [X0] :
( sQ101_spl
<=> ( memberP(nil,X0)
| X0 = sK57_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1155,plain,
! [X0] :
( ~ sQ101_spl
| memberP(nil,X0)
| X0 = sK57_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1154]) ).
fof(f1157,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1112,f1154,f526,f523,f467]) ).
fof(f1180,plain,
! [X0] :
( ~ sQ101_spl
| X0 = sK57_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1155,f279]) ).
fof(f1362,plain,
( ~ sQ17_spl
| ~ ssList(nil)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl))
| ~ ssItem(sK52_skl)
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)))
| memberP(sK47_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f563,f480]) ).
fof(f1363,plain,
! [X0] :
( ~ sQ17_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f563,f271]) ).
fof(f1366,definition,
( sQ146_spl
<=> memberP(sK47_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1367,plain,
( ~ sQ146_spl
| memberP(sK47_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f1366]) ).
fof(f1369,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ60_spl
| ~ sQ12_spl
| sQ146_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1362,f554,f1366,f542,f883,f523,f562]) ).
fof(f1370,definition,
! [X0] :
( sQ147_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1371,plain,
! [X0] :
( ~ sQ147_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1370]) ).
fof(f1373,plain,
( ~ sQ17_spl
| ~ sQ61_spl
| ~ sQ60_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1363,f1370,f883,f886,f562]) ).
fof(f1379,plain,
! [X0] :
( ~ sQ147_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1371]) ).
fof(f1381,plain,
( ~ sQ101_spl
| ~ sQ146_spl
| sK52_skl = sK57_skl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f1367,f1180]) ).
fof(f1382,definition,
( sQ149_spl
<=> sK52_skl = sK57_skl ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
( ~ sQ149_spl
| sK52_skl = sK57_skl ),
inference(component_clause,[status(thm)],[f1382]) ).
fof(f1385,plain,
( ~ sQ101_spl
| ~ sQ146_spl
| sQ149_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1381,f554,f1382,f1366,f1154]) ).
fof(f1386,plain,
! [X0] :
( ~ sQ101_spl
| ~ sQ149_spl
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f1383,f1180]) ).
fof(f1388,plain,
( ~ sQ5_spl
| ~ sQ149_spl
| cons(sK52_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f1383,f520]) ).
fof(f1405,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ149_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1388,f275]) ).
fof(f1444,definition,
! [X0] :
( sQ157_spl
<=> ( memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1445,plain,
! [X0] :
( ~ sQ157_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1444]) ).
fof(f1447,plain,
( ~ sQ5_spl
| ~ sQ149_spl
| ~ sQ8_spl
| ~ sQ15_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f1405,f1444,f554,f523,f1382,f467]) ).
fof(f1460,plain,
! [X0] :
( ~ sQ157_spl
| X0 = sK52_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1445,f279]) ).
fof(f1482,plain,
( ~ sQ7_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f714]) ).
fof(f1529,definition,
( sQ161_spl
<=> ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1531,plain,
( sQ161_spl
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),sK54_skl),cons(sK52_skl,nil)),sK55_skl)) ),
inference(component_clause,[status(thm)],[f1529]) ).
fof(f1573,plain,
( sQ161_spl
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f431,f1531]) ).
fof(f1574,plain,
( sQ161_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1573,f420]) ).
fof(f1575,plain,
sQ161_spl,
inference(contradiction_clause,[status(thm)],[f1574]) ).
fof(f1577,plain,
! [X0] :
( ~ sQ147_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1379,f271]) ).
fof(f1578,plain,
! [X0] :
( ~ sQ147_spl
| ~ memberP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1379,f272]) ).
fof(f1580,definition,
! [X0] :
( sQ170_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1581,plain,
! [X0] :
( ~ sQ170_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1580]) ).
fof(f1583,plain,
( ~ sQ147_spl
| ~ sQ63_spl
| ~ sQ62_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1577,f1580,f891,f894,f1370]) ).
fof(f1584,definition,
! [X0] :
( sQ171_spl
<=> ( ~ memberP(sK54_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1585,plain,
! [X0] :
( ~ sQ171_spl
| ~ memberP(sK54_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1584]) ).
fof(f1587,plain,
( ~ sQ147_spl
| ~ sQ63_spl
| ~ sQ62_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1578,f1584,f891,f894,f1370]) ).
fof(f1589,plain,
! [X0] :
( ~ sQ170_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1581]) ).
fof(f1590,plain,
! [X0] :
( ~ sQ171_spl
| ~ memberP(sK54_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1585]) ).
fof(f1593,plain,
( ~ sQ170_spl
| ~ ssList(nil)
| ~ ssList(sK53_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| memberP(sK47_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1589,f480]) ).
fof(f1597,definition,
( sQ172_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1598,plain,
( ~ sQ172_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1597]) ).
fof(f1600,plain,
( ~ sQ170_spl
| ~ sQ8_spl
| ~ sQ64_spl
| ~ sQ62_spl
| sQ172_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1593,f551,f1597,f891,f908,f523,f1580]) ).
fof(f1669,plain,
( ~ sQ172_spl
| ~ sQ7_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f1482,f1598]) ).
fof(f1688,plain,
( ~ sQ172_spl
| ~ sQ7_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1669,f279]) ).
fof(f1689,plain,
( ~ sQ172_spl
| ~ sQ7_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1688,f551,f474,f1597]) ).
fof(f1843,plain,
( ~ sQ172_spl
| ~ sQ101_spl
| ~ sQ149_spl
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1386,f1598]) ).
fof(f1846,plain,
( ~ sQ172_spl
| ~ sQ101_spl
| ~ sQ149_spl
| sQ16_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1843,f551,f557,f1382,f1154,f1597]) ).
fof(f1861,plain,
( ~ sQ16_spl
| leq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f558,f432]) ).
fof(f1894,definition,
( sQ195_spl
<=> leq(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1896,plain,
( sQ195_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1894]) ).
fof(f1906,plain,
( sQ1_spl
| ~ sQ16_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f558,f454]) ).
fof(f1922,plain,
( sQ195_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1896,f1861]) ).
fof(f1923,plain,
( sQ195_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f1922]) ).
fof(f2047,plain,
! [X0] :
( ~ sQ157_spl
| ~ sQ16_spl
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f558,f1460]) ).
fof(f2054,plain,
( ~ sQ2_spl
| ~ sQ171_spl
| memberP(sK47_skl,sK56_skl)
| ~ ssItem(sK56_skl) ),
inference(resolution,[status(thm)],[f1590,f457]) ).
fof(f2056,definition,
( sQ213_spl
<=> memberP(sK47_skl,sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2057,plain,
( ~ sQ213_spl
| memberP(sK47_skl,sK56_skl) ),
inference(component_clause,[status(thm)],[f2056]) ).
fof(f2059,plain,
( ~ sQ2_spl
| ~ sQ171_spl
| sQ213_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2054,f449,f2056,f1584,f456]) ).
fof(f2135,plain,
( ~ sQ157_spl
| ~ sQ16_spl
| ~ sQ213_spl
| sK56_skl = sK51_skl
| ~ ssItem(sK56_skl) ),
inference(resolution,[status(thm)],[f2057,f2047]) ).
fof(f2136,definition,
( sQ227_spl
<=> sK56_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( ~ sQ227_spl
| sK56_skl = sK51_skl ),
inference(component_clause,[status(thm)],[f2136]) ).
fof(f2139,plain,
( ~ sQ157_spl
| ~ sQ16_spl
| ~ sQ213_spl
| sQ227_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2135,f449,f2136,f2056,f557,f1444]) ).
fof(f2141,plain,
( sQ3_spl
| ~ sQ227_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f2137,f462]) ).
fof(f2144,plain,
( sQ3_spl
| ~ sQ227_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f2141,f1894,f2136,f460]) ).
fof(f2203,plain,
( sQ4_spl
| ~ sQ16_spl
| ~ leq(sK56_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f558,f465]) ).
fof(f2204,plain,
( sQ1_spl
| ~ sQ16_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f1906,f1894,f557,f452]) ).
fof(f2207,plain,
( sQ4_spl
| ~ sQ16_spl
| ~ sQ227_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f2137,f2203]) ).
fof(f2208,plain,
( sQ4_spl
| ~ sQ16_spl
| ~ sQ227_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2207,f1861]) ).
fof(f2209,plain,
( sQ4_spl
| ~ sQ16_spl
| ~ sQ227_spl ),
inference(contradiction_clause,[status(thm)],[f2208]) ).
fof(f2210,plain,
$false,
inference(sat_refutation,[status(thm)],[f455,f459,f466,f477,f538,f565,f567,f591,f593,f889,f897,f899,f901,f914,f916,f918,f1103,f1157,f1369,f1373,f1385,f1447,f1575,f1583,f1587,f1600,f1689,f1846,f1923,f2059,f2139,f2144,f2204,f2209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC152+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n017.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Mon Sep 21 07:54:27 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.55 % Drodi V4.1.1
% 0.14/0.97 % Refutation found
% 0.14/0.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/1.00 % Elapsed time: 0.449371 seconds
% 0.14/1.00 % CPU time: 3.311012 seconds
% 0.14/1.00 % Total memory used: 152.273 MB
% 0.14/1.00 % Net memory used: 149.008 MB
%------------------------------------------------------------------------------