%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC098+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 02:39:57 PM UTC 2026
% Result : Theorem 0.13s 0.59s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 126 ( 8 unt; 19 def)
% Number of atoms : 524 ( 120 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 664 ( 266 ~; 260 |; 89 &)
% ( 21 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 19 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 141 ( 120 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
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(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( leq(V,U)
& leq(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(V,W)
& leq(U,V) )
=> leq(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] :
( ssItem(U)
=> leq(U,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 )
& ! [X1] :
( ssItem(X1)
=> ( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( memberP(V,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Y,Z)
| ~ memberP(V,Z) ) )
& cons(Y,nil) = U
& ssItem(Y) )
| 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 )
& ! [X1] :
( ssItem(X1)
=> ( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( memberP(V,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Y,Z)
| ~ memberP(V,Z) ) )
& cons(Y,nil) = U
& ssItem(Y) )
| 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(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(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f250,plain,
! [U] :
( ! [V] :
( U = V
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f251,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
! [U] :
( ! [V] :
( ! [W] :
( leq(U,W)
| ~ leq(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f253,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
! [U] :
( leq(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f255,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X1] :
( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ memberP(V,Y)
| ? [Z] :
( Y != Z
& leq(Y,Z)
& memberP(V,Z)
& ssItem(Z) )
| cons(Y,nil) != U
| ~ 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,X1] :
( sP0_prd(X1,X,W)
<=> ( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X1] : sP0_prd(X1,X,W) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ memberP(V,Y)
| ? [Z] :
( Y != Z
& leq(Y,Z)
& memberP(V,Z)
& ssItem(Z) )
| cons(Y,nil) != U
| ~ ssItem(Y) )
& 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) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ memberP(sK48_skl,Y)
| ( Y != sK51_skl(Y)
& leq(Y,sK51_skl(Y))
& memberP(sK48_skl,sK51_skl(Y))
& ssItem(sK51_skl(Y)) )
| cons(Y,nil) != sK47_skl
| ~ ssItem(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl(Y)),skolemize(X1,sK52_skl)],[f417]) ).
fof(f422,plain,
ssList(sK50_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,
! [X0] :
( ~ memberP(sK48_skl,X0)
| ssItem(sK51_skl(X0))
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| memberP(sK48_skl,sK51_skl(X0))
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| leq(X0,sK51_skl(X0))
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| X0 != sK51_skl(X0)
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( nil = sK50_skl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
( nil = sK49_skl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
! [W,X,X1] :
( ( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W
| ~ ssItem(X1)
| sP0_prd(X1,X,W) )
& ( ( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) )
| ~ sP0_prd(X1,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f433,plain,
( ! [W,X,X1] :
( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W
| ~ ssItem(X1)
| sP0_prd(X1,X,W) )
& ! [W,X,X1] :
( ( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) )
| ~ sP0_prd(X1,X,W) ) ),
inference(miniscoping,[status(thm)],[f432]) ).
fof(f434,plain,
( ! [W,X,X1] :
( ( leq(X1,sK53_skl(X1,X,W))
& memberP(X,sK53_skl(X1,X,W))
& X1 != sK53_skl(X1,X,W)
& ssItem(sK53_skl(X1,X,W)) )
| ~ memberP(X,X1)
| cons(X1,nil) != W
| ~ ssItem(X1)
| sP0_prd(X1,X,W) )
& ! [W,X,X1] :
( ( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) )
| ~ sP0_prd(X1,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(X2,sK53_skl(X1,X,W))],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f437,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,plain,
! [X0,X1,X2,X3] :
( ~ leq(X0,X3)
| ~ memberP(X1,X3)
| X0 = X3
| ~ ssItem(X3)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f443,definition,
( sQ0_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ0_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,definition,
( sQ1_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ1_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f429,f443,f446]) ).
fof(f450,definition,
( sQ2_spl
<=> sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ2_spl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ3_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f430,f450,f453]) ).
fof(f457,definition,
( sQ4_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f431,f450,f457]) ).
fof(f464,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f497,plain,
( sQ0_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f498,plain,
( ~ sQ2_spl
| ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f451,f435]) ).
fof(f499,plain,
( ~ sQ2_spl
| memberP(sK50_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f437,f451]) ).
fof(f502,plain,
( ~ sQ2_spl
| cons(sK52_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f436,f451]) ).
fof(f506,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ6_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ6_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f521,plain,
( sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f498]) ).
fof(f522,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f497]) ).
fof(f524,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f223]) ).
fof(f526,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ1_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f424,f448]) ).
fof(f529,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| ssItem(sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f425]) ).
fof(f530,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| ssItem(sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f529]) ).
fof(f545,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f546,definition,
! [X0] :
( sQ9_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f547,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,definition,
! [X1] :
( sQ10_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f545,f546,f549]) ).
fof(f553,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f547]) ).
fof(f562,plain,
( ~ sQ9_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f422,f553]) ).
fof(f564,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f575,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| memberP(sK48_skl,sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f426]) ).
fof(f576,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| memberP(sK50_skl,sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f575]) ).
fof(f577,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| memberP(sK50_skl,sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f576]) ).
fof(f578,plain,
( ~ sQ2_spl
| ~ memberP(sK50_skl,sK52_skl)
| memberP(sK50_skl,sK51_skl(sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f502,f577]) ).
fof(f580,definition,
( sQ13_spl
<=> memberP(sK50_skl,sK51_skl(sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ13_spl
| memberP(sK50_skl,sK51_skl(sK52_skl)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,definition,
( sQ14_spl
<=> memberP(sK50_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ14_spl
| ~ memberP(sK50_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| sQ13_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f578,f509,f580,f583,f450]) ).
fof(f605,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f464,f222]) ).
fof(f607,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( ~ sQ5_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f605,f607,f506]) ).
fof(f617,plain,
! [X0] :
( ~ sQ2_spl
| ~ leq(sK52_skl,X0)
| ~ memberP(sK50_skl,X0)
| sK52_skl = X0
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f438,f451]) ).
fof(f618,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ leq(sK52_skl,sK51_skl(sK52_skl))
| sK52_skl = sK51_skl(sK52_skl)
| ~ ssItem(sK51_skl(sK52_skl)) ),
inference(resolution,[status(thm)],[f617,f581]) ).
fof(f620,definition,
( sQ19_spl
<=> ssItem(sK51_skl(sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f623,definition,
( sQ20_spl
<=> sK52_skl = sK51_skl(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f626,definition,
( sQ21_spl
<=> leq(sK52_skl,sK51_skl(sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ21_spl
| sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f618,f620,f623,f626,f450,f580]) ).
fof(f630,definition,
( sQ22_spl
<=> sK52_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f633,definition,
( sQ23_spl
<=> leq(sK52_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( ~ sQ23_spl
| leq(sK52_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f635,plain,
( sQ23_spl
| ~ leq(sK52_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f637,plain,
( sQ14_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f499]) ).
fof(f638,plain,
( sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f639,plain,
( sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f527,f457,f446]) ).
fof(f640,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| leq(X0,sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f427]) ).
fof(f641,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| leq(X0,sK51_skl(X0))
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f640]) ).
fof(f642,plain,
( sQ23_spl
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f635,f255]) ).
fof(f643,plain,
( sQ23_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f642,f509,f633]) ).
fof(f644,plain,
! [X0] :
( ~ sQ23_spl
| leq(X0,sK52_skl)
| ~ leq(X0,sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f634,f253]) ).
fof(f645,plain,
( ~ sQ23_spl
| sK52_skl = sK52_skl
| ~ leq(sK52_skl,sK52_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f634,f251]) ).
fof(f646,definition,
! [X0] :
( sQ24_spl
<=> ( leq(X0,sK52_skl)
| ~ leq(X0,sK52_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( ~ sQ23_spl
| ~ sQ6_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f644,f646,f509,f633]) ).
fof(f650,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f645,f509,f633,f630]) ).
fof(f657,plain,
( ~ sQ2_spl
| ~ memberP(sK50_skl,sK52_skl)
| leq(sK52_skl,sK51_skl(sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f502,f641]) ).
fof(f666,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| sQ21_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f657,f509,f626,f583,f450]) ).
fof(f704,plain,
! [X0] :
( ~ memberP(sK48_skl,X0)
| X0 != sK51_skl(X0)
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f705,plain,
! [X0] :
( ~ memberP(sK50_skl,X0)
| X0 != sK51_skl(X0)
| cons(X0,nil) != sK49_skl
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f704]) ).
fof(f706,plain,
( ~ sQ2_spl
| ~ memberP(sK50_skl,sK52_skl)
| sK52_skl != sK51_skl(sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f705,f502]) ).
fof(f708,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f706,f509,f623,f583,f450]) ).
fof(f710,plain,
( ~ sQ2_spl
| ~ memberP(sK50_skl,sK52_skl)
| ssItem(sK51_skl(sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f530,f502]) ).
fof(f712,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| sQ19_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f710,f509,f620,f583,f450]) ).
fof(f714,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f456,f460,f522,f524,f526,f552,f564,f586,f610,f629,f638,f639,f643,f649,f650,f666,f708,f712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC098+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n017.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 07:50:58 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.56 % Drodi V4.1.1
% 0.13/0.59 % Refutation found
% 0.13/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.63 % Elapsed time: 0.078373 seconds
% 0.13/0.63 % CPU time: 0.202700 seconds
% 0.13/0.63 % Total memory used: 111.721 MB
% 0.13/0.63 % Net memory used: 111.541 MB
%------------------------------------------------------------------------------