%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:03 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 25
% Syntax : Number of formulae : 122 ( 13 unt; 17 def)
% Number of atoms : 482 ( 93 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 607 ( 247 ~; 238 |; 75 &)
% ( 21 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 17 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 145 ( 126 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ( ? [X1] :
( leq(X1,Z)
& memberP(X,X1)
& Z != X1
& ssItem(X1) )
| ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ( memberP(V,Y)
| ~ memberP(U,Y) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ( ? [X1] :
( leq(X1,Z)
& memberP(X,X1)
& Z != X1
& ssItem(X1) )
| ~ memberP(X,Z)
| cons(Z,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ( memberP(V,Y)
| ~ memberP(U,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(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
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(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
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(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
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 )
| ? [Z] :
( ! [X1] :
( ~ leq(X1,Z)
| ~ memberP(X,X1)
| Z = X1
| ~ ssItem(X1) )
& memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) ) )
& ? [Y] :
( ~ memberP(V,Y)
& memberP(U,Y)
& 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,Z] :
( sP0_prd(Z,X,W)
<=> ( ! [X1] :
( ~ leq(X1,Z)
| ~ memberP(X,X1)
| Z = X1
| ~ ssItem(X1) )
& memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] : sP0_prd(Z,X,W) )
& ? [Y] :
( ~ memberP(V,Y)
& memberP(U,Y)
& 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) )
& ~ memberP(sK48_skl,sK51_skl)
& memberP(sK47_skl,sK51_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl)],[f417]) ).
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,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
memberP(sK47_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
~ memberP(sK48_skl,sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( nil = sK50_skl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( nil = sK49_skl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
! [W,X,Z] :
( ( ? [X1] :
( leq(X1,Z)
& memberP(X,X1)
& Z != X1
& ssItem(X1) )
| ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ( ( ! [X1] :
( ~ leq(X1,Z)
| ~ memberP(X,X1)
| Z = X1
| ~ ssItem(X1) )
& memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [W,X,Z] :
( ? [X1] :
( leq(X1,Z)
& memberP(X,X1)
& Z != X1
& ssItem(X1) )
| ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ! [W,X,Z] :
( ( ! [X1] :
( ~ leq(X1,Z)
| ~ memberP(X,X1)
| Z = X1
| ~ ssItem(X1) )
& memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Z] :
( ( leq(sK53_skl(Z,X,W),Z)
& memberP(X,sK53_skl(Z,X,W))
& Z != sK53_skl(Z,X,W)
& ssItem(sK53_skl(Z,X,W)) )
| ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ! [W,X,Z] :
( ( ! [X1] :
( ~ leq(X1,Z)
| ~ memberP(X,X1)
| Z = X1
| ~ ssItem(X1) )
& memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl]),skolemize(X1,sK53_skl(Z,X,W))],[f431]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f435,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f441,definition,
( sQ0_spl
<=> sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ0_spl
| sP0_prd(sK52_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f441,f444]) ).
fof(f448,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f429,f441,f448]) ).
fof(f455,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f488,plain,
memberP(sK49_skl,sK51_skl),
inference(forward_demodulation,[status(thm)],[f424,f426]) ).
fof(f489,plain,
~ memberP(sK50_skl,sK51_skl),
inference(forward_demodulation,[status(thm)],[f423,f427]) ).
fof(f490,plain,
( ~ sQ0_spl
| ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f442,f433]) ).
fof(f491,plain,
( ~ sQ0_spl
| memberP(sK50_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f435,f442]) ).
fof(f494,plain,
( ~ sQ0_spl
| cons(sK52_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f434,f442]) ).
fof(f497,definition,
( sQ3_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ3_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f511,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f223]) ).
fof(f512,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f524,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| memberP(sK50_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f527,f488]) ).
fof(f527,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f445,f449]) ).
fof(f528,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f489]) ).
fof(f529,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( ~ sQ0_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f502]) ).
fof(f531,plain,
( ~ sQ0_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f533,definition,
! [X0] :
( sQ7_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f534,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
! [X1] :
( sQ8_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f532,f533,f536]) ).
fof(f540,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f534]) ).
fof(f541,plain,
( ~ sQ7_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f540]) ).
fof(f544,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f564,plain,
( ~ singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sK4_skl(nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f225,f117]) ).
fof(f566,definition,
( sQ12_spl
<=> ssItem(sK4_skl(nil)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ12_spl
| ~ ssItem(sK4_skl(nil)) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,definition,
( sQ13_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f564,f497,f566,f569]) ).
fof(f574,plain,
( sQ12_spl
| ~ singletonP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f568,f116]) ).
fof(f575,plain,
( sQ12_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f574,f497,f569,f566]) ).
fof(f588,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f228,f117]) ).
fof(f593,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f594,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,plain,
( sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f588,f497,f593]) ).
fof(f606,definition,
! [X1] :
( sQ18_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f607,plain,
! [X0] :
( ~ sQ18_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f610,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f116]) ).
fof(f623,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f455,f222]) ).
fof(f625,definition,
! [X0] :
( sQ21_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f626,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f628,plain,
( ~ sQ3_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f623,f625,f497]) ).
fof(f633,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(duplicate_literals_removal,[status(thm)],[f626]) ).
fof(f638,definition,
( sQ23_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f675,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ singletonP(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f610,f222]) ).
fof(f676,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ15_spl
| ~ ssItem(X0)
| nil = nil
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f675,f633]) ).
fof(f678,plain,
( ~ sQ21_spl
| ~ sQ15_spl
| sQ23_spl
| sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f676,f497,f606,f638,f593,f625]) ).
fof(f680,plain,
! [X0] :
( ~ sQ18_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f607]) ).
fof(f684,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f490,f680]) ).
fof(f688,plain,
( ~ sQ0_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f684]) ).
fof(f697,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f494,f275]) ).
fof(f698,definition,
! [X0] :
( sQ31_spl
<=> ( memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f699,plain,
! [X0] :
( ~ sQ31_spl
| memberP(nil,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f697,f698,f500,f497,f441]) ).
fof(f702,plain,
! [X0] :
( ~ sQ31_spl
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f279]) ).
fof(f729,plain,
( ~ sQ31_spl
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f702,f488]) ).
fof(f731,definition,
( sQ37_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f733,plain,
( sQ37_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f731]) ).
fof(f734,definition,
( sQ38_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f735,plain,
( ~ sQ38_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f734]) ).
fof(f737,plain,
( ~ sQ31_spl
| sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f729,f731,f734,f698]) ).
fof(f738,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f733,f425]) ).
fof(f739,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f742,plain,
( ~ sQ38_spl
| ~ memberP(sK50_skl,sK52_skl) ),
inference(backward_demodulation,[status(thm)],[f735,f489]) ).
fof(f743,plain,
( ~ sQ38_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f742,f491]) ).
fof(f744,plain,
( ~ sQ38_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f743]) ).
fof(f745,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f451,f512,f529,f531,f539,f544,f572,f575,f596,f628,f678,f688,f701,f737,f739,f744]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC392+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:20:58 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.059864 seconds
% 0.12/0.43 % CPU time: 0.190322 seconds
% 0.12/0.43 % Total memory used: 107.999 MB
% 0.12/0.43 % Net memory used: 107.805 MB
%------------------------------------------------------------------------------