%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC310+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 : n010.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 02:40:44 PM UTC 2026
% Result : Theorem 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 39
% Syntax : Number of formulae : 179 ( 13 unt; 26 def)
% Number of atoms : 691 ( 193 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 896 ( 384 ~; 365 |; 87 &)
% ( 28 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 26 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 169 ( 141 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( ? [X3] :
( neq(nil,V)
& ? [X4] :
( neq(nil,V)
& hd(V) = X4
& cons(X4,nil) = X3
& ssItem(X4) )
& app(X2,X3) = X1
& tl(V) = X2
& ssList(X3) )
& ssList(X2) )
& U = X1
& ssList(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != W
| app(cons(Y,nil),Z) != X
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( ? [X3] :
( neq(nil,V)
& ? [X4] :
( neq(nil,V)
& hd(V) = X4
& cons(X4,nil) = X3
& ssItem(X4) )
& app(X2,X3) = X1
& tl(V) = X2
& ssList(X3) )
& ssList(X2) )
& U = X1
& ssList(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != W
| app(cons(Y,nil),Z) != X
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X
| ~ ssList(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(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(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(f238,plain,
! [U] :
( ! [V] :
( hd(cons(V,U)) = V
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f239,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f242,plain,
! [U] :
( ! [V] :
( tl(cons(V,U)) = U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f243,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
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(f246,plain,
! [U] :
( ! [V] :
( ! [W] :
( cons(W,app(V,U)) = app(cons(W,V),U)
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f247,plain,
! [X0,X1,X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
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(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
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] :
( ( ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ neq(nil,V)
| ! [X4] :
( ~ neq(nil,V)
| hd(V) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4) )
| app(X2,X3) != X1
| tl(V) != X2
| ~ ssList(X3) )
| ~ ssList(X2) )
| U != X1
| ~ ssList(X1) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = W
& app(cons(Y,nil),Z) = X
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ neq(nil,V)
| ! [X4] :
( ~ neq(nil,V)
| hd(V) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4) )
| app(X2,X3) != X1
| tl(V) != X2
| ~ ssList(X3) )
| ~ ssList(X2) )
| U != X1
| ~ ssList(X1) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = W
& app(cons(Y,nil),Z) = X
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& 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] :
( ( ( ! [X1] :
( ! [X2] :
( ~ neq(nil,V)
| ! [X3] :
( ~ neq(nil,V)
| ! [X4] :
( hd(V) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4) )
| app(X2,X3) != X1
| tl(V) != X2
| ~ ssList(X3) )
| ~ ssList(X2) )
| U != X1
| ~ ssList(X1) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = W
& app(cons(Y,nil),Z) = X
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( ! [X1] :
( ! [X2] :
( ~ neq(nil,sK48_skl)
| ! [X3] :
( ~ neq(nil,sK48_skl)
| ! [X4] :
( hd(sK48_skl) != X4
| cons(X4,nil) != X3
| ~ ssItem(X4) )
| app(X2,X3) != X1
| tl(sK48_skl) != X2
| ~ ssList(X3) )
| ~ ssList(X2) )
| sK47_skl != X1
| ~ ssList(X1) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| ( app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl
& app(cons(sK51_skl,nil),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssItem(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_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)],[f418]) ).
fof(f420,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f421,plain,
ssList(sK48_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,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
( ~ neq(sK50_skl,nil)
| app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ neq(nil,sK48_skl)
| ~ neq(nil,sK48_skl)
| hd(sK48_skl) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sK48_skl) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sK47_skl != X0
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f433,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f434,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f437,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f445,f448]) ).
fof(f452,definition,
( sQ4_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ4_spl
| ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f428,f452,f448]) ).
fof(f456,definition,
( sQ5_spl
<=> app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK50_skl ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f429,f456,f448]) ).
fof(f460,definition,
( sQ6_spl
<=> app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ6_spl
| app(sK52_skl,cons(sK51_skl,nil)) = sK49_skl ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f430,f460,f448]) ).
fof(f464,definition,
( sQ7_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ7_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
( sQ8_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ8_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f431,f464,f467]) ).
fof(f471,definition,
! [X0,X1,X2,X3] :
( sQ9_spl
<=> ( hd(sK48_skl) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sK48_skl) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sK47_skl != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f472,plain,
! [X0,X1,X2,X3] :
( ~ sQ9_spl
| hd(sK48_skl) != X3
| cons(X3,nil) != X2
| ~ ssItem(X3)
| app(X1,X2) != X0
| tl(sK48_skl) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| sK47_skl != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,definition,
( sQ10_spl
<=> neq(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ10_spl
| ~ neq(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( ~ sQ10_spl
| sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f432,f464,f471,f474]) ).
fof(f493,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f494,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f493]) ).
fof(f508,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f509,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f437]) ).
fof(f512,plain,
( sQ3_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f424,f450]) ).
fof(f513,plain,
( ~ sQ7_spl
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f435,f465]) ).
fof(f523,definition,
( sQ13_spl
<=> sK48_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ13_spl
| sK48_skl = nil ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f527,plain,
( sQ3_spl
| sK48_skl = nil
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f220,f512]) ).
fof(f530,definition,
( sQ14_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ14_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( sQ3_spl
| sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f527,f530,f533,f523,f448]) ).
fof(f537,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sP0_prd(sK48_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f540,f465]) ).
fof(f540,plain,
( ~ sQ0_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f439]) ).
fof(f542,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sP0_prd(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f513,f537]) ).
fof(f549,definition,
( sQ16_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f223]) ).
fof(f555,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f556,plain,
( sQ10_spl
| nil = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f476,f220]) ).
fof(f558,plain,
( sQ10_spl
| sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f556,f533,f530,f523,f474]) ).
fof(f563,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f564,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f565,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f567,definition,
! [X1] :
( sQ18_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f563,f564,f567]) ).
fof(f571,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f565]) ).
fof(f581,plain,
( ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f421,f571]) ).
fof(f584,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f590,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f524,f468]) ).
fof(f592,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f590,f494]) ).
fof(f593,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f592,f533,f523,f467]) ).
fof(f595,plain,
( ~ sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f513,f523,f464]) ).
fof(f596,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f508]) ).
fof(f597,plain,
( ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f613,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f509,f435]) ).
fof(f614,definition,
! [X0] :
( sQ25_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f615,plain,
! [X0] :
( ~ sQ25_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,plain,
( sQ16_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f613,f614,f549]) ).
fof(f618,plain,
! [X0,X1] :
( ~ sQ25_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f615,f615]) ).
fof(f627,plain,
( ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f618]) ).
fof(f628,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f631,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f421]) ).
fof(f632,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f633,plain,
( sQ1_spl
| nil != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f443]) ).
fof(f637,plain,
( ~ sQ5_spl
| app(cons(sK51_skl,nil),sK52_skl) = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f457]) ).
fof(f638,plain,
( ~ sQ5_spl
| cons(sK51_skl,app(nil,sK52_skl)) = sK48_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f637,f247]) ).
fof(f639,definition,
( sQ26_spl
<=> cons(sK51_skl,app(nil,sK52_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( ~ sQ26_spl
| cons(sK51_skl,app(nil,sK52_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f639]) ).
fof(f642,plain,
( ~ sQ5_spl
| sQ26_spl
| ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f638,f452,f533,f445,f639,f456]) ).
fof(f649,plain,
( ~ sQ6_spl
| app(sK52_skl,cons(sK51_skl,nil)) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f461]) ).
fof(f655,plain,
( ~ sQ13_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f633]) ).
fof(f656,plain,
( ~ sQ13_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f659,plain,
( ~ sQ9_spl
| ~ ssItem(hd(sK48_skl))
| app(tl(sK48_skl),cons(hd(sK48_skl),nil)) != sK47_skl
| ~ ssList(cons(hd(sK48_skl),nil))
| ~ ssList(tl(sK48_skl))
| ~ ssList(sK47_skl) ),
inference(destructive_equality_resolution,[status(thm)],[f472]) ).
fof(f660,plain,
( ~ sQ9_spl
| ~ ssItem(hd(sK48_skl))
| app(tl(sK48_skl),cons(hd(sK48_skl),nil)) != sK47_skl
| ~ ssList(cons(hd(sK48_skl),nil))
| ~ ssList(tl(sK48_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f420]) ).
fof(f677,plain,
( ~ sQ26_spl
| hd(sK48_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(app(nil,sK52_skl)) ),
inference(paramodulation,[status(thm)],[f640,f239]) ).
fof(f681,plain,
( ~ sQ26_spl
| tl(sK48_skl) = app(nil,sK52_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(nil,sK52_skl)) ),
inference(paramodulation,[status(thm)],[f640,f243]) ).
fof(f684,definition,
( sQ27_spl
<=> ssList(app(nil,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( sQ27_spl
| ~ ssList(app(nil,sK52_skl)) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,definition,
( sQ28_spl
<=> hd(sK48_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f688,plain,
( ~ sQ28_spl
| hd(sK48_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( ~ sQ26_spl
| sQ28_spl
| ~ sQ2_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f677,f684,f445,f687,f639]) ).
fof(f697,definition,
( sQ30_spl
<=> tl(sK48_skl) = app(nil,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( ~ sQ30_spl
| tl(sK48_skl) = app(nil,sK52_skl) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f700,plain,
( ~ sQ26_spl
| sQ30_spl
| ~ sQ2_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f681,f684,f445,f697,f639]) ).
fof(f731,plain,
( sQ27_spl
| ~ ssList(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f686,f245]) ).
fof(f732,plain,
( sQ27_spl
| ~ sQ4_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f731,f533,f452,f684]) ).
fof(f754,definition,
( sQ39_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ39_spl
| ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f756,plain,
( sQ39_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f771,plain,
( ~ sQ30_spl
| tl(sK48_skl) = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f698,f249]) ).
fof(f775,definition,
( sQ42_spl
<=> tl(sK48_skl) = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ42_spl
| tl(sK48_skl) = sK52_skl ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f778,plain,
( ~ sQ30_spl
| sQ42_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f771,f452,f775,f697]) ).
fof(f933,plain,
( sQ39_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f756,f222]) ).
fof(f934,plain,
( sQ39_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f933,f533,f445,f754]) ).
fof(f1000,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f389]) ).
fof(f1012,definition,
! [X0] :
( sQ77_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1015,plain,
( ~ sQ15_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1000,f1012,f533]) ).
fof(f1086,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ ssItem(hd(sK48_skl))
| app(tl(sK48_skl),cons(hd(sK48_skl),nil)) != sK47_skl
| ~ ssList(cons(hd(sK48_skl),nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f776,f660]) ).
fof(f1087,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ ssItem(hd(sK48_skl))
| app(tl(sK48_skl),cons(hd(sK48_skl),nil)) != sK47_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f688,f1086]) ).
fof(f1088,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ ssItem(hd(sK48_skl))
| app(sK52_skl,cons(hd(sK48_skl),nil)) != sK47_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f776,f1087]) ).
fof(f1089,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ ssItem(hd(sK48_skl))
| app(sK52_skl,cons(sK51_skl,nil)) != sK47_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f688,f1088]) ).
fof(f1090,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ ssItem(hd(sK48_skl))
| sK47_skl != sK47_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f649,f1089]) ).
fof(f1091,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ ssItem(sK51_skl)
| sK47_skl != sK47_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f688,f1090]) ).
fof(f1092,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ ssItem(sK51_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(trivial_equality_resolution,[status(thm)],[f1091]) ).
fof(f1093,plain,
( ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ ssItem(sK51_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1092,f453]) ).
fof(f1094,plain,
( ~ sQ39_spl
| ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1093,f755]) ).
fof(f1096,plain,
( ~ sQ39_spl
| ~ sQ9_spl
| ~ sQ42_spl
| ~ sQ28_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1094,f445,f452,f460,f687,f775,f471,f754]) ).
fof(f1098,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f451,f455,f459,f463,f470,f477,f536,f555,f558,f570,f584,f593,f595,f597,f617,f628,f632,f642,f656,f690,f700,f732,f778,f934,f1015,f1096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC310+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:15:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.52 % Refutation found
% 0.14/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.163670 seconds
% 0.14/0.53 % CPU time: 0.969373 seconds
% 0.14/0.53 % Total memory used: 124.228 MB
% 0.14/0.53 % Net memory used: 123.141 MB
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