%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC048+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 : n003.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 02:39:44 PM UTC 2026
% Result : Theorem 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 34
% Syntax : Number of formulae : 161 ( 13 unt; 24 def)
% Number of atoms : 540 ( 99 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 651 ( 272 ~; 264 |; 63 &)
% ( 30 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 23 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 121 ( 106 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( rearsegP(U,Y)
& rearsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f300,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(U,W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f301,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
! [U] :
( ! [V] :
( U = V
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f303,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& 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,definition,
! [W,X] :
( sP1_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| sP1_prd(X,W) )
& ( ( ! [Y] :
( ~ rearsegP(U,Y)
| ~ rearsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| sP0_prd(V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
( ( ( rearsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP1_prd(sK50_skl,sK49_skl) )
& ( ( ! [Y] :
( ~ rearsegP(sK47_skl,Y)
| ~ rearsegP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f418]) ).
fof(f422,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f423,plain,
ssList(sK50_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,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
! [X0] :
( ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( neq(sK49_skl,nil)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( rearsegP(sK50_skl,sK49_skl)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,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(f431,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)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f435,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP1_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f436,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP1_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( nil = X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f440,definition,
( sQ0_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f440,f443]) ).
fof(f447,definition,
! [X0] :
( sQ2_spl
<=> ( ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK47_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f440,f447]) ).
fof(f451,definition,
( sQ3_spl
<=> sP1_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ3_spl
| sP1_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ4_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ4_spl
| neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f451,f454]) ).
fof(f458,definition,
( sQ5_spl
<=> rearsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ5_spl
| rearsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f429,f451,f458]) ).
fof(f477,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f478,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f477]) ).
fof(f492,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f433]) ).
fof(f493,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f434]) ).
fof(f497,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f441]) ).
fof(f498,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f497]) ).
fof(f503,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f432,f498]) ).
fof(f504,plain,
( ~ sQ0_spl
| sP0_prd(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f498]) ).
fof(f505,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| sP1_prd(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f452]) ).
fof(f510,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f493,f432]) ).
fof(f511,definition,
! [X0] :
( sQ6_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f512,plain,
! [X0] :
( ~ sQ6_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ7_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f510,f511,f514]) ).
fof(f518,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f512,f512]) ).
fof(f532,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f518]) ).
fof(f533,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f553,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f438,f505]) ).
fof(f557,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sP0_prd(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f553,f504]) ).
fof(f559,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f492]) ).
fof(f560,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f567,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK49_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f448]) ).
fof(f569,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f424,f444]) ).
fof(f571,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f452,f437]) ).
fof(f580,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f571,f569]) ).
fof(f586,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f580,f478]) ).
fof(f587,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f586,f223]) ).
fof(f588,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f594,definition,
( sQ12_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ12_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,definition,
( sQ13_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ13_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,definition,
( sQ14_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ14_spl
| rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ14_spl
| ~ rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,definition,
( sQ15_spl
<=> sK49_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( ~ sQ15_spl
| sK49_skl = nil ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f611,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| rearsegP(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f503,f459]) ).
fof(f619,definition,
( sQ17_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ17_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f619]) ).
fof(f625,definition,
( sQ19_spl
<=> sK49_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ sQ19_spl
| sK49_skl = sK50_skl ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f627,plain,
( sQ19_spl
| sK49_skl != sK50_skl ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f629,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f422]) ).
fof(f630,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f629]) ).
fof(f632,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f223]) ).
fof(f633,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f638,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f309,f303]) ).
fof(f639,definition,
! [X0] :
( sQ20_spl
<=> ( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( ~ sQ13_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f638,f639,f597]) ).
fof(f645,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f312,f301]) ).
fof(f648,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( ~ sQ13_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f645,f648,f597]) ).
fof(f656,plain,
( ~ sQ19_spl
| ~ sQ0_spl
| sK49_skl = nil ),
inference(forward_demodulation,[status(thm)],[f503,f626]) ).
fof(f657,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ0_spl
| neq(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f656,f455]) ).
fof(f658,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f657,f478]) ).
fof(f659,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f658,f597,f440,f625,f454]) ).
fof(f660,plain,
( sQ14_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f602,f309]) ).
fof(f662,plain,
( sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f660,f594,f600]) ).
fof(f672,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f423]) ).
fof(f673,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f672]) ).
fof(f678,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f309]) ).
fof(f686,definition,
! [X0] :
( sQ25_spl
<=> ( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( ~ sQ13_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f678,f686,f597]) ).
fof(f694,plain,
( ~ sQ14_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f601,f129]) ).
fof(f695,plain,
( ~ sQ14_spl
| nil = sK49_skl
| ~ rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f601,f303]) ).
fof(f696,definition,
( sQ26_spl
<=> app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f699,plain,
( ~ sQ14_spl
| sQ26_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f694,f594,f597,f696,f600]) ).
fof(f700,definition,
( sQ27_spl
<=> rearsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f702,plain,
( sQ27_spl
| ~ rearsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f700]) ).
fof(f703,plain,
( ~ sQ14_spl
| sQ15_spl
| ~ sQ27_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f695,f597,f594,f700,f603,f600]) ).
fof(f704,plain,
! [X0] :
( ~ sQ2_spl
| ~ rearsegP(sK49_skl,X0)
| ~ rearsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f567]) ).
fof(f706,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ rearsegP(sK49_skl,sK49_skl)
| ~ rearsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f704,f455]) ).
fof(f708,definition,
( sQ28_spl
<=> rearsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( sQ28_spl
| ~ rearsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f712,definition,
( sQ29_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ29_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ29_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f706,f594,f458,f712,f447,f454]) ).
fof(f723,plain,
! [X0] :
( sQ27_spl
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f702,f301]) ).
fof(f724,definition,
! [X0] :
( sQ31_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( sQ27_spl
| ~ sQ12_spl
| sQ31_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f723,f597,f724,f594,f700]) ).
fof(f752,plain,
( sQ28_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f710,f305]) ).
fof(f757,plain,
( sQ28_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f752,f619,f708]) ).
fof(f761,plain,
( sQ29_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f714,f305]) ).
fof(f766,plain,
( sQ29_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f761,f594,f712]) ).
fof(f767,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f611,f702]) ).
fof(f768,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f773,plain,
( sQ19_spl
| ~ sQ0_spl
| sK49_skl != nil ),
inference(forward_demodulation,[status(thm)],[f503,f627]) ).
fof(f774,plain,
( ~ sQ15_spl
| sQ19_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f773]) ).
fof(f775,plain,
( ~ sQ15_spl
| sQ19_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f776,plain,
$false,
inference(sat_refutation,[status(thm)],[f446,f450,f457,f461,f517,f533,f560,f588,f630,f633,f642,f651,f659,f662,f673,f689,f699,f703,f715,f727,f757,f766,f768,f775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC048+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.35 % Computer : n003.cluster.edu
% 0.09/5.35 % Model : x86_64 x86_64
% 0.09/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.35 % Memory : 8046.5625MB
% 0.09/5.35 % OS : Linux 6.8.0-71-generic
% 0.09/5.35 % CPULimit : 300
% 0.09/5.35 % WCLimit : 300
% 0.09/5.35 % DateTime : Mon Sep 21 07:53:06 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.050510 seconds
% 0.13/5.41 % CPU time: 0.136171 seconds
% 0.13/5.41 % Total memory used: 48.801 MB
% 0.13/5.41 % Net memory used: 48.722 MB
%------------------------------------------------------------------------------