%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC415+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 : n001.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 02:41:09 PM UTC 2026
% Result : Theorem 0.13s 10.66s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 86 ( 8 unt; 12 def)
% Number of atoms : 341 ( 74 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 422 ( 167 ~; 160 |; 68 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 120 ( 104 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ? [Z] :
( neq(nil,V)
& U = Z
& tl(V) = Z
& ssList(Z) )
| ? [Y] :
( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ? [Z] :
( neq(nil,V)
& U = Z
& tl(V) = Z
& ssList(Z) )
| ? [Y] :
( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ! [Z] :
( ~ neq(nil,V)
| U != Z
| tl(V) != Z
| ~ ssList(Z) )
& ! [Y] :
( ~ neq(nil,X)
| tl(X) != Y
| W = Y
| ~ ssList(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ! [Z] :
( ~ neq(nil,V)
| U != Z
| tl(V) != Z
| ~ ssList(Z) )
& ! [Y] :
( ~ neq(nil,X)
| tl(X) != Y
| W = Y
| ~ ssList(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,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)],[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,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,definition,
! [W,X,Y] :
( sP1_prd(Y,X,W)
<=> ( ~ neq(nil,X)
| tl(X) != Y
| W = Y
| ~ ssList(Y) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f428,plain,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ! [Z] :
( ~ neq(nil,V)
| U != Z
| tl(V) != Z
| ~ ssList(Z) )
& ! [Y] : sP1_prd(Y,X,W)
& neq(V,nil) ) ),
inference(formula_renaming,[status(thm)],[f416,f427]) ).
fof(f429,plain,
! [U,V,W,X] :
( ( ? [Z] :
( neq(nil,V)
& U = Z
& tl(V) = Z
& ssList(Z) )
| ? [Y] : ~ sP1_prd(Y,X,W)
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ! [Z] :
( ~ neq(nil,V)
| U != Z
| tl(V) != Z
| ~ ssList(Z) )
& ! [Y] : sP1_prd(Y,X,W)
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f428]) ).
fof(f430,plain,
( ! [U,V,W,X] :
( ( neq(nil,V)
& ? [Z] :
( U = Z
& tl(V) = Z
& ssList(Z) ) )
| ? [Y] : ~ sP1_prd(Y,X,W)
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ( ~ neq(nil,V)
| ! [Z] :
( U != Z
| tl(V) != Z
| ~ ssList(Z) ) )
& ! [Y] : sP1_prd(Y,X,W)
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
( ! [U,V,W,X] :
( ( neq(nil,V)
& U = sK52_skl(X,W,V,U)
& tl(V) = sK52_skl(X,W,V,U)
& ssList(sK52_skl(X,W,V,U)) )
| ~ sP1_prd(sK51_skl(X,W,V,U),X,W)
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ( ~ neq(nil,V)
| ! [Z] :
( U != Z
| tl(V) != Z
| ~ ssList(Z) ) )
& ! [Y] : sP1_prd(Y,X,W)
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f430]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1,X2,X3,X4] :
( sP1_prd(X4,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1,X2,X3,X4] :
( ~ neq(nil,X2)
| X3 != X4
| tl(X2) != X4
| ~ ssList(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f439,plain,
! [W,X,Y] :
( ( ( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| sP1_prd(Y,X,W) )
& ( ~ neq(nil,X)
| tl(X) != Y
| W = Y
| ~ ssList(Y)
| ~ sP1_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f427]) ).
fof(f440,plain,
( ! [W,X,Y] :
( ( neq(nil,X)
& tl(X) = Y
& W != Y
& ssList(Y) )
| sP1_prd(Y,X,W) )
& ! [W,X,Y] :
( ~ neq(nil,X)
| tl(X) != Y
| W = Y
| ~ ssList(Y)
| ~ sP1_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f439]) ).
fof(f441,plain,
! [X0,X1,X2] :
( ~ neq(nil,X1)
| tl(X1) != X0
| X2 = X0
| ~ ssList(X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f446,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f446,f449]) ).
fof(f453,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f446,f453]) ).
fof(f472,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f473,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f472]) ).
fof(f487,plain,
! [X0,X1,X2] :
( ~ neq(nil,X2)
| ~ ssList(tl(X2))
| ~ sP0_prd(X0,X1,X2,tl(X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f434]) ).
fof(f488,plain,
! [X0,X1] :
( ~ neq(nil,X0)
| X1 = tl(X0)
| ~ ssList(tl(X0))
| ~ sP1_prd(tl(X0),X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f441]) ).
fof(f492,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f447]) ).
fof(f493,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f492]) ).
fof(f494,plain,
( ~ sQ0_spl
| neq(sK50_skl,nil) ),
inference(resolution,[status(thm)],[f432,f493]) ).
fof(f499,plain,
! [X0] :
( ~ sQ0_spl
| sP1_prd(X0,sK50_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f433,f493]) ).
fof(f500,plain,
( ~ sQ0_spl
| ~ neq(nil,sK50_skl)
| sK49_skl = tl(sK50_skl)
| ~ ssList(tl(sK50_skl)) ),
inference(resolution,[status(thm)],[f488,f499]) ).
fof(f505,definition,
( sQ3_spl
<=> ssList(tl(sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ3_spl
| ~ ssList(tl(sK50_skl)) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,definition,
( sQ4_spl
<=> sK49_skl = tl(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ4_spl
| sK49_skl = tl(sK50_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
( sQ5_spl
<=> neq(nil,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ5_spl
| ~ neq(nil,sK50_skl) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f500,f505,f508,f511,f446]) ).
fof(f515,plain,
( sQ5_spl
| nil = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f513,f220]) ).
fof(f517,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,definition,
( sQ7_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ7_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ8_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ8_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( sQ5_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f515,f517,f520,f523,f511]) ).
fof(f534,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f422]) ).
fof(f535,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f223]) ).
fof(f537,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f545,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| neq(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f524,f494]) ).
fof(f562,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f545,f473]) ).
fof(f564,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f562,f520,f523,f446]) ).
fof(f565,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f450]) ).
fof(f566,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| neq(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f524,f565]) ).
fof(f570,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f566,f473]) ).
fof(f572,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f570,f520,f523,f449]) ).
fof(f579,plain,
( sQ3_spl
| nil = sK50_skl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f241,f507]) ).
fof(f580,plain,
( sQ3_spl
| sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f579,f520,f523,f505]) ).
fof(f602,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ neq(nil,sK50_skl)
| ~ ssList(tl(sK50_skl))
| ~ sP0_prd(X0,X1,sK50_skl,sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f487]) ).
fof(f603,definition,
! [X0,X1] :
( sQ15_spl
<=> ~ sP0_prd(X0,X1,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f604,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ sP0_prd(X0,X1,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f602,f603,f505,f511,f508]) ).
fof(f607,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f493,f604]) ).
fof(f608,plain,
( ~ sQ0_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
( sQ2_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f455,f220]) ).
fof(f611,plain,
( sQ2_spl
| sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f609,f520,f517,f523,f453]) ).
fof(f613,plain,
$false,
inference(sat_refutation,[status(thm)],[f452,f456,f514,f526,f535,f537,f564,f572,f580,f606,f608,f611]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC415+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.60 % Computer : n001.cluster.edu
% 0.13/10.60 % Model : x86_64 x86_64
% 0.13/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.60 % Memory : 8046.5625MB
% 0.13/10.60 % OS : Linux 6.8.0-71-generic
% 0.13/10.60 % CPULimit : 300
% 0.13/10.60 % WCLimit : 300
% 0.13/10.60 % DateTime : Mon Sep 21 08:28:42 UTC 2026
% 0.13/10.61 % CPUTime :
% 0.13/10.63 % Drodi V4.1.1
% 0.13/10.66 % Refutation found
% 0.13/10.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/10.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.68 % Elapsed time: 0.070348 seconds
% 0.13/10.68 % CPU time: 0.230469 seconds
% 0.13/10.68 % Total memory used: 63.249 MB
% 0.13/10.68 % Net memory used: 63.133 MB
%------------------------------------------------------------------------------