%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC016+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 : n026.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 02:39:36 PM UTC 2026
% Result : Theorem 0.13s 15.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 6 unt; 13 def)
% Number of atoms : 300 ( 62 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 359 ( 143 ~; 134 |; 55 &)
% ( 15 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 59 ( 47 !; 12 ?)
% 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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Z] :
( frontsegP(U,Z)
& frontsegP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| 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)
=> ( ( ( ? [Z] :
( frontsegP(U,Z)
& frontsegP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| 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(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Z] :
( ~ frontsegP(U,Z)
| ~ frontsegP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(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] :
( ( ( ! [Z] :
( ~ frontsegP(U,Z)
| ~ frontsegP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(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,
( ( ( ! [Z] :
( ~ frontsegP(sK47_skl,Z)
| ~ frontsegP(sK48_skl,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| ( frontsegP(sK49_skl,sK51_skl)
& frontsegP(sK50_skl,sK51_skl)
& neq(sK51_skl,nil)
& ssList(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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_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,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| neq(sK51_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| frontsegP(sK50_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| frontsegP(sK49_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,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(f433,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)],[f432]) ).
fof(f434,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f436,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f437,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f442,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f437,f440]) ).
fof(f444,definition,
( sQ2_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ3_spl
| neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f444,f447]) ).
fof(f451,definition,
( sQ4_spl
<=> neq(sK51_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f451,f447]) ).
fof(f455,definition,
( sQ5_spl
<=> frontsegP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f428,f455,f447]) ).
fof(f459,definition,
( sQ6_spl
<=> frontsegP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ6_spl
| frontsegP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f459]) ).
fof(f462,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f429,f459,f447]) ).
fof(f463,definition,
( sQ7_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ7_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ8_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ8_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f430,f463,f466]) ).
fof(f470,definition,
! [X0] :
( sQ9_spl
<=> ( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f471,plain,
! [X0] :
( ~ sQ9_spl
| ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f431,f463,f470]) ).
fof(f489,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f490,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f489]) ).
fof(f504,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f435]) ).
fof(f505,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f508,plain,
( ~ sQ0_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f438,f424]) ).
fof(f510,plain,
( ~ sQ7_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f464]) ).
fof(f511,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sP0_prd(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f508,f510]) ).
fof(f512,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f504]) ).
fof(f513,plain,
( ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f514,plain,
( ~ sQ8_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f467]) ).
fof(f515,plain,
( ~ sQ8_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f449]) ).
fof(f516,plain,
( ~ sQ8_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f521,plain,
( ~ sQ7_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f510]) ).
fof(f522,plain,
( ~ sQ7_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f521,f434]) ).
fof(f523,plain,
( ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f442]) ).
fof(f524,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
! [X0] :
( ~ sQ9_spl
| ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f471]) ).
fof(f526,plain,
! [X0] :
( ~ sQ9_spl
| ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f525]) ).
fof(f530,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f441,f448]) ).
fof(f539,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f530,f490]) ).
fof(f540,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f223]) ).
fof(f541,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f543,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f505,f434]) ).
fof(f544,definition,
! [X0] :
( sQ10_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f545,plain,
! [X0] :
( ~ sQ10_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ11_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f543,f544,f547]) ).
fof(f551,plain,
( sQ1_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f442,f545]) ).
fof(f565,plain,
( sQ1_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f566,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ frontsegP(sK50_skl,sK51_skl)
| ~ neq(sK51_skl,nil)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f526,f460]) ).
fof(f567,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f566,f444,f451,f455,f470,f459]) ).
fof(f568,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f450,f454,f458,f462,f469,f473,f513,f516,f524,f541,f550,f565,f567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC016+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/15.37 % Computer : n026.cluster.edu
% 0.08/15.37 % Model : x86_64 x86_64
% 0.08/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/15.37 % Memory : 8046.5625MB
% 0.08/15.37 % OS : Linux 6.8.0-71-generic
% 0.08/15.37 % CPULimit : 300
% 0.08/15.37 % WCLimit : 300
% 0.08/15.37 % DateTime : Mon Sep 21 07:52:23 UTC 2026
% 0.08/15.37 % CPUTime :
% 0.08/15.39 % Drodi V4.1.1
% 0.13/15.41 % Refutation found
% 0.13/15.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/15.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/15.43 % Elapsed time: 0.054371 seconds
% 0.13/15.43 % CPU time: 0.160296 seconds
% 0.13/15.43 % Total memory used: 83.184 MB
% 0.13/15.43 % Net memory used: 83.072 MB
%------------------------------------------------------------------------------