%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC023+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 : 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 02:39:38 PM UTC 2026
% Result : Theorem 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 7 unt; 7 def)
% Number of atoms : 221 ( 30 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 264 ( 101 ~; 92 |; 50 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 62 ( 50 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssList(Z)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& 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)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssList(Z)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& 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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] :
( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& ssList(Z) ) )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ 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,
! [W,X,Z] :
( sP0_prd(Z,X,W)
<=> ( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& ssList(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] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& 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(sK51_skl,sK50_skl,sK49_skl) )
& ! [Y] :
( ~ frontsegP(sK47_skl,Y)
| ~ frontsegP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil)
& 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(Z,sK51_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),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X,Z] :
( ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil)
| ~ ssList(Z)
| sP0_prd(Z,X,W) )
& ( ( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X,Z] :
( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil)
| ~ ssList(Z)
| sP0_prd(Z,X,W) )
& ! [W,X,Z] :
( ( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2] :
( ssList(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( neq(X0,nil)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f433,plain,
! [X0,X1,X2] :
( frontsegP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f436,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f436,f439]) ).
fof(f462,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f463,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f462]) ).
fof(f479,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f480,plain,
( ~ sQ0_spl
| ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f437,f431]) ).
fof(f481,plain,
( ~ sQ0_spl
| frontsegP(sK50_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f433,f437]) ).
fof(f484,plain,
( ~ sQ0_spl
| frontsegP(sK49_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f434,f437]) ).
fof(f485,plain,
( ~ sQ0_spl
| neq(sK51_skl,nil) ),
inference(resolution,[status(thm)],[f432,f437]) ).
fof(f486,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f487,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f486]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ frontsegP(sK49_skl,sK51_skl)
| ~ frontsegP(sK50_skl,sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f487,f485]) ).
fof(f491,definition,
( sQ3_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( sQ3_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
( sQ4_spl
<=> frontsegP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ4_spl
| ~ frontsegP(sK50_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
( sQ5_spl
<=> frontsegP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ5_spl
| ~ frontsegP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f488,f491,f494,f497,f436]) ).
fof(f501,definition,
( sQ6_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ6_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f518,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f422]) ).
fof(f519,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( sQ5_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f484]) ).
fof(f521,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f538,plain,
( ~ sQ1_spl
| neq(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f440,f479]) ).
fof(f551,plain,
( ~ sQ1_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f538,f463]) ).
fof(f553,plain,
( ~ sQ1_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f551,f501,f439]) ).
fof(f554,plain,
( ~ sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f493]) ).
fof(f555,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f577,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f481]) ).
fof(f578,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f579,plain,
$false,
inference(sat_refutation,[status(thm)],[f442,f500,f519,f521,f553,f555,f578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 07:51:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.057142 seconds
% 0.11/0.44 % CPU time: 0.155258 seconds
% 0.11/0.44 % Total memory used: 66.116 MB
% 0.11/0.44 % Net memory used: 66.021 MB
%------------------------------------------------------------------------------