%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC020+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 : n012.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 02:39:37 PM UTC 2026
% Result : Theorem 0.06s 10.34s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 9 unt; 9 def)
% Number of atoms : 202 ( 50 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 223 ( 82 ~; 80 |; 43 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 39 ( 29 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| 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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f285,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f286,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X] :
( sP0_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| sP0_prd(X,W) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( frontsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ frontsegP(sK47_skl,Y)
| ~ frontsegP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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(f421,plain,
ssList(sK49_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,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( neq(sK49_skl,nil)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( frontsegP(sK50_skl,sK49_skl)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP0_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP0_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,definition,
( sQ0_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ0_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ1_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ1_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f434,f437]) ).
fof(f441,definition,
( sQ2_spl
<=> sP0_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ2_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ3_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ3_spl
| neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f441,f444]) ).
fof(f448,definition,
( sQ4_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f428,f441,f448]) ).
fof(f485,plain,
( sQ0_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f490,plain,
( ~ sQ2_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f431,f442]) ).
fof(f492,plain,
( ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f485]) ).
fof(f493,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f494,plain,
( sQ1_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f424,f439]) ).
fof(f495,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f496,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f495]) ).
fof(f497,plain,
( ~ sQ3_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ frontsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f496,f445]) ).
fof(f498,definition,
( sQ5_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ5_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ6_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ6_spl
| ~ frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f497,f498,f448,f501,f444]) ).
fof(f509,plain,
( sQ6_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f503,f286]) ).
fof(f510,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f421]) ).
fof(f511,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f421]) ).
fof(f513,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f515,plain,
( ~ sQ2_spl
| sP0_prd(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f490,f442]) ).
fof(f535,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f542,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f223]) ).
fof(f543,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f432,f515]) ).
fof(f546,plain,
( ~ sQ2_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f494]) ).
fof(f547,plain,
( ~ sQ2_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f447,f451,f493,f504,f511,f513,f543,f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC020+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/10.32 % Computer : n012.cluster.edu
% 0.06/10.32 % Model : x86_64 x86_64
% 0.06/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/10.32 % Memory : 8046.5625MB
% 0.06/10.32 % OS : Linux 6.8.0-71-generic
% 0.06/10.32 % CPULimit : 300
% 0.06/10.32 % WCLimit : 300
% 0.06/10.32 % DateTime : Mon Sep 21 07:49:21 UTC 2026
% 0.06/10.32 % CPUTime :
% 0.06/10.33 % Drodi V4.1.1
% 0.06/10.34 % Refutation found
% 0.06/10.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/10.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/10.36 % Elapsed time: 0.041545 seconds
% 0.06/10.36 % CPU time: 0.115873 seconds
% 0.06/10.36 % Total memory used: 107.176 MB
% 0.06/10.36 % Net memory used: 107.039 MB
%------------------------------------------------------------------------------