%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC038+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 : n006.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 02:39:42 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 12 unt; 5 def)
% Number of atoms : 143 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 151 ( 52 ~; 47 |; 36 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 34 ( 26 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('/export/starexec/sandbox2/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
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& nil != U
& U = W
& V = X
& nil = V
& 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
& U = W
& V = X
& nil = V
& 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
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& nil = sK48_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,
nil = sK48_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
nil != sK47_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(f432,plain,
! [X0,X1] :
( nil = X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f441,definition,
( sQ2_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ2_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f434,f441]) ).
fof(f476,plain,
nil = sK50_skl,
inference(backward_demodulation,[status(thm)],[f424,f423]) ).
fof(f479,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f425,f426]) ).
fof(f480,plain,
sK50_skl != sK49_skl,
inference(backward_demodulation,[status(thm)],[f476,f479]) ).
fof(f497,plain,
! [X0,X1] :
( sK50_skl = X1
| ~ sP0_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f476,f432]) ).
fof(f498,plain,
( ~ sQ0_spl
| sK50_skl = sK49_skl ),
inference(resolution,[status(thm)],[f497,f435]) ).
fof(f500,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f480]) ).
fof(f501,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f509,plain,
! [X0] :
( nil = X0
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f476,f298]) ).
fof(f510,plain,
! [X0] :
( sK50_skl = X0
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f476,f509]) ).
fof(f511,plain,
( ~ sQ2_spl
| sK50_skl = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f510,f442]) ).
fof(f514,definition,
( sQ3_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ3_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,definition,
( sQ4_spl
<=> sK50_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( ~ sQ4_spl
| sK50_skl = sK49_skl ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f511,f514,f517,f441]) ).
fof(f529,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f516,f421]) ).
fof(f530,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f533,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f480]) ).
fof(f534,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f501,f520,f530,f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC038+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n006.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 07:50:30 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.49 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56 % Elapsed time: 0.098711 seconds
% 0.17/0.56 % CPU time: 0.112699 seconds
% 0.17/0.56 % Total memory used: 6.933 MB
% 0.17/0.56 % Net memory used: 6.926 MB
%------------------------------------------------------------------------------