%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC381+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 : n008.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 02:41:01 PM UTC 2026
% Result : Theorem 0.15s 0.43s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 4 unt; 4 def)
% Number of atoms : 182 ( 35 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 225 ( 81 ~; 74 |; 56 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 86 ( 70 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [Z] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(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] :
( ssItem(Z)
=> ( ~ memberP(X,Z)
| cons(Z,nil) != W ) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(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] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(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(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,plain,
! [U,V,W,X] :
( ( ! [Z] :
( ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [Z] :
( ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z) )
| ? [Y] :
( memberP(V,Y)
& cons(Y,nil) = U
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [Z] :
( memberP(X,Z)
& cons(Z,nil) = W
& ssItem(Z) )
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [Z] :
( ~ memberP(X,Z)
| cons(Z,nil) != W
| ~ ssItem(Z) )
| ( memberP(V,sK52_skl(X,W,V,U))
& cons(sK52_skl(X,W,V,U),nil) = U
& ssItem(sK52_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( memberP(X,sK51_skl(X,W,V,U))
& cons(sK51_skl(X,W,V,U),nil) = W
& ssItem(sK51_skl(X,W,V,U))
& ! [Y] :
( ~ memberP(V,Y)
| cons(Y,nil) != U
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Z,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U))],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4] :
( ~ memberP(X2,X4)
| cons(X4,nil) != X3
| ~ ssItem(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( cons(sK51_skl(X0,X1,X2,X3),nil) = X1
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( memberP(X0,sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f438,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f438,f445]) ).
fof(f475,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f439]) ).
fof(f476,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f475]) ).
fof(f499,plain,
! [X0] :
( ~ sQ0_spl
| ~ memberP(sK48_skl,X0)
| cons(X0,nil) != sK47_skl
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f431,f476]) ).
fof(f567,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK47_skl,X1,X2)
| ~ memberP(sK48_skl,sK51_skl(X0,sK47_skl,X1,X2))
| ~ ssItem(sK51_skl(X0,sK47_skl,X1,X2)) ),
inference(resolution,[status(thm)],[f499,f433]) ).
fof(f568,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK47_skl,X1,X2)
| ~ memberP(sK48_skl,sK51_skl(X0,sK47_skl,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f432]) ).
fof(f599,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK48_skl,sK47_skl,X0,X1)
| ~ sP0_prd(sK48_skl,sK47_skl,X0,X1) ),
inference(resolution,[status(thm)],[f568,f434]) ).
fof(f600,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK48_skl,sK47_skl,X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f599]) ).
fof(f601,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f476,f600]) ).
fof(f602,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f603,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f447]) ).
fof(f642,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f442]) ).
fof(f643,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f644,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f448,f602,f643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC381+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 08:20:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 0.15/0.43 % Refutation found
% 0.15/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.47 % Elapsed time: 0.085048 seconds
% 0.15/0.47 % CPU time: 0.382730 seconds
% 0.15/0.47 % Total memory used: 105.052 MB
% 0.15/0.47 % Net memory used: 104.598 MB
%------------------------------------------------------------------------------