%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC096+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 02:39:56 PM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 4 unt; 4 def)
% Number of atoms : 208 ( 59 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 266 ( 98 ~; 90 |; 66 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 133 ( 109 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ ssList(Z) )
| ~ 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)
<=> ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ ssList(Z) )
| ~ 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] :
( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ( app(sK54_skl(X,W,V,U),cons(sK53_skl(X,W,V,U),nil)) = V
& cons(sK53_skl(X,W,V,U),nil) = U
& ssList(sK54_skl(X,W,V,U))
& ssItem(sK53_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( app(sK52_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil)) = X
& cons(sK51_skl(X,W,V,U),nil) = W
& ssList(sK52_skl(X,W,V,U))
& ssItem(sK51_skl(X,W,V,U))
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X1,sK51_skl(X,W,V,U)),skolemize(X2,sK52_skl(X,W,V,U)),skolemize(Y,sK53_skl(X,W,V,U)),skolemize(Z,sK54_skl(X,W,V,U))],[f428]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5] :
( app(X5,cons(X4,nil)) != X2
| cons(X4,nil) != X3
| ~ ssList(X5)
| ~ 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] :
( ssList(sK52_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,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(f435,plain,
! [X0,X1,X2,X3] :
( app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f440,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f440,f443]) ).
fof(f447,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f440,f447]) ).
fof(f473,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f441]) ).
fof(f474,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f473]) ).
fof(f577,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( cons(sK51_skl(X0,X1,X2,X3),nil) != X6
| ~ ssList(sK52_skl(X0,X1,X2,X3))
| ~ ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X0,X6)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f435,f431]) ).
fof(f584,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( cons(sK51_skl(X0,X1,X2,X3),nil) != X6
| ~ ssList(sK52_skl(X0,X1,X2,X3))
| ~ sP0_prd(X4,X5,X0,X6)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f432]) ).
fof(f1012,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f449]) ).
fof(f1013,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1012,f444]) ).
fof(f1014,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1013]) ).
fof(f1652,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( cons(sK51_skl(X0,X1,X2,X3),nil) != X6
| ~ sP0_prd(X4,X5,X0,X6)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f433]) ).
fof(f1653,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X1,X2,X3)
| ~ sP0_prd(X4,X5,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f1652,f434]) ).
fof(f1668,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X4,X5,X0,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(duplicate_literals_removal,[status(thm)],[f1653]) ).
fof(f1822,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sP0_prd(sK48_skl,sK47_skl,X0,X1) ),
inference(resolution,[status(thm)],[f1668,f474]) ).
fof(f1829,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f474,f1822]) ).
fof(f1830,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1829]) ).
fof(f1831,plain,
$false,
inference(sat_refutation,[status(thm)],[f446,f450,f1014,f1830]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 07:54:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.40 % Elapsed time: 0.096934 seconds
% 0.08/0.40 % CPU time: 0.553056 seconds
% 0.08/0.40 % Total memory used: 124.703 MB
% 0.08/0.40 % Net memory used: 123.526 MB
%------------------------------------------------------------------------------