%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC322+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 : n007.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 02:40:47 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 7 unt; 7 def)
% Number of atoms : 219 ( 86 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 257 ( 94 ~; 89 |; 55 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 61 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = U
| nil != V )
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) != W
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = U
| nil != V )
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) != W
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != U
& nil = V )
| ? [X1] :
( ? [X2] :
( app(cons(X1,nil),X2) != U
& app(X2,cons(X1,nil)) = V
& ssList(X2) )
& ssItem(X1) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) = W
| ~ ssList(Z) )
| ~ ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,X1] :
( sP0_prd(X1,V,U)
<=> ( ? [X2] :
( app(cons(X1,nil),X2) != U
& app(X2,cons(X1,nil)) = V
& ssList(X2) )
& ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != U
& nil = V )
| ? [X1] : sP0_prd(X1,V,U) )
& ( nil != X
| nil = W )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) = W
| ~ ssList(Z) )
| ~ ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil != sK47_skl
& nil = sK48_skl )
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != sK50_skl
| app(cons(Y,nil),Z) = sK49_skl
| ~ ssList(Z) )
| ~ ssItem(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,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X1,sK51_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,X1] :
( app(X1,cons(X0,nil)) != sK50_skl
| app(cons(X0,nil),X1) = sK49_skl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( nil = sK48_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( nil != sK47_skl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [U,V,X1] :
( ( ! [X2] :
( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V
| ~ ssList(X2) )
| ~ ssItem(X1)
| sP0_prd(X1,V,U) )
& ( ( ? [X2] :
( app(cons(X1,nil),X2) != U
& app(X2,cons(X1,nil)) = V
& ssList(X2) )
& ssItem(X1) )
| ~ sP0_prd(X1,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [U,V,X1] :
( ! [X2] :
( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V
| ~ ssList(X2) )
| ~ ssItem(X1)
| sP0_prd(X1,V,U) )
& ! [U,V,X1] :
( ( ? [X2] :
( app(cons(X1,nil),X2) != U
& app(X2,cons(X1,nil)) = V
& ssList(X2) )
& ssItem(X1) )
| ~ sP0_prd(X1,V,U) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
( ! [U,V,X1] :
( ! [X2] :
( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V
| ~ ssList(X2) )
| ~ ssItem(X1)
| sP0_prd(X1,V,U) )
& ! [U,V,X1] :
( ( app(cons(X1,nil),sK52_skl(X1,V,U)) != U
& app(sK52_skl(X1,V,U),cons(X1,nil)) = V
& ssList(sK52_skl(X1,V,U))
& ssItem(X1) )
| ~ sP0_prd(X1,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl]),skolemize(X2,sK52_skl(X1,V,U))],[f430]) ).
fof(f432,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1,X2] :
( app(sK52_skl(X0,X1,X2),cons(X0,nil)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f435,plain,
! [X0,X1,X2] :
( app(cons(X0,nil),sK52_skl(X0,X1,X2)) != X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f437,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f437,f440]) ).
fof(f444,definition,
( sQ2_spl
<=> sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,definition,
( sQ3_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ3_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f444,f447]) ).
fof(f451,definition,
( sQ4_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ4_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,plain,
( ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f428,f444,f451]) ).
fof(f489,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f445]) ).
fof(f490,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f489]) ).
fof(f539,definition,
( sQ9_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ9_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f594,plain,
! [X0,X1] :
( ~ sP0_prd(X0,X1,sK49_skl)
| app(sK52_skl(X0,X1,sK49_skl),cons(X0,nil)) != sK50_skl
| ~ ssList(sK52_skl(X0,X1,sK49_skl))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f425,f435]) ).
fof(f595,plain,
! [X0,X1] :
( ~ sP0_prd(X0,X1,sK49_skl)
| app(sK52_skl(X0,X1,sK49_skl),cons(X0,nil)) != sK50_skl
| ~ ssList(sK52_skl(X0,X1,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f432]) ).
fof(f597,plain,
! [X0,X1] :
( ~ sP0_prd(X0,X1,sK49_skl)
| app(sK52_skl(X0,X1,sK49_skl),cons(X0,nil)) != sK50_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f433]) ).
fof(f598,plain,
! [X0] :
( ~ sP0_prd(X0,sK50_skl,sK49_skl)
| ~ sP0_prd(X0,sK50_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f597,f434]) ).
fof(f599,plain,
! [X0] : ~ sP0_prd(X0,sK50_skl,sK49_skl),
inference(duplicate_literals_removal,[status(thm)],[f598]) ).
fof(f600,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f490,f599]) ).
fof(f601,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f423,f448]) ).
fof(f603,plain,
( ~ sQ3_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f442]) ).
fof(f604,plain,
( ~ sQ3_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
( sQ4_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f424,f453]) ).
fof(f608,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f421]) ).
fof(f609,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f608]) ).
fof(f610,plain,
( sQ4_spl
| ~ sQ3_spl
| sK50_skl != sK49_skl ),
inference(backward_demodulation,[status(thm)],[f602,f605]) ).
fof(f633,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sK50_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f602,f438]) ).
fof(f645,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| sK50_skl != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f633,f610]) ).
fof(f646,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f645]) ).
fof(f647,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f648,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f450,f454,f601,f604,f609,f647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC322+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n007.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 08:13:05 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.59 % Elapsed time: 0.131197 seconds
% 0.27/0.59 % CPU time: 0.128465 seconds
% 0.27/0.59 % Total memory used: 17.426 MB
% 0.27/0.59 % Net memory used: 17.393 MB
%------------------------------------------------------------------------------