%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC402+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 : 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 02:41:06 PM UTC 2026
% Result : Theorem 0.24s 0.52s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 17 unt; 8 def)
% Number of atoms : 289 ( 48 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 365 ( 136 ~; 133 |; 73 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 96 ( 66 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( nil = W
& nil != X )
| ! [X9] :
( memberP(V,X9)
| ~ memberP(U,X9)
| ~ ssItem(X9) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X
| ~ ssList(Z) ) )
| 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] :
( ( nil = W
& nil != X )
| ! [X9] :
( memberP(V,X9)
| ~ memberP(U,X9)
| ~ ssItem(X9) )
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( leq(X7,X5)
& app(X8,cons(X7,nil)) = W
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = Z
& ssList(X6) )
& ssItem(X5) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( leq(X1,X3)
& app(cons(X3,nil),X4) = W
& ssList(X4) )
& ssItem(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ totalorderedP(W)
| app(app(Y,W),Z) != X
| ~ ssList(Z) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X9] :
( ~ memberP(V,X9)
& memberP(U,X9)
& ssItem(X9) )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ leq(X7,X5)
| app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ leq(X1,X3)
| app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X9] :
( ~ memberP(V,X9)
& memberP(U,X9)
& ssItem(X9) )
& ? [Y] :
( ? [Z] :
( ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != W
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != Z
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != W
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( nil != sK49_skl
| nil = sK50_skl )
& ~ memberP(sK48_skl,sK53_skl)
& memberP(sK47_skl,sK53_skl)
& ssItem(sK53_skl)
& ! [X5] :
( ! [X7] :
( ~ leq(X7,X5)
| ! [X8] :
( app(X8,cons(X7,nil)) != sK49_skl
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ! [X6] :
( app(cons(X5,nil),X6) != sK52_skl
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X1] :
( ! [X3] :
( ~ leq(X1,X3)
| ! [X4] :
( app(cons(X3,nil),X4) != sK49_skl
| ~ ssList(X4) )
| ~ ssItem(X3) )
| ! [X2] :
( app(X2,cons(X1,nil)) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& totalorderedP(sK49_skl)
& app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_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,sK51_skl,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X9,sK53_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(app(sK51_skl,sK49_skl),sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
ssItem(sK53_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
memberP(sK47_skl,sK53_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
~ memberP(sK48_skl,sK53_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f475,plain,
memberP(sK49_skl,sK53_skl),
inference(forward_demodulation,[status(thm)],[f423,f431]) ).
fof(f476,plain,
~ memberP(sK50_skl,sK53_skl),
inference(forward_demodulation,[status(thm)],[f422,f432]) ).
fof(f498,definition,
( sQ2_spl
<=> ssList(app(sK51_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ2_spl
| ~ ssList(app(sK51_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ3_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ3_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f530,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f425]) ).
fof(f531,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f532,plain,
( sQ2_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f500,f245]) ).
fof(f533,definition,
( sQ7_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( sQ7_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,definition,
( sQ8_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f538,plain,
( sQ8_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( sQ2_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f532,f533,f536,f498]) ).
fof(f540,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f424]) ).
fof(f541,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f420]) ).
fof(f543,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f776,plain,
! [X0] :
( ~ memberP(app(sK51_skl,sK49_skl),X0)
| memberP(sK50_skl,X0)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK51_skl,sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f426,f271]) ).
fof(f778,definition,
! [X0] :
( sQ43_spl
<=> ( ~ memberP(app(sK51_skl,sK49_skl),X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f779,plain,
! [X0] :
( ~ sQ43_spl
| ~ memberP(app(sK51_skl,sK49_skl),X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f778]) ).
fof(f781,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f776,f778,f498,f501]) ).
fof(f804,plain,
! [X0] :
( ~ sQ43_spl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK51_skl)
| ~ ssItem(X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f779,f272]) ).
fof(f806,definition,
! [X0] :
( sQ48_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f807,plain,
! [X0] :
( ~ sQ48_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f806]) ).
fof(f809,plain,
( ~ sQ43_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f804,f806,f533,f536,f778]) ).
fof(f814,plain,
! [X0] :
( ~ sQ48_spl
| ~ memberP(sK49_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f807]) ).
fof(f816,plain,
( ~ sQ48_spl
| memberP(sK50_skl,sK53_skl)
| ~ ssItem(sK53_skl) ),
inference(resolution,[status(thm)],[f814,f475]) ).
fof(f817,definition,
( sQ50_spl
<=> ssItem(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( sQ50_spl
| ~ ssItem(sK53_skl) ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f820,definition,
( sQ51_spl
<=> memberP(sK50_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ51_spl
| memberP(sK50_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,plain,
( ~ sQ48_spl
| sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f816,f817,f820,f806]) ).
fof(f824,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f819,f430]) ).
fof(f825,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f824]) ).
fof(f826,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f821,f476]) ).
fof(f827,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f828,plain,
$false,
inference(sat_refutation,[status(thm)],[f531,f539,f541,f543,f781,f809,f823,f825,f827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC402+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 08:19:21 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.24/0.52 % Refutation found
% 0.24/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58 % Elapsed time: 0.123667 seconds
% 0.24/0.58 % CPU time: 0.265610 seconds
% 0.24/0.58 % Total memory used: 39.582 MB
% 0.24/0.58 % Net memory used: 39.416 MB
%------------------------------------------------------------------------------