%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC220+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 : n010.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 02:40:26 PM UTC 2026
% Result : Theorem 0.17s 25.72s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 8 unt; 12 def)
% Number of atoms : 294 ( 47 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 383 ( 152 ~; 153 |; 50 &)
% ( 12 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 73 ( 57 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( leq(X3,X6)
& memberP(X5,X6)
& memberP(X4,X6)
& ~ leq(X6,X3)
& ssItem(X6) )
| app(app(X4,cons(X3,nil)),X5) != W ) ) ) )
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(X2,Y)
| ~ leq(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| 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)
=> ( ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( leq(X3,X6)
& memberP(X5,X6)
& memberP(X4,X6)
& ~ leq(X6,X3)
& ssItem(X6) )
| app(app(X4,cons(X3,nil)),X5) != W ) ) ) )
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(X2,Y)
| ~ leq(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ~ leq(X3,X6)
| ~ memberP(X5,X6)
| ~ memberP(X4,X6)
| leq(X6,X3)
| ~ ssItem(X6) )
& app(app(X4,cons(X3,nil)),X5) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
| nil = W )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ? [X2] :
( ~ leq(X2,Y)
& leq(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ( ! [X6] :
( ~ leq(sK52_skl,X6)
| ~ memberP(sK54_skl,X6)
| ~ memberP(sK53_skl,X6)
| leq(X6,sK52_skl)
| ~ ssItem(X6) )
& app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl) )
| nil = sK49_skl )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ leq(sK51_skl(X1,Z,Y),Y)
& leq(Y,sK51_skl(X1,Z,Y))
& memberP(X1,sK51_skl(X1,Z,Y))
& memberP(Z,sK51_skl(X1,Z,Y))
& ssItem(sK51_skl(X1,Z,Y)) )
| app(app(Z,cons(Y,nil)),X1) != sK47_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != 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,sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X2,sK51_skl(X1,Z,Y)),skolemize(X3,sK52_skl),skolemize(X4,sK53_skl),skolemize(X5,sK54_skl)],[f415]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ssItem(sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
! [X0,X1,X2] :
( memberP(X1,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
! [X0,X1,X2] :
( memberP(X2,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
! [X0,X1,X2] :
( leq(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
! [X0,X1,X2] :
( ~ leq(sK51_skl(X2,X1,X0),X0)
| app(app(X1,cons(X0,nil)),X2) != sK47_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ssItem(sK52_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ssList(sK53_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ssList(sK54_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f432,plain,
( app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f433,plain,
! [X0] :
( ~ leq(sK52_skl,X0)
| ~ memberP(sK54_skl,X0)
| ~ memberP(sK53_skl,X0)
| leq(X0,sK52_skl)
| ~ ssItem(X0)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f434,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ1_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f429,f434,f437]) ).
fof(f441,definition,
( sQ2_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f430,f434,f441]) ).
fof(f445,definition,
( sQ3_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f431,f434,f445]) ).
fof(f449,definition,
( sQ4_spl
<=> app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ4_spl
| app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f434,f449]) ).
fof(f453,definition,
! [X0] :
( sQ5_spl
<=> ( ~ leq(sK52_skl,X0)
| ~ memberP(sK54_skl,X0)
| ~ memberP(sK53_skl,X0)
| leq(X0,sK52_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f454,plain,
! [X0] :
( ~ sQ5_spl
| ~ leq(sK52_skl,X0)
| ~ memberP(sK54_skl,X0)
| ~ memberP(sK53_skl,X0)
| leq(X0,sK52_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f434,f453]) ).
fof(f489,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f422,f423]) ).
fof(f490,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f489]) ).
fof(f491,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f490]) ).
fof(f494,plain,
! [X0,X1,X2] :
( ssItem(sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f495,plain,
( ~ sQ4_spl
| ssItem(sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f494,f450]) ).
fof(f497,definition,
( sQ6_spl
<=> ssItem(sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ4_spl
| sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f495,f437,f441,f445,f497,f449]) ).
fof(f505,plain,
! [X0,X1,X2] :
( memberP(X1,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f425]) ).
fof(f506,plain,
( ~ sQ4_spl
| memberP(sK53_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f505,f450]) ).
fof(f508,definition,
( sQ8_spl
<=> memberP(sK53_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ8_spl
| memberP(sK53_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( ~ sQ4_spl
| sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f506,f437,f441,f445,f508,f449]) ).
fof(f513,plain,
! [X0,X1,X2] :
( memberP(X2,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f426]) ).
fof(f514,plain,
( ~ sQ4_spl
| memberP(sK54_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f513,f450]) ).
fof(f516,definition,
( sQ9_spl
<=> memberP(sK54_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ4_spl
| sQ9_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f514,f437,f441,f445,f516,f449]) ).
fof(f529,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ leq(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ memberP(sK54_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| leq(sK51_skl(sK54_skl,sK53_skl,sK52_skl),sK52_skl)
| ~ ssItem(sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
inference(resolution,[status(thm)],[f509,f454]) ).
fof(f530,definition,
( sQ12_spl
<=> leq(sK51_skl(sK54_skl,sK53_skl,sK52_skl),sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f533,definition,
( sQ13_spl
<=> leq(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| sQ12_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f529,f497,f530,f516,f533,f508,f453]) ).
fof(f543,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f547,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f223]) ).
fof(f548,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f578,plain,
! [X0,X1,X2] :
( leq(X0,sK51_skl(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f579,plain,
( ~ sQ4_spl
| leq(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f578,f450]) ).
fof(f581,plain,
( ~ sQ4_spl
| sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f579,f437,f441,f445,f533,f449]) ).
fof(f583,plain,
! [X0,X1,X2] :
( ~ leq(sK51_skl(X2,X1,X0),X0)
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f428]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ leq(sK51_skl(sK54_skl,sK53_skl,sK52_skl),sK52_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f583,f450]) ).
fof(f586,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f584,f437,f441,f445,f530,f449]) ).
fof(f588,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f444,f448,f452,f456,f491,f500,f511,f519,f536,f548,f581,f586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/25.67 % Computer : n010.cluster.edu
% 0.13/25.67 % Model : x86_64 x86_64
% 0.13/25.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/25.67 % Memory : 8046.5625MB
% 0.13/25.67 % OS : Linux 6.8.0-71-generic
% 0.13/25.67 % CPULimit : 300
% 0.13/25.67 % WCLimit : 300
% 0.13/25.67 % DateTime : Mon Sep 21 08:06:08 UTC 2026
% 0.13/25.67 % CPUTime :
% 0.13/25.69 % Drodi V4.1.1
% 0.17/25.72 % Refutation found
% 0.17/25.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/25.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/25.76 % Elapsed time: 0.069457 seconds
% 0.17/25.76 % CPU time: 0.177604 seconds
% 0.17/25.76 % Total memory used: 111.263 MB
% 0.17/25.76 % Net memory used: 111.099 MB
%------------------------------------------------------------------------------