%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC241+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 : 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 02:40:29 PM UTC 2026
% Result : Theorem 0.23s 0.57s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 8 unt; 9 def)
% Number of atoms : 274 ( 52 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 351 ( 131 ~; 127 |; 70 &)
% ( 11 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 78 ( 54 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(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) ) ) )
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( leq(Y,X2)
| ~ lt(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) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(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) ) ) )
& nil != W )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( leq(Y,X2)
| ~ lt(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) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f406,plain,
! [U] :
( ! [V] :
( ( lt(U,V)
<=> ( leq(U,V)
& U != V ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f407,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f406]) ).
fof(f409,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f407]) ).
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(Y,X2)
& lt(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,
? [U] :
( ? [V] :
( ? [W] :
( ( ? [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(Y,X2)
& lt(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
& ? [X] :
( V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,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(Y,sK51_skl(X1,Z,Y))
& lt(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)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
nil != sK47_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,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)],[f417]) ).
fof(f428,plain,
! [X0,X1,X2] :
( lt(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)],[f417]) ).
fof(f429,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)],[f417]) ).
fof(f430,plain,
( ssItem(sK52_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f431,plain,
( ssList(sK53_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f432,plain,
( ssList(sK54_skl)
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f433,plain,
( app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f435,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ1_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f430,f435,f438]) ).
fof(f442,definition,
( sQ2_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f431,f435,f442]) ).
fof(f446,definition,
( sQ3_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f435,f446]) ).
fof(f450,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(f451,plain,
( ~ sQ4_spl
| app(app(sK53_skl,cons(sK52_skl,nil)),sK54_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f435,f450]) ).
fof(f490,plain,
nil != sK49_skl,
inference(forward_demodulation,[status(thm)],[f423,f424]) ).
fof(f491,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f436,f490]) ).
fof(f492,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f495,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)],[f423,f425]) ).
fof(f496,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)],[f495,f451]) ).
fof(f498,definition,
( sQ6_spl
<=> ssItem(sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ4_spl
| sQ6_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f496,f438,f442,f446,f498,f450]) ).
fof(f534,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(f544,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f548,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f223]) ).
fof(f549,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f578,plain,
! [X0,X1,X2] :
( lt(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)],[f423,f428]) ).
fof(f579,plain,
( ~ sQ4_spl
| lt(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssList(sK54_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f578,f451]) ).
fof(f581,definition,
( sQ20_spl
<=> lt(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( ~ sQ20_spl
| lt(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl)) ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f584,plain,
( ~ sQ4_spl
| sQ20_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f579,f438,f442,f446,f581,f450]) ).
fof(f586,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)],[f423,f429]) ).
fof(f587,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)],[f586,f451]) ).
fof(f589,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f587,f438,f442,f446,f534,f450]) ).
fof(f660,plain,
( ~ sQ20_spl
| leq(sK52_skl,sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssItem(sK51_skl(sK54_skl,sK53_skl,sK52_skl))
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f409,f582]) ).
fof(f661,plain,
( ~ sQ20_spl
| sQ13_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f660,f438,f498,f534,f581]) ).
fof(f662,plain,
$false,
inference(sat_refutation,[status(thm)],[f441,f445,f449,f453,f492,f501,f549,f584,f589,f661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC241+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.46 % Computer : n010.cluster.edu
% 0.17/0.46 % Model : x86_64 x86_64
% 0.17/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.46 % Memory : 8046.5625MB
% 0.17/0.46 % OS : Linux 6.8.0-71-generic
% 0.17/0.47 % CPULimit : 300
% 0.17/0.47 % WCLimit : 300
% 0.17/0.47 % DateTime : Mon Sep 21 08:08:25 UTC 2026
% 0.17/0.47 % CPUTime :
% 0.17/0.52 % Drodi V4.1.1
% 0.23/0.57 % Refutation found
% 0.23/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.63 % Elapsed time: 0.126172 seconds
% 0.23/0.63 % CPU time: 0.282967 seconds
% 0.23/0.63 % Total memory used: 50.319 MB
% 0.23/0.63 % Net memory used: 50.152 MB
%------------------------------------------------------------------------------