%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC279+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 : n008.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 02:40:37 PM UTC 2026
% Result : Theorem 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 10 unt; 1 def)
% Number of atoms : 241 ( 25 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 308 ( 114 ~; 113 |; 64 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 84 ( 60 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& 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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ( ~ leq(X3,X6)
& memberP(X5,X6) )
| ( ~ leq(X6,X3)
& memberP(X4,X6) ) )
& ssItem(X6) )
& app(app(X4,cons(X3,nil)),X5) = U
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != W
| ~ ssList(X1) )
| ~ 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,
! [X3,X4,X6] :
( sP0_prd(X6,X4,X3)
<=> ( ~ leq(X6,X3)
& memberP(X4,X6) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ( ~ leq(X3,X6)
& memberP(X5,X6) )
| sP0_prd(X6,X4,X3) )
& ssItem(X6) )
& app(app(X4,cons(X3,nil)),X5) = U
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != W
| ~ ssList(X1) )
| ~ 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,
( ( ( ~ leq(sK51_skl,sK54_skl)
& memberP(sK53_skl,sK54_skl) )
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) )
& ssItem(sK54_skl)
& app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssItem(sK51_skl)
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != sK49_skl
| ~ ssList(X1) )
| ~ 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,sK52_skl,sK53_skl,sK54_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(X3,sK51_skl),skolemize(X4,sK52_skl),skolemize(X5,sK53_skl),skolemize(X6,sK54_skl)],[f417]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X2,X3)
| leq(X0,X3)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
! [X0,X1,X2,X3] :
( ~ memberP(X1,X3)
| leq(X3,X0)
| ~ ssItem(X3)
| app(app(X1,cons(X0,nil)),X2) != sK49_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
ssItem(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( memberP(sK53_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
( ~ leq(sK51_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f434,plain,
! [X3,X4,X6] :
( ( leq(X6,X3)
| ~ memberP(X4,X6)
| sP0_prd(X6,X4,X3) )
& ( ( ~ leq(X6,X3)
& memberP(X4,X6) )
| ~ sP0_prd(X6,X4,X3) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f435,plain,
( ! [X3,X4,X6] :
( leq(X6,X3)
| ~ memberP(X4,X6)
| sP0_prd(X6,X4,X3) )
& ! [X3,X4,X6] :
( ( ~ leq(X6,X3)
& memberP(X4,X6) )
| ~ sP0_prd(X6,X4,X3) ) ),
inference(miniscoping,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ~ leq(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f477,plain,
( ~ leq(sK54_skl,sK51_skl)
| memberP(sK53_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f432,f437]) ).
fof(f478,plain,
( memberP(sK52_skl,sK54_skl)
| memberP(sK53_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f432,f436]) ).
fof(f479,plain,
( ~ leq(sK54_skl,sK51_skl)
| ~ leq(sK51_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f433,f437]) ).
fof(f480,plain,
( memberP(sK52_skl,sK54_skl)
| ~ leq(sK51_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f433,f436]) ).
fof(f494,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f430]) ).
fof(f495,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| leq(X0,sK51_skl)
| ~ ssItem(X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f494,f426]) ).
fof(f496,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f494,f425]) ).
fof(f500,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| leq(X0,sK51_skl)
| ~ ssItem(X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f427]) ).
fof(f501,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK53_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f427]) ).
fof(f506,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| leq(X0,sK51_skl)
| ~ ssItem(X0)
| ~ ssList(sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f428]) ).
fof(f507,plain,
( ~ leq(sK51_skl,sK54_skl)
| leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f506,f480]) ).
fof(f508,plain,
( ~ leq(sK51_skl,sK54_skl)
| leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f429]) ).
fof(f509,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f428]) ).
fof(f510,plain,
( memberP(sK52_skl,sK54_skl)
| leq(sK51_skl,sK54_skl)
| ~ ssItem(sK54_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f509,f478]) ).
fof(f511,plain,
( ~ leq(sK54_skl,sK51_skl)
| leq(sK51_skl,sK54_skl)
| ~ ssItem(sK54_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f509,f477]) ).
fof(f512,plain,
( memberP(sK52_skl,sK54_skl)
| leq(sK51_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f429]) ).
fof(f513,plain,
( ~ leq(sK54_skl,sK51_skl)
| leq(sK51_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f429]) ).
fof(f524,plain,
~ leq(sK51_skl,sK54_skl),
inference(backward_subsumption_resolution,[status(thm)],[f479,f525]) ).
fof(f525,plain,
( ~ leq(sK51_skl,sK54_skl)
| leq(sK54_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f431]) ).
fof(f529,plain,
( memberP(sK52_skl,sK54_skl)
| leq(sK51_skl,sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f431]) ).
fof(f530,plain,
( leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl)
| ~ ssList(sK53_skl)
| leq(sK51_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f529,f506]) ).
fof(f531,plain,
( leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl)
| ~ ssList(sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f530,f524]) ).
fof(f558,plain,
( leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f429]) ).
fof(f564,plain,
( ~ leq(sK54_skl,sK51_skl)
| leq(sK51_skl,sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f431]) ).
fof(f565,plain,
( ~ ssItem(sK54_skl)
| leq(sK51_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f564,f558]) ).
fof(f567,plain,
~ ssItem(sK54_skl),
inference(forward_subsumption_resolution,[status(thm)],[f565,f524]) ).
fof(f569,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f567,f431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.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 08:12:26 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.50 % Refutation found
% 0.18/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.52 % Elapsed time: 0.071691 seconds
% 0.18/0.52 % CPU time: 0.204884 seconds
% 0.18/0.52 % Total memory used: 52.562 MB
% 0.18/0.52 % Net memory used: 52.462 MB
%------------------------------------------------------------------------------