%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 : Fri Sep 25 03:05:43 PM UTC 2026
% Result : Theorem 24.24s 3.91s
% Output : Proof 24.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 249 ( 79 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 303 ( 110 ~; 127 |; 50 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn 24 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,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/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,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)],[f95]) ).
fof(f95_nnf,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(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y,Z,X1,X6] :
( ( ( ( ~ leq(sk52,X6)
| ~ memberP(sk54,X6)
| ~ memberP(sk53,X6)
| leq(X6,sk52)
| ~ ssItem(X6) )
& app(app(sk53,cons(sk52,nil)),sk54) = sk49
& ssList(sk54)
& ssList(sk53)
& ssItem(sk52) )
| nil = sk49 )
& ( ( ~ leq(sk51(Y,Z,X1),Y)
& leq(Y,sk51(Y,Z,X1))
& memberP(X1,sk51(Y,Z,X1))
& memberP(Z,sk51(Y,Z,X1))
& ssItem(sk51(Y,Z,X1)) )
| app(app(Z,cons(Y,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(Z)
| ~ ssItem(Y) )
& nil != sk47
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51,sk52,sk53,sk54])],[f95_nnf]) ).
cnf(c197,plain,
( ssItem(sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c202,plain,
( ssItem(sk52)
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p207,plain,
( ssItem(sk52)
| nil = sk47 ),
inference(superposition,[status(thm)],[c195,c202]) ).
cnf(c196,plain,
nil != sk47,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p211,plain,
ssItem(sk52),
inference(resolution,[status(thm)],[p207,c196]) ).
cnf(p221,plain,
( ssItem(sk51(sk52,X0,X1))
| app(app(X0,cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c197,p211]) ).
cnf(c203,plain,
( ssList(sk53)
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p215,plain,
( ssList(sk53)
| nil = sk47 ),
inference(superposition,[status(thm)],[c195,c203]) ).
cnf(p217,plain,
ssList(sk53),
inference(resolution,[status(thm)],[p215,c196]) ).
cnf(p240,plain,
( ssItem(sk51(sk52,sk53,X0))
| app(app(sk53,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p221,p217]) ).
cnf(c204,plain,
( ssList(sk54)
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
( ssList(sk54)
| nil = sk47 ),
inference(superposition,[status(thm)],[c195,c204]) ).
cnf(p212,plain,
ssList(sk54),
inference(resolution,[status(thm)],[p209,c196]) ).
cnf(p290,plain,
( ssItem(sk51(sk52,sk53,sk54))
| app(app(sk53,cons(sk52,nil)),sk54) != sk47 ),
inference(resolution,[status(thm)],[p240,p212]) ).
cnf(c205,plain,
( app(app(sk53,cons(sk52,nil)),sk54) = sk49
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p213,plain,
( app(app(sk53,cons(sk52,nil)),sk54) = sk47
| nil = sk49 ),
inference(superposition,[status(thm)],[c195,c205]) ).
cnf(p294,plain,
( nil = sk49
| ssItem(sk51(sk52,sk53,sk54)) ),
inference(resolution,[status(thm)],[p290,p213]) ).
cnf(c206,plain,
( ~ leq(sk52,X11)
| ~ memberP(sk54,X11)
| ~ memberP(sk53,X11)
| leq(X11,sk52)
| ~ ssItem(X11)
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p295,plain,
( ~ leq(sk52,sk51(sk52,sk53,sk54))
| ~ memberP(sk54,sk51(sk52,sk53,sk54))
| ~ memberP(sk53,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49
| nil = sk49 ),
inference(resolution,[status(thm)],[p294,c206]) ).
cnf(p813,plain,
( ~ leq(sk52,sk51(sk52,sk53,sk54))
| ~ memberP(sk54,sk51(sk52,sk53,sk54))
| ~ memberP(sk53,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(factoring,[status(thm)],[p295]) ).
cnf(c198,plain,
( memberP(X5,sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p299,plain,
( memberP(X0,sk51(sk52,X0,X1))
| app(app(X0,cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c198,p211]) ).
cnf(p320,plain,
( memberP(sk53,sk51(sk52,sk53,X0))
| app(app(sk53,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p299,p217]) ).
cnf(p370,plain,
( memberP(sk53,sk51(sk52,sk53,sk54))
| app(app(sk53,cons(sk52,nil)),sk54) != sk47 ),
inference(resolution,[status(thm)],[p320,p212]) ).
cnf(p374,plain,
( nil = sk49
| memberP(sk53,sk51(sk52,sk53,sk54)) ),
inference(resolution,[status(thm)],[p370,p213]) ).
cnf(p814,plain,
( nil = sk49
| ~ leq(sk52,sk51(sk52,sk53,sk54))
| ~ memberP(sk54,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(resolution,[status(thm)],[p813,p374]) ).
cnf(p815,plain,
( ~ leq(sk52,sk51(sk52,sk53,sk54))
| ~ memberP(sk54,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(factoring,[status(thm)],[p814]) ).
cnf(c199,plain,
( memberP(X6,sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p375,plain,
( memberP(X1,sk51(sk52,X0,X1))
| app(app(X0,cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c199,p211]) ).
cnf(p382,plain,
( memberP(X0,sk51(sk52,sk53,X0))
| app(app(sk53,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p375,p217]) ).
cnf(p432,plain,
( memberP(sk54,sk51(sk52,sk53,sk54))
| app(app(sk53,cons(sk52,nil)),sk54) != sk47 ),
inference(resolution,[status(thm)],[p382,p212]) ).
cnf(p436,plain,
( nil = sk49
| memberP(sk54,sk51(sk52,sk53,sk54)) ),
inference(resolution,[status(thm)],[p432,p213]) ).
cnf(p816,plain,
( nil = sk49
| ~ leq(sk52,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(resolution,[status(thm)],[p815,p436]) ).
cnf(p817,plain,
( ~ leq(sk52,sk51(sk52,sk53,sk54))
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(factoring,[status(thm)],[p816]) ).
cnf(c200,plain,
( leq(X4,sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p438,plain,
( leq(sk52,sk51(sk52,X0,X1))
| app(app(X0,cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c200,p211]) ).
cnf(p459,plain,
( leq(sk52,sk51(sk52,sk53,X0))
| app(app(sk53,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p438,p217]) ).
cnf(p509,plain,
( leq(sk52,sk51(sk52,sk53,sk54))
| app(app(sk53,cons(sk52,nil)),sk54) != sk47 ),
inference(resolution,[status(thm)],[p459,p212]) ).
cnf(p513,plain,
( nil = sk49
| leq(sk52,sk51(sk52,sk53,sk54)) ),
inference(resolution,[status(thm)],[p509,p213]) ).
cnf(p818,plain,
( nil = sk49
| leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(resolution,[status(thm)],[p817,p513]) ).
cnf(p819,plain,
( leq(sk51(sk52,sk53,sk54),sk52)
| nil = sk49 ),
inference(factoring,[status(thm)],[p818]) ).
cnf(c201,plain,
( ~ leq(sk51(X4,X5,X6),X4)
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p515,plain,
( ~ leq(sk51(sk52,X0,X1),sk52)
| app(app(X0,cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c201,p211]) ).
cnf(p536,plain,
( ~ leq(sk51(sk52,sk53,X0),sk52)
| app(app(sk53,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p515,p217]) ).
cnf(p586,plain,
( ~ leq(sk51(sk52,sk53,sk54),sk52)
| app(app(sk53,cons(sk52,nil)),sk54) != sk47 ),
inference(resolution,[status(thm)],[p536,p212]) ).
cnf(p590,plain,
( nil = sk49
| ~ leq(sk51(sk52,sk53,sk54),sk52) ),
inference(resolution,[status(thm)],[p586,p213]) ).
cnf(p820,plain,
( nil = sk49
| nil = sk49 ),
inference(resolution,[status(thm)],[p819,p590]) ).
cnf(p821,plain,
nil = sk49,
inference(factoring,[status(thm)],[p820]) ).
cnf(p822,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p821,c195]) ).
cnf(p823,plain,
nil != nil,
inference(demodulation,[status(thm)],[p822,c196]) ).
cnf(p1180,plain,
$false,
inference(equality_resolution,[status(thm)],[p823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC220+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 17:04:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.24/3.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.24/3.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------