%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC098+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 : n016.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 03:05:20 PM UTC 2026
% Result : Theorem 24.71s 14.07s
% Output : Proof 24.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 1
% Syntax : Number of formulae : 83 ( 10 unt; 0 def)
% Number of atoms : 301 ( 159 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 322 ( 104 ~; 160 |; 46 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X1] :
( ssItem(X1)
=> ( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( memberP(V,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Y,Z)
| ~ memberP(V,Z) ) )
& cons(Y,nil) = U
& ssItem(Y) )
| 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)
=> ( ( ( nil != W
| nil != X )
& ! [X1] :
( ssItem(X1)
=> ( ? [X2] :
( leq(X1,X2)
& memberP(X,X2)
& X1 != X2
& ssItem(X2) )
| ~ memberP(X,X1)
| cons(X1,nil) != W ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( memberP(V,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Y,Z)
| ~ memberP(V,Z) ) )
& cons(Y,nil) = U
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X1] :
( ! [X2] :
( ~ leq(X1,X2)
| ~ memberP(X,X2)
| X1 = X2
| ~ ssItem(X2) )
& memberP(X,X1)
& cons(X1,nil) = W
& ssItem(X1) ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ memberP(V,Y)
| ? [Z] :
( Y != Z
& leq(Y,Z)
& memberP(V,Z)
& ssItem(Z) )
| cons(Y,nil) != U
| ~ ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y,X2] :
( ( ( nil = sk49
& nil = sk50 )
| ( ( ~ leq(sk52,X2)
| ~ memberP(sk50,X2)
| sk52 = X2
| ~ ssItem(X2) )
& memberP(sk50,sk52)
& cons(sk52,nil) = sk49
& ssItem(sk52) ) )
& ( nil != sk47
| nil != sk48 )
& ( ~ memberP(sk48,Y)
| ( Y != sk51(Y)
& leq(Y,sk51(Y))
& memberP(sk48,sk51(Y))
& ssItem(sk51(Y)) )
| cons(Y,nil) != sk47
| ~ ssItem(Y) )
& 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])],[f95_nnf]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c207,plain,
( nil = sk50
| ~ leq(sk52,X7)
| ~ memberP(sk50,X7)
| sk52 = X7
| ~ ssItem(X7) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c196,plain,
( ~ memberP(sk48,X4)
| ssItem(sk51(X4))
| cons(X4,nil) != sk47
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c200,plain,
( nil != sk47
| nil != sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c201,plain,
( nil = sk50
| ssItem(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
( nil = sk48
| ssItem(sk52) ),
inference(superposition,[status(thm)],[c194,c201]) ).
cnf(p213,plain,
( ssItem(sk52)
| nil != sk47 ),
inference(resolution,[status(thm)],[c200,p209]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c202,plain,
( nil = sk49
| ssItem(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p211,plain,
( nil = sk47
| ssItem(sk52) ),
inference(superposition,[status(thm)],[c195,c202]) ).
cnf(p214,plain,
( ssItem(sk52)
| ssItem(sk52) ),
inference(resolution,[status(thm)],[p213,p211]) ).
cnf(p215,plain,
ssItem(sk52),
inference(factoring,[status(thm)],[p214]) ).
cnf(p225,plain,
( ~ memberP(sk48,sk52)
| ssItem(sk51(sk52))
| cons(sk52,nil) != sk47 ),
inference(resolution,[status(thm)],[c196,p215]) ).
cnf(c203,plain,
( nil = sk50
| cons(sk52,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p218,plain,
( nil = sk50
| cons(sk52,nil) = sk47 ),
inference(superposition,[status(thm)],[c195,c203]) ).
cnf(p228,plain,
( nil = sk50
| ~ memberP(sk48,sk52)
| ssItem(sk51(sk52)) ),
inference(resolution,[status(thm)],[p225,p218]) ).
cnf(c205,plain,
( nil = sk50
| memberP(sk50,sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p216,plain,
( nil = sk50
| memberP(sk48,sk52) ),
inference(superposition,[status(thm)],[c194,c205]) ).
cnf(p230,plain,
( nil = sk50
| nil = sk50
| ssItem(sk51(sk52)) ),
inference(resolution,[status(thm)],[p228,p216]) ).
cnf(p233,plain,
( nil = sk50
| ssItem(sk51(sk52)) ),
inference(factoring,[status(thm)],[p230]) ).
cnf(p268,plain,
( nil = sk50
| nil = sk50
| ~ leq(sk52,sk51(sk52))
| ~ memberP(sk50,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[c207,p233]) ).
cnf(p271,plain,
( nil = sk50
| ~ leq(sk52,sk51(sk52))
| ~ memberP(sk50,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p268]) ).
cnf(p272,plain,
( nil = sk50
| ~ leq(sk52,sk51(sk52))
| ~ memberP(sk48,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(superposition,[status(thm)],[c194,p271]) ).
cnf(c197,plain,
( ~ memberP(sk48,X4)
| memberP(sk48,sk51(X4))
| cons(X4,nil) != sk47
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p237,plain,
( ~ memberP(sk48,sk52)
| memberP(sk48,sk51(sk52))
| cons(sk52,nil) != sk47 ),
inference(resolution,[status(thm)],[c197,p215]) ).
cnf(p242,plain,
( nil = sk50
| ~ memberP(sk48,sk52)
| memberP(sk48,sk51(sk52)) ),
inference(resolution,[status(thm)],[p237,p218]) ).
cnf(p244,plain,
( nil = sk50
| nil = sk50
| memberP(sk48,sk51(sk52)) ),
inference(resolution,[status(thm)],[p242,p216]) ).
cnf(p247,plain,
( nil = sk50
| memberP(sk48,sk51(sk52)) ),
inference(factoring,[status(thm)],[p244]) ).
cnf(p273,plain,
( nil = sk50
| nil = sk50
| ~ leq(sk52,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[p272,p247]) ).
cnf(p275,plain,
( nil = sk50
| ~ leq(sk52,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p273]) ).
cnf(c198,plain,
( ~ memberP(sk48,X4)
| leq(X4,sk51(X4))
| cons(X4,nil) != sk47
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p249,plain,
( ~ memberP(sk48,sk52)
| leq(sk52,sk51(sk52))
| cons(sk52,nil) != sk47 ),
inference(resolution,[status(thm)],[c198,p215]) ).
cnf(p254,plain,
( nil = sk50
| ~ memberP(sk48,sk52)
| leq(sk52,sk51(sk52)) ),
inference(resolution,[status(thm)],[p249,p218]) ).
cnf(p256,plain,
( nil = sk50
| nil = sk50
| leq(sk52,sk51(sk52)) ),
inference(resolution,[status(thm)],[p254,p216]) ).
cnf(p259,plain,
( nil = sk50
| leq(sk52,sk51(sk52)) ),
inference(factoring,[status(thm)],[p256]) ).
cnf(p276,plain,
( nil = sk50
| nil = sk50
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[p275,p259]) ).
cnf(p278,plain,
( nil = sk50
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p276]) ).
cnf(c199,plain,
( ~ memberP(sk48,X4)
| X4 != sk51(X4)
| cons(X4,nil) != sk47
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p261,plain,
( ~ memberP(sk48,sk52)
| sk52 != sk51(sk52)
| cons(sk52,nil) != sk47 ),
inference(resolution,[status(thm)],[c199,p215]) ).
cnf(p266,plain,
( nil = sk50
| ~ memberP(sk48,sk52)
| sk52 != sk51(sk52) ),
inference(resolution,[status(thm)],[p261,p218]) ).
cnf(p281,plain,
( nil = sk50
| ~ memberP(sk48,sk52)
| nil = sk50 ),
inference(resolution,[status(thm)],[p278,p266]) ).
cnf(p292,plain,
( ~ memberP(sk48,sk52)
| nil = sk50 ),
inference(factoring,[status(thm)],[p281]) ).
cnf(p293,plain,
( nil = sk50
| nil = sk50 ),
inference(resolution,[status(thm)],[p292,p216]) ).
cnf(p295,plain,
nil = sk50,
inference(factoring,[status(thm)],[p293]) ).
cnf(c208,plain,
( nil = sk49
| ~ leq(sk52,X7)
| ~ memberP(sk50,X7)
| sk52 = X7
| ~ ssItem(X7) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c204,plain,
( nil = sk49
| cons(sk52,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p219,plain,
( nil = sk49
| cons(sk52,nil) = sk47 ),
inference(superposition,[status(thm)],[c195,c204]) ).
cnf(p229,plain,
( nil = sk49
| ~ memberP(sk48,sk52)
| ssItem(sk51(sk52)) ),
inference(resolution,[status(thm)],[p225,p219]) ).
cnf(c206,plain,
( nil = sk49
| memberP(sk50,sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p217,plain,
( nil = sk49
| memberP(sk48,sk52) ),
inference(superposition,[status(thm)],[c194,c206]) ).
cnf(p232,plain,
( nil = sk49
| nil = sk49
| ssItem(sk51(sk52)) ),
inference(resolution,[status(thm)],[p229,p217]) ).
cnf(p235,plain,
( nil = sk49
| ssItem(sk51(sk52)) ),
inference(factoring,[status(thm)],[p232]) ).
cnf(p270,plain,
( nil = sk49
| nil = sk49
| ~ leq(sk52,sk51(sk52))
| ~ memberP(sk50,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[c208,p235]) ).
cnf(p310,plain,
( nil = sk49
| ~ leq(sk52,sk51(sk52))
| ~ memberP(sk50,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p270]) ).
cnf(p311,plain,
( nil = sk49
| ~ leq(sk52,sk51(sk52))
| ~ memberP(nil,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(superposition,[status(thm)],[p295,p310]) ).
cnf(p296,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p295,c194]) ).
cnf(p243,plain,
( nil = sk49
| ~ memberP(sk48,sk52)
| memberP(sk48,sk51(sk52)) ),
inference(resolution,[status(thm)],[p237,p219]) ).
cnf(p246,plain,
( nil = sk49
| nil = sk49
| memberP(sk48,sk51(sk52)) ),
inference(resolution,[status(thm)],[p243,p217]) ).
cnf(p248,plain,
( nil = sk49
| memberP(sk48,sk51(sk52)) ),
inference(factoring,[status(thm)],[p246]) ).
cnf(p303,plain,
( nil = sk49
| memberP(nil,sk51(sk52)) ),
inference(demodulation,[status(thm)],[p296,p248]) ).
cnf(p312,plain,
( nil = sk49
| nil = sk49
| ~ leq(sk52,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[p311,p303]) ).
cnf(p313,plain,
( nil = sk49
| ~ leq(sk52,sk51(sk52))
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p312]) ).
cnf(p255,plain,
( nil = sk49
| ~ memberP(sk48,sk52)
| leq(sk52,sk51(sk52)) ),
inference(resolution,[status(thm)],[p249,p219]) ).
cnf(p258,plain,
( nil = sk49
| nil = sk49
| leq(sk52,sk51(sk52)) ),
inference(resolution,[status(thm)],[p255,p217]) ).
cnf(p260,plain,
( nil = sk49
| leq(sk52,sk51(sk52)) ),
inference(factoring,[status(thm)],[p258]) ).
cnf(p314,plain,
( nil = sk49
| nil = sk49
| sk52 = sk51(sk52) ),
inference(resolution,[status(thm)],[p313,p260]) ).
cnf(p315,plain,
( nil = sk49
| sk52 = sk51(sk52) ),
inference(factoring,[status(thm)],[p314]) ).
cnf(p267,plain,
( nil = sk49
| ~ memberP(sk48,sk52)
| sk52 != sk51(sk52) ),
inference(resolution,[status(thm)],[p261,p219]) ).
cnf(p308,plain,
( nil = sk49
| ~ memberP(nil,sk52)
| sk52 != sk51(sk52) ),
inference(demodulation,[status(thm)],[p296,p267]) ).
cnf(p317,plain,
( nil = sk49
| ~ memberP(nil,sk52)
| nil = sk49 ),
inference(resolution,[status(thm)],[p315,p308]) ).
cnf(p321,plain,
( ~ memberP(nil,sk52)
| nil = sk49 ),
inference(factoring,[status(thm)],[p317]) ).
cnf(p298,plain,
( nil = sk49
| memberP(nil,sk52) ),
inference(demodulation,[status(thm)],[p296,p217]) ).
cnf(p322,plain,
( nil = sk49
| nil = sk49 ),
inference(resolution,[status(thm)],[p321,p298]) ).
cnf(p323,plain,
nil = sk49,
inference(factoring,[status(thm)],[p322]) ).
cnf(p324,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p323,c195]) ).
cnf(p297,plain,
( nil != sk47
| nil != nil ),
inference(demodulation,[status(thm)],[p296,c200]) ).
cnf(p309,plain,
nil != sk47,
inference(equality_resolution,[status(thm)],[p297]) ).
cnf(p329,plain,
nil != nil,
inference(demodulation,[status(thm)],[p324,p309]) ).
cnf(p330,plain,
$false,
inference(equality_resolution,[status(thm)],[p329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC098+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n016.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 16:27:38 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.71/14.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.71/14.07 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------