%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC016+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 : n001.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 03:05:05 PM UTC 2026
% Result : Theorem 29.02s 4.14s
% Output : Proof 29.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 58 ( 14 unt; 0 def)
% Number of atoms : 195 ( 62 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 221 ( 84 ~; 89 |; 38 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 25 ( 0 sgn 12 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ? [Z] :
( frontsegP(U,Z)
& frontsegP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| 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)
=> ( ( ( ? [Z] :
( frontsegP(U,Z)
& frontsegP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssList(Y)
=> ( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Z] :
( ~ frontsegP(U,Z)
| ~ frontsegP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Z] :
( ( ( ( ~ frontsegP(sk47,Z)
| ~ frontsegP(sk48,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(sk48,nil) )
| ( nil != sk47
& nil = sk48 ) )
& ( ~ neq(sk50,nil)
| ( frontsegP(sk49,sk51)
& frontsegP(sk50,sk51)
& neq(sk51,nil)
& ssList(sk51) ) )
& ( nil != sk50
| nil = sk49 )
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51])],[f95_nnf]) ).
cnf(c203,plain,
( neq(sk48,nil)
| nil != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c201,plain,
( neq(sk48,nil)
| nil = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c197,plain,
( ~ neq(sk50,nil)
| ssList(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p210,plain,
( ~ neq(sk48,nil)
| ssList(sk51) ),
inference(superposition,[status(thm)],[c194,c197]) ).
cnf(p212,plain,
( ssList(sk51)
| nil = sk48 ),
inference(resolution,[status(thm)],[c201,p210]) ).
cnf(p213,plain,
( nil = sk50
| ssList(sk51) ),
inference(superposition,[status(thm)],[p212,c194]) ).
cnf(c196,plain,
( nil != sk50
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p217,plain,
( nil = sk49
| ssList(sk51) ),
inference(resolution,[status(thm)],[p213,c196]) ).
cnf(p219,plain,
( nil = sk47
| ssList(sk51) ),
inference(superposition,[status(thm)],[c195,p217]) ).
cnf(p239,plain,
( ssList(sk51)
| neq(sk48,nil) ),
inference(resolution,[status(thm)],[c203,p219]) ).
cnf(p240,plain,
( ssList(sk51)
| ssList(sk51) ),
inference(resolution,[status(thm)],[p239,p210]) ).
cnf(p244,plain,
ssList(sk51),
inference(factoring,[status(thm)],[p240]) ).
cnf(c202,plain,
( ~ frontsegP(sk47,X5)
| ~ frontsegP(sk48,X5)
| ~ neq(X5,nil)
| ~ ssList(X5)
| nil = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p245,plain,
( ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51)
| ~ neq(sk51,nil)
| nil = sk48 ),
inference(resolution,[status(thm)],[p244,c202]) ).
cnf(c198,plain,
( ~ neq(sk50,nil)
| neq(sk51,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
( ~ neq(sk48,nil)
| neq(sk51,nil) ),
inference(superposition,[status(thm)],[c194,c198]) ).
cnf(p222,plain,
( nil = sk48
| neq(sk51,nil) ),
inference(resolution,[status(thm)],[p209,c201]) ).
cnf(p247,plain,
( nil = sk48
| ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51)
| nil = sk48 ),
inference(resolution,[status(thm)],[p245,p222]) ).
cnf(p248,plain,
( ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51)
| nil = sk48 ),
inference(factoring,[status(thm)],[p247]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| frontsegP(sk50,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p220,plain,
( ~ neq(sk48,nil)
| frontsegP(sk50,sk51) ),
inference(superposition,[status(thm)],[c194,c199]) ).
cnf(p226,plain,
( nil = sk48
| frontsegP(sk50,sk51) ),
inference(resolution,[status(thm)],[p220,c201]) ).
cnf(p228,plain,
( nil = sk48
| frontsegP(sk48,sk51) ),
inference(superposition,[status(thm)],[c194,p226]) ).
cnf(p249,plain,
( nil = sk48
| ~ frontsegP(sk47,sk51)
| nil = sk48 ),
inference(resolution,[status(thm)],[p248,p228]) ).
cnf(p250,plain,
( ~ frontsegP(sk47,sk51)
| nil = sk48 ),
inference(factoring,[status(thm)],[p249]) ).
cnf(c200,plain,
( ~ neq(sk50,nil)
| frontsegP(sk49,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p223,plain,
( ~ neq(sk48,nil)
| frontsegP(sk49,sk51) ),
inference(superposition,[status(thm)],[c194,c200]) ).
cnf(p227,plain,
( nil = sk48
| frontsegP(sk49,sk51) ),
inference(resolution,[status(thm)],[p223,c201]) ).
cnf(p229,plain,
( nil = sk48
| frontsegP(sk47,sk51) ),
inference(superposition,[status(thm)],[c195,p227]) ).
cnf(p251,plain,
( nil = sk48
| nil = sk48 ),
inference(resolution,[status(thm)],[p250,p229]) ).
cnf(p252,plain,
nil = sk48,
inference(factoring,[status(thm)],[p251]) ).
cnf(p211,plain,
( nil != sk48
| nil = sk49 ),
inference(superposition,[status(thm)],[c194,c196]) ).
cnf(p255,plain,
nil = sk49,
inference(resolution,[status(thm)],[p252,p211]) ).
cnf(p261,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p255,c195]) ).
cnf(p253,plain,
nil = sk50,
inference(superposition,[status(thm)],[p252,c194]) ).
cnf(p258,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p253,c194]) ).
cnf(c204,plain,
( ~ frontsegP(sk47,X5)
| ~ frontsegP(sk48,X5)
| ~ neq(X5,nil)
| ~ ssList(X5)
| nil != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p260,plain,
( ~ frontsegP(sk47,X0)
| ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != sk47 ),
inference(demodulation,[status(thm)],[p258,c204]) ).
cnf(p263,plain,
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != nil ),
inference(demodulation,[status(thm)],[p261,p260]) ).
cnf(p269,plain,
( ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| nil != nil ),
inference(factoring,[status(thm)],[p263]) ).
cnf(p270,plain,
( ~ frontsegP(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[p269]) ).
cnf(p273,plain,
( ~ frontsegP(nil,sk51)
| ~ neq(sk51,nil) ),
inference(resolution,[status(thm)],[p270,p244]) ).
cnf(p259,plain,
( neq(nil,nil)
| nil != sk47 ),
inference(demodulation,[status(thm)],[p258,c203]) ).
cnf(p262,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[p261,p259]) ).
cnf(p264,plain,
neq(nil,nil),
inference(equality_resolution,[status(thm)],[p262]) ).
cnf(p254,plain,
( ~ neq(nil,nil)
| neq(sk51,nil) ),
inference(superposition,[status(thm)],[p252,p209]) ).
cnf(p265,plain,
neq(sk51,nil),
inference(resolution,[status(thm)],[p264,p254]) ).
cnf(p276,plain,
~ frontsegP(nil,sk51),
inference(resolution,[status(thm)],[p273,p265]) ).
cnf(p256,plain,
( ~ neq(nil,nil)
| frontsegP(sk50,sk51) ),
inference(superposition,[status(thm)],[p252,p220]) ).
cnf(p266,plain,
frontsegP(sk50,sk51),
inference(resolution,[status(thm)],[p264,p256]) ).
cnf(p268,plain,
frontsegP(nil,sk51),
inference(superposition,[status(thm)],[p253,p266]) ).
cnf(p277,plain,
$false,
inference(resolution,[status(thm)],[p276,p268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC016+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 : n001.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 16:01:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.02/4.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.02/4.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------