%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC185+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 : n015.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 03:05:36 PM UTC 2026
% Result : Theorem 26.06s 3.75s
% Output : Proof 26.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 110 ( 25 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 142 ( 53 ~; 41 |; 34 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 20 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& 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',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ( ~ memberP(X4,X2)
& ~ memberP(X3,X2) )
| app(app(X3,cons(X2,nil)),X4) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( memberP(X4,X2)
| memberP(X3,X2) )
& app(app(X3,cons(X2,nil)),X4) = U
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| 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(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y,Z,X1] :
( ( memberP(sk53,sk51)
| memberP(sk52,sk51) )
& app(app(sk52,cons(sk51,nil)),sk53) = sk47
& ssList(sk53)
& ssList(sk52)
& ssItem(sk51)
& ( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != sk49
| ~ ssList(X1)
| ~ ssList(Z)
| ~ 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,sk53])],[f95_nnf]) ).
cnf(c197,plain,
( ~ memberP(X6,X4)
| app(app(X5,cons(X4,nil)),X6) != sk49
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c198,plain,
ssItem(sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p258,plain,
( ~ memberP(X1,sk51)
| app(app(X0,cons(sk51,nil)),X1) != sk49
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c197,c198]) ).
cnf(c199,plain,
ssList(sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p336,plain,
( ~ memberP(X0,sk51)
| app(app(sk52,cons(sk51,nil)),X0) != sk49
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p258,c199]) ).
cnf(c200,plain,
ssList(sk53),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p378,plain,
( ~ memberP(sk53,sk51)
| sk47 != sk49 ),
inference(resolution,[status(thm)],[p336,c200]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p379,plain,
~ memberP(sk53,sk51),
inference(resolution,[status(thm)],[p378,c195]) ).
cnf(c202,plain,
( memberP(sk53,sk51)
| memberP(sk52,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p380,plain,
memberP(sk52,sk51),
inference(resolution,[status(thm)],[p379,c202]) ).
cnf(c196,plain,
( ~ memberP(X5,X4)
| app(app(X5,cons(X4,nil)),X6) != sk49
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p204,plain,
( ~ memberP(X0,sk51)
| app(app(X0,cons(sk51,nil)),X1) != sk49
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c196,c198]) ).
cnf(p263,plain,
( ~ memberP(sk52,sk51)
| app(app(sk52,cons(sk51,nil)),X0) != sk49
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c199,p204]) ).
cnf(p320,plain,
( ~ memberP(sk52,sk51)
| sk47 != sk49 ),
inference(resolution,[status(thm)],[p263,c200]) ).
cnf(p321,plain,
~ memberP(sk52,sk51),
inference(resolution,[status(thm)],[p320,c195]) ).
cnf(p381,plain,
$false,
inference(resolution,[status(thm)],[p380,p321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC185+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 : n015.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 16:54:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 26.06/3.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.06/3.75 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------