%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 03:06:15 PM UTC 2026
% Result : Theorem 22.00s 3.73s
% Output : Proof 22.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 103 ( 18 equ)
% Maximal formula atoms : 22 ( 6 avg)
% Number of connectives : 126 ( 38 ~; 34 |; 42 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X1] :
( ssItem(X1)
=> ( memberP(V,X1)
| ~ memberP(U,X1) ) )
| ? [Y] :
( ( ( ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y) )
& memberP(W,Y) )
| ( memberP(X,Y)
& ! [Z] :
( ssItem(Z)
=> ( Y = Z
| ~ leq(Z,Y)
| ~ memberP(X,Z) ) )
& ~ memberP(W,Y) ) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X1] :
( ~ memberP(V,X1)
& memberP(U,X1)
& ssItem(X1) )
& ! [Y] :
( ( ( ( ! [Z] :
( ~ leq(Z,Y)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y) )
| ~ memberP(W,Y) )
& ( ~ memberP(X,Y)
| ? [Z] :
( Y != Z
& leq(Z,Y)
& memberP(X,Z)
& ssItem(Z) )
| memberP(W,Y) ) )
| ~ 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] :
( ~ memberP(sk48,sk52)
& memberP(sk47,sk52)
& ssItem(sk52)
& ( ( ( ( ( ~ leq(Z,Y)
| ~ memberP(sk50,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(sk50,Y) )
| ~ memberP(sk49,Y) )
& ( ~ memberP(sk50,Y)
| ( Y != sk51(Y)
& leq(sk51(Y),Y)
& memberP(sk50,sk51(Y))
& ssItem(sk51(Y)) )
| memberP(sk49,Y) ) )
| ~ 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(c203,plain,
memberP(sk47,sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c200,plain,
( memberP(sk50,X4)
| ~ memberP(sk49,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c202,plain,
ssItem(sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p205,plain,
( memberP(sk50,sk52)
| ~ memberP(sk49,sk52) ),
inference(resolution,[status(thm)],[c200,c202]) ).
cnf(p206,plain,
( memberP(sk50,sk52)
| ~ memberP(sk47,sk52) ),
inference(superposition,[status(thm)],[c195,p205]) ).
cnf(p210,plain,
memberP(sk50,sk52),
inference(resolution,[status(thm)],[c203,p206]) ).
cnf(p211,plain,
memberP(sk48,sk52),
inference(superposition,[status(thm)],[c194,p210]) ).
cnf(c204,plain,
~ memberP(sk48,sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p214,plain,
$false,
inference(resolution,[status(thm)],[p211,c204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 18:03:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.00/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.00/3.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------