%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC279+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 : n011.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 03:05:52 PM UTC 2026
% Result : Theorem 25.45s 4.08s
% Output : Proof 25.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 173 ( 25 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 220 ( 80 ~; 78 |; 46 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 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] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = W
& ssList(X1) )
& ssList(Z) )
& 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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> ( ( leq(X3,X6)
| ~ memberP(X5,X6) )
& ( leq(X6,X3)
| ~ memberP(X4,X6) ) ) )
| app(app(X4,cons(X3,nil)),X5) != U ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( memberP(Z,X2)
& ~ leq(X2,Y) )
| ( memberP(X1,X2)
& ~ leq(Y,X2) ) )
& ssItem(X2) )
& 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] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ( ( ~ leq(X3,X6)
& memberP(X5,X6) )
| ( ~ leq(X6,X3)
& memberP(X4,X6) ) )
& ssItem(X6) )
& app(app(X4,cons(X3,nil)),X5) = U
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2) )
| 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,X2] :
( ( ( ~ leq(sk51,sk54)
& memberP(sk53,sk54) )
| ( ~ leq(sk54,sk51)
& memberP(sk52,sk54) ) )
& ssItem(sk54)
& app(app(sk52,cons(sk51,nil)),sk53) = sk47
& ssList(sk53)
& ssList(sk52)
& ssItem(sk51)
& ( ( ( ~ memberP(Z,X2)
| leq(X2,Y) )
& ( ~ memberP(X1,X2)
| leq(Y,X2) ) )
| ~ ssItem(X2)
| 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,sk54])],[f95_nnf]) ).
cnf(c197,plain,
( ~ memberP(X5,X7)
| leq(X7,X4)
| ~ ssItem(X7)
| 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(p422,plain,
( ~ memberP(X0,X2)
| leq(X2,sk51)
| ~ ssItem(X2)
| 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(p478,plain,
( ~ memberP(sk52,X1)
| leq(X1,sk51)
| ~ ssItem(X1)
| app(app(sk52,cons(sk51,nil)),X0) != sk49
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p422,c199]) ).
cnf(c200,plain,
ssList(sk53),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p536,plain,
( ~ memberP(sk52,X0)
| leq(X0,sk51)
| ~ ssItem(X0)
| sk47 != sk49 ),
inference(resolution,[status(thm)],[p478,c200]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p537,plain,
( ~ memberP(sk52,X0)
| leq(X0,sk51)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[p536,c195]) ).
cnf(c202,plain,
ssItem(sk54),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p539,plain,
( ~ memberP(sk52,sk54)
| leq(sk54,sk51) ),
inference(resolution,[status(thm)],[p537,c202]) ).
cnf(c196,plain,
( ~ memberP(X6,X7)
| leq(X4,X7)
| ~ ssItem(X7)
| app(app(X5,cons(X4,nil)),X6) != sk49
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( ~ memberP(X1,X2)
| leq(sk51,X2)
| ~ ssItem(X2)
| app(app(X0,cons(sk51,nil)),X1) != sk49
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c196,c198]) ).
cnf(p264,plain,
( ~ memberP(X0,X1)
| leq(sk51,X1)
| ~ ssItem(X1)
| app(app(sk52,cons(sk51,nil)),X0) != sk49
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p208,c199]) ).
cnf(p314,plain,
( ~ memberP(sk53,X0)
| leq(sk51,X0)
| ~ ssItem(X0)
| sk47 != sk49 ),
inference(resolution,[status(thm)],[p264,c200]) ).
cnf(p315,plain,
( ~ memberP(sk53,X0)
| leq(sk51,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[p314,c195]) ).
cnf(p317,plain,
( ~ memberP(sk53,sk54)
| leq(sk51,sk54) ),
inference(resolution,[status(thm)],[p315,c202]) ).
cnf(c203,plain,
( memberP(sk53,sk54)
| memberP(sk52,sk54) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p318,plain,
( memberP(sk52,sk54)
| leq(sk51,sk54) ),
inference(resolution,[status(thm)],[p317,c203]) ).
cnf(c204,plain,
( ~ leq(sk51,sk54)
| memberP(sk52,sk54) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p319,plain,
( memberP(sk52,sk54)
| memberP(sk52,sk54) ),
inference(resolution,[status(thm)],[p318,c204]) ).
cnf(p320,plain,
memberP(sk52,sk54),
inference(factoring,[status(thm)],[p319]) ).
cnf(p540,plain,
leq(sk54,sk51),
inference(resolution,[status(thm)],[p539,p320]) ).
cnf(c205,plain,
( memberP(sk53,sk54)
| ~ leq(sk54,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p541,plain,
memberP(sk53,sk54),
inference(resolution,[status(thm)],[p540,c205]) ).
cnf(p543,plain,
leq(sk51,sk54),
inference(resolution,[status(thm)],[p541,p317]) ).
cnf(c206,plain,
( ~ leq(sk51,sk54)
| ~ leq(sk54,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p542,plain,
~ leq(sk51,sk54),
inference(resolution,[status(thm)],[p540,c206]) ).
cnf(p544,plain,
$false,
inference(resolution,[status(thm)],[p543,p542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 17:22:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.45/4.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.45/4.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------