%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC010+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 : n019.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 03:05:04 PM UTC 2026
% Result : Theorem 24.10s 3.87s
% Output : Proof 24.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 157 ( 44 equ)
% Maximal formula atoms : 23 ( 4 avg)
% Number of connectives : 191 ( 68 ~; 65 |; 44 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 22 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( geq(X5,X2)
& memberP(X,X5)
& X2 != X5
& ssItem(X5) )
| app(X3,X4) != W
| app(app(X3,cons(X2,nil)),X4) != X ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Z,X1) = U
& app(app(Z,cons(Y,nil)),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ geq(X5,X2)
| ~ memberP(X,X5)
| X2 = X5
| ~ ssItem(X5) )
& app(X3,X4) = W
& app(app(X3,cons(X2,nil)),X4) = X
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Z,X1) != U
| app(app(Z,cons(Y,nil)),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& neq(V,nil) ) )
& 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,X5] :
( ( ( ~ neq(sk50,nil)
& neq(sk48,nil) )
| ( ( ~ geq(X5,sk51)
| ~ memberP(sk50,X5)
| sk51 = X5
| ~ ssItem(X5) )
& app(sk52,sk53) = sk49
& app(app(sk52,cons(sk51,nil)),sk53) = sk50
& ssList(sk53)
& ssList(sk52)
& ssItem(sk51)
& ( app(Z,X1) != sk47
| app(app(Z,cons(Y,nil)),X1) != sk48
| ~ ssList(X1)
| ~ ssList(Z)
| ~ ssItem(Y) )
& neq(sk48,nil) ) )
& 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(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c207,plain,
( ~ neq(sk50,nil)
| app(app(sk52,cons(sk51,nil)),sk53) = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p229,plain,
( ~ neq(sk48,nil)
| app(app(sk52,cons(sk51,nil)),sk53) = sk50 ),
inference(superposition,[status(thm)],[c194,c207]) ).
cnf(c196,plain,
( neq(sk48,nil)
| neq(sk48,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p224,plain,
neq(sk48,nil),
inference(factoring,[status(thm)],[c196]) ).
cnf(p230,plain,
app(app(sk52,cons(sk51,nil)),sk53) = sk50,
inference(resolution,[status(thm)],[p229,p224]) ).
cnf(p231,plain,
sk50 = sk48,
inference(superposition,[status(thm)],[c194,p230]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| app(X5,X6) != sk47
| app(app(X5,cons(X4,nil)),X6) != sk48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p232,plain,
( ~ neq(sk48,nil)
| app(X1,X2) != sk47
| app(app(X1,cons(X0,nil)),X2) != sk48
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[p231,c199]) ).
cnf(c201,plain,
( ~ neq(sk50,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p212,plain,
( ~ neq(sk48,nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c194,c201]) ).
cnf(c200,plain,
( neq(sk48,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p215,plain,
( ssItem(sk51)
| ssItem(sk51) ),
inference(resolution,[status(thm)],[p212,c200]) ).
cnf(p218,plain,
ssItem(sk51),
inference(factoring,[status(thm)],[p215]) ).
cnf(p236,plain,
( ~ neq(sk48,nil)
| app(X0,X1) != sk47
| app(app(X0,cons(sk51,nil)),X1) != sk48
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p232,p218]) ).
cnf(c203,plain,
( ~ neq(sk50,nil)
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p213,plain,
( ~ neq(sk48,nil)
| ssList(sk52) ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(c202,plain,
( neq(sk48,nil)
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p219,plain,
( ssList(sk52)
| ssList(sk52) ),
inference(resolution,[status(thm)],[p213,c202]) ).
cnf(p221,plain,
ssList(sk52),
inference(factoring,[status(thm)],[p219]) ).
cnf(p244,plain,
( ~ neq(sk48,nil)
| app(sk52,X0) != sk47
| app(app(sk52,cons(sk51,nil)),X0) != sk48
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p236,p221]) ).
cnf(c205,plain,
( ~ neq(sk50,nil)
| ssList(sk53) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p214,plain,
( ~ neq(sk48,nil)
| ssList(sk53) ),
inference(superposition,[status(thm)],[c194,c205]) ).
cnf(c204,plain,
( neq(sk48,nil)
| ssList(sk53) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p222,plain,
( ssList(sk53)
| ssList(sk53) ),
inference(resolution,[status(thm)],[p214,c204]) ).
cnf(p223,plain,
ssList(sk53),
inference(factoring,[status(thm)],[p222]) ).
cnf(p254,plain,
( ~ neq(sk48,nil)
| sk47 != sk47
| sk48 != sk48 ),
inference(resolution,[status(thm)],[p244,p223]) ).
cnf(p255,plain,
( ~ neq(sk48,nil)
| sk47 != sk47 ),
inference(equality_resolution,[status(thm)],[p254]) ).
cnf(p257,plain,
~ neq(sk48,nil),
inference(equality_resolution,[status(thm)],[p255]) ).
cnf(p258,plain,
$false,
inference(resolution,[status(thm)],[p257,p224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC010+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.59 % Computer : n019.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Thu Sep 24 15:54:05 UTC 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.10/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.10/3.87 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------