%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC009+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 : 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 03:05:04 PM UTC 2026
% Result : Theorem 30.44s 4.38s
% Output : Proof 30.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 128 ( 55 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 163 ( 59 ~; 49 |; 44 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 27 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f83_nnf,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f83]) ).
fof(f83_sk,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f83_nnf]) ).
cnf(c176,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f83_sk]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| ! [X2] :
( ssList(X2)
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( lt(X5,X3)
& app(X6,cons(X5,nil)) = W
& ssList(X6) )
& ssItem(X5) )
& app(cons(X3,nil),X4) = X2
& ssList(X4) )
& ssItem(X3) )
| ~ strictorderedP(W)
| app(W,X2) != X ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(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)
=> ( ( nil = W
& nil != X )
| ! [X2] :
( ssList(X2)
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( lt(X5,X3)
& app(X6,cons(X5,nil)) = W
& ssList(X6) )
& ssItem(X5) )
& app(cons(X3,nil),X4) = X2
& ssList(X4) )
& ssItem(X3) )
| ~ strictorderedP(W)
| app(W,X2) != X ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( ~ lt(X5,X3)
| app(X6,cons(X5,nil)) != W
| ~ ssList(X6) )
| ~ ssItem(X5) )
| app(cons(X3,nil),X4) != X2
| ~ ssList(X4) )
| ~ ssItem(X3) )
& strictorderedP(W)
& app(W,X2) = X
& ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(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,X3,X4,X5,X6] :
( ( nil != sk49
| nil = sk50 )
& ( ~ lt(X5,X3)
| app(X6,cons(X5,nil)) != sk49
| ~ ssList(X6)
| ~ ssItem(X5)
| app(cons(X3,nil),X4) != sk51
| ~ ssList(X4)
| ~ ssItem(X3) )
& strictorderedP(sk49)
& app(sk49,sk51) = sk50
& ssList(sk51)
& ( app(Y,X1) != sk47
| app(app(Y,Z),X1) != sk48
| ~ ssList(X1)
| ~ ssList(Z)
| ~ ssList(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])],[f95_nnf]) ).
cnf(c191,plain,
ssList(sk48),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p610,plain,
app(sk48,nil) = sk48,
inference(resolution,[status(thm)],[c176,c191]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p603,plain,
app(sk47,nil) = sk47,
inference(resolution,[status(thm)],[c176,c190]) ).
fof(f16,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f16_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c83,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(c196,plain,
( app(X4,X6) != sk47
| app(app(X4,X5),X6) != sk48
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssList(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p210,plain,
( app(sk47,X1) != sk47
| app(app(sk47,X0),X1) != sk48
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c196,c190]) ).
cnf(c197,plain,
ssList(sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p297,plain,
( app(sk47,X0) != sk47
| app(sk48,X0) != sk48
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p210,c197]) ).
cnf(p363,plain,
( app(sk47,nil) != sk47
| app(sk48,nil) != sk48 ),
inference(resolution,[status(thm)],[c83,p297]) ).
cnf(p607,plain,
( sk47 != sk47
| app(sk48,nil) != sk48 ),
inference(demodulation,[status(thm)],[p603,p363]) ).
cnf(p616,plain,
( sk47 != sk47
| sk48 != sk48 ),
inference(demodulation,[status(thm)],[p610,p607]) ).
cnf(p624,plain,
sk47 != sk47,
inference(equality_resolution,[status(thm)],[p616]) ).
cnf(p626,plain,
$false,
inference(equality_resolution,[status(thm)],[p624]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC009+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 15:53:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.44/4.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.44/4.38 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------