%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC189+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 : n020.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 03:05:37 PM UTC 2026
% Result : Theorem 25.10s 13.78s
% Output : Proof 25.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 100 ( 37 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 120 ( 37 ~; 33 |; 34 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 24 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(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)
=> ( ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( X3 = X4
| app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) != U ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = W
& Y != Z
& ssList(X2) )
& ssList(X1) )
& ssItem(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] :
( X3 != X4
& app(app(app(X5,cons(X3,nil)),cons(X4,nil)),X6) = U
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ssItem(X3) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != W
| Y = Z
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(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] :
( sk51 != sk52
& app(app(app(sk53,cons(sk51,nil)),cons(sk52,nil)),sk54) = sk47
& ssList(sk54)
& ssList(sk53)
& ssItem(sk52)
& ssItem(sk51)
& ( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != sk49
| Y = Z
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(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(c196,plain,
( app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != sk49
| X4 = X5
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c197,plain,
ssItem(sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p205,plain,
( app(app(app(X1,cons(sk51,nil)),cons(X0,nil)),X2) != sk49
| sk51 = X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c196,c197]) ).
cnf(c198,plain,
ssItem(sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p309,plain,
( app(app(app(X0,cons(sk51,nil)),cons(sk52,nil)),X1) != sk49
| sk51 = sk52
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p205,c198]) ).
cnf(c199,plain,
ssList(sk53),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p314,plain,
( app(app(app(sk53,cons(sk51,nil)),cons(sk52,nil)),X0) != sk49
| sk51 = sk52
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p309,c199]) ).
cnf(c200,plain,
ssList(sk54),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p352,plain,
( sk47 != sk49
| sk51 = sk52 ),
inference(resolution,[status(thm)],[p314,c200]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p353,plain,
sk51 = sk52,
inference(resolution,[status(thm)],[p352,c195]) ).
cnf(c202,plain,
sk51 != sk52,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p354,plain,
$false,
inference(resolution,[status(thm)],[p353,c202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC189+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.40 % Computer : n020.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Thu Sep 24 16:54:29 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.10/13.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.10/13.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------