%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC096+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 : n026.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 03:05:20 PM UTC 2026
% Result : Theorem 27.54s 13.99s
% Output : Proof 27.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 120 ( 44 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 146 ( 57 ~; 49 |; 32 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X1] :
( ssItem(X1)
=> ! [X2] :
( app(X2,cons(X1,nil)) != X
| cons(X1,nil) != W
| ~ ssList(X2) ) )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = V
& cons(Y,nil) = U
& ssList(Z) )
& ssItem(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = X
& cons(X1,nil) = W
& ssList(X2) )
& ssItem(X1) )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != V
| cons(Y,nil) != U
| ~ 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] :
( ( ( ~ neq(sk50,nil)
& neq(sk48,nil) )
| ( app(sk52,cons(sk51,nil)) = sk50
& cons(sk51,nil) = sk49
& ssList(sk52)
& ssItem(sk51)
& ( app(Z,cons(Y,nil)) != sk48
| cons(Y,nil) != sk47
| ~ 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])],[f95_nnf]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c205,plain,
( ~ neq(sk50,nil)
| cons(sk51,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p213,plain,
( ~ neq(sk48,nil)
| cons(sk51,nil) = sk49 ),
inference(superposition,[status(thm)],[c194,c205]) ).
cnf(c196,plain,
( neq(sk48,nil)
| neq(sk48,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
neq(sk48,nil),
inference(factoring,[status(thm)],[c196]) ).
cnf(p214,plain,
cons(sk51,nil) = sk49,
inference(resolution,[status(thm)],[p213,p209]) ).
cnf(p216,plain,
sk49 = sk47,
inference(superposition,[status(thm)],[c195,p214]) ).
cnf(c207,plain,
( ~ neq(sk50,nil)
| app(sk52,cons(sk51,nil)) = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p215,plain,
( ~ neq(sk50,nil)
| app(sk52,sk49) = sk50 ),
inference(demodulation,[status(thm)],[p214,c207]) ).
cnf(p218,plain,
( ~ neq(sk50,nil)
| app(sk52,sk47) = sk50 ),
inference(demodulation,[status(thm)],[p216,p215]) ).
cnf(p219,plain,
( ~ neq(sk48,nil)
| app(sk52,sk47) = sk50 ),
inference(superposition,[status(thm)],[c194,p218]) ).
cnf(p220,plain,
app(sk52,sk47) = sk50,
inference(resolution,[status(thm)],[p219,p209]) ).
cnf(p221,plain,
sk50 = sk48,
inference(superposition,[status(thm)],[c194,p220]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| app(X5,cons(X4,nil)) != sk48
| cons(X4,nil) != sk47
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p222,plain,
( ~ neq(sk48,nil)
| app(X1,cons(X0,nil)) != sk48
| cons(X0,nil) != sk47
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[p221,c199]) ).
cnf(c201,plain,
( ~ neq(sk50,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( ~ neq(sk48,nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c194,c201]) ).
cnf(p211,plain,
ssItem(sk51),
inference(resolution,[status(thm)],[p208,p209]) ).
cnf(p224,plain,
( ~ neq(sk48,nil)
| app(X0,sk47) != sk48
| sk47 != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p222,p211]) ).
cnf(p225,plain,
( ~ neq(sk48,nil)
| app(X0,sk47) != sk48
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[p224]) ).
cnf(c203,plain,
( ~ neq(sk50,nil)
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p210,plain,
( ~ neq(sk48,nil)
| ssList(sk52) ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(p212,plain,
ssList(sk52),
inference(resolution,[status(thm)],[p210,p209]) ).
cnf(p228,plain,
( ~ neq(sk48,nil)
| sk48 != sk48 ),
inference(resolution,[status(thm)],[p225,p212]) ).
cnf(p229,plain,
~ neq(sk48,nil),
inference(equality_resolution,[status(thm)],[p228]) ).
cnf(p230,plain,
$false,
inference(resolution,[status(thm)],[p229,p209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/10.36 % Computer : n026.cluster.edu
% 0.09/10.36 % Model : x86_64 x86_64
% 0.09/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.36 % Memory : 8046.5625MB
% 0.09/10.36 % OS : Linux 6.8.0-71-generic
% 0.09/10.36 % CPULimit : 300
% 0.09/10.36 % WCLimit : 300
% 0.09/10.36 % DateTime : Thu Sep 24 16:25:05 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.54/13.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.54/13.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------