%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC254+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 : n015.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 03:05:48 PM UTC 2026
% Result : Theorem 22.61s 8.72s
% Output : Proof 22.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 117 ( 36 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 128 ( 44 ~; 39 |; 31 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 17 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( ( ( cons(V,nil) != U
| ~ ssItem(V)
| singletonP(U) )
& ( ( cons(sk4(U),nil) = U
& ssItem(sk4(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f3_nnf]) ).
cnf(c11,plain,
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ 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) )
& ( singletonP(U)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ 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) )
| ( ~ singletonP(U)
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& 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,
( ( ( ~ neq(sk50,nil)
& neq(sk48,nil) )
| ( ~ singletonP(sk47)
& app(sk52,cons(sk51,nil)) = sk50
& cons(sk51,nil) = sk49
& ssList(sk52)
& ssItem(sk51)
& 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(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p270,plain,
( cons(X0,nil) != sk47
| ~ ssItem(X0)
| singletonP(sk47) ),
inference(resolution,[status(thm)],[c11,c190]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p217,plain,
( ~ neq(sk48,nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c194,c199]) ).
cnf(c196,plain,
( neq(sk48,nil)
| neq(sk48,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p211,plain,
neq(sk48,nil),
inference(factoring,[status(thm)],[c196]) ).
cnf(p220,plain,
ssItem(sk51),
inference(resolution,[status(thm)],[p217,p211]) ).
cnf(p301,plain,
( sk47 != sk47
| singletonP(sk47) ),
inference(resolution,[status(thm)],[p270,p220]) ).
cnf(p302,plain,
singletonP(sk47),
inference(equality_resolution,[status(thm)],[p301]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c203,plain,
( ~ neq(sk50,nil)
| cons(sk51,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p216,plain,
( ~ neq(sk48,nil)
| cons(sk51,nil) = sk49 ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(p223,plain,
cons(sk51,nil) = sk49,
inference(resolution,[status(thm)],[p216,p211]) ).
cnf(p225,plain,
sk49 = sk47,
inference(superposition,[status(thm)],[c195,p223]) ).
cnf(c205,plain,
( ~ neq(sk50,nil)
| app(sk52,cons(sk51,nil)) = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p224,plain,
( ~ neq(sk50,nil)
| app(sk52,sk49) = sk50 ),
inference(demodulation,[status(thm)],[p223,c205]) ).
cnf(p227,plain,
( ~ neq(sk50,nil)
| app(sk52,sk47) = sk50 ),
inference(demodulation,[status(thm)],[p225,p224]) ).
cnf(p228,plain,
( ~ neq(sk48,nil)
| app(sk52,sk47) = sk50 ),
inference(superposition,[status(thm)],[c194,p227]) ).
cnf(p229,plain,
app(sk52,sk47) = sk50,
inference(resolution,[status(thm)],[p228,p211]) ).
cnf(p234,plain,
sk50 = sk48,
inference(superposition,[status(thm)],[c194,p229]) ).
cnf(c207,plain,
( ~ neq(sk50,nil)
| ~ singletonP(sk47) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p235,plain,
( ~ neq(sk48,nil)
| ~ singletonP(sk47) ),
inference(demodulation,[status(thm)],[p234,c207]) ).
cnf(p307,plain,
~ neq(sk48,nil),
inference(resolution,[status(thm)],[p302,p235]) ).
cnf(p310,plain,
$false,
inference(resolution,[status(thm)],[p307,p211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 17:18:32 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 22.61/8.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.61/8.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------