%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC252+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 : n012.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 36.94s 21.45s
% Output : Proof 36.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 190 ( 78 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 210 ( 74 ~; 81 |; 40 &)
% ( 0 <=>; 15 =>; 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 : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 27 !; 12 ?)
% 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 )
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(Y,X2)
| ~ lt(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| 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 )
& ! [X3] :
( ssItem(X3)
=> ( ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X2] :
( ssItem(X2)
=> ( leq(Y,X2)
| ~ lt(Y,X2)
| ~ memberP(X1,X2)
| ~ memberP(Z,X2) ) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| nil = U
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ? [X2] :
( ~ leq(Y,X2)
& lt(Y,X2)
& memberP(X1,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y) )
& nil != U
& 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] :
( ( ( nil = sk49
& nil = sk50 )
| ( memberP(sk50,sk52)
& cons(sk52,nil) = sk49
& ssItem(sk52) ) )
& ( ( ~ leq(Y,sk51(Y,Z,X1))
& lt(Y,sk51(Y,Z,X1))
& memberP(X1,sk51(Y,Z,X1))
& memberP(Z,sk51(Y,Z,X1))
& ssItem(sk51(Y,Z,X1)) )
| app(app(Z,cons(Y,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(Z)
| ~ ssItem(Y) )
& nil != sk47
& 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(p15934,plain,
app(sk47,nil) = sk47,
inference(resolution,[status(thm)],[c176,c190]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f27_nnf,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c97,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(c192,plain,
ssList(sk49),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p15696,plain,
app(nil,sk49) = sk49,
inference(resolution,[status(thm)],[c97,c192]) ).
cnf(p15767,plain,
sk49 = sk47,
inference(superposition,[status(thm)],[c195,p15696]) ).
cnf(p15626,plain,
app(nil,sk47) = sk47,
inference(resolution,[status(thm)],[c97,c190]) ).
cnf(c205,plain,
( nil = sk49
| cons(sk52,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p212,plain,
( nil = sk49
| cons(sk52,nil) = sk47 ),
inference(superposition,[status(thm)],[c195,c205]) ).
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(c198,plain,
( memberP(X5,sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p410,plain,
( memberP(X1,sk51(X0,X1,X1))
| app(app(X1,cons(X0,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(factoring,[status(thm)],[c198]) ).
cnf(c203,plain,
( nil = sk49
| ssItem(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p218,plain,
( nil = sk47
| ssItem(sk52) ),
inference(superposition,[status(thm)],[c195,c203]) ).
cnf(c196,plain,
nil != sk47,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p220,plain,
ssItem(sk52),
inference(resolution,[status(thm)],[p218,c196]) ).
cnf(p412,plain,
( memberP(X0,sk51(sk52,X0,X0))
| app(app(X0,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p410,p220]) ).
cnf(p1510,plain,
( memberP(nil,sk51(sk52,nil,nil))
| app(app(nil,cons(sk52,nil)),nil) != sk47 ),
inference(resolution,[status(thm)],[c83,p412]) ).
cnf(p1628,plain,
( memberP(nil,sk51(sk52,nil,nil))
| app(app(nil,sk47),nil) != sk47
| nil = sk49 ),
inference(superposition,[status(thm)],[p212,p1510]) ).
cnf(p15630,plain,
( memberP(nil,sk51(sk52,nil,nil))
| app(sk47,nil) != sk47
| nil = sk49 ),
inference(demodulation,[status(thm)],[p15626,p1628]) ).
cnf(p15866,plain,
( memberP(nil,sk51(sk52,nil,nil))
| app(sk47,nil) != sk47
| nil = sk47 ),
inference(demodulation,[status(thm)],[p15767,p15630]) ).
cnf(p15936,plain,
( memberP(nil,sk51(sk52,nil,nil))
| sk47 != sk47
| nil = sk47 ),
inference(demodulation,[status(thm)],[p15934,p15866]) ).
cnf(p15986,plain,
( memberP(nil,sk51(sk52,nil,nil))
| nil = sk47 ),
inference(equality_resolution,[status(thm)],[p15936]) ).
cnf(c197,plain,
( ssItem(sk51(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sk47
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p216,plain,
( ssItem(sk51(X0,X1,X1))
| app(app(X1,cons(X0,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(factoring,[status(thm)],[c197]) ).
cnf(p224,plain,
( ssItem(sk51(sk52,X0,X0))
| app(app(X0,cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p216,p220]) ).
cnf(p1504,plain,
( ssItem(sk51(sk52,nil,nil))
| app(app(nil,cons(sk52,nil)),nil) != sk47 ),
inference(resolution,[status(thm)],[c83,p224]) ).
cnf(p1594,plain,
( ssItem(sk51(sk52,nil,nil))
| app(app(nil,sk47),nil) != sk47
| nil = sk49 ),
inference(superposition,[status(thm)],[p212,p1504]) ).
cnf(p15628,plain,
( ssItem(sk51(sk52,nil,nil))
| app(sk47,nil) != sk47
| nil = sk49 ),
inference(demodulation,[status(thm)],[p15626,p1594]) ).
cnf(p15865,plain,
( ssItem(sk51(sk52,nil,nil))
| app(sk47,nil) != sk47
| nil = sk47 ),
inference(demodulation,[status(thm)],[p15767,p15628]) ).
cnf(p15935,plain,
( ssItem(sk51(sk52,nil,nil))
| sk47 != sk47
| nil = sk47 ),
inference(demodulation,[status(thm)],[p15934,p15865]) ).
cnf(p15944,plain,
( ssItem(sk51(sk52,nil,nil))
| nil = sk47 ),
inference(equality_resolution,[status(thm)],[p15935]) ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f37_nnf,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c113,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p15955,plain,
( ~ memberP(nil,sk51(sk52,nil,nil))
| nil = sk47 ),
inference(resolution,[status(thm)],[p15944,c113]) ).
cnf(p15987,plain,
( nil = sk47
| nil = sk47 ),
inference(resolution,[status(thm)],[p15986,p15955]) ).
cnf(p15989,plain,
nil = sk47,
inference(factoring,[status(thm)],[p15987]) ).
cnf(p15990,plain,
$false,
inference(resolution,[status(thm)],[p15989,c196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC252+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.04/16.69 % Computer : n012.cluster.edu
% 0.04/16.69 % Model : x86_64 x86_64
% 0.04/16.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/16.69 % Memory : 8046.5625MB
% 0.04/16.69 % OS : Linux 6.8.0-71-generic
% 0.04/16.69 % CPULimit : 300
% 0.04/16.69 % WCLimit : 300
% 0.04/16.69 % DateTime : Thu Sep 24 17:14:10 UTC 2026
% 0.04/16.69 % CPUTime :
% 0.04/16.69 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.94/21.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.94/21.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------