%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC320+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 : 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 03:05:59 PM UTC 2026
% Result : Theorem 22.86s 3.81s
% Output : Proof 22.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 1
% Syntax : Number of formulae : 55 ( 11 unt; 0 def)
% Number of atoms : 190 ( 105 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 215 ( 80 ~; 89 |; 38 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 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 : 38 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| 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] :
( ( ( ? [X1] :
( ? [X2] :
( app(X2,cons(X1,nil)) = V
& app(cons(X1,nil),X2) = U
& ssList(X2) )
& ssItem(X1) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W
| ~ ssList(Z) ) ) )
| ( nil = X
& nil != W )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [X1] :
( ! [X2] :
( app(X2,cons(X1,nil)) != V
| app(cons(X1,nil),X2) != U
| ~ ssList(X2) )
| ~ ssItem(X1) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [X1,X2] :
( ( ( ( app(X2,cons(X1,nil)) != sk48
| app(cons(X1,nil),X2) != sk47
| ~ ssList(X2)
| ~ ssItem(X1) )
& neq(sk48,nil) )
| ( nil != sk47
& nil = sk48 ) )
& ( ~ neq(sk50,nil)
| ( app(sk52,cons(sk51,nil)) = sk50
& app(cons(sk51,nil),sk52) = sk49
& ssList(sk52)
& ssItem(sk51) ) )
& ( nil != sk50
| nil = sk49 )
& 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(c203,plain,
( neq(sk48,nil)
| nil != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c197,plain,
( ~ neq(sk50,nil)
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( ~ neq(sk48,nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c194,c197]) ).
cnf(c201,plain,
( neq(sk48,nil)
| nil = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( nil = sk48
| ssItem(sk51) ),
inference(resolution,[status(thm)],[p206,c201]) ).
cnf(p213,plain,
( nil = sk50
| ssItem(sk51) ),
inference(superposition,[status(thm)],[p208,c194]) ).
cnf(c196,plain,
( nil != sk50
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p218,plain,
( nil = sk49
| ssItem(sk51) ),
inference(resolution,[status(thm)],[p213,c196]) ).
cnf(p222,plain,
( nil = sk47
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c195,p218]) ).
cnf(p233,plain,
( ssItem(sk51)
| neq(sk48,nil) ),
inference(resolution,[status(thm)],[c203,p222]) ).
cnf(p239,plain,
( ssItem(sk51)
| ssItem(sk51) ),
inference(resolution,[status(thm)],[p233,p206]) ).
cnf(p242,plain,
ssItem(sk51),
inference(factoring,[status(thm)],[p239]) ).
cnf(c202,plain,
( app(X7,cons(X6,nil)) != sk48
| app(cons(X6,nil),X7) != sk47
| ~ ssList(X7)
| ~ ssItem(X6)
| nil = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p243,plain,
( app(X0,cons(sk51,nil)) != sk48
| app(cons(sk51,nil),X0) != sk47
| ~ ssList(X0)
| nil = sk48 ),
inference(resolution,[status(thm)],[p242,c202]) ).
cnf(c198,plain,
( ~ neq(sk50,nil)
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p205,plain,
( ~ neq(sk48,nil)
| ssList(sk52) ),
inference(superposition,[status(thm)],[c194,c198]) ).
cnf(p207,plain,
( nil = sk48
| ssList(sk52) ),
inference(resolution,[status(thm)],[p205,c201]) ).
cnf(p210,plain,
( nil = sk50
| ssList(sk52) ),
inference(superposition,[status(thm)],[p207,c194]) ).
cnf(p216,plain,
( nil = sk49
| ssList(sk52) ),
inference(resolution,[status(thm)],[p210,c196]) ).
cnf(p220,plain,
( nil = sk47
| ssList(sk52) ),
inference(superposition,[status(thm)],[c195,p216]) ).
cnf(p231,plain,
( ssList(sk52)
| neq(sk48,nil) ),
inference(resolution,[status(thm)],[c203,p220]) ).
cnf(p234,plain,
( ssList(sk52)
| ssList(sk52) ),
inference(resolution,[status(thm)],[p231,p205]) ).
cnf(p238,plain,
ssList(sk52),
inference(factoring,[status(thm)],[p234]) ).
cnf(p253,plain,
( app(sk52,cons(sk51,nil)) != sk48
| app(cons(sk51,nil),sk52) != sk47
| nil = sk48 ),
inference(resolution,[status(thm)],[p243,p238]) ).
cnf(c199,plain,
( ~ neq(sk50,nil)
| app(cons(sk51,nil),sk52) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p225,plain,
( ~ neq(sk48,nil)
| app(cons(sk51,nil),sk52) = sk49 ),
inference(superposition,[status(thm)],[c194,c199]) ).
cnf(p227,plain,
( nil = sk48
| app(cons(sk51,nil),sk52) = sk49 ),
inference(resolution,[status(thm)],[p225,c201]) ).
cnf(p229,plain,
( nil = sk48
| app(cons(sk51,nil),sk52) = sk47 ),
inference(superposition,[status(thm)],[c195,p227]) ).
cnf(p257,plain,
( nil = sk48
| app(sk52,cons(sk51,nil)) != sk48
| nil = sk48 ),
inference(resolution,[status(thm)],[p253,p229]) ).
cnf(p258,plain,
( app(sk52,cons(sk51,nil)) != sk48
| nil = sk48 ),
inference(factoring,[status(thm)],[p257]) ).
cnf(c200,plain,
( ~ neq(sk50,nil)
| app(sk52,cons(sk51,nil)) = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p226,plain,
( ~ neq(sk48,nil)
| app(sk52,cons(sk51,nil)) = sk50 ),
inference(superposition,[status(thm)],[c194,c200]) ).
cnf(p228,plain,
( nil = sk48
| app(sk52,cons(sk51,nil)) = sk50 ),
inference(resolution,[status(thm)],[p226,c201]) ).
cnf(p244,plain,
( nil = sk48
| app(sk52,cons(sk51,nil)) = sk48 ),
inference(superposition,[status(thm)],[c194,p228]) ).
cnf(p260,plain,
( nil = sk48
| nil = sk48 ),
inference(resolution,[status(thm)],[p258,p244]) ).
cnf(p261,plain,
nil = sk48,
inference(factoring,[status(thm)],[p260]) ).
cnf(p209,plain,
( nil != sk48
| nil = sk49 ),
inference(superposition,[status(thm)],[c194,c196]) ).
cnf(p263,plain,
nil = sk49,
inference(resolution,[status(thm)],[p261,p209]) ).
cnf(p269,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p263,c195]) ).
cnf(p262,plain,
nil = sk50,
inference(superposition,[status(thm)],[p261,c194]) ).
cnf(p266,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p262,c194]) ).
cnf(c204,plain,
( app(X7,cons(X6,nil)) != sk48
| app(cons(X6,nil),X7) != sk47
| ~ ssList(X7)
| ~ ssItem(X6)
| nil != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p268,plain,
( app(X1,cons(X0,nil)) != nil
| app(cons(X0,nil),X1) != sk47
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != sk47 ),
inference(demodulation,[status(thm)],[p266,c204]) ).
cnf(p271,plain,
( app(X1,cons(X0,nil)) != nil
| app(cons(X0,nil),X1) != nil
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != nil ),
inference(demodulation,[status(thm)],[p269,p268]) ).
cnf(p280,plain,
( app(X1,cons(X0,nil)) != nil
| app(cons(X0,nil),X1) != nil
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[p271]) ).
cnf(p284,plain,
( app(X0,cons(sk51,nil)) != nil
| app(cons(sk51,nil),X0) != nil
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p280,p242]) ).
cnf(p290,plain,
( nil != nil
| nil != nil ),
inference(resolution,[status(thm)],[p284,p238]) ).
cnf(p291,plain,
nil != nil,
inference(factoring,[status(thm)],[p290]) ).
cnf(p292,plain,
$false,
inference(equality_resolution,[status(thm)],[p291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 17:37:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.86/3.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.86/3.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------