%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC322+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 : n003.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 03:06:00 PM UTC 2026
% Result : Theorem 26.68s 3.89s
% Output : Proof 26.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 147 ( 96 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 148 ( 48 ~; 54 |; 34 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 16 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = U
| nil != V )
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) != W
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil = U
| nil != V )
& ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(cons(X1,nil),X2) = U
| app(X2,cons(X1,nil)) != V ) ) ) )
| ( nil = X
& nil != W )
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) != W
& ssList(Z) )
& ssItem(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil != U
& nil = V )
| ? [X1] :
( ? [X2] :
( app(cons(X1,nil),X2) != U
& app(X2,cons(X1,nil)) = V
& ssList(X2) )
& ssItem(X1) ) )
& ( nil != X
| nil = W )
& ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) = W
| ~ ssList(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] :
( ( ( nil != sk47
& nil = sk48 )
| ( app(cons(sk51,nil),sk52) != sk47
& app(sk52,cons(sk51,nil)) = sk48
& ssList(sk52)
& ssItem(sk51) ) )
& ( nil != sk50
| nil = sk49 )
& ( app(Z,cons(Y,nil)) != sk50
| app(cons(Y,nil),Z) = sk49
| ~ ssList(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])],[f95_nnf]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c202,plain,
( nil = sk48
| app(sk52,cons(sk51,nil)) = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c196,plain,
( app(X5,cons(X4,nil)) != sk50
| app(cons(X4,nil),X5) = sk49
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c199,plain,
( nil != sk47
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c197,plain,
( nil != sk50
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c198,plain,
( nil = sk48
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( nil = sk50
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c198,c194]) ).
cnf(p209,plain,
( ssItem(sk51)
| nil = sk49 ),
inference(resolution,[status(thm)],[c197,p206]) ).
cnf(p211,plain,
( ssItem(sk51)
| nil = sk47 ),
inference(superposition,[status(thm)],[c195,p209]) ).
cnf(p213,plain,
( ssItem(sk51)
| ssItem(sk51) ),
inference(resolution,[status(thm)],[c199,p211]) ).
cnf(p214,plain,
ssItem(sk51),
inference(factoring,[status(thm)],[p213]) ).
cnf(p225,plain,
( app(X0,cons(sk51,nil)) != sk50
| app(cons(sk51,nil),X0) = sk49
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c196,p214]) ).
cnf(c200,plain,
( nil = sk48
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( nil != sk48
| nil = sk49 ),
inference(superposition,[status(thm)],[c194,c197]) ).
cnf(p216,plain,
( nil = sk49
| ssList(sk52) ),
inference(resolution,[status(thm)],[c200,p208]) ).
cnf(p219,plain,
( nil = sk47
| ssList(sk52) ),
inference(superposition,[status(thm)],[c195,p216]) ).
cnf(c201,plain,
( nil != sk47
| ssList(sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p223,plain,
( ssList(sk52)
| ssList(sk52) ),
inference(resolution,[status(thm)],[p219,c201]) ).
cnf(p224,plain,
ssList(sk52),
inference(factoring,[status(thm)],[p223]) ).
cnf(p230,plain,
( app(sk52,cons(sk51,nil)) != sk50
| app(cons(sk51,nil),sk52) = sk49 ),
inference(resolution,[status(thm)],[p225,p224]) ).
cnf(p237,plain,
( sk48 != sk50
| app(cons(sk51,nil),sk52) = sk49
| nil = sk48 ),
inference(superposition,[status(thm)],[c202,p230]) ).
cnf(p241,plain,
( app(cons(sk51,nil),sk52) = sk49
| nil = sk48 ),
inference(resolution,[status(thm)],[p237,c194]) ).
cnf(p242,plain,
( app(cons(sk51,nil),sk52) = sk47
| nil = sk48 ),
inference(superposition,[status(thm)],[c195,p241]) ).
cnf(c204,plain,
( nil = sk48
| app(cons(sk51,nil),sk52) != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p245,plain,
( nil = sk48
| nil = sk48 ),
inference(resolution,[status(thm)],[p242,c204]) ).
cnf(p247,plain,
nil = sk48,
inference(factoring,[status(thm)],[p245]) ).
cnf(p249,plain,
nil = sk49,
inference(resolution,[status(thm)],[p247,p208]) ).
cnf(p264,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p249,c195]) ).
cnf(p248,plain,
nil = sk50,
inference(superposition,[status(thm)],[p247,c194]) ).
cnf(p257,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p248,c194]) ).
cnf(c203,plain,
( nil != sk47
| app(sk52,cons(sk51,nil)) = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p258,plain,
( nil != sk47
| app(sk52,cons(sk51,nil)) = nil ),
inference(demodulation,[status(thm)],[p257,c203]) ).
cnf(p267,plain,
( nil != nil
| app(sk52,cons(sk51,nil)) = nil ),
inference(demodulation,[status(thm)],[p264,p258]) ).
cnf(p270,plain,
app(sk52,cons(sk51,nil)) = nil,
inference(equality_resolution,[status(thm)],[p267]) ).
cnf(p271,plain,
( nil != sk50
| app(cons(sk51,nil),sk52) = sk49 ),
inference(demodulation,[status(thm)],[p270,p230]) ).
cnf(p273,plain,
app(cons(sk51,nil),sk52) = sk49,
inference(resolution,[status(thm)],[p271,p248]) ).
cnf(c205,plain,
( nil != sk47
| app(cons(sk51,nil),sk52) != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p265,plain,
( nil != nil
| app(cons(sk51,nil),sk52) != nil ),
inference(demodulation,[status(thm)],[p264,c205]) ).
cnf(p269,plain,
app(cons(sk51,nil),sk52) != nil,
inference(equality_resolution,[status(thm)],[p265]) ).
cnf(p274,plain,
sk49 != nil,
inference(demodulation,[status(thm)],[p273,p269]) ).
cnf(p275,plain,
nil != nil,
inference(superposition,[status(thm)],[p249,p274]) ).
cnf(p276,plain,
$false,
inference(equality_resolution,[status(thm)],[p275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC322+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.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 17:38:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.68/3.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.68/3.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------