%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC153+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 : n001.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 03:05:32 PM UTC 2026
% Result : Theorem 32.04s 4.46s
% Output : Proof 32.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 285 ( 34 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 406 ( 167 ~; 161 |; 58 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 32 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( leq(X5,X6)
& ! [X10] :
( ssItem(X10)
=> ( ( leq(X5,X10)
& leq(X10,X6) )
| ~ memberP(X8,X10) ) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != U ) ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( ( ~ leq(X4,Z)
| ~ leq(Y,X4) )
& memberP(X2,X4)
& ssItem(X4) )
| ~ leq(Y,Z) )
& leq(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = W
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| W != U
| X != V ) ) ) ) ),
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)
=> ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( ( leq(X5,X6)
& ! [X10] :
( ssItem(X10)
=> ( ( leq(X5,X10)
& leq(X10,X6) )
| ~ memberP(X8,X10) ) ) )
| ~ leq(X6,X5)
| app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) != U ) ) ) ) ) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( ( ~ leq(X4,Z)
| ~ leq(Y,X4) )
& memberP(X2,X4)
& ssItem(X4) )
| ~ leq(Y,Z) )
& leq(Z,Y)
& app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) = W
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
| W != U
| X != V ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ( ~ leq(X5,X6)
| ? [X10] :
( ( ~ leq(X5,X10)
| ~ leq(X10,X6) )
& memberP(X8,X10)
& ssItem(X10) ) )
& leq(X6,X5)
& app(app(app(app(X7,cons(X5,nil)),X8),cons(X6,nil)),X9) = U
& ssList(X9) )
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
& ssItem(X5) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ! [X4] :
( ( leq(X4,Z)
& leq(Y,X4) )
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& leq(Y,Z) )
| ~ leq(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != W
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z) )
| ~ ssItem(Y) )
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y,Z,X1,X2,X3,X4] :
( ( ~ leq(sk51,sk52)
| ( ( ~ leq(sk51,sk56)
| ~ leq(sk56,sk52) )
& memberP(sk54,sk56)
& ssItem(sk56) ) )
& leq(sk52,sk51)
& app(app(app(app(sk53,cons(sk51,nil)),sk54),cons(sk52,nil)),sk55) = sk47
& ssList(sk55)
& ssList(sk54)
& ssList(sk53)
& ssItem(sk52)
& ssItem(sk51)
& ( ( ( ( leq(X4,Z)
& leq(Y,X4) )
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& leq(Y,Z) )
| ~ leq(Z,Y)
| app(app(app(app(X1,cons(Y,nil)),X2),cons(Z,nil)),X3) != sk49
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(Z)
| ~ ssItem(Y) )
& sk49 = sk47
& sk50 = sk48
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51,sk52,sk53,sk54,sk55,sk56])],[f95_nnf]) ).
cnf(c207,plain,
( ~ leq(sk51,sk52)
| memberP(sk54,sk56) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c196,plain,
( leq(X4,X5)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sk49
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c199,plain,
ssItem(sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p212,plain,
( leq(sk51,X0)
| ~ leq(X0,sk51)
| app(app(app(app(X1,cons(sk51,nil)),X2),cons(X0,nil)),X3) != sk47
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c196,c199]) ).
cnf(c200,plain,
ssItem(sk52),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p307,plain,
( leq(sk51,sk52)
| ~ leq(sk52,sk51)
| app(app(app(app(X0,cons(sk51,nil)),X1),cons(sk52,nil)),X2) != sk47
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p212,c200]) ).
cnf(c201,plain,
ssList(sk53),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p311,plain,
( leq(sk51,sk52)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),X0),cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p307,c201]) ).
cnf(c202,plain,
ssList(sk54),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p362,plain,
( leq(sk51,sk52)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),sk54),cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p311,c202]) ).
cnf(c203,plain,
ssList(sk55),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p370,plain,
( leq(sk51,sk52)
| ~ leq(sk52,sk51)
| sk47 != sk47 ),
inference(resolution,[status(thm)],[p362,c203]) ).
cnf(p371,plain,
( leq(sk51,sk52)
| ~ leq(sk52,sk51) ),
inference(equality_resolution,[status(thm)],[p370]) ).
cnf(c205,plain,
leq(sk52,sk51),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p372,plain,
leq(sk51,sk52),
inference(resolution,[status(thm)],[p371,c205]) ).
cnf(p4351,plain,
memberP(sk54,sk56),
inference(resolution,[status(thm)],[c207,p372]) ).
cnf(c198,plain,
( leq(X9,X5)
| ~ memberP(X7,X9)
| ~ ssItem(X9)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sk49
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p2603,plain,
( leq(X4,X0)
| ~ memberP(X2,X4)
| ~ ssItem(X4)
| ~ leq(X0,sk51)
| app(app(app(app(X1,cons(sk51,nil)),X2),cons(X0,nil)),X3) != sk47
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c198,c199]) ).
cnf(p3637,plain,
( leq(X3,sk52)
| ~ memberP(X1,X3)
| ~ ssItem(X3)
| ~ leq(sk52,sk51)
| app(app(app(app(X0,cons(sk51,nil)),X1),cons(sk52,nil)),X2) != sk47
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p2603,c200]) ).
cnf(p3642,plain,
( leq(X2,sk52)
| ~ memberP(X0,X2)
| ~ ssItem(X2)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),X0),cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p3637,c201]) ).
cnf(p3693,plain,
( leq(X1,sk52)
| ~ memberP(sk54,X1)
| ~ ssItem(X1)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),sk54),cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p3642,c202]) ).
cnf(p3701,plain,
( leq(X0,sk52)
| ~ memberP(sk54,X0)
| ~ ssItem(X0)
| ~ leq(sk52,sk51)
| sk47 != sk47 ),
inference(resolution,[status(thm)],[p3693,c203]) ).
cnf(p3702,plain,
( leq(X0,sk52)
| ~ memberP(sk54,X0)
| ~ ssItem(X0)
| ~ leq(sk52,sk51) ),
inference(equality_resolution,[status(thm)],[p3701]) ).
cnf(p3703,plain,
( leq(X0,sk52)
| ~ memberP(sk54,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[p3702,c205]) ).
cnf(c206,plain,
( ~ leq(sk51,sk52)
| ssItem(sk56) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p373,plain,
ssItem(sk56),
inference(resolution,[status(thm)],[p372,c206]) ).
cnf(p3705,plain,
( leq(sk56,sk52)
| ~ memberP(sk54,sk56) ),
inference(resolution,[status(thm)],[p3703,p373]) ).
cnf(p4353,plain,
leq(sk56,sk52),
inference(resolution,[status(thm)],[p4351,p3705]) ).
cnf(c208,plain,
( ~ leq(sk51,sk52)
| ~ leq(sk51,sk56)
| ~ leq(sk56,sk52) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p4354,plain,
( ~ leq(sk51,sk52)
| ~ leq(sk51,sk56) ),
inference(resolution,[status(thm)],[p4353,c208]) ).
cnf(c197,plain,
( leq(X4,X9)
| ~ memberP(X7,X9)
| ~ ssItem(X9)
| ~ leq(X5,X4)
| app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) != sk49
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p1064,plain,
( leq(sk51,X4)
| ~ memberP(X2,X4)
| ~ ssItem(X4)
| ~ leq(X0,sk51)
| app(app(app(app(X1,cons(sk51,nil)),X2),cons(X0,nil)),X3) != sk47
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c197,c199]) ).
cnf(p2098,plain,
( leq(sk51,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3)
| ~ leq(sk52,sk51)
| app(app(app(app(X0,cons(sk51,nil)),X1),cons(sk52,nil)),X2) != sk47
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p1064,c200]) ).
cnf(p2103,plain,
( leq(sk51,X2)
| ~ memberP(X0,X2)
| ~ ssItem(X2)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),X0),cons(sk52,nil)),X1) != sk47
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p2098,c201]) ).
cnf(p2154,plain,
( leq(sk51,X1)
| ~ memberP(sk54,X1)
| ~ ssItem(X1)
| ~ leq(sk52,sk51)
| app(app(app(app(sk53,cons(sk51,nil)),sk54),cons(sk52,nil)),X0) != sk47
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[p2103,c202]) ).
cnf(p2162,plain,
( leq(sk51,X0)
| ~ memberP(sk54,X0)
| ~ ssItem(X0)
| ~ leq(sk52,sk51)
| sk47 != sk47 ),
inference(resolution,[status(thm)],[p2154,c203]) ).
cnf(p2163,plain,
( leq(sk51,X0)
| ~ memberP(sk54,X0)
| ~ ssItem(X0)
| ~ leq(sk52,sk51) ),
inference(equality_resolution,[status(thm)],[p2162]) ).
cnf(p2164,plain,
( leq(sk51,X0)
| ~ memberP(sk54,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[p2163,c205]) ).
cnf(p2166,plain,
( leq(sk51,sk56)
| ~ memberP(sk54,sk56) ),
inference(resolution,[status(thm)],[p2164,p373]) ).
cnf(p4352,plain,
leq(sk51,sk56),
inference(resolution,[status(thm)],[p4351,p2166]) ).
cnf(p4355,plain,
~ leq(sk51,sk52),
inference(resolution,[status(thm)],[p4354,p4352]) ).
cnf(p4356,plain,
$false,
inference(resolution,[status(thm)],[p4355,p372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC153+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 : n001.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 16:46:38 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.04/4.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.04/4.46 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------