%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC179+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 : n008.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 03:05:35 PM UTC 2026
% Result : Theorem 23.95s 3.93s
% Output : Proof 23.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 112 ( 31 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 120 ( 33 ~; 34 |; 38 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 21 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| duplicatefreeP(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 )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W ) ) ) ) )
| duplicatefreeP(U)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& ~ duplicatefreeP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [X2,X3] :
( ( ( nil = sk49
& nil = sk50 )
| ( ( ~ lt(X3,sk51)
| ~ memberP(sk53,X3)
| ~ ssItem(X3) )
& ( ~ lt(sk51,X2)
| ~ memberP(sk52,X2)
| ~ ssItem(X2) )
& app(app(sk52,sk49),sk53) = sk50
& cons(sk51,nil) = sk49
& ssList(sk53)
& ssList(sk52)
& ssItem(sk51) ) )
& ~ duplicatefreeP(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,sk53])],[f95_nnf]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c204,plain,
( nil = sk49
| cons(sk51,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
fof(f70,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f70_nnf,plain,
! [U] :
( duplicatefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [U] :
( duplicatefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c159,plain,
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
fof(f71,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f71_nnf,plain,
duplicatefreeP(nil),
inference(nnf_transformation,[status(thm)],[f71]) ).
cnf(c160,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[status(esa)],[f71_nnf]) ).
cnf(c198,plain,
( nil = sk49
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p211,plain,
( nil = sk47
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c195,c198]) ).
cnf(c196,plain,
~ duplicatefreeP(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p217,plain,
( ~ duplicatefreeP(nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[p211,c196]) ).
cnf(p252,plain,
ssItem(sk51),
inference(resolution,[status(thm)],[c160,p217]) ).
cnf(p534,plain,
duplicatefreeP(cons(sk51,nil)),
inference(resolution,[status(thm)],[c159,p252]) ).
cnf(p536,plain,
( duplicatefreeP(sk49)
| nil = sk49 ),
inference(superposition,[status(thm)],[c204,p534]) ).
cnf(p547,plain,
( sk47 = nil
| duplicatefreeP(sk49) ),
inference(superposition,[status(thm)],[p536,c195]) ).
cnf(p571,plain,
( ~ duplicatefreeP(nil)
| duplicatefreeP(sk49) ),
inference(superposition,[status(thm)],[p547,c196]) ).
cnf(p572,plain,
duplicatefreeP(sk49),
inference(resolution,[status(thm)],[p571,c160]) ).
cnf(p573,plain,
duplicatefreeP(sk47),
inference(superposition,[status(thm)],[c195,p572]) ).
cnf(p574,plain,
$false,
inference(resolution,[status(thm)],[p573,c196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC179+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 16:50:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.95/3.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.95/3.93 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------