%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC258+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 03:05:49 PM UTC 2026
% Result : Theorem 22.76s 3.73s
% Output : Proof 22.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 96 ( 31 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 100 ( 29 ~; 30 |; 30 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(U)
| 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 != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ( ? [Z] :
( leq(Z,Y)
& memberP(X,Z)
& Y != Z
& ssItem(Z) )
| ~ memberP(X,Y)
| cons(Y,nil) != W ) ) )
| totalorderedP(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] :
( ~ leq(Z,Y)
| ~ memberP(X,Z)
| Y = Z
| ~ ssItem(Z) )
& memberP(X,Y)
& cons(Y,nil) = W
& ssItem(Y) ) )
& ~ totalorderedP(U)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Z] :
( ( ( nil = sk49
& nil = sk50 )
| ( ( ~ leq(Z,sk51)
| ~ memberP(sk50,Z)
| sk51 = Z
| ~ ssItem(Z) )
& memberP(sk50,sk51)
& cons(sk51,nil) = sk49
& ssItem(sk51) ) )
& ~ totalorderedP(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])],[f95_nnf]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c200,plain,
( nil = sk49
| cons(sk51,nil) = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
fof(f64,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f64_nnf,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c145,plain,
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
fof(f65,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f65_nnf,plain,
totalorderedP(nil),
inference(nnf_transformation,[status(thm)],[f65]) ).
cnf(c146,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(esa)],[f65_nnf]) ).
cnf(c198,plain,
( nil = sk49
| ssItem(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( nil = sk47
| ssItem(sk51) ),
inference(superposition,[status(thm)],[c195,c198]) ).
cnf(c196,plain,
~ totalorderedP(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p210,plain,
( ~ totalorderedP(nil)
| ssItem(sk51) ),
inference(superposition,[status(thm)],[p206,c196]) ).
cnf(p227,plain,
ssItem(sk51),
inference(resolution,[status(thm)],[c146,p210]) ).
cnf(p407,plain,
totalorderedP(cons(sk51,nil)),
inference(resolution,[status(thm)],[c145,p227]) ).
cnf(p409,plain,
( totalorderedP(sk49)
| nil = sk49 ),
inference(superposition,[status(thm)],[c200,p407]) ).
cnf(p420,plain,
( sk47 = nil
| totalorderedP(sk49) ),
inference(superposition,[status(thm)],[p409,c195]) ).
cnf(p444,plain,
( ~ totalorderedP(nil)
| totalorderedP(sk49) ),
inference(superposition,[status(thm)],[p420,c196]) ).
cnf(p445,plain,
totalorderedP(sk49),
inference(resolution,[status(thm)],[p444,c146]) ).
cnf(p446,plain,
totalorderedP(sk47),
inference(superposition,[status(thm)],[c195,p445]) ).
cnf(p447,plain,
$false,
inference(resolution,[status(thm)],[p446,c196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC258+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 17:17:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.76/3.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.76/3.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------