%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC023+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 : n009.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 03:05:07 PM UTC 2026
% Result : Theorem 26.25s 3.77s
% Output : Proof 26.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 2
% Syntax : Number of formulae : 63 ( 20 unt; 0 def)
% Number of atoms : 177 ( 51 equ)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 177 ( 63 ~; 71 |; 32 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 24 ( 0 sgn 15 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssList(Z)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| 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 )
& ! [Z] :
( ssList(Z)
=> ( ~ frontsegP(W,Z)
| ~ frontsegP(X,Z)
| ~ neq(Z,nil) ) ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] :
( frontsegP(W,Z)
& frontsegP(X,Z)
& neq(Z,nil)
& ssList(Z) ) )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [Y] :
( ( ( nil = sk49
& nil = sk50 )
| ( frontsegP(sk49,sk51)
& frontsegP(sk50,sk51)
& neq(sk51,nil)
& ssList(sk51) ) )
& ( ~ frontsegP(sk47,Y)
| ~ frontsegP(sk48,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sk48,nil)
& 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(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c198,plain,
( nil = sk50
| ssList(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( nil = sk48
| ssList(sk51) ),
inference(superposition,[status(thm)],[c194,c198]) ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f41_nnf,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c117,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(c191,plain,
ssList(sk48),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p264,plain,
frontsegP(sk48,sk48),
inference(resolution,[status(thm)],[c117,c191]) ).
cnf(c197,plain,
( ~ frontsegP(sk47,X4)
| ~ frontsegP(sk48,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p216,plain,
( ~ frontsegP(sk47,sk48)
| ~ frontsegP(sk48,sk48)
| ~ neq(sk48,nil) ),
inference(resolution,[status(thm)],[c197,c191]) ).
cnf(c196,plain,
neq(sk48,nil),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p220,plain,
( ~ frontsegP(sk47,sk48)
| ~ frontsegP(sk48,sk48) ),
inference(resolution,[status(thm)],[p216,c196]) ).
cnf(p272,plain,
~ frontsegP(sk47,sk48),
inference(resolution,[status(thm)],[p264,p220]) ).
cnf(p282,plain,
( ~ frontsegP(sk47,nil)
| ssList(sk51) ),
inference(superposition,[status(thm)],[p206,p272]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c199,plain,
( nil = sk49
| ssList(sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p211,plain,
( nil = sk47
| ssList(sk51) ),
inference(superposition,[status(thm)],[c195,c199]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p263,plain,
frontsegP(sk47,sk47),
inference(resolution,[status(thm)],[c117,c190]) ).
cnf(p269,plain,
( frontsegP(sk47,nil)
| ssList(sk51) ),
inference(superposition,[status(thm)],[p211,p263]) ).
cnf(p288,plain,
( ssList(sk51)
| ssList(sk51) ),
inference(resolution,[status(thm)],[p282,p269]) ).
cnf(p289,plain,
ssList(sk51),
inference(factoring,[status(thm)],[p288]) ).
cnf(p290,plain,
( ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51)
| ~ neq(sk51,nil) ),
inference(resolution,[status(thm)],[p289,c197]) ).
cnf(c201,plain,
( nil = sk49
| neq(sk51,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p292,plain,
( nil = sk49
| ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51) ),
inference(resolution,[status(thm)],[p290,c201]) ).
cnf(c203,plain,
( nil = sk49
| frontsegP(sk50,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p214,plain,
( nil = sk49
| frontsegP(sk48,sk51) ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(p295,plain,
( nil = sk49
| nil = sk49
| ~ frontsegP(sk47,sk51) ),
inference(resolution,[status(thm)],[p292,p214]) ).
cnf(p301,plain,
( nil = sk49
| ~ frontsegP(sk47,sk51) ),
inference(factoring,[status(thm)],[p295]) ).
cnf(c205,plain,
( nil = sk49
| frontsegP(sk49,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p213,plain,
( nil = sk49
| frontsegP(sk47,sk51) ),
inference(superposition,[status(thm)],[c195,c205]) ).
cnf(p303,plain,
( nil = sk49
| nil = sk49 ),
inference(resolution,[status(thm)],[p301,p213]) ).
cnf(p313,plain,
nil = sk49,
inference(factoring,[status(thm)],[p303]) ).
cnf(p314,plain,
sk47 = nil,
inference(superposition,[status(thm)],[p313,c195]) ).
cnf(c200,plain,
( nil = sk50
| neq(sk51,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p293,plain,
( nil = sk50
| ~ frontsegP(sk47,sk51)
| ~ frontsegP(sk48,sk51) ),
inference(resolution,[status(thm)],[p290,c200]) ).
cnf(c202,plain,
( nil = sk50
| frontsegP(sk50,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( nil = sk50
| frontsegP(sk48,sk51) ),
inference(superposition,[status(thm)],[c194,c202]) ).
cnf(p296,plain,
( nil = sk50
| nil = sk50
| ~ frontsegP(sk47,sk51) ),
inference(resolution,[status(thm)],[p293,p208]) ).
cnf(p326,plain,
( nil = sk50
| nil = sk50
| ~ frontsegP(nil,sk51) ),
inference(demodulation,[status(thm)],[p314,p296]) ).
cnf(p330,plain,
( nil = sk50
| ~ frontsegP(nil,sk51) ),
inference(factoring,[status(thm)],[p326]) ).
cnf(c204,plain,
( nil = sk50
| frontsegP(sk49,sk51) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p209,plain,
( nil = sk50
| frontsegP(sk47,sk51) ),
inference(superposition,[status(thm)],[c195,c204]) ).
cnf(p316,plain,
( nil = sk50
| frontsegP(nil,sk51) ),
inference(demodulation,[status(thm)],[p314,p209]) ).
cnf(p331,plain,
( nil = sk50
| nil = sk50 ),
inference(resolution,[status(thm)],[p330,p316]) ).
cnf(p332,plain,
nil = sk50,
inference(factoring,[status(thm)],[p331]) ).
cnf(p333,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p332,c194]) ).
cnf(c193,plain,
ssList(sk50),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p266,plain,
frontsegP(sk50,sk50),
inference(resolution,[status(thm)],[c117,c193]) ).
cnf(p280,plain,
frontsegP(sk48,sk50),
inference(superposition,[status(thm)],[c194,p266]) ).
cnf(p335,plain,
frontsegP(nil,sk50),
inference(demodulation,[status(thm)],[p333,p280]) ).
cnf(p218,plain,
( ~ frontsegP(sk47,sk50)
| ~ frontsegP(sk48,sk50)
| ~ neq(sk50,nil) ),
inference(resolution,[status(thm)],[c197,c193]) ).
cnf(p227,plain,
( ~ frontsegP(sk47,sk50)
| ~ frontsegP(sk48,sk50)
| ~ neq(sk48,nil) ),
inference(superposition,[status(thm)],[c194,p218]) ).
cnf(p228,plain,
( ~ frontsegP(sk47,sk50)
| ~ frontsegP(sk48,sk50) ),
inference(resolution,[status(thm)],[p227,c196]) ).
cnf(p230,plain,
( ~ frontsegP(sk47,sk50)
| ~ frontsegP(sk48,sk48) ),
inference(superposition,[status(thm)],[c194,p228]) ).
cnf(p273,plain,
~ frontsegP(sk47,sk50),
inference(resolution,[status(thm)],[p264,p230]) ).
cnf(p321,plain,
~ frontsegP(nil,sk50),
inference(demodulation,[status(thm)],[p314,p273]) ).
cnf(p343,plain,
$false,
inference(resolution,[status(thm)],[p335,p321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC023+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 15:58:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.25/3.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.25/3.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------