%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC105+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 : 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 03:05:22 PM UTC 2026
% Result : Theorem 223.39s 33.33s
% Output : Proof 223.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 17 unt; 0 def)
% Number of atoms : 165 ( 73 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 172 ( 60 ~; 66 |; 32 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f14_nnf,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [U,V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c80,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ( rearsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| 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)
=> ( ( ( ~ rearsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ( rearsegP(V,U)
& neq(U,nil) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( rearsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
( ( ( rearsegP(sk50,sk49)
& neq(sk49,nil) )
| ( nil = sk49
& nil = sk50 ) )
& ( ( ( ~ rearsegP(sk48,sk47)
| ~ neq(sk47,nil) )
& neq(sk48,nil) )
| ( nil != sk47
& nil = sk48 ) )
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50])],[f95_nnf]) ).
cnf(c193,plain,
ssList(sk50),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p8872,plain,
( sk50 != X0
| ~ neq(sk50,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c80,c193]) ).
cnf(p34681,plain,
( ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[status(thm)],[p8872]) ).
fof(f16,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f16_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c83,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(p34731,plain,
~ neq(nil,nil),
inference(resolution,[status(thm)],[p34681,c83]) ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f51_nnf,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c130,plain,
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p18140,plain,
( nil = sk47
| ~ rearsegP(nil,sk47) ),
inference(resolution,[status(thm)],[c130,c190]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f27_nnf,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c97,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(c192,plain,
ssList(sk49),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p14181,plain,
app(nil,sk49) = sk49,
inference(resolution,[status(thm)],[c97,c192]) ).
cnf(p14319,plain,
sk49 = sk47,
inference(superposition,[status(thm)],[c195,p14181]) ).
cnf(c200,plain,
( neq(sk49,nil)
| nil = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p206,plain,
( neq(sk47,nil)
| nil = sk50 ),
inference(superposition,[status(thm)],[c195,c200]) ).
cnf(c197,plain,
( ~ rearsegP(sk48,sk47)
| ~ neq(sk47,nil)
| nil = sk48 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p219,plain,
( ~ rearsegP(sk48,sk47)
| nil = sk48
| nil = sk50 ),
inference(resolution,[status(thm)],[p206,c197]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c201,plain,
( rearsegP(sk50,sk49)
| nil = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p208,plain,
( rearsegP(sk50,sk47)
| nil = sk50 ),
inference(superposition,[status(thm)],[c195,c201]) ).
cnf(p214,plain,
( rearsegP(sk48,sk47)
| nil = sk50 ),
inference(superposition,[status(thm)],[c194,p208]) ).
cnf(p226,plain,
( nil = sk50
| nil = sk48
| nil = sk50 ),
inference(resolution,[status(thm)],[p219,p214]) ).
cnf(p309,plain,
( nil = sk48
| nil = sk50 ),
inference(factoring,[status(thm)],[p226]) ).
cnf(p316,plain,
( sk48 != sk50
| nil = sk48 ),
inference(equality_factoring,[status(thm)],[p309]) ).
cnf(p320,plain,
nil = sk48,
inference(resolution,[status(thm)],[p316,c194]) ).
cnf(c203,plain,
( rearsegP(sk50,sk49)
| nil = sk49 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p210,plain,
( rearsegP(sk48,sk49)
| nil = sk49 ),
inference(superposition,[status(thm)],[c194,c203]) ).
cnf(p322,plain,
( rearsegP(nil,sk49)
| nil = sk49 ),
inference(superposition,[status(thm)],[p320,p210]) ).
cnf(p14322,plain,
( rearsegP(nil,sk47)
| nil = sk47 ),
inference(demodulation,[status(thm)],[p14319,p322]) ).
cnf(p18779,plain,
( nil = sk47
| nil = sk47 ),
inference(resolution,[status(thm)],[p18140,p14322]) ).
cnf(p18906,plain,
nil = sk47,
inference(factoring,[status(thm)],[p18779]) ).
cnf(p321,plain,
nil = sk50,
inference(superposition,[status(thm)],[p320,c194]) ).
cnf(p334,plain,
sk48 = nil,
inference(superposition,[status(thm)],[p321,c194]) ).
cnf(c198,plain,
( neq(sk48,nil)
| nil != sk47 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(p335,plain,
( neq(nil,nil)
| nil != sk47 ),
inference(demodulation,[status(thm)],[p334,c198]) ).
cnf(p18923,plain,
neq(nil,nil),
inference(resolution,[status(thm)],[p18906,p335]) ).
cnf(p34732,plain,
$false,
inference(resolution,[status(thm)],[p34731,p18923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC105+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:24:58 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 223.39/33.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 223.39/33.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------