%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC030+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:54:00 AM UTC 2026
% Result : Theorem 19.72s 4.72s
% Output : CNFRefutation 19.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 68 ( 27 unt; 0 def)
% Number of atoms : 176 ( 77 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 181 ( 73 ~; 81 |; 4 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ) ).
fof(ax46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,X4) != X2
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,X4) != X2
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c14,plain,
( ~ ssList(X2)
| app(X2,X0) != X1
| ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
cnf(c17,plain,
( app(X0,X2) != X1
| ~ ssList(X2)
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax6]) ).
cnf(c137,plain,
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax46]) ).
cnf(c144,plain,
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax52]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
sK254 = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
ssList(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
app(sK257,sK258) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
app(sK258,sK257) = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( nil = sK253
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( nil != sK254
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(sK257,sK258) = sK254,
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d1,plain,
( rearsegP(X0,sK258)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(sK257)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( rearsegP(X0,sK258)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c215,d1]) ).
cnf(d3,plain,
( rearsegP(X0,sK258)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c214,d2]) ).
cnf(d4,plain,
( rearsegP(sK254,sK258)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
rearsegP(sK254,sK258),
inference(resolution,[status(thm)],[c209,d4]) ).
cnf(d6,plain,
( nil = sK253
| rearsegP(nil,sK258) ),
inference(superposition,[status(thm)],[c218,d5]) ).
cnf(d7,plain,
( nil = sK253
| ~ ssList(sK258)
| nil = sK258 ),
inference(resolution,[status(thm)],[c144,d6]) ).
cnf(d8,plain,
( nil = sK258
| nil = sK253 ),
inference(resolution,[status(thm)],[c215,d7]) ).
cnf(d9,plain,
app(sK258,nil) = sK258,
inference(resolution,[status(thm)],[c194,c215]) ).
cnf(d10,plain,
app(sK258,sK257) = sK253,
inference(demodulation,[status(thm)],[c217,c213]) ).
cnf(d11,plain,
( frontsegP(X0,sK257)
| ~ ssList(X0)
| ~ ssList(sK258)
| ~ ssList(sK257)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d0,c14]) ).
cnf(d12,plain,
( frontsegP(X0,sK257)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c215,d11]) ).
cnf(d13,plain,
( frontsegP(X0,sK257)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c214,d12]) ).
cnf(d14,plain,
( frontsegP(sK254,sK257)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d13]) ).
cnf(d15,plain,
frontsegP(sK254,sK257),
inference(resolution,[status(thm)],[c209,d14]) ).
cnf(d16,plain,
( nil = sK253
| frontsegP(nil,sK257) ),
inference(superposition,[status(thm)],[c218,d15]) ).
cnf(d17,plain,
( nil = sK253
| ~ ssList(sK257)
| nil = sK257 ),
inference(resolution,[status(thm)],[c137,d16]) ).
cnf(d18,plain,
( nil = sK257
| nil = sK253 ),
inference(resolution,[status(thm)],[c214,d17]) ).
cnf(d19,plain,
( nil = sK253
| app(sK258,nil) = sK253 ),
inference(superposition,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( nil = sK253
| sK258 = sK253 ),
inference(demodulation,[status(thm)],[d19,d9]) ).
cnf(d21,plain,
( nil = sK253
| nil = sK253
| nil = sK253 ),
inference(superposition,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
app(sK253,nil) = sK253,
inference(resolution,[status(thm)],[c194,c208]) ).
cnf(d23,plain,
app(nil,nil) = sK253,
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
app(nil,nil) = nil,
inference(demodulation,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
( frontsegP(X0,sK258)
| ~ ssList(X0)
| ~ ssList(sK257)
| ~ ssList(sK258)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d10,c14]) ).
cnf(d26,plain,
( frontsegP(X0,sK258)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c215,d25]) ).
cnf(d27,plain,
( frontsegP(X0,sK258)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c214,d26]) ).
cnf(d28,plain,
( frontsegP(sK253,sK258)
| ~ ssList(sK253) ),
inference(equality_resolution,[status(thm)],[d27]) ).
cnf(d29,plain,
frontsegP(sK253,sK258),
inference(resolution,[status(thm)],[c208,d28]) ).
cnf(d30,plain,
frontsegP(nil,sK258),
inference(demodulation,[status(thm)],[d29,d21]) ).
cnf(d31,plain,
( ~ ssList(sK258)
| nil = sK258 ),
inference(resolution,[status(thm)],[d30,c137]) ).
cnf(d32,plain,
nil = sK258,
inference(resolution,[status(thm)],[c215,d31]) ).
cnf(d33,plain,
( rearsegP(X0,sK257)
| ~ ssList(sK257)
| ~ ssList(X0)
| ~ ssList(sK258)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d10,c17]) ).
cnf(d34,plain,
( rearsegP(X0,sK257)
| ~ ssList(sK257)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c215,d33]) ).
cnf(d35,plain,
( rearsegP(X0,sK257)
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c214,d34]) ).
cnf(d36,plain,
( rearsegP(sK253,sK257)
| ~ ssList(sK253) ),
inference(equality_resolution,[status(thm)],[d35]) ).
cnf(d37,plain,
rearsegP(sK253,sK257),
inference(resolution,[status(thm)],[c208,d36]) ).
cnf(d38,plain,
rearsegP(nil,sK257),
inference(demodulation,[status(thm)],[d37,d21]) ).
cnf(d39,plain,
( ~ ssList(sK257)
| nil = sK257 ),
inference(resolution,[status(thm)],[d38,c144]) ).
cnf(d40,plain,
nil = sK257,
inference(resolution,[status(thm)],[c214,d39]) ).
cnf(d41,plain,
app(nil,sK258) = sK254,
inference(demodulation,[status(thm)],[d0,d40]) ).
cnf(d42,plain,
app(nil,nil) = sK254,
inference(demodulation,[status(thm)],[d41,d32]) ).
cnf(d43,plain,
nil = sK254,
inference(demodulation,[status(thm)],[d42,d24]) ).
cnf(d44,plain,
nil != sK254,
inference(resolution,[status(thm)],[d21,c221]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,d43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC030+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n001.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 12:11:57 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.72/4.72 % SZS status Theorem for theBenchmark.p
% 19.72/4.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------