%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 07:55:40 AM UTC 2026
% Result : Theorem 124.49s 32.99s
% Output : CNFRefutation 124.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 40 unt; 0 def)
% Number of atoms : 78 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 16 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 5 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_01,axiom,
! [X0,X1,X2] : '\'+\''('\'+\''(X0,X1),X2) = '\'+\''(X0,'\'+\''(X1,X2)) ).
fof(sos_02,axiom,
! [X0,X1] : '\'+\''(X0,X1) = '\'+\''(X1,X0) ).
fof(sos_03,axiom,
! [X0] : '\'+\''(X0,'\'0\'') = X0 ).
fof(sos_04,axiom,
! [X0] : '\'>=\''(X0,X0) ).
fof(sos_06,axiom,
! [X0,X1] :
( ( '\'>=\''(X1,X0)
& '\'>=\''(X0,X1) )
=> X0 = X1 ) ).
fof(sos_07,axiom,
! [X0,X1,X2] :
( '\'>=\''('\'+\''(X0,X1),X2)
<=> '\'>=\''(X1,'\'==>\''(X0,X2)) ) ).
fof(sos_08,axiom,
! [X0] : '\'>=\''(X0,'\'0\'') ).
fof(sos_09,axiom,
! [X0,X1,X2] :
( '\'>=\''(X0,X1)
=> '\'>=\''('\'+\''(X0,X2),'\'+\''(X1,X2)) ) ).
fof(sos_13,axiom,
! [X0,X1] : '\'==>\''('\'==>\''(X0,X1),X1) = '\'==>\''('\'==>\''(X1,X0),X0) ).
fof(sos_14,axiom,
! [X0] : '\'+\''(X0,X0) = X0 ).
fof(goals_15,conjecture,
! [X0] : '\'==>\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X0) = '\'0\'' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : '\'==>\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X0) = '\'0\'',
inference(negate_conjecture,[status(cth)],[goals_15]) ).
cnf(c0,plain,
'\'+\''(X0,'\'+\''(X1,X2)) = '\'+\''('\'+\''(X0,X1),X2),
inference(clausification,[status(esa)],[sos_01]) ).
cnf(c1,plain,
'\'+\''(X0,X1) = '\'+\''(X1,X0),
inference(clausification,[status(esa)],[sos_02]) ).
cnf(c2,plain,
'\'+\''(X0,'\'0\'') = X0,
inference(clausification,[status(esa)],[sos_03]) ).
cnf(c3,plain,
'\'>=\''(X0,X0),
inference(clausification,[status(esa)],[sos_04]) ).
cnf(c5,plain,
( X0 = X1
| ~ '\'>=\''(X1,X0)
| ~ '\'>=\''(X0,X1) ),
inference(clausification,[status(esa)],[sos_06]) ).
cnf(c6,plain,
( '\'>=\''(X1,'\'==>\''(X0,X2))
| ~ '\'>=\''('\'+\''(X0,X1),X2) ),
inference(clausification,[status(esa)],[sos_07]) ).
cnf(c7,plain,
( ~ '\'>=\''(X1,'\'==>\''(X0,X2))
| '\'>=\''('\'+\''(X0,X1),X2) ),
inference(clausification,[status(esa)],[sos_07]) ).
cnf(c8,plain,
'\'>=\''(X0,'\'0\''),
inference(clausification,[status(esa)],[sos_08]) ).
cnf(c9,plain,
( '\'>=\''('\'+\''(X0,X2),'\'+\''(X1,X2))
| ~ '\'>=\''(X0,X1) ),
inference(clausification,[status(esa)],[sos_09]) ).
cnf(c13,plain,
'\'==>\''('\'==>\''(X0,X1),X1) = '\'==>\''('\'==>\''(X1,X0),X0),
inference(clausification,[status(esa)],[sos_13]) ).
cnf(c14,plain,
'\'+\''(X0,X0) = X0,
inference(clausification,[status(esa)],[sos_14]) ).
cnf(c15,plain,
'\'==>\''('\'==>\''('\'==>\''(sK29,'\'1\''),sK29),sK29) != '\'0\'',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ '\'>=\''('\'0\'',X0)
| '\'0\'' = X0 ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d1,plain,
'\'>=\''(X0,'\'==>\''(X1,'\'+\''(X1,X0))),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d2,plain,
'\'>=\''('\'0\'','\'==>\''(X0,X0)),
inference(superposition,[status(thm)],[c2,d1]) ).
cnf(d3,plain,
'\'0\'' = '\'==>\''(X0,X0),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
X0 = '\'+\''('\'0\'',X0),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d5,plain,
( ~ '\'>=\''(X1,'\'0\'')
| '\'>=\''('\'+\''(X1,X0),X0) ),
inference(superposition,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
'\'>=\''('\'+\''(X0,X1),X1),
inference(resolution,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
'\'>=\''(X0,'\'==>\''(X1,X0)),
inference(resolution,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
( ~ '\'>=\''('\'==>\''(X0,X1),X1)
| '\'==>\''(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
( '\'>=\''('\'0\'','\'==>\''(X0,X1))
| ~ '\'>=\''(X0,X1) ),
inference(superposition,[status(thm)],[c2,c6]) ).
cnf(d10,plain,
( '\'>=\''('\'+\''('\'==>\''(X0,X1),X2),X1)
| ~ '\'>=\''(X2,'\'==>\''('\'==>\''(X1,X0),X0)) ),
inference(superposition,[status(thm)],[c13,c7]) ).
cnf(d11,plain,
( ~ '\'>=\''('\'==>\''(X1,X0),X0)
| '\'>=\''('\'+\''('\'==>\''(X0,X1),'\'0\''),X1) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( ~ '\'>=\''('\'==>\''(X1,X0),X0)
| '\'>=\''('\'==>\''(X0,X1),X1) ),
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
'\'>=\''('\'+\''(X0,'\'==>\''(X0,X1)),X1),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d14,plain,
'\'>=\''('\'+\''(X0,'\'+\''(X1,'\'==>\''(X1,'\'==>\''(X0,X2)))),X2),
inference(resolution,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
'\'+\''(X0,'\'+\''(X1,X2)) = '\'+\''(X2,'\'+\''(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d16,plain,
X0 = '\'+\''(X0,X0),
inference(superposition,[status(thm)],[c14,c1]) ).
cnf(d17,plain,
'\'+\''(X0,'\'+\''(X0,X1)) = '\'+\''(X1,X0),
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
'\'>=\''('\'+\''('\'==>\''(X0,'\'==>\''(X0,X1)),X0),X1),
inference(superposition,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
'\'>=\''('\'+\''(X0,'\'==>\''(X0,'\'==>\''(X0,X1))),X1),
inference(demodulation,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
'\'>=\''('\'==>\''(X0,'\'==>\''(X0,X1)),'\'==>\''(X0,X1)),
inference(resolution,[status(thm)],[d19,c6]) ).
cnf(d21,plain,
'\'>=\''('\'==>\''('\'==>\''(X0,X1),X0),X0),
inference(resolution,[status(thm)],[d20,d12]) ).
cnf(d22,plain,
'\'==>\''('\'==>\''(X0,X1),X0) = X0,
inference(resolution,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
'\'==>\''(sK29,sK29) != '\'0\'',
inference(demodulation,[status(thm)],[c15,d22]) ).
cnf(d24,plain,
'\'0\'' != '\'0\'',
inference(demodulation,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
'\'>=\''(X0,'\'==>\''('\'0\'',X0)),
inference(superposition,[status(thm)],[d4,d1]) ).
cnf(d26,plain,
( ~ '\'>=\''('\'==>\''('\'0\'',X0),X0)
| '\'==>\''('\'0\'',X0) = X0 ),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
'\'>=\''('\'==>\''('\'0\'',X0),X0),
inference(superposition,[status(thm)],[d4,d13]) ).
cnf(d28,plain,
'\'==>\''('\'0\'',X0) = X0,
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
( ~ '\'>=\''(X0,'\'==>\''('\'0\'',X0))
| X0 = '\'==>\''('\'0\'',X0) ),
inference(resolution,[status(thm)],[d27,c5]) ).
cnf(d30,plain,
( ~ '\'>=\''(X0,'\'==>\''('\'0\'',X0))
| X0 = X0 ),
inference(demodulation,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
( ~ '\'>=\''(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d30,d28]) ).
cnf(d32,plain,
X0 = X0,
inference(resolution,[status(thm)],[c3,d31]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL901+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 : Fri Sep 25 23:46:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 124.49/32.99 % SZS status Theorem for theBenchmark.p
% 124.49/32.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------