%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL903+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 : n014.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 137.64s 35.74s
% Output : CNFRefutation 137.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 46 unt; 0 def)
% Number of atoms : 117 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 76 ( 36 ~; 33 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 135 ( 13 sgn 26 !; 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_05,axiom,
! [X0,X1,X2] :
( ( '\'>=\''(X1,X2)
& '\'>=\''(X0,X1) )
=> '\'>=\''(X0,X2) ) ).
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_10,axiom,
! [X0,X1,X2] :
( '\'>=\''(X0,X1)
=> '\'>=\''('\'==>\''(X1,X2),'\'==>\''(X0,X2)) ) ).
fof(sos_12,axiom,
! [X0] : '\'+\''(X0,'\'1\'') = '\'1\'' ).
fof(sos_13,axiom,
! [X0] : '\'==>\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X0) = '\'0\'' ).
fof(goals_14,conjecture,
! [X0] : '\'+\''(X0,X0) = X0 ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : '\'+\''(X0,X0) = X0,
inference(negate_conjecture,[status(cth)],[goals_14]) ).
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(c4,plain,
( '\'>=\''(X2,X1)
| ~ '\'>=\''(X2,X0)
| ~ '\'>=\''(X0,X1) ),
inference(clausification,[status(esa)],[sos_05]) ).
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(c10,plain,
( '\'>=\''('\'==>\''(X1,X2),'\'==>\''(X0,X2))
| ~ '\'>=\''(X0,X1) ),
inference(clausification,[status(esa)],[sos_10]) ).
cnf(c12,plain,
'\'+\''(X0,'\'1\'') = '\'1\'',
inference(clausification,[status(esa)],[sos_12]) ).
cnf(c13,plain,
'\'==>\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X0) = '\'0\'',
inference(clausification,[status(esa)],[sos_13]) ).
cnf(c14,plain,
'\'+\''(sK27,sK27) != sK27,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'\'+\''('\'0\'',X0) = X0,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
( ~ '\'>=\''('\'+\''(X1,X2),'\'+\''(X0,X2))
| '\'+\''(X1,X2) = '\'+\''(X0,X2)
| ~ '\'>=\''(X0,X1) ),
inference(resolution,[status(thm)],[c9,c5]) ).
cnf(d2,plain,
X0 = '\'+\''('\'0\'',X0),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d3,plain,
( ~ '\'>=\''(X1,'\'0\'')
| '\'+\''('\'0\'',X0) = '\'+\''(X1,X0)
| ~ '\'>=\''(X0,'\'+\''(X1,X0)) ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ '\'>=\''(X0,'\'+\''(X1,X0))
| ~ '\'>=\''(X1,'\'0\'')
| X0 = '\'+\''(X1,X0) ),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ '\'>=\''(X0,'\'+\''(X1,X0))
| X0 = '\'+\''(X1,X0) ),
inference(resolution,[status(thm)],[c8,d4]) ).
cnf(d6,plain,
'\'>=\''('\'+\''(X0,'\'==>\''(X0,X1)),X1),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d7,plain,
'\'>=\''(X0,'\'==>\''(X1,'\'+\''(X1,X0))),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d8,plain,
'\'>=\''(X1,'\'==>\''(X0,'\'+\''(X1,X0))),
inference(superposition,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
X0 = '\'+\''(X0,'\'0\''),
inference(superposition,[status(thm)],[d0,c1]) ).
cnf(d10,plain,
( '\'>=\''('\'0\'','\'==>\''(X0,X1))
| ~ '\'>=\''(X0,X1) ),
inference(superposition,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( ~ '\'>=\''('\'==>\''(X0,X1),'\'0\'')
| '\'==>\''(X0,X1) = '\'0\''
| ~ '\'>=\''(X0,X1) ),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
( ~ '\'>=\''(X0,X1)
| '\'==>\''(X0,X1) = '\'0\'' ),
inference(resolution,[status(thm)],[c8,d11]) ).
cnf(d13,plain,
'\'==>\''(X0,'\'==>\''(X1,'\'+\''(X0,X1))) = '\'0\'',
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ '\'>=\''(X1,'\'0\'')
| '\'>=\''('\'+\''(X1,X0),X0) ),
inference(superposition,[status(thm)],[d2,c9]) ).
cnf(d15,plain,
'\'>=\''('\'+\''(X0,X1),X1),
inference(resolution,[status(thm)],[c8,d14]) ).
cnf(d16,plain,
'\'>=\''(X0,'\'==>\''(X1,X0)),
inference(resolution,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
( ~ '\'>=\''('\'==>\''(X0,X1),X1)
| '\'==>\''(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( '\'>=\''(X2,'\'==>\''('\'+\''(X0,X1),X3))
| ~ '\'>=\''('\'+\''(X0,'\'+\''(X1,X2)),X3) ),
inference(superposition,[status(thm)],[c0,c6]) ).
cnf(d19,plain,
'\'1\'' = '\'+\''('\'1\'',X0),
inference(superposition,[status(thm)],[c12,c1]) ).
cnf(d20,plain,
'\'>=\''('\'1\'',X0),
inference(superposition,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
( ~ '\'>=\''(X0,'\'1\'')
| X0 = '\'1\'' ),
inference(resolution,[status(thm)],[d20,c5]) ).
cnf(d22,plain,
'\'+\''(X0,'\'==>\''(X0,'\'1\'')) = '\'1\'',
inference(resolution,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
( '\'>=\''('\'==>\''(X0,'\'1\''),'\'==>\''('\'+\''(X1,X0),X2))
| ~ '\'>=\''('\'+\''(X1,'\'1\''),X2) ),
inference(superposition,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
( '\'>=\''('\'==>\''(X2,'\'1\''),'\'==>\''('\'+\''(X0,X2),X1))
| ~ '\'>=\''('\'1\'',X1) ),
inference(demodulation,[status(thm)],[d23,c12]) ).
cnf(d25,plain,
'\'>=\''('\'==>\''(X0,'\'1\''),'\'==>\''('\'+\''(X1,X0),X2)),
inference(resolution,[status(thm)],[d20,d24]) ).
cnf(d26,plain,
'\'>=\''('\'==>\''(X0,'\'1\''),'\'==>\''(X0,X1)),
inference(superposition,[status(thm)],[d2,d25]) ).
cnf(d27,plain,
( '\'>=\''('\'==>\''(X1,X2),X3)
| ~ '\'>=\''('\'==>\''(X0,X2),X3)
| ~ '\'>=\''(X0,X1) ),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d28,plain,
( '\'>=\''('\'+\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X1),X0)
| ~ '\'>=\''(X1,'\'0\'') ),
inference(superposition,[status(thm)],[c13,c7]) ).
cnf(d29,plain,
'\'>=\''('\'+\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X1),X0),
inference(resolution,[status(thm)],[c8,d28]) ).
cnf(d30,plain,
'\'>=\''('\'==>\''('\'==>\''(X0,'\'1\''),X0),X0),
inference(superposition,[status(thm)],[d9,d29]) ).
cnf(d31,plain,
( '\'>=\''('\'==>\''(X1,X0),X0)
| ~ '\'>=\''('\'==>\''(X0,'\'1\''),X1) ),
inference(resolution,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
'\'>=\''('\'==>\''('\'==>\''(X0,X1),X0),X0),
inference(resolution,[status(thm)],[d31,d26]) ).
cnf(d33,plain,
'\'==>\''('\'==>\''(X0,X1),X0) = X0,
inference(resolution,[status(thm)],[d32,d17]) ).
cnf(d34,plain,
'\'==>\''(X0,'\'==>\''(X0,X1)) = '\'==>\''(X0,X1),
inference(superposition,[status(thm)],[d33,d33]) ).
cnf(d35,plain,
'\'==>\''(X0,'\'+\''(X0,X0)) = '\'0\'',
inference(superposition,[status(thm)],[d34,d13]) ).
cnf(d36,plain,
'\'>=\''('\'+\''(X0,'\'0\''),'\'+\''(X0,X0)),
inference(superposition,[status(thm)],[d35,d6]) ).
cnf(d37,plain,
'\'>=\''(X0,'\'+\''(X0,X0)),
inference(demodulation,[status(thm)],[d36,c2]) ).
cnf(d38,plain,
X0 = '\'+\''(X0,X0),
inference(resolution,[status(thm)],[d37,d5]) ).
cnf(d39,plain,
sK27 != sK27,
inference(demodulation,[status(thm)],[c14,d38]) ).
cnf(d40,plain,
'\'>=\''(X0,'\'==>\''('\'0\'',X0)),
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d41,plain,
( ~ '\'>=\''('\'==>\''('\'0\'',X0),X0)
| '\'==>\''('\'0\'',X0) = X0 ),
inference(resolution,[status(thm)],[d40,c5]) ).
cnf(d42,plain,
'\'>=\''('\'==>\''('\'0\'',X0),X0),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d43,plain,
'\'==>\''('\'0\'',X0) = X0,
inference(resolution,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
( ~ '\'>=\''(X0,'\'==>\''('\'0\'',X0))
| X0 = '\'==>\''('\'0\'',X0) ),
inference(resolution,[status(thm)],[d42,c5]) ).
cnf(d45,plain,
( ~ '\'>=\''(X0,'\'==>\''('\'0\'',X0))
| X0 = X0 ),
inference(demodulation,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
( ~ '\'>=\''(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d45,d43]) ).
cnf(d47,plain,
X0 = X0,
inference(resolution,[status(thm)],[c3,d46]) ).
cnf(d48,plain,
$false,
inference(resolution,[status(thm)],[d47,d39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL903+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
% 0.08/0.35 % Computer : n014.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 : Fri Sep 25 23:47:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 137.64/35.74 % SZS status Theorem for theBenchmark.p
% 137.64/35.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------