%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL896+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 : n008.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 07:55:39 AM UTC 2026
% Result : Theorem 157.66s 44.31s
% Output : CNFRefutation 157.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 52 unt; 0 def)
% Number of atoms : 84 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 14 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 10 ( 2 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 : 152 ( 12 sgn 20 !; 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_12,axiom,
! [X0,X1,X2] : '\'+\''('\'+\''(X0,'\'==>\''(X0,X1)),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2)) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))) ).
fof(goals_13,conjecture,
! [X0,X1] : '\'+\''(X0,'\'==>\''(X0,X1)) = '\'+\''(X1,'\'==>\''(X1,X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : '\'+\''(X0,'\'==>\''(X0,X1)) = '\'+\''(X1,'\'==>\''(X1,X0)),
inference(negate_conjecture,[status(cth)],[goals_13]) ).
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(c12,plain,
'\'+\''('\'+\''(X0,'\'==>\''(X0,X1)),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2)) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))),
inference(clausification,[status(esa)],[sos_12]) ).
cnf(c13,plain,
'\'+\''(sK28,'\'==>\''(sK28,sK29)) != '\'+\''(sK29,'\'==>\''(sK29,sK28)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2))) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))),
inference(demodulation,[status(thm)],[c12,c0]) ).
cnf(d1,plain,
( ~ '\'>=\''('\'0\'',X0)
| X0 = '\'0\'' ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d2,plain,
'\'>=\''(X0,'\'==>\''(X1,'\'+\''(X1,X0))),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d3,plain,
'\'>=\''('\'0\'','\'==>\''(X0,X0)),
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
'\'==>\''(X0,X0) = '\'0\'',
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( '\'>=\''('\'+\''(X0,X1),X0)
| ~ '\'>=\''(X1,'\'0\'') ),
inference(superposition,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
'\'>=\''('\'+\''(X0,X1),X0),
inference(resolution,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
'\'>=\''('\'+\''(X1,X0),X0),
inference(superposition,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
'\'>=\''('\'+\''(X0,'\'+\''(X1,X2)),X2),
inference(superposition,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
'\'>=\''('\'+\''('\'+\''(X1,X2),X0),X2),
inference(superposition,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
'\'>=\''('\'+\''(X0,'\'+\''(X1,X2)),X1),
inference(demodulation,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( '\'>=\''(X1,'\'==>\''(X0,X2))
| ~ '\'>=\''('\'+\''(X1,X0),X2) ),
inference(superposition,[status(thm)],[c1,c6]) ).
cnf(d12,plain,
'\'>=\''(X0,'\'==>\''('\'+\''(X1,X2),X1)),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
'\'==>\''('\'+\''(X0,X1),X0) = '\'0\'',
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'0\'')) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),
inference(superposition,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
'\'+\''(X0,'\'==>\''(X0,X1)) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),
inference(demodulation,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'\'+\''('\'0\'',X0) = X0,
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d17,plain,
'\'+\''('\'+\''(X1,X0),X2) = '\'+\''(X0,'\'+\''(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d18,plain,
'\'+\''(X1,'\'+\''(X0,X2)) = '\'+\''(X0,'\'+\''(X1,X2)),
inference(superposition,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
'\'+\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))),X3) = '\'+\''(X0,'\'+\''('\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2)),X3)),
inference(superposition,[status(thm)],[d0,c0]) ).
cnf(d20,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2))),X3)) = '\'+\''(X0,'\'+\''('\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2)),X3)),
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2))),X3)) = '\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'+\''('\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2),X3))),
inference(demodulation,[status(thm)],[d20,c0]) ).
cnf(d22,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0))),X2)) = '\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'+\''('\'0\'',X2))),
inference(superposition,[status(thm)],[d13,d21]) ).
cnf(d23,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0))),X2)) = '\'+\''(X0,'\'+\''('\'0\'','\'+\''('\'==>\''(X0,X1),X2))),
inference(demodulation,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0))),X2)) = '\'+\''(X0,'\'+\''('\'==>\''(X0,X1),X2)),
inference(demodulation,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'0\'')) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))))),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d26,plain,
'\'+\''(X0,'\'==>\''(X0,X1)) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))))),
inference(demodulation,[status(thm)],[d25,c2]) ).
cnf(d27,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1))))),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2))) = '\'+\''(X0,'\'==>\''(X0,'\'+\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),'\'==>\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),X2)))),
inference(superposition,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
'\'+\''(X1,'\'+\''('\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1))),'\'==>\''('\'+\''(X1,'\'==>\''(X1,X0)),X2))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),'\'==>\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),X2)))),
inference(demodulation,[status(thm)],[d27,d15]) ).
cnf(d29,plain,
'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2))) = '\'+\''(X0,'\'==>\''(X0,'\'+\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),'\'==>\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),X2)))),
inference(demodulation,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
'\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))) = '\'+\''(X0,'\'==>\''(X0,'\'+\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),'\'==>\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),X2)))),
inference(demodulation,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X2)))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'+\''('\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0))),'\'==>\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),X2))))),
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X2)))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),X2))))),
inference(demodulation,[status(thm)],[d31,d24]) ).
cnf(d33,plain,
'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X2)))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'+\''('\'==>\''(X0,X1),'\'==>\''('\'+\''(X0,'\'==>\''(X0,X1)),X2))))),
inference(demodulation,[status(thm)],[d32,d15]) ).
cnf(d34,plain,
'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X2)))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X2)))))),
inference(demodulation,[status(thm)],[d33,d0]) ).
cnf(d35,plain,
'\'>=\''('\'+\''(X0,'\'==>\''(X0,X1)),X1),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d36,plain,
( ~ '\'>=\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))
| '\'+\''(X0,'\'==>\''(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[d35,c5]) ).
cnf(d37,plain,
( '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1))))
| ~ '\'>=\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),'\'+\''(X0,'\'==>\''(X0,X1))) ),
inference(superposition,[status(thm)],[d26,d36]) ).
cnf(d38,plain,
( ~ '\'>=\''('\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))),'\'+\''(X0,'\'==>\''(X0,X1)))
| '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X1)))) = '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1)))) ),
inference(demodulation,[status(thm)],[d37,d34]) ).
cnf(d39,plain,
( ~ '\'>=\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),'\'+\''(X1,'\'==>\''(X1,X0)))
| '\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'0\''))) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))) ),
inference(demodulation,[status(thm)],[d38,d4]) ).
cnf(d40,plain,
( ~ '\'>=\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),'\'+\''(X1,'\'==>\''(X1,X0)))
| '\'+\''(X1,'\'==>\''(X1,X0)) = '\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))) ),
inference(demodulation,[status(thm)],[d39,c2]) ).
cnf(d41,plain,
( ~ '\'>=\''('\'+\''(X0,'\'==>\''(X0,'\'+\''(X1,'\'==>\''(X1,X0)))),'\'+\''(X1,'\'==>\''(X1,X0)))
| '\'+\''(X1,'\'==>\''(X1,X0)) = '\'+\''(X0,'\'==>\''(X0,X1)) ),
inference(demodulation,[status(thm)],[d40,d15]) ).
cnf(d42,plain,
( ~ '\'>=\''('\'+\''(X0,'\'==>\''(X0,X1)),'\'+\''(X1,'\'==>\''(X1,X0)))
| '\'+\''(X1,'\'==>\''(X1,X0)) = '\'+\''(X0,'\'==>\''(X0,X1)) ),
inference(demodulation,[status(thm)],[d41,d15]) ).
cnf(d43,plain,
'\'>=\''('\'+\''(X0,'\'==>\''(X0,X1)),'\'+\''(X1,'\'==>\''(X1,'\'+\''(X0,'\'==>\''(X0,X1))))),
inference(superposition,[status(thm)],[d26,d35]) ).
cnf(d44,plain,
'\'>=\''('\'+\''(X1,'\'==>\''(X1,X0)),'\'+\''(X0,'\'==>\''(X0,X1))),
inference(demodulation,[status(thm)],[d43,d15]) ).
cnf(d45,plain,
'\'+\''(X0,'\'==>\''(X0,X1)) = '\'+\''(X1,'\'==>\''(X1,X0)),
inference(resolution,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
$false,
inference(resolution,[status(thm)],[d45,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL896+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 23:47:39 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 157.66/44.31 % SZS status Theorem for theBenchmark.p
% 157.66/44.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------