%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 06:57:00 AM UTC 2026
% Result : Unsatisfiable 20.81s 5.81s
% Output : CNFRefutation 20.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 14 unt; 0 nHn; 33 RR)
% Number of literals : 64 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Comb_Odiamond__strip__lemmaE_0,axiom,
( 'c$uin'('c$uPair'(X3,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'(X0,X4,X3,X1),X1,X1),'c$uTransitive$u$uClosure$uOrtrancl'(X0,X1),'tc$uprod'(X1,X1))
| ~ 'c$uin'('c$uPair'(X2,X4,X1,X1),'c$uTransitive$u$uClosure$uOrtrancl'(X0,X1),'tc$uprod'(X1,X1))
| ~ 'c$uin'('c$uPair'(X2,X3,X1,X1),X0,'tc$uprod'(X1,X1))
| ~ 'c$uComb$uOdiamond'(X0,X1) ) ).
cnf(cls_Comb_Odiamond__strip__lemmaE_1,axiom,
( 'c$uin'('c$uPair'(X4,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'(X0,X4,X3,X1),X1,X1),X0,'tc$uprod'(X1,X1))
| ~ 'c$uin'('c$uPair'(X2,X4,X1,X1),'c$uTransitive$u$uClosure$uOrtrancl'(X0,X1),'tc$uprod'(X1,X1))
| ~ 'c$uin'('c$uPair'(X2,X3,X1,X1),X0,'tc$uprod'(X1,X1))
| ~ 'c$uComb$uOdiamond'(X0,X1) ) ).
cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
( 'c$uin'(X0,'c$uTransitive$u$uClosure$uOrtrancl'(X1,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'(X0,X1,'tc$uprod'(X2,X2)) ) ).
cnf(cls_Transitive__Closure_Ortrancl__trans_0,axiom,
( 'c$uin'('c$uPair'(X4,X1,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X4,X0,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uComb$uOdiamond'('v$ur','t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uPair'('v$uya','v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ).
cnf(cls_conjecture_3,negated_conjecture,
'c$uin'('c$uPair'('v$uy','v$uxaa','t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$uy',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'('v$uya','v$ux'(X0),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$uy',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$ux'(X0),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$uz',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uxaa',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ) ).
cnf(c0,plain,
( 'c$uin'('c$uPair'(X4,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'(X3,X1,X4,X2),X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X4,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uComb$uOdiamond'(X3,X2)
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Comb_Odiamond__strip__lemmaE_0]) ).
cnf(c1,plain,
( 'c$uin'('c$uPair'(X1,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'(X3,X1,X4,X2),X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X4,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uComb$uOdiamond'(X3,X2)
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Comb_Odiamond__strip__lemmaE_1]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uTransitive$u$uClosure$uOrtrancl'(X1,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'(X0,X1,'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Transitive__Closure_Or__into__rtrancl_0]) ).
cnf(c3,plain,
( 'c$uin'('c$uPair'(X0,X4,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X1,X4,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTransitive$u$uClosure$uOrtrancl'(X3,X2),'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Transitive__Closure_Ortrancl__trans_0]) ).
cnf(c4,plain,
'c$uComb$uOdiamond'('v$ur','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c5,plain,
'c$uin'('c$uPair'('v$uya','v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
'c$uin'('c$uPair'('v$uy','v$uxaa','t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c7,plain,
( ~ 'c$uin'('c$uPair'('v$uy',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'('v$uya','v$ux'(X0),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c8,plain,
( ~ 'c$uin'('c$uPair'('v$uy',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$ux'(X0),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c9,plain,
( ~ 'c$uin'('c$uPair'('v$uz',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uxaa',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_6]) ).
cnf(d0,plain,
'c$uin'('c$uPair'('v$uxaa','v$ux'('v$uxaa'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d1,plain,
'c$uin'('c$uPair'('v$uya','v$ux'('v$uxaa'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d2,plain,
( ~ 'c$uComb$uOdiamond'('v$ur','t$ua')
| ~ 'c$uin'('c$uPair'('v$uya',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur',X0,'v$uz','t$ua'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c1,c5]) ).
cnf(d3,plain,
( ~ 'c$uin'('c$uPair'('v$uya',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur',X0,'v$uz','t$ua'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
'c$uin'('c$uPair'('v$ux'('v$uxaa'),'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'c$uin'('c$uPair'('v$ux'('v$uxaa'),'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ 'c$uin'('c$uPair'(X0,'v$ux'('v$uxaa'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
'c$uin'('c$uPair'('v$uxaa','c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( ~ 'c$uComb$uOdiamond'('v$ur','t$ua')
| ~ 'c$uin'('c$uPair'('v$uya',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'('v$uz','c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur',X0,'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d9,plain,
( 'c$uin'('c$uPair'('v$uz','c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur',X0,'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uya',X0,'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c4,d8]) ).
cnf(d10,plain,
'c$uin'('c$uPair'('v$uz','c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
~ 'c$uin'('c$uPair'('v$uxaa','c$uComb$uOdiamond$u$ustrip$u$ulemmaE$u$u1'('v$ur','v$ux'('v$uxaa'),'v$uz','t$ua'),'t$ua','t$ua'),'c$uTransitive$u$uClosure$uOrtrancl'('v$ur','t$ua'),'tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL121-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 % Computer : n017.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Sat Sep 26 23:12:49 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.81/5.81 % SZS status Unsatisfiable for theBenchmark.p
% 20.81/5.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------