%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL123-2 : 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 : n020.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 06:57:01 AM UTC 2026
% Result : Unsatisfiable 11.64s 11.88s
% Output : CNFRefutation 11.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 6 unt; 0 nHn; 27 RR)
% Number of literals : 60 ( 0 equ; 41 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uprod'(X2,X2)) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('c$uPair'('v$uy','v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uPair'('v$ux','v$uxb','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$uxaa'(X0),'t$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$ux',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'('v$uy','v$uxaa'(X0),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$uxb',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',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ 'c$uin'('c$uPair'(X1,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$uxa'(X1,X0,X2),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(cls_conjecture_7,negated_conjecture,
( ~ 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X1,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$uxa'(X1,X2,X0),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ) ).
cnf(c0,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(c1,plain,
( '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$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Transitive__Closure_Ortrancl__trans_0]) ).
cnf(c2,plain,
'c$uin'('c$uPair'('v$uy','v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c3,plain,
'c$uin'('c$uPair'('v$ux','v$uxb','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c4,plain,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'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_3]) ).
cnf(c5,plain,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'('v$uy','v$uxaa'(X0),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c6,plain,
( ~ 'c$uin'('c$uPair'('v$uxb',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',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c7,plain,
( ~ 'c$uin'('c$uPair'(X1,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$uxa'(X1,X0,X2),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_6]) ).
cnf(c8,plain,
( ~ 'c$uin'('c$uPair'(X1,X2,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X1,X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,'v$uxa'(X1,X2,X0),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_7]) ).
cnf(d0,plain,
( ~ 'c$uin'('c$uPair'(X4,X1,X2,X2),X3,'tc$uprod'(X2,X2))
| ~ 'c$uin'('c$uPair'(X0,X4,X2,X2),'c$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$uprod'(X2,X2)) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| 'c$uin'('c$uPair'(X0,X1,'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),X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ 'c$uin'('c$uPair'('v$uz',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uxaa'('v$uxb'),X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$ux','v$uxb','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ 'c$uin'('c$uPair'('v$uxaa'('v$uxb'),X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uz',X0,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
( ~ 'c$uin'('c$uPair'(X0,'v$uxaa'('v$uxb'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X0,X1,'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uz','v$uxa'(X0,'v$uxaa'('v$uxb'),X1),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( ~ 'c$uin'('c$uPair'(X0,'v$uxaa'('v$uxb'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X0,'v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X0,'v$uxaa'('v$uxb'),'t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'(X0,'v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( ~ 'c$uin'('c$uPair'('v$ux','v$uxb','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua'))
| ~ 'c$uin'('c$uPair'('v$uy','v$uz','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')) ),
inference(resolution,[status(thm)],[d5,c5]) ).
cnf(d7,plain,
~ 'c$uin'('c$uPair'('v$ux','v$uxb','t$ua','t$ua'),'v$ur','tc$uprod'('t$ua','t$ua')),
inference(resolution,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c3,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL123-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.37 % Computer : n020.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 23:18:14 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.64/11.88 % SZS status Unsatisfiable for theBenchmark.p
% 11.64/11.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------