%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL102-2 : 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 : n004.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 06:56:56 AM UTC 2026
% Result : Unsatisfiable 10.99s 2.86s
% Output : CNFRefutation 10.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 15 RR)
% Number of literals : 27 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('c$uPair'('v$uy','v$uza','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),'c$uComb$uOcomb$uOop$uA$uD$uD'('v$uy','v$uz'),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(cls_conjecture_3,negated_conjecture,
~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),'c$uComb$uOcomb$uOop$uA$uD$uD'('v$uza','v$uz'),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(cls_Comb_Ocontract_OAp1_0,axiom,
( 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X2),'c$uComb$uOcomb$uOop$uA$uD$uD'(X1,X2),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'(X0,X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Transitive__Closure_Or__into__rtrancl_0,axiom,
( 'c$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(c0,plain,
'c$uin'('c$uPair'('v$uy','v$uza','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c1,plain,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),'c$uComb$uOcomb$uOop$uA$uD$uD'('v$uy','v$uz'),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c2,plain,
~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),'c$uComb$uOcomb$uOop$uA$uD$uD'('v$uza','v$uz'),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c3,plain,
( 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X2),'c$uComb$uOcomb$uOop$uA$uD$uD'(X1,X2),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'(X0,X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(clausification,[status(esa)],[cls_Comb_Ocontract_OAp1_0]) ).
cnf(c4,plain,
( 'c$uin'(X0,'c$uTransitive$u$uClosure$uOrtrancl'(X1,X2),'tc$uprod'(X2,X2))
| ~ 'c$uin'(X0,X1,'tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Transitive__Closure_Or__into__rtrancl_0]) ).
cnf(c5,plain,
( 'c$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(d0,plain,
( 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$uy','v$uz'),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$uy','v$uz'),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$ux','v$uz'),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uTransitive$u$uClosure$uOrtrancl'('c$uComb$uOcontract','tc$uComb$uOcomb'),'tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$uy','v$uz'),'c$uComb$uOcomb$uOop$uA$uD$uD'('v$uza','v$uz'),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
~ 'c$uin'('c$uPair'('v$uy','v$uza','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c0,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL102-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:15:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.99/2.86 % SZS status Unsatisfiable for theBenchmark.p
% 10.99/2.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------