%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT002-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 08:27:39 AM UTC 2026
% Result : Unsatisfiable 54.13s 31.09s
% Output : CNFRefutation 54.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 13 unt; 0 nHn; 20 RR)
% Number of literals : 35 ( 3 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 31 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_trancl__id_0,axiom,
( ~ 'c$uRelation$uOtrans'(X0,X1)
| 'c$uTransitive$u$uClosure$uOtrancl'(X0,X1) = X0 ) ).
cnf(cls_r__r__into__trancl_0,axiom,
( ~ hBOOL('c$uin'('c$uPair'(X0,X4,X2,X2),X3,'tc$uprod'(X2,X2)))
| ~ hBOOL('c$uin'('c$uPair'(X4,X1,X2,X2),X3,'tc$uprod'(X2,X2)))
| hBOOL('c$uin'('c$uPair'(X0,X1,X2,X2),'c$uTransitive$u$uClosure$uOtrancl'(X3,X2),'tc$uprod'(X2,X2))) ) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X1,X0))
| hBOOL('c$uin'(X0,X1,X2)) ) ).
cnf(cls_mem__def_0,axiom,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uRelation$uOtrans'('v$uL','tc$uArrow$u$uOrder$u$uMirabelle$uOalt') ).
cnf(cls_conjecture_2,negated_conjecture,
~ hBOOL('c$uin'('c$uPair'(X0,X0,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))) ).
cnf(cls_conjecture_3,negated_conjecture,
hBOOL('c$uin'('c$uPair'('v$uy','v$ux','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))) ).
cnf(cls_conjecture_4,negated_conjecture,
hBOOL('c$uin'('c$uPair'('v$ux','v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))) ).
cnf(c552,plain,
( ~ 'c$uRelation$uOtrans'(X0,X1)
| 'c$uTransitive$u$uClosure$uOtrancl'(X0,X1) = X0 ),
inference(clausification,[status(esa)],[cls_trancl__id_0]) ).
cnf(c614,plain,
( ~ hBOOL('c$uin'('c$uPair'(X4,X0,X2,X2),X3,'tc$uprod'(X2,X2)))
| hBOOL('c$uin'('c$uPair'(X4,X1,X2,X2),'c$uTransitive$u$uClosure$uOtrancl'(X3,X2),'tc$uprod'(X2,X2)))
| ~ hBOOL('c$uin'('c$uPair'(X0,X1,X2,X2),X3,'tc$uprod'(X2,X2))) ),
inference(clausification,[status(esa)],[cls_r__r__into__trancl_0]) ).
cnf(c647,plain,
( ~ hBOOL(hAPP(X1,X0))
| hBOOL('c$uin'(X0,X1,X2)) ),
inference(clausification,[status(esa)],[cls_mem__def_1]) ).
cnf(c648,plain,
( ~ hBOOL('c$uin'(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_mem__def_0]) ).
cnf(c650,plain,
'c$uRelation$uOtrans'('v$uL','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c651,plain,
~ hBOOL('c$uin'('c$uPair'(X0,X0,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c652,plain,
hBOOL('c$uin'('c$uPair'('v$uy','v$ux','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c653,plain,
hBOOL('c$uin'('c$uPair'('v$ux','v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(d0,plain,
hBOOL(hAPP('v$uL','c$uPair'('v$ux','v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(resolution,[status(thm)],[c653,c648]) ).
cnf(d1,plain,
hBOOL('c$uin'('c$uPair'('v$ux','v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL',X0)),
inference(resolution,[status(thm)],[d0,c647]) ).
cnf(d2,plain,
'c$uTransitive$u$uClosure$uOtrancl'('v$uL','tc$uArrow$u$uOrder$u$uMirabelle$uOalt') = 'v$uL',
inference(resolution,[status(thm)],[c552,c650]) ).
cnf(d3,plain,
( ~ hBOOL('c$uin'('c$uPair'(X0,'v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')))
| hBOOL('c$uin'('c$uPair'(X0,'v$ux','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'c$uTransitive$u$uClosure$uOtrancl'('v$uL','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))) ),
inference(resolution,[status(thm)],[c652,c614]) ).
cnf(d4,plain,
( ~ hBOOL('c$uin'('c$uPair'(X0,'v$uy','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')))
| hBOOL('c$uin'('c$uPair'(X0,'v$ux','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))) ),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
hBOOL('c$uin'('c$uPair'('v$ux','v$ux','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uL','tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c651,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT002-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 26 06:17:35 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.13/31.09 % SZS status Unsatisfiable for theBenchmark.p
% 54.13/31.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------