%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL106-2 : 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 : n019.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 06:56:57 AM UTC 2026
% Result : Unsatisfiable 68.01s 11.76s
% Output : CNFRefutation 68.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of clauses : 48 ( 11 unt; 24 nHn; 43 RR)
% Number of literals : 133 ( 99 equ; 30 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 64 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya'),'v$uxb','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('v$uxb',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Comb_OAp__parcontractE_0,axiom,
( X2 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'(X0,X1,X2),'v$usko$u$uuTH'(X0,X1,X2))
| X0 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'(X0,X1,X2)),'v$usko$u$uuTG'(X0,X1,X2))
| X0 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2)
| X2 = 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1)
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Comb_OAp__parcontractE_2,axiom,
( X0 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'(X0,X1,X2)),'v$usko$u$uuTG'(X0,X1,X2))
| X0 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2)
| X2 = 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1)
| 'c$uin'('c$uPair'(X0,'v$usko$u$uuTI'(X0,X1,X2),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Comb_Ocomb_Odistinct__3__iff1_0,axiom,
'c$uComb$uOcomb$uOK' != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_0,axiom,
( X0 = X2
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X2,X3) ) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_1,axiom,
( X1 = X3
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X2,X3) ) ).
cnf(cls_Comb_OK1__parcontractD__dest_0,axiom,
( X1 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'(X0,X1))
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Comb_OK1__parcontractD__dest_1,axiom,
( 'c$uin'('c$uPair'(X0,'v$usko$u$uuTE'(X0,X1),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ) ).
cnf(cls_Comb_Oparcontract_Ointros__1_0,axiom,
'c$uin'('c$uPair'(X0,X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(cls_Comb_Oparcontract_Ointros__2_0,axiom,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ).
cnf(c0,plain,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya'),'v$uxb','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('v$uxb',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2) = X0
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) = X2
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'(X0,X1,X2),'v$usko$u$uuTH'(X0,X1,X2)) = X2
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'(X0,X1,X2)),'v$usko$u$uuTG'(X0,X1,X2)) = X0 ),
inference(clausification,[status(esa)],[cls_Comb_OAp__parcontractE_0]) ).
cnf(c3,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2) = X0
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) = X2
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uin'('c$uPair'(X0,'v$usko$u$uuTI'(X0,X1,X2),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'(X0,X1,X2)),'v$usko$u$uuTG'(X0,X1,X2)) = X0 ),
inference(clausification,[status(esa)],[cls_Comb_OAp__parcontractE_2]) ).
cnf(c4,plain,
'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOK',
inference(clausification,[status(esa)],[cls_Comb_Ocomb_Odistinct__3__iff1_0]) ).
cnf(c5,plain,
( X0 = X2
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X2,X3) ),
inference(clausification,[status(esa)],[cls_Comb_Ocomb_Oinject__iff1_0]) ).
cnf(c6,plain,
( X1 = X3
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X2,X3) ),
inference(clausification,[status(esa)],[cls_Comb_Ocomb_Oinject__iff1_1]) ).
cnf(c7,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'(X0,X1)) = X1
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(clausification,[status(esa)],[cls_Comb_OK1__parcontractD__dest_0]) ).
cnf(c8,plain,
( 'c$uin'('c$uPair'(X0,'v$usko$u$uuTE'(X0,X1),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(clausification,[status(esa)],[cls_Comb_OK1__parcontractD__dest_1]) ).
cnf(c9,plain,
'c$uin'('c$uPair'(X0,X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_Comb_Oparcontract_Ointros__1_0]) ).
cnf(c10,plain,
'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1),X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')),
inference(clausification,[status(esa)],[cls_Comb_Oparcontract_Ointros__2_0]) ).
cnf(d0,plain,
( ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0)
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0)
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1) = X2
| 'c$uin'('c$uPair'(X0,'v$usko$u$uuTE'(X0,'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d1,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'(X0,'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2))) = 'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)
| ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1),X2,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X2) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0)
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1,X2)) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0)
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK',X0),X1) = X2 ),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d2,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'))) = 'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'))) = 'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = X0
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux') != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) ),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOK'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'))) = 'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'))) = 'v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[c4,d4]) ).
cnf(d6,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'),X0),'v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(superposition,[status(thm)],[d5,c10]) ).
cnf(d7,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'),'v$usko$u$uuTH'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d8,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'),'v$usko$u$uuTH'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = X0
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux') != 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) ),
inference(superposition,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOK'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'),'v$usko$u$uuTH'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'),'v$usko$u$uuTH'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[c4,d9]) ).
cnf(d11,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uin'('c$uPair'('v$uxb','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( ~ 'c$uin'('c$uPair'('v$ux','v$usko$u$uuTE'('v$ux','v$usko$u$uuTI'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
( ~ 'c$uin'('c$uPair'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya'),'v$uxb','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')),'v$usko$u$uuTG'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(resolution,[status(thm)],[c0,d13]) ).
cnf(d15,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| X0 = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux') ),
inference(superposition,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOK' = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOS','v$usko$u$uuTF'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya','v$uxb')) ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb'
| 'c$uComb$uOcomb$uOK' != 'c$uComb$uOcomb$uOK' ),
inference(superposition,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),'v$uya') = 'v$uxb' ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux')
| 'c$uin'('c$uPair'('v$uxb','v$ux','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(superposition,[status(thm)],[d18,c10]) ).
cnf(d20,plain,
( ~ 'c$uin'('c$uPair'('v$ux','v$ux','tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux') ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$uxb') = 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux'),
inference(resolution,[status(thm)],[c9,d20]) ).
cnf(d22,plain,
( X1 = 'v$uxb'
| 'c$uComb$uOcomb$uOop$uA$uD$uD'(X0,X1) != 'c$uComb$uOcomb$uOop$uA$uD$uD'('c$uComb$uOcomb$uOK','v$ux') ),
inference(superposition,[status(thm)],[d21,c6]) ).
cnf(d23,plain,
'v$ux' = 'v$uxb',
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
( ~ 'c$uin'('c$uPair'('v$ux',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb'))
| ~ 'c$uin'('c$uPair'('v$ux',X0,'tc$uComb$uOcomb','tc$uComb$uOcomb'),'c$uComb$uOparcontract','tc$uprod'('tc$uComb$uOcomb','tc$uComb$uOcomb')) ),
inference(demodulation,[status(thm)],[c1,d23]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 23:16:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.01/11.76 % SZS status Unsatisfiable for theBenchmark.p
% 68.01/11.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------