%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT075-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:27:45 AM UTC 2026
% Result : Unsatisfiable 94.61s 12.56s
% Output : CNFRefutation 94.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 18 unt; 7 nHn; 18 RR)
% Number of literals : 62 ( 26 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 72 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_insert__absorb_0,axiom,
( ~ 'c$uin'(X0,X1,X2)
| 'c$uSet$uOinsert'(X0,X1,X2) = X1 ) ).
cnf(cls_insert__code_1,axiom,
hBOOL(hAPP('c$uSet$uOinsert'(X0,X1,X2),X0)) ).
cnf(cls_Domain__Id__on_0,axiom,
'c$uRelation$uODomain'('c$uRelation$uOId$u$uon'(X0,X1),X1,X1) = X0 ).
cnf(cls_sym__conv__converse__eq_0,axiom,
( ~ 'c$uRelation$uOsym'(X0,X1)
| 'c$uRelation$uOconverse'(X0,X1,X1) = X0 ) ).
cnf(cls_sym__Id__on_0,axiom,
'c$uRelation$uOsym'('c$uRelation$uOId$u$uon'(X0,X1),X1) ).
cnf(cls_Range__converse_0,axiom,
'c$uRelation$uORange'('c$uRelation$uOconverse'(X0,X1,X2),X2,X1) = 'c$uRelation$uODomain'(X0,X1,X2) ).
cnf(cls_Range__Id__on_0,axiom,
'c$uRelation$uORange'('c$uRelation$uOId$u$uon'(X0,X1),X1,X1) = X0 ).
cnf(cls_complete__Lin_1,axiom,
( X0 = X1
| 'c$uin'('c$uPair'(X0,X1,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ) ).
cnf(cls_complete__Lin_0,axiom,
( X0 = X1
| 'c$uin'('v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')) ) ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X1,X0))
| 'c$uin'(X0,X1,X2) ) ).
cnf(cls_that_0,axiom,
( ~ 'c$uin'('c$uPair'('v$ub','v$ua','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),X0,'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'(X0,'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))
| 'v$uthesis' ) ).
cnf(cls_CHAINED_0,axiom,
'v$ua' != 'v$ub' ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'v$uthesis' ).
cnf(c115,plain,
( ~ 'c$uin'(X0,X1,X2)
| 'c$uSet$uOinsert'(X0,X1,X2) = X1 ),
inference(clausification,[status(esa)],[cls_insert__absorb_0]) ).
cnf(c187,plain,
hBOOL(hAPP('c$uSet$uOinsert'(X0,X1,X2),X0)),
inference(clausification,[status(esa)],[cls_insert__code_1]) ).
cnf(c399,plain,
'c$uRelation$uODomain'('c$uRelation$uOId$u$uon'(X0,X1),X1,X1) = X0,
inference(clausification,[status(esa)],[cls_Domain__Id__on_0]) ).
cnf(c400,plain,
( ~ 'c$uRelation$uOsym'(X0,X1)
| 'c$uRelation$uOconverse'(X0,X1,X1) = X0 ),
inference(clausification,[status(esa)],[cls_sym__conv__converse__eq_0]) ).
cnf(c404,plain,
'c$uRelation$uOsym'('c$uRelation$uOId$u$uon'(X0,X1),X1),
inference(clausification,[status(esa)],[cls_sym__Id__on_0]) ).
cnf(c415,plain,
'c$uRelation$uORange'('c$uRelation$uOconverse'(X0,X1,X2),X2,X1) = 'c$uRelation$uODomain'(X0,X1,X2),
inference(clausification,[status(esa)],[cls_Range__converse_0]) ).
cnf(c416,plain,
'c$uRelation$uORange'('c$uRelation$uOId$u$uon'(X0,X1),X1,X1) = X0,
inference(clausification,[status(esa)],[cls_Range__Id__on_0]) ).
cnf(c458,plain,
( X0 = X1
| 'c$uin'('c$uPair'(X0,X1,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(clausification,[status(esa)],[cls_complete__Lin_1]) ).
cnf(c459,plain,
( X0 = X1
| 'c$uin'('v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')) ),
inference(clausification,[status(esa)],[cls_complete__Lin_0]) ).
cnf(c522,plain,
( ~ hBOOL(hAPP(X1,X0))
| 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_mem__def_1]) ).
cnf(c524,plain,
( ~ 'c$uin'('c$uPair'('v$ub','v$ua','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),X0,'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'(X0,'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool'))
| 'v$uthesis' ),
inference(clausification,[status(esa)],[cls_that_0]) ).
cnf(c526,plain,
'v$ua' != 'v$ub',
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c527,plain,
~ 'v$uthesis',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
'c$uin'(X0,'c$uSet$uOinsert'(X0,X1,X2),X3),
inference(resolution,[status(thm)],[c522,c187]) ).
cnf(d1,plain,
( ~ 'c$uin'(X0,X1,X2)
| 'c$uin'(X0,X1,X3) ),
inference(superposition,[status(thm)],[c115,d0]) ).
cnf(d2,plain,
( 'c$uin'('v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),'c$uArrow$u$uOrder$u$uMirabelle$uOLin',X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[c459,d1]) ).
cnf(d3,plain,
( 'c$uin'('c$uPair'(X0,X1,'tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'(X0,X1),X2)
| X0 = X1 ),
inference(resolution,[status(thm)],[c458,d1]) ).
cnf(d4,plain,
( ~ 'c$uin'('c$uPair'('v$ub','v$ua','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),X0,'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'(X0,'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')) ),
inference(resolution,[status(thm)],[c527,c524]) ).
cnf(d5,plain,
( 'v$ub' = 'v$ua'
| ~ 'c$uin'('v$usko$u$uArrow$u$uOrder$u$uMirabelle$u$uXcomplete$u$uLin$u$u1'('v$ub','v$ua'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$ubool')) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( 'v$ub' = 'v$ua'
| 'v$ub' = 'v$ua' ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
'v$ub' != 'v$ub',
inference(demodulation,[status(thm)],[c526,d6]) ).
cnf(d8,plain,
( ~ 'c$uRelation$uOsym'(X0,X1)
| 'c$uRelation$uORange'(X0,X1,X1) = 'c$uRelation$uODomain'(X0,X1,X1) ),
inference(superposition,[status(thm)],[c400,c415]) ).
cnf(d9,plain,
( ~ 'c$uRelation$uOsym'('c$uRelation$uOId$u$uon'(X0,X1),X1)
| 'c$uRelation$uODomain'('c$uRelation$uOId$u$uon'(X0,X1),X1,X1) = X0 ),
inference(superposition,[status(thm)],[d8,c416]) ).
cnf(d10,plain,
( ~ 'c$uRelation$uOsym'('c$uRelation$uOId$u$uon'(X0,X1),X1)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d9,c399]) ).
cnf(d11,plain,
X0 = X0,
inference(resolution,[status(thm)],[c404,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT075-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n020.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Sat Sep 26 06:26:19 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.10/0.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 94.61/12.56 % SZS status Unsatisfiable for theBenchmark.p
% 94.61/12.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------