%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT070-1 : 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 : n001.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 08:27:44 AM UTC 2026
% Result : Unsatisfiable 115.46s 17.18s
% Output : CNFRefutation 115.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 7 unt; 22 nHn; 38 RR)
% Number of literals : 143 ( 42 equ; 72 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 43 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_COMBK__def_0,axiom,
hAPP('c$uCOMBK'(X0,X1,X2),X3) = X0 ).
cnf(cls_mem__def_1,axiom,
( ~ hBOOL(hAPP(X1,X0))
| 'c$uin'(X0,X1,X2) ) ).
cnf(cls_mem__def_0,axiom,
( ~ 'c$uin'(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ) ).
cnf(cls_CHAINED_1,axiom,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ) ).
cnf(cls_CHAINED_0,axiom,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ) ).
cnf(cls_CHAINED_1_01,axiom,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ) ).
cnf(cls_CHAINED_0_02,axiom,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ) ).
cnf(cls_CHAINED_1_03,axiom,
( 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH' ) ).
cnf(cls_CHAINED_0_04,axiom,
( 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH' ) ).
cnf(cls_CHAINED_1_05,axiom,
( 'v$ua' = 'v$ub$uH'
| 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ) ).
cnf(cls_CHAINED_0_06,axiom,
( 'v$ua' = 'v$ub$uH'
| 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ) ).
cnf(c6,plain,
hAPP('c$uCOMBK'(X0,X1,X2),X3) = X0,
inference(clausification,[status(esa)],[cls_COMBK__def_0]) ).
cnf(c654,plain,
( ~ hBOOL(hAPP(X1,X0))
| 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_mem__def_1]) ).
cnf(c655,plain,
( ~ 'c$uin'(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(clausification,[status(esa)],[cls_mem__def_0]) ).
cnf(c656,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_1]) ).
cnf(c657,plain,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c658,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_1_01]) ).
cnf(c659,plain,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| 'v$ub' != 'v$ua$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_0_02]) ).
cnf(c660,plain,
( 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_1_03]) ).
cnf(c661,plain,
( 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH' ),
inference(clausification,[status(esa)],[cls_CHAINED_0_04]) ).
cnf(c662,plain,
( 'v$ua' = 'v$ub$uH'
| 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(clausification,[status(esa)],[cls_CHAINED_1_05]) ).
cnf(c663,plain,
( 'v$ua' = 'v$ub$uH'
| 'v$ub' = 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(clausification,[status(esa)],[cls_CHAINED_0_06]) ).
cnf(c664,plain,
( ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c665,plain,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(d0,plain,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ub' != 'v$ua$uH'
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ub' != 'v$ua$uH' ),
inference(resolution,[status(thm)],[c657,c659]) ).
cnf(d1,plain,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d0,c663]) ).
cnf(d2,plain,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d0,c661]) ).
cnf(d3,plain,
( 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ub' != 'v$ua$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ub' != 'v$ua$uH' ),
inference(resolution,[status(thm)],[c656,c658]) ).
cnf(d5,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' = 'v$ub$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d4,c662]) ).
cnf(d6,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'v$ua' != 'v$ub$uH'
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d4,c660]) ).
cnf(d7,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))
| ~ 'c$uin'('c$uPair'('v$ua$uH','v$ub$uH','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP$uH'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')) ),
inference(resolution,[status(thm)],[d7,c664]) ).
cnf(d9,plain,
~ 'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
( 'c$uin'(X3,'c$uCOMBK'(X0,X1,X2),X4)
| ~ hBOOL(X0) ),
inference(superposition,[status(thm)],[c6,c654]) ).
cnf(d11,plain,
( hBOOL(hAPP('c$uCOMBK'(X0,X1,X2),X3))
| ~ hBOOL(X0) ),
inference(resolution,[status(thm)],[d10,c655]) ).
cnf(d12,plain,
( hBOOL(X0)
| ~ hBOOL(X0) ),
inference(demodulation,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
( 'c$uin'(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(resolution,[status(thm)],[d12,c654]) ).
cnf(d14,plain,
( 'c$uin'(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(resolution,[status(thm)],[d12,d13]) ).
cnf(d15,plain,
( ~ 'c$uin'(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(resolution,[status(thm)],[d12,c655]) ).
cnf(d16,plain,
( ~ 'c$uin'(X1,X0,X2)
| hBOOL(hAPP(X0,X1)) ),
inference(resolution,[status(thm)],[d12,d15]) ).
cnf(d17,plain,
'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),'tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),
inference(resolution,[status(thm)],[d8,c665]) ).
cnf(d18,plain,
hBOOL(hAPP('v$uF'('v$uP'),'c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'))),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
'c$uin'('c$uPair'('v$ua','v$ub','tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$uF'('v$uP'),X0),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT070-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 06:30:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 115.46/17.18 % SZS status Unsatisfiable for theBenchmark.p
% 115.46/17.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------