%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT123+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:27:49 AM UTC 2026
% Result : Theorem 147.92s 26.78s
% Output : CNFRefutation 147.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 17 unt; 0 def)
% Number of atoms : 38 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 0 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-5 aty)
% Number of variables : 67 ( 26 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X1 = X0 ) ).
fof(fact_mem__def,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP('c$umember'(X2),X1),X0))
<=> hBOOL(hAPP(X0,X1)) ) ).
fof(fact_Prof__def,axiom,
'c$uArrow$u$uOrder$u$uMirabelle$uOProf' = 'c$uFuncSet$uOPi'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$uHOL$uObool')),'c$uCOMBK'('tc$ufun'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'tc$uHOL$uObool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi','c$uArrow$u$uOrder$u$uMirabelle$uOLin')) ).
fof(fact_funcsetI,axiom,
! [X0,X1,X2,X3,X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP('c$umember'(X4),X5),X3))
=> hBOOL(hAPP(hAPP('c$umember'(X2),hAPP(X1,X5)),X0)) )
=> hBOOL(hAPP(hAPP('c$umember'('tc$ufun'(X4,X2)),X1),'c$uFuncSet$uOPi'(X4,X2,X3,'c$uCOMBK'('tc$ufun'(X2,'tc$uHOL$uObool'),X4,X0)))) ) ).
fof(help_c__COMBK__1,axiom,
! [X0,X1,X2,X3] : hAPP('c$uCOMBK'(X3,X2,X1),X0) = X1 ).
fof(conj_0,hypothesis,
hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool')),'v$uL'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')) ).
fof(conj_1,conjecture,
hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'))),'c$uCOMBK'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi','v$uL')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'))),'c$uCOMBK'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi','v$uL')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')),
inference(negate_conjecture,[status(cth)],[conj_1]) ).
cnf(c0,plain,
( X0 = X1
| hAPP(X0,sK2(X0,X1)) != hAPP(X1,sK2(X0,X1)) ),
inference(clausification,[status(esa)],[fact_ext]) ).
cnf(c6,plain,
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c7,plain,
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP('c$umember'(X0),X1),X2)) ),
inference(clausification,[status(esa)],[fact_mem__def]) ).
cnf(c20,plain,
'c$uFuncSet$uOPi'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$uHOL$uObool')),'c$uCOMBK'('tc$ufun'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'tc$uHOL$uObool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi','c$uArrow$u$uOrder$u$uMirabelle$uOLin')) = 'c$uArrow$u$uOrder$u$uMirabelle$uOProf',
inference(clausification,[status(esa)],[fact_Prof__def]) ).
cnf(c22,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$ufun'(X4,X0)),X1),'c$uFuncSet$uOPi'(X4,X0,X3,'c$uCOMBK'('tc$ufun'(X0,'tc$uHOL$uObool'),X4,X2))))
| ~ hBOOL(hAPP(hAPP('c$umember'(X0),hAPP(X1,sK44(X2,X1,X0,X3,X4))),X2)) ),
inference(clausification,[status(esa)],[fact_funcsetI]) ).
cnf(c30,plain,
hAPP('c$uCOMBK'(X0,X1,X2),X3) = X2,
inference(clausification,[status(esa)],[help_c__COMBK__1]) ).
cnf(c31,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool')),'v$uL'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c32,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'))),'c$uCOMBK'('tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'tc$uArrow$u$uOrder$u$uMirabelle$uOindi','v$uL')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uOLin','v$uL')),
inference(resolution,[status(thm)],[c31,c6]) ).
cnf(d1,plain,
hBOOL(hAPP(hAPP('c$umember'(X0),'v$uL'),'c$uArrow$u$uOrder$u$uMirabelle$uOLin')),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$ufun'(X6,X4)),'c$uCOMBK'(X0,X1,X2)),'c$uFuncSet$uOPi'(X6,X4,X5,'c$uCOMBK'('tc$ufun'(X4,'tc$uHOL$uObool'),X6,X3))))
| ~ hBOOL(hAPP(hAPP('c$umember'(X4),X2),X3)) ),
inference(superposition,[status(thm)],[c30,c22]) ).
cnf(d3,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$ufun'(X0,X1)),'c$uCOMBK'(X2,X3,'v$uL')),'c$uFuncSet$uOPi'(X0,X1,X4,'c$uCOMBK'('tc$ufun'(X1,'tc$uHOL$uObool'),X0,'c$uArrow$u$uOrder$u$uMirabelle$uOLin')))),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( 'c$uCOMBK'(X0,X1,X2) = X3
| X2 != hAPP(X3,sK2('c$uCOMBK'(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c30,c0]) ).
cnf(d5,plain,
( 'c$uCOMBK'(X3,X4,X5) = 'c$uCOMBK'(X0,X1,X2)
| X5 != X2 ),
inference(superposition,[status(thm)],[c30,d4]) ).
cnf(d6,plain,
'c$uCOMBK'(X0,X1,X2) = 'c$uCOMBK'(X3,X4,X2),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
'c$uFuncSet$uOPi'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'),'c$uOrderings$uOtop$u$uclass$uOtop'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$uHOL$uObool')),'c$uCOMBK'(X0,X1,'c$uArrow$u$uOrder$u$uMirabelle$uOLin')) = 'c$uArrow$u$uOrder$u$uMirabelle$uOProf',
inference(superposition,[status(thm)],[d6,c20]) ).
cnf(d8,plain,
hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'))),'c$uCOMBK'(X0,X1,'v$uL')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')),
inference(superposition,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$ufun'('tc$uArrow$u$uOrder$u$uMirabelle$uOindi','tc$ufun'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'tc$uHOL$uObool'))),'c$uCOMBK'(X0,X1,'v$uL')),'c$uArrow$u$uOrder$u$uMirabelle$uOProf')),
inference(superposition,[status(thm)],[d6,c32]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT123+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.55 % Computer : n018.cluster.edu
% 0.12/5.55 % Model : x86_64 x86_64
% 0.12/5.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.55 % Memory : 8046.5625MB
% 0.12/5.55 % OS : Linux 6.8.0-71-generic
% 0.12/5.55 % CPULimit : 300
% 0.12/5.55 % WCLimit : 300
% 0.12/5.55 % DateTime : Sat Sep 26 06:32:41 UTC 2026
% 0.12/5.55 % CPUTime :
% 0.12/5.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 147.92/26.78 % SZS status Theorem for theBenchmark.p
% 147.92/26.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------