%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SCT146+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:27:50 AM UTC 2026
% Result : Theorem 30.43s 6.05s
% Output : CNFRefutation 30.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 13 ~; 11 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096,axiom,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',X0)))
<=> hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub'))) ) ).
fof(fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096,axiom,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')))
<=> hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua'))) ) ).
fof(fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096,axiom,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')))
<=> hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc'))) ) ).
fof(conj_0,conjecture,
! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc')))
<=> hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',X0))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc')))
<=> hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',X0))) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c4,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')))
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',X0))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096]) ).
cnf(c5,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',X0))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_096]) ).
cnf(c6,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')))
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub'))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096]) ).
cnf(c7,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub'))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062below_A_IP_Ai_J_Ac_Ab_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_096]) ).
cnf(c8,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc')))
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua'))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096]) ).
cnf(c9,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc')))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',X0)),'v$uc'),'v$ub')),'v$ub'),'v$ua'))) ),
inference(clausification,[status(esa)],[fact__096ALL_Ai_O_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_092_060_094esub_062_Ac_J_A_061_A_Ib_A_060_092_060_094bsub_062below_A_Ibelow_A_Ibelow_A_IP_Ai_J_Ac_Ab_J_Ab_Aa_J_Aa_Ac_092_060_094esub_062_Aa_J_096]) ).
cnf(c875,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031)))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc'))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c876,plain,
( ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc')))
| ~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')),'v$ub'),'v$ua')))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031))) ),
inference(resolution,[status(thm)],[c875,c9]) ).
cnf(d1,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031))) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031)))
| hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031))) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$ua')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')),'v$ub'),'v$ua')),'v$ua'),'v$uc'))),
inference(resolution,[status(thm)],[d2,c876]) ).
cnf(d4,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ub'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub')),'v$ub'),'v$ua'))),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$uc')),hAPP(hAPP(hAPP('c$uArrow$u$uOrder$u$uMirabelle$uObelow',hAPP('v$uP',sK2031)),'v$uc'),'v$ub'))),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
~ hBOOL(hAPP(hAPP('c$umember'('tc$uprod'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt')),hAPP(hAPP('c$uProduct$u$uType$uOPair'('tc$uArrow$u$uOrder$u$uMirabelle$uOalt','tc$uArrow$u$uOrder$u$uMirabelle$uOalt'),'v$ua'),'v$ub')),hAPP('v$uP',sK2031))),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d2,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT146+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.03/0.37 % CPULimit : 300
% 0.03/0.37 % WCLimit : 300
% 0.03/0.37 % DateTime : Sat Sep 26 06:33:24 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.43/6.05 % SZS status Theorem for theBenchmark.p
% 30.43/6.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------