%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW293+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 : n016.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 09:11:38 AM UTC 2026
% Result : Theorem 107.21s 14.20s
% Output : CNFRefutation 107.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 20 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 2 |; 0 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 24 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_triple__valid__def2,axiom,
! [X0,X1,X2,X3,X4] :
( 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X4,X3,hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X4),X2),X1),X0))
<=> ! [X5,X6] :
( hBOOL(hAPP(hAPP(X2,X5),X6))
=> ! [X7] :
( 'c$uNatural$uOevaln'(X1,X6,X3,X7)
=> hBOOL(hAPP(hAPP(X0,X5),X7)) ) ) ) ).
fof(fact_evaln__elim__cases_I6_J,axiom,
! [X0,X1,X2,X3] :
( 'c$uNatural$uOevaln'(hAPP('c$uCom$uOcom$uOBODY',X3),X2,X1,X0)
=> ~ ! [X4] :
( X1 = hAPP('c$uNat$uOSuc',X4)
=> ~ 'c$uNatural$uOevaln'(hAPP('c$uOption$uOthe'('tc$uCom$uOcom'),hAPP('c$uCom$uObody',X3)),X2,X4,X0) ) ) ).
fof(fact_Suc__neq__Zero,axiom,
! [X0] : hAPP('c$uNat$uOSuc',X0) != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ).
fof(conj_0,conjecture,
'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP'),hAPP('c$uCom$uOcom$uOBODY','v$upn')),'v$uQ')) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP'),hAPP('c$uCom$uOcom$uOBODY','v$upn')),'v$uQ')),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c15,plain,
( 'c$uNatural$uOevaln'(X3,sK44(X4,X3,X2,X1),X1,sK45(X4,X3,X2,X1))
| 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'(X0,X1,hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'(X0),X2),X3),X4)) ),
inference(clausification,[status(esa)],[fact_triple__valid__def2]) ).
cnf(c299,plain,
( X2 = hAPP('c$uNat$uOSuc',sK856(X3,X2,X1,X0))
| ~ 'c$uNatural$uOevaln'(hAPP('c$uCom$uOcom$uOBODY',X0),X1,X2,X3) ),
inference(clausification,[status(esa)],[fact_evaln__elim__cases_I6_J]) ).
cnf(c314,plain,
hAPP('c$uNat$uOSuc',X0) != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(clausification,[status(esa)],[fact_Suc__neq__Zero]) ).
cnf(c7494,plain,
~ 'c$uHoare$u$uMirabelle$uOtriple$u$uvalid'('t$ua','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),hAPP(hAPP(hAPP('c$uHoare$u$uMirabelle$uOtriple$uOtriple'('t$ua'),'v$uP'),hAPP('c$uCom$uOcom$uOBODY','v$upn')),'v$uQ')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'c$uNatural$uOevaln'(hAPP('c$uCom$uOcom$uOBODY','v$upn'),sK44('v$uQ',hAPP('c$uCom$uOcom$uOBODY','v$upn'),'v$uP','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),sK45('v$uQ',hAPP('c$uCom$uOcom$uOBODY','v$upn'),'v$uP','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))),
inference(resolution,[status(thm)],[c15,c7494]) ).
cnf(d1,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') = hAPP('c$uNat$uOSuc',sK856(sK45('v$uQ',hAPP('c$uCom$uOcom$uOBODY','v$upn'),'v$uP','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),sK44('v$uQ',hAPP('c$uCom$uOcom$uOBODY','v$upn'),'v$uP','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')),'v$upn')),
inference(resolution,[status(thm)],[c299,d0]) ).
cnf(d2,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(superposition,[status(thm)],[d1,c314]) ).
cnf(d3,plain,
$false,
inference(equality_resolution,[status(thm)],[d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW293+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n016.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 15:41:00 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 107.21/14.20 % SZS status Theorem for theBenchmark.p
% 107.21/14.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------