%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG202+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 06:48:04 AM UTC 2026
% Result : Theorem 9.76s 1.76s
% Output : CNFRefutation 9.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 67 ( 26 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 60 ( 18 ~; 12 |; 8 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ) ).
fof(ax3,axiom,
! [X0] :
( sorti1(X0)
=> op1(X0,X0) = X0 ) ).
fof(ax4,axiom,
~ ! [X0] :
( sorti2(X0)
=> op2(X0,X0) = X0 ) ).
fof(co1,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c1,plain,
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c2,plain,
( op1(X0,X0) = X0
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c3,plain,
sorti2(sK5),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c4,plain,
op2(sK5,sK5) != sK5,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c6,plain,
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
( j(op2(X0,X1)) = op1(j(X0),j(X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
h(j(sK5)) = sK5,
inference(resolution,[status(thm)],[c3,c9]) ).
cnf(d1,plain,
( ~ sorti2(X0)
| op1(j(X0),j(X0)) = j(X0) ),
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d2,plain,
op1(j(sK5),j(sK5)) = j(sK5),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ sorti2(X0)
| j(op2(sK5,X0)) = op1(j(sK5),j(X0)) ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d4,plain,
j(op2(sK5,sK5)) = op1(j(sK5),j(sK5)),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
j(op2(sK5,sK5)) = j(sK5),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ sorti2(X1)
| ~ sorti2(X0)
| h(j(op2(X0,X1))) = op2(X0,X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d7,plain,
( ~ sorti2(X0)
| h(j(op2(sK5,X0))) = op2(sK5,X0) ),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
h(j(op2(sK5,sK5))) = op2(sK5,sK5),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
h(j(sK5)) = op2(sK5,sK5),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
sK5 = op2(sK5,sK5),
inference(demodulation,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
sK5 != sK5,
inference(demodulation,[status(thm)],[c4,d10]) ).
cnf(d12,plain,
$false,
inference(equality_resolution,[status(thm)],[d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG202+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 21:25:17 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.76/1.76 % SZS status Theorem for theBenchmark.p
% 9.76/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------