%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG178+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 : n012.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 06:47:43 AM UTC 2026
% Result : Theorem 6.66s 2.14s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 14 unt; 0 def)
% Number of atoms : 88 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 82 ( 28 ~; 22 |; 8 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ) ).
fof(ax3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,op1(X0,X1)) = X1 ) ) ).
fof(ax4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,op2(X0,X1)) = X1 ) ) ).
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,op1(X0,X1)) = X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c3,plain,
sorti2(sK6),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c4,plain,
sorti2(sK7),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c5,plain,
op2(sK6,op2(sK6,sK7)) != sK7,
inference(clausification,[status(esa)],[ax4]) ).
cnf(c6,plain,
( sorti1(j(X0))
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
( op1(j(X0),j(X1)) = j(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
h(j(sK7)) = sK7,
inference(resolution,[status(thm)],[c4,c10]) ).
cnf(d1,plain,
( ~ sorti2(X0)
| op1(j(sK6),j(X0)) = j(op2(sK6,X0)) ),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d2,plain,
op1(j(sK6),j(sK7)) = j(op2(sK6,sK7)),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ sorti2(X1)
| ~ sorti1(X0)
| op1(X0,op1(X0,j(X1))) = j(X1) ),
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d4,plain,
( ~ sorti1(X0)
| op1(X0,op1(X0,j(sK7))) = j(sK7) ),
inference(resolution,[status(thm)],[c4,d3]) ).
cnf(d5,plain,
( ~ sorti2(X0)
| op1(j(X0),op1(j(X0),j(sK7))) = j(sK7) ),
inference(resolution,[status(thm)],[d4,c6]) ).
cnf(d6,plain,
op1(j(sK6),op1(j(sK6),j(sK7))) = j(sK7),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
op1(j(sK6),j(op2(sK6,sK7))) = j(sK7),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( ~ sorti2(X1)
| ~ sorti2(X0)
| op1(j(sK6),j(op2(X0,X1))) = j(op2(sK6,op2(X0,X1))) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d9,plain,
( ~ sorti2(X0)
| op1(j(sK6),j(op2(sK6,X0))) = j(op2(sK6,op2(sK6,X0))) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
op1(j(sK6),j(op2(sK6,sK7))) = j(op2(sK6,op2(sK6,sK7))),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
j(sK7) = j(op2(sK6,op2(sK6,sK7))),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( h(j(op2(X0,X1))) = op2(X0,X1)
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(resolution,[status(thm)],[c1,c10]) ).
cnf(d13,plain,
( ~ sorti2(X0)
| h(j(op2(sK6,X0))) = op2(sK6,X0) ),
inference(resolution,[status(thm)],[c3,d12]) ).
cnf(d14,plain,
( ~ sorti2(X1)
| ~ sorti2(X0)
| h(j(op2(sK6,op2(X0,X1)))) = op2(sK6,op2(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
( ~ sorti2(X0)
| h(j(op2(sK6,op2(sK6,X0)))) = op2(sK6,op2(sK6,X0)) ),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
h(j(op2(sK6,op2(sK6,sK7)))) = op2(sK6,op2(sK6,sK7)),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
h(j(sK7)) = op2(sK6,op2(sK6,sK7)),
inference(demodulation,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
sK7 = op2(sK6,op2(sK6,sK7)),
inference(demodulation,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
sK7 != sK7,
inference(demodulation,[status(thm)],[c5,d18]) ).
cnf(d20,plain,
$false,
inference(equality_resolution,[status(thm)],[d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG178+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sat Sep 26 21:22:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.66/2.14 % SZS status Theorem for theBenchmark.p
% 6.66/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------