%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG073+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 : n015.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 06:47:22 AM UTC 2026
% Result : Theorem 3.88s 2.46s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 22 unt; 0 def)
% Number of atoms : 142 ( 60 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 148 ( 59 ~; 51 |; 16 &)
% ( 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ) ).
fof(ax2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ) ).
fof(ax3,axiom,
? [X0] :
( ? [X1] :
( op1(X0,X1) != X0
& op1(X1,X1) = X0
& op1(X0,X0) = X1
& sorti1(X1) )
& sorti1(X0) ) ).
fof(ax4,axiom,
~ ? [X0] :
( ? [X1] :
( op2(X0,X1) != X0
& op2(X1,X1) = X0
& op2(X0,X0) = X1
& sorti2(X1) )
& sorti2(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(c0,plain,
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[ax1]) ).
cnf(c1,plain,
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[ax2]) ).
cnf(c2,plain,
sorti1(sK4),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c3,plain,
sorti1(sK5),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c4,plain,
op1(sK4,sK4) = sK5,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c5,plain,
op1(sK5,sK5) = sK4,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c6,plain,
op1(sK4,sK5) != sK4,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c7,plain,
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1 ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c8,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c10,plain,
( h(op1(X0,X1)) = op2(h(X0),h(X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
( h(j(X0)) = X0
| ~ sorti2(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c13,plain,
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
j(h(sK4)) = sK4,
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d1,plain,
( ~ sorti1(X0)
| h(op1(sK5,X0)) = op2(h(sK5),h(X0)) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d2,plain,
h(op1(sK5,sK5)) = op2(h(sK5),h(sK5)),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
h(sK4) = op2(h(sK5),h(sK5)),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( ~ sorti1(X0)
| h(op1(sK4,X0)) = op2(h(sK4),h(X0)) ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d5,plain,
h(op1(sK4,sK5)) = op2(h(sK4),h(sK5)),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
h(op1(sK4,sK4)) = op2(h(sK4),h(sK4)),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d7,plain,
h(sK5) = op2(h(sK4),h(sK4)),
inference(demodulation,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( ~ sorti2(X0)
| ~ sorti2(op2(X0,X0))
| op2(op2(X0,X0),X0) = op2(X0,X0)
| op2(op2(X0,X0),op2(X0,X0)) != X0 ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d9,plain,
( ~ sorti2(op2(h(sK5),h(sK5)))
| ~ sorti2(h(sK5))
| op2(op2(h(sK5),h(sK5)),h(sK5)) = op2(h(sK5),h(sK5))
| op2(op2(h(sK5),h(sK5)),h(sK4)) != h(sK5) ),
inference(superposition,[status(thm)],[d3,d8]) ).
cnf(d10,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(op2(h(sK5),h(sK5)))
| op2(op2(h(sK5),h(sK5)),h(sK5)) = op2(h(sK5),h(sK5))
| op2(h(sK4),h(sK4)) != h(sK5) ),
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(op2(h(sK5),h(sK5)))
| op2(op2(h(sK5),h(sK5)),h(sK5)) = op2(h(sK5),h(sK5))
| h(sK5) != h(sK5) ),
inference(demodulation,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(op2(h(sK5),h(sK5)))
| op2(h(sK4),h(sK5)) = op2(h(sK5),h(sK5))
| h(sK5) != h(sK5) ),
inference(demodulation,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(op2(h(sK5),h(sK5)))
| h(op1(sK4,sK5)) = op2(h(sK5),h(sK5))
| h(sK5) != h(sK5) ),
inference(demodulation,[status(thm)],[d12,d5]) ).
cnf(d14,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(op2(h(sK5),h(sK5)))
| h(op1(sK4,sK5)) = h(sK4)
| h(sK5) != h(sK5) ),
inference(demodulation,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK4,sK5)) = h(sK4)
| h(sK5) != h(sK5) ),
inference(demodulation,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
j(h(sK5)) = sK5,
inference(resolution,[status(thm)],[c3,c13]) ).
cnf(d17,plain,
( ~ sorti1(X0)
| h(j(h(X0))) = h(X0) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d18,plain,
h(j(h(sK5))) = h(sK5),
inference(resolution,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
h(sK5) = h(sK5),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK4,sK5)) = h(sK4) ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK5))
| sorti2(h(sK4)) ),
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d22,plain,
( ~ sorti1(sK5)
| sorti2(h(sK4)) ),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
sorti2(h(sK4)),
inference(resolution,[status(thm)],[c3,d22]) ).
cnf(d24,plain,
( ~ sorti2(h(sK5))
| h(op1(sK4,sK5)) = h(sK4) ),
inference(resolution,[status(thm)],[d23,d20]) ).
cnf(d25,plain,
( ~ sorti2(h(sK4))
| ~ sorti2(h(sK4))
| sorti2(h(sK5)) ),
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d26,plain,
sorti2(h(sK5)),
inference(resolution,[status(thm)],[d23,d25]) ).
cnf(d27,plain,
h(op1(sK4,sK5)) = h(sK4),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(op1(X0,X1))) = op1(X0,X1) ),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d29,plain,
( ~ sorti1(X0)
| j(h(op1(sK4,X0))) = op1(sK4,X0) ),
inference(resolution,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
j(h(op1(sK4,sK5))) = op1(sK4,sK5),
inference(resolution,[status(thm)],[d29,c3]) ).
cnf(d31,plain,
j(h(sK4)) = op1(sK4,sK5),
inference(demodulation,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
sK4 = op1(sK4,sK5),
inference(demodulation,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
sK4 != sK4,
inference(demodulation,[status(thm)],[c6,d32]) ).
cnf(d34,plain,
$false,
inference(equality_resolution,[status(thm)],[d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG073+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
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 21:10:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.88/2.46 % SZS status Theorem for theBenchmark.p
% 3.88/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------