%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG074+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 : n018.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 6.94s 5.85s
% Output : CNFRefutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 74 ( 29 unt; 0 def)
% Number of atoms : 190 ( 98 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 193 ( 77 ~; 80 |; 16 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 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 : 63 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ) ).
fof(ax3,axiom,
? [X0] :
( ? [X1] :
( op1(op1(X0,X1),X0) != X1
& op1(op1(X0,X1),X1) = X0
& op1(X1,X0) != op1(X0,X1)
& sorti1(X1) )
& sorti1(X0) ) ).
fof(ax4,axiom,
~ ? [X0] :
( ? [X1] :
( op2(op2(X0,X1),X0) != X1
& op2(op2(X0,X1),X1) = X0
& op2(X1,X0) != op2(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(c2,plain,
sorti1(sK4),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c3,plain,
sorti1(sK5),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c4,plain,
op1(sK5,sK4) != op1(sK4,sK5),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c5,plain,
op1(op1(sK4,sK5),sK5) = sK4,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c6,plain,
op1(op1(sK4,sK5),sK4) != sK5,
inference(clausification,[status(esa)],[ax3]) ).
cnf(c7,plain,
( op2(X1,X0) = op2(X0,X1)
| ~ sorti2(X1)
| ~ sorti2(X0)
| op2(op2(X0,X1),X0) = X1
| op2(op2(X0,X1),X1) != X0 ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c8,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c9,plain,
( sorti1(j(X0))
| ~ sorti2(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,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(op1(X0,X1))) = op1(X0,X1) ),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d1,plain,
( ~ sorti1(X0)
| j(h(op1(sK4,X0))) = op1(sK4,X0) ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
j(h(op1(sK4,sK5))) = op1(sK4,sK5),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
j(h(sK5)) = sK5,
inference(resolution,[status(thm)],[c3,c13]) ).
cnf(d4,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(op1(op1(X0,X1),X2))) = op1(op1(X0,X1),X2) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d5,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(op1(op1(sK4,X0),X1))) = op1(op1(sK4,X0),X1) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ sorti1(X0)
| j(h(op1(op1(sK4,sK5),X0))) = op1(op1(sK4,sK5),X0) ),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
j(h(op1(op1(sK4,sK5),sK4))) = op1(op1(sK4,sK5),sK4),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( ~ sorti2(X0)
| j(h(j(X0))) = j(X0) ),
inference(resolution,[status(thm)],[c13,c9]) ).
cnf(d9,plain,
( ~ sorti1(X0)
| j(h(j(h(X0)))) = j(h(X0)) ),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(j(h(op1(X0,X1))))) = j(h(op1(X0,X1))) ),
inference(resolution,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| ~ sorti1(X2)
| j(h(j(h(op1(op1(X0,X1),X2))))) = j(h(op1(op1(X0,X1),X2))) ),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| j(h(j(h(op1(op1(sK4,X0),X1))))) = j(h(op1(op1(sK4,X0),X1))) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( ~ sorti1(X0)
| j(h(j(h(op1(op1(sK4,sK5),X0))))) = j(h(op1(op1(sK4,sK5),X0))) ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
j(h(j(h(op1(op1(sK4,sK5),sK4))))) = j(h(op1(op1(sK4,sK5),sK4))),
inference(resolution,[status(thm)],[d13,c2]) ).
cnf(d15,plain,
j(h(op1(op1(sK4,sK5),sK4))) = j(h(op1(op1(sK4,sK5),sK4))),
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
op1(op1(sK4,sK5),sK4) = j(h(op1(op1(sK4,sK5),sK4))),
inference(demodulation,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| ~ sorti1(X2)
| h(op1(op1(X0,X1),X2)) = op2(h(op1(X0,X1)),h(X2)) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(d18,plain,
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(op1(sK4,X0),X1)) = op2(h(op1(sK4,X0)),h(X1)) ),
inference(resolution,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
( ~ sorti1(X0)
| h(op1(op1(sK4,sK5),X0)) = op2(h(op1(sK4,sK5)),h(X0)) ),
inference(resolution,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
h(op1(op1(sK4,sK5),sK4)) = op2(h(op1(sK4,sK5)),h(sK4)),
inference(resolution,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
h(op1(op1(sK4,sK5),sK5)) = op2(h(op1(sK4,sK5)),h(sK5)),
inference(resolution,[status(thm)],[d19,c3]) ).
cnf(d22,plain,
h(sK4) = op2(h(op1(sK4,sK5)),h(sK5)),
inference(demodulation,[status(thm)],[d21,c5]) ).
cnf(d23,plain,
( ~ sorti1(X0)
| h(op1(sK4,X0)) = op2(h(sK4),h(X0)) ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d24,plain,
h(op1(sK4,sK5)) = op2(h(sK4),h(sK5)),
inference(resolution,[status(thm)],[d23,c3]) ).
cnf(d25,plain,
( ~ sorti1(X0)
| h(op1(sK5,X0)) = op2(h(sK5),h(X0)) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d26,plain,
h(op1(sK5,sK4)) = op2(h(sK5),h(sK4)),
inference(resolution,[status(thm)],[d25,c2]) ).
cnf(d27,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| op2(op2(h(sK4),h(sK5)),h(sK4)) = h(sK5)
| op2(h(sK5),h(sK4)) = op2(h(sK4),h(sK5))
| op2(h(op1(sK4,sK5)),h(sK5)) != h(sK4) ),
inference(superposition,[status(thm)],[d24,c7]) ).
cnf(d28,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| op2(h(sK5),h(sK4)) = op2(h(sK4),h(sK5))
| op2(h(op1(sK4,sK5)),h(sK5)) != h(sK4)
| op2(h(op1(sK4,sK5)),h(sK4)) = h(sK5) ),
inference(demodulation,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = op2(h(sK4),h(sK5))
| op2(h(op1(sK4,sK5)),h(sK5)) != h(sK4)
| op2(h(op1(sK4,sK5)),h(sK4)) = h(sK5) ),
inference(demodulation,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| op2(h(op1(sK4,sK5)),h(sK5)) != h(sK4)
| op2(h(op1(sK4,sK5)),h(sK4)) = h(sK5) ),
inference(demodulation,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(sK4) != h(sK4)
| op2(h(op1(sK4,sK5)),h(sK4)) = h(sK5) ),
inference(demodulation,[status(thm)],[d30,d22]) ).
cnf(d32,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(sK4) != h(sK4)
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(demodulation,[status(thm)],[d31,d20]) ).
cnf(d33,plain,
j(h(sK4)) = sK4,
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d34,plain,
( ~ sorti1(X0)
| h(j(h(X0))) = h(X0) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d35,plain,
h(j(h(sK4))) = h(sK4),
inference(resolution,[status(thm)],[d34,c2]) ).
cnf(d36,plain,
h(sK4) = h(sK4),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( ~ sorti2(h(sK5))
| ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(resolution,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
( ~ sorti1(sK5)
| ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(resolution,[status(thm)],[d37,c8]) ).
cnf(d39,plain,
( ~ sorti2(h(sK4))
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(resolution,[status(thm)],[c3,d38]) ).
cnf(d40,plain,
( ~ sorti1(sK4)
| h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(resolution,[status(thm)],[d39,c8]) ).
cnf(d41,plain,
( h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| h(op1(op1(sK4,sK5),sK4)) = h(sK5) ),
inference(resolution,[status(thm)],[c2,d40]) ).
cnf(d42,plain,
( h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| op1(op1(sK4,sK5),sK4) = j(h(sK5)) ),
inference(superposition,[status(thm)],[d41,d16]) ).
cnf(d43,plain,
( h(op1(sK5,sK4)) = h(op1(sK4,sK5))
| op1(op1(sK4,sK5),sK4) = sK5 ),
inference(demodulation,[status(thm)],[d42,d3]) ).
cnf(d44,plain,
h(op1(sK5,sK4)) = h(op1(sK4,sK5)),
inference(resolution,[status(thm)],[c6,d43]) ).
cnf(d45,plain,
( ~ sorti1(X0)
| j(h(op1(sK5,X0))) = op1(sK5,X0) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d46,plain,
j(h(op1(sK5,sK4))) = op1(sK5,sK4),
inference(resolution,[status(thm)],[d45,c2]) ).
cnf(d47,plain,
j(h(op1(sK4,sK5))) = op1(sK5,sK4),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
op1(sK4,sK5) = op1(sK5,sK4),
inference(demodulation,[status(thm)],[d47,d2]) ).
cnf(d49,plain,
op1(sK4,sK5) != op1(sK4,sK5),
inference(demodulation,[status(thm)],[c4,d48]) ).
cnf(d50,plain,
( ~ sorti2(X0)
| j(h(op1(sK4,j(X0)))) = op1(sK4,j(X0)) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d51,plain,
( ~ sorti1(X0)
| j(h(op1(sK4,j(h(X0))))) = op1(sK4,j(h(X0))) ),
inference(resolution,[status(thm)],[d50,c8]) ).
cnf(d52,plain,
j(h(op1(sK4,j(h(sK5))))) = op1(sK4,j(h(sK5))),
inference(resolution,[status(thm)],[d51,c3]) ).
cnf(d53,plain,
j(h(op1(sK4,sK5))) = op1(sK4,j(h(sK5))),
inference(demodulation,[status(thm)],[d52,d3]) ).
cnf(d54,plain,
op1(sK4,sK5) = op1(sK4,j(h(sK5))),
inference(demodulation,[status(thm)],[d53,d2]) ).
cnf(d55,plain,
op1(sK4,sK5) = op1(sK4,sK5),
inference(demodulation,[status(thm)],[d54,d3]) ).
cnf(d56,plain,
$false,
inference(resolution,[status(thm)],[d55,d49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG074+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
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 21:08:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.94/5.85 % SZS status Theorem for theBenchmark.p
% 6.94/5.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------