%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:18:56 AM UTC 2026
% Result : Theorem 9.06s 1.91s
% Output : CNFRefutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 22 unt; 0 def)
% Number of atoms : 67 ( 25 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 69 ( 37 ~; 28 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 38 ( 2 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ) ).
fof(axiom_2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( X2 = X1
& r2(X0,X2) )
| ( X2 != X1
& ~ r2(X0,X2) ) ) ).
fof(axiom_3a,axiom,
! [X0,X1] :
( X0 = X1
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( X3 != X2
| ~ r2(X0,X3) ) ) ) ).
fof(axiom_7a,axiom,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( X2 != X1
| ~ r1(X2) ) ) ).
fof(oneuneqtwo,conjecture,
! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( X1 != X0
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X3] :
( ~ r2(X3,X0)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) )
| ! [X1] :
( X1 != X0
| ! [X2] :
( ~ r2(X2,X1)
| ~ r1(X2) ) ) ),
inference(negate_conjecture,[status(cth)],[oneuneqtwo]) ).
cnf(c1,plain,
( X0 = sK0
| ~ r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c5,plain,
( X1 = sK3(X0)
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c26,plain,
( X0 = X3
| ~ r2(X3,X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_3a]) ).
cnf(c38,plain,
( ~ r2(X2,X1)
| X0 != X1
| ~ r1(X0) ),
inference(clausification,[status(esa)],[axiom_7a]) ).
cnf(c39,plain,
r1(sK45),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c40,plain,
r2(sK45,sK44),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c41,plain,
sK44 = sK43,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c42,plain,
r1(sK47),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c43,plain,
r2(sK47,sK46),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c44,plain,
r2(sK46,sK43),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sK45 = sK0,
inference(resolution,[status(thm)],[c1,c39]) ).
cnf(d1,plain,
sK44 = sK3(sK45),
inference(resolution,[status(thm)],[c5,c40]) ).
cnf(d2,plain,
sK44 = sK3(sK0),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
sK47 = sK0,
inference(resolution,[status(thm)],[c42,c1]) ).
cnf(d4,plain,
sK46 = sK3(sK47),
inference(resolution,[status(thm)],[c43,c5]) ).
cnf(d5,plain,
sK46 = sK3(sK0),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
sK46 = sK44,
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
r2(sK46,sK44),
inference(demodulation,[status(thm)],[c44,c41]) ).
cnf(d8,plain,
r2(sK44,sK44),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
r2(sK0,sK44),
inference(demodulation,[status(thm)],[c40,d0]) ).
cnf(d10,plain,
( ~ r2(X1,X2)
| ~ r2(X0,X2)
| X0 = X1 ),
inference(equality_resolution,[status(thm)],[c26]) ).
cnf(d11,plain,
( ~ r2(X0,sK44)
| sK0 = X0 ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
sK0 = sK44,
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
r2(sK0,sK44),
inference(demodulation,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
r2(sK0,sK0),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c38]) ).
cnf(d16,plain,
~ r1(sK0),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
r1(sK0),
inference(demodulation,[status(thm)],[c39,d0]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 04:30:29 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.06/1.91 % SZS status Theorem for theBenchmark.p
% 9.06/1.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------