%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN084+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:18:58 AM UTC 2026
% Result : Theorem 7.11s 3.34s
% Output : CNFRefutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 44 unt; 0 def)
% Number of atoms : 121 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 93 ( 39 ~; 25 |; 29 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 143 ( 22 sgn 15 !; 29 ?)
% 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_3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r3(X0,X1,X3) )
| ( X3 != X2
& ~ r3(X0,X1,X3) ) ) ).
fof(axiom_4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( X3 = X2
& r4(X0,X1,X3) )
| ( X3 != X2
& ~ r4(X0,X1,X3) ) ) ).
fof(axiom_1a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( X3 = X2
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) ) ) ).
fof(axiom_2a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r4(X0,X1,X5)
& r3(X5,X0,X2) )
& ? [X3] :
( X3 = X2
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) ) ) ).
fof(axiom_4a,axiom,
! [X0] :
? [X1] :
( X1 = X0
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ) ).
fof(axiom_5a,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( X1 = X3
& r1(X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ) ).
fof(xtimesyeqtwo,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& X2 = X3 )
& r4(X0,X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( r2(X5,X4)
& r1(X5) )
& r2(X4,X3) )
& X2 = X3 )
& r4(X0,X1,X2) ),
inference(negate_conjecture,[status(cth)],[xtimesyeqtwo]) ).
cnf(c1,plain,
( X0 = sK0
| ~ r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c2,plain,
( r1(X0)
| X0 != sK0 ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c5,plain,
( X1 = sK3(X0)
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c6,plain,
( r2(X1,X0)
| X0 != sK3(X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c9,plain,
( X2 = sK7(X0,X1)
| ~ r3(X0,X1,X2) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c13,plain,
( X2 = sK11(X0,X1)
| ~ r4(X0,X1,X2) ),
inference(clausification,[status(esa)],[axiom_4]) ).
cnf(c16,plain,
r2(X0,sK17(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c17,plain,
r3(X0,sK17(X0,X1),sK16(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c18,plain,
sK16(X0,X1) = sK15(X0,X1),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c19,plain,
r2(sK18(X0,X1),sK15(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c20,plain,
r3(X0,X1,sK18(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c22,plain,
r4(X0,sK23(X0,X1),sK22(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c23,plain,
sK22(X0,X1) = sK21(X0,X1),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c24,plain,
r3(sK24(X0,X1),X0,sK21(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c25,plain,
r4(X0,X1,sK24(X0,X1)),
inference(clausification,[status(esa)],[axiom_2a]) ).
cnf(c27,plain,
r1(sK31(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c28,plain,
r3(X0,sK31(X0),sK30(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c29,plain,
sK30(X0) = X0,
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c30,plain,
r1(sK34(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c31,plain,
r4(X0,sK34(X0),sK33(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c32,plain,
r1(sK35(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c33,plain,
sK33(X0) = sK35(X0),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c39,plain,
( ~ r2(X1,X3)
| ~ r4(X4,X5,X2)
| X2 != X3
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
sK18(X0,X1) = sK7(X0,X1),
inference(resolution,[status(thm)],[c20,c9]) ).
cnf(d1,plain,
r2(X0,sK3(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d2,plain,
r2(sK18(X0,X1),sK16(X0,X1)),
inference(demodulation,[status(thm)],[c19,c18]) ).
cnf(d3,plain,
sK16(X0,X1) = sK3(sK18(X0,X1)),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
r2(sK18(X0,X1),sK16(X0,X1)),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
r2(sK7(X0,X1),sK16(X0,X1)),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ r4(X3,X4,X2)
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(d7,plain,
( ~ r2(X0,X1)
| ~ r2(X1,sK22(X2,X3))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c22,d6]) ).
cnf(d8,plain,
sK24(X0,X1) = sK11(X0,X1),
inference(resolution,[status(thm)],[c25,c13]) ).
cnf(d9,plain,
r3(sK24(X0,X1),X0,sK22(X0,X1)),
inference(demodulation,[status(thm)],[c24,c23]) ).
cnf(d10,plain,
sK22(X0,X1) = sK7(sK24(X0,X1),X0),
inference(resolution,[status(thm)],[d9,c9]) ).
cnf(d11,plain,
sK22(X0,X1) = sK7(sK11(X0,X1),X0),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
sK35(X0) = sK0,
inference(resolution,[status(thm)],[c32,c1]) ).
cnf(d13,plain,
sK33(X0) = sK0,
inference(demodulation,[status(thm)],[c33,d12]) ).
cnf(d14,plain,
sK34(X0) = sK0,
inference(resolution,[status(thm)],[c30,c1]) ).
cnf(d15,plain,
r4(X0,sK0,sK33(X0)),
inference(demodulation,[status(thm)],[c31,d14]) ).
cnf(d16,plain,
r4(X0,sK0,sK0),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
sK0 = sK11(X0,sK0),
inference(resolution,[status(thm)],[d16,c13]) ).
cnf(d18,plain,
sK22(X0,sK0) = sK7(sK0,X0),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
( ~ r2(X2,X1)
| ~ r1(X2)
| ~ r2(X1,sK7(sK0,X0)) ),
inference(superposition,[status(thm)],[d18,d7]) ).
cnf(d20,plain,
sK17(X0,X1) = sK3(X1),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d21,plain,
sK16(X0,X1) = sK7(X0,sK17(X0,X1)),
inference(resolution,[status(thm)],[c17,c9]) ).
cnf(d22,plain,
sK16(X0,X1) = sK7(X0,sK3(X1)),
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( ~ r2(X2,X1)
| ~ r1(X2)
| ~ r2(X1,sK16(sK0,X0)) ),
inference(superposition,[status(thm)],[d22,d19]) ).
cnf(d24,plain,
( ~ r2(X0,sK7(sK0,X1))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d23,d5]) ).
cnf(d25,plain,
( ~ r1(X1)
| ~ r2(X1,sK16(sK0,X0)) ),
inference(superposition,[status(thm)],[d22,d24]) ).
cnf(d26,plain,
~ r1(sK7(sK0,X0)),
inference(resolution,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
sK31(X0) = sK0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(d28,plain,
r3(X0,sK0,sK30(X0)),
inference(demodulation,[status(thm)],[c28,d27]) ).
cnf(d29,plain,
r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[d28,c29]) ).
cnf(d30,plain,
X0 = sK7(X0,sK0),
inference(resolution,[status(thm)],[d29,c9]) ).
cnf(d31,plain,
~ r1(sK0),
inference(superposition,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
r1(sK0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN084+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n013.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 04:31:51 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.11/3.34 % SZS status Theorem for theBenchmark.p
% 7.11/3.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------