%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN056+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:18:52 AM UTC 2026
% Result : Theorem 99.17s 15.71s
% Output : CNFRefutation 99.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 17 unt; 0 def)
% Number of atoms : 364 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 577 ( 291 ~; 254 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 0 con; 1-2 aty)
% Number of variables : 342 ( 6 sgn 18 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ) ).
fof(axiom_3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ) ).
fof(axiom_5,axiom,
! [X0] : id(X0,X0) ).
fof(axiom_6,axiom,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ) ).
fof(axiom_7,axiom,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ) ).
fof(axiom_9,axiom,
! [X0,X1,X2,X3] :
( ( r2(X2,X3)
& r2(X0,X1) )
| ( ~ r2(X2,X3)
& ~ r2(X0,X1) )
| ~ id(X1,X3)
| ~ id(X0,X2) ) ).
fof(axiom_1a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) )
& id(X3,X2) ) ) ).
fof(axiom_4a,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ) ).
fof(oneplustwoidthree,conjecture,
? [X0] :
( ? [X5] :
( ? [X8] :
( ? [X9] :
( r2(X9,X8)
& r1(X9) )
& r2(X8,X5) )
& ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r3(X6,X5,X0) ) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X4,X3)
& r1(X4) )
& r2(X3,X2) )
& r2(X2,X1) )
& id(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ? [X5] :
( ? [X8] :
( ? [X9] :
( r2(X9,X8)
& r1(X9) )
& r2(X8,X5) )
& ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r3(X6,X5,X0) ) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X4,X3)
& r1(X4) )
& r2(X3,X2) )
& r2(X2,X1) )
& id(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[oneplustwoidthree]) ).
cnf(c4,plain,
( ~ r2(X1,X0)
| id(X0,sK3(X1)) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c7,plain,
( ~ id(X1,sK3(X0))
| r2(X0,X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c8,plain,
( ~ r3(X1,X2,X0)
| id(X0,sK7(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c16,plain,
id(X0,X0),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c17,plain,
( id(X1,X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_6]) ).
cnf(c18,plain,
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_7]) ).
cnf(c24,plain,
( r2(X1,X3)
| ~ r2(X0,X2)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c35,plain,
id(sK40(X0,X1),sK39(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c36,plain,
r2(X0,sK41(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c37,plain,
r3(X0,sK41(X0,X1),sK40(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c38,plain,
r2(sK42(X0,X1),sK39(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c39,plain,
r3(X0,X1,sK42(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c46,plain,
id(sK54(X0),X0),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c47,plain,
r1(sK55(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c48,plain,
r3(X0,sK55(X0),sK54(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c58,plain,
( ~ r2(X7,X4)
| ~ r1(X6)
| ~ r1(X2)
| ~ r2(X9,X0)
| ~ r1(X9)
| ~ id(X8,X5)
| ~ r3(X3,X1,X8)
| ~ r2(X6,X7)
| ~ r2(X4,X5)
| ~ r2(X2,X3)
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(d1,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c17,c46]) ).
cnf(d2,plain,
( ~ r3(X1,X2,X3)
| ~ id(X0,X3)
| id(X0,sK7(X1,X2)) ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d3,plain,
( r2(X1,X2)
| ~ id(sK3(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c24,d0]) ).
cnf(d4,plain,
( ~ r3(X2,X3,X4)
| ~ id(sK3(X0),X4)
| r2(X1,sK7(X2,X3))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ r2(X0,X1)
| id(sK3(X0),X1) ),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d6,plain,
id(sK39(X0,X1),sK40(X0,X1)),
inference(resolution,[status(thm)],[c35,c17]) ).
cnf(d7,plain,
( ~ id(X0,sK39(X1,X2))
| id(X0,sK40(X1,X2)) ),
inference(resolution,[status(thm)],[c18,d6]) ).
cnf(d8,plain,
( ~ r2(X0,sK39(X1,X2))
| id(sK3(X0),sK40(X1,X2)) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ r2(X1,X2)
| ~ id(X0,X2)
| id(X0,sK3(X1)) ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d10,plain,
( ~ id(X0,X1)
| id(X0,sK54(X1)) ),
inference(resolution,[status(thm)],[c18,d1]) ).
cnf(d11,plain,
( ~ id(X2,X0)
| id(X2,sK54(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d10,c18]) ).
cnf(d12,plain,
( id(sK54(X1),X0)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d10,c17]) ).
cnf(d13,plain,
( ~ id(X0,sK54(X1))
| id(X0,X1) ),
inference(resolution,[status(thm)],[c18,c46]) ).
cnf(d14,plain,
id(sK54(sK54(X0)),X0),
inference(resolution,[status(thm)],[d13,c46]) ).
cnf(d15,plain,
id(X0,sK54(sK54(X0))),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d16,plain,
r2(X0,sK54(sK54(sK3(X0)))),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d17,plain,
( ~ r2(X2,X8)
| ~ r2(X8,X7)
| ~ r2(X7,X5)
| ~ r2(X1,X6)
| ~ r2(X6,sK41(X3,X4))
| ~ r2(X0,X3)
| ~ id(sK40(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c37,c58]) ).
cnf(d18,plain,
( ~ r2(X2,X3)
| ~ r2(X1,X4)
| ~ r2(X0,X6)
| ~ r2(X7,X5)
| ~ r2(X6,X7)
| ~ id(sK40(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d17,c36]) ).
cnf(d19,plain,
( ~ r2(X5,X7)
| ~ r2(X4,X1)
| ~ r2(X3,X0)
| ~ r2(X7,X6)
| ~ r2(X6,sK54(X2))
| ~ r1(X5)
| ~ r1(X4)
| ~ r1(X3)
| ~ id(sK40(X0,X1),X2) ),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
( ~ r2(X6,X0)
| ~ r2(X5,X1)
| ~ r2(X4,X7)
| ~ r2(X8,sK54(sK54(X3)))
| ~ r2(X7,X8)
| ~ r1(X6)
| ~ r1(X5)
| ~ r1(X4)
| ~ id(X2,X3)
| ~ id(sK40(X0,X1),X2) ),
inference(resolution,[status(thm)],[d11,d19]) ).
cnf(d21,plain,
( ~ r2(X2,X7)
| ~ r2(X1,X6)
| ~ r2(X0,X5)
| ~ r2(X7,X4)
| ~ id(sK40(X5,X6),X3)
| ~ id(X3,sK3(X4))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
( ~ r2(X2,X3)
| ~ r2(X1,X4)
| ~ r2(X0,X6)
| ~ r2(X6,X5)
| ~ id(sK54(sK54(sK40(X3,X4))),sK3(X5))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
( ~ id(sK3(X4),sK54(sK40(X5,X6)))
| ~ r2(X2,X3)
| ~ r2(X1,X6)
| ~ r2(X0,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
( ~ id(X7,sK40(X6,X5))
| ~ id(sK3(X4),X7)
| ~ r2(X2,X6)
| ~ r2(X1,X5)
| ~ r2(X0,X3)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d23,d11]) ).
cnf(d25,plain,
( ~ id(sK40(X6,X7),X4)
| ~ r2(X2,X5)
| ~ r2(X1,X7)
| ~ r2(X0,X6)
| ~ r2(X5,X3)
| ~ id(sK3(X3),sK54(X4))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d24,d12]) ).
cnf(d26,plain,
( ~ r2(X2,X4)
| ~ r2(X1,X5)
| ~ r2(X0,X6)
| ~ r2(X6,X3)
| ~ id(sK3(X3),sK54(sK39(X4,X5)))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d25,c35]) ).
cnf(d27,plain,
( ~ id(X7,sK39(X5,X6))
| ~ id(sK3(X4),X7)
| ~ r2(X2,X3)
| ~ r2(X1,X6)
| ~ r2(X0,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d26,d11]) ).
cnf(d28,plain,
( ~ r2(X4,sK39(X7,X6))
| ~ r2(X2,X7)
| ~ r2(X1,X6)
| ~ r2(X0,X5)
| ~ r2(X5,X3)
| ~ id(sK3(X3),sK3(X4))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d27,d5]) ).
cnf(d29,plain,
( ~ r2(X2,X6)
| ~ r2(X1,X5)
| ~ r2(X0,X4)
| ~ r2(X6,X3)
| ~ id(sK3(X3),sK3(sK42(X4,X5)))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d28,c38]) ).
cnf(d30,plain,
( ~ r2(sK42(X6,X5),X7)
| ~ id(sK3(X4),X7)
| ~ r2(X2,X6)
| ~ r2(X1,X5)
| ~ r2(X0,X3)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d29,d9]) ).
cnf(d31,plain,
( ~ r2(X2,X7)
| ~ r2(X1,X6)
| ~ r2(X0,X5)
| ~ r2(X7,X3)
| ~ id(sK3(X3),sK41(X4,sK42(X5,X6)))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d30,c36]) ).
cnf(d32,plain,
( ~ r2(X4,sK41(X7,sK42(X6,X5)))
| ~ r2(X2,X6)
| ~ r2(X1,X5)
| ~ r2(X0,X3)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d31,d5]) ).
cnf(d33,plain,
( r2(X1,X3)
| ~ id(sK41(X2,X0),X3)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c24,c36]) ).
cnf(d34,plain,
( r2(X1,sK41(X2,X0))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d33,c16]) ).
cnf(d35,plain,
( ~ r2(X5,X6)
| ~ r2(X4,X1)
| ~ r2(X3,X0)
| ~ r2(X6,X2)
| ~ r1(X5)
| ~ r1(X4)
| ~ r1(X3)
| ~ id(sK42(X0,X1),X2) ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( ~ r3(X4,X5,sK42(X7,X6))
| ~ r2(X2,X7)
| ~ r2(X1,X6)
| ~ r2(X0,X3)
| ~ r2(X3,sK7(X4,X5))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d35,c8]) ).
cnf(d37,plain,
( ~ r2(X2,X3)
| ~ r2(X1,X5)
| ~ r2(X0,X4)
| ~ r2(X3,sK7(X4,X5))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d36,c39]) ).
cnf(d38,plain,
( ~ r2(X7,X3)
| ~ r2(X6,X4)
| ~ r2(X5,X1)
| ~ r1(X7)
| ~ r1(X6)
| ~ r1(X5)
| ~ r3(X3,X4,X2)
| ~ id(sK3(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d4,d37]) ).
cnf(d39,plain,
( ~ r2(X2,X4)
| ~ r2(X1,sK41(X5,X6))
| ~ r2(X0,X5)
| ~ id(sK3(X3),sK40(X5,X6))
| ~ id(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d38,c37]) ).
cnf(d40,plain,
( ~ r2(X3,sK39(X5,X6))
| ~ r2(X2,X5)
| ~ r2(X1,sK41(X5,X6))
| ~ r2(X0,X4)
| ~ id(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d39,d8]) ).
cnf(d41,plain,
( ~ r2(X2,X4)
| ~ r2(X0,X5)
| ~ r2(X3,sK39(X5,X1))
| ~ id(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d40,c36]) ).
cnf(d42,plain,
( ~ r2(X2,X3)
| ~ r2(X0,X4)
| ~ id(sK42(X3,X1),X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d41,c38]) ).
cnf(d43,plain,
( ~ r3(X4,X5,sK42(X3,X1))
| ~ r2(X2,sK7(X4,X5))
| ~ r2(X0,X3)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d42,c8]) ).
cnf(d44,plain,
( ~ r2(X2,X3)
| ~ r2(X0,sK7(X3,X1))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d43,c39]) ).
cnf(d45,plain,
( ~ r3(X3,X1,X5)
| ~ id(sK3(X4),X5)
| ~ id(X4,X2)
| ~ r2(X0,X3)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d44,d4]) ).
cnf(d46,plain,
( ~ r2(X2,X1)
| ~ id(sK3(X3),sK54(X1))
| ~ id(X3,X0)
| ~ r1(X2)
| ~ r1(sK55(X1))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d45,c48]) ).
cnf(d47,plain,
( ~ r2(X0,X3)
| ~ id(sK3(X2),sK54(X3))
| ~ id(X2,X1)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c47,d46]) ).
cnf(d48,plain,
( ~ r2(X1,sK3(X2))
| ~ id(X2,X0)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d47,d1]) ).
cnf(d49,plain,
( ~ id(X0,X1)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d48,d0]) ).
cnf(d50,plain,
( ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d49,c16]) ).
cnf(d51,plain,
$false,
inference(resolution,[status(thm)],[d50,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN056+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 04:28:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 99.17/15.71 % SZS status Theorem for theBenchmark.p
% 99.17/15.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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