%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN075+1 : 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 08:18:56 AM UTC 2026
% Result : Theorem 52.64s 22.19s
% Output : CNFRefutation 52.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 11
% Syntax : Number of formulae : 112 ( 24 unt; 0 def)
% Number of atoms : 742 ( 0 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 1250 ( 620 ~; 570 |; 60 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 744 ( 2 sgn 21 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ) ).
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_8,axiom,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ 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(sevenplustwoidnine,conjecture,
? [X0] :
( ? [X11] :
( ? [X15] :
( ? [X16] :
( ? [X17] :
( ? [X18] :
( ? [X19] :
( ? [X20] :
( ? [X21] :
( r2(X21,X20)
& r1(X21) )
& r2(X20,X19) )
& r2(X19,X18) )
& r2(X18,X17) )
& r2(X17,X16) )
& r2(X16,X15) )
& r2(X15,X11) )
& ? [X12] :
( ? [X13] :
( ? [X14] :
( r2(X14,X13)
& r1(X14) )
& r2(X13,X12) )
& r3(X11,X12,X0) ) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( r2(X10,X9)
& r1(X10) )
& r2(X9,X8) )
& r2(X8,X7) )
& r2(X7,X6) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r2(X3,X2) )
& r2(X2,X1) )
& id(X0,X1) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ? [X11] :
( ? [X15] :
( ? [X16] :
( ? [X17] :
( ? [X18] :
( ? [X19] :
( ? [X20] :
( ? [X21] :
( r2(X21,X20)
& r1(X21) )
& r2(X20,X19) )
& r2(X19,X18) )
& r2(X18,X17) )
& r2(X17,X16) )
& r2(X16,X15) )
& r2(X15,X11) )
& ? [X12] :
( ? [X13] :
( ? [X14] :
( r2(X14,X13)
& r1(X14) )
& r2(X13,X12) )
& r3(X11,X12,X0) ) )
& ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( ? [X10] :
( r2(X10,X9)
& r1(X10) )
& r2(X9,X8) )
& r2(X8,X7) )
& r2(X7,X6) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r2(X3,X2) )
& r2(X2,X1) )
& id(X0,X1) ) ),
inference(negate_conjecture,[status(cth)],[sevenplustwoidnine]) ).
cnf(c3,plain,
( ~ id(X0,sK0)
| r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
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(c20,plain,
( r1(X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c21,plain,
( r1(X0)
| ~ r1(X1)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_8]) ).
cnf(c24,plain,
( r2(X1,X3)
| ~ r2(X0,X2)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_9]) ).
cnf(c25,plain,
( r2(X0,X2)
| ~ r2(X1,X3)
| ~ 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(X19,X20)
| ~ r2(X8,X21)
| ~ r2(X21,X18)
| ~ r2(X15,X7)
| ~ r1(X16)
| ~ r3(X5,X6,X9)
| ~ r2(X20,X14)
| ~ r2(X17,X19)
| ~ r2(X18,X10)
| ~ r2(X16,X17)
| ~ r2(X1,X15)
| ~ r1(X2)
| ~ r1(X12)
| ~ r2(X14,X13)
| ~ r2(X13,X4)
| ~ r2(X12,X11)
| ~ r2(X11,X0)
| ~ id(X9,X10)
| ~ r2(X7,X8)
| ~ r2(X3,X6)
| ~ r2(X4,X5)
| ~ r2(X2,X3)
| ~ r2(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ r3(X0,X1,X2)
| r1(X2)
| ~ r1(sK7(X0,X1)) ),
inference(resolution,[status(thm)],[c21,c8]) ).
cnf(d1,plain,
( ~ r1(sK7(X0,X1))
| r1(sK42(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c39]) ).
cnf(d2,plain,
( ~ r3(X0,X1,X2)
| id(sK7(X0,X1),X2) ),
inference(resolution,[status(thm)],[c17,c8]) ).
cnf(d3,plain,
( ~ id(X0,sK54(X1))
| id(X0,X1) ),
inference(resolution,[status(thm)],[c18,c46]) ).
cnf(d4,plain,
( ~ r3(X0,X1,sK54(X2))
| id(sK7(X0,X1),X2) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
id(sK7(X0,sK55(X0)),X0),
inference(resolution,[status(thm)],[d4,c48]) ).
cnf(d6,plain,
r1(sK7(sK0,sK55(sK0))),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
r1(sK42(sK0,sK55(sK0))),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
id(X0,sK54(X0)),
inference(resolution,[status(thm)],[c17,c46]) ).
cnf(d9,plain,
( ~ r1(X0)
| r1(sK54(X0)) ),
inference(resolution,[status(thm)],[c20,d8]) ).
cnf(d10,plain,
( ~ r3(X1,X2,X3)
| ~ id(X0,X3)
| id(X0,sK7(X1,X2)) ),
inference(resolution,[status(thm)],[c18,c8]) ).
cnf(d11,plain,
( id(X0,sK7(X1,X2))
| ~ id(X0,sK42(X1,X2)) ),
inference(resolution,[status(thm)],[d10,c39]) ).
cnf(d12,plain,
id(sK42(X0,X1),sK7(X0,X1)),
inference(resolution,[status(thm)],[d11,c16]) ).
cnf(d13,plain,
( ~ id(X0,sK7(X1,sK55(X1)))
| id(X0,X1) ),
inference(resolution,[status(thm)],[d5,c18]) ).
cnf(d14,plain,
id(sK42(X0,sK55(X0)),X0),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ r2(X0,X1)
| id(sK3(X0),X1) ),
inference(resolution,[status(thm)],[c17,c4]) ).
cnf(d16,plain,
r2(X0,sK3(X0)),
inference(resolution,[status(thm)],[c7,c16]) ).
cnf(d17,plain,
( r2(X1,X2)
| ~ id(sK3(X0),X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c24,d16]) ).
cnf(d18,plain,
( ~ r2(X0,X2)
| r2(X1,X2)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( r2(X2,sK39(X0,X1))
| ~ id(sK42(X0,X1),X2) ),
inference(resolution,[status(thm)],[d18,c38]) ).
cnf(d20,plain,
r2(X0,sK39(X0,sK55(X0))),
inference(resolution,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
id(X0,sK42(X0,sK55(X0))),
inference(resolution,[status(thm)],[d14,c17]) ).
cnf(d22,plain,
( ~ id(X0,X1)
| id(X0,sK54(X1)) ),
inference(resolution,[status(thm)],[d8,c18]) ).
cnf(d23,plain,
( r2(X2,X3)
| ~ id(sK39(X0,X1),X3)
| ~ id(sK42(X0,X1),X2) ),
inference(resolution,[status(thm)],[c38,c24]) ).
cnf(d24,plain,
( r2(sK54(sK42(X0,X1)),X2)
| ~ id(sK39(X0,X1),X2) ),
inference(resolution,[status(thm)],[d23,d8]) ).
cnf(d25,plain,
( ~ id(X0,sK40(X1,X2))
| id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[c35,c18]) ).
cnf(d26,plain,
( ~ r3(X0,X1,sK40(X2,X3))
| id(sK7(X0,X1),sK39(X2,X3)) ),
inference(resolution,[status(thm)],[d25,d2]) ).
cnf(d27,plain,
( r2(X0,X3)
| ~ id(X3,sK39(X1,X2))
| ~ id(X0,sK42(X1,X2)) ),
inference(resolution,[status(thm)],[c38,c25]) ).
cnf(d28,plain,
( r2(sK54(sK42(X1,X2)),X0)
| ~ id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[d27,c46]) ).
cnf(d29,plain,
( ~ r2(X1,X2)
| ~ id(X0,X2)
| id(X0,sK3(X1)) ),
inference(resolution,[status(thm)],[c18,c4]) ).
cnf(d30,plain,
( id(X0,sK3(sK42(X1,X2)))
| ~ id(X0,sK39(X1,X2)) ),
inference(resolution,[status(thm)],[d29,c38]) ).
cnf(d31,plain,
id(sK54(sK54(X0)),X0),
inference(resolution,[status(thm)],[d3,c46]) ).
cnf(d32,plain,
id(X0,sK54(sK54(X0))),
inference(resolution,[status(thm)],[d31,c17]) ).
cnf(d33,plain,
( r2(X1,sK54(sK54(sK3(X0))))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d32,d17]) ).
cnf(d34,plain,
( ~ id(X0,X1)
| id(X0,sK54(sK54(X1))) ),
inference(resolution,[status(thm)],[d32,c18]) ).
cnf(d35,plain,
( ~ r2(X14,X20)
| ~ r2(X20,X18)
| ~ r2(X2,X16)
| ~ r2(X13,X19)
| ~ r2(X19,X10)
| ~ r2(X18,X5)
| ~ r2(X9,X17)
| ~ r2(X17,X12)
| ~ r2(X16,X15)
| ~ r2(X15,X7)
| ~ r2(X11,X14)
| ~ r2(X12,X13)
| ~ r2(X8,X11)
| ~ r2(X10,X3)
| ~ r2(X1,X9)
| ~ r2(X7,X8)
| ~ r2(X0,X6)
| ~ r2(X6,sK41(X3,X4))
| ~ id(sK40(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c58,c37]) ).
cnf(d36,plain,
( ~ r2(X2,X4)
| ~ r2(X1,X18)
| ~ r2(X0,X12)
| ~ r2(X14,X19)
| ~ r2(X19,X17)
| ~ r2(X18,X10)
| ~ r2(X9,X3)
| ~ r2(X17,X15)
| ~ r2(X11,X16)
| ~ r2(X16,X8)
| ~ r2(X15,X6)
| ~ r2(X13,X14)
| ~ r2(X12,X13)
| ~ r2(X10,X11)
| ~ r2(X7,X5)
| ~ r2(X8,X9)
| ~ r2(X6,X7)
| ~ id(sK40(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d35,c36]) ).
cnf(d37,plain,
( ~ id(sK40(X16,X19),X18)
| ~ r2(X2,X13)
| ~ r2(X1,X5)
| ~ r2(X0,X19)
| ~ r2(X10,X17)
| ~ r2(X17,sK54(sK54(X18)))
| ~ r2(X9,X15)
| ~ r2(X15,X16)
| ~ r2(X6,X14)
| ~ r2(X14,X8)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X3)
| ~ r2(X7,X10)
| ~ r2(X8,X9)
| ~ r2(X4,X7)
| ~ r2(X5,X6)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d36,d34]) ).
cnf(d38,plain,
( ~ id(X5,X14)
| ~ r2(X2,X4)
| ~ r2(X1,X18)
| ~ r2(X0,X9)
| ~ r2(X12,X19)
| ~ r2(X19,X16)
| ~ r2(X18,X17)
| ~ r2(X17,X7)
| ~ r2(X16,X13)
| ~ r2(X8,X15)
| ~ r2(X15,X6)
| ~ r2(X13,X14)
| ~ r2(X11,X12)
| ~ r2(X10,X11)
| ~ r2(X9,X10)
| ~ r2(X7,X8)
| ~ r2(X6,X3)
| ~ id(sK40(X3,X4),sK3(X5))
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
( ~ id(sK40(X19,X20),sK39(X3,X4))
| ~ r2(X2,X17)
| ~ r2(X1,X8)
| ~ r2(X0,X20)
| ~ r2(X13,X19)
| ~ r2(X10,X18)
| ~ r2(X18,X12)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X6)
| ~ r2(X11,X5)
| ~ r2(X12,X13)
| ~ r2(X7,X11)
| ~ r2(X9,X10)
| ~ r2(X8,X9)
| ~ r2(X6,X7)
| ~ id(sK42(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d38,d30]) ).
cnf(d40,plain,
( ~ r2(X2,X4)
| ~ r2(X1,X17)
| ~ r2(X0,X8)
| ~ r2(X12,X18)
| ~ r2(X18,X14)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X6)
| ~ r2(X14,X5)
| ~ r2(X7,X13)
| ~ r2(X13,X3)
| ~ r2(X11,X12)
| ~ r2(X10,X11)
| ~ r2(X9,X10)
| ~ r2(X8,X9)
| ~ r2(X6,X7)
| ~ id(sK42(X3,X4),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d39,c35]) ).
cnf(d41,plain,
( ~ r3(X9,X10,sK42(X12,X19))
| ~ r2(X2,X17)
| ~ r2(X1,X5)
| ~ r2(X0,X19)
| ~ r2(X8,X18)
| ~ r2(X18,X11)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X3)
| ~ r2(X11,X12)
| ~ r2(X4,sK7(X9,X10))
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d40,c8]) ).
cnf(d42,plain,
( ~ r2(X2,X17)
| ~ r2(X1,X15)
| ~ r2(X0,X5)
| ~ r2(X10,X16)
| ~ r2(X16,sK7(X11,X17))
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X3)
| ~ r2(X4,X11)
| ~ r2(X9,X10)
| ~ r2(X8,X9)
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d41,c39]) ).
cnf(d43,plain,
( ~ id(sK7(X17,X18),sK39(X9,X10))
| ~ r2(X2,X15)
| ~ r2(X1,X3)
| ~ r2(X0,X18)
| ~ r2(X7,X16)
| ~ r2(X16,X17)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X8)
| ~ r2(X8,sK54(sK42(X9,X10)))
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d42,d28]) ).
cnf(d44,plain,
( ~ r3(X4,X18,sK40(X11,X12))
| ~ r2(X2,X18)
| ~ r2(X1,X17)
| ~ r2(X0,X5)
| ~ r2(X17,X16)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X3)
| ~ r2(X10,sK54(sK42(X11,X12)))
| ~ r2(X9,X10)
| ~ r2(X8,X9)
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d43,d26]) ).
cnf(d45,plain,
( ~ r2(X2,X16)
| ~ r2(X1,X3)
| ~ r2(X0,sK41(X10,X11))
| ~ r2(X8,X10)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X9)
| ~ r2(X9,sK54(sK42(X10,X11)))
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d44,c37]) ).
cnf(d46,plain,
( ~ id(sK39(X8,X9),sK54(sK42(X11,X17)))
| ~ r2(X2,sK41(X11,X17))
| ~ r2(X1,X16)
| ~ r2(X0,X3)
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X10)
| ~ r2(X10,X11)
| ~ r2(X7,sK54(sK42(X8,X9)))
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d45,d24]) ).
cnf(d47,plain,
( ~ id(sK39(X11,X12),sK42(X9,X17))
| ~ r2(X2,X16)
| ~ r2(X1,X3)
| ~ r2(X0,sK41(X9,X17))
| ~ r2(X16,X15)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X10)
| ~ r2(X10,sK54(sK42(X11,X12)))
| ~ r2(X8,X9)
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d46,d22]) ).
cnf(d48,plain,
( ~ r2(X2,sK41(sK39(X8,X9),sK55(sK39(X8,X9))))
| ~ r2(X1,X15)
| ~ r2(X0,X3)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,sK39(X8,X9))
| ~ r2(X7,sK54(sK42(X8,X9)))
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d21,d47]) ).
cnf(d49,plain,
( ~ r2(X3,X14)
| ~ r2(X2,X4)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,sK54(sK42(X0,X1)))
| ~ r2(X9,sK39(X0,X1))
| ~ r2(X8,X9)
| ~ r2(X7,X8)
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r1(X3)
| ~ r1(X2)
| ~ r1(sK55(sK39(X0,X1))) ),
inference(resolution,[status(thm)],[d48,c36]) ).
cnf(d50,plain,
( ~ r2(X1,X14)
| ~ r2(X0,X2)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,sK39(X7,X8))
| ~ r2(X6,sK54(sK42(X7,X8)))
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c47,d49]) ).
cnf(d51,plain,
( ~ id(sK39(X11,X12),sK54(sK42(X8,X9)))
| ~ r2(X1,X15)
| ~ r2(X0,X2)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X10)
| ~ r2(X10,sK54(sK42(X11,X12)))
| ~ r2(X7,sK39(X8,X9))
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d50,d24]) ).
cnf(d52,plain,
( ~ id(sK39(X6,X7),sK42(X9,X10))
| ~ r2(X1,X15)
| ~ r2(X0,X2)
| ~ r2(X15,X14)
| ~ r2(X14,X13)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X8)
| ~ r2(X8,sK39(X9,X10))
| ~ r2(X5,sK54(sK42(X6,X7)))
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d51,d22]) ).
cnf(d53,plain,
( ~ r2(X1,X13)
| ~ r2(X0,X2)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,sK54(sK42(X8,X9)))
| ~ r2(X7,sK39(sK39(X8,X9),sK55(sK39(X8,X9))))
| ~ r2(X6,X7)
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d52,d21]) ).
cnf(d54,plain,
( ~ r2(X1,X12)
| ~ r2(X0,X2)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,sK39(X6,X7))
| ~ r2(X5,sK54(sK42(X6,X7)))
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d53,d20]) ).
cnf(d55,plain,
( ~ id(sK39(X10,X11),sK54(sK42(X7,X8)))
| ~ r2(X1,X13)
| ~ r2(X0,X2)
| ~ r2(X13,X12)
| ~ r2(X12,X9)
| ~ r2(X9,sK54(sK42(X10,X11)))
| ~ r2(X6,sK39(X7,X8))
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d54,d24]) ).
cnf(d56,plain,
( ~ id(sK39(X5,X6),sK42(X8,X9))
| ~ r2(X1,X13)
| ~ r2(X0,X2)
| ~ r2(X13,X12)
| ~ r2(X12,X11)
| ~ r2(X11,X10)
| ~ r2(X10,X7)
| ~ r2(X7,sK39(X8,X9))
| ~ r2(X4,sK54(sK42(X5,X6)))
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d55,d22]) ).
cnf(d57,plain,
( ~ r2(X1,X11)
| ~ r2(X0,X2)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,sK54(sK42(X7,X8)))
| ~ r2(X6,sK39(sK39(X7,X8),sK55(sK39(X7,X8))))
| ~ r2(X5,X6)
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d56,d21]) ).
cnf(d58,plain,
( ~ r2(X1,X10)
| ~ r2(X0,X2)
| ~ r2(X10,X9)
| ~ r2(X9,X8)
| ~ r2(X8,X7)
| ~ r2(X7,sK39(X5,X6))
| ~ r2(X4,sK54(sK42(X5,X6)))
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d57,d20]) ).
cnf(d59,plain,
( ~ id(sK39(X9,X10),sK54(sK42(X6,X7)))
| ~ r2(X1,X11)
| ~ r2(X0,X2)
| ~ r2(X11,X8)
| ~ r2(X8,sK54(sK42(X9,X10)))
| ~ r2(X5,sK39(X6,X7))
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d58,d24]) ).
cnf(d60,plain,
( ~ id(sK39(X4,X5),sK42(X7,X8))
| ~ r2(X1,X11)
| ~ r2(X0,X2)
| ~ r2(X11,X10)
| ~ r2(X10,X9)
| ~ r2(X9,X6)
| ~ r2(X6,sK39(X7,X8))
| ~ r2(X3,sK54(sK42(X4,X5)))
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d59,d22]) ).
cnf(d61,plain,
( ~ r2(X1,X9)
| ~ r2(X0,X2)
| ~ r2(X9,X8)
| ~ r2(X8,sK54(sK42(X6,X7)))
| ~ r2(X5,sK39(sK39(X6,X7),sK55(sK39(X6,X7))))
| ~ r2(X4,X5)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d60,d21]) ).
cnf(d62,plain,
( ~ r2(X1,X8)
| ~ r2(X0,X2)
| ~ r2(X8,X7)
| ~ r2(X7,X6)
| ~ r2(X6,sK39(X4,X5))
| ~ r2(X3,sK54(sK42(X4,X5)))
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d61,d20]) ).
cnf(d63,plain,
( ~ id(sK39(X8,X9),sK54(sK42(X5,X6)))
| ~ r2(X1,X7)
| ~ r2(X0,X2)
| ~ r2(X7,sK54(sK42(X8,X9)))
| ~ r2(X4,sK39(X5,X6))
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d62,d24]) ).
cnf(d64,plain,
( ~ id(sK39(X3,X4),sK42(X6,X7))
| ~ r2(X1,X9)
| ~ r2(X0,X2)
| ~ r2(X9,X8)
| ~ r2(X8,X5)
| ~ r2(X5,sK39(X6,X7))
| ~ r2(X2,sK54(sK42(X3,X4)))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d63,d22]) ).
cnf(d65,plain,
( ~ r2(X1,X7)
| ~ r2(X0,X2)
| ~ r2(X7,sK54(sK42(X5,X6)))
| ~ r2(X4,sK39(sK39(X5,X6),sK55(sK39(X5,X6))))
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d64,d21]) ).
cnf(d66,plain,
( ~ r2(X1,X6)
| ~ r2(X0,X2)
| ~ r2(X6,X5)
| ~ r2(X5,sK39(X3,X4))
| ~ r2(X2,sK54(sK42(X3,X4)))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d65,d20]) ).
cnf(d67,plain,
( ~ id(sK39(X6,X7),sK54(sK42(X4,X5)))
| ~ r2(X1,sK54(sK42(X6,X7)))
| ~ r2(X0,X2)
| ~ r2(X3,sK39(X4,X5))
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d66,d24]) ).
cnf(d68,plain,
( ~ id(sK39(X6,X7),sK42(X3,X4))
| ~ r2(X1,X5)
| ~ r2(X0,sK54(sK42(X6,X7)))
| ~ r2(X5,X2)
| ~ r2(X2,sK39(X3,X4))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d67,d22]) ).
cnf(d69,plain,
( ~ r2(X1,sK54(sK42(X4,X5)))
| ~ r2(X0,X2)
| ~ r2(X3,sK39(sK39(X4,X5),sK55(sK39(X4,X5))))
| ~ r2(X2,X3)
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d68,d21]) ).
cnf(d70,plain,
( ~ r2(X1,X2)
| ~ r2(X0,sK54(sK42(X3,X4)))
| ~ r2(X2,sK39(X3,X4))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d69,d20]) ).
cnf(d71,plain,
( ~ id(sK39(X1,X2),sK54(sK42(X4,X5)))
| ~ r2(X0,X3)
| ~ r2(X3,sK39(X4,X5))
| ~ r1(sK54(sK42(X1,X2)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d70,d24]) ).
cnf(d72,plain,
( ~ id(sK39(X1,X2),sK42(X4,X5))
| ~ r2(X0,X3)
| ~ r2(X3,sK39(X4,X5))
| ~ r1(sK54(sK42(X1,X2)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d71,d22]) ).
cnf(d73,plain,
( ~ r2(X0,X3)
| ~ r2(X3,sK39(sK39(X1,X2),sK55(sK39(X1,X2))))
| ~ r1(sK54(sK42(X1,X2)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d72,d21]) ).
cnf(d74,plain,
( ~ r2(X0,sK39(X1,X2))
| ~ r1(sK54(sK42(X1,X2)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d73,d20]) ).
cnf(d75,plain,
( ~ r1(sK54(sK42(X0,sK55(X0))))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d74,d20]) ).
cnf(d76,plain,
( ~ r1(sK42(X0,sK55(X0)))
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d75,d9]) ).
cnf(d77,plain,
~ r1(sK0),
inference(resolution,[status(thm)],[d76,d7]) ).
cnf(d78,plain,
r1(sK0),
inference(resolution,[status(thm)],[c3,c16]) ).
cnf(d79,plain,
$false,
inference(resolution,[status(thm)],[d78,d77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN075+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n013.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 04:30:22 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.64/22.19 % SZS status Theorem for theBenchmark.p
% 52.64/22.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------