%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 42.75s 11.71s
% Output : CNFRefutation 42.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 21 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 188 ( 91 ~; 72 |; 25 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 169 ( 7 sgn 29 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ) ).
fof(axiom_3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r3(X0,X1,X3) )
| ( r3(X0,X1,X3)
& id(X3,X2) ) ) ).
fof(axiom_4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ id(X3,X2)
& ~ r4(X0,X1,X3) )
| ( r4(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_10,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r3(X3,X4,X5)
& r3(X0,X1,X2) )
| ( ~ r3(X3,X4,X5)
& ~ r3(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ) ).
fof(axiom_11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( r4(X3,X4,X5)
& r4(X0,X1,X2) )
| ( ~ r4(X3,X4,X5)
& ~ r4(X0,X1,X2) )
| ~ id(X2,X5)
| ~ id(X1,X4)
| ~ id(X0,X3) ) ).
fof(axiom_4a,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ) ).
fof(axiom_5a,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( r1(X3)
& id(X1,X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ) ).
fof(fermattothepoweroftwoid,conjecture,
? [X0,X1,X2,X3] :
( ? [X5] :
( ? [X6] :
( r3(X6,X5,X3)
& r4(X0,X0,X6) )
& r4(X1,X1,X5) )
& ? [X4] :
( r4(X2,X2,X4)
& id(X3,X4) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2,X3] :
( ? [X5] :
( ? [X6] :
( r3(X6,X5,X3)
& r4(X0,X0,X6) )
& r4(X1,X1,X5) )
& ? [X4] :
( r4(X2,X2,X4)
& id(X3,X4) ) ),
inference(negate_conjecture,[status(cth)],[fermattothepoweroftwoid]) ).
cnf(c0,plain,
( ~ r1(X0)
| id(X0,sK0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c8,plain,
( ~ r3(X1,X2,X0)
| id(X0,sK7(X1,X2)) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c11,plain,
( ~ id(X2,sK7(X0,X1))
| r3(X0,X1,X2) ),
inference(clausification,[status(esa)],[axiom_3]) ).
cnf(c15,plain,
( ~ id(X2,sK11(X0,X1))
| r4(X0,X1,X2) ),
inference(clausification,[status(esa)],[axiom_4]) ).
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(X0,X2)
| ~ id(X1,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(c28,plain,
( ~ r3(X1,X3,X5)
| r3(X0,X2,X4)
| ~ id(X4,X5)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_10]) ).
cnf(c32,plain,
( r4(X0,X2,X4)
| ~ r4(X1,X3,X5)
| ~ id(X4,X5)
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(clausification,[status(esa)],[axiom_11]) ).
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(c49,plain,
r1(sK58(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c50,plain,
r4(X0,sK58(X0),sK57(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c51,plain,
id(sK57(X0),sK59(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c52,plain,
r1(sK59(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c58,plain,
( ~ r4(X6,X6,X3)
| ~ r4(X5,X5,X4)
| ~ r3(X4,X1,X2)
| ~ id(X2,X3)
| ~ r4(X0,X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
r4(X0,X1,sK11(X0,X1)),
inference(resolution,[status(thm)],[c15,c16]) ).
cnf(d1,plain,
( ~ r1(X0)
| id(sK0,X0) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d2,plain,
r4(X0,X1,sK54(sK11(X0,X1))),
inference(resolution,[status(thm)],[c15,c46]) ).
cnf(d3,plain,
( ~ r4(X5,X5,X3)
| ~ r4(X4,X4,X2)
| ~ r3(X2,X3,X0)
| ~ id(X0,sK54(sK11(X1,X1))) ),
inference(resolution,[status(thm)],[d2,c58]) ).
cnf(d4,plain,
( ~ r3(X0,X1,X2)
| id(sK7(X0,X1),X2) ),
inference(resolution,[status(thm)],[c17,c8]) ).
cnf(d5,plain,
( ~ r4(X6,X6,X3)
| ~ r4(X5,X5,X4)
| ~ r3(X3,X4,sK7(X0,X1))
| ~ r3(X0,X1,sK54(sK11(X2,X2))) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ r4(X4,X4,X1)
| ~ r4(X3,X3,X0)
| ~ r3(X0,X1,sK7(sK11(X2,X2),sK55(sK11(X2,X2)))) ),
inference(resolution,[status(thm)],[d5,c48]) ).
cnf(d7,plain,
r3(X0,X1,sK7(X0,X1)),
inference(resolution,[status(thm)],[c11,c16]) ).
cnf(d8,plain,
( r3(X0,X4,X2)
| ~ id(X4,X3)
| ~ id(X2,sK7(X1,X3))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[c28,d7]) ).
cnf(d9,plain,
( r3(X2,X0,sK7(X3,X1))
| ~ id(X2,X3)
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d8,c16]) ).
cnf(d10,plain,
( ~ r4(X4,X4,X0)
| ~ r4(X3,X3,X2)
| ~ id(X2,sK55(sK11(X1,X1)))
| ~ id(X0,sK11(X1,X1)) ),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
( ~ r1(sK55(sK11(X1,X1)))
| ~ r4(X3,X3,sK0)
| ~ r4(X2,X2,X0)
| ~ id(X0,sK11(X1,X1)) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( ~ r4(X3,X3,X0)
| ~ r4(X2,X2,sK0)
| ~ id(X0,sK11(X1,X1)) ),
inference(resolution,[status(thm)],[c47,d11]) ).
cnf(d13,plain,
( ~ r4(X2,X2,sK0)
| ~ r4(X0,X0,sK11(X1,X1)) ),
inference(resolution,[status(thm)],[d12,c16]) ).
cnf(d14,plain,
~ r4(X0,X0,sK0),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( r4(X3,X0,X2)
| ~ id(X3,X1)
| ~ id(X2,sK57(X1))
| ~ id(X0,sK58(X1)) ),
inference(resolution,[status(thm)],[c32,c50]) ).
cnf(d16,plain,
( r4(X0,sK58(X1),X2)
| ~ id(X2,sK57(X1))
| ~ id(X0,X1) ),
inference(resolution,[status(thm)],[d15,c16]) ).
cnf(d17,plain,
( ~ id(sK58(X0),X0)
| ~ id(sK0,sK57(X0)) ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
id(sK59(X0),sK57(X0)),
inference(resolution,[status(thm)],[c17,c51]) ).
cnf(d19,plain,
( ~ id(X0,sK59(X1))
| id(X0,sK57(X1)) ),
inference(resolution,[status(thm)],[c18,d18]) ).
cnf(d20,plain,
( ~ r1(X1)
| ~ id(X0,X1)
| id(X0,sK0) ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(d21,plain,
( id(sK59(X0),sK0)
| ~ r1(sK57(X0)) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( r1(sK57(X0))
| ~ r1(sK59(X0)) ),
inference(resolution,[status(thm)],[c20,c51]) ).
cnf(d23,plain,
r1(sK57(X0)),
inference(resolution,[status(thm)],[c52,d22]) ).
cnf(d24,plain,
id(sK59(X0),sK0),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
id(sK0,sK59(X0)),
inference(resolution,[status(thm)],[d24,c17]) ).
cnf(d26,plain,
id(sK0,sK57(X0)),
inference(resolution,[status(thm)],[d25,d19]) ).
cnf(d27,plain,
~ id(sK58(X0),X0),
inference(resolution,[status(thm)],[d26,d17]) ).
cnf(d28,plain,
~ r1(sK58(sK0)),
inference(resolution,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[c49,d28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n020.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 04:29:24 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.75/11.71 % SZS status Theorem for theBenchmark.p
% 42.75/11.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------