%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUN062+1 : TPTP v9.0.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 12:34:37 PM UTC 2025
% Result : Theorem 13.05s 1.98s
% Output : CNFRefutation 13.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 19 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 63 ~; 54 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 103 ( 5 sgn 24 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(infiniteNumbersid,plain,
! [X1] :
? [Y2,Y1] :
( ! [Y4] :
( ~ id(Y1,Y4)
| ~ r1(Y4) )
& ? [Y3] :
( id(Y3,Y2)
& r3(X1,Y1,Y3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(infiniteNumbersid_negated,plain,
~ ! [X1] :
? [Y2,Y1] :
( ! [Y4] :
( ~ id(Y1,Y4)
| ~ r1(Y4) )
& ? [Y3] :
( id(Y3,Y2)
& r3(X1,Y1,Y3) ) ),
inference(negate_conjecture,[status(cth)],[infiniteNumbersid]) ).
cnf(58,plain,
( ~ id(X0,X1)
| ~ r3(sK21,X2,X0)
| id(X2,sK22(X1,X2)) ),
inference(cnf,[status(esa)],[infiniteNumbersid_negated]) ).
cnf(l0,plain,
( ~ id(sK6(sK21,X0_459),sK2(sK13(sK13(sK8(sK21,X0_459)))))
| ~ r3(sK21,sK7(sK21,X0_459),sK6(sK21,X0_459))
| id(sK7(sK21,X0_459),sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459))) ),
inference(instantiation,[status(thm)],[58]) ).
fof(axiom_1a,plain,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( id(Y5,Y4)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
file('Axioms/NUM009+0.ax',axiom_1a) ).
cnf(37,plain,
r3(X0,sK7(X0,X1),sK6(X0,X1)),
inference(cnf,[status(esa)],[axiom_1a]) ).
cnf(l1,plain,
r3(sK21,sK7(sK21,X0_459),sK6(sK21,X0_459)),
inference(instantiation,[status(thm)],[37]) ).
fof(axiom_2,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( id(X12,Y21)
& r2(X11,X12) )
| ( ~ r2(X11,X12)
& ~ id(X12,Y21) ) ),
file('Axioms/NUM009+0.ax',axiom_2) ).
cnf(4,plain,
( id(X0,sK2(X1))
| sP1(X1,X0) ),
inference(cnf,[status(esa)],[axiom_2]) ).
cnf(l2,plain,
( id(sK6(sK21,X0_459),sK2(sK13(sK13(sK8(sK21,X0_459)))))
| sP1(sK13(sK13(sK8(sK21,X0_459))),sK6(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(7,plain,
( ~ r2(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf,[status(esa)],[axiom_2]) ).
cnf(l254,plain,
( ~ r2(sK13(sK13(sK8(sK21,X0_459))),sK6(sK21,X0_459))
| ~ sP1(sK13(sK13(sK8(sK21,X0_459))),sK6(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[7]) ).
fof(axiom_9,plain,
! [X28,X29,X30,X31] :
( ~ id(X28,X30)
| ~ id(X29,X31)
| ( ~ r2(X28,X29)
& ~ r2(X30,X31) )
| ( r2(X28,X29)
& r2(X30,X31) ) ),
file('Axioms/NUM009+0.ax',axiom_9) ).
cnf(26,plain,
( r2(X0,X1)
| ~ sP5(X1,X0,X2,X3) ),
inference(cnf,[status(esa)],[axiom_9]) ).
cnf(l271,plain,
( r2(sK13(sK13(sK8(sK21,X0_459))),sK6(sK21,X0_459))
| ~ sP5(sK6(sK21,X0_459),sK13(sK13(sK8(sK21,X0_459))),sK5(sK21,X0_459),sK8(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[26]) ).
fof(axiom_6,plain,
! [X21,X22] :
( ~ id(X21,X22)
| id(X22,X21) ),
file('Axioms/NUM009+0.ax',axiom_6) ).
cnf(17,plain,
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf,[status(esa)],[axiom_6]) ).
cnf(l4,plain,
( ~ id(sK7(sK21,X0_459),sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)))
| id(sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)),sK7(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[17]) ).
fof(axiom_8,plain,
! [X26,X27] :
( ~ id(X26,X27)
| ( ~ r1(X26)
& ~ r1(X27) )
| ( r1(X26)
& r1(X27) ) ),
file('Axioms/NUM009+0.ax',axiom_8) ).
cnf(20,plain,
( ~ id(X0,X1)
| ~ r1(X1)
| sP4(X1,X0) ),
inference(cnf,[status(esa)],[axiom_8]) ).
cnf(l82,plain,
( ~ id(sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)),sK7(sK21,X0_459))
| ~ r1(sK7(sK21,X0_459))
| sP4(sK7(sK21,X0_459),sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459))) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(24,plain,
( ~ id(X0,X1)
| ~ id(X2,X3)
| ~ r2(X1,X3)
| sP5(X2,X0,X3,X1) ),
inference(cnf,[status(esa)],[axiom_9]) ).
cnf(l425,plain,
( ~ id(sK13(sK13(sK8(sK21,X0_459))),sK8(sK21,X0_459))
| ~ id(sK6(sK21,X0_459),sK5(sK21,X0_459))
| ~ r2(sK8(sK21,X0_459),sK5(sK21,X0_459))
| sP5(sK6(sK21,X0_459),sK13(sK13(sK8(sK21,X0_459))),sK5(sK21,X0_459),sK8(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[24]) ).
cnf(38,plain,
r2(sK8(X0,X1),sK5(X0,X1)),
inference(cnf,[status(esa)],[axiom_1a]) ).
cnf(l429,plain,
r2(sK8(sK21,X0_459),sK5(sK21,X0_459)),
inference(instantiation,[status(thm)],[38]) ).
fof(axiom_7,plain,
! [X23,X24,X25] :
( ~ id(X23,X24)
| id(X23,X25)
| ~ id(X24,X25) ),
file('Axioms/NUM009+0.ax',axiom_7) ).
cnf(18,plain,
( ~ id(X0,X1)
| ~ id(X1,X2)
| id(X0,X2) ),
inference(cnf,[status(esa)],[axiom_7]) ).
cnf(l435,plain,
( ~ id(sK13(sK13(sK8(sK21,X0_459))),sK13(sK8(sK21,X0_459)))
| ~ id(sK13(sK8(sK21,X0_459)),sK8(sK21,X0_459))
| id(sK13(sK13(sK8(sK21,X0_459))),sK8(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[18]) ).
fof(axiom_4a,plain,
! [X4] :
? [Y9] :
( id(Y9,X4)
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
file('Axioms/NUM009+0.ax',axiom_4a) ).
cnf(46,plain,
id(sK13(X0),X0),
inference(cnf,[status(esa)],[axiom_4a]) ).
cnf(l436,plain,
id(sK13(sK8(sK21,X0_459)),sK8(sK21,X0_459)),
inference(instantiation,[status(thm)],[46]) ).
cnf(35,plain,
id(sK6(X0,X1),sK5(X0,X1)),
inference(cnf,[status(esa)],[axiom_1a]) ).
cnf(l433,plain,
id(sK6(sK21,X0_459),sK5(sK21,X0_459)),
inference(instantiation,[status(thm)],[35]) ).
cnf(l442,plain,
id(sK13(sK13(sK8(sK21,X0_459))),sK13(sK8(sK21,X0_459))),
inference(instantiation,[status(thm)],[46]) ).
cnf(22,plain,
( r1(X0)
| ~ sP4(X1,X0) ),
inference(cnf,[status(esa)],[axiom_8]) ).
cnf(l447,plain,
( r1(sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)))
| ~ sP4(sK7(sK21,X0_459),sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(l86,plain,
( r1(sK7(sK21,X0_459))
| ~ sP4(sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459)),sK7(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[22]) ).
fof(axiom_7a,plain,
! [X7,Y10] :
( ! [Y20] :
( ~ id(Y20,Y10)
| ~ r1(Y20) )
| ~ r2(X7,Y10) ),
file('Axioms/NUM009+0.ax',axiom_7a) ).
cnf(57,plain,
( ~ id(X0,X1)
| ~ r1(X0)
| ~ r2(X2,X1) ),
inference(cnf,[status(esa)],[axiom_7a]) ).
cnf(l458,plain,
( ~ id(sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)),sK7(sK21,X0_459))
| ~ r1(sK22(sK2(sK13(sK13(sK8(sK21,X0_459)))),sK7(sK21,X0_459)))
| ~ r2(X0_459,sK7(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(l247,plain,
( ~ id(sK7(sK21,X0_459),sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459)))
| ~ r1(sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459)))
| sP4(sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459)),sK7(sK21,X0_459)) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(36,plain,
r2(X0,sK7(X1,X0)),
inference(cnf,[status(esa)],[axiom_1a]) ).
cnf(l459,plain,
r2(X0_459,sK7(sK21,X0_459)),
inference(instantiation,[status(thm)],[36]) ).
cnf(l248,plain,
( ~ id(sK8(sK21,sK7(sK21,X0_459)),sK8(sK21,sK7(sK21,X0_459)))
| ~ r3(sK21,sK7(sK21,X0_459),sK8(sK21,sK7(sK21,X0_459)))
| id(sK7(sK21,X0_459),sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459))) ),
inference(instantiation,[status(thm)],[58]) ).
cnf(59,plain,
( ~ id(X0,X1)
| ~ r3(sK21,X2,X0)
| r1(sK22(X1,X2)) ),
inference(cnf,[status(esa)],[infiniteNumbersid_negated]) ).
cnf(l249,plain,
( ~ id(sK8(sK21,sK7(sK21,X0_459)),sK8(sK21,sK7(sK21,X0_459)))
| ~ r3(sK21,sK7(sK21,X0_459),sK8(sK21,sK7(sK21,X0_459)))
| r1(sK22(sK8(sK21,sK7(sK21,X0_459)),sK7(sK21,X0_459))) ),
inference(instantiation,[status(thm)],[59]) ).
fof(axiom_5,plain,
! [X20] : id(X20,X20),
file('Axioms/NUM009+0.ax',axiom_5) ).
cnf(16,plain,
id(X0,X0),
inference(cnf,[status(esa)],[axiom_5]) ).
cnf(l405,plain,
id(sK8(sK21,sK7(sK21,X0_459)),sK8(sK21,sK7(sK21,X0_459))),
inference(instantiation,[status(thm)],[16]) ).
cnf(39,plain,
r3(X0,X1,sK8(X0,X1)),
inference(cnf,[status(esa)],[axiom_1a]) ).
cnf(l250,plain,
r3(sK21,sK7(sK21,X0_459),sK8(sK21,sK7(sK21,X0_459))),
inference(instantiation,[status(thm)],[39]) ).
cnf(l251,plain,
id(sK8(sK21,sK7(sK21,X0_459)),sK8(sK21,sK7(sK21,X0_459))),
inference(instantiation,[status(thm)],[16]) ).
cnf(l402,plain,
r3(sK21,sK7(sK21,X0_459),sK8(sK21,sK7(sK21,X0_459))),
inference(instantiation,[status(thm)],[39]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l254,l271,l4,l82,l425,l429,l435,l436,l433,l442,l447,l86,l458,l247,l459,l248,l249,l405,l250,l251,l402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN062+1 : TPTP v9.0.0. Bugfixed v7.4.0.
% 0.06/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 14:42:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.18/0.40 % launching worker at depth: 11
% 13.05/1.98 % SZS status Theorem for theBenchmark
% 13.05/1.98 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------