%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM925+6 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:29:29 PM UTC 2025
% Result : Theorem 18.44s 2.68s
% Output : CNFRefutation 18.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 17 unt; 0 def)
% Number of atoms : 48 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 15 |; 0 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 20 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_0_negated,plain,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(881,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(cnf,[status(esa)],[conj_0_negated]) ).
cnf(l0,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(instantiation,[status(thm)],[881]) ).
fof(fact_409_ord__eq__less__trans,plain,
! [X_a] :
( ord(X_a)
=> ! [C_1,A_1,B] :
( A_1 = B
=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C_1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_ord__eq__less__trans) ).
cnf(637,plain,
( X0 != X1
| ~ ord(X2)
| ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X1),X3))
| hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X0),X3)) ),
inference(cnf,[status(esa)],[fact_409_ord__eq__less__trans]) ).
cnf(l1,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| ~ ord(int)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(instantiation,[status(thm)],[637]) ).
fof(arity_Int_Oint___Orderings_Oord,plain,
ord(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
cnf(799,plain,
ord(int),
inference(cnf,[status(esa)],[arity_Int_Oint___Orderings_Oord]) ).
cnf(l3,plain,
ord(int),
inference(instantiation,[status(thm)],[799]) ).
fof(fact_421_not__less__iff__gr__or__eq,plain,
! [X_a] :
( linorder(X_a)
=> ! [Xa,Ya] :
( ~ hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Xa),Ya))
<=> ( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ya),Xa))
| ti(X_a,Xa) = ti(X_a,Ya) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_not__less__iff__gr__or__eq) ).
cnf(651,plain,
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X1),X2))
| ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),X2),X1))
| ~ linorder(X0) ),
inference(cnf,[status(esa)],[fact_421_not__less__iff__gr__or__eq]) ).
cnf(l4,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| ~ linorder(int) ),
inference(instantiation,[status(thm)],[651]) ).
fof(arity_Int_Oint___Orderings_Olinorder,plain,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
cnf(790,plain,
linorder(int),
inference(cnf,[status(esa)],[arity_Int_Oint___Orderings_Olinorder]) ).
cnf(l5,plain,
linorder(int),
inference(instantiation,[status(thm)],[790]) ).
fof(fact_178_zero__less__power,plain,
! [X_a] :
( linordered_semidom(X_a)
=> ! [N,A_1] :
( hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1))
=> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,power_power(X_a,A_1),N))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_zero__less__power) ).
cnf(297,plain,
( ~ hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),X1))
| ~ linordered_semidom(X0)
| hBOOL(hAPP(X0,bool,hAPP(X0,fun(X0,bool),ord_less(X0),zero_zero(X0)),hAPP(nat,X0,power_power(X0,X1),X2))) ),
inference(cnf,[status(esa)],[fact_178_zero__less__power]) ).
cnf(l2,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))
| ~ linordered_semidom(int)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),
inference(instantiation,[status(thm)],[297]) ).
fof(fact_0_n1pos,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
cnf(46,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(cnf,[status(esa)],[fact_0_n1pos]) ).
cnf(l13,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(instantiation,[status(thm)],[46]) ).
fof(arity_Int_Oint___Rings_Olinordered__semidom,plain,
linordered_semidom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
cnf(779,plain,
linordered_semidom(int),
inference(cnf,[status(esa)],[arity_Int_Oint___Rings_Olinordered__semidom]) ).
cnf(l12,plain,
linordered_semidom(int),
inference(instantiation,[status(thm)],[779]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l4,l5,l2,l13,l12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : NUM925+6 : TPTP v9.0.0. Released v5.3.0.
% 0.08/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.29 % Computer : n018.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 21 14:28:49 EDT 2025
% 0.08/0.29 % CPUTime :
% 0.14/0.34 % launching worker at depth: 4
% 0.14/0.34 % launching worker at depth: 8
% 0.14/0.34 % launching worker at depth: 5
% 0.14/0.34 % launching worker at depth: 1
% 0.14/0.34 % launching worker at depth: 6
% 0.14/0.34 % launching worker at depth: 7
% 0.14/0.34 % launching worker at depth: 3
% 0.14/0.34 % launching worker at depth: 2
% 0.14/0.34 % launching worker at depth: 9
% 1.73/0.62 % launching worker at depth: 10
% 18.44/2.68 % SZS status Theorem for theBenchmark
% 18.44/2.68 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------