%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925_1 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:22:23 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 33 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 47 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 15 ~; 4 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_int_type,type,
ord_less_int: ( int * int ) > $o ).
tff(plus_plus_int_type,type,
plus_plus_int: ( int * int ) > int ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: nat > int ).
tff(n_type,type,
n: nat ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(pls_type,type,
pls: int ).
tff(power_power_int_type,type,
power_power_int: ( int * nat ) > int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(bit0_type,type,
bit0: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(1,plain,
( ( pls = zero_zero_int )
<=> ( pls = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pls__def) ).
tff(3,plain,
pls = zero_zero_int,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
zero_zero_int = pls,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
^ [A_1: int] :
refl(( ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
<=> ! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).
tff(9,plain,
! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
inference(skolemize,[status(sab)],[9]) ).
tff(11,plain,
! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ~ ! [A_1: int] :
( ( power_power_int(A_1,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( A_1 = zero_zero_int ) )
| ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(17,plain,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) )
| ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) ),
inference(tautology,[status(thm)],[]) ).
tff(20,plain,
( ~ ( ( power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) )
| ( plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = zero_zero_int,
inference(unit_resolution,[status(thm)],[20,13]) ).
tff(22,plain,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(transitivity,[status(thm)],[21,4]) ).
tff(23,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n)))
<=> ord_less_int(pls,pls) ),
inference(monotonicity,[status(thm)],[4,22]) ).
tff(24,plain,
( ord_less_int(pls,pls)
<=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ ord_less_int(pls,pls)
<=> ~ ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ ord_less_int(pls,pls)
<=> ~ ord_less_int(pls,pls) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
~ ord_less_int(pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_rel__simps_I2_J) ).
tff(28,plain,
~ ord_less_int(pls,pls),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
( ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n)))
<=> ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(32,plain,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM925_1 : TPTP v9.0.0. Released v5.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 02:04:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------