%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925+5 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:22:25 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 64 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 112 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 193 ( 69 ~; 58 |; 0 &)
% ( 60 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 104 ( 95 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_type,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(semiring_1_of_nat_type,type,
semiring_1_of_nat: ( $i * $i ) > $i ).
tff(n_type,type,
n: $i ).
tff(int_type,type,
int: $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(pls_type,type,
pls: $i ).
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(power_power_type,type,
power_power: ( $i * $i * $i ) > $i ).
tff(number_number_of_type,type,
number_number_of: ( $i * $i ) > $i ).
tff(bit0_type,type,
bit0: $i > $i ).
tff(bit1_type,type,
bit1: $i > $i ).
tff(nat_type,type,
nat: $i ).
tff(ring_11004092258visors_type,type,
ring_11004092258visors: $i > $o ).
tff(number_semiring_type,type,
number_semiring: $i > $o ).
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/sandbox2/benchmark/theBenchmark.p',fact_73_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,
( ring_11004092258visors(int)
<=> ring_11004092258visors(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(7,plain,
ring_11004092258visors(int),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [X_a: $i] :
refl(( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X_a: $i] :
rewrite(( ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(transitivity,[status(thm)],[11,9]) ).
tff(13,plain,
( ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [X_a: $i] :
rewrite(( ( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [X_a: $i] :
( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
<=> ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [X_a: $i] :
( ring_11004092258visors(X_a)
=> ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
tff(17,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) )
<=> ( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [X_a: $i] :
( ~ ring_11004092258visors(X_a)
| ! [A_2: $i] :
( ( power_power(X_a,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X_a) )
<=> ( ti(X_a,A_2) = zero_zero(X_a) ) ) )
| ~ ring_11004092258visors(int)
| ! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[23,20,7]) ).
tff(25,plain,
( ~ ! [A_2: $i] :
( ( power_power(int,A_2,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,A_2) = zero_zero(int) ) )
| ( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ) )
<=> ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
~ ( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(30,plain,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ~ ( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) )
| ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) )
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
( ~ ( ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int) )
<=> ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) )
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = zero_zero(int),
inference(unit_resolution,[status(thm)],[33,26]) ).
tff(35,plain,
( number_semiring(int)
<=> number_semiring(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(37,plain,
number_semiring(int),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
^ [B_1: $i,B_2: $i,X_a: $i] :
refl(( ( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
<=> ( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
<=> ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
<=> ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [B_1: $i,B_2: $i,X_a: $i] :
rewrite(( ( number_semiring(X_a)
=> ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
<=> ( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [B_1: $i,B_2: $i,X_a: $i] :
( number_semiring(X_a)
=> ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
<=> ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( number_semiring(X_a)
=> ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
tff(44,plain,
! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
| ~ number_semiring(int)
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) ) )
<=> ( ~ ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
| ~ number_semiring(int)
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
| ~ number_semiring(int)
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [B_1: $i,B_2: $i,X_a: $i] :
( ~ number_semiring(X_a)
| ( ti(X_a,plus_plus(X_a,B_1,B_2)) = plus_plus(X_a,B_1,B_2) ) )
| ~ number_semiring(int)
| ( ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,plain,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = pls,
inference(transitivity,[status(thm)],[52,34,4]) ).
tff(54,plain,
( ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
<=> ord_less(int,pls,pls) ),
inference(monotonicity,[status(thm)],[4,53]) ).
tff(55,plain,
( ord_less(int,pls,pls)
<=> ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ~ ord_less(int,pls,pls)
<=> ~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ~ ord_less(int,pls,pls)
<=> ~ ord_less(int,pls,pls) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
tff(59,plain,
~ ord_less(int,pls,pls),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,plain,
( ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
<=> ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(63,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM925+5 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:04:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------