%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924+6 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 1.24s 1.38s
% Output : Proof 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 61
% Syntax : Number of formulae : 151 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 652 ( 268 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 656 ( 198 ~; 273 |; 10 &)
% ( 155 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 263 ( 239 !; 0 ?; 263 :)
% Comments :
%------------------------------------------------------------------------------
tff(ti_type,type,
ti: ( $i * $i ) > $i ).
tff(times_times_type,type,
times_times: ( $i * $i * $i ) > $i ).
tff(zero_zero_type,type,
zero_zero: $i > $i ).
tff(int_type,type,
int: $i ).
tff(plus_plus_type,type,
plus_plus: ( $i * $i * $i ) > $i ).
tff(one_one_type,type,
one_one: $i > $i ).
tff(m_type,type,
m: $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(pls_type,type,
pls: $i ).
tff(t_type,type,
t: $i ).
tff(power_type,type,
power: $i > $o ).
tff(ring_n68954251visors_type,type,
ring_n68954251visors: $i > $o ).
tff(ord_less_type,type,
ord_less: ( $i * $i * $i ) > $o ).
tff(ord_less_eq_type,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
tff(power_power_type,type,
power_power: ( $i * $i * $i ) > $i ).
tff(nat_type,type,
nat: $i ).
tff(s_type,type,
s: $i ).
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_120_Pls__def) ).
tff(3,plain,
pls = zero_zero(int),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( power(int)
<=> power(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
power(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(10,plain,
power(int),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [B_1_1: $i,B_2_1: $i,X_a: $i] :
refl(( ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
^ [B_1_1: $i,B_2_1: $i,X_a: $i] :
rewrite(( ( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
<=> ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( power(X_a)
=> ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_4_res) ).
tff(17,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) ) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [B_1_1: $i,B_2_1: $i,X_a: $i] :
( ~ power(X_a)
| ( ti(X_a,times_times(X_a,B_1_1,B_2_1)) = times_times(X_a,B_1_1,B_2_1) ) )
| ~ power(int)
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls),
inference(unit_resolution,[status(thm)],[23,20,10]) ).
tff(25,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),pls)),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
zero_zero(int) = pls,
inference(symmetry,[status(thm)],[3]) ).
tff(27,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_one__is__num__one) ).
tff(29,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)) = plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls),
inference(monotonicity,[status(thm)],[30,26]) ).
tff(32,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ring_n68954251visors(int)
<=> ring_n68954251visors(int) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
ring_n68954251visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__no__zero__divisors) ).
tff(35,plain,
ring_n68954251visors(int),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
^ [X_a: $i] :
refl(( ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
^ [X_a: $i] :
rewrite(( ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [X_a: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [A_2: $i,B_1: $i] :
rewrite(( ( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) )
<=> ( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ))),
( ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) )
<=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )),
( ( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) ) )
<=> ( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) )),
rewrite(( ( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
<=> ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) )),
( ( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) ) )
<=> ( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [X_a: $i] :
( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) ) )
<=> ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X_a: $i] :
( ring_n68954251visors(X_a)
=> ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,A_2) = zero_zero(X_a) )
| ( ti(X_a,B_1) = zero_zero(X_a) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_mult__eq__0__iff) ).
tff(45,plain,
! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
| ~ ring_n68954251visors(int)
| ! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) ) )
<=> ( ~ ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
| ~ ring_n68954251visors(int)
| ! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
| ~ ring_n68954251visors(int)
| ! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X_a: $i] :
( ~ ring_n68954251visors(X_a)
| ! [A_2: $i,B_1: $i] :
( ( times_times(X_a,A_2,B_1) = zero_zero(X_a) )
<=> ( ( ti(X_a,B_1) = zero_zero(X_a) )
| ( ti(X_a,A_2) = zero_zero(X_a) ) ) ) )
| ~ ring_n68954251visors(int)
| ! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) ),
inference(unit_resolution,[status(thm)],[51,48,35]) ).
tff(53,plain,
( ~ ! [A_2: $i,B_1: $i] :
( ( times_times(int,A_2,B_1) = zero_zero(int) )
<=> ( ( ti(int,B_1) = zero_zero(int) )
| ( ti(int,A_2) = zero_zero(int) ) ) )
| ( ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) )
<=> ( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) )
<=> ( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ( ti(int,pls) = pls )
<=> ( ti(int,pls) = pls ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
ti(int,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
tff(57,plain,
ti(int,pls) = pls,
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
ti(int,pls) = zero_zero(int),
inference(transitivity,[status(thm)],[57,3]) ).
tff(59,plain,
( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) )
| ( ti(int,pls) != zero_zero(int) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ( ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) )
<=> ( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ) )
| ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) )
| ~ ( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
( ~ ( ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) )
<=> ( ( ti(int,pls) = zero_zero(int) )
| ( ti(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls)))) = zero_zero(int) ) ) )
| ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int) ) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls) = zero_zero(int),
inference(unit_resolution,[status(thm)],[62,54]) ).
tff(64,plain,
zero_zero(int) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),number_number_of(int,bit1(pls))),pls),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
<=> ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(66,plain,
( ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
<=> ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
<=> ~ ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
^ [Z_1: $i] :
refl(( ( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
<=> ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_int__one__le__iff__zero__less) ).
tff(72,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [Z_1: $i] :
( ord_less_eq(int,one_one(int),Z_1)
<=> ord_less(int,zero_zero(int),Z_1) )
| ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ ord_less_eq(int,one_one(int),t)
<=> ~ ord_less_eq(int,one_one(int),t) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
~ ord_less_eq(int,one_one(int),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(79,plain,
~ ord_less_eq(int,one_one(int),t),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) )
| ord_less_eq(int,one_one(int),t)
| ~ ord_less(int,zero_zero(int),t) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
( ~ ( ord_less_eq(int,one_one(int),t)
<=> ord_less(int,zero_zero(int),t) )
| ~ ord_less(int,zero_zero(int),t) ),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
~ ord_less(int,zero_zero(int),t),
inference(unit_resolution,[status(thm)],[81,76]) ).
tff(83,plain,
^ [B: $i,A_1: $i] :
refl(( ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [B: $i,A_1: $i] :
trans(monotonicity(rewrite(( ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) )
<=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) )),
( ( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),A_1)
=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) ) )),
rewrite(( ( ord_less(int,zero_zero(int),A_1)
=> ( ~ ord_less(int,zero_zero(int),times_times(int,A_1,B))
| ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
( ( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) )
<=> ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),A_1)
=> ( ord_less(int,zero_zero(int),times_times(int,A_1,B))
=> ord_less(int,zero_zero(int),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_pos__zmult__pos) ).
tff(89,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
( ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
<=> ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
tff(95,plain,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) )
<=> ( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [B: $i,A_1: $i] :
( ord_less(int,zero_zero(int),B)
| ~ ord_less(int,zero_zero(int),A_1)
| ~ ord_less(int,zero_zero(int),times_times(int,A_1,B)) )
| ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)))
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ord_less(int,zero_zero(int),t)
| ~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(unit_resolution,[status(thm)],[98,95,92]) ).
tff(100,plain,
~ ord_less(int,zero_zero(int),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(unit_resolution,[status(thm)],[99,82]) ).
tff(101,plain,
~ ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(modus_ponens,[status(thm)],[100,67]) ).
tff(102,plain,
( ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) )
<=> ( plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(104,plain,
plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)) = times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t) = plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
<=> ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)) ),
inference(monotonicity,[status(thm)],[105,3]) ).
tff(107,plain,
( ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls) ),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
( ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
<=> ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int))
<=> ~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(111,plain,
~ ord_less(int,plus_plus(int,power_power(int,s,number_number_of(nat,bit0(bit1(pls)))),one_one(int)),zero_zero(int)),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls),
inference(modus_ponens,[status(thm)],[111,108]) ).
tff(113,plain,
^ [X: $i,Y: $i] :
refl(( ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [X: $i,Y: $i] :
trans(monotonicity(rewrite(( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) ) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y) ) )),
( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
rewrite(( ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
( ( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [X: $i,Y: $i] :
( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) )
<=> ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [X: $i,Y: $i] :
( ord_less(int,X,Y)
| ( ti(int,X) = ti(int,Y) )
| ord_less(int,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_zless__linear) ).
tff(119,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
( ( ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) )
<=> ( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) ) ),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) ) ),
inference(transitivity,[status(thm)],[125,123]) ).
tff(127,plain,
( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [X: $i,Y: $i] :
( ( ti(int,X) = ti(int,Y) )
| ord_less(int,X,Y)
| ord_less(int,Y,X) )
| ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),pls)
| ord_less(int,pls,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,pls),
inference(unit_resolution,[status(thm)],[128,122,112,101]) ).
tff(130,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(transitivity,[status(thm)],[129,57,3,64,32,5,25,7]) ).
tff(131,plain,
^ [Z_1: $i,W_1: $i] :
refl(( ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) )
<=> ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) )
<=> ! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
^ [Z_1: $i,W_1: $i] :
trans(trans(monotonicity(rewrite(( ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) )
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) )),
( ( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) ) )),
rewrite(( ( ord_less(int,Z_1,W_1)
<=> ~ ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) ) )
<=> ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) )),
( ( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) )),
rewrite(( ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) )
<=> ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) )),
( ( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) )),
inference(bind,[status(th)],[]) ).
tff(134,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,plain,
( ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) )
<=> ! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_zless__le) ).
tff(137,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [Z_1: $i,W_1: $i] :
( ord_less(int,Z_1,W_1)
<=> ( ord_less_eq(int,Z_1,W_1)
& ( ti(int,Z_1) != ti(int,W_1) ) ) ),
inference(skolemize,[status(sab)],[137]) ).
tff(139,plain,
! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
( ~ ! [Z_1: $i,W_1: $i] :
~ ( ( ~ ord_less_eq(int,Z_1,W_1)
| ( ti(int,Z_1) = ti(int,W_1) ) )
<=> ord_less(int,Z_1,W_1) )
| ~ ( ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) )
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
~ ( ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) )
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ),
inference(unit_resolution,[status(thm)],[141,140]) ).
tff(143,plain,
( ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(145,plain,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ( ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) )
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) )
| ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) )
| ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ),
inference(tautology,[status(thm)],[]) ).
tff(147,plain,
( ( ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) )
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) )
| ~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) ) ),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
~ ( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) ),
inference(unit_resolution,[status(thm)],[147,142]) ).
tff(149,plain,
( ~ ord_less_eq(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int)))
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) = ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) )
| ( ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) != ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(150,plain,
ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)) != ti(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),zero_zero(int))),
inference(unit_resolution,[status(thm)],[149,148]) ).
tff(151,plain,
$false,
inference(unit_resolution,[status(thm)],[150,130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM924+6 : TPTP v9.0.0. Released v5.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.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 02:04:39 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.24/1.38 % SZS status Theorem
% 1.24/1.38 % SZS output start Proof
% See solution above
% 1.24/1.44 % E exiting
%------------------------------------------------------------------------------