%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924+5 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:22:22 AM UTC 2025
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 31
% Syntax : Number of formulae : 79 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 53 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 116 ( 41 ~; 30 |; 0 &)
% ( 42 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 94 ( 84 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(ord_less_eq_type,type,
ord_less_eq: ( $i * $i * $i ) > $o ).
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(ord_less_type,type,
ord_less: ( $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,
^ [K_1: $i] :
refl(( ( number_number_of(int,K_1) = K_1 )
<=> ( number_number_of(int,K_1) = K_1 ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
<=> ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
<=> ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_number__of__is__id) ).
tff(5,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [K_1: $i] : ( number_number_of(int,K_1) = K_1 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [K_1: $i] : ( number_number_of(int,K_1) = K_1 )
| ( number_number_of(int,pls) = pls ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
number_number_of(int,pls) = pls,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
pls = number_number_of(int,pls),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [W: $i] :
refl(( ( times_times(int,pls,W) = pls )
<=> ( times_times(int,pls,W) = pls ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W: $i] : ( times_times(int,pls,W) = pls )
<=> ! [W: $i] : ( times_times(int,pls,W) = pls ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W: $i] : ( times_times(int,pls,W) = pls )
<=> ! [W: $i] : ( times_times(int,pls,W) = pls ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [W: $i] : ( times_times(int,pls,W) = pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_mult__Pls) ).
tff(15,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [W: $i] : ( times_times(int,pls,W) = pls ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [W: $i] : ( times_times(int,pls,W) = pls )
| ( times_times(int,pls,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(19,plain,
times_times(int,pls,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = pls,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) = times_times(int,pls,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(monotonicity,[status(thm)],[9]) ).
tff(21,plain,
^ [Z: $i,W: $i] :
refl(( ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ( times_times(int,Z,W) = times_times(int,W,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
<=> ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zmult__commute) ).
tff(25,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Z: $i,W: $i] : ( times_times(int,Z,W) = times_times(int,W,Z) )
| ( times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,pls)) = times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),number_number_of(int,pls)) = times_times(int,number_number_of(int,pls),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ( zero_zero(int) = number_number_of(int,pls) )
<=> ( zero_zero(int) = number_number_of(int,pls) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__is__num__zero) ).
tff(32,plain,
zero_zero(int) = number_number_of(int,pls),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,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)),number_number_of(int,pls)),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,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)) = number_number_of(int,pls),
inference(transitivity,[status(thm)],[33,29,20,19,10]) ).
tff(35,plain,
( ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(int,pls)) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(int,pls))
<=> ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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)],[35]) ).
tff(37,plain,
( ~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(int,pls))
<=> ~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
^ [W_1: $i,Z_1: $i] :
refl(( ( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) )
<=> ( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) )
<=> ! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) )
<=> ! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add1__zle__eq) ).
tff(42,plain,
! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [W_1: $i,Z_1: $i] :
( ord_less_eq(int,plus_plus(int,W_1,one_one(int)),Z_1)
<=> ord_less(int,W_1,Z_1) )
| ( ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(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),number_number_of(int,pls)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(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),number_number_of(int,pls)) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
number_number_of(int,pls) = zero_zero(int),
inference(symmetry,[status(thm)],[32]) ).
tff(48,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(49,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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(50,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)],[49,48]) ).
tff(51,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)],[50]) ).
tff(52,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),number_number_of(int,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)],[51,47]) ).
tff(53,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),number_number_of(int,pls)) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,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),number_number_of(int,pls)) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,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(56,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/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(57,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)],[56,55]) ).
tff(58,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),number_number_of(int,pls)),
inference(modus_ponens,[status(thm)],[57,54]) ).
tff(59,plain,
( ~ ( ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(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),number_number_of(int,pls)) )
| ~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(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),number_number_of(int,pls)) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(int)),number_number_of(int,pls)),
inference(unit_resolution,[status(thm)],[59,58,46]) ).
tff(61,plain,
~ ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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(modus_ponens,[status(thm)],[60,37]) ).
tff(62,plain,
^ [W: $i,Z: $i] :
refl(( ( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
<=> ( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
<=> ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
<=> ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [W: $i,Z: $i] :
rewrite(( ( ord_less(int,W,Z)
=> ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
<=> ( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W: $i,Z: $i] :
( ord_less(int,W,Z)
=> ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
<=> ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [W: $i,Z: $i] :
( ord_less(int,W,Z)
=> ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zless__imp__add1__zle) ).
tff(68,plain,
! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,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(73,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/sandbox/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(74,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)],[73,72]) ).
tff(75,plain,
( ( ~ ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
| ~ 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,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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))) )
<=> ( ~ ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
| ~ 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,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
| ~ 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,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W: $i,Z: $i] :
( ~ ord_less(int,W,Z)
| ord_less_eq(int,plus_plus(int,W,one_one(int)),Z) )
| ~ 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,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
ord_less_eq(int,plus_plus(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t),one_one(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)],[77,74,71]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM924+5 : TPTP v9.0.0. Released v5.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:04:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------