TSTP Solution File: NUM768^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM768^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n004.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 : 600s
% DateTime : Mon Jul 18 11:55:17 EDT 2022
% Result : Theorem 128.64s 128.87s
% Output : CNFRefutation 128.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 28
% Syntax : Number of formulae : 177 ( 69 unt; 17 typ; 0 def)
% Number of atoms : 1071 ( 478 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2803 ( 44 ~; 180 |; 0 &;2567 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 504 ( 77 ^ 427 !; 0 ?; 504 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_amone,type,
amone: ( nat > $o ) > $o ).
thf(tp_den,type,
den: frac > nat ).
thf(tp_eq,type,
eq: frac > frac > $o ).
thf(tp_fr,type,
fr: nat > nat > frac ).
thf(tp_ind,type,
ind: ( nat > $o ) > nat ).
thf(tp_num,type,
num: frac > nat ).
thf(tp_pf,type,
pf: frac > frac > frac ).
thf(tp_pl,type,
pl: nat > nat > nat ).
thf(tp_sK1_E,type,
sK1_E: nat > nat > nat ).
thf(tp_sK2_E,type,
sK2_E: nat ).
thf(tp_sK3_E,type,
sK3_E: nat > nat > nat ).
thf(tp_some,type,
some: ( nat > $o ) > $o ).
thf(tp_ts,type,
ts: nat > nat > nat ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(1,axiom,
! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40a) ).
thf(2,axiom,
! [Xp: nat > $o] :
( ~ ( ( amone @ Xp )
=> ~ ( some @ Xp ) )
=> ( Xp @ ( ind @ Xp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneax) ).
thf(3,axiom,
! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz57) ).
thf(4,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(5,axiom,
! [Xx: frac] : ( eq @ Xx @ Xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz37) ).
thf(6,axiom,
! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz40) ).
thf(7,axiom,
! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(8,axiom,
! [Xx: frac,Xy: frac,Xz: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xy @ Xz )
=> ( eq @ Xx @ Xz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(9,axiom,
! [Xx: nat,Xy: nat] :
( amone
@ ^ [Xz: nat] :
( Xx
= ( pl @ Xy @ Xz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz8b) ).
thf(10,axiom,
( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(11,conjecture,
( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz67c) ).
thf(12,negated_conjecture,
( ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x )
= $false ),
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,plain,
( ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x )
= $false ),
inference(unfold_def,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [Xp: nat > $o] :
( ~ ( ( amone @ Xp )
=> ~ ( some @ Xp ) )
=> ( Xp @ ( ind @ Xp ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac,Xu: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xz @ Xu )
=> ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [Xx: frac,Xy: frac,Xz: frac] :
( ( eq @ Xx @ Xy )
=> ( ( eq @ Xy @ Xz )
=> ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [Xx: nat,Xy: nat] :
( amone
@ ^ [Xz: nat] :
( Xx
= ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [Xp: nat > $o] :
( ~ ( amone @ Xp )
| ~ ( some @ Xp )
| ( Xp @ ( ind @ Xp ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(26,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac,Xu: frac] :
( ~ ( eq @ Xz @ Xu )
| ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(27,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xy @ Xz )
| ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(28,plain,
( ( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
( ( ! [Xx: nat,Xy: nat] :
( amone
@ ^ [Xz: nat] :
( Xx
= ( pl @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(30,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac] :
( ~ ( eq @ Xy @ Xz )
| ( eq @ Xx @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [Xx: frac,Xy: frac] :
( ~ ( eq @ Xx @ Xy )
| ! [Xz: frac,Xu: frac] :
( ~ ( eq @ Xz @ Xu )
| ( eq @ ( pf @ Xx @ Xz ) @ ( pf @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(32,plain,
( ( ! [Xx: frac,Xn: nat] : ( eq @ Xx @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(33,plain,
( ( ! [Xx: frac] : ( eq @ Xx @ Xx ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(34,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(35,plain,
( ( ! [Xx1: nat,Xx2: nat,Xn: nat] : ( eq @ ( pf @ ( fr @ Xx1 @ Xn ) @ ( fr @ Xx2 @ Xn ) ) @ ( fr @ ( pl @ Xx1 @ Xx2 ) @ Xn ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(36,plain,
( ( ! [Xp: nat > $o] :
( ~ ( amone @ Xp )
| ~ ( some @ Xp )
| ( Xp @ ( ind @ Xp ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [Xx: frac,Xn: nat] : ( eq @ ( fr @ ( ts @ ( num @ Xx ) @ Xn ) @ ( ts @ ( den @ Xx ) @ Xn ) ) @ Xx ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(38,plain,
( ( ~ ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(39,plain,
! [SV1: nat] :
( ( ! [SY62: nat] :
( amone
@ ^ [SY63: nat] :
( SV1
= ( pl @ SY62 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV2: frac] :
( ( ! [SY64: frac] :
( ~ ( eq @ SV2 @ SY64 )
| ! [SY65: frac] :
( ~ ( eq @ SY64 @ SY65 )
| ( eq @ SV2 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV3: frac] :
( ( ! [SY66: frac] :
( ~ ( eq @ SV3 @ SY66 )
| ! [SY67: frac,SY68: frac] :
( ~ ( eq @ SY67 @ SY68 )
| ( eq @ ( pf @ SV3 @ SY67 ) @ ( pf @ SY66 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
! [SV4: frac] :
( ( ! [SY69: nat] : ( eq @ SV4 @ ( fr @ ( ts @ ( num @ SV4 ) @ SY69 ) @ ( ts @ ( den @ SV4 ) @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(43,plain,
! [SV5: frac] :
( ( eq @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(44,plain,
! [SV6: nat] :
( ( ! [SY70: nat] :
( ( ts @ SV6 @ SY70 )
= ( ts @ SY70 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(45,plain,
! [SV7: nat] :
( ( ! [SY71: nat,SY72: nat] : ( eq @ ( pf @ ( fr @ SV7 @ SY72 ) @ ( fr @ SY71 @ SY72 ) ) @ ( fr @ ( pl @ SV7 @ SY71 ) @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(46,plain,
! [SV8: nat > $o] :
( ( ~ ( amone @ SV8 )
| ~ ( some @ SV8 )
| ( SV8 @ ( ind @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(47,plain,
! [SV9: frac] :
( ( ! [SY73: nat] : ( eq @ ( fr @ ( ts @ ( num @ SV9 ) @ SY73 ) @ ( ts @ ( den @ SV9 ) @ SY73 ) ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(48,plain,
( ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV10: nat,SV1: nat] :
( ( amone
@ ^ [SY74: nat] :
( SV1
= ( pl @ SV10 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV11: frac,SV2: frac] :
( ( ~ ( eq @ SV2 @ SV11 )
| ! [SY75: frac] :
( ~ ( eq @ SV11 @ SY75 )
| ( eq @ SV2 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV12: frac,SV3: frac] :
( ( ~ ( eq @ SV3 @ SV12 )
| ! [SY76: frac,SY77: frac] :
( ~ ( eq @ SY76 @ SY77 )
| ( eq @ ( pf @ SV3 @ SY76 ) @ ( pf @ SV12 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(52,plain,
! [SV13: nat,SV4: frac] :
( ( eq @ SV4 @ ( fr @ ( ts @ ( num @ SV4 ) @ SV13 ) @ ( ts @ ( den @ SV4 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(53,plain,
! [SV14: nat,SV6: nat] :
( ( ( ts @ SV6 @ SV14 )
= ( ts @ SV14 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(54,plain,
! [SV15: nat,SV7: nat] :
( ( ! [SY78: nat] : ( eq @ ( pf @ ( fr @ SV7 @ SY78 ) @ ( fr @ SV15 @ SY78 ) ) @ ( fr @ ( pl @ SV7 @ SV15 ) @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(55,plain,
! [SV8: nat > $o] :
( ( ( ~ ( amone @ SV8 )
| ~ ( some @ SV8 ) )
= $true )
| ( ( SV8 @ ( ind @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(56,plain,
! [SV16: nat,SV9: frac] :
( ( eq @ ( fr @ ( ts @ ( num @ SV9 ) @ SV16 ) @ ( ts @ ( den @ SV9 ) @ SV16 ) ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV11: frac,SV2: frac] :
( ( ( ~ ( eq @ SV2 @ SV11 ) )
= $true )
| ( ( ! [SY75: frac] :
( ~ ( eq @ SV11 @ SY75 )
| ( eq @ SV2 @ SY75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV12: frac,SV3: frac] :
( ( ( ~ ( eq @ SV3 @ SV12 ) )
= $true )
| ( ( ! [SY76: frac,SY77: frac] :
( ~ ( eq @ SY76 @ SY77 )
| ( eq @ ( pf @ SV3 @ SY76 ) @ ( pf @ SV12 @ SY77 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV15: nat,SV17: nat,SV7: nat] :
( ( eq @ ( pf @ ( fr @ SV7 @ SV17 ) @ ( fr @ SV15 @ SV17 ) ) @ ( fr @ ( pl @ SV7 @ SV15 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV8: nat > $o] :
( ( ( ~ ( amone @ SV8 ) )
= $true )
| ( ( ~ ( some @ SV8 ) )
= $true )
| ( ( SV8 @ ( ind @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV11: frac,SV2: frac] :
( ( ( eq @ SV2 @ SV11 )
= $false )
| ( ( ! [SY75: frac] :
( ~ ( eq @ SV11 @ SY75 )
| ( eq @ SV2 @ SY75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV12: frac,SV3: frac] :
( ( ( eq @ SV3 @ SV12 )
= $false )
| ( ( ! [SY76: frac,SY77: frac] :
( ~ ( eq @ SY76 @ SY77 )
| ( eq @ ( pf @ SV3 @ SY76 ) @ ( pf @ SV12 @ SY77 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV8: nat > $o] :
( ( ( amone @ SV8 )
= $false )
| ( ( ~ ( some @ SV8 ) )
= $true )
| ( ( SV8 @ ( ind @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV2: frac,SV18: frac,SV11: frac] :
( ( ( ~ ( eq @ SV11 @ SV18 )
| ( eq @ SV2 @ SV18 ) )
= $true )
| ( ( eq @ SV2 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV12: frac,SV3: frac,SV19: frac] :
( ( ( ! [SY79: frac] :
( ~ ( eq @ SV19 @ SY79 )
| ( eq @ ( pf @ SV3 @ SV19 ) @ ( pf @ SV12 @ SY79 ) ) ) )
= $true )
| ( ( eq @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV8: nat > $o] :
( ( ( some @ SV8 )
= $false )
| ( ( amone @ SV8 )
= $false )
| ( ( SV8 @ ( ind @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV2: frac,SV18: frac,SV11: frac] :
( ( ( ~ ( eq @ SV11 @ SV18 ) )
= $true )
| ( ( eq @ SV2 @ SV18 )
= $true )
| ( ( eq @ SV2 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV12: frac,SV3: frac,SV20: frac,SV19: frac] :
( ( ( ~ ( eq @ SV19 @ SV20 )
| ( eq @ ( pf @ SV3 @ SV19 ) @ ( pf @ SV12 @ SV20 ) ) )
= $true )
| ( ( eq @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV2: frac,SV18: frac,SV11: frac] :
( ( ( eq @ SV11 @ SV18 )
= $false )
| ( ( eq @ SV2 @ SV18 )
= $true )
| ( ( eq @ SV2 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV12: frac,SV3: frac,SV20: frac,SV19: frac] :
( ( ( ~ ( eq @ SV19 @ SV20 ) )
= $true )
| ( ( eq @ ( pf @ SV3 @ SV19 ) @ ( pf @ SV12 @ SV20 ) )
= $true )
| ( ( eq @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV12: frac,SV3: frac,SV20: frac,SV19: frac] :
( ( ( eq @ SV19 @ SV20 )
= $false )
| ( ( eq @ ( pf @ SV3 @ SV19 ) @ ( pf @ SV12 @ SV20 ) )
= $true )
| ( ( eq @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(72,plain,
! [SV25: frac] :
( ( eq @ SV25 @ SV25 )
= $true ),
inference(rename,[status(thm)],[43]) ).
thf(73,plain,
! [SV25: frac] :
( ( ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x )
= ( eq @ SV25 @ SV25 ) )
= $false ),
inference(res,[status(thm)],[48,72]) ).
thf(75,plain,
( ( x
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[73:[bind(SV25,$thf( pf @ y @ ( fr @ ( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ))]]) ).
thf(76,plain,
! [SV26: nat,SV27: nat] :
( ( amone
@ ^ [SX0: nat] :
( SV27
= ( pl @ SV26 @ SX0 ) ) )
= $true ),
inference(rename,[status(thm)],[49]) ).
thf(78,plain,
! [SV28: nat,SV29: frac] :
( ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) )
= $true ),
inference(rename,[status(thm)],[52]) ).
thf(79,plain,
! [SV28: nat,SV29: frac] :
( ( ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) )
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $false ),
inference(res,[status(thm)],[78,48]) ).
thf(80,plain,
! [SV28: nat] :
( ( ( fr
@ ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ SV28 )
@ ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ SV28 ) )
= x )
= $false ),
inference(extuni,[status(esa)],[79:[bind(SV29,$thf( pf @ y @ ( fr @ ( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ))]]) ).
thf(81,plain,
! [SV30: nat,SV31: nat] :
( ( ( ts @ SV31 @ SV30 )
= ( ts @ SV30 @ SV31 ) )
= $true ),
inference(rename,[status(thm)],[53]) ).
thf(83,plain,
! [SV32: nat,SV33: frac] :
( ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 )
= $true ),
inference(rename,[status(thm)],[56]) ).
thf(84,plain,
! [SV32: nat,SV33: frac] :
( ( ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 )
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $false ),
inference(res,[status(thm)],[83,48]) ).
thf(85,plain,
! [SV32: nat] :
( ( ( fr @ ( ts @ ( num @ x ) @ SV32 ) @ ( ts @ ( den @ x ) @ SV32 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ),
inference(extuni,[status(esa)],[84:[bind(SV33,$thf( x ))]]) ).
thf(86,plain,
! [SV34: nat,SV35: nat,SV36: nat] :
( ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) )
= $true ),
inference(rename,[status(thm)],[59]) ).
thf(87,plain,
! [SV34: nat,SV35: nat,SV36: nat] :
( ( ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) )
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $false ),
inference(res,[status(thm)],[86,48]) ).
thf(88,plain,
! [SV36: nat] :
( ( ( ( fr
@ ( pl @ SV36
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= x )
= $false )
| ( ( ( fr @ SV36 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(extuni,[status(esa)],[87:[bind(SV35,$thf( ts @ ( den @ x ) @ ( den @ y ) )),bind(SV34,$thf( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(89,plain,
! [SV35: nat,SV34: nat,SV36: nat] :
( ( ( ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )
= x )
= $false )
| ( ( ( fr @ SV34 @ SV35 )
= ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= $false )
| ( ( ( fr @ SV36 @ SV35 )
= y )
= $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(90,plain,
! [SV35: nat,SV34: nat,SV36: nat] :
( ( ( ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )
= x )
= $false )
| ( ( ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(91,plain,
! [SV37: nat > $o] :
( ( ( some @ SV37 )
= $false )
| ( ( amone @ SV37 )
= $false )
| ( ( SV37 @ ( ind @ SV37 ) )
= $true ) ),
inference(rename,[status(thm)],[66]) ).
thf(104,plain,
! [SV37: nat > $o,SV26: nat,SV27: nat] :
( ( ( ( amone @ SV37 )
= ( amone
@ ^ [SX0: nat] :
( SV27
= ( pl @ SV26 @ SX0 ) ) ) )
= $false )
| ( ( some @ SV37 )
= $false )
| ( ( SV37 @ ( ind @ SV37 ) )
= $true ) ),
inference(res,[status(thm)],[91,76]) ).
thf(110,plain,
! [SV37: nat > $o] :
( ( ( ( some @ SV37 )
= ( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) )
= $false )
| ( ( amone @ SV37 )
= $false )
| ( ( SV37 @ ( ind @ SV37 ) )
= $true ) ),
inference(res,[status(thm)],[91,28]) ).
thf(111,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true )
| ( ( amone
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[110:[bind(SV37,$thf( ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(112,plain,
! [SV26: nat,SV27: nat] :
( ( ( SV27
= ( pl @ SV26
@ ( ind
@ ^ [SX0: nat] :
( SV27
= ( pl @ SV26 @ SX0 ) ) ) ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( SV27
= ( pl @ SV26 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[104:[bind(SV37,$thf( ^ [SX0: nat] : ( SV27 = ( pl @ SV26 @ SX0 ) ) ))]]) ).
thf(113,plain,
! [SV78: frac,SV79: frac,SV80: frac] :
( ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(rename,[status(thm)],[69]) ).
thf(122,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( ( eq @ SV78 @ SV80 )
= ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) ) )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true ) ),
inference(res,[status(thm)],[113,86]) ).
thf(123,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( ( eq @ SV80 @ SV79 )
= ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) ) )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[113,86]) ).
thf(124,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV32: nat,SV33: frac] :
( ( ( ( eq @ SV78 @ SV80 )
= ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 ) )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true ) ),
inference(res,[status(thm)],[113,83]) ).
thf(125,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV32: nat,SV33: frac] :
( ( ( ( eq @ SV80 @ SV79 )
= ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 ) )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[113,83]) ).
thf(128,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV28: nat,SV29: frac] :
( ( ( ( eq @ SV78 @ SV80 )
= ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) ) )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true ) ),
inference(res,[status(thm)],[113,78]) ).
thf(129,plain,
! [SV78: frac,SV79: frac,SV80: frac,SV28: nat,SV29: frac] :
( ( ( ( eq @ SV80 @ SV79 )
= ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) ) )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[113,78]) ).
thf(134,plain,
! [SV78: frac,SV79: frac,SV80: frac] :
( ( ( ( eq @ SV78 @ SV79 )
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[113,48]) ).
thf(137,plain,
! [SV80: frac] :
( ( ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ SV80 )
= $false )
| ( ( eq @ SV80 @ x )
= $false ) ),
inference(extuni,[status(esa)],[134:[bind(SV79,$thf( x )),bind(SV78,$thf( pf @ y @ ( fr @ ( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ))]]) ).
thf(140,plain,
! [SV28: nat,SV29: frac,SV78: frac] :
( ( ( eq @ SV78 @ SV29 )
= $false )
| ( ( eq @ SV78 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[129:[bind(SV79,$thf( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) )),bind(SV80,$thf( SV29 ))]]) ).
thf(141,plain,
! [SV28: nat,SV79: frac,SV29: frac] :
( ( ( eq @ SV29 @ SV79 )
= $true )
| ( ( eq @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) @ SV79 )
= $false ) ),
inference(extuni,[status(esa)],[128:[bind(SV80,$thf( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) )),bind(SV78,$thf( SV29 ))]]) ).
thf(142,plain,
! [SV32: nat,SV33: frac,SV78: frac] :
( ( ( eq @ SV78 @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) )
= $false )
| ( ( eq @ SV78 @ SV33 )
= $true ) ),
inference(extuni,[status(esa)],[125:[bind(SV79,$thf( SV33 )),bind(SV80,$thf( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ))]]) ).
thf(143,plain,
! [SV79: frac,SV32: nat,SV33: frac] :
( ( ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV79 )
= $true )
| ( ( eq @ SV33 @ SV79 )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV80,$thf( SV33 )),bind(SV78,$thf( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ))]]) ).
thf(144,plain,
! [SV34: nat,SV35: nat,SV36: nat,SV78: frac] :
( ( ( eq @ SV78 @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) )
= $false )
| ( ( eq @ SV78 @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) )
= $true ) ),
inference(extuni,[status(esa)],[123:[bind(SV79,$thf( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )),bind(SV80,$thf( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ))]]) ).
thf(145,plain,
! [SV79: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ SV79 )
= $true )
| ( ( eq @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) @ SV79 )
= $false ) ),
inference(extuni,[status(esa)],[122:[bind(SV80,$thf( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )),bind(SV78,$thf( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ))]]) ).
thf(150,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac] :
( ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(rename,[status(thm)],[71]) ).
thf(155,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV78: frac,SV79: frac,SV80: frac] :
( ( ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= ( eq @ SV78 @ SV80 ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true ) ),
inference(res,[status(thm)],[150,113]) ).
thf(156,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV78: frac,SV79: frac,SV80: frac] :
( ( ( ( eq @ SV82 @ SV81 )
= ( eq @ SV78 @ SV79 ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[150,113]) ).
thf(157,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV78: frac,SV79: frac,SV80: frac] :
( ( ( ( eq @ SV84 @ SV83 )
= ( eq @ SV78 @ SV79 ) )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[150,113]) ).
thf(158,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV78: frac,SV79: frac,SV80: frac] :
( ( ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= ( eq @ SV80 @ SV79 ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV78 @ SV79 )
= $true )
| ( ( eq @ SV78 @ SV80 )
= $false ) ),
inference(res,[status(thm)],[150,113]) ).
thf(163,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( ( eq @ SV82 @ SV81 )
= ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true ) ),
inference(res,[status(thm)],[150,86]) ).
thf(164,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( ( eq @ SV84 @ SV83 )
= ( eq @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) ) )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(res,[status(thm)],[150,86]) ).
thf(165,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV32: nat,SV33: frac] :
( ( ( ( eq @ SV82 @ SV81 )
= ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true ) ),
inference(res,[status(thm)],[150,83]) ).
thf(166,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV32: nat,SV33: frac] :
( ( ( ( eq @ SV84 @ SV83 )
= ( eq @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV33 ) )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(res,[status(thm)],[150,83]) ).
thf(169,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV28: nat,SV29: frac] :
( ( ( ( eq @ SV82 @ SV81 )
= ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true ) ),
inference(res,[status(thm)],[150,78]) ).
thf(170,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV28: nat,SV29: frac] :
( ( ( ( eq @ SV84 @ SV83 )
= ( eq @ SV29 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) ) )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(res,[status(thm)],[150,78]) ).
thf(173,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV25: frac] :
( ( ( ( eq @ SV82 @ SV81 )
= ( eq @ SV25 @ SV25 ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true ) ),
inference(res,[status(thm)],[150,72]) ).
thf(174,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac,SV25: frac] :
( ( ( ( eq @ SV84 @ SV83 )
= ( eq @ SV25 @ SV25 ) )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(res,[status(thm)],[150,72]) ).
thf(175,plain,
! [SV81: frac,SV82: frac,SV83: frac,SV84: frac] :
( ( ( ( eq @ ( pf @ SV82 @ SV84 ) @ ( pf @ SV81 @ SV83 ) )
= ( eq
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
@ x ) )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( eq @ SV82 @ SV81 )
= $false ) ),
inference(res,[status(thm)],[150,48]) ).
thf(178,plain,
! [SV83: frac,SV81: frac] :
( ( ( eq @ y @ SV81 )
= $false )
| ( ( eq
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ SV83 )
= $false )
| ( ( ( pf @ SV81 @ SV83 )
= x )
= $false ) ),
inference(extuni,[status(esa)],[175:[bind(SV84,$thf( fr @ ( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) @ ( ts @ ( den @ x ) @ ( den @ y ) ) )),bind(SV82,$thf( y ))]]) ).
thf(179,plain,
! [SV83: frac,SV84: frac,SV81: frac,SV82: frac] :
( ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false )
| ( ( ( pf @ SV81 @ SV83 )
= x )
= $false )
| ( ( ( pf @ SV82 @ SV84 )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [Xt: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xt ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[175]) ).
thf(180,plain,
! [SV25: frac,SV81: frac,SV82: frac] :
( ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV25 ) @ ( pf @ SV81 @ SV25 ) )
= $true ) ),
inference(extuni,[status(esa)],[174:[bind(SV83,$thf( SV25 )),bind(SV84,$thf( SV25 ))]]) ).
thf(181,plain,
! [SV83: frac,SV84: frac,SV25: frac] :
( ( ( eq @ ( pf @ SV25 @ SV84 ) @ ( pf @ SV25 @ SV83 ) )
= $true )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[173:[bind(SV81,$thf( SV25 )),bind(SV82,$thf( SV25 ))]]) ).
thf(182,plain,
! [SV28: nat,SV29: frac,SV81: frac,SV82: frac] :
( ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV29 ) @ ( pf @ SV81 @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[170:[bind(SV83,$thf( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) )),bind(SV84,$thf( SV29 ))]]) ).
thf(183,plain,
! [SV83: frac,SV28: nat,SV84: frac,SV29: frac] :
( ( ( eq @ ( pf @ SV29 @ SV84 ) @ ( pf @ ( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) ) @ SV83 ) )
= $true )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[169:[bind(SV81,$thf( fr @ ( ts @ ( num @ SV29 ) @ SV28 ) @ ( ts @ ( den @ SV29 ) @ SV28 ) )),bind(SV82,$thf( SV29 ))]]) ).
thf(184,plain,
! [SV32: nat,SV33: frac,SV81: frac,SV82: frac] :
( ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ ( pf @ SV82 @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) ) @ ( pf @ SV81 @ SV33 ) )
= $true ) ),
inference(extuni,[status(esa)],[166:[bind(SV83,$thf( SV33 )),bind(SV84,$thf( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ))]]) ).
thf(185,plain,
! [SV83: frac,SV84: frac,SV32: nat,SV33: frac] :
( ( ( eq @ ( pf @ ( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ) @ SV84 ) @ ( pf @ SV33 @ SV83 ) )
= $true )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[165:[bind(SV81,$thf( SV33 )),bind(SV82,$thf( fr @ ( ts @ ( num @ SV33 ) @ SV32 ) @ ( ts @ ( den @ SV33 ) @ SV32 ) ))]]) ).
thf(186,plain,
! [SV34: nat,SV35: nat,SV36: nat,SV81: frac,SV82: frac] :
( ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ ( pf @ SV82 @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) ) @ ( pf @ SV81 @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[164:[bind(SV83,$thf( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )),bind(SV84,$thf( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ))]]) ).
thf(187,plain,
! [SV83: frac,SV84: frac,SV34: nat,SV35: nat,SV36: nat] :
( ( ( eq @ ( pf @ ( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ) @ SV84 ) @ ( pf @ ( fr @ ( pl @ SV36 @ SV34 ) @ SV35 ) @ SV83 ) )
= $true )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[163:[bind(SV81,$thf( fr @ ( pl @ SV36 @ SV34 ) @ SV35 )),bind(SV82,$thf( pf @ ( fr @ SV36 @ SV35 ) @ ( fr @ SV34 @ SV35 ) ))]]) ).
thf(188,plain,
! [SV83: frac,SV81: frac,SV84: frac,SV82: frac,SV78: frac] :
( ( ( eq @ SV78 @ ( pf @ SV82 @ SV84 ) )
= $false )
| ( ( eq @ SV78 @ ( pf @ SV81 @ SV83 ) )
= $true )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[158:[bind(SV79,$thf( pf @ SV81 @ SV83 )),bind(SV80,$thf( pf @ SV82 @ SV84 ))]]) ).
thf(189,plain,
! [SV81: frac,SV82: frac,SV79: frac,SV80: frac,SV78: frac] :
( ( ( eq @ SV78 @ SV80 )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ ( pf @ SV82 @ SV78 ) @ ( pf @ SV81 @ SV79 ) )
= $true ) ),
inference(extuni,[status(esa)],[157:[bind(SV83,$thf( SV79 )),bind(SV84,$thf( SV78 ))]]) ).
thf(190,plain,
! [SV83: frac,SV84: frac,SV79: frac,SV80: frac,SV78: frac] :
( ( ( eq @ SV78 @ SV80 )
= $false )
| ( ( eq @ SV80 @ SV79 )
= $false )
| ( ( eq @ ( pf @ SV78 @ SV84 ) @ ( pf @ SV79 @ SV83 ) )
= $true )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[156:[bind(SV81,$thf( SV79 )),bind(SV82,$thf( SV78 ))]]) ).
thf(191,plain,
! [SV83: frac,SV81: frac,SV79: frac,SV84: frac,SV82: frac] :
( ( ( eq @ ( pf @ SV82 @ SV84 ) @ SV79 )
= $true )
| ( ( eq @ ( pf @ SV81 @ SV83 ) @ SV79 )
= $false )
| ( ( eq @ SV82 @ SV81 )
= $false )
| ( ( eq @ SV84 @ SV83 )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV80,$thf( pf @ SV81 @ SV83 )),bind(SV78,$thf( pf @ SV82 @ SV84 ))]]) ).
thf(202,plain,
! [SV85: nat] :
( ( ( fr
@ ( ts
@ ( num
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ SV85 )
@ ( ts
@ ( den
@ ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
@ SV85 ) )
= x )
= $false ),
inference(rename,[status(thm)],[80]) ).
thf(213,plain,
! [SV86: nat] :
( ( ( fr @ ( ts @ ( num @ x ) @ SV86 ) @ ( ts @ ( den @ x ) @ SV86 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ),
inference(rename,[status(thm)],[85]) ).
thf(224,plain,
! [SV87: nat] :
( ( ( ( fr
@ ( pl @ SV87
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= x )
= $false )
| ( ( ( fr @ SV87 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(rename,[status(thm)],[88]) ).
thf(246,plain,
! [SV88: nat,SV89: nat,SV90: nat] :
( ( ( ( fr @ ( pl @ SV90 @ SV89 ) @ SV88 )
= x )
= $false )
| ( ( ( fr @ SV89 @ SV88 )
= ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= $false )
| ( ( ( fr @ SV90 @ SV88 )
= y )
= $false ) ),
inference(rename,[status(thm)],[89]) ).
thf(277,plain,
! [SV91: nat,SV92: nat,SV93: nat] :
( ( ( ( fr @ ( pl @ SV93 @ SV92 ) @ SV91 )
= x )
= $false )
| ( ( ( pf @ ( fr @ SV93 @ SV91 ) @ ( fr @ SV92 @ SV91 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false ) ),
inference(rename,[status(thm)],[90]) ).
thf(298,plain,
! [SV91: nat,SV92: nat,SV93: nat] :
( ( ( ( pf @ ( fr @ SV93 @ SV91 ) @ ( fr @ SV92 @ SV91 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( ( fr @ ( pl @ SV93 @ SV92 ) @ SV91 )
= x )
= ( ( pf @ ( fr @ SV93 @ SV91 ) @ ( fr @ SV92 @ SV91 ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[277]) ).
thf(299,plain,
! [SV93: nat] :
( ( ( ( fr
@ ( pl @ SV93
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( x
= ( pf @ ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298:[bind(SV91,$thf( ts @ ( den @ x ) @ ( den @ y ) )),bind(SV92,$thf( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(300,plain,
! [SV93: nat] :
( ( ( x
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( fr
@ ( pl @ SV93
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= ( pf @ ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298:[bind(SV91,$thf( ts @ ( den @ x ) @ ( den @ y ) )),bind(SV92,$thf( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(301,plain,
! [SV93: nat] :
( ( ( ( fr
@ ( pl @ SV93
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= x )
= $true )
| ( ( ( pf @ ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $true )
| ( ( ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298:[bind(SV91,$thf( ts @ ( den @ x ) @ ( den @ y ) )),bind(SV92,$thf( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(302,plain,
! [SV93: nat] :
( ( ( ( fr
@ ( pl @ SV93
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= x )
= $false )
| ( ( ( pf @ ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( fr @ SV93 @ ( ts @ ( den @ x ) @ ( den @ y ) ) )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298:[bind(SV91,$thf( ts @ ( den @ x ) @ ( den @ y ) )),bind(SV92,$thf( ind @ ^ [SX0: nat] : ( ( ts @ ( num @ x ) @ ( den @ y ) ) = ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ))]]) ).
thf(303,plain,
! [SV91: nat,SV92: nat,SV93: nat] :
( ( ( ( fr @ ( pl @ SV93 @ SV92 ) @ SV91 )
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( x
= ( pf @ ( fr @ SV93 @ SV91 ) @ ( fr @ SV92 @ SV91 ) ) )
= $false )
| ( ( ( fr @ SV92 @ SV91 )
= ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= $false )
| ( ( ( fr @ SV93 @ SV91 )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298]) ).
thf(304,plain,
! [SV91: nat,SV92: nat,SV93: nat] :
( ( ( x
= ( pf @ y
@ ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) ) )
= $false )
| ( ( ( fr @ ( pl @ SV93 @ SV92 ) @ SV91 )
= ( pf @ ( fr @ SV93 @ SV91 ) @ ( fr @ SV92 @ SV91 ) ) )
= $false )
| ( ( ( fr @ SV92 @ SV91 )
= ( fr
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
@ ( ts @ ( den @ x ) @ ( den @ y ) ) ) )
= $false )
| ( ( ( fr @ SV93 @ SV91 )
= y )
= $false ) ),
inference(extuni,[status(esa)],[298]) ).
thf(329,plain,
! [SV26: nat,SV27: nat] :
( ( ( ( amone
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) )
= ( amone
@ ^ [SX0: nat] :
( SV27
= ( pl @ SV26 @ SX0 ) ) ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true ) ),
inference(res,[status(thm)],[111,76]) ).
thf(334,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true ),
inference(extuni,[status(esa)],[329:[bind(SV26,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV27,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(335,plain,
! [SV26: nat] :
( ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true )
| ( ( ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK1_E @ SV26 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
= ( pl @ SV26 @ ( sK1_E @ SV26 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[329:[bind(SV27,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(336,plain,
! [SV27: nat,SV26: nat] :
( ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true )
| ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK1_E @ SV26 @ SV27 ) ) )
= $true )
| ( ( SV27
= ( pl @ SV26 @ ( sK1_E @ SV26 @ SV27 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[329]) ).
thf(337,plain,
! [SV27: nat,SV26: nat] :
( ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true )
| ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK1_E @ SV26 @ SV27 ) ) )
= $false )
| ( ( SV27
= ( pl @ SV26 @ ( sK1_E @ SV26 @ SV27 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[329]) ).
thf(338,plain,
! [SV94: nat,SV95: nat] :
( ( ( SV95
= ( pl @ SV94
@ ( ind
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) ) ) )
= $true )
| ( ( some
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) )
= $false ) ),
inference(rename,[status(thm)],[112]) ).
thf(369,plain,
! [SV94: nat,SV95: nat] :
( ( ( ( some
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) )
= ( some
@ ^ [Xu: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ Xu ) ) ) )
= $false )
| ( ( SV95
= ( pl @ SV94
@ ( ind
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) ) ) )
= $true ) ),
inference(res,[status(thm)],[338,28]) ).
thf(370,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) )
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SX0 ) ) ) ) )
= $true ),
inference(extuni,[status(esa)],[369:[bind(SV94,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV95,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(371,plain,
! [SV94: nat] :
( ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ SV94
@ ( ind
@ ^ [SX0: nat] :
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ SV94 @ SX0 ) ) ) ) )
= $true )
| ( ( ( pl @ SV94 @ ( sK3_E @ SV94 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK3_E @ SV94 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[369:[bind(SV95,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(372,plain,
! [SV94: nat,SV95: nat] :
( ( ( SV95
= ( pl @ SV94
@ ( ind
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) ) ) )
= $true )
| ( ( SV95
= ( pl @ SV94 @ ( sK3_E @ SV94 @ SV95 ) ) )
= $true )
| ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK3_E @ SV94 @ SV95 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[369]) ).
thf(373,plain,
! [SV94: nat,SV95: nat] :
( ( ( SV95
= ( pl @ SV94
@ ( ind
@ ^ [SX0: nat] :
( SV95
= ( pl @ SV94 @ SX0 ) ) ) ) )
= $true )
| ( ( SV95
= ( pl @ SV94 @ ( sK3_E @ SV94 @ SV95 ) ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( pl @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ ( sK3_E @ SV94 @ SV95 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[369]) ).
thf(374,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,373,372,371,370,338,337,336,335,334,304,303,302,301,300,299,277,246,224,213,202,191,190,189,188,187,186,185,184,183,182,181,180,179,178,150,145,144,143,142,141,140,137,113,111,91,86,83,81,78,76,75,72,48]) ).
thf(375,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM768^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n004.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 : 600
% 0.13/0.34 % DateTime : Tue Jul 5 09:19:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 10
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: true
% 0.13/0.36 (rf:0,axioms:10,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)...eprover: CPU time limit exceeded, terminating
% 25.22/25.44 .eprover: CPU time limit exceeded, terminating
% 50.40/50.65 .
% 50.50/50.75
% 50.50/50.75 Prim_subst applied to clause
% 50.50/50.75
% 50.50/50.75 85:[ 0:<some@SV37 = $false>-w(1)-i() 1:<amone@SV37 = $false>-w(1)-i() 2:<SV37@(ind@SV37) = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 55)-o(AXIOM)-fv([ SV37 ])
% 50.71/50.94 .eprover: CPU time limit exceeded, terminating
% 75.04/75.26
% 75.04/75.26 (rf:0,axioms:10,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:12,loop_count:0,foatp_calls:0,translation:fof_full)....eprover: CPU time limit exceeded, terminating
% 100.04/100.34 ..
% 100.21/100.51
% 100.21/100.51 Prim_subst applied to clause
% 100.21/100.51
% 100.21/100.51 91:[ 0:<some@SV37 = $false>-w(1)-i() 1:<amone@SV37 = $false>-w(1)-i() 2:<SV37@(ind@SV37) = $true>-w(1)-i() ]-mln(3)-w(3)-i(rename 66)-o(AXIOM)-fv([ SV37 ])
% 125.36/125.60 eprover: CPU time limit exceeded, terminating
% 125.80/126.04 ......
% 128.64/128.87
% 128.64/128.87 ********************************
% 128.64/128.87 * All subproblems solved! *
% 128.64/128.87 ********************************
% 128.64/128.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:21,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:374,loop_count:20,foatp_calls:3,translation:fof_full)
% 128.66/128.89
% 128.66/128.89 %**** Beginning of derivation protocol ****
% 128.66/128.89 % SZS output start CNFRefutation
% See solution above
% 128.66/128.89
% 128.66/128.89 %**** End of derivation protocol ****
% 128.66/128.89 %**** no. of clauses in derivation: 160 ****
% 128.66/128.89 %**** clause counter: 374 ****
% 128.66/128.89
% 128.66/128.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:0,u:1,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:21,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:374,loop_count:20,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------