TSTP Solution File: NUM727^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM727^1 : 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 : n006.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 11:54:44 EDT 2022
% Result : Theorem 51.50s 51.84s
% Output : CNFRefutation 51.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 252 ( 49 unt; 8 typ; 0 def)
% Number of atoms : 1703 (1151 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1847 ( 8 ~; 317 |; 0 &;1520 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 220 ( 0 ^ 220 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_den,type,
den: frac > nat ).
thf(tp_num,type,
num: frac > nat ).
thf(tp_ts,type,
ts: nat > nat > nat ).
thf(tp_x,type,
x: frac ).
thf(tp_y,type,
y: frac ).
thf(tp_z,type,
z: frac ).
thf(1,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
= ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz31) ).
thf(2,axiom,
! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).
thf(3,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( ( ts @ Xx @ Xz )
= ( ts @ Xy @ Xz ) )
=> ( Xx = Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz33b) ).
thf(4,axiom,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f) ).
thf(5,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(6,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz39) ).
thf(7,negated_conjecture,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
= ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( ( ts @ Xx @ Xz )
= ( ts @ Xy @ Xz ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xz: nat] :
( ( ts @ Xx @ Xz )
!= ( ts @ Xy @ Xz ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(16,plain,
( ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xz: nat] :
( ( ts @ Xx @ Xz )
!= ( ts @ Xy @ Xz ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
= ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(21,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(22,plain,
! [SV1: nat] :
( ( ! [SY8: nat] :
( ! [SY9: nat] :
( ( ts @ SV1 @ SY9 )
!= ( ts @ SY8 @ SY9 ) )
| ( SV1 = SY8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: nat] :
( ( ! [SY10: nat] :
( ( ts @ SV2 @ SY10 )
= ( ts @ SY10 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV3: nat] :
( ( ! [SY11: nat,SY12: nat] :
( ( ts @ ( ts @ SV3 @ SY11 ) @ SY12 )
= ( ts @ SV3 @ ( ts @ SY11 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV4: nat,SV1: nat] :
( ( ! [SY13: nat] :
( ( ts @ SV1 @ SY13 )
!= ( ts @ SV4 @ SY13 ) )
| ( SV1 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV5: nat,SV2: nat] :
( ( ( ts @ SV2 @ SV5 )
= ( ts @ SV5 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV6: nat,SV3: nat] :
( ( ! [SY14: nat] :
( ( ts @ ( ts @ SV3 @ SV6 ) @ SY14 )
= ( ts @ SV3 @ ( ts @ SV6 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV4: nat,SV1: nat] :
( ( ( ! [SY13: nat] :
( ( ts @ SV1 @ SY13 )
!= ( ts @ SV4 @ SY13 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV7: nat,SV6: nat,SV3: nat] :
( ( ( ts @ ( ts @ SV3 @ SV6 ) @ SV7 )
= ( ts @ SV3 @ ( ts @ SV6 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: nat,SV8: nat,SV1: nat] :
( ( ( ( ( ts @ SV1 @ SV8 )
!= ( ts @ SV4 @ SV8 ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV4: nat,SV8: nat,SV1: nat] :
( ( ( ( ts @ SV1 @ SV8 )
= ( ts @ SV4 @ SV8 ) )
= $false )
| ( ( SV1 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
( ( ( z = x )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(34,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(35,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(36,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(38,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false ),
inference(res,[status(thm)],[25,17]) ).
thf(39,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false ),
inference(res,[status(thm)],[25,16]) ).
thf(40,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(41,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(42,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(43,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(44,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(45,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(46,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(47,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(48,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(49,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(50,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(51,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(52,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(53,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(54,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(55,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(56,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(57,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(58,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(59,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(60,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(61,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(62,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(63,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(64,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(65,plain,
( ( ( z = y )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(66,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(67,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(68,plain,
( ( ( z = y )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(69,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(70,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(71,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(72,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(73,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[39]) ).
thf(74,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(75,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(76,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(77,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(78,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(79,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(80,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(81,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(82,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(83,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(84,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(85,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(86,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(87,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(88,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(89,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(90,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(91,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(92,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(93,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(94,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(95,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(96,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(97,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(98,plain,
( ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(99,plain,
( ( ( x = y )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(100,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(101,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(102,plain,
( ( ( x = y )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(103,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(104,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(105,plain,
( ( ( x = y )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(106,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(107,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[38]) ).
thf(108,plain,
( ( ( z = x )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(109,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(110,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(111,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[25]) ).
thf(112,plain,
( ( z = y )
= $false ),
inference(sim,[status(thm)],[65]) ).
thf(113,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(sim,[status(thm)],[51]) ).
thf(114,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(sim,[status(thm)],[50]) ).
thf(115,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false ) ),
inference(sim,[status(thm)],[47]) ).
thf(116,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false )
| ( ( ( den @ x )
= ( den @ y ) )
= $false ) ),
inference(sim,[status(thm)],[45]) ).
thf(117,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false )
| ( ( x = y )
= $false ) ),
inference(sim,[status(thm)],[42]) ).
thf(118,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = y )
= $false )
| ( ( z = x )
= $false ) ),
inference(sim,[status(thm)],[41]) ).
thf(119,plain,
( ( ( z = x )
= $false )
| ( ( x = y )
= $false ) ),
inference(sim,[status(thm)],[40]) ).
thf(120,plain,
( ( x = y )
= $false ),
inference(sim,[status(thm)],[99]) ).
thf(121,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(sim,[status(thm)],[85]) ).
thf(122,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(sim,[status(thm)],[84]) ).
thf(123,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false ) ),
inference(sim,[status(thm)],[81]) ).
thf(124,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( den @ z ) )
= $false ) ),
inference(sim,[status(thm)],[79]) ).
thf(125,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(sim,[status(thm)],[76]) ).
thf(126,plain,
( ( ( ( den @ z )
= ( den @ y ) )
= $false )
| ( ( x = z )
= $false )
| ( ( z = y )
= $false ) ),
inference(sim,[status(thm)],[75]) ).
thf(127,plain,
( ( ( z = y )
= $false )
| ( ( x = z )
= $false ) ),
inference(sim,[status(thm)],[74]) ).
thf(128,plain,
! [SV9: nat,SV10: nat] :
( ( ( ts @ SV10 @ SV9 )
= ( ts @ SV9 @ SV10 ) )
= $true ),
inference(rename,[status(thm)],[27]) ).
thf(129,plain,
! [SV9: nat,SV10: nat] :
( ( ( ( ts @ SV10 @ SV9 )
= ( ts @ SV9 @ SV10 ) )
= ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $false ),
inference(res,[status(thm)],[128,25]) ).
thf(130,plain,
( ( ( ( num @ x )
= ( den @ x ) )
= $false )
| ( ( ( den @ z )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[129:[bind(SV10,$thf( den @ z )),bind(SV9,$thf( num @ x ))]]) ).
thf(131,plain,
( ( ( ts @ ( den @ z ) @ ( num @ x ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(extuni,[status(esa)],[129:[bind(SV10,$thf( den @ z )),bind(SV9,$thf( num @ x ))]]) ).
thf(132,plain,
( ( ( ts @ ( den @ x ) @ ( num @ z ) )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ),
inference(extuni,[status(esa)],[129:[bind(SV9,$thf( den @ x )),bind(SV10,$thf( num @ z ))]]) ).
thf(133,plain,
! [SV9: nat,SV10: nat] :
( ( ( ( ts @ SV10 @ SV9 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV9 @ SV10 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[129]) ).
thf(134,plain,
( ( ( ( num @ x )
= ( den @ x ) )
= $false )
| ( ( ( den @ z )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[129:[bind(SV9,$thf( den @ z )),bind(SV10,$thf( num @ x ))]]) ).
thf(135,plain,
( ( ( ts @ ( den @ z ) @ ( num @ x ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(extuni,[status(esa)],[129:[bind(SV9,$thf( den @ z )),bind(SV10,$thf( num @ x ))]]) ).
thf(136,plain,
( ( ( ts @ ( den @ x ) @ ( num @ z ) )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ),
inference(extuni,[status(esa)],[129:[bind(SV10,$thf( den @ x )),bind(SV9,$thf( num @ z ))]]) ).
thf(137,plain,
! [SV10: nat,SV9: nat] :
( ( ( ( ts @ SV9 @ SV10 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV10 @ SV9 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[129]) ).
thf(138,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $true ),
inference(rename,[status(thm)],[30]) ).
thf(139,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $false ),
inference(res,[status(thm)],[138,25]) ).
thf(140,plain,
! [SV12: nat] :
( ( ( ( ts @ ( num @ x ) @ SV12 )
= ( num @ z ) )
= $false )
| ( ( ( ts @ SV12 @ ( den @ x ) )
= ( den @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV11,$thf( den @ x )),bind(SV13,$thf( num @ x ))]]) ).
thf(141,plain,
! [SV11: nat,SV12: nat] :
( ( ( ( ts @ ( ts @ ( num @ x ) @ SV12 ) @ SV11 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV12 @ SV11 )
= ( den @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV13,$thf( num @ x ))]]) ).
thf(142,plain,
! [SV12: nat,SV13: nat] :
( ( ( ( ts @ SV13 @ SV12 )
= ( num @ z ) )
= $false )
| ( ( ( ts @ SV13 @ ( ts @ SV12 @ ( den @ x ) ) )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV11,$thf( den @ x ))]]) ).
thf(143,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[139]) ).
thf(144,plain,
! [SV12: nat] :
( ( ( ( ts @ SV12 @ ( den @ z ) )
= ( den @ x ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ SV12 )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV13,$thf( num @ z )),bind(SV11,$thf( den @ z ))]]) ).
thf(145,plain,
! [SV12: nat,SV13: nat] :
( ( ( ( ts @ SV13 @ ( ts @ SV12 @ ( den @ z ) ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV13 @ SV12 )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV11,$thf( den @ z ))]]) ).
thf(146,plain,
! [SV11: nat,SV12: nat] :
( ( ( ( ts @ SV12 @ SV11 )
= ( den @ x ) )
= $false )
| ( ( ( ts @ ( ts @ ( num @ z ) @ SV12 ) @ SV11 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[139:[bind(SV13,$thf( num @ z ))]]) ).
thf(147,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[139]) ).
thf(148,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= $false )
| ( ( SV16 = SV14 )
= $true ) ),
inference(rename,[status(thm)],[32]) ).
thf(151,plain,
! [SV14: nat,SV15: nat,SV16: nat,SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) ) )
= $false )
| ( ( SV16 = SV14 )
= $true ) ),
inference(res,[status(thm)],[148,138]) ).
thf(152,plain,
! [SV14: nat,SV15: nat,SV16: nat,SV9: nat,SV10: nat] :
( ( ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= ( ( ts @ SV10 @ SV9 )
= ( ts @ SV9 @ SV10 ) ) )
= $false )
| ( ( SV16 = SV14 )
= $true ) ),
inference(res,[status(thm)],[148,128]) ).
thf(153,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( SV16 = SV14 )
= ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= $false ) ),
inference(res,[status(thm)],[148,25]) ).
thf(154,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( SV16 = SV14 )
= $true ) ),
inference(res,[status(thm)],[148,17]) ).
thf(155,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( SV16 = SV14 )
= $true ) ),
inference(res,[status(thm)],[148,16]) ).
thf(156,plain,
( ( ( ( num @ y )
= ( num @ x ) )
= $true )
| ( ( y = x )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV16,$thf( num @ y )),bind(SV15,$thf( den @ y )),bind(SV14,$thf( num @ x ))]]) ).
thf(157,plain,
( ( ( ( num @ y )
= ( num @ x ) )
= $true )
| ( ( ( den @ y )
= ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV16,$thf( num @ y )),bind(SV15,$thf( den @ y )),bind(SV14,$thf( num @ x ))]]) ).
thf(158,plain,
! [SV16: nat] :
( ( ( SV16
= ( num @ x ) )
= $true )
| ( ( ( ts @ SV16 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV15,$thf( den @ y )),bind(SV14,$thf( num @ x ))]]) ).
thf(159,plain,
! [SV14: nat] :
( ( ( ( num @ y )
= SV14 )
= $true )
| ( ( ( ts @ SV14 @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV15,$thf( den @ x )),bind(SV16,$thf( num @ y ))]]) ).
thf(160,plain,
! [SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155]) ).
thf(161,plain,
( ( ( ( num @ x )
= ( num @ y ) )
= $true )
| ( ( y = x )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV14,$thf( num @ y )),bind(SV15,$thf( den @ y )),bind(SV16,$thf( num @ x ))]]) ).
thf(162,plain,
( ( ( ( num @ x )
= ( num @ y ) )
= $true )
| ( ( ( den @ y )
= ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV14,$thf( num @ y )),bind(SV15,$thf( den @ y )),bind(SV16,$thf( num @ x ))]]) ).
thf(163,plain,
! [SV14: nat] :
( ( ( ( num @ x )
= SV14 )
= $true )
| ( ( ( ts @ SV14 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV15,$thf( den @ y )),bind(SV16,$thf( num @ x ))]]) ).
thf(164,plain,
! [SV16: nat] :
( ( ( SV16
= ( num @ y ) )
= $true )
| ( ( ( ts @ SV16 @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155:[bind(SV15,$thf( den @ x )),bind(SV14,$thf( num @ y ))]]) ).
thf(165,plain,
! [SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[155]) ).
thf(166,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $true )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV16,$thf( num @ z )),bind(SV15,$thf( den @ z )),bind(SV14,$thf( num @ y ))]]) ).
thf(167,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $true )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV16,$thf( num @ z )),bind(SV15,$thf( den @ z )),bind(SV14,$thf( num @ y ))]]) ).
thf(168,plain,
! [SV16: nat] :
( ( ( SV16
= ( num @ y ) )
= $true )
| ( ( ( ts @ SV16 @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV15,$thf( den @ z )),bind(SV14,$thf( num @ y ))]]) ).
thf(169,plain,
! [SV14: nat] :
( ( ( ( num @ z )
= SV14 )
= $true )
| ( ( ( ts @ SV14 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV15,$thf( den @ y )),bind(SV16,$thf( num @ z ))]]) ).
thf(170,plain,
! [SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154]) ).
thf(171,plain,
( ( ( ( num @ y )
= ( num @ z ) )
= $true )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV14,$thf( num @ z )),bind(SV15,$thf( den @ z )),bind(SV16,$thf( num @ y ))]]) ).
thf(172,plain,
( ( ( ( num @ y )
= ( num @ z ) )
= $true )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV14,$thf( num @ z )),bind(SV15,$thf( den @ z )),bind(SV16,$thf( num @ y ))]]) ).
thf(173,plain,
! [SV14: nat] :
( ( ( ( num @ y )
= SV14 )
= $true )
| ( ( ( ts @ SV14 @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV15,$thf( den @ z )),bind(SV16,$thf( num @ y ))]]) ).
thf(174,plain,
! [SV16: nat] :
( ( ( SV16
= ( num @ z ) )
= $true )
| ( ( ( ts @ SV16 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154:[bind(SV15,$thf( den @ y )),bind(SV14,$thf( num @ z ))]]) ).
thf(175,plain,
! [SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[154]) ).
thf(176,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(177,plain,
( ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(178,plain,
( ( ( x = z )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(179,plain,
( ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( ( num @ z )
= ( num @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(180,plain,
( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(181,plain,
! [SV15: nat] :
( ( ( ts @ ( ts @ ( num @ z ) @ ( den @ x ) ) @ SV15 )
= ( ts @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ SV15 ) )
= $false ),
inference(extuni,[status(esa)],[153:[bind(SV16,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV14,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(182,plain,
( ( ( z = x )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(183,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(184,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(185,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( ( num @ x )
= ( num @ z ) )
= $false ) ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(186,plain,
( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(187,plain,
! [SV15: nat] :
( ( ( ts @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ SV15 )
= ( ts @ ( ts @ ( num @ z ) @ ( den @ x ) ) @ SV15 ) )
= $false ),
inference(extuni,[status(esa)],[153:[bind(SV14,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV16,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(189,plain,
! [SV9: nat,SV10: nat,SV16: nat] :
( ( ( SV16 = SV10 )
= $true )
| ( ( ( ts @ SV16 @ SV9 )
= ( ts @ SV9 @ SV10 ) )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV15,$thf( SV9 )),bind(SV14,$thf( SV10 ))]]) ).
thf(190,plain,
! [SV10: nat,SV14: nat,SV9: nat] :
( ( ( SV9 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV10 )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV15,$thf( SV10 )),bind(SV16,$thf( SV9 ))]]) ).
thf(191,plain,
! [SV10: nat,SV9: nat,SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[152]) ).
thf(193,plain,
! [SV9: nat,SV14: nat,SV10: nat] :
( ( ( SV10 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV9 )
= ( ts @ SV9 @ SV10 ) )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV15,$thf( SV9 )),bind(SV16,$thf( SV10 ))]]) ).
thf(194,plain,
! [SV10: nat,SV9: nat,SV16: nat] :
( ( ( SV16 = SV9 )
= $true )
| ( ( ( ts @ SV16 @ SV10 )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[152:[bind(SV15,$thf( SV10 )),bind(SV14,$thf( SV9 ))]]) ).
thf(195,plain,
! [SV10: nat,SV9: nat,SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[152]) ).
thf(196,plain,
! [SV11: nat,SV12: nat,SV13: nat,SV16: nat] :
( ( ( SV16
= ( ts @ SV13 @ SV12 ) )
= $true )
| ( ( ( ts @ SV16 @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[151:[bind(SV15,$thf( SV11 )),bind(SV14,$thf( ts @ SV13 @ SV12 ))]]) ).
thf(197,plain,
! [SV11: nat,SV12: nat,SV14: nat,SV13: nat] :
( ( ( SV13 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ ( ts @ SV12 @ SV11 ) )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[151:[bind(SV15,$thf( ts @ SV12 @ SV11 )),bind(SV16,$thf( SV13 ))]]) ).
thf(198,plain,
! [SV11: nat,SV12: nat,SV13: nat,SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[151]) ).
thf(199,plain,
! [SV11: nat,SV14: nat,SV12: nat,SV13: nat] :
( ( ( ( ts @ SV13 @ SV12 )
= SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[151:[bind(SV15,$thf( SV11 )),bind(SV16,$thf( ts @ SV13 @ SV12 ))]]) ).
thf(200,plain,
! [SV11: nat,SV12: nat,SV13: nat,SV16: nat] :
( ( ( SV16 = SV13 )
= $true )
| ( ( ( ts @ SV16 @ ( ts @ SV12 @ SV11 ) )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[151:[bind(SV15,$thf( ts @ SV12 @ SV11 )),bind(SV14,$thf( SV13 ))]]) ).
thf(201,plain,
! [SV11: nat,SV12: nat,SV13: nat,SV15: nat,SV14: nat,SV16: nat] :
( ( ( SV16 = SV14 )
= $true )
| ( ( ( ts @ SV14 @ SV15 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[151]) ).
thf(213,plain,
( ( ( x = z )
= $false )
| ( ( ( z = x )
= ( x = z ) )
= $false ) ),
inference(fac_restr,[status(thm)],[33]) ).
thf(214,plain,
( ( x = z )
= $false ),
inference(extuni,[status(esa)],[213]) ).
thf(215,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[213]) ).
thf(216,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false ) ),
inference(sim,[status(thm)],[215]) ).
thf(218,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( ( den @ z )
= ( den @ x ) )
= ( SV16 = SV14 ) )
= $false )
| ( ( x = z )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= $false ) ),
inference(res,[status(thm)],[34,148]) ).
thf(220,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ( den @ z )
= ( den @ x ) )
= ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(res,[status(thm)],[34,138]) ).
thf(222,plain,
! [SV9: nat,SV10: nat] :
( ( ( ( ( den @ z )
= ( den @ x ) )
= ( ( ts @ SV10 @ SV9 )
= ( ts @ SV9 @ SV10 ) ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(res,[status(thm)],[34,128]) ).
thf(224,plain,
( ( ( ( ( den @ z )
= ( den @ x ) )
= ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(res,[status(thm)],[34,17]) ).
thf(226,plain,
( ( ( ( ( den @ z )
= ( den @ x ) )
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(res,[status(thm)],[34,16]) ).
thf(228,plain,
( ( ( x = z )
= $false )
| ( ( ( den @ z )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ x )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[226]) ).
thf(229,plain,
( ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ z )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[226]) ).
thf(230,plain,
( ( ( x = z )
= $false )
| ( ( ( den @ z )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( den @ x )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[224]) ).
thf(231,plain,
( ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( den @ z )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[224]) ).
thf(232,plain,
! [SV10: nat,SV9: nat] :
( ( ( x = z )
= $false )
| ( ( ( den @ z )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( den @ x )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[222]) ).
thf(233,plain,
! [SV10: nat,SV9: nat] :
( ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( den @ z )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[222]) ).
thf(234,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( x = z )
= $false )
| ( ( ( den @ z )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( den @ x )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[220]) ).
thf(235,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( x = z )
= $false )
| ( ( ( den @ x )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( den @ z )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[220]) ).
thf(236,plain,
( ( ( x = z )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ z )),bind(SV16,$thf( den @ x ))]]) ).
thf(237,plain,
( ( ( ( den @ x )
= ( den @ z ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ z )),bind(SV16,$thf( den @ x ))]]) ).
thf(238,plain,
! [SV15: nat] :
( ( ( ( ts @ ( den @ x ) @ SV15 )
= ( ts @ ( den @ z ) @ SV15 ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ z )),bind(SV16,$thf( den @ x ))]]) ).
thf(239,plain,
( ( ( z = x )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ x )),bind(SV16,$thf( den @ z ))]]) ).
thf(240,plain,
( ( ( ( den @ z )
= ( den @ x ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ x )),bind(SV16,$thf( den @ z ))]]) ).
thf(241,plain,
! [SV15: nat] :
( ( ( ( ts @ ( den @ z ) @ SV15 )
= ( ts @ ( den @ x ) @ SV15 ) )
= $false )
| ( ( x = z )
= $false ) ),
inference(extuni,[status(esa)],[218:[bind(SV14,$thf( den @ x )),bind(SV16,$thf( den @ z ))]]) ).
thf(242,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[34]) ).
thf(243,plain,
( ( x = z )
= $false ),
inference(sim,[status(thm)],[236]) ).
thf(244,plain,
! [SV14: nat,SV15: nat,SV16: nat] :
( ( ( ( ( num @ x )
= ( num @ z ) )
= ( SV16 = SV14 ) )
= $false )
| ( ( z = x )
= $false )
| ( ( ( ts @ SV16 @ SV15 )
= ( ts @ SV14 @ SV15 ) )
= $false ) ),
inference(res,[status(thm)],[35,148]) ).
thf(246,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( ( ( num @ x )
= ( num @ z ) )
= ( ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(res,[status(thm)],[35,138]) ).
thf(248,plain,
! [SV9: nat,SV10: nat] :
( ( ( ( ( num @ x )
= ( num @ z ) )
= ( ( ts @ SV10 @ SV9 )
= ( ts @ SV9 @ SV10 ) ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(res,[status(thm)],[35,128]) ).
thf(250,plain,
( ( ( ( ( num @ x )
= ( num @ z ) )
= ( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(res,[status(thm)],[35,17]) ).
thf(252,plain,
( ( ( ( ( num @ x )
= ( num @ z ) )
= ( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(res,[status(thm)],[35,16]) ).
thf(255,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[252]) ).
thf(256,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ z )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( num @ x )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[252]) ).
thf(257,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[250]) ).
thf(258,plain,
( ( ( z = x )
= $false )
| ( ( ( num @ z )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( num @ x )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[250]) ).
thf(259,plain,
! [SV10: nat,SV9: nat] :
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( num @ z )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[248]) ).
thf(260,plain,
! [SV10: nat,SV9: nat] :
( ( ( z = x )
= $false )
| ( ( ( num @ z )
= ( ts @ SV9 @ SV10 ) )
= $false )
| ( ( ( num @ x )
= ( ts @ SV10 @ SV9 ) )
= $false ) ),
inference(extuni,[status(esa)],[248]) ).
thf(261,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( z = x )
= $false )
| ( ( ( num @ x )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[246]) ).
thf(262,plain,
! [SV11: nat,SV12: nat,SV13: nat] :
( ( ( z = x )
= $false )
| ( ( ( num @ z )
= ( ts @ SV13 @ ( ts @ SV12 @ SV11 ) ) )
= $false )
| ( ( ( num @ x )
= ( ts @ ( ts @ SV13 @ SV12 ) @ SV11 ) )
= $false ) ),
inference(extuni,[status(esa)],[246]) ).
thf(263,plain,
( ( ( z = x )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ x )),bind(SV16,$thf( num @ z ))]]) ).
thf(264,plain,
( ( ( ( num @ z )
= ( num @ x ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ x )),bind(SV16,$thf( num @ z ))]]) ).
thf(265,plain,
! [SV15: nat] :
( ( ( ( ts @ ( num @ z ) @ SV15 )
= ( ts @ ( num @ x ) @ SV15 ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ x )),bind(SV16,$thf( num @ z ))]]) ).
thf(266,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ z )),bind(SV16,$thf( num @ x ))]]) ).
thf(267,plain,
( ( ( ( num @ x )
= ( num @ z ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ z )),bind(SV16,$thf( num @ x ))]]) ).
thf(268,plain,
! [SV15: nat] :
( ( ( ( ts @ ( num @ x ) @ SV15 )
= ( ts @ ( num @ z ) @ SV15 ) )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[244:[bind(SV14,$thf( num @ z )),bind(SV16,$thf( num @ x ))]]) ).
thf(269,plain,
( ( ( x = z )
= $false )
| ( ( z = x )
= $false ) ),
inference(extuni,[status(esa)],[35]) ).
thf(270,plain,
( ( z = x )
= $false ),
inference(sim,[status(thm)],[263]) ).
thf(271,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,270,269,268,267,266,265,264,262,261,260,259,258,257,256,255,243,242,241,240,239,238,237,235,234,233,232,231,230,229,228,216,214,201,200,199,198,197,196,195,194,193,191,190,189,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,148,147,146,145,144,143,142,141,140,138,137,136,135,134,133,132,131,130,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,98,97,96,95,94,93,92,91,90,89,88,87,86,83,82,80,78,77,73,72,71,70,69,68,67,66,64,63,62,61,60,59,58,57,56,55,54,53,52,49,48,46,44,43,36,35,34,33,25,17]) ).
thf(272,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM727^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n006.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 : 600
% 0.12/0.33 % DateTime : Wed Jul 6 08:14:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 5
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:5,ps:3,u:6,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:7,loop_count:0,foatp_calls:0,translation:fof_full).eprover: CPU time limit exceeded, terminating
% 25.23/25.41 .eprover: CPU time limit exceeded, terminating
% 50.22/50.47 ....
% 51.50/51.84
% 51.50/51.84 ********************************
% 51.50/51.84 * All subproblems solved! *
% 51.50/51.84 ********************************
% 51.50/51.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:10,foatp_calls:3,translation:fof_full)
% 51.50/51.87
% 51.50/51.87 %**** Beginning of derivation protocol ****
% 51.50/51.87 % SZS output start CNFRefutation
% See solution above
% 51.50/51.87
% 51.50/51.87 %**** End of derivation protocol ****
% 51.50/51.87 %**** no. of clauses in derivation: 244 ****
% 51.50/51.87 %**** clause counter: 271 ****
% 51.50/51.87
% 51.50/51.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:271,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------