TSTP Solution File: NUM741^1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM741^1 : 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 11:54:53 EDT 2022
% Result : Theorem 34.36s 34.55s
% Output : CNFRefutation 34.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 145 ( 44 unt; 9 typ; 0 def)
% Number of atoms : 853 ( 427 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 1471 ( 22 ~; 151 |; 0 &;1292 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 259 ( 0 ^ 259 !; 0 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_frac,type,
frac: $tType ).
thf(tp_nat,type,
nat: $tType ).
thf(tp_den,type,
den: frac > nat ).
thf(tp_less,type,
less: nat > nat > $o ).
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,Xu: nat] :
( ( less @ Xx @ Xy )
=> ( ( less @ Xz @ Xu )
=> ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34a) ).
thf(4,axiom,
! [Xx: nat,Xy: nat,Xz: nat] :
( ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
=> ( less @ Xx @ Xy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz33c) ).
thf(5,axiom,
less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(6,axiom,
less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(7,conjecture,
less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50) ).
thf(8,negated_conjecture,
( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,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(11,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
( ( less @ Xx @ Xy )
=> ( ( less @ Xz @ Xu )
=> ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
=> ( less @ Xx @ Xy ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ! [Xz: nat,Xu: nat] :
( ~ ( less @ Xz @ Xu )
| ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(18,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xz: nat] :
~ ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
| ( less @ Xx @ Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(19,plain,
( ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(20,plain,
( ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ! [Xx: nat,Xy: nat] :
( ! [Xz: nat] :
~ ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
| ( less @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [Xx: nat,Xy: nat] :
( ~ ( less @ Xx @ Xy )
| ! [Xz: nat,Xu: nat] :
( ~ ( less @ Xz @ Xu )
| ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [Xx: nat,Xy: nat] :
( ( ts @ Xx @ Xy )
= ( ts @ Xy @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [Xx: nat,Xy: nat,Xz: nat] :
( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
= ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(25,plain,
( ( ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(26,plain,
! [SV1: nat] :
( ( ! [SY12: nat] :
( ! [SY13: nat] :
~ ( less @ ( ts @ SV1 @ SY13 ) @ ( ts @ SY12 @ SY13 ) )
| ( less @ SV1 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV2: nat] :
( ( ! [SY14: nat] :
( ~ ( less @ SV2 @ SY14 )
| ! [SY15: nat,SY16: nat] :
( ~ ( less @ SY15 @ SY16 )
| ( less @ ( ts @ SV2 @ SY15 ) @ ( ts @ SY14 @ SY16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV3: nat] :
( ( ! [SY17: nat] :
( ( ts @ SV3 @ SY17 )
= ( ts @ SY17 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV4: nat] :
( ( ! [SY18: nat,SY19: nat] :
( ( ts @ ( ts @ SV4 @ SY18 ) @ SY19 )
= ( ts @ SV4 @ ( ts @ SY18 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV5: nat,SV1: nat] :
( ( ! [SY20: nat] :
~ ( less @ ( ts @ SV1 @ SY20 ) @ ( ts @ SV5 @ SY20 ) )
| ( less @ SV1 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV6: nat,SV2: nat] :
( ( ~ ( less @ SV2 @ SV6 )
| ! [SY21: nat,SY22: nat] :
( ~ ( less @ SY21 @ SY22 )
| ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV7: nat,SV3: nat] :
( ( ( ts @ SV3 @ SV7 )
= ( ts @ SV7 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV8: nat,SV4: nat] :
( ( ! [SY23: nat] :
( ( ts @ ( ts @ SV4 @ SV8 ) @ SY23 )
= ( ts @ SV4 @ ( ts @ SV8 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
! [SV5: nat,SV1: nat] :
( ( ( ! [SY20: nat] :
~ ( less @ ( ts @ SV1 @ SY20 ) @ ( ts @ SV5 @ SY20 ) ) )
= $true )
| ( ( less @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV6: nat,SV2: nat] :
( ( ( ~ ( less @ SV2 @ SV6 ) )
= $true )
| ( ( ! [SY21: nat,SY22: nat] :
( ~ ( less @ SY21 @ SY22 )
| ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV9: nat,SV8: nat,SV4: nat] :
( ( ( ts @ ( ts @ SV4 @ SV8 ) @ SV9 )
= ( ts @ SV4 @ ( ts @ SV8 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV5: nat,SV10: nat,SV1: nat] :
( ( ( ~ ( less @ ( ts @ SV1 @ SV10 ) @ ( ts @ SV5 @ SV10 ) ) )
= $true )
| ( ( less @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV6: nat,SV2: nat] :
( ( ( less @ SV2 @ SV6 )
= $false )
| ( ( ! [SY21: nat,SY22: nat] :
( ~ ( less @ SY21 @ SY22 )
| ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: nat,SV10: nat,SV1: nat] :
( ( ( less @ ( ts @ SV1 @ SV10 ) @ ( ts @ SV5 @ SV10 ) )
= $false )
| ( ( less @ SV1 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV6: nat,SV2: nat,SV11: nat] :
( ( ( ! [SY24: nat] :
( ~ ( less @ SV11 @ SY24 )
| ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SY24 ) ) ) )
= $true )
| ( ( less @ SV2 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
( ( ( ~ ( less @ SV11 @ SV12 )
| ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) ) )
= $true )
| ( ( less @ SV2 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
( ( ( ~ ( less @ SV11 @ SV12 ) )
= $true )
| ( ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) )
= $true )
| ( ( less @ SV2 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
( ( ( less @ SV11 @ SV12 )
= $false )
| ( ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) )
= $true )
| ( ( less @ SV2 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
( ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false ),
inference(res,[status(thm)],[30,20]) ).
thf(46,plain,
( ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
= ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false ),
inference(res,[status(thm)],[30,19]) ).
thf(47,plain,
( ( ( z = y )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(48,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(49,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(50,plain,
( ( ( z = y )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(51,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(52,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(53,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(54,plain,
( ( ( ( num @ z )
= ( num @ y ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[46]) ).
thf(55,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)],[46]) ).
thf(56,plain,
( ( ( x = y )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(57,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(58,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( x = y )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(59,plain,
( ( ( x = y )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(60,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(61,plain,
( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( num @ x )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(62,plain,
( ( ( x = y )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(63,plain,
( ( ( ( den @ x )
= ( den @ y ) )
= $false )
| ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[45]) ).
thf(64,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)],[45]) ).
thf(65,plain,
( ( z = y )
= $false ),
inference(sim,[status(thm)],[47]) ).
thf(66,plain,
( ( x = y )
= $false ),
inference(sim,[status(thm)],[56]) ).
thf(67,plain,
! [SV13: nat,SV14: nat] :
( ( ( ts @ SV14 @ SV13 )
= ( ts @ SV13 @ SV14 ) )
= $true ),
inference(rename,[status(thm)],[33]) ).
thf(69,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
= $true ),
inference(rename,[status(thm)],[37]) ).
thf(71,plain,
! [SV18: nat,SV19: nat,SV20: nat] :
( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false )
| ( ( less @ SV20 @ SV18 )
= $true ) ),
inference(rename,[status(thm)],[40]) ).
thf(76,plain,
! [SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ SV20 @ SV18 )
= ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $false )
| ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false ) ),
inference(res,[status(thm)],[71,30]) ).
thf(77,plain,
! [SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( less @ SV20 @ SV18 )
= $true ) ),
inference(res,[status(thm)],[71,20]) ).
thf(78,plain,
! [SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( less @ SV20 @ SV18 )
= $true ) ),
inference(res,[status(thm)],[71,19]) ).
thf(79,plain,
( ( ( less @ ( num @ x ) @ ( num @ y ) )
= $true )
| ( ( y = x )
= $false ) ),
inference(extuni,[status(esa)],[78:[bind(SV18,$thf( num @ y )),bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).
thf(80,plain,
( ( ( less @ ( num @ x ) @ ( num @ y ) )
= $true )
| ( ( ( den @ y )
= ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[78:[bind(SV18,$thf( num @ y )),bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).
thf(81,plain,
! [SV18: nat] :
( ( ( less @ ( num @ x ) @ SV18 )
= $true )
| ( ( ( ts @ SV18 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[78:[bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).
thf(82,plain,
! [SV20: nat] :
( ( ( less @ SV20 @ ( num @ y ) )
= $true )
| ( ( ( ts @ SV20 @ ( den @ x ) )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[78:[bind(SV19,$thf( den @ x )),bind(SV18,$thf( num @ y ))]]) ).
thf(83,plain,
! [SV19: nat,SV18: nat,SV20: nat] :
( ( ( less @ SV20 @ SV18 )
= $true )
| ( ( ( ts @ SV18 @ SV19 )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV20 @ SV19 )
= ( ts @ ( num @ x ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[78]) ).
thf(84,plain,
( ( ( less @ ( num @ y ) @ ( num @ z ) )
= $true )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV18,$thf( num @ z )),bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).
thf(85,plain,
( ( ( less @ ( num @ y ) @ ( num @ z ) )
= $true )
| ( ( ( den @ z )
= ( den @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV18,$thf( num @ z )),bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).
thf(86,plain,
! [SV18: nat] :
( ( ( less @ ( num @ y ) @ SV18 )
= $true )
| ( ( ( ts @ SV18 @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).
thf(87,plain,
! [SV20: nat] :
( ( ( less @ SV20 @ ( num @ z ) )
= $true )
| ( ( ( ts @ SV20 @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[77:[bind(SV19,$thf( den @ y )),bind(SV18,$thf( num @ z ))]]) ).
thf(88,plain,
! [SV19: nat,SV18: nat,SV20: nat] :
( ( ( less @ SV20 @ SV18 )
= $true )
| ( ( ( ts @ SV18 @ SV19 )
= ( ts @ ( num @ z ) @ ( den @ y ) ) )
= $false )
| ( ( ( ts @ SV20 @ SV19 )
= ( ts @ ( num @ y ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[77]) ).
thf(89,plain,
! [SV19: nat] :
( ( less @ ( ts @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ SV19 ) @ ( ts @ ( ts @ ( num @ z ) @ ( den @ x ) ) @ SV19 ) )
= $false ),
inference(extuni,[status(esa)],[76:[bind(SV18,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV20,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).
thf(90,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true )
| ( ( less @ SV22 @ SV21 )
= $false ) ),
inference(rename,[status(thm)],[44]) ).
thf(95,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ SV22 @ SV21 )
= ( less @ SV20 @ SV18 ) )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true )
| ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false ) ),
inference(res,[status(thm)],[90,71]) ).
thf(96,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ SV24 @ SV23 )
= ( less @ SV20 @ SV18 ) )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true )
| ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false ) ),
inference(res,[status(thm)],[90,71]) ).
thf(97,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
( ( ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) ) )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ SV20 @ SV18 )
= $true ) ),
inference(res,[status(thm)],[90,71]) ).
thf(102,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ SV22 @ SV21 )
= $false ) ),
inference(res,[status(thm)],[90,30]) ).
thf(103,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( ( less @ SV22 @ SV21 )
= ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true ) ),
inference(res,[status(thm)],[90,20]) ).
thf(104,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( ( less @ SV24 @ SV23 )
= ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true )
| ( ( less @ SV22 @ SV21 )
= $false ) ),
inference(res,[status(thm)],[90,20]) ).
thf(105,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( ( less @ SV22 @ SV21 )
= ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true ) ),
inference(res,[status(thm)],[90,19]) ).
thf(106,plain,
! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
( ( ( ( less @ SV24 @ SV23 )
= ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $false )
| ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
= $true )
| ( ( less @ SV22 @ SV21 )
= $false ) ),
inference(res,[status(thm)],[90,19]) ).
thf(107,plain,
! [SV21: nat,SV22: nat] :
( ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ ( ts @ SV22 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ SV21 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[106:[bind(SV23,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV24,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(108,plain,
! [SV23: nat,SV24: nat] :
( ( ( less @ ( ts @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ SV24 ) @ ( ts @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SV23 ) )
= $true )
| ( ( less @ SV24 @ SV23 )
= $false ) ),
inference(extuni,[status(esa)],[105:[bind(SV21,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV22,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).
thf(109,plain,
! [SV21: nat,SV22: nat] :
( ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ ( ts @ SV22 @ ( ts @ ( num @ y ) @ ( den @ z ) ) ) @ ( ts @ SV21 @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[104:[bind(SV23,$thf( ts @ ( num @ z ) @ ( den @ y ) )),bind(SV24,$thf( ts @ ( num @ y ) @ ( den @ z ) ))]]) ).
thf(110,plain,
! [SV23: nat,SV24: nat] :
( ( ( less @ ( ts @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ SV24 ) @ ( ts @ ( ts @ ( num @ z ) @ ( den @ y ) ) @ SV23 ) )
= $true )
| ( ( less @ SV24 @ SV23 )
= $false ) ),
inference(extuni,[status(esa)],[103:[bind(SV21,$thf( ts @ ( num @ z ) @ ( den @ y ) )),bind(SV22,$thf( ts @ ( num @ y ) @ ( den @ z ) ))]]) ).
thf(111,plain,
( ( ( less @ ( num @ x ) @ ( num @ z ) )
= $false )
| ( ( less @ ( den @ z ) @ ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[102:[bind(SV23,$thf( den @ x )),bind(SV21,$thf( num @ z )),bind(SV24,$thf( den @ z )),bind(SV22,$thf( num @ x ))]]) ).
thf(112,plain,
! [SV23: nat,SV21: nat] :
( ( ( less @ ( num @ x ) @ SV21 )
= $false )
| ( ( less @ ( den @ z ) @ SV23 )
= $false )
| ( ( ( ts @ SV21 @ SV23 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false ) ),
inference(extuni,[status(esa)],[102:[bind(SV24,$thf( den @ z )),bind(SV22,$thf( num @ x ))]]) ).
thf(113,plain,
! [SV24: nat,SV22: nat] :
( ( ( less @ SV22 @ ( num @ z ) )
= $false )
| ( ( less @ SV24 @ ( den @ x ) )
= $false )
| ( ( ( ts @ SV22 @ SV24 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[102:[bind(SV23,$thf( den @ x )),bind(SV21,$thf( num @ z ))]]) ).
thf(114,plain,
! [SV23: nat,SV24: nat,SV21: nat,SV22: nat] :
( ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( ( ts @ SV21 @ SV23 )
= ( ts @ ( num @ z ) @ ( den @ x ) ) )
= $false )
| ( ( ( ts @ SV22 @ SV24 )
= ( ts @ ( num @ x ) @ ( den @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[102]) ).
thf(116,plain,
! [SV23: nat,SV19: nat,SV21: nat,SV18: nat,SV20: nat] :
( ( ( less @ SV20 @ SV18 )
= $true )
| ( ( less @ SV20 @ SV21 )
= $false )
| ( ( less @ SV19 @ SV23 )
= $false )
| ( ( ( ts @ SV21 @ SV23 )
= ( ts @ SV18 @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[97:[bind(SV24,$thf( SV19 )),bind(SV22,$thf( SV20 ))]]) ).
thf(117,plain,
! [SV19: nat,SV24: nat,SV22: nat,SV18: nat,SV20: nat] :
( ( ( less @ SV20 @ SV18 )
= $true )
| ( ( less @ SV22 @ SV18 )
= $false )
| ( ( less @ SV24 @ SV19 )
= $false )
| ( ( ( ts @ SV22 @ SV24 )
= ( ts @ SV20 @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[97:[bind(SV23,$thf( SV19 )),bind(SV21,$thf( SV18 ))]]) ).
thf(118,plain,
! [SV19: nat,SV23: nat,SV24: nat,SV21: nat,SV22: nat,SV18: nat,SV20: nat] :
( ( ( less @ SV20 @ SV18 )
= $true )
| ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ SV24 @ SV23 )
= $false )
| ( ( ( ts @ SV21 @ SV23 )
= ( ts @ SV18 @ SV19 ) )
= $false )
| ( ( ( ts @ SV22 @ SV24 )
= ( ts @ SV20 @ SV19 ) )
= $false ) ),
inference(extuni,[status(esa)],[97]) ).
thf(119,plain,
! [SV21: nat,SV22: nat,SV18: nat,SV19: nat,SV20: nat] :
( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false )
| ( ( less @ SV22 @ SV21 )
= $false )
| ( ( less @ ( ts @ SV22 @ SV20 ) @ ( ts @ SV21 @ SV18 ) )
= $true ) ),
inference(extuni,[status(esa)],[96:[bind(SV23,$thf( SV18 )),bind(SV24,$thf( SV20 ))]]) ).
thf(120,plain,
! [SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
= $false )
| ( ( less @ ( ts @ SV20 @ SV24 ) @ ( ts @ SV18 @ SV23 ) )
= $true )
| ( ( less @ SV24 @ SV23 )
= $false ) ),
inference(extuni,[status(esa)],[95:[bind(SV21,$thf( SV18 )),bind(SV22,$thf( SV20 ))]]) ).
thf(126,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( ( ( num @ z )
= ( num @ y ) )
= ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(res,[status(thm)],[48,69]) ).
thf(128,plain,
! [SV13: nat,SV14: nat] :
( ( ( ( ( num @ z )
= ( num @ y ) )
= ( ( ts @ SV14 @ SV13 )
= ( ts @ SV13 @ SV14 ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(res,[status(thm)],[48,67]) ).
thf(134,plain,
! [SV14: nat,SV13: nat] :
( ( ( z = y )
= $false )
| ( ( ( num @ z )
= ( ts @ SV13 @ SV14 ) )
= $false )
| ( ( ( num @ y )
= ( ts @ SV14 @ SV13 ) )
= $false ) ),
inference(extuni,[status(esa)],[128]) ).
thf(135,plain,
! [SV14: nat,SV13: nat] :
( ( ( z = y )
= $false )
| ( ( ( num @ y )
= ( ts @ SV13 @ SV14 ) )
= $false )
| ( ( ( num @ z )
= ( ts @ SV14 @ SV13 ) )
= $false ) ),
inference(extuni,[status(esa)],[128]) ).
thf(136,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( num @ z )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
= $false )
| ( ( ( num @ y )
= ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[126]) ).
thf(137,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( num @ y )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[126]) ).
thf(138,plain,
( ( ( z = y )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[48]) ).
thf(139,plain,
( ( z = y )
= $false ),
inference(sim,[status(thm)],[138]) ).
thf(145,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(res,[status(thm)],[49,69]) ).
thf(147,plain,
! [SV13: nat,SV14: nat] :
( ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) )
= ( ( ts @ SV14 @ SV13 )
= ( ts @ SV13 @ SV14 ) ) )
= $false )
| ( ( z = y )
= $false ) ),
inference(res,[status(thm)],[49,67]) ).
thf(153,plain,
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( num @ y ) )
= $false )
| ( ( ( num @ z )
= ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ y ))]]) ).
thf(154,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( den @ x ) @ ( num @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ y ))]]) ).
thf(155,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ ( den @ x ) @ ( num @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV14,$thf( den @ x )),bind(SV13,$thf( num @ z ))]]) ).
thf(156,plain,
! [SV14: nat,SV13: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ SV13 @ SV14 ) )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ SV14 @ SV13 ) )
= $false ) ),
inference(extuni,[status(esa)],[147]) ).
thf(157,plain,
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( num @ z ) )
= $false )
| ( ( ( num @ y )
= ( den @ x ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ z ))]]) ).
thf(158,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ ( den @ x ) @ ( num @ z ) ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ z ))]]) ).
thf(159,plain,
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( den @ x ) @ ( num @ y ) ) )
= $false ) ),
inference(extuni,[status(esa)],[147:[bind(SV14,$thf( den @ x )),bind(SV13,$thf( num @ y ))]]) ).
thf(160,plain,
! [SV14: nat,SV13: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ SV13 @ SV14 ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ SV14 @ SV13 ) )
= $false ) ),
inference(extuni,[status(esa)],[147]) ).
thf(161,plain,
! [SV16: nat] :
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( ts @ SV16 @ ( den @ x ) ) )
= $false )
| ( ( ( num @ y )
= ( ts @ ( num @ z ) @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ z )),bind(SV15,$thf( den @ x ))]]) ).
thf(162,plain,
! [SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ SV17 @ ( ts @ SV16 @ ( den @ x ) ) ) )
= $false )
| ( ( ( num @ y )
= ( ts @ SV17 @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV15,$thf( den @ x ))]]) ).
thf(163,plain,
! [SV15: nat,SV16: nat] :
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( ts @ SV16 @ SV15 ) )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ ( ts @ ( num @ z ) @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ z ))]]) ).
thf(164,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[145]) ).
thf(165,plain,
! [SV16: nat] :
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( ts @ SV16 @ ( den @ x ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ ( num @ y ) @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ y )),bind(SV15,$thf( den @ x ))]]) ).
thf(166,plain,
! [SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ SV17 @ ( ts @ SV16 @ ( den @ x ) ) ) )
= $false )
| ( ( ( num @ z )
= ( ts @ SV17 @ SV16 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV15,$thf( den @ x ))]]) ).
thf(167,plain,
! [SV15: nat,SV16: nat] :
( ( ( z = y )
= $false )
| ( ( ( den @ x )
= ( ts @ SV16 @ SV15 ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( ts @ ( num @ y ) @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ y ))]]) ).
thf(168,plain,
! [SV15: nat,SV16: nat,SV17: nat] :
( ( ( z = y )
= $false )
| ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
= ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
= $false )
| ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
= ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
= $false ) ),
inference(extuni,[status(esa)],[145]) ).
thf(169,plain,
( ( ( z = y )
= $false )
| ( ( z = y )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(170,plain,
( ( ( z = y )
= $false )
| ( ( ( num @ z )
= ( num @ y ) )
= $false ) ),
inference(extuni,[status(esa)],[49]) ).
thf(171,plain,
( ( z = y )
= $false ),
inference(sim,[status(thm)],[169]) ).
thf(172,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,171,170,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,139,137,136,135,134,120,119,118,117,116,114,113,112,111,110,109,108,107,90,89,88,87,86,85,84,83,82,81,80,79,71,69,67,66,65,64,63,62,61,60,59,58,57,55,54,53,52,51,50,49,48,30,20]) ).
thf(173,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM741^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n006.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 : Thu Jul 7 01:27:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 6
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:6,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:8,loop_count:0,foatp_calls:0,translation:fof_full)..eprover: CPU time limit exceeded, terminating
% 25.27/25.47 ...
% 34.36/34.55
% 34.36/34.55 ********************************
% 34.36/34.55 * All subproblems solved! *
% 34.36/34.55 ********************************
% 34.36/34.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:172,loop_count:10,foatp_calls:2,translation:fof_full)
% 34.36/34.57
% 34.36/34.57 %**** Beginning of derivation protocol ****
% 34.36/34.57 % SZS output start CNFRefutation
% See solution above
% 34.36/34.57
% 34.36/34.57 %**** End of derivation protocol ****
% 34.36/34.57 %**** no. of clauses in derivation: 136 ****
% 34.36/34.57 %**** clause counter: 172 ****
% 34.36/34.57
% 34.36/34.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:172,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------