TSTP Solution File: HEN008-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HEN008-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 12:57:23 EDT 2022
% Result : Unsatisfiable 2.93s 3.15s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 31
% Syntax : Number of formulae : 166 ( 99 unt; 10 typ; 0 def)
% Number of atoms : 896 ( 248 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1583 ( 218 ~; 286 |; 0 &;1079 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 9 con; 0-3 aty)
% Number of variables : 511 ( 0 ^ 511 !; 0 ?; 511 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_aQc,type,
aQc: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bQc,type,
bQc: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_divide,type,
divide: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_less_equal,type,
less_equal: $i > $i > $o ).
thf(tp_quotient,type,
quotient: $i > $i > $i > $o ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( quotient @ Z @ Y @ W1 )
| ~ ( quotient @ Z @ X @ W2 )
| ( less_equal @ W1 @ W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_zQyLEzQx) ).
thf(2,axiom,
! [X: $i,Y: $i,W1: $i,Z: $i,W2: $i] :
( ~ ( quotient @ X @ Y @ W1 )
| ~ ( less_equal @ W1 @ Z )
| ~ ( quotient @ X @ Z @ W2 )
| ( less_equal @ W2 @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz_implies_xQzLEy) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_equal) ).
thf(4,axiom,
! [X: $i] : ( quotient @ X @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
thf(5,axiom,
! [X: $i] : ( quotient @ X @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(6,axiom,
! [X: $i] : ( quotient @ zero @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(7,axiom,
! [X: $i] : ( quotient @ X @ identity @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined) ).
thf(9,axiom,
! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(10,axiom,
! [X: $i] : ( less_equal @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(12,axiom,
! [X: $i] : ( less_equal @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(13,axiom,
! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i,V5: $i] :
( ~ ( quotient @ X @ Y @ V1 )
| ~ ( quotient @ Y @ Z @ V2 )
| ~ ( quotient @ X @ Z @ V3 )
| ~ ( quotient @ V3 @ V2 @ V4 )
| ~ ( quotient @ V1 @ Z @ V5 )
| ( less_equal @ V4 @ V5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(17,axiom,
quotient @ b @ c @ bQc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bQc) ).
thf(18,axiom,
quotient @ a @ c @ aQc,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aQc) ).
thf(19,axiom,
less_equal @ a @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLEb) ).
thf(20,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(21,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,negated_conjecture,
~ ( less_equal @ aQc @ bQc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aQcLEbQc) ).
thf(23,plain,
$false = $false,
inference(unfold_def,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( quotient @ Z @ Y @ W1 )
| ~ ( quotient @ Z @ X @ W2 )
| ( less_equal @ W1 @ W2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,W1: $i,Z: $i,W2: $i] :
( ~ ( quotient @ X @ Y @ W1 )
| ~ ( less_equal @ W1 @ Z )
| ~ ( quotient @ X @ Z @ W2 )
| ( less_equal @ W2 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i,V4: $i,V5: $i] :
( ~ ( quotient @ X @ Y @ V1 )
| ~ ( quotient @ Y @ Z @ V2 )
| ~ ( quotient @ X @ Z @ V3 )
| ~ ( quotient @ V3 @ V2 @ V4 )
| ~ ( quotient @ V1 @ Z @ V5 )
| ( less_equal @ V4 @ V5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( quotient @ b @ c @ bQc )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( quotient @ a @ c @ aQc )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( less_equal @ a @ b )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ~ ( less_equal @ aQc @ bQc ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(44,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ! [W1: $i] :
( ~ ( quotient @ Z @ Y @ W1 )
| ! [W2: $i] :
( ~ ( quotient @ Z @ X @ W2 )
| ( less_equal @ W1 @ W2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i,W1: $i] :
( ~ ( quotient @ X @ Y @ W1 )
| ! [Z: $i] :
( ~ ( less_equal @ W1 @ Z )
| ! [W2: $i] :
( ~ ( quotient @ X @ Z @ W2 )
| ( less_equal @ W2 @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] :
( ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i] :
( ~ ( quotient @ X @ Y @ V1 )
| ~ ( quotient @ Y @ Z @ V2 )
| ~ ( quotient @ X @ Z @ V3 )
| ! [V4: $i] :
( ~ ( quotient @ V3 @ V2 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ V1 @ Z @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(50,plain,
( ( ~ ( less_equal @ aQc @ bQc ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(51,plain,
( ( less_equal @ a @ b )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( quotient @ a @ c @ aQc )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(53,plain,
( ( quotient @ b @ c @ bQc )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i,V1: $i,Z: $i,V2: $i,V3: $i] :
( ~ ( quotient @ X @ Y @ V1 )
| ~ ( quotient @ Y @ Z @ V2 )
| ~ ( quotient @ X @ Z @ V3 )
| ! [V4: $i] :
( ~ ( quotient @ V3 @ V2 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ V1 @ Z @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(58,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(63,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] :
( ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,W1: $i] :
( ~ ( quotient @ X @ Y @ W1 )
| ! [Z: $i] :
( ~ ( less_equal @ W1 @ Z )
| ! [W2: $i] :
( ~ ( quotient @ X @ Z @ W2 )
| ( less_equal @ W2 @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ! [W1: $i] :
( ~ ( quotient @ Z @ Y @ W1 )
| ! [W2: $i] :
( ~ ( quotient @ Z @ X @ W2 )
| ( less_equal @ W1 @ W2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(70,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(71,plain,
( ( less_equal @ aQc @ bQc )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(72,plain,
! [SV1: $i] :
( ( ! [SY42: $i] :
( ~ ( less_equal @ SV1 @ SY42 )
| ( quotient @ SV1 @ SY42 @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
! [SV2: $i] :
( ( ! [SY43: $i] :
( ~ ( quotient @ SV2 @ SY43 @ zero )
| ( less_equal @ SV2 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(74,plain,
! [SV3: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( quotient @ SV3 @ SY44 @ SY45 )
| ( less_equal @ SY45 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(75,plain,
! [SV4: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i,SY49: $i,SY50: $i] :
( ~ ( quotient @ SV4 @ SY46 @ SY47 )
| ~ ( quotient @ SY46 @ SY48 @ SY49 )
| ~ ( quotient @ SV4 @ SY48 @ SY50 )
| ! [V4: $i] :
( ~ ( quotient @ SY50 @ SY49 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ SY47 @ SY48 @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV5: $i] :
( ( less_equal @ zero @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV6: $i] :
( ( ! [SY53: $i] :
( ~ ( less_equal @ SV6 @ SY53 )
| ~ ( less_equal @ SY53 @ SV6 )
| ( SV6 = SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV7: $i] :
( ( less_equal @ SV7 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV8: $i] :
( ( ! [SY54: $i] : ( quotient @ SV8 @ SY54 @ ( divide @ SV8 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV9: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( quotient @ SV9 @ SY55 @ SY56 )
| ! [SY57: $i] :
( ~ ( quotient @ SV9 @ SY55 @ SY57 )
| ( SY56 = SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV10: $i] :
( ( quotient @ SV10 @ identity @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV11: $i] :
( ( quotient @ zero @ SV11 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
! [SV12: $i] :
( ( quotient @ SV12 @ SV12 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(84,plain,
! [SV13: $i] :
( ( quotient @ SV13 @ zero @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
! [SV14: $i] :
( ( ! [SY58: $i] :
( ~ ( less_equal @ SV14 @ SY58 )
| ! [SY59: $i] :
( ~ ( less_equal @ SY58 @ SY59 )
| ( less_equal @ SV14 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(86,plain,
! [SV15: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( quotient @ SV15 @ SY60 @ SY61 )
| ! [SY62: $i] :
( ~ ( less_equal @ SY61 @ SY62 )
| ! [SY63: $i] :
( ~ ( quotient @ SV15 @ SY62 @ SY63 )
| ( less_equal @ SY63 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(87,plain,
! [SV16: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( less_equal @ SV16 @ SY64 )
| ! [SY66: $i] :
( ~ ( quotient @ SY65 @ SY64 @ SY66 )
| ! [SY67: $i] :
( ~ ( quotient @ SY65 @ SV16 @ SY67 )
| ( less_equal @ SY66 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(88,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(89,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( less_equal @ SV1 @ SV17 )
| ( quotient @ SV1 @ SV17 @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(90,plain,
! [SV18: $i,SV2: $i] :
( ( ~ ( quotient @ SV2 @ SV18 @ zero )
| ( less_equal @ SV2 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(91,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY68: $i] :
( ~ ( quotient @ SV3 @ SV19 @ SY68 )
| ( less_equal @ SY68 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(92,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i,SY72: $i] :
( ~ ( quotient @ SV4 @ SV20 @ SY69 )
| ~ ( quotient @ SV20 @ SY70 @ SY71 )
| ~ ( quotient @ SV4 @ SY70 @ SY72 )
| ! [V4: $i] :
( ~ ( quotient @ SY72 @ SY71 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ SY69 @ SY70 @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV21: $i,SV6: $i] :
( ( ~ ( less_equal @ SV6 @ SV21 )
| ~ ( less_equal @ SV21 @ SV6 )
| ( SV6 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV22: $i,SV8: $i] :
( ( quotient @ SV8 @ SV22 @ ( divide @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY75: $i] :
( ~ ( quotient @ SV9 @ SV23 @ SY75 )
| ! [SY76: $i] :
( ~ ( quotient @ SV9 @ SV23 @ SY76 )
| ( SY75 = SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV24: $i,SV14: $i] :
( ( ~ ( less_equal @ SV14 @ SV24 )
| ! [SY77: $i] :
( ~ ( less_equal @ SV24 @ SY77 )
| ( less_equal @ SV14 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV25: $i,SV15: $i] :
( ( ! [SY78: $i] :
( ~ ( quotient @ SV15 @ SV25 @ SY78 )
| ! [SY79: $i] :
( ~ ( less_equal @ SY78 @ SY79 )
| ! [SY80: $i] :
( ~ ( quotient @ SV15 @ SY79 @ SY80 )
| ( less_equal @ SY80 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV26: $i,SV16: $i] :
( ( ! [SY81: $i] :
( ~ ( less_equal @ SV16 @ SV26 )
| ! [SY82: $i] :
( ~ ( quotient @ SY81 @ SV26 @ SY82 )
| ! [SY67: $i] :
( ~ ( quotient @ SY81 @ SV16 @ SY67 )
| ( less_equal @ SY82 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV17: $i,SV1: $i] :
( ( ( ~ ( less_equal @ SV1 @ SV17 ) )
= $true )
| ( ( quotient @ SV1 @ SV17 @ zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV18: $i,SV2: $i] :
( ( ( ~ ( quotient @ SV2 @ SV18 @ zero ) )
= $true )
| ( ( less_equal @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV27: $i,SV19: $i,SV3: $i] :
( ( ~ ( quotient @ SV3 @ SV19 @ SV27 )
| ( less_equal @ SV27 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV28: $i,SV20: $i,SV4: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i] :
( ~ ( quotient @ SV4 @ SV20 @ SV28 )
| ~ ( quotient @ SV20 @ SY84 @ SY85 )
| ~ ( quotient @ SV4 @ SY84 @ SY86 )
| ! [SY87: $i] :
( ~ ( quotient @ SY86 @ SY85 @ SY87 )
| ! [SY88: $i] :
( ~ ( quotient @ SV28 @ SY84 @ SY88 )
| ( less_equal @ SY87 @ SY88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV21: $i,SV6: $i] :
( ( ( ~ ( less_equal @ SV6 @ SV21 ) )
= $true )
| ( ( ~ ( less_equal @ SV21 @ SV6 )
| ( SV6 = SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ~ ( quotient @ SV9 @ SV23 @ SV29 )
| ! [SY89: $i] :
( ~ ( quotient @ SV9 @ SV23 @ SY89 )
| ( SV29 = SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV24: $i,SV14: $i] :
( ( ( ~ ( less_equal @ SV14 @ SV24 ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( less_equal @ SV24 @ SY77 )
| ( less_equal @ SV14 @ SY77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV30: $i,SV25: $i,SV15: $i] :
( ( ~ ( quotient @ SV15 @ SV25 @ SV30 )
| ! [SY90: $i] :
( ~ ( less_equal @ SV30 @ SY90 )
| ! [SY80: $i] :
( ~ ( quotient @ SV15 @ SY90 @ SY80 )
| ( less_equal @ SY80 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV31: $i,SV26: $i,SV16: $i] :
( ( ~ ( less_equal @ SV16 @ SV26 )
| ! [SY92: $i] :
( ~ ( quotient @ SV31 @ SV26 @ SY92 )
| ! [SY93: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY93 )
| ( less_equal @ SY92 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV17: $i,SV1: $i] :
( ( ( less_equal @ SV1 @ SV17 )
= $false )
| ( ( quotient @ SV1 @ SV17 @ zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV18: $i,SV2: $i] :
( ( ( quotient @ SV2 @ SV18 @ zero )
= $false )
| ( ( less_equal @ SV2 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV27: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( quotient @ SV3 @ SV19 @ SV27 ) )
= $true )
| ( ( less_equal @ SV27 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV32: $i,SV28: $i,SV20: $i,SV4: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( quotient @ SV4 @ SV20 @ SV28 )
| ~ ( quotient @ SV20 @ SV32 @ SY94 )
| ~ ( quotient @ SV4 @ SV32 @ SY95 )
| ! [SY96: $i] :
( ~ ( quotient @ SY95 @ SY94 @ SY96 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY96 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV21: $i,SV6: $i] :
( ( ( less_equal @ SV6 @ SV21 )
= $false )
| ( ( ~ ( less_equal @ SV21 @ SV6 )
| ( SV6 = SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV23 @ SV29 ) )
= $true )
| ( ( ! [SY89: $i] :
( ~ ( quotient @ SV9 @ SV23 @ SY89 )
| ( SV29 = SY89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV24: $i,SV14: $i] :
( ( ( less_equal @ SV14 @ SV24 )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( less_equal @ SV24 @ SY77 )
| ( less_equal @ SV14 @ SY77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV30: $i,SV25: $i,SV15: $i] :
( ( ( ~ ( quotient @ SV15 @ SV25 @ SV30 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( less_equal @ SV30 @ SY90 )
| ! [SY80: $i] :
( ~ ( quotient @ SV15 @ SY90 @ SY80 )
| ( less_equal @ SY80 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV31: $i,SV26: $i,SV16: $i] :
( ( ( ~ ( less_equal @ SV16 @ SV26 ) )
= $true )
| ( ( ! [SY92: $i] :
( ~ ( quotient @ SV31 @ SV26 @ SY92 )
| ! [SY93: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY93 )
| ( less_equal @ SY92 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV27: $i,SV19: $i,SV3: $i] :
( ( ( quotient @ SV3 @ SV19 @ SV27 )
= $false )
| ( ( less_equal @ SV27 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV33: $i,SV32: $i,SV28: $i,SV20: $i,SV4: $i] :
( ( ! [SY98: $i] :
( ~ ( quotient @ SV4 @ SV20 @ SV28 )
| ~ ( quotient @ SV20 @ SV32 @ SV33 )
| ~ ( quotient @ SV4 @ SV32 @ SY98 )
| ! [SY99: $i] :
( ~ ( quotient @ SY98 @ SV33 @ SY99 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY99 @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV6: $i,SV21: $i] :
( ( ( ~ ( less_equal @ SV21 @ SV6 ) )
= $true )
| ( ( SV6 = SV21 )
= $true )
| ( ( less_equal @ SV6 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV29: $i,SV23: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV23 @ SV29 )
= $false )
| ( ( ! [SY89: $i] :
( ~ ( quotient @ SV9 @ SV23 @ SY89 )
| ( SV29 = SY89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV14: $i,SV34: $i,SV24: $i] :
( ( ( ~ ( less_equal @ SV24 @ SV34 )
| ( less_equal @ SV14 @ SV34 ) )
= $true )
| ( ( less_equal @ SV14 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV30: $i,SV25: $i,SV15: $i] :
( ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( less_equal @ SV30 @ SY90 )
| ! [SY80: $i] :
( ~ ( quotient @ SV15 @ SY90 @ SY80 )
| ( less_equal @ SY80 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV31: $i,SV26: $i,SV16: $i] :
( ( ( less_equal @ SV16 @ SV26 )
= $false )
| ( ( ! [SY92: $i] :
( ~ ( quotient @ SV31 @ SV26 @ SY92 )
| ! [SY93: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY93 )
| ( less_equal @ SY92 @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV35: $i,SV33: $i,SV32: $i,SV28: $i,SV20: $i,SV4: $i] :
( ( ~ ( quotient @ SV4 @ SV20 @ SV28 )
| ~ ( quotient @ SV20 @ SV32 @ SV33 )
| ~ ( quotient @ SV4 @ SV32 @ SV35 )
| ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(125,plain,
! [SV6: $i,SV21: $i] :
( ( ( less_equal @ SV21 @ SV6 )
= $false )
| ( ( SV6 = SV21 )
= $true )
| ( ( less_equal @ SV6 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(126,plain,
! [SV29: $i,SV36: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV23 @ SV36 )
| ( SV29 = SV36 ) )
= $true )
| ( ( quotient @ SV9 @ SV23 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV14: $i,SV34: $i,SV24: $i] :
( ( ( ~ ( less_equal @ SV24 @ SV34 ) )
= $true )
| ( ( less_equal @ SV14 @ SV34 )
= $true )
| ( ( less_equal @ SV14 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV25: $i,SV15: $i,SV37: $i,SV30: $i] :
( ( ( ~ ( less_equal @ SV30 @ SV37 )
| ! [SY103: $i] :
( ~ ( quotient @ SV15 @ SV37 @ SY103 )
| ( less_equal @ SY103 @ SV25 ) ) )
= $true )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV16: $i,SV38: $i,SV26: $i,SV31: $i] :
( ( ( ~ ( quotient @ SV31 @ SV26 @ SV38 )
| ! [SY104: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY104 )
| ( less_equal @ SV38 @ SY104 ) ) )
= $true )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV35: $i,SV33: $i,SV32: $i,SV28: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( quotient @ SV20 @ SV32 @ SV33 )
| ~ ( quotient @ SV4 @ SV32 @ SV35 )
| ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV29: $i,SV36: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV23 @ SV36 ) )
= $true )
| ( ( SV29 = SV36 )
= $true )
| ( ( quotient @ SV9 @ SV23 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(132,plain,
! [SV14: $i,SV34: $i,SV24: $i] :
( ( ( less_equal @ SV24 @ SV34 )
= $false )
| ( ( less_equal @ SV14 @ SV34 )
= $true )
| ( ( less_equal @ SV14 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV25: $i,SV15: $i,SV37: $i,SV30: $i] :
( ( ( ~ ( less_equal @ SV30 @ SV37 ) )
= $true )
| ( ( ! [SY103: $i] :
( ~ ( quotient @ SV15 @ SV37 @ SY103 )
| ( less_equal @ SY103 @ SV25 ) ) )
= $true )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(134,plain,
! [SV16: $i,SV38: $i,SV26: $i,SV31: $i] :
( ( ( ~ ( quotient @ SV31 @ SV26 @ SV38 ) )
= $true )
| ( ( ! [SY104: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY104 )
| ( less_equal @ SV38 @ SY104 ) ) )
= $true )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(135,plain,
! [SV35: $i,SV33: $i,SV32: $i,SV28: $i,SV20: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false )
| ( ( ~ ( quotient @ SV20 @ SV32 @ SV33 )
| ~ ( quotient @ SV4 @ SV32 @ SV35 )
| ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(136,plain,
! [SV29: $i,SV36: $i,SV23: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV23 @ SV36 )
= $false )
| ( ( SV29 = SV36 )
= $true )
| ( ( quotient @ SV9 @ SV23 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(137,plain,
! [SV25: $i,SV15: $i,SV37: $i,SV30: $i] :
( ( ( less_equal @ SV30 @ SV37 )
= $false )
| ( ( ! [SY103: $i] :
( ~ ( quotient @ SV15 @ SV37 @ SY103 )
| ( less_equal @ SY103 @ SV25 ) ) )
= $true )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV16: $i,SV38: $i,SV26: $i,SV31: $i] :
( ( ( quotient @ SV31 @ SV26 @ SV38 )
= $false )
| ( ( ! [SY104: $i] :
( ~ ( quotient @ SV31 @ SV16 @ SY104 )
| ( less_equal @ SV38 @ SY104 ) ) )
= $true )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV28: $i,SV35: $i,SV4: $i,SV33: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( quotient @ SV20 @ SV32 @ SV33 ) )
= $true )
| ( ( ~ ( quotient @ SV4 @ SV32 @ SV35 )
| ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV30: $i,SV25: $i,SV39: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( quotient @ SV15 @ SV37 @ SV39 )
| ( less_equal @ SV39 @ SV25 ) )
= $true )
| ( ( less_equal @ SV30 @ SV37 )
= $false )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV26: $i,SV38: $i,SV40: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( quotient @ SV31 @ SV16 @ SV40 )
| ( less_equal @ SV38 @ SV40 ) )
= $true )
| ( ( quotient @ SV31 @ SV26 @ SV38 )
= $false )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV28: $i,SV35: $i,SV4: $i,SV33: $i,SV32: $i,SV20: $i] :
( ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( ~ ( quotient @ SV4 @ SV32 @ SV35 )
| ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(143,plain,
! [SV30: $i,SV25: $i,SV39: $i,SV37: $i,SV15: $i] :
( ( ( ~ ( quotient @ SV15 @ SV37 @ SV39 ) )
= $true )
| ( ( less_equal @ SV39 @ SV25 )
= $true )
| ( ( less_equal @ SV30 @ SV37 )
= $false )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(144,plain,
! [SV26: $i,SV38: $i,SV40: $i,SV16: $i,SV31: $i] :
( ( ( ~ ( quotient @ SV31 @ SV16 @ SV40 ) )
= $true )
| ( ( less_equal @ SV38 @ SV40 )
= $true )
| ( ( quotient @ SV31 @ SV26 @ SV38 )
= $false )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV20: $i,SV28: $i,SV33: $i,SV35: $i,SV32: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV32 @ SV35 ) )
= $true )
| ( ( ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV30: $i,SV25: $i,SV39: $i,SV37: $i,SV15: $i] :
( ( ( quotient @ SV15 @ SV37 @ SV39 )
= $false )
| ( ( less_equal @ SV39 @ SV25 )
= $true )
| ( ( less_equal @ SV30 @ SV37 )
= $false )
| ( ( quotient @ SV15 @ SV25 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(147,plain,
! [SV26: $i,SV38: $i,SV40: $i,SV16: $i,SV31: $i] :
( ( ( quotient @ SV31 @ SV16 @ SV40 )
= $false )
| ( ( less_equal @ SV38 @ SV40 )
= $true )
| ( ( quotient @ SV31 @ SV26 @ SV38 )
= $false )
| ( ( less_equal @ SV16 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV20: $i,SV28: $i,SV33: $i,SV35: $i,SV32: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( ! [SY101: $i] :
( ~ ( quotient @ SV35 @ SV33 @ SY101 )
| ! [SY97: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY97 )
| ( less_equal @ SY101 @ SY97 ) ) ) )
= $true )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(149,plain,
! [SV20: $i,SV4: $i,SV32: $i,SV28: $i,SV41: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( quotient @ SV35 @ SV33 @ SV41 )
| ! [SY105: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY105 )
| ( less_equal @ SV41 @ SY105 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(150,plain,
! [SV20: $i,SV4: $i,SV32: $i,SV28: $i,SV41: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( quotient @ SV35 @ SV33 @ SV41 ) )
= $true )
| ( ( ! [SY105: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY105 )
| ( less_equal @ SV41 @ SY105 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV20: $i,SV4: $i,SV32: $i,SV28: $i,SV41: $i,SV33: $i,SV35: $i] :
( ( ( quotient @ SV35 @ SV33 @ SV41 )
= $false )
| ( ( ! [SY105: $i] :
( ~ ( quotient @ SV28 @ SV32 @ SY105 )
| ( less_equal @ SV41 @ SY105 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(152,plain,
! [SV20: $i,SV4: $i,SV33: $i,SV35: $i,SV41: $i,SV42: $i,SV32: $i,SV28: $i] :
( ( ( ~ ( quotient @ SV28 @ SV32 @ SV42 )
| ( less_equal @ SV41 @ SV42 ) )
= $true )
| ( ( quotient @ SV35 @ SV33 @ SV41 )
= $false )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(153,plain,
! [SV20: $i,SV4: $i,SV33: $i,SV35: $i,SV41: $i,SV42: $i,SV32: $i,SV28: $i] :
( ( ( ~ ( quotient @ SV28 @ SV32 @ SV42 ) )
= $true )
| ( ( less_equal @ SV41 @ SV42 )
= $true )
| ( ( quotient @ SV35 @ SV33 @ SV41 )
= $false )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(154,plain,
! [SV20: $i,SV4: $i,SV33: $i,SV35: $i,SV41: $i,SV42: $i,SV32: $i,SV28: $i] :
( ( ( quotient @ SV28 @ SV32 @ SV42 )
= $false )
| ( ( less_equal @ SV41 @ SV42 )
= $true )
| ( ( quotient @ SV35 @ SV33 @ SV41 )
= $false )
| ( ( quotient @ SV4 @ SV32 @ SV35 )
= $false )
| ( ( quotient @ SV20 @ SV32 @ SV33 )
= $false )
| ( ( quotient @ SV4 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(155,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[51,154,147,146,136,132,125,117,109,108,94,88,84,83,82,81,78,76,71,53,52]) ).
thf(156,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN008-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 13:12:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 20
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:20,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:22,loop_count:0,foatp_calls:0,translation:fof_full).........
% 2.93/3.15
% 2.93/3.15 ********************************
% 2.93/3.15 * All subproblems solved! *
% 2.93/3.15 ********************************
% 2.93/3.15 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.93/3.16
% 2.93/3.16 %**** Beginning of derivation protocol ****
% 2.93/3.16 % SZS output start CNFRefutation
% See solution above
% 2.93/3.16
% 2.93/3.16 %**** End of derivation protocol ****
% 2.93/3.16 %**** no. of clauses in derivation: 156 ****
% 2.93/3.16 %**** clause counter: 155 ****
% 2.93/3.16
% 2.93/3.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:155,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------