TSTP Solution File: HEN006-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HEN006-2 : 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 : n015.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 12:57:19 EDT 2022
% Result : Unsatisfiable 11.12s 11.34s
% Output : CNFRefutation 11.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 29
% Syntax : Number of formulae : 136 ( 87 unt; 10 typ; 0 def)
% Number of atoms : 660 ( 190 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1127 ( 152 ~; 196 |; 0 &; 779 @)
% ( 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 : 361 ( 0 ^ 361 !; 0 ?; 361 :)
% Comments :
%------------------------------------------------------------------------------
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_x,type,
x: $i ).
thf(tp_xQy,type,
xQy: $i ).
thf(tp_xQz,type,
xQz: $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,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(2,axiom,
! [X: $i] : ( quotient @ X @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
thf(3,axiom,
! [X: $i] : ( quotient @ X @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(4,axiom,
! [X: $i] : ( quotient @ zero @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(5,axiom,
! [X: $i] : ( quotient @ X @ identity @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(6,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(7,axiom,
! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(8,axiom,
! [X: $i] : ( less_equal @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(9,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(10,axiom,
! [X: $i] : ( less_equal @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(11,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(12,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(13,axiom,
! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(15,axiom,
quotient @ x @ z @ xQz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQz) ).
thf(16,axiom,
less_equal @ xQy @ z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQyLEz) ).
thf(17,axiom,
quotient @ x @ y @ xQy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xQy) ).
thf(18,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(19,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,negated_conjecture,
~ ( less_equal @ xQz @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xQzLEy) ).
thf(21,plain,
$false = $false,
inference(unfold_def,[status(thm)],[19]) ).
thf(22,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)],[1]) ).
thf(23,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,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)],[6]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(32,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)],[11]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,plain,
( ( quotient @ x @ z @ xQz )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(37,plain,
( ( less_equal @ xQy @ z )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( quotient @ x @ y @ xQy )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ~ ( less_equal @ xQz @ y ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(41,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)],[22]) ).
thf(42,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)],[27]) ).
thf(43,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)],[32]) ).
thf(44,plain,
( ( ~ ( less_equal @ xQz @ y ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(45,plain,
( ( quotient @ x @ y @ xQy )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( less_equal @ xQy @ z )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,plain,
( ( quotient @ x @ z @ xQz )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(51,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)],[43]) ).
thf(52,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(54,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ! [W: $i] :
( ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(57,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(58,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(60,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] :
( ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(62,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(63,plain,
( ( less_equal @ xQz @ y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY32: $i] :
( ~ ( less_equal @ SV1 @ SY32 )
| ( quotient @ SV1 @ SY32 @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(65,plain,
! [SV2: $i] :
( ( ! [SY33: $i] :
( ~ ( quotient @ SV2 @ SY33 @ zero )
| ( less_equal @ SV2 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(66,plain,
! [SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( quotient @ SV3 @ SY34 @ SY35 )
| ( less_equal @ SY35 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i,SY39: $i,SY40: $i] :
( ~ ( quotient @ SV4 @ SY36 @ SY37 )
| ~ ( quotient @ SY36 @ SY38 @ SY39 )
| ~ ( quotient @ SV4 @ SY38 @ SY40 )
| ! [V4: $i] :
( ~ ( quotient @ SY40 @ SY39 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ SY37 @ SY38 @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(68,plain,
! [SV5: $i] :
( ( less_equal @ zero @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY43: $i] :
( ~ ( less_equal @ SV6 @ SY43 )
| ~ ( less_equal @ SY43 @ SV6 )
| ( SV6 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(70,plain,
! [SV7: $i] :
( ( less_equal @ SV7 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(71,plain,
! [SV8: $i] :
( ( ! [SY44: $i] : ( quotient @ SV8 @ SY44 @ ( divide @ SV8 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(72,plain,
! [SV9: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( quotient @ SV9 @ SY45 @ SY46 )
| ! [SY47: $i] :
( ~ ( quotient @ SV9 @ SY45 @ SY47 )
| ( SY46 = SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV10: $i] :
( ( quotient @ SV10 @ identity @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV11: $i] :
( ( quotient @ zero @ SV11 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV12: $i] :
( ( quotient @ SV12 @ SV12 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV13: $i] :
( ( quotient @ SV13 @ zero @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV14: $i] :
( ( ! [SY48: $i] :
( ~ ( less_equal @ SV14 @ SY48 )
| ! [SY49: $i] :
( ~ ( less_equal @ SY48 @ SY49 )
| ( less_equal @ SV14 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV15: $i,SV1: $i] :
( ( ~ ( less_equal @ SV1 @ SV15 )
| ( quotient @ SV1 @ SV15 @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV16: $i,SV2: $i] :
( ( ~ ( quotient @ SV2 @ SV16 @ zero )
| ( less_equal @ SV2 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV17: $i,SV3: $i] :
( ( ! [SY50: $i] :
( ~ ( quotient @ SV3 @ SV17 @ SY50 )
| ( less_equal @ SY50 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV18: $i,SV4: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ~ ( quotient @ SV4 @ SV18 @ SY51 )
| ~ ( quotient @ SV18 @ SY52 @ SY53 )
| ~ ( quotient @ SV4 @ SY52 @ SY54 )
| ! [V4: $i] :
( ~ ( quotient @ SY54 @ SY53 @ V4 )
| ! [V5: $i] :
( ~ ( quotient @ SY51 @ SY52 @ V5 )
| ( less_equal @ V4 @ V5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV19: $i,SV6: $i] :
( ( ~ ( less_equal @ SV6 @ SV19 )
| ~ ( less_equal @ SV19 @ SV6 )
| ( SV6 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV20: $i,SV8: $i] :
( ( quotient @ SV8 @ SV20 @ ( divide @ SV8 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(85,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY57: $i] :
( ~ ( quotient @ SV9 @ SV21 @ SY57 )
| ! [SY58: $i] :
( ~ ( quotient @ SV9 @ SV21 @ SY58 )
| ( SY57 = SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV22: $i,SV14: $i] :
( ( ~ ( less_equal @ SV14 @ SV22 )
| ! [SY59: $i] :
( ~ ( less_equal @ SV22 @ SY59 )
| ( less_equal @ SV14 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV15: $i,SV1: $i] :
( ( ( ~ ( less_equal @ SV1 @ SV15 ) )
= $true )
| ( ( quotient @ SV1 @ SV15 @ zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV16: $i,SV2: $i] :
( ( ( ~ ( quotient @ SV2 @ SV16 @ zero ) )
= $true )
| ( ( less_equal @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV23: $i,SV17: $i,SV3: $i] :
( ( ~ ( quotient @ SV3 @ SV17 @ SV23 )
| ( less_equal @ SV23 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV24: $i,SV18: $i,SV4: $i] :
( ( ! [SY60: $i,SY61: $i,SY62: $i] :
( ~ ( quotient @ SV4 @ SV18 @ SV24 )
| ~ ( quotient @ SV18 @ SY60 @ SY61 )
| ~ ( quotient @ SV4 @ SY60 @ SY62 )
| ! [SY63: $i] :
( ~ ( quotient @ SY62 @ SY61 @ SY63 )
| ! [SY64: $i] :
( ~ ( quotient @ SV24 @ SY60 @ SY64 )
| ( less_equal @ SY63 @ SY64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV19: $i,SV6: $i] :
( ( ( ~ ( less_equal @ SV6 @ SV19 ) )
= $true )
| ( ( ~ ( less_equal @ SV19 @ SV6 )
| ( SV6 = SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV25: $i,SV21: $i,SV9: $i] :
( ( ~ ( quotient @ SV9 @ SV21 @ SV25 )
| ! [SY65: $i] :
( ~ ( quotient @ SV9 @ SV21 @ SY65 )
| ( SV25 = SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV22: $i,SV14: $i] :
( ( ( ~ ( less_equal @ SV14 @ SV22 ) )
= $true )
| ( ( ! [SY59: $i] :
( ~ ( less_equal @ SV22 @ SY59 )
| ( less_equal @ SV14 @ SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV15: $i,SV1: $i] :
( ( ( less_equal @ SV1 @ SV15 )
= $false )
| ( ( quotient @ SV1 @ SV15 @ zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV16: $i,SV2: $i] :
( ( ( quotient @ SV2 @ SV16 @ zero )
= $false )
| ( ( less_equal @ SV2 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV23: $i,SV17: $i,SV3: $i] :
( ( ( ~ ( quotient @ SV3 @ SV17 @ SV23 ) )
= $true )
| ( ( less_equal @ SV23 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV26: $i,SV24: $i,SV18: $i,SV4: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( quotient @ SV4 @ SV18 @ SV24 )
| ~ ( quotient @ SV18 @ SV26 @ SY66 )
| ~ ( quotient @ SV4 @ SV26 @ SY67 )
| ! [SY68: $i] :
( ~ ( quotient @ SY67 @ SY66 @ SY68 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY68 @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV19: $i,SV6: $i] :
( ( ( less_equal @ SV6 @ SV19 )
= $false )
| ( ( ~ ( less_equal @ SV19 @ SV6 )
| ( SV6 = SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV25: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV21 @ SV25 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( quotient @ SV9 @ SV21 @ SY65 )
| ( SV25 = SY65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV22: $i,SV14: $i] :
( ( ( less_equal @ SV14 @ SV22 )
= $false )
| ( ( ! [SY59: $i] :
( ~ ( less_equal @ SV22 @ SY59 )
| ( less_equal @ SV14 @ SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV23: $i,SV17: $i,SV3: $i] :
( ( ( quotient @ SV3 @ SV17 @ SV23 )
= $false )
| ( ( less_equal @ SV23 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV27: $i,SV26: $i,SV24: $i,SV18: $i,SV4: $i] :
( ( ! [SY70: $i] :
( ~ ( quotient @ SV4 @ SV18 @ SV24 )
| ~ ( quotient @ SV18 @ SV26 @ SV27 )
| ~ ( quotient @ SV4 @ SV26 @ SY70 )
| ! [SY71: $i] :
( ~ ( quotient @ SY70 @ SV27 @ SY71 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY71 @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV6: $i,SV19: $i] :
( ( ( ~ ( less_equal @ SV19 @ SV6 ) )
= $true )
| ( ( SV6 = SV19 )
= $true )
| ( ( less_equal @ SV6 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV25: $i,SV21: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV21 @ SV25 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( quotient @ SV9 @ SV21 @ SY65 )
| ( SV25 = SY65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV14: $i,SV28: $i,SV22: $i] :
( ( ( ~ ( less_equal @ SV22 @ SV28 )
| ( less_equal @ SV14 @ SV28 ) )
= $true )
| ( ( less_equal @ SV14 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV29: $i,SV27: $i,SV26: $i,SV24: $i,SV18: $i,SV4: $i] :
( ( ~ ( quotient @ SV4 @ SV18 @ SV24 )
| ~ ( quotient @ SV18 @ SV26 @ SV27 )
| ~ ( quotient @ SV4 @ SV26 @ SV29 )
| ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV6: $i,SV19: $i] :
( ( ( less_equal @ SV19 @ SV6 )
= $false )
| ( ( SV6 = SV19 )
= $true )
| ( ( less_equal @ SV6 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV25: $i,SV30: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV21 @ SV30 )
| ( SV25 = SV30 ) )
= $true )
| ( ( quotient @ SV9 @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV14: $i,SV28: $i,SV22: $i] :
( ( ( ~ ( less_equal @ SV22 @ SV28 ) )
= $true )
| ( ( less_equal @ SV14 @ SV28 )
= $true )
| ( ( less_equal @ SV14 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV29: $i,SV27: $i,SV26: $i,SV24: $i,SV18: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV18 @ SV24 ) )
= $true )
| ( ( ~ ( quotient @ SV18 @ SV26 @ SV27 )
| ~ ( quotient @ SV4 @ SV26 @ SV29 )
| ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV25: $i,SV30: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV21 @ SV30 ) )
= $true )
| ( ( SV25 = SV30 )
= $true )
| ( ( quotient @ SV9 @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV14: $i,SV28: $i,SV22: $i] :
( ( ( less_equal @ SV22 @ SV28 )
= $false )
| ( ( less_equal @ SV14 @ SV28 )
= $true )
| ( ( less_equal @ SV14 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV29: $i,SV27: $i,SV26: $i,SV24: $i,SV18: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false )
| ( ( ~ ( quotient @ SV18 @ SV26 @ SV27 )
| ~ ( quotient @ SV4 @ SV26 @ SV29 )
| ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV25: $i,SV30: $i,SV21: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV21 @ SV30 )
= $false )
| ( ( SV25 = SV30 )
= $true )
| ( ( quotient @ SV9 @ SV21 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(115,plain,
! [SV24: $i,SV29: $i,SV4: $i,SV27: $i,SV26: $i,SV18: $i] :
( ( ( ~ ( quotient @ SV18 @ SV26 @ SV27 ) )
= $true )
| ( ( ~ ( quotient @ SV4 @ SV26 @ SV29 )
| ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV24: $i,SV29: $i,SV4: $i,SV27: $i,SV26: $i,SV18: $i] :
( ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( ~ ( quotient @ SV4 @ SV26 @ SV29 )
| ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(117,plain,
! [SV18: $i,SV24: $i,SV27: $i,SV29: $i,SV26: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV26 @ SV29 ) )
= $true )
| ( ( ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(118,plain,
! [SV18: $i,SV24: $i,SV27: $i,SV29: $i,SV26: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( ! [SY73: $i] :
( ~ ( quotient @ SV29 @ SV27 @ SY73 )
| ! [SY69: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY69 )
| ( less_equal @ SY73 @ SY69 ) ) ) )
= $true )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(119,plain,
! [SV18: $i,SV4: $i,SV26: $i,SV24: $i,SV31: $i,SV27: $i,SV29: $i] :
( ( ( ~ ( quotient @ SV29 @ SV27 @ SV31 )
| ! [SY75: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY75 )
| ( less_equal @ SV31 @ SY75 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(120,plain,
! [SV18: $i,SV4: $i,SV26: $i,SV24: $i,SV31: $i,SV27: $i,SV29: $i] :
( ( ( ~ ( quotient @ SV29 @ SV27 @ SV31 ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY75 )
| ( less_equal @ SV31 @ SY75 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(121,plain,
! [SV18: $i,SV4: $i,SV26: $i,SV24: $i,SV31: $i,SV27: $i,SV29: $i] :
( ( ( quotient @ SV29 @ SV27 @ SV31 )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( quotient @ SV24 @ SV26 @ SY75 )
| ( less_equal @ SV31 @ SY75 ) ) )
= $true )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(122,plain,
! [SV18: $i,SV4: $i,SV27: $i,SV29: $i,SV31: $i,SV32: $i,SV26: $i,SV24: $i] :
( ( ( ~ ( quotient @ SV24 @ SV26 @ SV32 )
| ( less_equal @ SV31 @ SV32 ) )
= $true )
| ( ( quotient @ SV29 @ SV27 @ SV31 )
= $false )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(123,plain,
! [SV18: $i,SV4: $i,SV27: $i,SV29: $i,SV31: $i,SV32: $i,SV26: $i,SV24: $i] :
( ( ( ~ ( quotient @ SV24 @ SV26 @ SV32 ) )
= $true )
| ( ( less_equal @ SV31 @ SV32 )
= $true )
| ( ( quotient @ SV29 @ SV27 @ SV31 )
= $false )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(124,plain,
! [SV18: $i,SV4: $i,SV27: $i,SV29: $i,SV31: $i,SV32: $i,SV26: $i,SV24: $i] :
( ( ( quotient @ SV24 @ SV26 @ SV32 )
= $false )
| ( ( less_equal @ SV31 @ SV32 )
= $true )
| ( ( quotient @ SV29 @ SV27 @ SV31 )
= $false )
| ( ( quotient @ SV4 @ SV26 @ SV29 )
= $false )
| ( ( quotient @ SV18 @ SV26 @ SV27 )
= $false )
| ( ( quotient @ SV4 @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(125,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,124,114,112,107,101,95,94,84,78,76,75,74,73,70,68,63,47,46]) ).
thf(126,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n015.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 13:07:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 18
% 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:18,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:20,loop_count:0,foatp_calls:0,translation:fof_full).......
% 11.12/11.34
% 11.12/11.34 ********************************
% 11.12/11.34 * All subproblems solved! *
% 11.12/11.34 ********************************
% 11.12/11.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:125,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.12/11.34
% 11.12/11.34 %**** Beginning of derivation protocol ****
% 11.12/11.34 % SZS output start CNFRefutation
% See solution above
% 11.12/11.34
% 11.12/11.34 %**** End of derivation protocol ****
% 11.12/11.34 %**** no. of clauses in derivation: 126 ****
% 11.12/11.34 %**** clause counter: 125 ****
% 11.12/11.34
% 11.12/11.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,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:125,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------