TSTP Solution File: HEN010-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HEN010-4 : 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 : n012.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 12:57:28 EDT 2022
% Result : Unsatisfiable 19.63s 19.81s
% Output : CNFRefutation 19.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 117 ( 84 unt; 5 typ; 0 def)
% Number of atoms : 429 ( 166 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 742 ( 71 ~; 81 |; 0 &; 590 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 211 ( 0 ^ 211 !; 0 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $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_zero,type,
zero: $i ).
thf(1,axiom,
! [X: $i] :
( ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ X ) ) )
= ( divide @ identity @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ( less_equal @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide3) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ( less_equal @ ( divide @ Z @ Y ) @ ( divide @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide2) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ ( divide @ X @ Y ) @ Z )
| ( less_equal @ ( divide @ X @ Z ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_divide1) ).
thf(5,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(6,axiom,
( ( divide @ a @ zero )
= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
thf(7,axiom,
! [X: $i] :
( ( divide @ X @ X )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(8,axiom,
! [X: $i] :
( ( divide @ zero @ X )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(9,axiom,
! [X: $i] :
( ( divide @ X @ identity )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_id_is_zero) ).
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,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
thf(14,axiom,
! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal2) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal1) ).
thf(17,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(18,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,negated_conjecture,
( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_inversion) ).
thf(20,plain,
$false = $false,
inference(unfold_def,[status(thm)],[18]) ).
thf(21,plain,
( ( ! [X: $i] :
( ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ X ) ) )
= ( divide @ identity @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ( less_equal @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ( less_equal @ ( divide @ Z @ Y ) @ ( divide @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ ( divide @ X @ Y ) @ Z )
| ( less_equal @ ( divide @ X @ Z ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(25,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)],[5]) ).
thf(26,plain,
( ( ( divide @ a @ zero )
= a )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( divide @ X @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(30,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(32,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(33,plain,
( ( ! [X: $i,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(37,plain,
( ( ( ( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(38,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] : ( less_equal @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] : ( less_equal @ ( divide @ Z @ Y ) @ ( divide @ Z @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
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)],[25]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(43,plain,
( ( ( ( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(44,plain,
( ( ( ( divide @ identity @ a )
!= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( ( divide @ X @ Y )
= zero ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( ( divide @ X @ Y )
!= zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] : ( less_equal @ ( divide @ X @ Y ) @ X ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(48,plain,
( ( ! [X: $i,Z: $i,Y: $i] : ( less_equal @ ( divide @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) @ ( divide @ ( divide @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(49,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( divide @ X @ identity )
= zero ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( divide @ zero @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( divide @ X @ X )
= zero ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(55,plain,
( ( ( divide @ a @ zero )
= a )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(56,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(57,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ ( divide @ X @ Y ) @ Z )
| ( less_equal @ ( divide @ X @ Z ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] : ( less_equal @ ( divide @ Z @ Y ) @ ( divide @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ! [Z: $i] : ( less_equal @ ( divide @ X @ Z ) @ ( divide @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ X ) ) )
= ( divide @ identity @ X ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(61,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(62,plain,
( ( ( divide @ identity @ a )
= ( divide @ ( divide @ identity @ a ) @ ( divide @ identity @ ( divide @ identity @ a ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(63,plain,
! [SV1: $i] :
( ( ! [SY29: $i] :
( ~ ( less_equal @ SV1 @ SY29 )
| ( ( divide @ SV1 @ SY29 )
= zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY30: $i] :
( ( ( divide @ SV2 @ SY30 )
!= zero )
| ( less_equal @ SV2 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(65,plain,
! [SV3: $i] :
( ( ! [SY31: $i] : ( less_equal @ ( divide @ SV3 @ SY31 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(66,plain,
! [SV4: $i] :
( ( ! [SY32: $i,SY33: $i] : ( less_equal @ ( divide @ ( divide @ SV4 @ SY32 ) @ ( divide @ SY33 @ SY32 ) ) @ ( divide @ ( divide @ SV4 @ SY33 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(67,plain,
! [SV5: $i] :
( ( less_equal @ zero @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(68,plain,
! [SV6: $i] :
( ( ! [SY34: $i] :
( ~ ( less_equal @ SV6 @ SY34 )
| ~ ( less_equal @ SY34 @ SV6 )
| ( SV6 = SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(69,plain,
! [SV7: $i] :
( ( less_equal @ SV7 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(70,plain,
! [SV8: $i] :
( ( ( divide @ SV8 @ identity )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(71,plain,
! [SV9: $i] :
( ( ( divide @ zero @ SV9 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(72,plain,
! [SV10: $i] :
( ( ( divide @ SV10 @ SV10 )
= zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
! [SV11: $i] :
( ( ! [SY35: $i] :
( ~ ( less_equal @ SV11 @ SY35 )
| ! [SY36: $i] :
( ~ ( less_equal @ SY35 @ SY36 )
| ( less_equal @ SV11 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(74,plain,
! [SV12: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( less_equal @ ( divide @ SV12 @ SY37 ) @ SY38 )
| ( less_equal @ ( divide @ SV12 @ SY38 ) @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(75,plain,
! [SV13: $i] :
( ( ! [SY39: $i] :
( ~ ( less_equal @ SV13 @ SY39 )
| ! [SY40: $i] : ( less_equal @ ( divide @ SY40 @ SY39 ) @ ( divide @ SY40 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(76,plain,
! [SV14: $i] :
( ( ! [SY41: $i] :
( ~ ( less_equal @ SV14 @ SY41 )
| ! [SY42: $i] : ( less_equal @ ( divide @ SV14 @ SY42 ) @ ( divide @ SY41 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(77,plain,
! [SV15: $i] :
( ( ( divide @ identity @ ( divide @ identity @ ( divide @ identity @ SV15 ) ) )
= ( divide @ identity @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(78,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(79,plain,
! [SV16: $i,SV1: $i] :
( ( ~ ( less_equal @ SV1 @ SV16 )
| ( ( divide @ SV1 @ SV16 )
= zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV17: $i,SV2: $i] :
( ( ( ( divide @ SV2 @ SV17 )
!= zero )
| ( less_equal @ SV2 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV18: $i,SV3: $i] :
( ( less_equal @ ( divide @ SV3 @ SV18 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(82,plain,
! [SV19: $i,SV4: $i] :
( ( ! [SY43: $i] : ( less_equal @ ( divide @ ( divide @ SV4 @ SV19 ) @ ( divide @ SY43 @ SV19 ) ) @ ( divide @ ( divide @ SV4 @ SY43 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(83,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ( less_equal @ SV6 @ SV20 )
| ~ ( less_equal @ SV20 @ SV6 )
| ( SV6 = SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV21: $i,SV11: $i] :
( ( ~ ( less_equal @ SV11 @ SV21 )
| ! [SY44: $i] :
( ~ ( less_equal @ SV21 @ SY44 )
| ( less_equal @ SV11 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV22: $i,SV12: $i] :
( ( ! [SY45: $i] :
( ~ ( less_equal @ ( divide @ SV12 @ SV22 ) @ SY45 )
| ( less_equal @ ( divide @ SV12 @ SY45 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( less_equal @ SV13 @ SV23 )
| ! [SY46: $i] : ( less_equal @ ( divide @ SY46 @ SV23 ) @ ( divide @ SY46 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV24: $i,SV14: $i] :
( ( ~ ( less_equal @ SV14 @ SV24 )
| ! [SY47: $i] : ( less_equal @ ( divide @ SV14 @ SY47 ) @ ( divide @ SV24 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( less_equal @ SV1 @ SV16 ) )
= $true )
| ( ( ( divide @ SV1 @ SV16 )
= zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV17: $i,SV2: $i] :
( ( ( ( ( divide @ SV2 @ SV17 )
!= zero ) )
= $true )
| ( ( less_equal @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV25: $i,SV19: $i,SV4: $i] :
( ( less_equal @ ( divide @ ( divide @ SV4 @ SV19 ) @ ( divide @ SV25 @ SV19 ) ) @ ( divide @ ( divide @ SV4 @ SV25 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( less_equal @ SV6 @ SV20 ) )
= $true )
| ( ( ~ ( less_equal @ SV20 @ SV6 )
| ( SV6 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV21: $i,SV11: $i] :
( ( ( ~ ( less_equal @ SV11 @ SV21 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( less_equal @ SV21 @ SY44 )
| ( less_equal @ SV11 @ SY44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV26: $i,SV22: $i,SV12: $i] :
( ( ~ ( less_equal @ ( divide @ SV12 @ SV22 ) @ SV26 )
| ( less_equal @ ( divide @ SV12 @ SV26 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( less_equal @ SV13 @ SV23 ) )
= $true )
| ( ( ! [SY46: $i] : ( less_equal @ ( divide @ SY46 @ SV23 ) @ ( divide @ SY46 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV24: $i,SV14: $i] :
( ( ( ~ ( less_equal @ SV14 @ SV24 ) )
= $true )
| ( ( ! [SY47: $i] : ( less_equal @ ( divide @ SV14 @ SY47 ) @ ( divide @ SV24 @ SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV16: $i,SV1: $i] :
( ( ( less_equal @ SV1 @ SV16 )
= $false )
| ( ( ( divide @ SV1 @ SV16 )
= zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV17: $i,SV2: $i] :
( ( ( ( divide @ SV2 @ SV17 )
= zero )
= $false )
| ( ( less_equal @ SV2 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV20: $i,SV6: $i] :
( ( ( less_equal @ SV6 @ SV20 )
= $false )
| ( ( ~ ( less_equal @ SV20 @ SV6 )
| ( SV6 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV21: $i,SV11: $i] :
( ( ( less_equal @ SV11 @ SV21 )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( less_equal @ SV21 @ SY44 )
| ( less_equal @ SV11 @ SY44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV26: $i,SV22: $i,SV12: $i] :
( ( ( ~ ( less_equal @ ( divide @ SV12 @ SV22 ) @ SV26 ) )
= $true )
| ( ( less_equal @ ( divide @ SV12 @ SV26 ) @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV23: $i,SV13: $i] :
( ( ( less_equal @ SV13 @ SV23 )
= $false )
| ( ( ! [SY46: $i] : ( less_equal @ ( divide @ SY46 @ SV23 ) @ ( divide @ SY46 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV24: $i,SV14: $i] :
( ( ( less_equal @ SV14 @ SV24 )
= $false )
| ( ( ! [SY47: $i] : ( less_equal @ ( divide @ SV14 @ SY47 ) @ ( divide @ SV24 @ SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV6: $i,SV20: $i] :
( ( ( ~ ( less_equal @ SV20 @ SV6 ) )
= $true )
| ( ( SV6 = SV20 )
= $true )
| ( ( less_equal @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV11: $i,SV27: $i,SV21: $i] :
( ( ( ~ ( less_equal @ SV21 @ SV27 )
| ( less_equal @ SV11 @ SV27 ) )
= $true )
| ( ( less_equal @ SV11 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV26: $i,SV22: $i,SV12: $i] :
( ( ( less_equal @ ( divide @ SV12 @ SV22 ) @ SV26 )
= $false )
| ( ( less_equal @ ( divide @ SV12 @ SV26 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV13: $i,SV23: $i,SV28: $i] :
( ( ( less_equal @ ( divide @ SV28 @ SV23 ) @ ( divide @ SV28 @ SV13 ) )
= $true )
| ( ( less_equal @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV24: $i,SV29: $i,SV14: $i] :
( ( ( less_equal @ ( divide @ SV14 @ SV29 ) @ ( divide @ SV24 @ SV29 ) )
= $true )
| ( ( less_equal @ SV14 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(108,plain,
! [SV6: $i,SV20: $i] :
( ( ( less_equal @ SV20 @ SV6 )
= $false )
| ( ( SV6 = SV20 )
= $true )
| ( ( less_equal @ SV6 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV11: $i,SV27: $i,SV21: $i] :
( ( ( ~ ( less_equal @ SV21 @ SV27 ) )
= $true )
| ( ( less_equal @ SV11 @ SV27 )
= $true )
| ( ( less_equal @ SV11 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV11: $i,SV27: $i,SV21: $i] :
( ( ( less_equal @ SV21 @ SV27 )
= $false )
| ( ( less_equal @ SV11 @ SV27 )
= $true )
| ( ( less_equal @ SV11 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(111,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,110,108,107,106,105,97,96,90,81,78,77,72,71,70,69,67,62]) ).
thf(112,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 14:31:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 17
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:17,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:19,loop_count:0,foatp_calls:0,translation:fof_full).....
% 19.63/19.81
% 19.63/19.81 ********************************
% 19.63/19.81 * All subproblems solved! *
% 19.63/19.81 ********************************
% 19.63/19.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:111,loop_count:0,foatp_calls:1,translation:fof_full)
% 19.63/19.82
% 19.63/19.82 %**** Beginning of derivation protocol ****
% 19.63/19.82 % SZS output start CNFRefutation
% See solution above
% 19.63/19.82
% 19.63/19.82 %**** End of derivation protocol ****
% 19.63/19.82 %**** no. of clauses in derivation: 112 ****
% 19.63/19.82 %**** clause counter: 111 ****
% 19.63/19.82
% 19.63/19.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:17,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:111,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------