%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:22:06 AM UTC 2026
% Result : Unsatisfiable 5.21s 1.06s
% Output : CNFRefutation 5.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 23
% Syntax : Number of formulae : 179 ( 116 unt; 0 typ; 0 def)
% Number of atoms : 1045 ( 295 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1916 ( 282 ~; 352 |; 0 &;1282 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 608 ( 0 ^; 608 !; 0 ?; 608 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_divide,type,
divide: $i > $i > $i ).
thf(tp_idQ_idQa,type,
idQ_idQa: $i ).
thf(tp_idQa,type,
idQa: $i ).
thf(tp_idQa_Q__idQ_idQa,type,
idQa_Q__idQ_idQa: $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,Y1: $i,Y2: $i,Y3: $i] :
( ~ ( quotient @ identity @ X @ Y1 )
| ~ ( quotient @ identity @ Y1 @ Y2 )
| ~ ( quotient @ identity @ Y2 @ Y3 )
| ( Y1 = Y3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_inversion_equals_three) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( quotient @ X @ Z @ W1 )
| ~ ( quotient @ Y @ Z @ W2 )
| ( less_equal @ W1 @ W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xLEy_implies_xQzLEyQz) ).
thf(3,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(4,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(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,
! [X: $i] : ( quotient @ X @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divde_zero_is_x) ).
thf(7,axiom,
! [X: $i] : ( quotient @ X @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_divide_x_is_zero) ).
thf(8,axiom,
! [X: $i] : ( quotient @ zero @ X @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_divide_anything_is_zero) ).
thf(9,axiom,
! [X: $i] : ( quotient @ X @ identity @ zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',everything_divide_identity_is_zero) ).
thf(10,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(11,axiom,
! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
thf(12,axiom,
! [X: $i] : ( less_equal @ X @ identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_is_largest) ).
thf(13,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(14,axiom,
! [X: $i] : ( less_equal @ zero @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(15,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(16,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(17,axiom,
! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(19,axiom,
quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
thf(20,axiom,
quotient @ identity @ idQa @ idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_idQa) ).
thf(21,axiom,
quotient @ identity @ a @ idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_divide_a) ).
thf(22,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(23,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[23]) ).
thf(26,plain,
( ( ! [X: $i,Y1: $i,Y2: $i,Y3: $i] :
( ~ ( quotient @ identity @ X @ Y1 )
| ~ ( quotient @ identity @ Y1 @ Y2 )
| ~ ( quotient @ identity @ Y2 @ Y3 )
| ( Y1 = Y3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( quotient @ X @ Z @ W1 )
| ~ ( quotient @ Y @ Z @ W2 )
| ( less_equal @ W1 @ W2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,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)],[3]) ).
thf(29,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)],[4]) ).
thf(30,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(31,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(32,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,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)],[10]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,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)],[15]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( quotient @ identity @ idQa @ idQ_idQa )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( quotient @ identity @ a @ idQa )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( idQa != idQa_Q__idQ_idQa )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( idQa != idQa_Q__idQ_idQa )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(50,plain,
( ( quotient @ identity @ a @ idQa )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(51,plain,
( ( quotient @ identity @ idQa @ idQ_idQa )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(52,plain,
( ( quotient @ idQa @ idQ_idQa @ idQa_Q__idQ_idQa )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ( quotient @ X @ Y @ zero ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( quotient @ X @ Y @ zero )
| ( less_equal @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ( less_equal @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(56,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(copy,[status(thm)],[40]) ).
thf(57,plain,
( ( ! [X: $i] : ( less_equal @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(59,plain,
( ( ! [X: $i] : ( less_equal @ X @ identity ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] : ( quotient @ X @ Y @ ( divide @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( quotient @ X @ Y @ Z )
| ~ ( quotient @ X @ Y @ W )
| ( Z = W ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(62,plain,
( ( ! [X: $i] : ( quotient @ X @ identity @ zero ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(63,plain,
( ( ! [X: $i] : ( quotient @ zero @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(64,plain,
( ( ! [X: $i] : ( quotient @ X @ X @ zero ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(65,plain,
( ( ! [X: $i] : ( quotient @ X @ zero @ X ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( less_equal @ Y @ Z )
| ( less_equal @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(67,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(copy,[status(thm)],[29]) ).
thf(68,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(copy,[status(thm)],[28]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i,W1: $i,W2: $i] :
( ~ ( less_equal @ X @ Y )
| ~ ( quotient @ X @ Z @ W1 )
| ~ ( quotient @ Y @ Z @ W2 )
| ( less_equal @ W1 @ W2 ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(70,plain,
( ( ! [X: $i,Y1: $i,Y2: $i,Y3: $i] :
( ~ ( quotient @ identity @ X @ Y1 )
| ~ ( quotient @ identity @ Y1 @ Y2 )
| ~ ( quotient @ identity @ Y2 @ Y3 )
| ( Y1 = Y3 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(71,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[48]) ).
thf(72,plain,
( ( idQa != idQa_Q__idQ_idQa )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY51: $i] :
( ~ ( less_equal @ SV1 @ SY51 )
| ( quotient @ SV1 @ SY51 @ zero ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(74,plain,
! [SV2: $i] :
( ( ! [SY52: $i] :
( ~ ( quotient @ SV2 @ SY52 @ zero )
| ( less_equal @ SV2 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(75,plain,
! [SV3: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ( quotient @ SV3 @ SY53 @ SY54 )
| ( less_equal @ SY54 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(76,plain,
! [SV4: $i] :
( ( ! [SY55: $i,SY56: $i,SY57: $i,SY58: $i,SY59: $i,SY60: $i,SY61: $i] :
( ~ ( quotient @ SV4 @ SY55 @ SY56 )
| ~ ( quotient @ SY55 @ SY57 @ SY58 )
| ~ ( quotient @ SV4 @ SY57 @ SY59 )
| ~ ( quotient @ SY59 @ SY58 @ SY60 )
| ~ ( quotient @ SY56 @ SY57 @ SY61 )
| ( less_equal @ SY60 @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(77,plain,
! [SV5: $i] :
( ( less_equal @ zero @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY62: $i] :
( ~ ( less_equal @ SV6 @ SY62 )
| ~ ( less_equal @ SY62 @ SV6 )
| ( SV6 = SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(79,plain,
! [SV7: $i] :
( ( less_equal @ SV7 @ identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(80,plain,
! [SV8: $i] :
( ( ! [SY63: $i] : ( quotient @ SV8 @ SY63 @ ( divide @ SV8 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(81,plain,
! [SV9: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
( ~ ( quotient @ SV9 @ SY64 @ SY65 )
| ~ ( quotient @ SV9 @ SY64 @ SY66 )
| ( SY65 = SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(82,plain,
! [SV10: $i] :
( ( quotient @ SV10 @ identity @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(83,plain,
! [SV11: $i] :
( ( quotient @ zero @ SV11 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(84,plain,
! [SV12: $i] :
( ( quotient @ SV12 @ SV12 @ zero )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(85,plain,
! [SV13: $i] :
( ( quotient @ SV13 @ zero @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(86,plain,
! [SV14: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( less_equal @ SV14 @ SY67 )
| ~ ( less_equal @ SY67 @ SY68 )
| ( less_equal @ SV14 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(87,plain,
! [SV15: $i] :
( ( ! [SY69: $i,SY70: $i,SY71: $i,SY72: $i] :
( ~ ( quotient @ SV15 @ SY69 @ SY70 )
| ~ ( less_equal @ SY70 @ SY71 )
| ~ ( quotient @ SV15 @ SY71 @ SY72 )
| ( less_equal @ SY72 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(88,plain,
! [SV16: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i,SY76: $i] :
( ~ ( less_equal @ SV16 @ SY73 )
| ~ ( quotient @ SY74 @ SY73 @ SY75 )
| ~ ( quotient @ SY74 @ SV16 @ SY76 )
| ( less_equal @ SY75 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(89,plain,
! [SV17: $i] :
( ( ! [SY77: $i,SY78: $i,SY79: $i,SY80: $i] :
( ~ ( less_equal @ SV17 @ SY77 )
| ~ ( quotient @ SV17 @ SY78 @ SY79 )
| ~ ( quotient @ SY77 @ SY78 @ SY80 )
| ( less_equal @ SY79 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(90,plain,
! [SV18: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ( quotient @ identity @ SV18 @ SY81 )
| ~ ( quotient @ identity @ SY81 @ SY82 )
| ~ ( quotient @ identity @ SY82 @ SY83 )
| ( SY81 = SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(91,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(92,plain,
( ( idQa = idQa_Q__idQ_idQa )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(93,plain,
! [SV19: $i,SV1: $i] :
( ( ~ ( less_equal @ SV1 @ SV19 )
| ( quotient @ SV1 @ SV19 @ zero ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(94,plain,
! [SV20: $i,SV2: $i] :
( ( ~ ( quotient @ SV2 @ SV20 @ zero )
| ( less_equal @ SV2 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(95,plain,
! [SV21: $i,SV3: $i] :
( ( ! [SY84: $i] :
( ~ ( quotient @ SV3 @ SV21 @ SY84 )
| ( less_equal @ SY84 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(96,plain,
! [SV22: $i,SV4: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i,SY88: $i,SY89: $i,SY90: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SY85 )
| ~ ( quotient @ SV22 @ SY86 @ SY87 )
| ~ ( quotient @ SV4 @ SY86 @ SY88 )
| ~ ( quotient @ SY88 @ SY87 @ SY89 )
| ~ ( quotient @ SY85 @ SY86 @ SY90 )
| ( less_equal @ SY89 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(97,plain,
! [SV23: $i,SV6: $i] :
( ( ~ ( less_equal @ SV6 @ SV23 )
| ~ ( less_equal @ SV23 @ SV6 )
| ( SV6 = SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV24: $i,SV8: $i] :
( ( quotient @ SV8 @ SV24 @ ( divide @ SV8 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(99,plain,
! [SV25: $i,SV9: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( quotient @ SV9 @ SV25 @ SY91 )
| ~ ( quotient @ SV9 @ SV25 @ SY92 )
| ( SY91 = SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY93: $i] :
( ~ ( less_equal @ SV14 @ SV26 )
| ~ ( less_equal @ SV26 @ SY93 )
| ( less_equal @ SV14 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i] :
( ~ ( quotient @ SV15 @ SV27 @ SY94 )
| ~ ( less_equal @ SY94 @ SY95 )
| ~ ( quotient @ SV15 @ SY95 @ SY96 )
| ( less_equal @ SY96 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV28: $i,SV16: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i] :
( ~ ( less_equal @ SV16 @ SV28 )
| ~ ( quotient @ SY97 @ SV28 @ SY98 )
| ~ ( quotient @ SY97 @ SV16 @ SY99 )
| ( less_equal @ SY98 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV29: $i,SV17: $i] :
( ( ! [SY100: $i,SY101: $i,SY102: $i] :
( ~ ( less_equal @ SV17 @ SV29 )
| ~ ( quotient @ SV17 @ SY100 @ SY101 )
| ~ ( quotient @ SV29 @ SY100 @ SY102 )
| ( less_equal @ SY101 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV30: $i,SV18: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( quotient @ identity @ SV18 @ SV30 )
| ~ ( quotient @ identity @ SV30 @ SY103 )
| ~ ( quotient @ identity @ SY103 @ SY104 )
| ( SV30 = SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV19: $i,SV1: $i] :
( ( ( ~ ( less_equal @ SV1 @ SV19 ) )
= $true )
| ( ( quotient @ SV1 @ SV19 @ zero )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV20: $i,SV2: $i] :
( ( ( ~ ( quotient @ SV2 @ SV20 @ zero ) )
= $true )
| ( ( less_equal @ SV2 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV31: $i,SV21: $i,SV3: $i] :
( ( ~ ( quotient @ SV3 @ SV21 @ SV31 )
| ( less_equal @ SV31 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV32: $i,SV22: $i,SV4: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i,SY108: $i,SY109: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SY105 @ SY106 )
| ~ ( quotient @ SV4 @ SY105 @ SY107 )
| ~ ( quotient @ SY107 @ SY106 @ SY108 )
| ~ ( quotient @ SV32 @ SY105 @ SY109 )
| ( less_equal @ SY108 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV23: $i,SV6: $i] :
( ( ( ~ ( less_equal @ SV6 @ SV23 ) )
= $true )
| ( ( ~ ( less_equal @ SV23 @ SV6 )
| ( SV6 = SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV33: $i,SV25: $i,SV9: $i] :
( ( ! [SY110: $i] :
( ~ ( quotient @ SV9 @ SV25 @ SV33 )
| ~ ( quotient @ SV9 @ SV25 @ SY110 )
| ( SV33 = SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV34: $i,SV26: $i,SV14: $i] :
( ( ~ ( less_equal @ SV14 @ SV26 )
| ~ ( less_equal @ SV26 @ SV34 )
| ( less_equal @ SV14 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV35: $i,SV27: $i,SV15: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( quotient @ SV15 @ SV27 @ SV35 )
| ~ ( less_equal @ SV35 @ SY111 )
| ~ ( quotient @ SV15 @ SY111 @ SY112 )
| ( less_equal @ SY112 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV36: $i,SV28: $i,SV16: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( less_equal @ SV16 @ SV28 )
| ~ ( quotient @ SV36 @ SV28 @ SY113 )
| ~ ( quotient @ SV36 @ SV16 @ SY114 )
| ( less_equal @ SY113 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV37: $i,SV29: $i,SV17: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( less_equal @ SV17 @ SV29 )
| ~ ( quotient @ SV17 @ SV37 @ SY115 )
| ~ ( quotient @ SV29 @ SV37 @ SY116 )
| ( less_equal @ SY115 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV38: $i,SV30: $i,SV18: $i] :
( ( ! [SY117: $i] :
( ~ ( quotient @ identity @ SV18 @ SV30 )
| ~ ( quotient @ identity @ SV30 @ SV38 )
| ~ ( quotient @ identity @ SV38 @ SY117 )
| ( SV30 = SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV19: $i,SV1: $i] :
( ( ( less_equal @ SV1 @ SV19 )
= $false )
| ( ( quotient @ SV1 @ SV19 @ zero )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV20: $i,SV2: $i] :
( ( ( quotient @ SV2 @ SV20 @ zero )
= $false )
| ( ( less_equal @ SV2 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV31: $i,SV21: $i,SV3: $i] :
( ( ( ~ ( quotient @ SV3 @ SV21 @ SV31 ) )
= $true )
| ( ( less_equal @ SV31 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ! [SY118: $i,SY119: $i,SY120: $i,SY121: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SV39 @ SY118 )
| ~ ( quotient @ SV4 @ SV39 @ SY119 )
| ~ ( quotient @ SY119 @ SY118 @ SY120 )
| ~ ( quotient @ SV32 @ SV39 @ SY121 )
| ( less_equal @ SY120 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV23: $i,SV6: $i] :
( ( ( less_equal @ SV6 @ SV23 )
= $false )
| ( ( ~ ( less_equal @ SV23 @ SV6 )
| ( SV6 = SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV40: $i,SV33: $i,SV25: $i,SV9: $i] :
( ( ~ ( quotient @ SV9 @ SV25 @ SV33 )
| ~ ( quotient @ SV9 @ SV25 @ SV40 )
| ( SV33 = SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV34: $i,SV26: $i,SV14: $i] :
( ( ( ~ ( less_equal @ SV14 @ SV26 ) )
= $true )
| ( ( ~ ( less_equal @ SV26 @ SV34 )
| ( less_equal @ SV14 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV41: $i,SV35: $i,SV27: $i,SV15: $i] :
( ( ! [SY122: $i] :
( ~ ( quotient @ SV15 @ SV27 @ SV35 )
| ~ ( less_equal @ SV35 @ SV41 )
| ~ ( quotient @ SV15 @ SV41 @ SY122 )
| ( less_equal @ SY122 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV42: $i,SV36: $i,SV28: $i,SV16: $i] :
( ( ! [SY123: $i] :
( ~ ( less_equal @ SV16 @ SV28 )
| ~ ( quotient @ SV36 @ SV28 @ SV42 )
| ~ ( quotient @ SV36 @ SV16 @ SY123 )
| ( less_equal @ SV42 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV43: $i,SV37: $i,SV29: $i,SV17: $i] :
( ( ! [SY124: $i] :
( ~ ( less_equal @ SV17 @ SV29 )
| ~ ( quotient @ SV17 @ SV37 @ SV43 )
| ~ ( quotient @ SV29 @ SV37 @ SY124 )
| ( less_equal @ SV43 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV44: $i,SV38: $i,SV30: $i,SV18: $i] :
( ( ~ ( quotient @ identity @ SV18 @ SV30 )
| ~ ( quotient @ identity @ SV30 @ SV38 )
| ~ ( quotient @ identity @ SV38 @ SV44 )
| ( SV30 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV31: $i,SV21: $i,SV3: $i] :
( ( ( quotient @ SV3 @ SV21 @ SV31 )
= $false )
| ( ( less_equal @ SV31 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(128,plain,
! [SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ! [SY125: $i,SY126: $i,SY127: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SY125 )
| ~ ( quotient @ SY125 @ SV45 @ SY126 )
| ~ ( quotient @ SV32 @ SV39 @ SY127 )
| ( less_equal @ SY126 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(129,plain,
! [SV6: $i,SV23: $i] :
( ( ( ~ ( less_equal @ SV23 @ SV6 ) )
= $true )
| ( ( SV6 = SV23 )
= $true )
| ( ( less_equal @ SV6 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV40: $i,SV33: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV25 @ SV33 ) )
= $true )
| ( ( ~ ( quotient @ SV9 @ SV25 @ SV40 )
| ( SV33 = SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(131,plain,
! [SV34: $i,SV26: $i,SV14: $i] :
( ( ( less_equal @ SV14 @ SV26 )
= $false )
| ( ( ~ ( less_equal @ SV26 @ SV34 )
| ( less_equal @ SV14 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(132,plain,
! [SV46: $i,SV41: $i,SV35: $i,SV27: $i,SV15: $i] :
( ( ~ ( quotient @ SV15 @ SV27 @ SV35 )
| ~ ( less_equal @ SV35 @ SV41 )
| ~ ( quotient @ SV15 @ SV41 @ SV46 )
| ( less_equal @ SV46 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV47: $i,SV42: $i,SV36: $i,SV28: $i,SV16: $i] :
( ( ~ ( less_equal @ SV16 @ SV28 )
| ~ ( quotient @ SV36 @ SV28 @ SV42 )
| ~ ( quotient @ SV36 @ SV16 @ SV47 )
| ( less_equal @ SV42 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(134,plain,
! [SV48: $i,SV43: $i,SV37: $i,SV29: $i,SV17: $i] :
( ( ~ ( less_equal @ SV17 @ SV29 )
| ~ ( quotient @ SV17 @ SV37 @ SV43 )
| ~ ( quotient @ SV29 @ SV37 @ SV48 )
| ( less_equal @ SV43 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(135,plain,
! [SV44: $i,SV38: $i,SV30: $i,SV18: $i] :
( ( ( ~ ( quotient @ identity @ SV18 @ SV30 ) )
= $true )
| ( ( ~ ( quotient @ identity @ SV30 @ SV38 )
| ~ ( quotient @ identity @ SV38 @ SV44 )
| ( SV30 = SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(136,plain,
! [SV49: $i,SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SY128 )
| ~ ( quotient @ SV32 @ SV39 @ SY129 )
| ( less_equal @ SY128 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV6: $i,SV23: $i] :
( ( ( less_equal @ SV23 @ SV6 )
= $false )
| ( ( SV6 = SV23 )
= $true )
| ( ( less_equal @ SV6 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV40: $i,SV33: $i,SV25: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV25 @ SV33 )
= $false )
| ( ( ~ ( quotient @ SV9 @ SV25 @ SV40 )
| ( SV33 = SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV14: $i,SV34: $i,SV26: $i] :
( ( ( ~ ( less_equal @ SV26 @ SV34 ) )
= $true )
| ( ( less_equal @ SV14 @ SV34 )
= $true )
| ( ( less_equal @ SV14 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV46: $i,SV41: $i,SV35: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( quotient @ SV15 @ SV27 @ SV35 ) )
= $true )
| ( ( ~ ( less_equal @ SV35 @ SV41 )
| ~ ( quotient @ SV15 @ SV41 @ SV46 )
| ( less_equal @ SV46 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV47: $i,SV42: $i,SV36: $i,SV28: $i,SV16: $i] :
( ( ( ~ ( less_equal @ SV16 @ SV28 ) )
= $true )
| ( ( ~ ( quotient @ SV36 @ SV28 @ SV42 )
| ~ ( quotient @ SV36 @ SV16 @ SV47 )
| ( less_equal @ SV42 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV48: $i,SV43: $i,SV37: $i,SV29: $i,SV17: $i] :
( ( ( ~ ( less_equal @ SV17 @ SV29 ) )
= $true )
| ( ( ~ ( quotient @ SV17 @ SV37 @ SV43 )
| ~ ( quotient @ SV29 @ SV37 @ SV48 )
| ( less_equal @ SV43 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV44: $i,SV38: $i,SV30: $i,SV18: $i] :
( ( ( quotient @ identity @ SV18 @ SV30 )
= $false )
| ( ( ~ ( quotient @ identity @ SV30 @ SV38 )
| ~ ( quotient @ identity @ SV38 @ SV44 )
| ( SV30 = SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(144,plain,
! [SV50: $i,SV49: $i,SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ! [SY130: $i] :
( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SY130 )
| ( less_equal @ SV50 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV33: $i,SV40: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( quotient @ SV9 @ SV25 @ SV40 ) )
= $true )
| ( ( SV33 = SV40 )
= $true )
| ( ( quotient @ SV9 @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV14: $i,SV34: $i,SV26: $i] :
( ( ( less_equal @ SV26 @ SV34 )
= $false )
| ( ( less_equal @ SV14 @ SV34 )
= $true )
| ( ( less_equal @ SV14 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV46: $i,SV41: $i,SV35: $i,SV27: $i,SV15: $i] :
( ( ( quotient @ SV15 @ SV27 @ SV35 )
= $false )
| ( ( ~ ( less_equal @ SV35 @ SV41 )
| ~ ( quotient @ SV15 @ SV41 @ SV46 )
| ( less_equal @ SV46 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV47: $i,SV42: $i,SV36: $i,SV28: $i,SV16: $i] :
( ( ( less_equal @ SV16 @ SV28 )
= $false )
| ( ( ~ ( quotient @ SV36 @ SV28 @ SV42 )
| ~ ( quotient @ SV36 @ SV16 @ SV47 )
| ( less_equal @ SV42 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV48: $i,SV43: $i,SV37: $i,SV29: $i,SV17: $i] :
( ( ( less_equal @ SV17 @ SV29 )
= $false )
| ( ( ~ ( quotient @ SV17 @ SV37 @ SV43 )
| ~ ( quotient @ SV29 @ SV37 @ SV48 )
| ( less_equal @ SV43 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV18: $i,SV44: $i,SV38: $i,SV30: $i] :
( ( ( ~ ( quotient @ identity @ SV30 @ SV38 ) )
= $true )
| ( ( ~ ( quotient @ identity @ SV38 @ SV44 )
| ( SV30 = SV44 ) )
= $true )
| ( ( quotient @ identity @ SV18 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ~ ( quotient @ SV4 @ SV22 @ SV32 )
| ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV33: $i,SV40: $i,SV25: $i,SV9: $i] :
( ( ( quotient @ SV9 @ SV25 @ SV40 )
= $false )
| ( ( SV33 = SV40 )
= $true )
| ( ( quotient @ SV9 @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV27: $i,SV46: $i,SV15: $i,SV41: $i,SV35: $i] :
( ( ( ~ ( less_equal @ SV35 @ SV41 ) )
= $true )
| ( ( ~ ( quotient @ SV15 @ SV41 @ SV46 )
| ( less_equal @ SV46 @ SV27 ) )
= $true )
| ( ( quotient @ SV15 @ SV27 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV47: $i,SV16: $i,SV42: $i,SV28: $i,SV36: $i] :
( ( ( ~ ( quotient @ SV36 @ SV28 @ SV42 ) )
= $true )
| ( ( ~ ( quotient @ SV36 @ SV16 @ SV47 )
| ( less_equal @ SV42 @ SV47 ) )
= $true )
| ( ( less_equal @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV48: $i,SV29: $i,SV43: $i,SV37: $i,SV17: $i] :
( ( ( ~ ( quotient @ SV17 @ SV37 @ SV43 ) )
= $true )
| ( ( ~ ( quotient @ SV29 @ SV37 @ SV48 )
| ( less_equal @ SV43 @ SV48 ) )
= $true )
| ( ( less_equal @ SV17 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV18: $i,SV44: $i,SV38: $i,SV30: $i] :
( ( ( quotient @ identity @ SV30 @ SV38 )
= $false )
| ( ( ~ ( quotient @ identity @ SV38 @ SV44 )
| ( SV30 = SV44 ) )
= $true )
| ( ( quotient @ identity @ SV18 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV22 @ SV32 ) )
= $true )
| ( ( ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV27: $i,SV46: $i,SV15: $i,SV41: $i,SV35: $i] :
( ( ( less_equal @ SV35 @ SV41 )
= $false )
| ( ( ~ ( quotient @ SV15 @ SV41 @ SV46 )
| ( less_equal @ SV46 @ SV27 ) )
= $true )
| ( ( quotient @ SV15 @ SV27 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(159,plain,
! [SV47: $i,SV16: $i,SV42: $i,SV28: $i,SV36: $i] :
( ( ( quotient @ SV36 @ SV28 @ SV42 )
= $false )
| ( ( ~ ( quotient @ SV36 @ SV16 @ SV47 )
| ( less_equal @ SV42 @ SV47 ) )
= $true )
| ( ( less_equal @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(160,plain,
! [SV48: $i,SV29: $i,SV43: $i,SV37: $i,SV17: $i] :
( ( ( quotient @ SV17 @ SV37 @ SV43 )
= $false )
| ( ( ~ ( quotient @ SV29 @ SV37 @ SV48 )
| ( less_equal @ SV43 @ SV48 ) )
= $true )
| ( ( less_equal @ SV17 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(161,plain,
! [SV18: $i,SV30: $i,SV44: $i,SV38: $i] :
( ( ( ~ ( quotient @ identity @ SV38 @ SV44 ) )
= $true )
| ( ( SV30 = SV44 )
= $true )
| ( ( quotient @ identity @ SV30 @ SV38 )
= $false )
| ( ( quotient @ identity @ SV18 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(162,plain,
! [SV51: $i,SV50: $i,SV49: $i,SV45: $i,SV39: $i,SV32: $i,SV22: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false )
| ( ( ~ ( quotient @ SV22 @ SV39 @ SV45 )
| ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(163,plain,
! [SV35: $i,SV27: $i,SV46: $i,SV41: $i,SV15: $i] :
( ( ( ~ ( quotient @ SV15 @ SV41 @ SV46 ) )
= $true )
| ( ( less_equal @ SV46 @ SV27 )
= $true )
| ( ( less_equal @ SV35 @ SV41 )
= $false )
| ( ( quotient @ SV15 @ SV27 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(164,plain,
! [SV28: $i,SV42: $i,SV47: $i,SV16: $i,SV36: $i] :
( ( ( ~ ( quotient @ SV36 @ SV16 @ SV47 ) )
= $true )
| ( ( less_equal @ SV42 @ SV47 )
= $true )
| ( ( quotient @ SV36 @ SV28 @ SV42 )
= $false )
| ( ( less_equal @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV17: $i,SV43: $i,SV48: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( quotient @ SV29 @ SV37 @ SV48 ) )
= $true )
| ( ( less_equal @ SV43 @ SV48 )
= $true )
| ( ( quotient @ SV17 @ SV37 @ SV43 )
= $false )
| ( ( less_equal @ SV17 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV18: $i,SV30: $i,SV44: $i,SV38: $i] :
( ( ( quotient @ identity @ SV38 @ SV44 )
= $false )
| ( ( SV30 = SV44 )
= $true )
| ( ( quotient @ identity @ SV30 @ SV38 )
= $false )
| ( ( quotient @ identity @ SV18 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV51: $i,SV32: $i,SV50: $i,SV49: $i,SV4: $i,SV45: $i,SV39: $i,SV22: $i] :
( ( ( ~ ( quotient @ SV22 @ SV39 @ SV45 ) )
= $true )
| ( ( ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(168,plain,
! [SV35: $i,SV27: $i,SV46: $i,SV41: $i,SV15: $i] :
( ( ( quotient @ SV15 @ SV41 @ SV46 )
= $false )
| ( ( less_equal @ SV46 @ SV27 )
= $true )
| ( ( less_equal @ SV35 @ SV41 )
= $false )
| ( ( quotient @ SV15 @ SV27 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(169,plain,
! [SV28: $i,SV42: $i,SV47: $i,SV16: $i,SV36: $i] :
( ( ( quotient @ SV36 @ SV16 @ SV47 )
= $false )
| ( ( less_equal @ SV42 @ SV47 )
= $true )
| ( ( quotient @ SV36 @ SV28 @ SV42 )
= $false )
| ( ( less_equal @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(170,plain,
! [SV17: $i,SV43: $i,SV48: $i,SV37: $i,SV29: $i] :
( ( ( quotient @ SV29 @ SV37 @ SV48 )
= $false )
| ( ( less_equal @ SV43 @ SV48 )
= $true )
| ( ( quotient @ SV17 @ SV37 @ SV43 )
= $false )
| ( ( less_equal @ SV17 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(171,plain,
! [SV51: $i,SV32: $i,SV50: $i,SV49: $i,SV4: $i,SV45: $i,SV39: $i,SV22: $i] :
( ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( ~ ( quotient @ SV4 @ SV39 @ SV49 )
| ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV22: $i,SV51: $i,SV32: $i,SV50: $i,SV45: $i,SV49: $i,SV39: $i,SV4: $i] :
( ( ( ~ ( quotient @ SV4 @ SV39 @ SV49 ) )
= $true )
| ( ( ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(173,plain,
! [SV22: $i,SV51: $i,SV32: $i,SV50: $i,SV45: $i,SV49: $i,SV39: $i,SV4: $i] :
( ( ( quotient @ SV4 @ SV39 @ SV49 )
= $false )
| ( ( ~ ( quotient @ SV49 @ SV45 @ SV50 )
| ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(174,plain,
! [SV22: $i,SV4: $i,SV51: $i,SV39: $i,SV32: $i,SV50: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( quotient @ SV49 @ SV45 @ SV50 ) )
= $true )
| ( ( ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV4 @ SV39 @ SV49 )
= $false )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(175,plain,
! [SV22: $i,SV4: $i,SV51: $i,SV39: $i,SV32: $i,SV50: $i,SV45: $i,SV49: $i] :
( ( ( quotient @ SV49 @ SV45 @ SV50 )
= $false )
| ( ( ~ ( quotient @ SV32 @ SV39 @ SV51 )
| ( less_equal @ SV50 @ SV51 ) )
= $true )
| ( ( quotient @ SV4 @ SV39 @ SV49 )
= $false )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(176,plain,
! [SV22: $i,SV4: $i,SV45: $i,SV49: $i,SV50: $i,SV51: $i,SV39: $i,SV32: $i] :
( ( ( ~ ( quotient @ SV32 @ SV39 @ SV51 ) )
= $true )
| ( ( less_equal @ SV50 @ SV51 )
= $true )
| ( ( quotient @ SV49 @ SV45 @ SV50 )
= $false )
| ( ( quotient @ SV4 @ SV39 @ SV49 )
= $false )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(177,plain,
! [SV22: $i,SV4: $i,SV45: $i,SV49: $i,SV50: $i,SV51: $i,SV39: $i,SV32: $i] :
( ( ( quotient @ SV32 @ SV39 @ SV51 )
= $false )
| ( ( less_equal @ SV50 @ SV51 )
= $true )
| ( ( quotient @ SV49 @ SV45 @ SV50 )
= $false )
| ( ( quotient @ SV4 @ SV39 @ SV49 )
= $false )
| ( ( quotient @ SV22 @ SV39 @ SV45 )
= $false )
| ( ( quotient @ SV4 @ SV22 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(178,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,177,170,169,168,166,152,146,137,127,117,116,98,92,91,85,84,83,82,79,77,52,51]) ).
thf(179,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n008.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 10:57:24 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.21/1.06
% 5.21/1.06 No.of.Axioms: 22
% 5.21/1.06
% 5.21/1.06 Length.of.Defs: 0
% 5.21/1.06
% 5.21/1.06 Contains.Choice.Funs: false
% 5.21/1.06 ....
% 5.21/1.06
% 5.21/1.06 ********************************
% 5.21/1.06 * All subproblems solved! *
% 5.21/1.06 ********************************
% 5.21/1.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:178,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.21/1.06
% 5.21/1.06 %**** Beginning of derivation protocol ****
% 5.21/1.06 % SZS output start CNFRefutation
% See solution above
% 5.21/1.06
% 5.21/1.06 %**** End of derivation protocol ****
% 5.21/1.06 %**** no. of clauses in derivation: 179 ****
% 5.21/1.06 %**** clause counter: 178 ****
% 5.21/1.06
% 5.21/1.06 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:22,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:178,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------