TSTP Solution File: SYN014-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN014-2 : 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 : n009.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 : Thu Jul 21 08:22:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of formulae : 199 ( 100 unt; 8 typ; 0 def)
% Number of atoms : 1153 ( 286 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1774 ( 182 ~; 390 |; 0 &;1202 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 259 ( 0 ^ 259 !; 0 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_k,type,
k: $i ).
thf(tp_m,type,
m: $i ).
thf(tp_n,type,
n: $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( element @ A @ B )
| ~ ( equalish @ A @ C )
| ( element @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish2) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ~ ( element @ C @ A )
| ( element @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish1) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivityish) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetryish) ).
thf(5,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivityish) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
equalish @ m @ k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).
thf(9,negated_conjecture,
~ ( equalish @ k @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_22) ).
thf(10,negated_conjecture,
~ ( equalish @ m @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_21) ).
thf(11,negated_conjecture,
equalish @ n @ k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
thf(12,negated_conjecture,
~ ( equalish @ m @ n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_19) ).
thf(13,negated_conjecture,
~ ( equalish @ n @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_18) ).
thf(14,negated_conjecture,
! [A: $i] :
( ~ ( element @ A @ k )
| ( equalish @ A @ n )
| ( equalish @ A @ m )
| ( equalish @ A @ k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).
thf(15,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ A @ n )
| ( element @ A @ k )
| ( equalish @ A @ k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
thf(16,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ A @ m )
| ( element @ A @ k )
| ( equalish @ A @ k ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
thf(17,negated_conjecture,
! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ n )
| ~ ( element @ B @ n )
| ( equalish @ B @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
thf(18,negated_conjecture,
! [A: $i] :
( ( element @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
thf(19,negated_conjecture,
! [A: $i] :
( ( element @ A @ ( g @ A ) )
| ( element @ A @ n )
| ( equalish @ A @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
thf(20,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
thf(21,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ n )
| ( element @ A @ n )
| ( equalish @ A @ n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
thf(22,negated_conjecture,
! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ m )
| ( element @ B @ m )
| ( equalish @ B @ m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
thf(23,negated_conjecture,
! [A: $i] :
( ( element @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
thf(24,negated_conjecture,
! [A: $i] :
( ( element @ A @ ( f @ A ) )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
thf(25,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
thf(26,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ m )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
thf(27,negated_conjecture,
! [A: $i] :
( ~ ( equalish @ A @ k )
| ( element @ A @ a )
| ( equalish @ A @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
thf(28,negated_conjecture,
! [A: $i] :
( ~ ( element @ A @ a )
| ( equalish @ A @ k )
| ( equalish @ A @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
thf(29,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ A @ B )
| ~ ( equalish @ A @ C )
| ( element @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ~ ( element @ C @ A )
| ( element @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(34,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(35,plain,
( ( equalish @ m @ k )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( ~ ( equalish @ k @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( ~ ( equalish @ m @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( equalish @ n @ k )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ~ ( equalish @ m @ n ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ~ ( equalish @ n @ a ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ k )
| ( equalish @ A @ n )
| ( equalish @ A @ m )
| ( equalish @ A @ k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ n )
| ( element @ A @ k )
| ( equalish @ A @ k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ m )
| ( element @ A @ k )
| ( equalish @ A @ k ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ n )
| ~ ( element @ B @ n )
| ( equalish @ B @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( element @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( element @ A @ ( g @ A ) )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ n )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ m )
| ( element @ B @ m )
| ( equalish @ B @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( element @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( element @ A @ ( f @ A ) )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(52,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(53,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ m )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(54,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ k )
| ( element @ A @ a )
| ( equalish @ A @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(55,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ a )
| ( equalish @ A @ k )
| ( equalish @ A @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(56,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ! [C: $i] :
( ~ ( equalish @ A @ C )
| ( element @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( element @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(60,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ a )
| ( equalish @ A @ k )
| ( equalish @ A @ a ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(61,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ k )
| ( element @ A @ a )
| ( equalish @ A @ a ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ m )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( element @ A @ ( f @ A ) )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( element @ ( f @ A ) @ A )
| ~ ( element @ A @ m )
| ( equalish @ A @ m ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ m )
| ( element @ B @ m )
| ( equalish @ B @ m ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(67,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ n )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(68,plain,
( ( ! [A: $i] :
( ~ ( equalish @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( element @ A @ ( g @ A ) )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( element @ ( g @ A ) @ A )
| ( element @ A @ n )
| ( equalish @ A @ n ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ~ ( element @ B @ A )
| ( equalish @ A @ B )
| ( equalish @ A @ n )
| ~ ( element @ B @ n )
| ( equalish @ B @ n ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(72,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ m )
| ( element @ A @ k )
| ( equalish @ A @ k ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(73,plain,
( ( ! [A: $i] :
( ~ ( equalish @ A @ n )
| ( element @ A @ k )
| ( equalish @ A @ k ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(74,plain,
( ( ! [A: $i] :
( ~ ( element @ A @ k )
| ( equalish @ A @ n )
| ( equalish @ A @ m )
| ( equalish @ A @ k ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(75,plain,
( ( ~ ( equalish @ n @ a ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(76,plain,
( ( ~ ( equalish @ m @ n ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(77,plain,
( ( equalish @ n @ k )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(78,plain,
( ( ~ ( equalish @ m @ a ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(79,plain,
( ( ~ ( equalish @ k @ a ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(80,plain,
( ( equalish @ m @ k )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(81,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(82,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(83,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i] :
( ~ ( element @ C @ A )
| ( element @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ! [C: $i] :
( ~ ( equalish @ A @ C )
| ( element @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(86,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(87,plain,
! [SV1: $i] :
( ( ~ ( element @ SV1 @ a )
| ( equalish @ SV1 @ k )
| ( equalish @ SV1 @ a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(88,plain,
! [SV2: $i] :
( ( ~ ( equalish @ SV2 @ k )
| ( element @ SV2 @ a )
| ( equalish @ SV2 @ a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(89,plain,
! [SV3: $i] :
( ( ~ ( equalish @ ( f @ SV3 ) @ m )
| ~ ( element @ SV3 @ m )
| ( equalish @ SV3 @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(90,plain,
! [SV4: $i] :
( ( ~ ( equalish @ ( f @ SV4 ) @ SV4 )
| ~ ( element @ SV4 @ m )
| ( equalish @ SV4 @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ ( f @ SV5 ) )
| ~ ( element @ SV5 @ m )
| ( equalish @ SV5 @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(92,plain,
! [SV6: $i] :
( ( ( element @ ( f @ SV6 ) @ SV6 )
| ~ ( element @ SV6 @ m )
| ( equalish @ SV6 @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(93,plain,
! [SV7: $i] :
( ( ! [SY29: $i] :
( ~ ( element @ SV7 @ SY29 )
| ~ ( element @ SY29 @ SV7 )
| ( equalish @ SV7 @ SY29 )
| ( equalish @ SV7 @ m )
| ( element @ SY29 @ m )
| ( equalish @ SY29 @ m ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(94,plain,
! [SV8: $i] :
( ( ~ ( equalish @ ( g @ SV8 ) @ n )
| ( element @ SV8 @ n )
| ( equalish @ SV8 @ n ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(95,plain,
! [SV9: $i] :
( ( ~ ( equalish @ ( g @ SV9 ) @ SV9 )
| ( element @ SV9 @ n )
| ( equalish @ SV9 @ n ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(96,plain,
! [SV10: $i] :
( ( ( element @ SV10 @ ( g @ SV10 ) )
| ( element @ SV10 @ n )
| ( equalish @ SV10 @ n ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(97,plain,
! [SV11: $i] :
( ( ( element @ ( g @ SV11 ) @ SV11 )
| ( element @ SV11 @ n )
| ( equalish @ SV11 @ n ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(98,plain,
! [SV12: $i] :
( ( ! [SY30: $i] :
( ~ ( element @ SV12 @ SY30 )
| ~ ( element @ SY30 @ SV12 )
| ( equalish @ SV12 @ SY30 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SY30 @ n )
| ( equalish @ SY30 @ n ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(99,plain,
! [SV13: $i] :
( ( ~ ( equalish @ SV13 @ m )
| ( element @ SV13 @ k )
| ( equalish @ SV13 @ k ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(100,plain,
! [SV14: $i] :
( ( ~ ( equalish @ SV14 @ n )
| ( element @ SV14 @ k )
| ( equalish @ SV14 @ k ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(101,plain,
! [SV15: $i] :
( ( ~ ( element @ SV15 @ k )
| ( equalish @ SV15 @ n )
| ( equalish @ SV15 @ m )
| ( equalish @ SV15 @ k ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(102,plain,
( ( equalish @ n @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(103,plain,
( ( equalish @ m @ n )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(104,plain,
( ( equalish @ m @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(105,plain,
( ( equalish @ k @ a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(106,plain,
! [SV16: $i] :
( ( equalish @ SV16 @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(107,plain,
! [SV17: $i] :
( ( ! [SY31: $i] :
( ~ ( equalish @ SV17 @ SY31 )
| ( equalish @ SY31 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(108,plain,
! [SV18: $i] :
( ( ! [SY32: $i] :
( ~ ( equalish @ SV18 @ SY32 )
| ! [SY33: $i] :
( ~ ( equalish @ SY32 @ SY33 )
| ( equalish @ SV18 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(109,plain,
! [SV19: $i] :
( ( ! [SY34: $i] :
( ~ ( equalish @ SV19 @ SY34 )
| ! [SY35: $i] :
( ~ ( element @ SY35 @ SV19 )
| ( element @ SY35 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(110,plain,
! [SV20: $i] :
( ( ! [SY36: $i] :
( ~ ( element @ SV20 @ SY36 )
| ! [SY37: $i] :
( ~ ( equalish @ SV20 @ SY37 )
| ( element @ SY37 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(111,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(112,plain,
! [SV1: $i] :
( ( ( ~ ( element @ SV1 @ a ) )
= $true )
| ( ( ( equalish @ SV1 @ k )
| ( equalish @ SV1 @ a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(113,plain,
! [SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ k ) )
= $true )
| ( ( ( element @ SV2 @ a )
| ( equalish @ SV2 @ a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(114,plain,
! [SV3: $i] :
( ( ( ~ ( equalish @ ( f @ SV3 ) @ m ) )
= $true )
| ( ( ~ ( element @ SV3 @ m )
| ( equalish @ SV3 @ m ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(115,plain,
! [SV4: $i] :
( ( ( ~ ( equalish @ ( f @ SV4 ) @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV4 @ m )
| ( equalish @ SV4 @ m ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(116,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ ( f @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV5 @ m )
| ( equalish @ SV5 @ m ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(117,plain,
! [SV6: $i] :
( ( ( element @ ( f @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( element @ SV6 @ m )
| ( equalish @ SV6 @ m ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(118,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV21 )
| ~ ( element @ SV21 @ SV7 )
| ( equalish @ SV7 @ SV21 )
| ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(119,plain,
! [SV8: $i] :
( ( ( ~ ( equalish @ ( g @ SV8 ) @ n ) )
= $true )
| ( ( ( element @ SV8 @ n )
| ( equalish @ SV8 @ n ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(120,plain,
! [SV9: $i] :
( ( ( ~ ( equalish @ ( g @ SV9 ) @ SV9 ) )
= $true )
| ( ( ( element @ SV9 @ n )
| ( equalish @ SV9 @ n ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(121,plain,
! [SV10: $i] :
( ( ( element @ SV10 @ ( g @ SV10 ) )
= $true )
| ( ( ( element @ SV10 @ n )
| ( equalish @ SV10 @ n ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(122,plain,
! [SV11: $i] :
( ( ( element @ ( g @ SV11 ) @ SV11 )
= $true )
| ( ( ( element @ SV11 @ n )
| ( equalish @ SV11 @ n ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(123,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ SV22 )
| ~ ( element @ SV22 @ SV12 )
| ( equalish @ SV12 @ SV22 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(124,plain,
! [SV13: $i] :
( ( ( ~ ( equalish @ SV13 @ m ) )
= $true )
| ( ( ( element @ SV13 @ k )
| ( equalish @ SV13 @ k ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(125,plain,
! [SV14: $i] :
( ( ( ~ ( equalish @ SV14 @ n ) )
= $true )
| ( ( ( element @ SV14 @ k )
| ( equalish @ SV14 @ k ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(126,plain,
! [SV15: $i] :
( ( ( ~ ( element @ SV15 @ k ) )
= $true )
| ( ( ( equalish @ SV15 @ n )
| ( equalish @ SV15 @ m )
| ( equalish @ SV15 @ k ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(127,plain,
! [SV23: $i,SV17: $i] :
( ( ~ ( equalish @ SV17 @ SV23 )
| ( equalish @ SV23 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(128,plain,
! [SV24: $i,SV18: $i] :
( ( ~ ( equalish @ SV18 @ SV24 )
| ! [SY38: $i] :
( ~ ( equalish @ SV24 @ SY38 )
| ( equalish @ SV18 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(129,plain,
! [SV25: $i,SV19: $i] :
( ( ~ ( equalish @ SV19 @ SV25 )
| ! [SY39: $i] :
( ~ ( element @ SY39 @ SV19 )
| ( element @ SY39 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(130,plain,
! [SV26: $i,SV20: $i] :
( ( ~ ( element @ SV20 @ SV26 )
| ! [SY40: $i] :
( ~ ( equalish @ SV20 @ SY40 )
| ( element @ SY40 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(131,plain,
! [SV1: $i] :
( ( ( element @ SV1 @ a )
= $false )
| ( ( ( equalish @ SV1 @ k )
| ( equalish @ SV1 @ a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV2: $i] :
( ( ( equalish @ SV2 @ k )
= $false )
| ( ( ( element @ SV2 @ a )
| ( equalish @ SV2 @ a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV3: $i] :
( ( ( equalish @ ( f @ SV3 ) @ m )
= $false )
| ( ( ~ ( element @ SV3 @ m )
| ( equalish @ SV3 @ m ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(134,plain,
! [SV4: $i] :
( ( ( equalish @ ( f @ SV4 ) @ SV4 )
= $false )
| ( ( ~ ( element @ SV4 @ m )
| ( equalish @ SV4 @ m ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 @ m ) )
= $true )
| ( ( equalish @ SV5 @ m )
= $true )
| ( ( element @ SV5 @ ( f @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV6: $i] :
( ( ( ~ ( element @ SV6 @ m ) )
= $true )
| ( ( equalish @ SV6 @ m )
= $true )
| ( ( element @ ( f @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ SV21 ) )
= $true )
| ( ( ~ ( element @ SV21 @ SV7 )
| ( equalish @ SV7 @ SV21 )
| ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV8: $i] :
( ( ( equalish @ ( g @ SV8 ) @ n )
= $false )
| ( ( ( element @ SV8 @ n )
| ( equalish @ SV8 @ n ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV9: $i] :
( ( ( equalish @ ( g @ SV9 ) @ SV9 )
= $false )
| ( ( ( element @ SV9 @ n )
| ( equalish @ SV9 @ n ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV10: $i] :
( ( ( element @ SV10 @ n )
= $true )
| ( ( equalish @ SV10 @ n )
= $true )
| ( ( element @ SV10 @ ( g @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV11: $i] :
( ( ( element @ SV11 @ n )
= $true )
| ( ( equalish @ SV11 @ n )
= $true )
| ( ( element @ ( g @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(142,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ SV22 ) )
= $true )
| ( ( ~ ( element @ SV22 @ SV12 )
| ( equalish @ SV12 @ SV22 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(143,plain,
! [SV13: $i] :
( ( ( equalish @ SV13 @ m )
= $false )
| ( ( ( element @ SV13 @ k )
| ( equalish @ SV13 @ k ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(144,plain,
! [SV14: $i] :
( ( ( equalish @ SV14 @ n )
= $false )
| ( ( ( element @ SV14 @ k )
| ( equalish @ SV14 @ k ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(145,plain,
! [SV15: $i] :
( ( ( element @ SV15 @ k )
= $false )
| ( ( ( equalish @ SV15 @ n )
| ( equalish @ SV15 @ m )
| ( equalish @ SV15 @ k ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV23: $i,SV17: $i] :
( ( ( ~ ( equalish @ SV17 @ SV23 ) )
= $true )
| ( ( equalish @ SV23 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(147,plain,
! [SV24: $i,SV18: $i] :
( ( ( ~ ( equalish @ SV18 @ SV24 ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( equalish @ SV24 @ SY38 )
| ( equalish @ SV18 @ SY38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(148,plain,
! [SV25: $i,SV19: $i] :
( ( ( ~ ( equalish @ SV19 @ SV25 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( element @ SY39 @ SV19 )
| ( element @ SY39 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV26: $i,SV20: $i] :
( ( ( ~ ( element @ SV20 @ SV26 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( equalish @ SV20 @ SY40 )
| ( element @ SY40 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV1: $i] :
( ( ( equalish @ SV1 @ k )
= $true )
| ( ( equalish @ SV1 @ a )
= $true )
| ( ( element @ SV1 @ a )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV2: $i] :
( ( ( element @ SV2 @ a )
= $true )
| ( ( equalish @ SV2 @ a )
= $true )
| ( ( equalish @ SV2 @ k )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV3: $i] :
( ( ( ~ ( element @ SV3 @ m ) )
= $true )
| ( ( equalish @ SV3 @ m )
= $true )
| ( ( equalish @ ( f @ SV3 ) @ m )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV4: $i] :
( ( ( ~ ( element @ SV4 @ m ) )
= $true )
| ( ( equalish @ SV4 @ m )
= $true )
| ( ( equalish @ ( f @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ m )
= $false )
| ( ( equalish @ SV5 @ m )
= $true )
| ( ( element @ SV5 @ ( f @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV6: $i] :
( ( ( element @ SV6 @ m )
= $false )
| ( ( equalish @ SV6 @ m )
= $true )
| ( ( element @ ( f @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV21: $i,SV7: $i] :
( ( ( element @ SV7 @ SV21 )
= $false )
| ( ( ~ ( element @ SV21 @ SV7 )
| ( equalish @ SV7 @ SV21 )
| ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV8: $i] :
( ( ( element @ SV8 @ n )
= $true )
| ( ( equalish @ SV8 @ n )
= $true )
| ( ( equalish @ ( g @ SV8 ) @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV9: $i] :
( ( ( element @ SV9 @ n )
= $true )
| ( ( equalish @ SV9 @ n )
= $true )
| ( ( equalish @ ( g @ SV9 ) @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV22: $i,SV12: $i] :
( ( ( element @ SV12 @ SV22 )
= $false )
| ( ( ~ ( element @ SV22 @ SV12 )
| ( equalish @ SV12 @ SV22 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(160,plain,
! [SV13: $i] :
( ( ( element @ SV13 @ k )
= $true )
| ( ( equalish @ SV13 @ k )
= $true )
| ( ( equalish @ SV13 @ m )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(161,plain,
! [SV14: $i] :
( ( ( element @ SV14 @ k )
= $true )
| ( ( equalish @ SV14 @ k )
= $true )
| ( ( equalish @ SV14 @ n )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(162,plain,
! [SV15: $i] :
( ( ( equalish @ SV15 @ n )
= $true )
| ( ( ( equalish @ SV15 @ m )
| ( equalish @ SV15 @ k ) )
= $true )
| ( ( element @ SV15 @ k )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(163,plain,
! [SV23: $i,SV17: $i] :
( ( ( equalish @ SV17 @ SV23 )
= $false )
| ( ( equalish @ SV23 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(164,plain,
! [SV24: $i,SV18: $i] :
( ( ( equalish @ SV18 @ SV24 )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( equalish @ SV24 @ SY38 )
| ( equalish @ SV18 @ SY38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(165,plain,
! [SV25: $i,SV19: $i] :
( ( ( equalish @ SV19 @ SV25 )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( element @ SY39 @ SV19 )
| ( element @ SY39 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(166,plain,
! [SV26: $i,SV20: $i] :
( ( ( element @ SV20 @ SV26 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( equalish @ SV20 @ SY40 )
| ( element @ SY40 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(167,plain,
! [SV3: $i] :
( ( ( element @ SV3 @ m )
= $false )
| ( ( equalish @ SV3 @ m )
= $true )
| ( ( equalish @ ( f @ SV3 ) @ m )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(168,plain,
! [SV4: $i] :
( ( ( element @ SV4 @ m )
= $false )
| ( ( equalish @ SV4 @ m )
= $true )
| ( ( equalish @ ( f @ SV4 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(169,plain,
! [SV7: $i,SV21: $i] :
( ( ( ~ ( element @ SV21 @ SV7 ) )
= $true )
| ( ( ( equalish @ SV7 @ SV21 )
| ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true )
| ( ( element @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV12: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ SV12 ) )
= $true )
| ( ( ( equalish @ SV12 @ SV22 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(171,plain,
! [SV15: $i] :
( ( ( equalish @ SV15 @ m )
= $true )
| ( ( equalish @ SV15 @ k )
= $true )
| ( ( equalish @ SV15 @ n )
= $true )
| ( ( element @ SV15 @ k )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV18: $i,SV27: $i,SV24: $i] :
( ( ( ~ ( equalish @ SV24 @ SV27 )
| ( equalish @ SV18 @ SV27 ) )
= $true )
| ( ( equalish @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV25: $i,SV19: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ SV19 )
| ( element @ SV28 @ SV25 ) )
= $true )
| ( ( equalish @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV26: $i,SV29: $i,SV20: $i] :
( ( ( ~ ( equalish @ SV20 @ SV29 )
| ( element @ SV29 @ SV26 ) )
= $true )
| ( ( element @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV7: $i,SV21: $i] :
( ( ( element @ SV21 @ SV7 )
= $false )
| ( ( ( equalish @ SV7 @ SV21 )
| ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true )
| ( ( element @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV12: $i,SV22: $i] :
( ( ( element @ SV22 @ SV12 )
= $false )
| ( ( ( equalish @ SV12 @ SV22 )
| ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(177,plain,
! [SV18: $i,SV27: $i,SV24: $i] :
( ( ( ~ ( equalish @ SV24 @ SV27 ) )
= $true )
| ( ( equalish @ SV18 @ SV27 )
= $true )
| ( ( equalish @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(178,plain,
! [SV25: $i,SV19: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ SV19 ) )
= $true )
| ( ( element @ SV28 @ SV25 )
= $true )
| ( ( equalish @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(179,plain,
! [SV26: $i,SV29: $i,SV20: $i] :
( ( ( ~ ( equalish @ SV20 @ SV29 ) )
= $true )
| ( ( element @ SV29 @ SV26 )
= $true )
| ( ( element @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(180,plain,
! [SV21: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV21 )
= $true )
| ( ( ( equalish @ SV7 @ m )
| ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true )
| ( ( element @ SV21 @ SV7 )
= $false )
| ( ( element @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(181,plain,
! [SV22: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV22 )
= $true )
| ( ( ( equalish @ SV12 @ n )
| ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true )
| ( ( element @ SV22 @ SV12 )
= $false )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(182,plain,
! [SV18: $i,SV27: $i,SV24: $i] :
( ( ( equalish @ SV24 @ SV27 )
= $false )
| ( ( equalish @ SV18 @ SV27 )
= $true )
| ( ( equalish @ SV18 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV25: $i,SV19: $i,SV28: $i] :
( ( ( element @ SV28 @ SV19 )
= $false )
| ( ( element @ SV28 @ SV25 )
= $true )
| ( ( equalish @ SV19 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV26: $i,SV29: $i,SV20: $i] :
( ( ( equalish @ SV20 @ SV29 )
= $false )
| ( ( element @ SV29 @ SV26 )
= $true )
| ( ( element @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV21: $i,SV7: $i] :
( ( ( equalish @ SV7 @ m )
= $true )
| ( ( ( element @ SV21 @ m )
| ( equalish @ SV21 @ m ) )
= $true )
| ( ( equalish @ SV7 @ SV21 )
= $true )
| ( ( element @ SV21 @ SV7 )
= $false )
| ( ( element @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(186,plain,
! [SV22: $i,SV12: $i] :
( ( ( equalish @ SV12 @ n )
= $true )
| ( ( ~ ( element @ SV22 @ n )
| ( equalish @ SV22 @ n ) )
= $true )
| ( ( equalish @ SV12 @ SV22 )
= $true )
| ( ( element @ SV22 @ SV12 )
= $false )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV7: $i,SV21: $i] :
( ( ( element @ SV21 @ m )
= $true )
| ( ( equalish @ SV21 @ m )
= $true )
| ( ( equalish @ SV7 @ m )
= $true )
| ( ( equalish @ SV7 @ SV21 )
= $true )
| ( ( element @ SV21 @ SV7 )
= $false )
| ( ( element @ SV7 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(188,plain,
! [SV12: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ n ) )
= $true )
| ( ( equalish @ SV22 @ n )
= $true )
| ( ( equalish @ SV12 @ n )
= $true )
| ( ( equalish @ SV12 @ SV22 )
= $true )
| ( ( element @ SV22 @ SV12 )
= $false )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(189,plain,
! [SV12: $i,SV22: $i] :
( ( ( element @ SV22 @ n )
= $false )
| ( ( equalish @ SV22 @ n )
= $true )
| ( ( equalish @ SV12 @ n )
= $true )
| ( ( equalish @ SV12 @ SV22 )
= $true )
| ( ( element @ SV22 @ SV12 )
= $false )
| ( ( element @ SV12 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(190,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[77,189,187,184,183,182,171,168,167,163,161,160,158,157,155,154,151,150,141,140,111,106,105,104,103,102,80]) ).
thf(191,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 23:22:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 26
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.36 (rf:0,axioms:26,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:28,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.43
% 0.20/0.43 ********************************
% 0.20/0.43 * All subproblems solved! *
% 0.20/0.43 ********************************
% 0.20/0.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.44
% 0.20/0.44 %**** Beginning of derivation protocol ****
% 0.20/0.44 % SZS output start CNFRefutation
% See solution above
% 0.20/0.44
% 0.20/0.44 %**** End of derivation protocol ****
% 0.20/0.44 %**** no. of clauses in derivation: 191 ****
% 0.20/0.44 %**** clause counter: 190 ****
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:26,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------