TSTP Solution File: COM003+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.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 : Fri Jul 15 01:28:32 EDT 2022
% Result : Theorem 0.18s 0.55s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 47
% Syntax : Number of formulae : 442 ( 240 unt; 31 typ; 0 def)
% Number of atoms : 2601 ( 599 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 5252 (1026 ~; 858 |; 88 &;3234 @)
% ( 22 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 10 con; 0-4 aty)
% Number of variables : 1272 ( 0 ^1256 !; 16 ?;1272 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_algorithm,type,
algorithm: $i > $o ).
thf(tp_algorithm_program_decides,type,
algorithm_program_decides: $i > $o ).
thf(tp_bad,type,
bad: $i ).
thf(tp_decides,type,
decides: $i > $i > $i > $o ).
thf(tp_good,type,
good: $i ).
thf(tp_halts2,type,
halts2: $i > $i > $o ).
thf(tp_halts2_outputs,type,
halts2_outputs: $i > $i > $i > $o ).
thf(tp_halts3,type,
halts3: $i > $i > $i > $o ).
thf(tp_halts3_outputs,type,
halts3_outputs: $i > $i > $i > $i > $o ).
thf(tp_outputs,type,
outputs: $i > $i > $o ).
thf(tp_program,type,
program: $i > $o ).
thf(tp_program_decides,type,
program_decides: $i > $o ).
thf(tp_program_halts2,type,
program_halts2: $i > $i > $o ).
thf(tp_program_halts2_halts2_outputs,type,
program_halts2_halts2_outputs: $i > $i > $i > $o ).
thf(tp_program_halts2_halts3_outputs,type,
program_halts2_halts3_outputs: $i > $i > $i > $i > $o ).
thf(tp_program_not_halts2,type,
program_not_halts2: $i > $i > $o ).
thf(tp_program_not_halts2_halts2_outputs,type,
program_not_halts2_halts2_outputs: $i > $i > $i > $o ).
thf(tp_program_not_halts2_halts3_outputs,type,
program_not_halts2_halts3_outputs: $i > $i > $i > $i > $o ).
thf(tp_program_program_decides,type,
program_program_decides: $i > $o ).
thf(tp_sK10_W,type,
sK10_W: $i ).
thf(tp_sK11_Y,type,
sK11_Y: $i > $i ).
thf(tp_sK12_SY48,type,
sK12_SY48: $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_U,type,
sK2_U: $i ).
thf(tp_sK3_Y,type,
sK3_Y: $i > $i ).
thf(tp_sK4_Y,type,
sK4_Y: $i > $i ).
thf(tp_sK5_REN,type,
sK5_REN: $o ).
thf(tp_sK6_V,type,
sK6_V: $i ).
thf(tp_sK7_Y,type,
sK7_Y: $i > $i ).
thf(tp_sK8_Y,type,
sK8_Y: $i > $i ).
thf(tp_sK9_REN,type,
sK9_REN: $o ).
thf(1,axiom,
( ? [V: $i] :
( ( program @ V )
& ! [Y: $i] :
( ( program_halts2_halts2_outputs @ V @ Y @ good )
& ( program_not_halts2_halts2_outputs @ V @ Y @ bad ) ) )
=> ? [U: $i] :
( ( program @ U )
& ! [Y: $i] :
( ( ( program_halts2 @ Y @ Y )
=> ~ ( halts2 @ U @ Y ) )
& ( program_not_halts2_halts2_outputs @ U @ Y @ good ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(2,axiom,
( ? [W: $i] :
( ( program @ W )
& ! [Y: $i] :
( ( program_halts2_halts3_outputs @ W @ Y @ Y @ good )
& ( program_not_halts2_halts3_outputs @ W @ Y @ Y @ bad ) ) )
=> ? [V: $i] :
( ( program @ V )
& ! [Y: $i] :
( ( program_halts2_halts2_outputs @ V @ Y @ good )
& ( program_not_halts2_halts2_outputs @ V @ Y @ bad ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(3,axiom,
! [W: $i] :
( ( program_program_decides @ W )
=> ! [Y: $i,Z: $i] :
( ( program_halts2_halts3_outputs @ W @ Y @ Z @ good )
& ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(4,axiom,
( ? [X: $i] : ( algorithm_program_decides @ X )
=> ? [W: $i] : ( program_program_decides @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(5,axiom,
! [X: $i,Y: $i,W: $i] :
( ( program_not_halts2_halts2_outputs @ X @ Y @ W )
<=> ( ( program_not_halts2 @ Y @ Y )
=> ( halts2_outputs @ X @ Y @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs_def) ).
thf(6,axiom,
! [X: $i,Y: $i,W: $i] :
( ( program_halts2_halts2_outputs @ X @ Y @ W )
<=> ( ( program_halts2 @ Y @ Y )
=> ( halts2_outputs @ X @ Y @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts2_outputs_def) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( program_not_halts2 @ Y @ Z )
=> ( halts3_outputs @ X @ Y @ Z @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts3_outputs_def) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( program_halts2 @ Y @ Z )
=> ( halts3_outputs @ X @ Y @ Z @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts3_outputs_def) ).
thf(9,axiom,
! [X: $i,Y: $i,W: $i] :
( ( halts2_outputs @ X @ Y @ W )
<=> ( ( halts2 @ X @ Y )
& ( outputs @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs_def) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( program_not_halts2 @ X @ Y )
<=> ( ( program @ X )
& ~ ( halts2 @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_def) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ( halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( halts3 @ X @ Y @ Z )
& ( outputs @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts3_outputs_def) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( program_halts2 @ X @ Y )
<=> ( ( program @ X )
& ( halts2 @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_def) ).
thf(13,axiom,
! [X: $i] :
( ( algorithm_program_decides @ X )
<=> ( ( algorithm @ X )
& ( program_decides @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',algorithm_program_decides_def) ).
thf(14,axiom,
! [X: $i] :
( ( program_program_decides @ X )
<=> ( ( program @ X )
& ( program_decides @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides_def) ).
thf(15,axiom,
! [X: $i] :
( ( program_decides @ X )
<=> ! [Y: $i] :
( ( program @ Y )
=> ! [Z: $i] : ( decides @ X @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_decides_def) ).
thf(16,conjecture,
~ ? [X: $i] : ( algorithm_program_decides @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(17,negated_conjecture,
( ( ~ ? [X: $i] : ( algorithm_program_decides @ X ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ~ ? [X: $i] : ( algorithm_program_decides @ X ) )
= $false ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ? [V: $i] :
( ( program @ V )
& ! [Y: $i] :
( ( program_halts2_halts2_outputs @ V @ Y @ good )
& ( program_not_halts2_halts2_outputs @ V @ Y @ bad ) ) )
=> ? [U: $i] :
( ( program @ U )
& ! [Y: $i] :
( ( ( program_halts2 @ Y @ Y )
=> ~ ( halts2 @ U @ Y ) )
& ( program_not_halts2_halts2_outputs @ U @ Y @ good ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ? [W: $i] :
( ( program @ W )
& ! [Y: $i] :
( ( program_halts2_halts3_outputs @ W @ Y @ Y @ good )
& ( program_not_halts2_halts3_outputs @ W @ Y @ Y @ bad ) ) )
=> ? [V: $i] :
( ( program @ V )
& ! [Y: $i] :
( ( program_halts2_halts2_outputs @ V @ Y @ good )
& ( program_not_halts2_halts2_outputs @ V @ Y @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [W: $i] :
( ( program_program_decides @ W )
=> ! [Y: $i,Z: $i] :
( ( program_halts2_halts3_outputs @ W @ Y @ Z @ good )
& ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ? [X: $i] : ( algorithm_program_decides @ X )
=> ? [W: $i] : ( program_program_decides @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( program_not_halts2_halts2_outputs @ X @ Y @ W )
<=> ( ( program_not_halts2 @ Y @ Y )
=> ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( program_halts2_halts2_outputs @ X @ Y @ W )
<=> ( ( program_halts2 @ Y @ Y )
=> ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( program_not_halts2 @ Y @ Z )
=> ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( program_halts2 @ Y @ Z )
=> ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( halts2_outputs @ X @ Y @ W )
<=> ( ( halts2 @ X @ Y )
& ( outputs @ X @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( program_not_halts2 @ X @ Y )
<=> ( ( program @ X )
& ~ ( halts2 @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ( halts3_outputs @ X @ Y @ Z @ W )
<=> ( ( halts3 @ X @ Y @ Z )
& ( outputs @ X @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ( program_halts2 @ X @ Y )
<=> ( ( program @ X )
& ( halts2 @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( algorithm_program_decides @ X )
<=> ( ( algorithm @ X )
& ( program_decides @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( ! [X: $i] :
( ( program_program_decides @ X )
<=> ( ( program @ X )
& ( program_decides @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( program_decides @ X )
<=> ! [Y: $i] :
( ( program @ Y )
=> ! [Z: $i] : ( decides @ X @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(34,plain,
( ( ? [X: $i] : ( algorithm_program_decides @ X ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( algorithm_program_decides @ sK1_X )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(36,plain,
( ( ( ! [V: $i] :
( ~ ( program_halts2_halts2_outputs @ V @ ( sK4_Y @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( sK3_Y @ V ) @ bad )
| ~ ( program @ V ) )
| sK5_REN )
& ( sK5_REN
=> ( ! [SY44: $i] :
( ~ ( program_halts2 @ SY44 @ SY44 )
| ~ ( halts2 @ sK2_U @ SY44 ) )
& ! [SY45: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SY45 @ good )
& ( program @ sK2_U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(37,plain,
( ( ( ! [W: $i] :
( ~ ( program_halts2_halts3_outputs @ W @ ( sK8_Y @ W ) @ ( sK8_Y @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( sK7_Y @ W ) @ ( sK7_Y @ W ) @ bad )
| ~ ( program @ W ) )
| sK9_REN )
& ( sK9_REN
=> ( ! [SY46: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SY46 @ good )
& ! [SY47: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SY47 @ bad )
& ( program @ sK6_V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(38,plain,
( ( ! [W: $i] :
( ~ ( program_program_decides @ W )
| ( ! [Y: $i,Z: $i] : ( program_halts2_halts3_outputs @ W @ Y @ Z @ good )
& ! [Y: $i,Z: $i] : ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(39,plain,
( ( ! [X: $i] :
~ ( algorithm_program_decides @ X )
| ( program_program_decides @ sK10_W ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(40,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( program_not_halts2 @ Y @ Y )
| ! [W: $i] : ( program_not_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( program_not_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ~ ( program_not_halts2 @ Y @ Y )
| ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(41,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( program_halts2 @ Y @ Y )
| ! [W: $i] : ( program_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( program_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ~ ( program_halts2 @ Y @ Y )
| ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
( ( program_not_halts2 @ Y @ Z )
| ! [W: $i] : ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ~ ( program_not_halts2 @ Y @ Z )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
( ( program_halts2 @ Y @ Z )
| ! [W: $i] : ( program_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( program_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ~ ( program_halts2 @ Y @ Z )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(44,plain,
( ( ! [X: $i] :
( ! [Y: $i,W: $i] :
( ~ ( halts2 @ X @ Y )
| ~ ( outputs @ X @ W )
| ( halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i] :
( ! [W: $i] :
~ ( halts2_outputs @ X @ Y @ W )
| ( halts2 @ X @ Y ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( outputs @ X @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program @ X )
| ( halts2 @ X @ Y )
| ( program_not_halts2 @ X @ Y ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( program_not_halts2 @ X @ Y )
| ( program @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i,W: $i] :
( ~ ( halts3 @ X @ Y @ Z )
| ~ ( outputs @ X @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i] :
( ! [W: $i] :
~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( halts3 @ X @ Y @ Z ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( outputs @ X @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( halts2 @ X @ Y )
| ~ ( program @ X )
| ( program_halts2 @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( halts2 @ X @ Y ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( program_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(48,plain,
( ( ! [X: $i] :
( ~ ( algorithm @ X )
| ~ ( program_decides @ X )
| ( algorithm_program_decides @ X ) )
& ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( algorithm @ X ) )
& ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(49,plain,
( ( ! [X: $i] :
( ~ ( program @ X )
| ~ ( program_decides @ X )
| ( program_program_decides @ X ) )
& ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program @ X ) )
& ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( ( program @ ( sK11_Y @ X ) )
& ~ ( decides @ X @ ( sK11_Y @ X ) @ ( sK12_SY48 @ X ) ) )
| ( program_decides @ X ) )
& ! [X: $i] :
( ~ ( program_decides @ X )
| ! [Y: $i] :
( ~ ( program @ Y )
| ! [Z: $i] : ( decides @ X @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( ( program @ ( sK11_Y @ X ) )
& ~ ( decides @ X @ ( sK11_Y @ X ) @ ( sK12_SY48 @ X ) ) )
| ( program_decides @ X ) )
& ! [X: $i] :
( ~ ( program_decides @ X )
| ! [Y: $i] :
( ~ ( program @ Y )
| ! [Z: $i] : ( decides @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(52,plain,
( ( ! [X: $i] :
( ~ ( program @ X )
| ~ ( program_decides @ X )
| ( program_program_decides @ X ) )
& ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program @ X ) )
& ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(53,plain,
( ( ! [X: $i] :
( ~ ( algorithm @ X )
| ~ ( program_decides @ X )
| ( algorithm_program_decides @ X ) )
& ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( algorithm @ X ) )
& ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( halts2 @ X @ Y )
| ~ ( program @ X )
| ( program_halts2 @ X @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( halts2 @ X @ Y ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( program_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i,W: $i] :
( ~ ( halts3 @ X @ Y @ Z )
| ~ ( outputs @ X @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i] :
( ! [W: $i] :
~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( halts3 @ X @ Y @ Z ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( outputs @ X @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program @ X )
| ( halts2 @ X @ Y )
| ( program_not_halts2 @ X @ Y ) )
& ! [X: $i] :
( ! [Y: $i] :
~ ( program_not_halts2 @ X @ Y )
| ( program @ X ) )
& ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [X: $i] :
( ! [Y: $i,W: $i] :
( ~ ( halts2 @ X @ Y )
| ~ ( outputs @ X @ W )
| ( halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i] :
( ! [W: $i] :
~ ( halts2_outputs @ X @ Y @ W )
| ( halts2 @ X @ Y ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( outputs @ X @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
( ( program_halts2 @ Y @ Z )
| ! [W: $i] : ( program_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( program_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ~ ( program_halts2 @ Y @ Z )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
( ( program_not_halts2 @ Y @ Z )
| ! [W: $i] : ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W ) )
& ! [Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ~ ( program_not_halts2 @ Y @ Z )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(60,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( program_halts2 @ Y @ Y )
| ! [W: $i] : ( program_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( program_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ~ ( program_halts2 @ Y @ Y )
| ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(61,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
( ( program_not_halts2 @ Y @ Y )
| ! [W: $i] : ( program_not_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( program_not_halts2_halts2_outputs @ X @ Y @ W ) )
& ! [Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ~ ( program_not_halts2 @ Y @ Y )
| ( halts2_outputs @ X @ Y @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(62,plain,
( ( ! [X: $i] :
~ ( algorithm_program_decides @ X )
| ( program_program_decides @ sK10_W ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(63,plain,
( ( ! [W: $i] :
( ~ ( program_program_decides @ W )
| ( ! [Y: $i,Z: $i] : ( program_halts2_halts3_outputs @ W @ Y @ Z @ good )
& ! [Y: $i,Z: $i] : ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(64,plain,
( ( ( ! [W: $i] :
( ~ ( program_halts2_halts3_outputs @ W @ ( sK8_Y @ W ) @ ( sK8_Y @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( sK7_Y @ W ) @ ( sK7_Y @ W ) @ bad )
| ~ ( program @ W ) )
| sK9_REN )
& ( sK9_REN
=> ( ! [SY46: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SY46 @ good )
& ! [SY47: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SY47 @ bad )
& ( program @ sK6_V ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(65,plain,
( ( ( ! [V: $i] :
( ~ ( program_halts2_halts2_outputs @ V @ ( sK4_Y @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( sK3_Y @ V ) @ bad )
| ~ ( program @ V ) )
| sK5_REN )
& ( sK5_REN
=> ( ! [SY44: $i] :
( ~ ( program_halts2 @ SY44 @ SY44 )
| ~ ( halts2 @ sK2_U @ SY44 ) )
& ! [SY45: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SY45 @ good )
& ( program @ sK2_U ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(66,plain,
( ( algorithm_program_decides @ sK1_X )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(67,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK8_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SX0 @ ( sK7_Y @ SX0 ) @ ( sK7_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ ( sK4_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SX0 @ ( sK3_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK5_REN )
| ~ ( ~ sK5_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( algorithm @ SX0 )
| ~ ( program_decides @ SX0 )
| ( algorithm_program_decides @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ( program_halts2 @ SX1 @ SX2 )
| ! [SX3: $i] : ( program_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ( program_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( program_halts2 @ SX1 @ SX2 )
| ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(71,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ( program_not_halts2 @ SX1 @ SX1 )
| ! [SX2: $i] : ( program_not_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( halts2_outputs @ SX0 @ SX1 @ SX2 )
| ( program_not_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 )
| ~ ( program_not_halts2 @ SX1 @ SX1 )
| ( halts2_outputs @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ( program_not_halts2 @ SX1 @ SX2 )
| ! [SX3: $i] : ( program_not_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ( program_not_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( program_not_halts2 @ SX1 @ SX2 )
| ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [SX0: $i] :
~ ( ~ ~ ( ~ ! [SX1: $i] :
( ( program_halts2 @ SX1 @ SX1 )
| ! [SX2: $i] : ( program_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( halts2_outputs @ SX0 @ SX1 @ SX2 )
| ( program_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ SX1 @ SX2 )
| ~ ( program_halts2 @ SX1 @ SX1 )
| ( halts2_outputs @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( halts3 @ SX0 @ SX1 @ SX2 )
| ~ ( outputs @ SX0 @ SX3 )
| ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ( halts3 @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( halts3_outputs @ SX0 @ SX1 @ SX2 @ SX3 )
| ( outputs @ SX0 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(75,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
| ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY48 @ SX0 ) ) )
| ( program_decides @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_decides @ SX0 )
| ! [SX1: $i] :
( ~ ( program @ SX1 )
| ! [SX2: $i] : ( decides @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] : ( program_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ good )
| ~ ! [SX1: $i,SX2: $i] : ( program_not_halts2_halts3_outputs @ SX0 @ SX1 @ SX2 @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(77,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( halts2 @ SX0 @ SX1 )
| ~ ( outputs @ SX0 @ SX2 )
| ( halts2_outputs @ SX0 @ SX1 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( halts2_outputs @ SX0 @ SX1 @ SX2 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( halts2_outputs @ SX0 @ SX1 @ SX2 )
| ( outputs @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(78,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( halts2 @ SX0 @ SX1 )
| ~ ( program @ SX0 )
| ( program_halts2 @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(79,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program @ SX0 )
| ( halts2 @ SX0 @ SX1 )
| ( program_not_halts2 @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(80,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( program @ SX0 )
| ~ ( program_decides @ SX0 )
| ( program_program_decides @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(81,plain,
( ( ( ! [X: $i] :
~ ( algorithm_program_decides @ X ) )
= $true )
| ( ( program_program_decides @ sK10_W )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(82,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK8_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SX0 @ ( sK7_Y @ SX0 ) @ ( sK7_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK9_REN )
| ~ ( ~ sK9_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(83,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ ( sK4_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SX0 @ ( sK3_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK5_REN )
| ~ ( ~ sK5_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(84,plain,
( ( ~ ! [SX0: $i] :
( ~ ( algorithm @ SX0 )
| ~ ( program_decides @ SX0 )
| ( algorithm_program_decides @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV1: $i] :
( ( ! [SY49: $i] :
~ ( ~ ~ ( ~ ! [SY50: $i] :
( ( program_halts2 @ SY49 @ SY50 )
| ! [SY51: $i] : ( program_halts2_halts3_outputs @ SV1 @ SY49 @ SY50 @ SY51 ) )
| ~ ! [SY52: $i,SY53: $i] :
( ~ ( halts3_outputs @ SV1 @ SY49 @ SY52 @ SY53 )
| ( program_halts2_halts3_outputs @ SV1 @ SY49 @ SY52 @ SY53 ) ) )
| ~ ! [SY54: $i,SY55: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SY49 @ SY54 @ SY55 )
| ~ ( program_halts2 @ SY49 @ SY54 )
| ( halts3_outputs @ SV1 @ SY49 @ SY54 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) )
| ~ ! [SY60: $i,SY61: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SY60 @ SY61 )
| ~ ( program_not_halts2 @ SY60 @ SY60 )
| ( halts2_outputs @ SV2 @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV3: $i] :
( ( ! [SY62: $i] :
~ ( ~ ~ ( ~ ! [SY63: $i] :
( ( program_not_halts2 @ SY62 @ SY63 )
| ! [SY64: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SY62 @ SY63 @ SY64 ) )
| ~ ! [SY65: $i,SY66: $i] :
( ~ ( halts3_outputs @ SV3 @ SY62 @ SY65 @ SY66 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SY62 @ SY65 @ SY66 ) ) )
| ~ ! [SY67: $i,SY68: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SY62 @ SY67 @ SY68 )
| ~ ( program_not_halts2 @ SY62 @ SY67 )
| ( halts3_outputs @ SV3 @ SY62 @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV4: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i] :
( ~ ( program_halts2_halts2_outputs @ SV4 @ SY73 @ SY74 )
| ~ ( program_halts2 @ SY73 @ SY73 )
| ( halts2_outputs @ SV4 @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV5: $i] :
( ( ! [SY75: $i] :
~ ( ~ ! [SY76: $i,SY77: $i] :
( ~ ( halts3 @ SV5 @ SY75 @ SY76 )
| ~ ( outputs @ SV5 @ SY77 )
| ( halts3_outputs @ SV5 @ SY75 @ SY76 @ SY77 ) )
| ~ ~ ( ~ ! [SY78: $i] :
( ! [SY79: $i] :
~ ( halts3_outputs @ SV5 @ SY75 @ SY78 @ SY79 )
| ( halts3 @ SV5 @ SY75 @ SY78 ) )
| ~ ! [SY80: $i,SY81: $i] :
( ~ ( halts3_outputs @ SV5 @ SY75 @ SY80 @ SY81 )
| ( outputs @ SV5 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
| ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY48 @ SX0 ) ) )
| ( program_decides @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_decides @ SX0 )
| ! [SX1: $i] :
( ~ ( program @ SX1 )
| ! [SX2: $i] : ( decides @ SX0 @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV6: $i] :
( ( ~ ( program_program_decides @ SV6 )
| ~ ( ~ ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good )
| ~ ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY86: $i,SY87: $i] :
( ~ ( halts2 @ SV7 @ SY86 )
| ~ ( outputs @ SV7 @ SY87 )
| ( halts2_outputs @ SV7 @ SY86 @ SY87 ) )
| ~ ~ ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) )
| ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( halts2 @ SX0 @ SX1 )
| ~ ( program @ SX0 )
| ( program_halts2 @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(94,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program @ SX0 )
| ( halts2 @ SX0 @ SX1 )
| ( program_not_halts2 @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(95,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program @ SX0 )
| ~ ( program_decides @ SX0 )
| ( program_program_decides @ SX0 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV8: $i] :
( ( ( ~ ( algorithm_program_decides @ SV8 ) )
= $true )
| ( ( program_program_decides @ sK10_W )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK8_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SX0 @ ( sK7_Y @ SX0 ) @ ( sK7_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK9_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(98,plain,
( ( ~ ( ~ sK9_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(99,plain,
( ( ~ ( ! [SX0: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ ( sK4_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SX0 @ ( sK3_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK5_REN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(100,plain,
( ( ~ ( ~ sK5_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(101,plain,
( ( ~ ! [SX0: $i] :
( ~ ( algorithm @ SX0 )
| ~ ( program_decides @ SX0 )
| ( algorithm_program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(102,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(103,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) )
| ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 )
| ~ ( program_halts2 @ SV9 @ SY96 )
| ( halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) )
| ~ ! [SY60: $i,SY61: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SY60 @ SY61 )
| ~ ( program_not_halts2 @ SY60 @ SY60 )
| ( halts2_outputs @ SV2 @ SY60 @ SY61 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 )
| ~ ( program_not_halts2 @ SV10 @ SY102 )
| ( halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) )
| ~ ! [SY73: $i,SY74: $i] :
( ~ ( program_halts2_halts2_outputs @ SV4 @ SY73 @ SY74 )
| ~ ( program_halts2 @ SY73 @ SY73 )
| ( halts2_outputs @ SV4 @ SY73 @ SY74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( halts3 @ SV5 @ SV11 @ SY104 )
| ~ ( outputs @ SV5 @ SY105 )
| ( halts3_outputs @ SV5 @ SV11 @ SY104 @ SY105 ) )
| ~ ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(108,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
| ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY48 @ SX0 ) ) )
| ( program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(109,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program_decides @ SX0 )
| ! [SX1: $i] :
( ~ ( program @ SX1 )
| ! [SX2: $i] : ( decides @ SX0 @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(110,plain,
! [SV6: $i] :
( ( ( ~ ( program_program_decides @ SV6 ) )
= $true )
| ( ( ~ ( ~ ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good )
| ~ ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV7: $i] :
( ( ~ ! [SY86: $i,SY87: $i] :
( ~ ( halts2 @ SV7 @ SY86 )
| ~ ( outputs @ SV7 @ SY87 )
| ( halts2_outputs @ SV7 @ SY86 @ SY87 ) )
| ~ ~ ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) )
| ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( halts2 @ SX0 @ SX1 )
| ~ ( program @ SX0 )
| ( program_halts2 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(113,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program @ SX0 )
| ( halts2 @ SX0 @ SX1 )
| ( program_not_halts2 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(115,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program @ SX0 )
| ~ ( program_decides @ SX0 )
| ( program_program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(117,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(118,plain,
! [SV8: $i] :
( ( ( algorithm_program_decides @ SV8 )
= $false )
| ( ( program_program_decides @ sK10_W )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK8_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SX0 @ ( sK7_Y @ SX0 ) @ ( sK7_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK9_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(120,plain,
( ( ~ sK9_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ ( sK4_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SX0 @ ( sK3_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) )
| sK5_REN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(122,plain,
( ( ~ sK5_REN
| ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(123,plain,
( ( ! [SX0: $i] :
( ~ ( algorithm @ SX0 )
| ~ ( program_decides @ SX0 )
| ( algorithm_program_decides @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(124,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(125,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) )
| ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) )
| ~ ! [SY96: $i,SY97: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 )
| ~ ( program_halts2 @ SV9 @ SY96 )
| ( halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(126,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(127,plain,
! [SV2: $i] :
( ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SY60 @ SY61 )
| ~ ( program_not_halts2 @ SY60 @ SY60 )
| ( halts2_outputs @ SV2 @ SY60 @ SY61 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(128,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ~ ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 )
| ~ ( program_not_halts2 @ SV10 @ SY102 )
| ( halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(129,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(130,plain,
! [SV4: $i] :
( ( ~ ! [SY73: $i,SY74: $i] :
( ~ ( program_halts2_halts2_outputs @ SV4 @ SY73 @ SY74 )
| ~ ( program_halts2 @ SY73 @ SY73 )
| ( halts2_outputs @ SV4 @ SY73 @ SY74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[106]) ).
thf(131,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( halts3 @ SV5 @ SV11 @ SY104 )
| ~ ( outputs @ SV5 @ SY105 )
| ( halts3_outputs @ SV5 @ SV11 @ SY104 @ SY105 ) )
| ~ ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(132,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( program @ ( sK11_Y @ SX0 ) )
| ~ ~ ( decides @ SX0 @ ( sK11_Y @ SX0 ) @ ( sK12_SY48 @ SX0 ) ) )
| ( program_decides @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(133,plain,
( ( ! [SX0: $i] :
( ~ ( program_decides @ SX0 )
| ! [SX1: $i] :
( ~ ( program @ SX1 )
| ! [SX2: $i] : ( decides @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(134,plain,
! [SV6: $i] :
( ( ( program_program_decides @ SV6 )
= $false )
| ( ( ~ ( ~ ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good )
| ~ ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV7: $i] :
( ( ~ ! [SY86: $i,SY87: $i] :
( ~ ( halts2 @ SV7 @ SY86 )
| ~ ( outputs @ SV7 @ SY87 )
| ( halts2_outputs @ SV7 @ SY86 @ SY87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(136,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) )
| ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( halts2 @ SX0 @ SX1 )
| ~ ( program @ SX0 )
| ( program_halts2 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(138,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( program @ SX0 )
| ( halts2 @ SX0 @ SX1 )
| ( program_not_halts2 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(140,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(141,plain,
( ( ! [SX0: $i] :
( ~ ( program @ SX0 )
| ~ ( program_decides @ SX0 )
| ( program_program_decides @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(142,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(143,plain,
( ( ( ! [SX0: $i] :
( ~ ( program_halts2_halts3_outputs @ SX0 @ ( sK8_Y @ SX0 ) @ ( sK8_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SX0 @ ( sK7_Y @ SX0 ) @ ( sK7_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(144,plain,
( ( ( ~ sK9_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(145,plain,
( ( ( ! [SX0: $i] :
( ~ ( program_halts2_halts2_outputs @ SX0 @ ( sK4_Y @ SX0 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SX0 @ ( sK3_Y @ SX0 ) @ bad )
| ~ ( program @ SX0 ) ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(146,plain,
( ( ( ~ sK5_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(147,plain,
! [SV12: $i] :
( ( ~ ( algorithm @ SV12 )
| ~ ( program_decides @ SV12 )
| ( algorithm_program_decides @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(148,plain,
( ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(149,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ~ ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) )
| ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(150,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ! [SY96: $i,SY97: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 )
| ~ ( program_halts2 @ SV9 @ SY96 )
| ( halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[125]) ).
thf(151,plain,
! [SV2: $i] :
( ( ~ ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(152,plain,
! [SV2: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SY60 @ SY61 )
| ~ ( program_not_halts2 @ SY60 @ SY60 )
| ( halts2_outputs @ SV2 @ SY60 @ SY61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(153,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ~ ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(154,plain,
! [SV10: $i,SV3: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 )
| ~ ( program_not_halts2 @ SV10 @ SY102 )
| ( halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(155,plain,
! [SV4: $i] :
( ( ~ ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(156,plain,
! [SV4: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ~ ( program_halts2_halts2_outputs @ SV4 @ SY73 @ SY74 )
| ~ ( program_halts2 @ SY73 @ SY73 )
| ( halts2_outputs @ SV4 @ SY73 @ SY74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(157,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( halts3 @ SV5 @ SV11 @ SY104 )
| ~ ( outputs @ SV5 @ SY105 )
| ( halts3_outputs @ SV5 @ SV11 @ SY104 @ SY105 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(158,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(159,plain,
! [SV13: $i] :
( ( ~ ( ~ ( program @ ( sK11_Y @ SV13 ) )
| ~ ~ ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) ) )
| ( program_decides @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(160,plain,
! [SV14: $i] :
( ( ~ ( program_decides @ SV14 )
| ! [SY110: $i] :
( ~ ( program @ SY110 )
| ! [SY111: $i] : ( decides @ SV14 @ SY110 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(161,plain,
! [SV6: $i] :
( ( ( ~ ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good )
| ~ ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) )
= $false )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(162,plain,
! [SV7: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( halts2 @ SV7 @ SY86 )
| ~ ( outputs @ SV7 @ SY87 )
| ( halts2_outputs @ SV7 @ SY86 @ SY87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(163,plain,
! [SV7: $i] :
( ( ~ ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) )
| ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(164,plain,
! [SV15: $i] :
( ( ! [SY112: $i] :
( ~ ( halts2 @ SV15 @ SY112 )
| ~ ( program @ SV15 )
| ( program_halts2 @ SV15 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(165,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) )
| ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(166,plain,
! [SV16: $i] :
( ( ! [SY113: $i] :
( ~ ( program @ SV16 )
| ( halts2 @ SV16 @ SY113 )
| ( program_not_halts2 @ SV16 @ SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(167,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(168,plain,
! [SV17: $i] :
( ( ~ ( program @ SV17 )
| ~ ( program_decides @ SV17 )
| ( program_program_decides @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(169,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(170,plain,
! [SV18: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad )
| ~ ( program @ SV18 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(171,plain,
( ( sK9_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(172,plain,
! [SV19: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad )
| ~ ( program @ SV19 ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(173,plain,
( ( sK5_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(174,plain,
! [SV12: $i] :
( ( ( ~ ( algorithm @ SV12 )
| ~ ( program_decides @ SV12 ) )
= $true )
| ( ( algorithm_program_decides @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(175,plain,
( ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(176,plain,
( ( ~ ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(177,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) )
| ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(178,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 )
| ~ ( program_halts2 @ SV9 @ SY96 )
| ( halts3_outputs @ SV1 @ SV9 @ SY96 @ SY97 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(179,plain,
! [SV2: $i] :
( ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(180,plain,
! [SV20: $i,SV2: $i] :
( ( ! [SY114: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SY114 )
| ~ ( program_not_halts2 @ SV20 @ SV20 )
| ( halts2_outputs @ SV2 @ SV20 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(181,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(182,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 )
| ~ ( program_not_halts2 @ SV10 @ SY102 )
| ( halts3_outputs @ SV3 @ SV10 @ SY102 @ SY103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(183,plain,
! [SV4: $i] :
( ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) )
| ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(184,plain,
! [SV21: $i,SV4: $i] :
( ( ! [SY115: $i] :
( ~ ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SY115 )
| ~ ( program_halts2 @ SV21 @ SV21 )
| ( halts2_outputs @ SV4 @ SV21 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(185,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( halts3 @ SV5 @ SV11 @ SY104 )
| ~ ( outputs @ SV5 @ SY105 )
| ( halts3_outputs @ SV5 @ SV11 @ SY104 @ SY105 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(186,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(187,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( program @ ( sK11_Y @ SV13 ) )
| ~ ~ ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) ) ) )
= $true )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(188,plain,
! [SV14: $i] :
( ( ( ~ ( program_decides @ SV14 ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( program @ SY110 )
| ! [SY111: $i] : ( decides @ SV14 @ SY110 @ SY111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(189,plain,
! [SV6: $i] :
( ( ( ~ ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good ) )
= $false )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(190,plain,
! [SV6: $i] :
( ( ( ~ ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) )
= $false )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(191,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY116: $i] :
( ~ ( halts2 @ SV7 @ SV22 )
| ~ ( outputs @ SV7 @ SY116 )
| ( halts2_outputs @ SV7 @ SV22 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(192,plain,
! [SV7: $i] :
( ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) )
| ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(193,plain,
! [SV23: $i,SV15: $i] :
( ( ~ ( halts2 @ SV15 @ SV23 )
| ~ ( program @ SV15 )
| ( program_halts2 @ SV15 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(194,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(195,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(196,plain,
! [SV24: $i,SV16: $i] :
( ( ~ ( program @ SV16 )
| ( halts2 @ SV16 @ SV24 )
| ( program_not_halts2 @ SV16 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(197,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(198,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(199,plain,
! [SV17: $i] :
( ( ( ~ ( program @ SV17 )
| ~ ( program_decides @ SV17 ) )
= $true )
| ( ( program_program_decides @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(200,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(201,plain,
( ( ~ ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(202,plain,
! [SV18: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV18 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(203,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
| ~ ( program @ sK6_V ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(204,plain,
! [SV19: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV19 ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(205,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
| ~ ( program @ sK2_U ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(206,plain,
! [SV12: $i] :
( ( ( ~ ( algorithm @ SV12 ) )
= $true )
| ( ( ~ ( program_decides @ SV12 ) )
= $true )
| ( ( algorithm_program_decides @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(207,plain,
( ( ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( algorithm @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(208,plain,
( ( ! [SX0: $i] :
( ~ ( algorithm_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(209,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) )
| ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(210,plain,
! [SV25: $i,SV9: $i,SV1: $i] :
( ( ! [SY117: $i] :
( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SY117 )
| ~ ( program_halts2 @ SV9 @ SV25 )
| ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(211,plain,
! [SV2: $i] :
( ( ~ ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(212,plain,
! [SV2: $i] :
( ( ~ ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(213,plain,
! [SV26: $i,SV20: $i,SV2: $i] :
( ( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SV26 )
| ~ ( program_not_halts2 @ SV20 @ SV20 )
| ( halts2_outputs @ SV2 @ SV20 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(214,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(215,plain,
! [SV27: $i,SV10: $i,SV3: $i] :
( ( ! [SY118: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SY118 )
| ~ ( program_not_halts2 @ SV10 @ SV27 )
| ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(216,plain,
! [SV4: $i] :
( ( ~ ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(217,plain,
! [SV4: $i] :
( ( ~ ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(218,plain,
! [SV28: $i,SV21: $i,SV4: $i] :
( ( ~ ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SV28 )
| ~ ( program_halts2 @ SV21 @ SV21 )
| ( halts2_outputs @ SV4 @ SV21 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV29: $i,SV11: $i,SV5: $i] :
( ( ! [SY119: $i] :
( ~ ( halts3 @ SV5 @ SV11 @ SV29 )
| ~ ( outputs @ SV5 @ SY119 )
| ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(220,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(221,plain,
! [SV13: $i] :
( ( ( ~ ( program @ ( sK11_Y @ SV13 ) )
| ~ ~ ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) ) )
= $false )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV14: $i] :
( ( ( program_decides @ SV14 )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( program @ SY110 )
| ! [SY111: $i] : ( decides @ SV14 @ SY110 @ SY111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV6: $i] :
( ( ( ! [SY82: $i,SY83: $i] : ( program_halts2_halts3_outputs @ SV6 @ SY82 @ SY83 @ good ) )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(224,plain,
! [SV6: $i] :
( ( ( ! [SY84: $i,SY85: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SY84 @ SY85 @ bad ) )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(225,plain,
! [SV30: $i,SV22: $i,SV7: $i] :
( ( ~ ( halts2 @ SV7 @ SV22 )
| ~ ( outputs @ SV7 @ SV30 )
| ( halts2_outputs @ SV7 @ SV22 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV7: $i] :
( ( ~ ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(227,plain,
! [SV7: $i] :
( ( ~ ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(228,plain,
! [SV23: $i,SV15: $i] :
( ( ( ~ ( halts2 @ SV15 @ SV23 )
| ~ ( program @ SV15 ) )
= $true )
| ( ( program_halts2 @ SV15 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(229,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( program_halts2 @ SX0 @ SX1 )
| ( halts2 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(230,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(231,plain,
! [SV24: $i,SV16: $i] :
( ( ( ~ ( program @ SV16 )
| ( halts2 @ SV16 @ SV24 ) )
= $true )
| ( ( program_not_halts2 @ SV16 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(232,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( program_not_halts2 @ SX0 @ SX1 )
| ( program @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( program_not_halts2 @ SX0 @ SX1 )
| ~ ( halts2 @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(234,plain,
! [SV17: $i] :
( ( ( ~ ( program @ SV17 ) )
= $true )
| ( ( ~ ( program_decides @ SV17 ) )
= $true )
| ( ( program_program_decides @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(235,plain,
( ( ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(236,plain,
( ( ! [SX0: $i] :
( ~ ( program_program_decides @ SX0 )
| ( program_decides @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(237,plain,
! [SV18: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV18 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(238,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(239,plain,
( ( ( ~ ( program @ sK6_V ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(240,plain,
! [SV19: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV19 ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(241,plain,
( ( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(242,plain,
( ( ( ~ ( program @ sK2_U ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(243,plain,
! [SV12: $i] :
( ( ( algorithm @ SV12 )
= $false )
| ( ( ~ ( program_decides @ SV12 ) )
= $true )
| ( ( algorithm_program_decides @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV31: $i] :
( ( ~ ( algorithm_program_decides @ SV31 )
| ( algorithm @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV32: $i] :
( ( ~ ( algorithm_program_decides @ SV32 )
| ( program_decides @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV1: $i,SV9: $i] :
( ( ~ ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(247,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(248,plain,
! [SV33: $i,SV25: $i,SV9: $i,SV1: $i] :
( ( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
| ~ ( program_halts2 @ SV9 @ SV25 )
| ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(249,plain,
! [SV2: $i] :
( ( ! [SY56: $i] :
( ( program_not_halts2 @ SY56 @ SY56 )
| ! [SY57: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SY56 @ SY57 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(250,plain,
! [SV2: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( halts2_outputs @ SV2 @ SY58 @ SY59 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SY58 @ SY59 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(251,plain,
! [SV26: $i,SV20: $i,SV2: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SV26 ) )
= $true )
| ( ( ~ ( program_not_halts2 @ SV20 @ SV20 )
| ( halts2_outputs @ SV2 @ SV20 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(252,plain,
! [SV3: $i,SV10: $i] :
( ( ~ ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(253,plain,
! [SV10: $i,SV3: $i] :
( ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(254,plain,
! [SV34: $i,SV27: $i,SV10: $i,SV3: $i] :
( ( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
| ~ ( program_not_halts2 @ SV10 @ SV27 )
| ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(255,plain,
! [SV4: $i] :
( ( ! [SY69: $i] :
( ( program_halts2 @ SY69 @ SY69 )
| ! [SY70: $i] : ( program_halts2_halts2_outputs @ SV4 @ SY69 @ SY70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(256,plain,
! [SV4: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( halts2_outputs @ SV4 @ SY71 @ SY72 )
| ( program_halts2_halts2_outputs @ SV4 @ SY71 @ SY72 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(257,plain,
! [SV28: $i,SV21: $i,SV4: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SV28 ) )
= $true )
| ( ( ~ ( program_halts2 @ SV21 @ SV21 )
| ( halts2_outputs @ SV4 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(258,plain,
! [SV35: $i,SV29: $i,SV11: $i,SV5: $i] :
( ( ~ ( halts3 @ SV5 @ SV11 @ SV29 )
| ~ ( outputs @ SV5 @ SV35 )
| ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(259,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(260,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(261,plain,
! [SV13: $i] :
( ( ( ~ ( program @ ( sK11_Y @ SV13 ) ) )
= $false )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(262,plain,
! [SV13: $i] :
( ( ( ~ ~ ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) ) )
= $false )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(263,plain,
! [SV14: $i,SV36: $i] :
( ( ( ~ ( program @ SV36 )
| ! [SY120: $i] : ( decides @ SV14 @ SV36 @ SY120 ) )
= $true )
| ( ( program_decides @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(264,plain,
! [SV37: $i,SV6: $i] :
( ( ( ! [SY121: $i] : ( program_halts2_halts3_outputs @ SV6 @ SV37 @ SY121 @ good ) )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(265,plain,
! [SV38: $i,SV6: $i] :
( ( ( ! [SY122: $i] : ( program_not_halts2_halts3_outputs @ SV6 @ SV38 @ SY122 @ bad ) )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(266,plain,
! [SV30: $i,SV22: $i,SV7: $i] :
( ( ( ~ ( halts2 @ SV7 @ SV22 )
| ~ ( outputs @ SV7 @ SV30 ) )
= $true )
| ( ( halts2_outputs @ SV7 @ SV22 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(267,plain,
! [SV7: $i] :
( ( ! [SY88: $i] :
( ! [SY89: $i] :
~ ( halts2_outputs @ SV7 @ SY88 @ SY89 )
| ( halts2 @ SV7 @ SY88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(268,plain,
! [SV7: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( halts2_outputs @ SV7 @ SY90 @ SY91 )
| ( outputs @ SV7 @ SY91 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(269,plain,
! [SV23: $i,SV15: $i] :
( ( ( ~ ( halts2 @ SV15 @ SV23 ) )
= $true )
| ( ( ~ ( program @ SV15 ) )
= $true )
| ( ( program_halts2 @ SV15 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(270,plain,
! [SV39: $i] :
( ( ! [SY123: $i] :
( ~ ( program_halts2 @ SV39 @ SY123 )
| ( halts2 @ SV39 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(271,plain,
! [SV40: $i] :
( ( ! [SY124: $i] :
~ ( program_halts2 @ SV40 @ SY124 )
| ( program @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(272,plain,
! [SV24: $i,SV16: $i] :
( ( ( ~ ( program @ SV16 ) )
= $true )
| ( ( halts2 @ SV16 @ SV24 )
= $true )
| ( ( program_not_halts2 @ SV16 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(273,plain,
! [SV41: $i] :
( ( ! [SY125: $i] :
~ ( program_not_halts2 @ SV41 @ SY125 )
| ( program @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(274,plain,
! [SV42: $i] :
( ( ! [SY126: $i] :
( ~ ( program_not_halts2 @ SV42 @ SY126 )
| ~ ( halts2 @ SV42 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(275,plain,
! [SV17: $i] :
( ( ( program @ SV17 )
= $false )
| ( ( ~ ( program_decides @ SV17 ) )
= $true )
| ( ( program_program_decides @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(276,plain,
! [SV43: $i] :
( ( ~ ( program_program_decides @ SV43 )
| ( program @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(277,plain,
! [SV44: $i] :
( ( ~ ( program_program_decides @ SV44 )
| ( program_decides @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(278,plain,
! [SV18: $i] :
( ( ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV18 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(279,plain,
( ( ( ~ ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) ) )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(280,plain,
( ( ( program @ sK6_V )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(281,plain,
! [SV19: $i] :
( ( ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad ) )
= $true )
| ( ( ~ ( program @ SV19 ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(282,plain,
( ( ( ~ ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(283,plain,
( ( ( program @ sK2_U )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(284,plain,
! [SV12: $i] :
( ( ( program_decides @ SV12 )
= $false )
| ( ( algorithm @ SV12 )
= $false )
| ( ( algorithm_program_decides @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(285,plain,
! [SV31: $i] :
( ( ( ~ ( algorithm_program_decides @ SV31 ) )
= $true )
| ( ( algorithm @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(286,plain,
! [SV32: $i] :
( ( ( ~ ( algorithm_program_decides @ SV32 ) )
= $true )
| ( ( program_decides @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(287,plain,
! [SV1: $i,SV9: $i] :
( ( ! [SY92: $i] :
( ( program_halts2 @ SV9 @ SY92 )
| ! [SY93: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY92 @ SY93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(288,plain,
! [SV9: $i,SV1: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SY94 @ SY95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(289,plain,
! [SV33: $i,SV25: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 ) )
= $true )
| ( ( ~ ( program_halts2 @ SV9 @ SV25 )
| ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(290,plain,
! [SV2: $i,SV45: $i] :
( ( ( program_not_halts2 @ SV45 @ SV45 )
| ! [SY127: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SV45 @ SY127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(291,plain,
! [SV46: $i,SV2: $i] :
( ( ! [SY128: $i] :
( ~ ( halts2_outputs @ SV2 @ SV46 @ SY128 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SV46 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(292,plain,
! [SV26: $i,SV20: $i,SV2: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SV26 )
= $false )
| ( ( ~ ( program_not_halts2 @ SV20 @ SV20 )
| ( halts2_outputs @ SV2 @ SV20 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(293,plain,
! [SV3: $i,SV10: $i] :
( ( ! [SY98: $i] :
( ( program_not_halts2 @ SV10 @ SY98 )
| ! [SY99: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY98 @ SY99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(294,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SY100 @ SY101 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(295,plain,
! [SV34: $i,SV27: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 ) )
= $true )
| ( ( ~ ( program_not_halts2 @ SV10 @ SV27 )
| ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(296,plain,
! [SV4: $i,SV47: $i] :
( ( ( program_halts2 @ SV47 @ SV47 )
| ! [SY129: $i] : ( program_halts2_halts2_outputs @ SV4 @ SV47 @ SY129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(297,plain,
! [SV48: $i,SV4: $i] :
( ( ! [SY130: $i] :
( ~ ( halts2_outputs @ SV4 @ SV48 @ SY130 )
| ( program_halts2_halts2_outputs @ SV4 @ SV48 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(298,plain,
! [SV28: $i,SV21: $i,SV4: $i] :
( ( ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SV28 )
= $false )
| ( ( ~ ( program_halts2 @ SV21 @ SV21 )
| ( halts2_outputs @ SV4 @ SV21 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(299,plain,
! [SV35: $i,SV29: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( halts3 @ SV5 @ SV11 @ SV29 )
| ~ ( outputs @ SV5 @ SV35 ) )
= $true )
| ( ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(300,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY106: $i] :
( ! [SY107: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SY106 @ SY107 )
| ( halts3 @ SV5 @ SV11 @ SY106 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(301,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SY108 @ SY109 )
| ( outputs @ SV5 @ SY109 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(302,plain,
! [SV13: $i] :
( ( ( program @ ( sK11_Y @ SV13 ) )
= $true )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(303,plain,
! [SV13: $i] :
( ( ( ~ ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) ) )
= $true )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(304,plain,
! [SV14: $i,SV36: $i] :
( ( ( ~ ( program @ SV36 ) )
= $true )
| ( ( ! [SY120: $i] : ( decides @ SV14 @ SV36 @ SY120 ) )
= $true )
| ( ( program_decides @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(305,plain,
! [SV49: $i,SV37: $i,SV6: $i] :
( ( ( program_halts2_halts3_outputs @ SV6 @ SV37 @ SV49 @ good )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(306,plain,
! [SV50: $i,SV38: $i,SV6: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV6 @ SV38 @ SV50 @ bad )
= $true )
| ( ( program_program_decides @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(307,plain,
! [SV30: $i,SV22: $i,SV7: $i] :
( ( ( ~ ( halts2 @ SV7 @ SV22 ) )
= $true )
| ( ( ~ ( outputs @ SV7 @ SV30 ) )
= $true )
| ( ( halts2_outputs @ SV7 @ SV22 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(308,plain,
! [SV51: $i,SV7: $i] :
( ( ! [SY131: $i] :
~ ( halts2_outputs @ SV7 @ SV51 @ SY131 )
| ( halts2 @ SV7 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(309,plain,
! [SV52: $i,SV7: $i] :
( ( ! [SY132: $i] :
( ~ ( halts2_outputs @ SV7 @ SV52 @ SY132 )
| ( outputs @ SV7 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(310,plain,
! [SV23: $i,SV15: $i] :
( ( ( halts2 @ SV15 @ SV23 )
= $false )
| ( ( ~ ( program @ SV15 ) )
= $true )
| ( ( program_halts2 @ SV15 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(311,plain,
! [SV53: $i,SV39: $i] :
( ( ~ ( program_halts2 @ SV39 @ SV53 )
| ( halts2 @ SV39 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(312,plain,
! [SV40: $i] :
( ( ( ! [SY124: $i] :
~ ( program_halts2 @ SV40 @ SY124 ) )
= $true )
| ( ( program @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(313,plain,
! [SV24: $i,SV16: $i] :
( ( ( program @ SV16 )
= $false )
| ( ( halts2 @ SV16 @ SV24 )
= $true )
| ( ( program_not_halts2 @ SV16 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(314,plain,
! [SV41: $i] :
( ( ( ! [SY125: $i] :
~ ( program_not_halts2 @ SV41 @ SY125 ) )
= $true )
| ( ( program @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(315,plain,
! [SV54: $i,SV42: $i] :
( ( ~ ( program_not_halts2 @ SV42 @ SV54 )
| ~ ( halts2 @ SV42 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(316,plain,
! [SV17: $i] :
( ( ( program_decides @ SV17 )
= $false )
| ( ( program @ SV17 )
= $false )
| ( ( program_program_decides @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(317,plain,
! [SV43: $i] :
( ( ( ~ ( program_program_decides @ SV43 ) )
= $true )
| ( ( program @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(318,plain,
! [SV44: $i] :
( ( ( ~ ( program_program_decides @ SV44 ) )
= $true )
| ( ( program_decides @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(319,plain,
! [SV18: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad )
= $false )
| ( ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good )
= $false )
| ( ( ~ ( program @ SV18 ) )
= $true )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(320,plain,
( ( ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(321,plain,
! [SV19: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad )
= $false )
| ( ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good )
= $false )
| ( ( ~ ( program @ SV19 ) )
= $true )
| ( sK5_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(322,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) )
| ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(323,plain,
! [SV31: $i] :
( ( ( algorithm_program_decides @ SV31 )
= $false )
| ( ( algorithm @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(324,plain,
! [SV32: $i] :
( ( ( algorithm_program_decides @ SV32 )
= $false )
| ( ( program_decides @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(325,plain,
! [SV1: $i,SV55: $i,SV9: $i] :
( ( ( program_halts2 @ SV9 @ SV55 )
| ! [SY133: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV55 @ SY133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(326,plain,
! [SV56: $i,SV9: $i,SV1: $i] :
( ( ! [SY134: $i] :
( ~ ( halts3_outputs @ SV1 @ SV9 @ SV56 @ SY134 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV56 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(327,plain,
! [SV33: $i,SV25: $i,SV9: $i,SV1: $i] :
( ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
= $false )
| ( ( ~ ( program_halts2 @ SV9 @ SV25 )
| ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(328,plain,
! [SV2: $i,SV45: $i] :
( ( ( program_not_halts2 @ SV45 @ SV45 )
= $true )
| ( ( ! [SY127: $i] : ( program_not_halts2_halts2_outputs @ SV2 @ SV45 @ SY127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(329,plain,
! [SV57: $i,SV46: $i,SV2: $i] :
( ( ~ ( halts2_outputs @ SV2 @ SV46 @ SV57 )
| ( program_not_halts2_halts2_outputs @ SV2 @ SV46 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(330,plain,
! [SV26: $i,SV2: $i,SV20: $i] :
( ( ( ~ ( program_not_halts2 @ SV20 @ SV20 ) )
= $true )
| ( ( halts2_outputs @ SV2 @ SV20 @ SV26 )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(331,plain,
! [SV3: $i,SV58: $i,SV10: $i] :
( ( ( program_not_halts2 @ SV10 @ SV58 )
| ! [SY135: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV58 @ SY135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(332,plain,
! [SV59: $i,SV10: $i,SV3: $i] :
( ( ! [SY136: $i] :
( ~ ( halts3_outputs @ SV3 @ SV10 @ SV59 @ SY136 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV59 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(333,plain,
! [SV34: $i,SV27: $i,SV10: $i,SV3: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
= $false )
| ( ( ~ ( program_not_halts2 @ SV10 @ SV27 )
| ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(334,plain,
! [SV4: $i,SV47: $i] :
( ( ( program_halts2 @ SV47 @ SV47 )
= $true )
| ( ( ! [SY129: $i] : ( program_halts2_halts2_outputs @ SV4 @ SV47 @ SY129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(335,plain,
! [SV60: $i,SV48: $i,SV4: $i] :
( ( ~ ( halts2_outputs @ SV4 @ SV48 @ SV60 )
| ( program_halts2_halts2_outputs @ SV4 @ SV48 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(336,plain,
! [SV28: $i,SV4: $i,SV21: $i] :
( ( ( ~ ( program_halts2 @ SV21 @ SV21 ) )
= $true )
| ( ( halts2_outputs @ SV4 @ SV21 @ SV28 )
= $true )
| ( ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(337,plain,
! [SV35: $i,SV29: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( halts3 @ SV5 @ SV11 @ SV29 ) )
= $true )
| ( ( ~ ( outputs @ SV5 @ SV35 ) )
= $true )
| ( ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(338,plain,
! [SV61: $i,SV11: $i,SV5: $i] :
( ( ! [SY137: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SV61 @ SY137 )
| ( halts3 @ SV5 @ SV11 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(339,plain,
! [SV62: $i,SV11: $i,SV5: $i] :
( ( ! [SY138: $i] :
( ~ ( halts3_outputs @ SV5 @ SV11 @ SV62 @ SY138 )
| ( outputs @ SV5 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(340,plain,
! [SV13: $i] :
( ( ( decides @ SV13 @ ( sK11_Y @ SV13 ) @ ( sK12_SY48 @ SV13 ) )
= $false )
| ( ( program_decides @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(341,plain,
! [SV14: $i,SV36: $i] :
( ( ( program @ SV36 )
= $false )
| ( ( ! [SY120: $i] : ( decides @ SV14 @ SV36 @ SY120 ) )
= $true )
| ( ( program_decides @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(342,plain,
! [SV30: $i,SV22: $i,SV7: $i] :
( ( ( halts2 @ SV7 @ SV22 )
= $false )
| ( ( ~ ( outputs @ SV7 @ SV30 ) )
= $true )
| ( ( halts2_outputs @ SV7 @ SV22 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(343,plain,
! [SV51: $i,SV7: $i] :
( ( ( ! [SY131: $i] :
~ ( halts2_outputs @ SV7 @ SV51 @ SY131 ) )
= $true )
| ( ( halts2 @ SV7 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(344,plain,
! [SV63: $i,SV52: $i,SV7: $i] :
( ( ~ ( halts2_outputs @ SV7 @ SV52 @ SV63 )
| ( outputs @ SV7 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(345,plain,
! [SV23: $i,SV15: $i] :
( ( ( program @ SV15 )
= $false )
| ( ( halts2 @ SV15 @ SV23 )
= $false )
| ( ( program_halts2 @ SV15 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(346,plain,
! [SV53: $i,SV39: $i] :
( ( ( ~ ( program_halts2 @ SV39 @ SV53 ) )
= $true )
| ( ( halts2 @ SV39 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(347,plain,
! [SV64: $i,SV40: $i] :
( ( ( ~ ( program_halts2 @ SV40 @ SV64 ) )
= $true )
| ( ( program @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(348,plain,
! [SV65: $i,SV41: $i] :
( ( ( ~ ( program_not_halts2 @ SV41 @ SV65 ) )
= $true )
| ( ( program @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(349,plain,
! [SV54: $i,SV42: $i] :
( ( ( ~ ( program_not_halts2 @ SV42 @ SV54 ) )
= $true )
| ( ( ~ ( halts2 @ SV42 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(350,plain,
! [SV43: $i] :
( ( ( program_program_decides @ SV43 )
= $false )
| ( ( program @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(351,plain,
! [SV44: $i] :
( ( ( program_program_decides @ SV44 )
= $false )
| ( ( program_decides @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(352,plain,
! [SV18: $i] :
( ( ( program @ SV18 )
= $false )
| ( ( program_halts2_halts3_outputs @ SV18 @ ( sK8_Y @ SV18 ) @ ( sK8_Y @ SV18 ) @ good )
= $false )
| ( ( program_not_halts2_halts3_outputs @ SV18 @ ( sK7_Y @ SV18 ) @ ( sK7_Y @ SV18 ) @ bad )
= $false )
| ( sK9_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(353,plain,
( ( ( ~ ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(354,plain,
( ( ( ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
= $false )
| ( sK9_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(355,plain,
! [SV19: $i] :
( ( ( program @ SV19 )
= $false )
| ( ( program_halts2_halts2_outputs @ SV19 @ ( sK4_Y @ SV19 ) @ good )
= $false )
| ( ( program_not_halts2_halts2_outputs @ SV19 @ ( sK3_Y @ SV19 ) @ bad )
= $false )
| ( sK5_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(356,plain,
( ( ( ~ ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(357,plain,
( ( ( ~ ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(358,plain,
! [SV1: $i,SV55: $i,SV9: $i] :
( ( ( program_halts2 @ SV9 @ SV55 )
= $true )
| ( ( ! [SY133: $i] : ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV55 @ SY133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(359,plain,
! [SV66: $i,SV56: $i,SV9: $i,SV1: $i] :
( ( ~ ( halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 )
| ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(360,plain,
! [SV33: $i,SV1: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( program_halts2 @ SV9 @ SV25 ) )
= $true )
| ( ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
= $true )
| ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(361,plain,
! [SV67: $i,SV45: $i,SV2: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV2 @ SV45 @ SV67 )
= $true )
| ( ( program_not_halts2 @ SV45 @ SV45 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(362,plain,
! [SV57: $i,SV46: $i,SV2: $i] :
( ( ( ~ ( halts2_outputs @ SV2 @ SV46 @ SV57 ) )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV2 @ SV46 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(363,plain,
! [SV26: $i,SV2: $i,SV20: $i] :
( ( ( program_not_halts2 @ SV20 @ SV20 )
= $false )
| ( ( halts2_outputs @ SV2 @ SV20 @ SV26 )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV2 @ SV20 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(364,plain,
! [SV3: $i,SV58: $i,SV10: $i] :
( ( ( program_not_halts2 @ SV10 @ SV58 )
= $true )
| ( ( ! [SY135: $i] : ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV58 @ SY135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(365,plain,
! [SV68: $i,SV59: $i,SV10: $i,SV3: $i] :
( ( ~ ( halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(366,plain,
! [SV34: $i,SV3: $i,SV27: $i,SV10: $i] :
( ( ( ~ ( program_not_halts2 @ SV10 @ SV27 ) )
= $true )
| ( ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(367,plain,
! [SV69: $i,SV47: $i,SV4: $i] :
( ( ( program_halts2_halts2_outputs @ SV4 @ SV47 @ SV69 )
= $true )
| ( ( program_halts2 @ SV47 @ SV47 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(368,plain,
! [SV60: $i,SV48: $i,SV4: $i] :
( ( ( ~ ( halts2_outputs @ SV4 @ SV48 @ SV60 ) )
= $true )
| ( ( program_halts2_halts2_outputs @ SV4 @ SV48 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(369,plain,
! [SV28: $i,SV4: $i,SV21: $i] :
( ( ( program_halts2 @ SV21 @ SV21 )
= $false )
| ( ( halts2_outputs @ SV4 @ SV21 @ SV28 )
= $true )
| ( ( program_halts2_halts2_outputs @ SV4 @ SV21 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(370,plain,
! [SV35: $i,SV29: $i,SV11: $i,SV5: $i] :
( ( ( halts3 @ SV5 @ SV11 @ SV29 )
= $false )
| ( ( ~ ( outputs @ SV5 @ SV35 ) )
= $true )
| ( ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(371,plain,
! [SV61: $i,SV11: $i,SV5: $i] :
( ( ( ! [SY137: $i] :
~ ( halts3_outputs @ SV5 @ SV11 @ SV61 @ SY137 ) )
= $true )
| ( ( halts3 @ SV5 @ SV11 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(372,plain,
! [SV70: $i,SV62: $i,SV11: $i,SV5: $i] :
( ( ~ ( halts3_outputs @ SV5 @ SV11 @ SV62 @ SV70 )
| ( outputs @ SV5 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(373,plain,
! [SV71: $i,SV36: $i,SV14: $i] :
( ( ( decides @ SV14 @ SV36 @ SV71 )
= $true )
| ( ( program @ SV36 )
= $false )
| ( ( program_decides @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(374,plain,
! [SV22: $i,SV30: $i,SV7: $i] :
( ( ( outputs @ SV7 @ SV30 )
= $false )
| ( ( halts2 @ SV7 @ SV22 )
= $false )
| ( ( halts2_outputs @ SV7 @ SV22 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(375,plain,
! [SV72: $i,SV51: $i,SV7: $i] :
( ( ( ~ ( halts2_outputs @ SV7 @ SV51 @ SV72 ) )
= $true )
| ( ( halts2 @ SV7 @ SV51 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(376,plain,
! [SV63: $i,SV52: $i,SV7: $i] :
( ( ( ~ ( halts2_outputs @ SV7 @ SV52 @ SV63 ) )
= $true )
| ( ( outputs @ SV7 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(377,plain,
! [SV53: $i,SV39: $i] :
( ( ( program_halts2 @ SV39 @ SV53 )
= $false )
| ( ( halts2 @ SV39 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(378,plain,
! [SV64: $i,SV40: $i] :
( ( ( program_halts2 @ SV40 @ SV64 )
= $false )
| ( ( program @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(379,plain,
! [SV65: $i,SV41: $i] :
( ( ( program_not_halts2 @ SV41 @ SV65 )
= $false )
| ( ( program @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(380,plain,
! [SV54: $i,SV42: $i] :
( ( ( program_not_halts2 @ SV42 @ SV54 )
= $false )
| ( ( ~ ( halts2 @ SV42 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(381,plain,
( ( ( ! [SX0: $i] : ( program_halts2_halts2_outputs @ sK6_V @ SX0 @ good ) )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(382,plain,
( ( ( ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK6_V @ SX0 @ bad ) )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(383,plain,
( ( ( ! [SX0: $i] :
( ~ ( program_halts2 @ SX0 @ SX0 )
| ~ ( halts2 @ sK2_U @ SX0 ) ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(384,plain,
( ( ( ! [SX0: $i] : ( program_not_halts2_halts2_outputs @ sK2_U @ SX0 @ good ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(385,plain,
! [SV73: $i,SV55: $i,SV9: $i,SV1: $i] :
( ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV55 @ SV73 )
= $true )
| ( ( program_halts2 @ SV9 @ SV55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(386,plain,
! [SV66: $i,SV56: $i,SV9: $i,SV1: $i] :
( ( ( ~ ( halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 ) )
= $true )
| ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(387,plain,
! [SV33: $i,SV1: $i,SV25: $i,SV9: $i] :
( ( ( program_halts2 @ SV9 @ SV25 )
= $false )
| ( ( halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
= $true )
| ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(388,plain,
! [SV57: $i,SV46: $i,SV2: $i] :
( ( ( halts2_outputs @ SV2 @ SV46 @ SV57 )
= $false )
| ( ( program_not_halts2_halts2_outputs @ SV2 @ SV46 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(389,plain,
! [SV74: $i,SV58: $i,SV10: $i,SV3: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV58 @ SV74 )
= $true )
| ( ( program_not_halts2 @ SV10 @ SV58 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(390,plain,
! [SV68: $i,SV59: $i,SV10: $i,SV3: $i] :
( ( ( ~ ( halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 ) )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(391,plain,
! [SV34: $i,SV3: $i,SV27: $i,SV10: $i] :
( ( ( program_not_halts2 @ SV10 @ SV27 )
= $false )
| ( ( halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV27 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(392,plain,
! [SV60: $i,SV48: $i,SV4: $i] :
( ( ( halts2_outputs @ SV4 @ SV48 @ SV60 )
= $false )
| ( ( program_halts2_halts2_outputs @ SV4 @ SV48 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV29: $i,SV11: $i,SV35: $i,SV5: $i] :
( ( ( outputs @ SV5 @ SV35 )
= $false )
| ( ( halts3 @ SV5 @ SV11 @ SV29 )
= $false )
| ( ( halts3_outputs @ SV5 @ SV11 @ SV29 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(394,plain,
! [SV75: $i,SV61: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( halts3_outputs @ SV5 @ SV11 @ SV61 @ SV75 ) )
= $true )
| ( ( halts3 @ SV5 @ SV11 @ SV61 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(395,plain,
! [SV70: $i,SV62: $i,SV11: $i,SV5: $i] :
( ( ( ~ ( halts3_outputs @ SV5 @ SV11 @ SV62 @ SV70 ) )
= $true )
| ( ( outputs @ SV5 @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(396,plain,
! [SV72: $i,SV51: $i,SV7: $i] :
( ( ( halts2_outputs @ SV7 @ SV51 @ SV72 )
= $false )
| ( ( halts2 @ SV7 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(397,plain,
! [SV63: $i,SV52: $i,SV7: $i] :
( ( ( halts2_outputs @ SV7 @ SV52 @ SV63 )
= $false )
| ( ( outputs @ SV7 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(398,plain,
! [SV54: $i,SV42: $i] :
( ( ( halts2 @ SV42 @ SV54 )
= $false )
| ( ( program_not_halts2 @ SV42 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(399,plain,
! [SV76: $i] :
( ( ( program_halts2_halts2_outputs @ sK6_V @ SV76 @ good )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(400,plain,
! [SV77: $i] :
( ( ( program_not_halts2_halts2_outputs @ sK6_V @ SV77 @ bad )
= $true )
| ( sK9_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(401,plain,
! [SV78: $i] :
( ( ( ~ ( program_halts2 @ SV78 @ SV78 )
| ~ ( halts2 @ sK2_U @ SV78 ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(402,plain,
! [SV79: $i] :
( ( ( program_not_halts2_halts2_outputs @ sK2_U @ SV79 @ good )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(403,plain,
! [SV66: $i,SV56: $i,SV9: $i,SV1: $i] :
( ( ( halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 )
= $false )
| ( ( program_halts2_halts3_outputs @ SV1 @ SV9 @ SV56 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(404,plain,
! [SV68: $i,SV59: $i,SV10: $i,SV3: $i] :
( ( ( halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 )
= $false )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV10 @ SV59 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(405,plain,
! [SV75: $i,SV61: $i,SV11: $i,SV5: $i] :
( ( ( halts3_outputs @ SV5 @ SV11 @ SV61 @ SV75 )
= $false )
| ( ( halts3 @ SV5 @ SV11 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(406,plain,
! [SV70: $i,SV62: $i,SV11: $i,SV5: $i] :
( ( ( halts3_outputs @ SV5 @ SV11 @ SV62 @ SV70 )
= $false )
| ( ( outputs @ SV5 @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(407,plain,
! [SV78: $i] :
( ( ( ~ ( program_halts2 @ SV78 @ SV78 ) )
= $true )
| ( ( ~ ( halts2 @ sK2_U @ SV78 ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(408,plain,
! [SV78: $i] :
( ( ( program_halts2 @ SV78 @ SV78 )
= $false )
| ( ( ~ ( halts2 @ sK2_U @ SV78 ) )
= $true )
| ( sK5_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(409,plain,
! [SV78: $i] :
( ( ( halts2 @ sK2_U @ SV78 )
= $false )
| ( ( program_halts2 @ SV78 @ SV78 )
= $false )
| ( sK5_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(410,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[66,409,406,405,404,403,402,400,399,398,397,396,393,392,391,389,388,387,385,379,378,377,374,373,369,367,363,361,355,352,351,350,345,340,324,323,316,313,306,305,302,284,283,280,118]) ).
thf(411,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COM003+2 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.12/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n005.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 : Thu Jun 16 20:09:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.18/0.35
% 0.18/0.35 No.of.Axioms: 15
% 0.18/0.35
% 0.18/0.35 Length.of.Defs: 0
% 0.18/0.35
% 0.18/0.35 Contains.Choice.Funs: false
% 0.18/0.36 (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full).................................
% 0.18/0.55
% 0.18/0.55 ********************************
% 0.18/0.55 * All subproblems solved! *
% 0.18/0.55 ********************************
% 0.18/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:410,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.45/0.63
% 0.45/0.63 %**** Beginning of derivation protocol ****
% 0.45/0.63 % SZS output start CNFRefutation
% See solution above
% 0.45/0.63
% 0.45/0.63 %**** End of derivation protocol ****
% 0.45/0.63 %**** no. of clauses in derivation: 411 ****
% 0.45/0.63 %**** clause counter: 410 ****
% 0.45/0.63
% 0.45/0.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:15,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:410,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------