%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:11:59 AM UTC 2026
% Result : Unsatisfiable 0.60s 0.37s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 371 ( 198 unt; 0 typ; 0 def)
% Number of atoms : 2042 ( 530 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3646 ( 489 ~; 611 |; 0 &;2546 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 8 con; 0-4 aty)
% Number of variables : 921 ( 0 ^; 921 !; 0 ?; 921 :)
% 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_c1,type,
c1: $i ).
thf(tp_c2,type,
c2: $i ).
thf(tp_c3,type,
c3: $i ).
thf(tp_c4,type,
c4: $i ).
thf(tp_decides,type,
decides: $i > $i > $i > $o ).
thf(tp_f1,type,
f1: $i > $i ).
thf(tp_f2,type,
f2: $i > $i ).
thf(tp_f3,type,
f3: $i > $i ).
thf(tp_f4,type,
f4: $i > $i ).
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(1,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_outputs3) ).
thf(2,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs2) ).
thf(3,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( program_not_halts2 @ Y @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts2_outputs1) ).
thf(4,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_outputs3) ).
thf(5,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts2_outputs2) ).
thf(6,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( program_halts2 @ Y @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts2_outputs1) ).
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_outputs3) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts3_outputs2) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_not_halts2 @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts2_halts3_outputs1) ).
thf(10,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_outputs3) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts3_outputs2) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_halts2 @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts2_halts3_outputs1) ).
thf(13,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_outputs3) ).
thf(14,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( outputs @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs2) ).
thf(15,axiom,
! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( halts2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts2_outputs1) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ( program_not_halts2 @ X @ Y )
| ~ ( program @ X )
| ( halts2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts3b) ).
thf(17,axiom,
! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ~ ( halts2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts3a) ).
thf(18,axiom,
! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ( program @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_not_halts1) ).
thf(19,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_outputs3) ).
thf(20,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( outputs @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts3_outputs2) ).
thf(21,axiom,
! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( halts3 @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',halts3_outputs1) ).
thf(22,axiom,
! [X: $i,Y: $i] :
( ( program_halts2 @ X @ Y )
| ~ ( program @ X )
| ~ ( halts2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts3b) ).
thf(23,axiom,
! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( halts2 @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts3a) ).
thf(24,axiom,
! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( program @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_halts1) ).
thf(25,axiom,
! [X: $i] :
( ( algorithm_program_decides @ X )
| ~ ( algorithm @ X )
| ~ ( program_decides @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',algorithm_program_decides3) ).
thf(26,axiom,
! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_decides @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',algorithm_program_decides2) ).
thf(27,axiom,
! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( algorithm @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',algorithm_program_decides1) ).
thf(28,axiom,
! [X: $i] :
( ( program_program_decides @ X )
| ~ ( program @ X )
| ~ ( program_decides @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides3) ).
thf(29,axiom,
! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program_decides @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides2) ).
thf(30,axiom,
! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_program_decides1) ).
thf(31,axiom,
! [X: $i] :
( ( program_decides @ X )
| ~ ( decides @ X @ ( f2 @ X ) @ ( f1 @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_decides3) ).
thf(32,axiom,
! [X: $i] :
( ( program_decides @ X )
| ( program @ ( f2 @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_decides2) ).
thf(33,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( program_decides @ X )
| ~ ( program @ Y )
| ( decides @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',program_decides1) ).
thf(34,axiom,
! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ Y @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4_3) ).
thf(35,axiom,
! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ~ ( program_halts2 @ Y @ Y )
| ( halts2 @ c3 @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4_2) ).
thf(36,axiom,
! [V: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program @ c3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4_1) ).
thf(37,axiom,
! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ Y @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3_3) ).
thf(38,axiom,
! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ Y @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3_2) ).
thf(39,axiom,
! [W: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program @ c2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3_1) ).
thf(40,axiom,
! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2_2) ).
thf(41,axiom,
! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_halts2_halts3_outputs @ W @ Y @ Z @ good ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2_1) ).
thf(42,axiom,
! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_program_decides @ c1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1_1) ).
thf(43,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(44,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[43]) ).
thf(45,negated_conjecture,
algorithm_program_decides @ c4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_algorithm_does_not_exist) ).
thf(46,plain,
$false = $false,
inference(unfold_def,[status(thm)],[44]) ).
thf(47,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)],[1]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( program_not_halts2 @ Y @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,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)],[4]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( program_halts2 @ Y @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(53,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(54,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_not_halts2 @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(56,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)],[10]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_halts2 @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( halts2_outputs @ X @ Y @ W )
| ~ ( halts2 @ X @ Y )
| ~ ( outputs @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( outputs @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] :
( ( program_not_halts2 @ X @ Y )
| ~ ( program @ X )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(65,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)],[19]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( outputs @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( halts3 @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( program_halts2 @ X @ Y )
| ~ ( program @ X )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(71,plain,
( ( ! [X: $i] :
( ( algorithm_program_decides @ X )
| ~ ( algorithm @ X )
| ~ ( program_decides @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(72,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(73,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( algorithm @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(74,plain,
( ( ! [X: $i] :
( ( program_program_decides @ X )
| ~ ( program @ X )
| ~ ( program_decides @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(75,plain,
( ( ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(76,plain,
( ( ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(77,plain,
( ( ! [X: $i] :
( ( program_decides @ X )
| ~ ( decides @ X @ ( f2 @ X ) @ ( f1 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(78,plain,
( ( ! [X: $i] :
( ( program_decides @ X )
| ( program @ ( f2 @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( program_decides @ X )
| ~ ( program @ Y )
| ( decides @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(80,plain,
( ( ! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ Y @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(81,plain,
( ( ! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ~ ( program_halts2 @ Y @ Y )
| ( halts2 @ c3 @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(82,plain,
( ( ! [V: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program @ c3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(83,plain,
( ( ! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ Y @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(84,plain,
( ( ! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ Y @ good ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(85,plain,
( ( ! [W: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program @ c2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(86,plain,
( ( ! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(87,plain,
( ( ! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_halts2_halts3_outputs @ W @ Y @ Z @ good ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(88,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_program_decides @ c1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(89,plain,
( ( algorithm_program_decides @ c4 )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(90,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(91,plain,
( ( algorithm_program_decides @ c4 )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(92,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_program_decides @ c1 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(93,plain,
( ( ! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_halts2_halts3_outputs @ W @ Y @ Z @ good ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(94,plain,
( ( ! [W: $i,Y: $i,Z: $i] :
( ~ ( program_program_decides @ W )
| ( program_not_halts2_halts3_outputs @ W @ Y @ Z @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(95,plain,
( ( ! [W: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program @ c2 ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(96,plain,
( ( ! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ Y @ good ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(97,plain,
( ( ! [W: $i,Y: $i] :
( ~ ( program @ W )
| ~ ( program_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ W @ ( f3 @ W ) @ ( f3 @ W ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ Y @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(98,plain,
( ( ! [V: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program @ c3 ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(99,plain,
( ( ! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ~ ( program_halts2 @ Y @ Y )
| ( halts2 @ c3 @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(100,plain,
( ( ! [V: $i,Y: $i] :
( ~ ( program @ V )
| ~ ( program_halts2_halts2_outputs @ V @ ( f4 @ V ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ V @ ( f4 @ V ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ Y @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(101,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( program_decides @ X )
| ~ ( program @ Y )
| ( decides @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(102,plain,
( ( ! [X: $i] :
( ( program_decides @ X )
| ( program @ ( f2 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(103,plain,
( ( ! [X: $i] :
( ( program_decides @ X )
| ~ ( decides @ X @ ( f2 @ X ) @ ( f1 @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(104,plain,
( ( ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program @ X ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(105,plain,
( ( ! [X: $i] :
( ~ ( program_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( program_program_decides @ X )
| ~ ( program @ X )
| ~ ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(107,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( algorithm @ X ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(108,plain,
( ( ! [X: $i] :
( ~ ( algorithm_program_decides @ X )
| ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(109,plain,
( ( ! [X: $i] :
( ( algorithm_program_decides @ X )
| ~ ( algorithm @ X )
| ~ ( program_decides @ X ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_halts2 @ X @ Y )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ( program_halts2 @ X @ Y )
| ~ ( program @ X )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( halts3 @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( halts3_outputs @ X @ Y @ Z @ W )
| ( outputs @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ( halts3_outputs @ X @ Y @ Z @ W )
| ~ ( halts3 @ X @ Y @ Z )
| ~ ( outputs @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ( program @ X ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( program_not_halts2 @ X @ Y )
| ~ ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ( program_not_halts2 @ X @ Y )
| ~ ( program @ X )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(119,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( halts2 @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(120,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( halts2_outputs @ X @ Y @ W )
| ( outputs @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ( halts2_outputs @ X @ Y @ W )
| ~ ( halts2 @ X @ Y )
| ~ ( outputs @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_halts2 @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(124,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(copy,[status(thm)],[56]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( program_not_halts2 @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(126,plain,
( ( ! [X: $i,Y: $i,Z: $i,W: $i] :
( ~ ( program_not_halts2_halts3_outputs @ X @ Y @ Z @ W )
| ( halts3_outputs @ X @ Y @ Z @ W ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(127,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(copy,[status(thm)],[53]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( program_halts2 @ Y @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(129,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(130,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(copy,[status(thm)],[50]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( program_not_halts2 @ Y @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i,W: $i] :
( ~ ( program_not_halts2_halts2_outputs @ X @ Y @ W )
| ( halts2_outputs @ X @ Y @ W ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(133,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(copy,[status(thm)],[47]) ).
thf(134,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[90]) ).
thf(135,plain,
! [SV1: $i] :
( ( ~ ( algorithm_program_decides @ SV1 )
| ( program_program_decides @ c1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(136,plain,
! [SV2: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( program_program_decides @ SV2 )
| ( program_halts2_halts3_outputs @ SV2 @ SY103 @ SY104 @ good ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(137,plain,
! [SV3: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( program_program_decides @ SV3 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SY105 @ SY106 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(138,plain,
! [SV4: $i] :
( ( ~ ( program @ SV4 )
| ~ ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
| ( program @ c2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(139,plain,
! [SV5: $i] :
( ( ! [SY107: $i] :
( ~ ( program @ SV5 )
| ~ ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SY107 @ good ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(140,plain,
! [SV6: $i] :
( ( ! [SY108: $i] :
( ~ ( program @ SV6 )
| ~ ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SY108 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(141,plain,
! [SV7: $i] :
( ( ~ ( program @ SV7 )
| ~ ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
| ( program @ c3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(142,plain,
! [SV8: $i] :
( ( ! [SY109: $i] :
( ~ ( program @ SV8 )
| ~ ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SY109 @ SY109 )
| ( halts2 @ c3 @ SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(143,plain,
! [SV9: $i] :
( ( ! [SY110: $i] :
( ~ ( program @ SV9 )
| ~ ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SY110 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(144,plain,
! [SV10: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( program_decides @ SV10 )
| ~ ( program @ SY111 )
| ( decides @ SV10 @ SY111 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(145,plain,
! [SV11: $i] :
( ( ( program_decides @ SV11 )
| ( program @ ( f2 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(146,plain,
! [SV12: $i] :
( ( ( program_decides @ SV12 )
| ~ ( decides @ SV12 @ ( f2 @ SV12 ) @ ( f1 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(147,plain,
! [SV13: $i] :
( ( ~ ( program_program_decides @ SV13 )
| ( program @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(148,plain,
! [SV14: $i] :
( ( ~ ( program_program_decides @ SV14 )
| ( program_decides @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(149,plain,
! [SV15: $i] :
( ( ( program_program_decides @ SV15 )
| ~ ( program @ SV15 )
| ~ ( program_decides @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(150,plain,
! [SV16: $i] :
( ( ~ ( algorithm_program_decides @ SV16 )
| ( algorithm @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(151,plain,
! [SV17: $i] :
( ( ~ ( algorithm_program_decides @ SV17 )
| ( program_decides @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(152,plain,
! [SV18: $i] :
( ( ( algorithm_program_decides @ SV18 )
| ~ ( algorithm @ SV18 )
| ~ ( program_decides @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(153,plain,
! [SV19: $i] :
( ( ! [SY113: $i] :
( ~ ( program_halts2 @ SV19 @ SY113 )
| ( program @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(154,plain,
! [SV20: $i] :
( ( ! [SY114: $i] :
( ~ ( program_halts2 @ SV20 @ SY114 )
| ( halts2 @ SV20 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(155,plain,
! [SV21: $i] :
( ( ! [SY115: $i] :
( ( program_halts2 @ SV21 @ SY115 )
| ~ ( program @ SV21 )
| ~ ( halts2 @ SV21 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(156,plain,
! [SV22: $i] :
( ( ! [SY116: $i,SY117: $i,SY118: $i] :
( ~ ( halts3_outputs @ SV22 @ SY116 @ SY117 @ SY118 )
| ( halts3 @ SV22 @ SY116 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(157,plain,
! [SV23: $i] :
( ( ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ( halts3_outputs @ SV23 @ SY119 @ SY120 @ SY121 )
| ( outputs @ SV23 @ SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(158,plain,
! [SV24: $i] :
( ( ! [SY122: $i,SY123: $i,SY124: $i] :
( ( halts3_outputs @ SV24 @ SY122 @ SY123 @ SY124 )
| ~ ( halts3 @ SV24 @ SY122 @ SY123 )
| ~ ( outputs @ SV24 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(159,plain,
! [SV25: $i] :
( ( ! [SY125: $i] :
( ~ ( program_not_halts2 @ SV25 @ SY125 )
| ( program @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(160,plain,
! [SV26: $i] :
( ( ! [SY126: $i] :
( ~ ( program_not_halts2 @ SV26 @ SY126 )
| ~ ( halts2 @ SV26 @ SY126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(161,plain,
! [SV27: $i] :
( ( ! [SY127: $i] :
( ( program_not_halts2 @ SV27 @ SY127 )
| ~ ( program @ SV27 )
| ( halts2 @ SV27 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(162,plain,
! [SV28: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( halts2_outputs @ SV28 @ SY128 @ SY129 )
| ( halts2 @ SV28 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(163,plain,
! [SV29: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( halts2_outputs @ SV29 @ SY130 @ SY131 )
| ( outputs @ SV29 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(164,plain,
! [SV30: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ( halts2_outputs @ SV30 @ SY132 @ SY133 )
| ~ ( halts2 @ SV30 @ SY132 )
| ~ ( outputs @ SV30 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(165,plain,
! [SV31: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i] :
( ~ ( program_halts2_halts3_outputs @ SV31 @ SY134 @ SY135 @ SY136 )
| ( program_halts2 @ SY134 @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(166,plain,
! [SV32: $i] :
( ( ! [SY137: $i,SY138: $i,SY139: $i] :
( ~ ( program_halts2_halts3_outputs @ SV32 @ SY137 @ SY138 @ SY139 )
| ( halts3_outputs @ SV32 @ SY137 @ SY138 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(167,plain,
! [SV33: $i] :
( ( ! [SY140: $i,SY141: $i,SY142: $i] :
( ( program_halts2_halts3_outputs @ SV33 @ SY140 @ SY141 @ SY142 )
| ~ ( program_halts2 @ SY140 @ SY141 )
| ~ ( halts3_outputs @ SV33 @ SY140 @ SY141 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(168,plain,
! [SV34: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV34 @ SY143 @ SY144 @ SY145 )
| ( program_not_halts2 @ SY143 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(169,plain,
! [SV35: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV35 @ SY146 @ SY147 @ SY148 )
| ( halts3_outputs @ SV35 @ SY146 @ SY147 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(170,plain,
! [SV36: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i] :
( ( program_not_halts2_halts3_outputs @ SV36 @ SY149 @ SY150 @ SY151 )
| ~ ( program_not_halts2 @ SY149 @ SY150 )
| ~ ( halts3_outputs @ SV36 @ SY149 @ SY150 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(171,plain,
! [SV37: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ( program_halts2_halts2_outputs @ SV37 @ SY152 @ SY153 )
| ( program_halts2 @ SY152 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(172,plain,
! [SV38: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ~ ( program_halts2_halts2_outputs @ SV38 @ SY154 @ SY155 )
| ( halts2_outputs @ SV38 @ SY154 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(173,plain,
! [SV39: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ( program_halts2_halts2_outputs @ SV39 @ SY156 @ SY157 )
| ~ ( program_halts2 @ SY156 @ SY156 )
| ~ ( halts2_outputs @ SV39 @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(174,plain,
! [SV40: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV40 @ SY158 @ SY159 )
| ( program_not_halts2 @ SY158 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(175,plain,
! [SV41: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV41 @ SY160 @ SY161 )
| ( halts2_outputs @ SV41 @ SY160 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(176,plain,
! [SV42: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ( program_not_halts2_halts2_outputs @ SV42 @ SY162 @ SY163 )
| ~ ( program_not_halts2 @ SY162 @ SY162 )
| ~ ( halts2_outputs @ SV42 @ SY162 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(177,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(178,plain,
! [SV1: $i] :
( ( ( ~ ( algorithm_program_decides @ SV1 ) )
= $true )
| ( ( program_program_decides @ c1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(179,plain,
! [SV43: $i,SV2: $i] :
( ( ! [SY164: $i] :
( ~ ( program_program_decides @ SV2 )
| ( program_halts2_halts3_outputs @ SV2 @ SV43 @ SY164 @ good ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(180,plain,
! [SV44: $i,SV3: $i] :
( ( ! [SY165: $i] :
( ~ ( program_program_decides @ SV3 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV44 @ SY165 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(181,plain,
! [SV4: $i] :
( ( ( ~ ( program @ SV4 ) )
= $true )
| ( ( ~ ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
| ( program @ c2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(182,plain,
! [SV45: $i,SV5: $i] :
( ( ~ ( program @ SV5 )
| ~ ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SV45 @ good ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(183,plain,
! [SV46: $i,SV6: $i] :
( ( ~ ( program @ SV6 )
| ~ ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(184,plain,
! [SV7: $i] :
( ( ( ~ ( program @ SV7 ) )
= $true )
| ( ( ~ ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
| ( program @ c3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(185,plain,
! [SV47: $i,SV8: $i] :
( ( ~ ( program @ SV8 )
| ~ ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(186,plain,
! [SV48: $i,SV9: $i] :
( ( ~ ( program @ SV9 )
| ~ ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(187,plain,
! [SV49: $i,SV10: $i] :
( ( ! [SY166: $i] :
( ~ ( program_decides @ SV10 )
| ~ ( program @ SV49 )
| ( decides @ SV10 @ SV49 @ SY166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(188,plain,
! [SV11: $i] :
( ( ( program_decides @ SV11 )
= $true )
| ( ( program @ ( f2 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(189,plain,
! [SV12: $i] :
( ( ( program_decides @ SV12 )
= $true )
| ( ( ~ ( decides @ SV12 @ ( f2 @ SV12 ) @ ( f1 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(190,plain,
! [SV13: $i] :
( ( ( ~ ( program_program_decides @ SV13 ) )
= $true )
| ( ( program @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(191,plain,
! [SV14: $i] :
( ( ( ~ ( program_program_decides @ SV14 ) )
= $true )
| ( ( program_decides @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(192,plain,
! [SV15: $i] :
( ( ( program_program_decides @ SV15 )
= $true )
| ( ( ~ ( program @ SV15 )
| ~ ( program_decides @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(193,plain,
! [SV16: $i] :
( ( ( ~ ( algorithm_program_decides @ SV16 ) )
= $true )
| ( ( algorithm @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(194,plain,
! [SV17: $i] :
( ( ( ~ ( algorithm_program_decides @ SV17 ) )
= $true )
| ( ( program_decides @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(195,plain,
! [SV18: $i] :
( ( ( algorithm_program_decides @ SV18 )
= $true )
| ( ( ~ ( algorithm @ SV18 )
| ~ ( program_decides @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(196,plain,
! [SV50: $i,SV19: $i] :
( ( ~ ( program_halts2 @ SV19 @ SV50 )
| ( program @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(197,plain,
! [SV51: $i,SV20: $i] :
( ( ~ ( program_halts2 @ SV20 @ SV51 )
| ( halts2 @ SV20 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(198,plain,
! [SV52: $i,SV21: $i] :
( ( ( program_halts2 @ SV21 @ SV52 )
| ~ ( program @ SV21 )
| ~ ( halts2 @ SV21 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(199,plain,
! [SV53: $i,SV22: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( halts3_outputs @ SV22 @ SV53 @ SY167 @ SY168 )
| ( halts3 @ SV22 @ SV53 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(200,plain,
! [SV54: $i,SV23: $i] :
( ( ! [SY169: $i,SY170: $i] :
( ~ ( halts3_outputs @ SV23 @ SV54 @ SY169 @ SY170 )
| ( outputs @ SV23 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(201,plain,
! [SV55: $i,SV24: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( halts3_outputs @ SV24 @ SV55 @ SY171 @ SY172 )
| ~ ( halts3 @ SV24 @ SV55 @ SY171 )
| ~ ( outputs @ SV24 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(202,plain,
! [SV56: $i,SV25: $i] :
( ( ~ ( program_not_halts2 @ SV25 @ SV56 )
| ( program @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(203,plain,
! [SV57: $i,SV26: $i] :
( ( ~ ( program_not_halts2 @ SV26 @ SV57 )
| ~ ( halts2 @ SV26 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(204,plain,
! [SV58: $i,SV27: $i] :
( ( ( program_not_halts2 @ SV27 @ SV58 )
| ~ ( program @ SV27 )
| ( halts2 @ SV27 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(205,plain,
! [SV59: $i,SV28: $i] :
( ( ! [SY173: $i] :
( ~ ( halts2_outputs @ SV28 @ SV59 @ SY173 )
| ( halts2 @ SV28 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(206,plain,
! [SV60: $i,SV29: $i] :
( ( ! [SY174: $i] :
( ~ ( halts2_outputs @ SV29 @ SV60 @ SY174 )
| ( outputs @ SV29 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(207,plain,
! [SV61: $i,SV30: $i] :
( ( ! [SY175: $i] :
( ( halts2_outputs @ SV30 @ SV61 @ SY175 )
| ~ ( halts2 @ SV30 @ SV61 )
| ~ ( outputs @ SV30 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(208,plain,
! [SV62: $i,SV31: $i] :
( ( ! [SY176: $i,SY177: $i] :
( ~ ( program_halts2_halts3_outputs @ SV31 @ SV62 @ SY176 @ SY177 )
| ( program_halts2 @ SV62 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(209,plain,
! [SV63: $i,SV32: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ~ ( program_halts2_halts3_outputs @ SV32 @ SV63 @ SY178 @ SY179 )
| ( halts3_outputs @ SV32 @ SV63 @ SY178 @ SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(210,plain,
! [SV64: $i,SV33: $i] :
( ( ! [SY180: $i,SY181: $i] :
( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SY180 @ SY181 )
| ~ ( program_halts2 @ SV64 @ SY180 )
| ~ ( halts3_outputs @ SV33 @ SV64 @ SY180 @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(211,plain,
! [SV65: $i,SV34: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV34 @ SV65 @ SY182 @ SY183 )
| ( program_not_halts2 @ SV65 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(212,plain,
! [SV66: $i,SV35: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV35 @ SV66 @ SY184 @ SY185 )
| ( halts3_outputs @ SV35 @ SV66 @ SY184 @ SY185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(213,plain,
! [SV67: $i,SV36: $i] :
( ( ! [SY186: $i,SY187: $i] :
( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SY186 @ SY187 )
| ~ ( program_not_halts2 @ SV67 @ SY186 )
| ~ ( halts3_outputs @ SV36 @ SV67 @ SY186 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(214,plain,
! [SV68: $i,SV37: $i] :
( ( ! [SY188: $i] :
( ~ ( program_halts2_halts2_outputs @ SV37 @ SV68 @ SY188 )
| ( program_halts2 @ SV68 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(215,plain,
! [SV69: $i,SV38: $i] :
( ( ! [SY189: $i] :
( ~ ( program_halts2_halts2_outputs @ SV38 @ SV69 @ SY189 )
| ( halts2_outputs @ SV38 @ SV69 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(216,plain,
! [SV70: $i,SV39: $i] :
( ( ! [SY190: $i] :
( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SY190 )
| ~ ( program_halts2 @ SV70 @ SV70 )
| ~ ( halts2_outputs @ SV39 @ SV70 @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(217,plain,
! [SV71: $i,SV40: $i] :
( ( ! [SY191: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV40 @ SV71 @ SY191 )
| ( program_not_halts2 @ SV71 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(218,plain,
! [SV72: $i,SV41: $i] :
( ( ! [SY192: $i] :
( ~ ( program_not_halts2_halts2_outputs @ SV41 @ SV72 @ SY192 )
| ( halts2_outputs @ SV41 @ SV72 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(219,plain,
! [SV73: $i,SV42: $i] :
( ( ! [SY193: $i] :
( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SY193 )
| ~ ( program_not_halts2 @ SV73 @ SV73 )
| ~ ( halts2_outputs @ SV42 @ SV73 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(220,plain,
! [SV1: $i] :
( ( ( algorithm_program_decides @ SV1 )
= $false )
| ( ( program_program_decides @ c1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(221,plain,
! [SV74: $i,SV43: $i,SV2: $i] :
( ( ~ ( program_program_decides @ SV2 )
| ( program_halts2_halts3_outputs @ SV2 @ SV43 @ SV74 @ good ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(222,plain,
! [SV75: $i,SV44: $i,SV3: $i] :
( ( ~ ( program_program_decides @ SV3 )
| ( program_not_halts2_halts3_outputs @ SV3 @ SV44 @ SV75 @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(223,plain,
! [SV4: $i] :
( ( ( program @ SV4 )
= $false )
| ( ( ~ ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
| ( program @ c2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(224,plain,
! [SV45: $i,SV5: $i] :
( ( ( ~ ( program @ SV5 ) )
= $true )
| ( ( ~ ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SV45 @ good ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(225,plain,
! [SV46: $i,SV6: $i] :
( ( ( ~ ( program @ SV6 ) )
= $true )
| ( ( ~ ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(226,plain,
! [SV7: $i] :
( ( ( program @ SV7 )
= $false )
| ( ( ~ ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
| ( program @ c3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(227,plain,
! [SV47: $i,SV8: $i] :
( ( ( ~ ( program @ SV8 ) )
= $true )
| ( ( ~ ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(228,plain,
! [SV48: $i,SV9: $i] :
( ( ( ~ ( program @ SV9 ) )
= $true )
| ( ( ~ ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(229,plain,
! [SV76: $i,SV49: $i,SV10: $i] :
( ( ~ ( program_decides @ SV10 )
| ~ ( program @ SV49 )
| ( decides @ SV10 @ SV49 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(230,plain,
! [SV12: $i] :
( ( ( decides @ SV12 @ ( f2 @ SV12 ) @ ( f1 @ SV12 ) )
= $false )
| ( ( program_decides @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(231,plain,
! [SV13: $i] :
( ( ( program_program_decides @ SV13 )
= $false )
| ( ( program @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(232,plain,
! [SV14: $i] :
( ( ( program_program_decides @ SV14 )
= $false )
| ( ( program_decides @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(233,plain,
! [SV15: $i] :
( ( ( ~ ( program @ SV15 ) )
= $true )
| ( ( ~ ( program_decides @ SV15 ) )
= $true )
| ( ( program_program_decides @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(234,plain,
! [SV16: $i] :
( ( ( algorithm_program_decides @ SV16 )
= $false )
| ( ( algorithm @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(235,plain,
! [SV17: $i] :
( ( ( algorithm_program_decides @ SV17 )
= $false )
| ( ( program_decides @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(236,plain,
! [SV18: $i] :
( ( ( ~ ( algorithm @ SV18 ) )
= $true )
| ( ( ~ ( program_decides @ SV18 ) )
= $true )
| ( ( algorithm_program_decides @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(237,plain,
! [SV50: $i,SV19: $i] :
( ( ( ~ ( program_halts2 @ SV19 @ SV50 ) )
= $true )
| ( ( program @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(238,plain,
! [SV51: $i,SV20: $i] :
( ( ( ~ ( program_halts2 @ SV20 @ SV51 ) )
= $true )
| ( ( halts2 @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(239,plain,
! [SV52: $i,SV21: $i] :
( ( ( program_halts2 @ SV21 @ SV52 )
= $true )
| ( ( ~ ( program @ SV21 )
| ~ ( halts2 @ SV21 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(240,plain,
! [SV77: $i,SV53: $i,SV22: $i] :
( ( ! [SY194: $i] :
( ~ ( halts3_outputs @ SV22 @ SV53 @ SV77 @ SY194 )
| ( halts3 @ SV22 @ SV53 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(241,plain,
! [SV78: $i,SV54: $i,SV23: $i] :
( ( ! [SY195: $i] :
( ~ ( halts3_outputs @ SV23 @ SV54 @ SV78 @ SY195 )
| ( outputs @ SV23 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(242,plain,
! [SV79: $i,SV55: $i,SV24: $i] :
( ( ! [SY196: $i] :
( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SY196 )
| ~ ( halts3 @ SV24 @ SV55 @ SV79 )
| ~ ( outputs @ SV24 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(243,plain,
! [SV56: $i,SV25: $i] :
( ( ( ~ ( program_not_halts2 @ SV25 @ SV56 ) )
= $true )
| ( ( program @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(244,plain,
! [SV57: $i,SV26: $i] :
( ( ( ~ ( program_not_halts2 @ SV26 @ SV57 ) )
= $true )
| ( ( ~ ( halts2 @ SV26 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(245,plain,
! [SV58: $i,SV27: $i] :
( ( ( program_not_halts2 @ SV27 @ SV58 )
= $true )
| ( ( ~ ( program @ SV27 )
| ( halts2 @ SV27 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(246,plain,
! [SV80: $i,SV59: $i,SV28: $i] :
( ( ~ ( halts2_outputs @ SV28 @ SV59 @ SV80 )
| ( halts2 @ SV28 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(247,plain,
! [SV81: $i,SV60: $i,SV29: $i] :
( ( ~ ( halts2_outputs @ SV29 @ SV60 @ SV81 )
| ( outputs @ SV29 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(248,plain,
! [SV82: $i,SV61: $i,SV30: $i] :
( ( ( halts2_outputs @ SV30 @ SV61 @ SV82 )
| ~ ( halts2 @ SV30 @ SV61 )
| ~ ( outputs @ SV30 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(249,plain,
! [SV83: $i,SV62: $i,SV31: $i] :
( ( ! [SY197: $i] :
( ~ ( program_halts2_halts3_outputs @ SV31 @ SV62 @ SV83 @ SY197 )
| ( program_halts2 @ SV62 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(250,plain,
! [SV84: $i,SV63: $i,SV32: $i] :
( ( ! [SY198: $i] :
( ~ ( program_halts2_halts3_outputs @ SV32 @ SV63 @ SV84 @ SY198 )
| ( halts3_outputs @ SV32 @ SV63 @ SV84 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(251,plain,
! [SV85: $i,SV64: $i,SV33: $i] :
( ( ! [SY199: $i] :
( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SY199 )
| ~ ( program_halts2 @ SV64 @ SV85 )
| ~ ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(252,plain,
! [SV86: $i,SV65: $i,SV34: $i] :
( ( ! [SY200: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV34 @ SV65 @ SV86 @ SY200 )
| ( program_not_halts2 @ SV65 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(253,plain,
! [SV87: $i,SV66: $i,SV35: $i] :
( ( ! [SY201: $i] :
( ~ ( program_not_halts2_halts3_outputs @ SV35 @ SV66 @ SV87 @ SY201 )
| ( halts3_outputs @ SV35 @ SV66 @ SV87 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(254,plain,
! [SV88: $i,SV67: $i,SV36: $i] :
( ( ! [SY202: $i] :
( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SY202 )
| ~ ( program_not_halts2 @ SV67 @ SV88 )
| ~ ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(255,plain,
! [SV89: $i,SV68: $i,SV37: $i] :
( ( ~ ( program_halts2_halts2_outputs @ SV37 @ SV68 @ SV89 )
| ( program_halts2 @ SV68 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(256,plain,
! [SV90: $i,SV69: $i,SV38: $i] :
( ( ~ ( program_halts2_halts2_outputs @ SV38 @ SV69 @ SV90 )
| ( halts2_outputs @ SV38 @ SV69 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(257,plain,
! [SV91: $i,SV70: $i,SV39: $i] :
( ( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SV91 )
| ~ ( program_halts2 @ SV70 @ SV70 )
| ~ ( halts2_outputs @ SV39 @ SV70 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(258,plain,
! [SV92: $i,SV71: $i,SV40: $i] :
( ( ~ ( program_not_halts2_halts2_outputs @ SV40 @ SV71 @ SV92 )
| ( program_not_halts2 @ SV71 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(259,plain,
! [SV93: $i,SV72: $i,SV41: $i] :
( ( ~ ( program_not_halts2_halts2_outputs @ SV41 @ SV72 @ SV93 )
| ( halts2_outputs @ SV41 @ SV72 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(260,plain,
! [SV94: $i,SV73: $i,SV42: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SV94 )
| ~ ( program_not_halts2 @ SV73 @ SV73 )
| ~ ( halts2_outputs @ SV42 @ SV73 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(261,plain,
! [SV74: $i,SV43: $i,SV2: $i] :
( ( ( ~ ( program_program_decides @ SV2 ) )
= $true )
| ( ( program_halts2_halts3_outputs @ SV2 @ SV43 @ SV74 @ good )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(262,plain,
! [SV75: $i,SV44: $i,SV3: $i] :
( ( ( ~ ( program_program_decides @ SV3 ) )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV44 @ SV75 @ bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(263,plain,
! [SV4: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
| ( program @ c2 ) )
= $true )
| ( ( program @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(264,plain,
! [SV45: $i,SV5: $i] :
( ( ( program @ SV5 )
= $false )
| ( ( ~ ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SV45 @ good ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(265,plain,
! [SV46: $i,SV6: $i] :
( ( ( program @ SV6 )
= $false )
| ( ( ~ ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
| ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(266,plain,
! [SV7: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
| ( program @ c3 ) )
= $true )
| ( ( program @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(267,plain,
! [SV47: $i,SV8: $i] :
( ( ( program @ SV8 )
= $false )
| ( ( ~ ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(268,plain,
! [SV48: $i,SV9: $i] :
( ( ( program @ SV9 )
= $false )
| ( ( ~ ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
| ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(269,plain,
! [SV76: $i,SV49: $i,SV10: $i] :
( ( ( ~ ( program_decides @ SV10 ) )
= $true )
| ( ( ~ ( program @ SV49 )
| ( decides @ SV10 @ SV49 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(270,plain,
! [SV15: $i] :
( ( ( program @ SV15 )
= $false )
| ( ( ~ ( program_decides @ SV15 ) )
= $true )
| ( ( program_program_decides @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(271,plain,
! [SV18: $i] :
( ( ( algorithm @ SV18 )
= $false )
| ( ( ~ ( program_decides @ SV18 ) )
= $true )
| ( ( algorithm_program_decides @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(272,plain,
! [SV50: $i,SV19: $i] :
( ( ( program_halts2 @ SV19 @ SV50 )
= $false )
| ( ( program @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(273,plain,
! [SV51: $i,SV20: $i] :
( ( ( program_halts2 @ SV20 @ SV51 )
= $false )
| ( ( halts2 @ SV20 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(274,plain,
! [SV52: $i,SV21: $i] :
( ( ( ~ ( program @ SV21 ) )
= $true )
| ( ( ~ ( halts2 @ SV21 @ SV52 ) )
= $true )
| ( ( program_halts2 @ SV21 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(275,plain,
! [SV95: $i,SV77: $i,SV53: $i,SV22: $i] :
( ( ~ ( halts3_outputs @ SV22 @ SV53 @ SV77 @ SV95 )
| ( halts3 @ SV22 @ SV53 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(276,plain,
! [SV96: $i,SV78: $i,SV54: $i,SV23: $i] :
( ( ~ ( halts3_outputs @ SV23 @ SV54 @ SV78 @ SV96 )
| ( outputs @ SV23 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(277,plain,
! [SV97: $i,SV79: $i,SV55: $i,SV24: $i] :
( ( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SV97 )
| ~ ( halts3 @ SV24 @ SV55 @ SV79 )
| ~ ( outputs @ SV24 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(278,plain,
! [SV56: $i,SV25: $i] :
( ( ( program_not_halts2 @ SV25 @ SV56 )
= $false )
| ( ( program @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(279,plain,
! [SV57: $i,SV26: $i] :
( ( ( program_not_halts2 @ SV26 @ SV57 )
= $false )
| ( ( ~ ( halts2 @ SV26 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(280,plain,
! [SV58: $i,SV27: $i] :
( ( ( ~ ( program @ SV27 ) )
= $true )
| ( ( halts2 @ SV27 @ SV58 )
= $true )
| ( ( program_not_halts2 @ SV27 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(281,plain,
! [SV80: $i,SV59: $i,SV28: $i] :
( ( ( ~ ( halts2_outputs @ SV28 @ SV59 @ SV80 ) )
= $true )
| ( ( halts2 @ SV28 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(282,plain,
! [SV81: $i,SV60: $i,SV29: $i] :
( ( ( ~ ( halts2_outputs @ SV29 @ SV60 @ SV81 ) )
= $true )
| ( ( outputs @ SV29 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(283,plain,
! [SV82: $i,SV61: $i,SV30: $i] :
( ( ( halts2_outputs @ SV30 @ SV61 @ SV82 )
= $true )
| ( ( ~ ( halts2 @ SV30 @ SV61 )
| ~ ( outputs @ SV30 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(284,plain,
! [SV98: $i,SV83: $i,SV62: $i,SV31: $i] :
( ( ~ ( program_halts2_halts3_outputs @ SV31 @ SV62 @ SV83 @ SV98 )
| ( program_halts2 @ SV62 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(285,plain,
! [SV99: $i,SV84: $i,SV63: $i,SV32: $i] :
( ( ~ ( program_halts2_halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 )
| ( halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(286,plain,
! [SV100: $i,SV85: $i,SV64: $i,SV33: $i] :
( ( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
| ~ ( program_halts2 @ SV64 @ SV85 )
| ~ ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(287,plain,
! [SV101: $i,SV86: $i,SV65: $i,SV34: $i] :
( ( ~ ( program_not_halts2_halts3_outputs @ SV34 @ SV65 @ SV86 @ SV101 )
| ( program_not_halts2 @ SV65 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(288,plain,
! [SV102: $i,SV87: $i,SV66: $i,SV35: $i] :
( ( ~ ( program_not_halts2_halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 )
| ( halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(289,plain,
! [SV103: $i,SV88: $i,SV67: $i,SV36: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
| ~ ( program_not_halts2 @ SV67 @ SV88 )
| ~ ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(290,plain,
! [SV89: $i,SV68: $i,SV37: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV37 @ SV68 @ SV89 ) )
= $true )
| ( ( program_halts2 @ SV68 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(291,plain,
! [SV90: $i,SV69: $i,SV38: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV38 @ SV69 @ SV90 ) )
= $true )
| ( ( halts2_outputs @ SV38 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(292,plain,
! [SV91: $i,SV70: $i,SV39: $i] :
( ( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SV91 )
= $true )
| ( ( ~ ( program_halts2 @ SV70 @ SV70 )
| ~ ( halts2_outputs @ SV39 @ SV70 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(293,plain,
! [SV92: $i,SV71: $i,SV40: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV40 @ SV71 @ SV92 ) )
= $true )
| ( ( program_not_halts2 @ SV71 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(294,plain,
! [SV93: $i,SV72: $i,SV41: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV41 @ SV72 @ SV93 ) )
= $true )
| ( ( halts2_outputs @ SV41 @ SV72 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(295,plain,
! [SV94: $i,SV73: $i,SV42: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SV94 )
= $true )
| ( ( ~ ( program_not_halts2 @ SV73 @ SV73 )
| ~ ( halts2_outputs @ SV42 @ SV73 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(296,plain,
! [SV74: $i,SV43: $i,SV2: $i] :
( ( ( program_program_decides @ SV2 )
= $false )
| ( ( program_halts2_halts3_outputs @ SV2 @ SV43 @ SV74 @ good )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(297,plain,
! [SV75: $i,SV44: $i,SV3: $i] :
( ( ( program_program_decides @ SV3 )
= $false )
| ( ( program_not_halts2_halts3_outputs @ SV3 @ SV44 @ SV75 @ bad )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(298,plain,
! [SV4: $i] :
( ( ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
| ( program @ c2 ) )
= $true )
| ( ( program @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(299,plain,
! [SV45: $i,SV5: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SV45 @ good ) )
= $true )
| ( ( program @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(300,plain,
! [SV46: $i,SV6: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad ) )
= $true )
| ( ( program @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(301,plain,
! [SV7: $i] :
( ( ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
| ( program @ c3 ) )
= $true )
| ( ( program @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(302,plain,
! [SV47: $i,SV8: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(303,plain,
! [SV48: $i,SV9: $i] :
( ( ( ~ ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good ) )
= $true )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad ) )
= $true )
| ( ( program @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(304,plain,
! [SV76: $i,SV49: $i,SV10: $i] :
( ( ( program_decides @ SV10 )
= $false )
| ( ( ~ ( program @ SV49 )
| ( decides @ SV10 @ SV49 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(305,plain,
! [SV15: $i] :
( ( ( program_decides @ SV15 )
= $false )
| ( ( program @ SV15 )
= $false )
| ( ( program_program_decides @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(306,plain,
! [SV18: $i] :
( ( ( program_decides @ SV18 )
= $false )
| ( ( algorithm @ SV18 )
= $false )
| ( ( algorithm_program_decides @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(307,plain,
! [SV52: $i,SV21: $i] :
( ( ( program @ SV21 )
= $false )
| ( ( ~ ( halts2 @ SV21 @ SV52 ) )
= $true )
| ( ( program_halts2 @ SV21 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(308,plain,
! [SV95: $i,SV77: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( halts3_outputs @ SV22 @ SV53 @ SV77 @ SV95 ) )
= $true )
| ( ( halts3 @ SV22 @ SV53 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(309,plain,
! [SV96: $i,SV78: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( halts3_outputs @ SV23 @ SV54 @ SV78 @ SV96 ) )
= $true )
| ( ( outputs @ SV23 @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(310,plain,
! [SV97: $i,SV79: $i,SV55: $i,SV24: $i] :
( ( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SV97 )
= $true )
| ( ( ~ ( halts3 @ SV24 @ SV55 @ SV79 )
| ~ ( outputs @ SV24 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(311,plain,
! [SV57: $i,SV26: $i] :
( ( ( halts2 @ SV26 @ SV57 )
= $false )
| ( ( program_not_halts2 @ SV26 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(312,plain,
! [SV58: $i,SV27: $i] :
( ( ( program @ SV27 )
= $false )
| ( ( halts2 @ SV27 @ SV58 )
= $true )
| ( ( program_not_halts2 @ SV27 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(313,plain,
! [SV80: $i,SV59: $i,SV28: $i] :
( ( ( halts2_outputs @ SV28 @ SV59 @ SV80 )
= $false )
| ( ( halts2 @ SV28 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(314,plain,
! [SV81: $i,SV60: $i,SV29: $i] :
( ( ( halts2_outputs @ SV29 @ SV60 @ SV81 )
= $false )
| ( ( outputs @ SV29 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(315,plain,
! [SV82: $i,SV61: $i,SV30: $i] :
( ( ( ~ ( halts2 @ SV30 @ SV61 ) )
= $true )
| ( ( ~ ( outputs @ SV30 @ SV82 ) )
= $true )
| ( ( halts2_outputs @ SV30 @ SV61 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(316,plain,
! [SV98: $i,SV83: $i,SV62: $i,SV31: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV31 @ SV62 @ SV83 @ SV98 ) )
= $true )
| ( ( program_halts2 @ SV62 @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(317,plain,
! [SV99: $i,SV84: $i,SV63: $i,SV32: $i] :
( ( ( ~ ( program_halts2_halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 ) )
= $true )
| ( ( halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(318,plain,
! [SV100: $i,SV85: $i,SV64: $i,SV33: $i] :
( ( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
= $true )
| ( ( ~ ( program_halts2 @ SV64 @ SV85 )
| ~ ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(319,plain,
! [SV101: $i,SV86: $i,SV65: $i,SV34: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV34 @ SV65 @ SV86 @ SV101 ) )
= $true )
| ( ( program_not_halts2 @ SV65 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(320,plain,
! [SV102: $i,SV87: $i,SV66: $i,SV35: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 ) )
= $true )
| ( ( halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(321,plain,
! [SV103: $i,SV88: $i,SV67: $i,SV36: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
= $true )
| ( ( ~ ( program_not_halts2 @ SV67 @ SV88 )
| ~ ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(322,plain,
! [SV89: $i,SV68: $i,SV37: $i] :
( ( ( program_halts2_halts2_outputs @ SV37 @ SV68 @ SV89 )
= $false )
| ( ( program_halts2 @ SV68 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(323,plain,
! [SV90: $i,SV69: $i,SV38: $i] :
( ( ( program_halts2_halts2_outputs @ SV38 @ SV69 @ SV90 )
= $false )
| ( ( halts2_outputs @ SV38 @ SV69 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(324,plain,
! [SV91: $i,SV39: $i,SV70: $i] :
( ( ( ~ ( program_halts2 @ SV70 @ SV70 ) )
= $true )
| ( ( ~ ( halts2_outputs @ SV39 @ SV70 @ SV91 ) )
= $true )
| ( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(325,plain,
! [SV92: $i,SV71: $i,SV40: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV40 @ SV71 @ SV92 )
= $false )
| ( ( program_not_halts2 @ SV71 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(326,plain,
! [SV93: $i,SV72: $i,SV41: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV41 @ SV72 @ SV93 )
= $false )
| ( ( halts2_outputs @ SV41 @ SV72 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(327,plain,
! [SV94: $i,SV42: $i,SV73: $i] :
( ( ( ~ ( program_not_halts2 @ SV73 @ SV73 ) )
= $true )
| ( ( ~ ( halts2_outputs @ SV42 @ SV73 @ SV94 ) )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV4: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad ) )
= $true )
| ( ( program @ c2 )
= $true )
| ( ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
= $false )
| ( ( program @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(329,plain,
! [SV45: $i,SV5: $i] :
( ( ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
| ( program_halts2_halts2_outputs @ c2 @ SV45 @ good ) )
= $true )
| ( ( program @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(330,plain,
! [SV46: $i,SV6: $i] :
( ( ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad ) )
= $true )
| ( ( program @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(331,plain,
! [SV7: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad ) )
= $true )
| ( ( program @ c3 )
= $true )
| ( ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
= $false )
| ( ( program @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(332,plain,
! [SV47: $i,SV8: $i] :
( ( ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
| ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(333,plain,
! [SV48: $i,SV9: $i] :
( ( ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
= $false )
| ( ( ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
| ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad ) )
= $true )
| ( ( program @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(334,plain,
! [SV76: $i,SV10: $i,SV49: $i] :
( ( ( ~ ( program @ SV49 ) )
= $true )
| ( ( decides @ SV10 @ SV49 @ SV76 )
= $true )
| ( ( program_decides @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(335,plain,
! [SV52: $i,SV21: $i] :
( ( ( halts2 @ SV21 @ SV52 )
= $false )
| ( ( program @ SV21 )
= $false )
| ( ( program_halts2 @ SV21 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(336,plain,
! [SV95: $i,SV77: $i,SV53: $i,SV22: $i] :
( ( ( halts3_outputs @ SV22 @ SV53 @ SV77 @ SV95 )
= $false )
| ( ( halts3 @ SV22 @ SV53 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(337,plain,
! [SV96: $i,SV78: $i,SV54: $i,SV23: $i] :
( ( ( halts3_outputs @ SV23 @ SV54 @ SV78 @ SV96 )
= $false )
| ( ( outputs @ SV23 @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(338,plain,
! [SV97: $i,SV79: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( halts3 @ SV24 @ SV55 @ SV79 ) )
= $true )
| ( ( ~ ( outputs @ SV24 @ SV97 ) )
= $true )
| ( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(339,plain,
! [SV82: $i,SV61: $i,SV30: $i] :
( ( ( halts2 @ SV30 @ SV61 )
= $false )
| ( ( ~ ( outputs @ SV30 @ SV82 ) )
= $true )
| ( ( halts2_outputs @ SV30 @ SV61 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(340,plain,
! [SV98: $i,SV83: $i,SV62: $i,SV31: $i] :
( ( ( program_halts2_halts3_outputs @ SV31 @ SV62 @ SV83 @ SV98 )
= $false )
| ( ( program_halts2 @ SV62 @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(341,plain,
! [SV99: $i,SV84: $i,SV63: $i,SV32: $i] :
( ( ( program_halts2_halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 )
= $false )
| ( ( halts3_outputs @ SV32 @ SV63 @ SV84 @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(342,plain,
! [SV100: $i,SV33: $i,SV85: $i,SV64: $i] :
( ( ( ~ ( program_halts2 @ SV64 @ SV85 ) )
= $true )
| ( ( ~ ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 ) )
= $true )
| ( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(343,plain,
! [SV101: $i,SV86: $i,SV65: $i,SV34: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV34 @ SV65 @ SV86 @ SV101 )
= $false )
| ( ( program_not_halts2 @ SV65 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(344,plain,
! [SV102: $i,SV87: $i,SV66: $i,SV35: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 )
= $false )
| ( ( halts3_outputs @ SV35 @ SV66 @ SV87 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(345,plain,
! [SV103: $i,SV36: $i,SV88: $i,SV67: $i] :
( ( ( ~ ( program_not_halts2 @ SV67 @ SV88 ) )
= $true )
| ( ( ~ ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 ) )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(346,plain,
! [SV91: $i,SV39: $i,SV70: $i] :
( ( ( program_halts2 @ SV70 @ SV70 )
= $false )
| ( ( ~ ( halts2_outputs @ SV39 @ SV70 @ SV91 ) )
= $true )
| ( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(347,plain,
! [SV94: $i,SV42: $i,SV73: $i] :
( ( ( program_not_halts2 @ SV73 @ SV73 )
= $false )
| ( ( ~ ( halts2_outputs @ SV42 @ SV73 @ SV94 ) )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(348,plain,
! [SV4: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ bad )
= $false )
| ( ( program @ c2 )
= $true )
| ( ( program_halts2_halts3_outputs @ SV4 @ ( f3 @ SV4 ) @ ( f3 @ SV4 ) @ good )
= $false )
| ( ( program @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(349,plain,
! [SV45: $i,SV5: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad ) )
= $true )
| ( ( program_halts2_halts2_outputs @ c2 @ SV45 @ good )
= $true )
| ( ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
= $false )
| ( ( program @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(350,plain,
! [SV46: $i,SV6: $i] :
( ( ( ~ ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad ) )
= $true )
| ( ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad )
= $true )
| ( ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
= $false )
| ( ( program @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(351,plain,
! [SV7: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ bad )
= $false )
| ( ( program @ c3 )
= $true )
| ( ( program_halts2_halts2_outputs @ SV7 @ ( f4 @ SV7 ) @ good )
= $false )
| ( ( program @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(352,plain,
! [SV47: $i,SV8: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad ) )
= $true )
| ( ( ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true )
| ( ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
= $false )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(353,plain,
! [SV48: $i,SV9: $i] :
( ( ( ~ ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad ) )
= $true )
| ( ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad )
= $true )
| ( ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
= $false )
| ( ( program @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(354,plain,
! [SV76: $i,SV10: $i,SV49: $i] :
( ( ( program @ SV49 )
= $false )
| ( ( decides @ SV10 @ SV49 @ SV76 )
= $true )
| ( ( program_decides @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(355,plain,
! [SV97: $i,SV79: $i,SV55: $i,SV24: $i] :
( ( ( halts3 @ SV24 @ SV55 @ SV79 )
= $false )
| ( ( ~ ( outputs @ SV24 @ SV97 ) )
= $true )
| ( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(356,plain,
! [SV61: $i,SV82: $i,SV30: $i] :
( ( ( outputs @ SV30 @ SV82 )
= $false )
| ( ( halts2 @ SV30 @ SV61 )
= $false )
| ( ( halts2_outputs @ SV30 @ SV61 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(357,plain,
! [SV100: $i,SV33: $i,SV85: $i,SV64: $i] :
( ( ( program_halts2 @ SV64 @ SV85 )
= $false )
| ( ( ~ ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 ) )
= $true )
| ( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(358,plain,
! [SV103: $i,SV36: $i,SV88: $i,SV67: $i] :
( ( ( program_not_halts2 @ SV67 @ SV88 )
= $false )
| ( ( ~ ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 ) )
= $true )
| ( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(359,plain,
! [SV91: $i,SV70: $i,SV39: $i] :
( ( ( halts2_outputs @ SV39 @ SV70 @ SV91 )
= $false )
| ( ( program_halts2 @ SV70 @ SV70 )
= $false )
| ( ( program_halts2_halts2_outputs @ SV39 @ SV70 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(360,plain,
! [SV94: $i,SV73: $i,SV42: $i] :
( ( ( halts2_outputs @ SV42 @ SV73 @ SV94 )
= $false )
| ( ( program_not_halts2 @ SV73 @ SV73 )
= $false )
| ( ( program_not_halts2_halts2_outputs @ SV42 @ SV73 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(361,plain,
! [SV45: $i,SV5: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ bad )
= $false )
| ( ( program_halts2_halts2_outputs @ c2 @ SV45 @ good )
= $true )
| ( ( program_halts2_halts3_outputs @ SV5 @ ( f3 @ SV5 ) @ ( f3 @ SV5 ) @ good )
= $false )
| ( ( program @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(362,plain,
! [SV46: $i,SV6: $i] :
( ( ( program_not_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ bad )
= $false )
| ( ( program_not_halts2_halts2_outputs @ c2 @ SV46 @ bad )
= $true )
| ( ( program_halts2_halts3_outputs @ SV6 @ ( f3 @ SV6 ) @ ( f3 @ SV6 ) @ good )
= $false )
| ( ( program @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(363,plain,
! [SV47: $i,SV8: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
= $false )
| ( ( ~ ( program_halts2 @ SV47 @ SV47 )
| ( halts2 @ c3 @ SV47 ) )
= $true )
| ( ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
= $false )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(364,plain,
! [SV48: $i,SV9: $i] :
( ( ( program_not_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ bad )
= $false )
| ( ( program_not_halts2_halts2_outputs @ c3 @ SV48 @ bad )
= $true )
| ( ( program_halts2_halts2_outputs @ SV9 @ ( f4 @ SV9 ) @ good )
= $false )
| ( ( program @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(365,plain,
! [SV79: $i,SV55: $i,SV97: $i,SV24: $i] :
( ( ( outputs @ SV24 @ SV97 )
= $false )
| ( ( halts3 @ SV24 @ SV55 @ SV79 )
= $false )
| ( ( halts3_outputs @ SV24 @ SV55 @ SV79 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(366,plain,
! [SV100: $i,SV85: $i,SV64: $i,SV33: $i] :
( ( ( halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
= $false )
| ( ( program_halts2 @ SV64 @ SV85 )
= $false )
| ( ( program_halts2_halts3_outputs @ SV33 @ SV64 @ SV85 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(367,plain,
! [SV103: $i,SV88: $i,SV67: $i,SV36: $i] :
( ( ( halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
= $false )
| ( ( program_not_halts2 @ SV67 @ SV88 )
= $false )
| ( ( program_not_halts2_halts3_outputs @ SV36 @ SV67 @ SV88 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(368,plain,
! [SV8: $i,SV47: $i] :
( ( ( ~ ( program_halts2 @ SV47 @ SV47 ) )
= $true )
| ( ( halts2 @ c3 @ SV47 )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
= $false )
| ( ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
= $false )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(369,plain,
! [SV8: $i,SV47: $i] :
( ( ( program_halts2 @ SV47 @ SV47 )
= $false )
| ( ( halts2 @ c3 @ SV47 )
= $true )
| ( ( program_not_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ bad )
= $false )
| ( ( program_halts2_halts2_outputs @ SV8 @ ( f4 @ SV8 ) @ good )
= $false )
| ( ( program @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(370,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,369,367,366,365,364,362,361,360,359,356,354,351,348,344,343,341,340,337,336,335,326,325,323,322,314,313,312,311,306,305,297,296,278,273,272,235,234,232,231,230,220,188,177]) ).
thf(371,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM003-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 18:37:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.37
% 0.60/0.37 No.of.Axioms: 43
% 0.60/0.37
% 0.60/0.37 Length.of.Defs: 0
% 0.60/0.37
% 0.60/0.37 Contains.Choice.Funs: false
% 0.60/0.37 .......
% 0.60/0.37
% 0.60/0.37 ********************************
% 0.60/0.37 * All subproblems solved! *
% 0.60/0.37 ********************************
% 0.60/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:43,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:370,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.37
% 0.60/0.37 %**** Beginning of derivation protocol ****
% 0.60/0.37 % SZS output start CNFRefutation
% See solution above
% 0.60/0.37
% 0.60/0.37 %**** End of derivation protocol ****
% 0.60/0.37 %**** no. of clauses in derivation: 371 ****
% 0.60/0.37 %**** clause counter: 370 ****
% 0.60/0.37
% 0.60/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:43,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:370,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------