TSTP Solution File: PUZ024-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n018.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 : Mon Jul 18 18:19:18 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 202 ( 82 unt; 10 typ; 0 def)
% Number of atoms : 1428 ( 360 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2341 ( 354 ~; 516 |; 0 &;1471 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 433 ( 0 ^ 433 !; 0 ?; 433 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_a_truth,type,
a_truth: $i > $o ).
thf(tp_all_are_liars,type,
all_are_liars: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_liar,type,
liar: $i > $i ).
thf(tp_one_truthteller,type,
one_truthteller: $i ).
thf(tp_people,type,
people: $i > $i > $i > $o ).
thf(tp_says,type,
says: $i > $i > $i ).
thf(tp_truthteller,type,
truthteller: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ all_are_liars )
| ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_truthtellers) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ ( says @ X @ all_are_liars ) )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',speaker_is_lying) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( liar @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',three_liars) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_truthtellers) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_truthteller_two_liars) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_not_the_truthteller) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_the_truth_teller) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ ( says @ X @ one_truthteller ) )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_says_one_truthteller) ).
thf(9,axiom,
! [Statement: $i,Liar: $i] :
( ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_are_told_by_liars) ).
thf(10,axiom,
! [Statement: $i,Truthteller: $i] :
( ~ ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truths_are_told_by_truthtellers) ).
thf(11,axiom,
! [Liar: $i,Statement: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lie) ).
thf(12,axiom,
! [Truthteller: $i,Statement: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthtellers_tell_truth) ).
thf(13,axiom,
! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_both) ).
thf(14,axiom,
! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
thf(15,axiom,
a_truth @ ( says @ b @ one_truthteller ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_one_truthteller) ).
thf(16,axiom,
a_truth @ ( says @ a @ all_are_liars ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_all_are_liars) ).
thf(17,axiom,
people @ c @ b @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_b_a_people) ).
thf(18,axiom,
people @ a @ c @ b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_c_b_people) ).
thf(19,axiom,
people @ b @ c @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_c_a_people) ).
thf(20,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(21,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,negated_conjecture,
! [Truthteller: $i] :
~ ( a_truth @ ( truthteller @ Truthteller ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_truthteller) ).
thf(23,plain,
$false = $false,
inference(unfold_def,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ all_are_liars )
| ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ ( says @ X @ all_are_liars ) )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( liar @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ one_truthteller )
| ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( a_truth @ ( says @ X @ one_truthteller ) )
| ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(32,plain,
( ( ! [Statement: $i,Liar: $i] :
( ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(33,plain,
( ( ! [Statement: $i,Truthteller: $i] :
( ~ ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(34,plain,
( ( ! [Liar: $i,Statement: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(35,plain,
( ( ! [Truthteller: $i,Statement: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(36,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(38,plain,
( ( a_truth @ ( says @ b @ one_truthteller ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(39,plain,
( ( a_truth @ ( says @ a @ all_are_liars ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(40,plain,
( ( people @ c @ b @ a )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(41,plain,
( ( people @ a @ c @ b )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(42,plain,
( ( people @ b @ c @ a )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [Truthteller: $i] :
~ ( a_truth @ ( truthteller @ Truthteller ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(44,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( a_truth @ all_are_liars )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(46,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( says @ X @ all_are_liars ) )
| ! [Y: $i,Z: $i] :
~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( liar @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(49,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(50,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(51,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(52,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( says @ X @ one_truthteller ) )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(53,plain,
( ( ! [Statement: $i] :
( ( a_truth @ Statement )
| ! [Liar: $i] :
( ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(54,plain,
( ( ! [Statement: $i] :
( ~ ( a_truth @ Statement )
| ! [Truthteller: $i] :
( ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(55,plain,
( ( ! [Liar: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ! [Statement: $i] :
( ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(56,plain,
( ( ! [Truthteller: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ! [Statement: $i] :
( ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(57,plain,
( ( ! [Truthteller: $i] :
~ ( a_truth @ ( truthteller @ Truthteller ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(58,plain,
( ( people @ b @ c @ a )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(59,plain,
( ( people @ a @ c @ b )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(60,plain,
( ( people @ c @ b @ a )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(61,plain,
( ( a_truth @ ( says @ a @ all_are_liars ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(62,plain,
( ( a_truth @ ( says @ b @ one_truthteller ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(64,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(65,plain,
( ( ! [Truthteller: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ! [Statement: $i] :
( ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(66,plain,
( ( ! [Liar: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ! [Statement: $i] :
( ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(67,plain,
( ( ! [Statement: $i] :
( ~ ( a_truth @ Statement )
| ! [Truthteller: $i] :
( ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(68,plain,
( ( ! [Statement: $i] :
( ( a_truth @ Statement )
| ! [Liar: $i] :
( ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(69,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( says @ X @ one_truthteller ) )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(70,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(71,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(72,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(73,plain,
( ( ! [X: $i] :
( ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(74,plain,
( ( ! [X: $i] :
( ( a_truth @ one_truthteller )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( liar @ X ) )
| ~ ( a_truth @ ( liar @ Y ) )
| ( a_truth @ ( liar @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(75,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( says @ X @ all_are_liars ) )
| ! [Y: $i,Z: $i] :
~ ( people @ X @ Y @ Z )
| ~ ( a_truth @ ( truthteller @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(76,plain,
( ( ! [X: $i] :
( ( a_truth @ all_are_liars )
| ! [Y: $i,Z: $i] :
( ~ ( people @ X @ Y @ Z )
| ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( truthteller @ Y ) )
| ( a_truth @ ( truthteller @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(77,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(78,plain,
! [SV1: $i] :
( ( ~ ( a_truth @ ( truthteller @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(79,plain,
! [SV2: $i] :
( ( ( a_truth @ ( truthteller @ SV2 ) )
| ( a_truth @ ( liar @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV3: $i] :
( ( ~ ( a_truth @ ( truthteller @ SV3 ) )
| ~ ( a_truth @ ( liar @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV4: $i] :
( ( ~ ( a_truth @ ( truthteller @ SV4 ) )
| ! [SY35: $i] :
( ~ ( a_truth @ ( says @ SV4 @ SY35 ) )
| ( a_truth @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(82,plain,
! [SV5: $i] :
( ( ~ ( a_truth @ ( liar @ SV5 ) )
| ! [SY36: $i] :
( ~ ( a_truth @ ( says @ SV5 @ SY36 ) )
| ~ ( a_truth @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(83,plain,
! [SV6: $i] :
( ( ~ ( a_truth @ SV6 )
| ! [SY37: $i] :
( ~ ( a_truth @ ( says @ SY37 @ SV6 ) )
| ( a_truth @ ( truthteller @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(84,plain,
! [SV7: $i] :
( ( ( a_truth @ SV7 )
| ! [SY38: $i] :
( ~ ( a_truth @ ( says @ SY38 @ SV7 ) )
| ( a_truth @ ( liar @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(85,plain,
! [SV8: $i] :
( ( ~ ( a_truth @ ( says @ SV8 @ one_truthteller ) )
| ! [SY39: $i,SY40: $i] :
( ~ ( people @ SV8 @ SY39 @ SY40 )
| ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SY39 ) )
| ~ ( a_truth @ ( truthteller @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(86,plain,
! [SV9: $i] :
( ( ~ ( a_truth @ one_truthteller )
| ! [SY41: $i,SY42: $i] :
( ~ ( people @ SV9 @ SY41 @ SY42 )
| ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SY41 ) )
| ( a_truth @ ( truthteller @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(87,plain,
! [SV10: $i] :
( ( ~ ( a_truth @ one_truthteller )
| ! [SY43: $i,SY44: $i] :
( ~ ( people @ SV10 @ SY43 @ SY44 )
| ~ ( a_truth @ ( truthteller @ SY43 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV11: $i] :
( ( ~ ( a_truth @ one_truthteller )
| ! [SY45: $i,SY46: $i] :
( ~ ( people @ SV11 @ SY45 @ SY46 )
| ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SY45 ) )
| ( a_truth @ ( liar @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV12: $i] :
( ( ( a_truth @ one_truthteller )
| ! [SY47: $i,SY48: $i] :
( ~ ( people @ SV12 @ SY47 @ SY48 )
| ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SY47 ) )
| ( a_truth @ ( truthteller @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(90,plain,
! [SV13: $i] :
( ( ( a_truth @ one_truthteller )
| ! [SY49: $i,SY50: $i] :
( ~ ( people @ SV13 @ SY49 @ SY50 )
| ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SY49 ) )
| ( a_truth @ ( liar @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(91,plain,
! [SV14: $i] :
( ( ~ ( a_truth @ ( says @ SV14 @ all_are_liars ) )
| ! [SY51: $i,SY52: $i] :
~ ( people @ SV14 @ SY51 @ SY52 )
| ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(92,plain,
! [SV15: $i] :
( ( ( a_truth @ all_are_liars )
| ! [SY53: $i,SY54: $i] :
( ~ ( people @ SV15 @ SY53 @ SY54 )
| ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SY53 ) )
| ( a_truth @ ( truthteller @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(93,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(94,plain,
! [SV1: $i] :
( ( a_truth @ ( truthteller @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(95,plain,
! [SV2: $i] :
( ( ( a_truth @ ( truthteller @ SV2 ) )
= $true )
| ( ( a_truth @ ( liar @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(96,plain,
! [SV3: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV3 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(97,plain,
! [SV4: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV4 ) ) )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( a_truth @ ( says @ SV4 @ SY35 ) )
| ( a_truth @ SY35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV5 ) ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( a_truth @ ( says @ SV5 @ SY36 ) )
| ~ ( a_truth @ SY36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(99,plain,
! [SV6: $i] :
( ( ( ~ ( a_truth @ SV6 ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( a_truth @ ( says @ SY37 @ SV6 ) )
| ( a_truth @ ( truthteller @ SY37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(100,plain,
! [SV7: $i] :
( ( ( a_truth @ SV7 )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( a_truth @ ( says @ SY38 @ SV7 ) )
| ( a_truth @ ( liar @ SY38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV8: $i] :
( ( ( ~ ( a_truth @ ( says @ SV8 @ one_truthteller ) ) )
= $true )
| ( ( ! [SY39: $i,SY40: $i] :
( ~ ( people @ SV8 @ SY39 @ SY40 )
| ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SY39 ) )
| ~ ( a_truth @ ( truthteller @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV9: $i] :
( ( ( ~ ( a_truth @ one_truthteller ) )
= $true )
| ( ( ! [SY41: $i,SY42: $i] :
( ~ ( people @ SV9 @ SY41 @ SY42 )
| ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SY41 ) )
| ( a_truth @ ( truthteller @ SY42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV10: $i] :
( ( ( ~ ( a_truth @ one_truthteller ) )
= $true )
| ( ( ! [SY43: $i,SY44: $i] :
( ~ ( people @ SV10 @ SY43 @ SY44 )
| ~ ( a_truth @ ( truthteller @ SY43 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SY44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV11: $i] :
( ( ( ~ ( a_truth @ one_truthteller ) )
= $true )
| ( ( ! [SY45: $i,SY46: $i] :
( ~ ( people @ SV11 @ SY45 @ SY46 )
| ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SY45 ) )
| ( a_truth @ ( liar @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV12: $i] :
( ( ( a_truth @ one_truthteller )
= $true )
| ( ( ! [SY47: $i,SY48: $i] :
( ~ ( people @ SV12 @ SY47 @ SY48 )
| ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SY47 ) )
| ( a_truth @ ( truthteller @ SY48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV13: $i] :
( ( ( a_truth @ one_truthteller )
= $true )
| ( ( ! [SY49: $i,SY50: $i] :
( ~ ( people @ SV13 @ SY49 @ SY50 )
| ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SY49 ) )
| ( a_truth @ ( liar @ SY50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV14: $i] :
( ( ( ~ ( a_truth @ ( says @ SV14 @ all_are_liars ) ) )
= $true )
| ( ( ! [SY51: $i,SY52: $i] :
~ ( people @ SV14 @ SY51 @ SY52 )
| ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV15: $i] :
( ( ( a_truth @ all_are_liars )
= $true )
| ( ( ! [SY53: $i,SY54: $i] :
( ~ ( people @ SV15 @ SY53 @ SY54 )
| ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SY53 ) )
| ( a_truth @ ( truthteller @ SY54 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV3: $i] :
( ( ( a_truth @ ( truthteller @ SV3 ) )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(110,plain,
! [SV4: $i] :
( ( ( a_truth @ ( truthteller @ SV4 ) )
= $false )
| ( ( ! [SY35: $i] :
( ~ ( a_truth @ ( says @ SV4 @ SY35 ) )
| ( a_truth @ SY35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( a_truth @ ( liar @ SV5 ) )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( a_truth @ ( says @ SV5 @ SY36 ) )
| ~ ( a_truth @ SY36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV6: $i] :
( ( ( a_truth @ SV6 )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( a_truth @ ( says @ SY37 @ SV6 ) )
| ( a_truth @ ( truthteller @ SY37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(113,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( a_truth @ ( says @ SV16 @ SV7 ) )
| ( a_truth @ ( liar @ SV16 ) ) )
= $true )
| ( ( a_truth @ SV7 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(114,plain,
! [SV8: $i] :
( ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false )
| ( ( ! [SY39: $i,SY40: $i] :
( ~ ( people @ SV8 @ SY39 @ SY40 )
| ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SY39 ) )
| ~ ( a_truth @ ( truthteller @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(115,plain,
! [SV9: $i] :
( ( ( a_truth @ one_truthteller )
= $false )
| ( ( ! [SY41: $i,SY42: $i] :
( ~ ( people @ SV9 @ SY41 @ SY42 )
| ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SY41 ) )
| ( a_truth @ ( truthteller @ SY42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(116,plain,
! [SV10: $i] :
( ( ( a_truth @ one_truthteller )
= $false )
| ( ( ! [SY43: $i,SY44: $i] :
( ~ ( people @ SV10 @ SY43 @ SY44 )
| ~ ( a_truth @ ( truthteller @ SY43 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SY44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(117,plain,
! [SV11: $i] :
( ( ( a_truth @ one_truthteller )
= $false )
| ( ( ! [SY45: $i,SY46: $i] :
( ~ ( people @ SV11 @ SY45 @ SY46 )
| ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SY45 ) )
| ( a_truth @ ( liar @ SY46 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV17: $i,SV12: $i] :
( ( ( ! [SY55: $i] :
( ~ ( people @ SV12 @ SV17 @ SY55 )
| ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SY55 ) ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV18: $i,SV13: $i] :
( ( ( ! [SY56: $i] :
( ~ ( people @ SV13 @ SV18 @ SY56 )
| ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SY56 ) ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(120,plain,
! [SV14: $i] :
( ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false )
| ( ( ! [SY51: $i,SY52: $i] :
~ ( people @ SV14 @ SY51 @ SY52 )
| ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(121,plain,
! [SV19: $i,SV15: $i] :
( ( ( ! [SY57: $i] :
( ~ ( people @ SV15 @ SV19 @ SY57 )
| ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SV19 ) )
| ( a_truth @ ( truthteller @ SY57 ) ) ) )
= $true )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(122,plain,
! [SV3: $i] :
( ( ( a_truth @ ( liar @ SV3 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(123,plain,
! [SV20: $i,SV4: $i] :
( ( ( ~ ( a_truth @ ( says @ SV4 @ SV20 ) )
| ( a_truth @ SV20 ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV4 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(124,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ( a_truth @ ( says @ SV5 @ SV21 ) )
| ~ ( a_truth @ SV21 ) )
= $true )
| ( ( a_truth @ ( liar @ SV5 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( a_truth @ ( says @ SV22 @ SV6 ) )
| ( a_truth @ ( truthteller @ SV22 ) ) )
= $true )
| ( ( a_truth @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV7: $i,SV16: $i] :
( ( ( ~ ( a_truth @ ( says @ SV16 @ SV7 ) ) )
= $true )
| ( ( a_truth @ ( liar @ SV16 ) )
= $true )
| ( ( a_truth @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV23: $i,SV8: $i] :
( ( ( ! [SY58: $i] :
( ~ ( people @ SV8 @ SV23 @ SY58 )
| ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SY58 ) ) ) )
= $true )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(128,plain,
! [SV24: $i,SV9: $i] :
( ( ( ! [SY59: $i] :
( ~ ( people @ SV9 @ SV24 @ SY59 )
| ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SV24 ) )
| ( a_truth @ ( truthteller @ SY59 ) ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV25: $i,SV10: $i] :
( ( ( ! [SY60: $i] :
( ~ ( people @ SV10 @ SV25 @ SY60 )
| ~ ( a_truth @ ( truthteller @ SV25 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SY60 ) ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV26: $i,SV11: $i] :
( ( ( ! [SY61: $i] :
( ~ ( people @ SV11 @ SV26 @ SY61 )
| ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SY61 ) ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV27: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( people @ SV12 @ SV17 @ SV27 )
| ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SV27 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV28: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( people @ SV13 @ SV18 @ SV28 )
| ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SV28 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(133,plain,
! [SV14: $i] :
( ( ( ! [SY51: $i,SY52: $i] :
~ ( people @ SV14 @ SY51 @ SY52 ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(134,plain,
! [SV29: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( people @ SV15 @ SV19 @ SV29 )
| ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SV19 ) )
| ( a_truth @ ( truthteller @ SV29 ) ) )
= $true )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV20: $i,SV4: $i] :
( ( ( ~ ( a_truth @ ( says @ SV4 @ SV20 ) ) )
= $true )
| ( ( a_truth @ SV20 )
= $true )
| ( ( a_truth @ ( truthteller @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ( a_truth @ ( says @ SV5 @ SV21 ) ) )
= $true )
| ( ( ~ ( a_truth @ SV21 ) )
= $true )
| ( ( a_truth @ ( liar @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( a_truth @ ( says @ SV22 @ SV6 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV22 ) )
= $true )
| ( ( a_truth @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV7: $i,SV16: $i] :
( ( ( a_truth @ ( says @ SV16 @ SV7 ) )
= $false )
| ( ( a_truth @ ( liar @ SV16 ) )
= $true )
| ( ( a_truth @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV30: $i,SV23: $i,SV8: $i] :
( ( ( ~ ( people @ SV8 @ SV23 @ SV30 )
| ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(140,plain,
! [SV31: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( people @ SV9 @ SV24 @ SV31 )
| ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SV24 ) )
| ( a_truth @ ( truthteller @ SV31 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV32: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( people @ SV10 @ SV25 @ SV32 )
| ~ ( a_truth @ ( truthteller @ SV25 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( ~ ( people @ SV11 @ SV26 @ SV33 )
| ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SV33 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV27: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( people @ SV12 @ SV17 @ SV27 ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SV27 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV28: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( people @ SV13 @ SV18 @ SV28 ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SV28 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV34: $i,SV14: $i] :
( ( ( ! [SY62: $i] :
~ ( people @ SV14 @ SV34 @ SY62 ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV29: $i,SV19: $i,SV15: $i] :
( ( ( ~ ( people @ SV15 @ SV19 @ SV29 ) )
= $true )
| ( ( ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SV19 ) )
| ( a_truth @ ( truthteller @ SV29 ) ) )
= $true )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV20: $i,SV4: $i] :
( ( ( a_truth @ ( says @ SV4 @ SV20 ) )
= $false )
| ( ( a_truth @ SV20 )
= $true )
| ( ( a_truth @ ( truthteller @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV21: $i,SV5: $i] :
( ( ( a_truth @ ( says @ SV5 @ SV21 ) )
= $false )
| ( ( ~ ( a_truth @ SV21 ) )
= $true )
| ( ( a_truth @ ( liar @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV6: $i,SV22: $i] :
( ( ( a_truth @ ( says @ SV22 @ SV6 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV22 ) )
= $true )
| ( ( a_truth @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV30: $i,SV23: $i,SV8: $i] :
( ( ( ~ ( people @ SV8 @ SV23 @ SV30 ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV31: $i,SV24: $i,SV9: $i] :
( ( ( ~ ( people @ SV9 @ SV24 @ SV31 ) )
= $true )
| ( ( ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SV24 ) )
| ( a_truth @ ( truthteller @ SV31 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV32: $i,SV25: $i,SV10: $i] :
( ( ( ~ ( people @ SV10 @ SV25 @ SV32 ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV25 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( ~ ( people @ SV11 @ SV26 @ SV33 ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SV33 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV27: $i,SV17: $i,SV12: $i] :
( ( ( people @ SV12 @ SV17 @ SV27 )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV12 ) )
| ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SV27 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV28: $i,SV18: $i,SV13: $i] :
( ( ( people @ SV13 @ SV18 @ SV28 )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV13 ) )
| ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SV28 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV35: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( people @ SV14 @ SV34 @ SV35 ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV29: $i,SV19: $i,SV15: $i] :
( ( ( people @ SV15 @ SV19 @ SV29 )
= $false )
| ( ( ( a_truth @ ( truthteller @ SV15 ) )
| ( a_truth @ ( truthteller @ SV19 ) )
| ( a_truth @ ( truthteller @ SV29 ) ) )
= $true )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV5: $i,SV21: $i] :
( ( ( a_truth @ SV21 )
= $false )
| ( ( a_truth @ ( says @ SV5 @ SV21 ) )
= $false )
| ( ( a_truth @ ( liar @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV30: $i,SV23: $i,SV8: $i] :
( ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV8 ) )
| ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(160,plain,
! [SV31: $i,SV24: $i,SV9: $i] :
( ( ( people @ SV9 @ SV24 @ SV31 )
= $false )
| ( ( ( a_truth @ ( truthteller @ SV9 ) )
| ( a_truth @ ( truthteller @ SV24 ) )
| ( a_truth @ ( truthteller @ SV31 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV32: $i,SV25: $i,SV10: $i] :
( ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV25 ) )
| ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( people @ SV11 @ SV26 @ SV33 )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV11 ) )
| ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SV33 ) ) )
= $true )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV27: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV12 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SV27 ) ) )
= $true )
| ( ( people @ SV12 @ SV17 @ SV27 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV28: $i,SV18: $i,SV13: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV13 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SV28 ) ) )
= $true )
| ( ( people @ SV13 @ SV18 @ SV28 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV35: $i,SV34: $i,SV14: $i] :
( ( ( people @ SV14 @ SV34 @ SV35 )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV14 ) ) )
= $true )
| ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(166,plain,
! [SV29: $i,SV19: $i,SV15: $i] :
( ( ( a_truth @ ( truthteller @ SV15 ) )
= $true )
| ( ( ( a_truth @ ( truthteller @ SV19 ) )
| ( a_truth @ ( truthteller @ SV29 ) ) )
= $true )
| ( ( people @ SV15 @ SV19 @ SV29 )
= $false )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(167,plain,
! [SV30: $i,SV23: $i,SV8: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV8 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV31: $i,SV24: $i,SV9: $i] :
( ( ( a_truth @ ( truthteller @ SV9 ) )
= $true )
| ( ( ( a_truth @ ( truthteller @ SV24 ) )
| ( a_truth @ ( truthteller @ SV31 ) ) )
= $true )
| ( ( people @ SV9 @ SV24 @ SV31 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(169,plain,
! [SV32: $i,SV10: $i,SV25: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV25 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(170,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV11 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SV33 ) ) )
= $true )
| ( ( people @ SV11 @ SV26 @ SV33 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(171,plain,
! [SV27: $i,SV17: $i,SV12: $i] :
( ( ( a_truth @ ( liar @ SV12 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV17 ) )
| ( a_truth @ ( truthteller @ SV27 ) ) )
= $true )
| ( ( people @ SV12 @ SV17 @ SV27 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV28: $i,SV18: $i,SV13: $i] :
( ( ( a_truth @ ( liar @ SV13 ) )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV18 ) )
| ( a_truth @ ( liar @ SV28 ) ) )
= $true )
| ( ( people @ SV13 @ SV18 @ SV28 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(173,plain,
! [SV35: $i,SV34: $i,SV14: $i] :
( ( ( a_truth @ ( truthteller @ SV14 ) )
= $false )
| ( ( people @ SV14 @ SV34 @ SV35 )
= $false )
| ( ( a_truth @ ( says @ SV14 @ all_are_liars ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(174,plain,
! [SV15: $i,SV29: $i,SV19: $i] :
( ( ( a_truth @ ( truthteller @ SV19 ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV29 ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV15 ) )
= $true )
| ( ( people @ SV15 @ SV19 @ SV29 )
= $false )
| ( ( a_truth @ all_are_liars )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(175,plain,
! [SV30: $i,SV23: $i,SV8: $i] :
( ( ( a_truth @ ( truthteller @ SV8 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV23 ) )
| ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(176,plain,
! [SV9: $i,SV31: $i,SV24: $i] :
( ( ( a_truth @ ( truthteller @ SV24 ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV31 ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV9 ) )
= $true )
| ( ( people @ SV9 @ SV24 @ SV31 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(177,plain,
! [SV32: $i,SV10: $i,SV25: $i] :
( ( ( a_truth @ ( truthteller @ SV25 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV10 ) )
| ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV33: $i,SV26: $i,SV11: $i] :
( ( ( a_truth @ ( liar @ SV11 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV26 ) )
| ( a_truth @ ( liar @ SV33 ) ) )
= $true )
| ( ( people @ SV11 @ SV26 @ SV33 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV12: $i,SV27: $i,SV17: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV17 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV27 ) )
= $true )
| ( ( a_truth @ ( liar @ SV12 ) )
= $false )
| ( ( people @ SV12 @ SV17 @ SV27 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV13: $i,SV28: $i,SV18: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV18 ) ) )
= $true )
| ( ( a_truth @ ( liar @ SV28 ) )
= $true )
| ( ( a_truth @ ( liar @ SV13 ) )
= $false )
| ( ( people @ SV13 @ SV18 @ SV28 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV8: $i,SV30: $i,SV23: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV23 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV8 ) )
= $false )
| ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV25: $i,SV32: $i,SV10: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV10 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV25 ) )
= $false )
| ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV11: $i,SV33: $i,SV26: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV26 ) ) )
= $true )
| ( ( a_truth @ ( liar @ SV33 ) )
= $true )
| ( ( a_truth @ ( liar @ SV11 ) )
= $false )
| ( ( people @ SV11 @ SV26 @ SV33 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(184,plain,
! [SV12: $i,SV27: $i,SV17: $i] :
( ( ( a_truth @ ( truthteller @ SV17 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV27 ) )
= $true )
| ( ( a_truth @ ( liar @ SV12 ) )
= $false )
| ( ( people @ SV12 @ SV17 @ SV27 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(185,plain,
! [SV13: $i,SV28: $i,SV18: $i] :
( ( ( a_truth @ ( liar @ SV18 ) )
= $false )
| ( ( a_truth @ ( liar @ SV28 ) )
= $true )
| ( ( a_truth @ ( liar @ SV13 ) )
= $false )
| ( ( people @ SV13 @ SV18 @ SV28 )
= $false )
| ( ( a_truth @ one_truthteller )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(186,plain,
! [SV8: $i,SV30: $i,SV23: $i] :
( ( ( a_truth @ ( truthteller @ SV23 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV30 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV8 ) )
= $false )
| ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(187,plain,
! [SV25: $i,SV32: $i,SV10: $i] :
( ( ( a_truth @ ( truthteller @ SV10 ) )
= $false )
| ( ( ~ ( a_truth @ ( truthteller @ SV32 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV25 ) )
= $false )
| ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(188,plain,
! [SV11: $i,SV33: $i,SV26: $i] :
( ( ( a_truth @ ( truthteller @ SV26 ) )
= $false )
| ( ( a_truth @ ( liar @ SV33 ) )
= $true )
| ( ( a_truth @ ( liar @ SV11 ) )
= $false )
| ( ( people @ SV11 @ SV26 @ SV33 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(189,plain,
! [SV8: $i,SV23: $i,SV30: $i] :
( ( ( a_truth @ ( truthteller @ SV30 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV23 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV8 ) )
= $false )
| ( ( people @ SV8 @ SV23 @ SV30 )
= $false )
| ( ( a_truth @ ( says @ SV8 @ one_truthteller ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(190,plain,
! [SV25: $i,SV10: $i,SV32: $i] :
( ( ( a_truth @ ( truthteller @ SV32 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV10 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV25 ) )
= $false )
| ( ( people @ SV10 @ SV25 @ SV32 )
= $false )
| ( ( a_truth @ one_truthteller )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(191,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[58,190,189,188,185,184,176,174,173,158,149,147,138,122,95,94,93,62,61,60,59]) ).
thf(192,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : PUZ024-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 01:22:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 20
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.36 (rf:0,axioms:20,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:22,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.18/0.44
% 0.18/0.44 ********************************
% 0.18/0.44 * All subproblems solved! *
% 0.18/0.44 ********************************
% 0.18/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:191,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.46
% 0.18/0.46 %**** Beginning of derivation protocol ****
% 0.18/0.46 % SZS output start CNFRefutation
% See solution above
% 0.18/0.46
% 0.18/0.46 %**** End of derivation protocol ****
% 0.18/0.46 %**** no. of clauses in derivation: 192 ****
% 0.18/0.46 %**** clause counter: 191 ****
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:20,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:191,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------