TSTP Solution File: HWV003-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n014.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 : Sat Jul 16 18:17:40 EDT 2022
% Result : Unsatisfiable 34.31s 34.49s
% Output : CNFRefutation 34.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 57
% Syntax : Number of formulae : 180 ( 156 unt; 20 typ; 0 def)
% Number of atoms : 417 ( 284 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 716 ( 13 ~; 7 |; 0 &; 696 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 18 con; 0-2 aty)
% Number of variables : 206 ( 0 ^ 206 !; 0 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_and,type,
and: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_carry,type,
carry: $i ).
thf(tp_carry_def,type,
carry_def: $i ).
thf(tp_cin,type,
cin: $i ).
thf(tp_ll0,type,
ll0: $i ).
thf(tp_ll1,type,
ll1: $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_sum,type,
sum: $i ).
thf(tp_sum_def,type,
sum_def: $i ).
thf(tp_t1,type,
t1: $i ).
thf(tp_t2,type,
t2: $i ).
thf(tp_t3,type,
t3: $i ).
thf(tp_t4,type,
t4: $i ).
thf(tp_t5,type,
t5: $i ).
thf(tp_t6,type,
t6: $i ).
thf(tp_t7,type,
t7: $i ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( xor @ X @ ( xor @ Y @ Z ) )
= ( xor @ ( xor @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutative) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( or @ ( and @ ( not @ X ) @ Y ) @ ( and @ X @ ( not @ Y ) ) )
= ( xor @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( not @ ( and @ X @ Y ) )
= ( or @ ( not @ X ) @ ( not @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_demorgan) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( not @ ( or @ X @ Y ) )
= ( and @ ( not @ X ) @ ( not @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_demorgan) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( and @ X @ ( or @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_absorption) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( or @ X @ ( and @ X @ Y ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_absorption) ).
thf(8,axiom,
! [X: $i] :
( ( and @ X @ ll0 )
= ll0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_boundedness) ).
thf(9,axiom,
! [X: $i] :
( ( or @ X @ ll1 )
= ll1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_boundedness) ).
thf(10,axiom,
( ( not @ ll1 )
= ll0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll1_inverse) ).
thf(11,axiom,
( ( not @ ll0 )
= ll1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ll0_inverse) ).
thf(12,axiom,
! [X: $i] :
( ( not @ ( not @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_involution) ).
thf(13,axiom,
! [X: $i] :
( ( and @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_idempotent) ).
thf(14,axiom,
! [X: $i] :
( ( or @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_idempotent) ).
thf(15,axiom,
! [X: $i] :
( ( and @ X @ ( not @ X ) )
= ll0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_complement) ).
thf(16,axiom,
! [X: $i] :
( ( or @ X @ ( not @ X ) )
= ll1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_complement) ).
thf(17,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( or @ X @ ( and @ Y @ Z ) )
= ( and @ ( or @ X @ Y ) @ ( or @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_distributive) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( and @ X @ ( or @ Y @ Z ) )
= ( or @ ( and @ X @ Y ) @ ( and @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_distributive) ).
thf(19,axiom,
! [X: $i] :
( ( and @ X @ ll1 )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_identity) ).
thf(20,axiom,
! [X: $i] :
( ( or @ X @ ll0 )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_identity) ).
thf(21,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( and @ ( and @ X @ Y ) @ Z )
= ( and @ X @ ( and @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associative) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( or @ ( or @ X @ Y ) @ Z )
= ( or @ X @ ( or @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associative) ).
thf(23,axiom,
! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( and @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutative) ).
thf(24,axiom,
! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( or @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutative) ).
thf(25,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(26,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[25]) ).
thf(27,negated_conjecture,
( ( sum != sum_def )
| ( carry != carry_def ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_circuit) ).
thf(28,negated_conjecture,
( ( not @ ( and @ t1 @ t5 ) )
= carry ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry) ).
thf(29,negated_conjecture,
( ( not @ ( and @ t6 @ t7 ) )
= sum ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(30,negated_conjecture,
( ( not @ ( and @ t5 @ cin ) )
= t7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).
thf(31,negated_conjecture,
( ( not @ ( and @ t4 @ t5 ) )
= t6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
thf(32,negated_conjecture,
( ( not @ ( and @ t4 @ cin ) )
= t5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5) ).
thf(33,negated_conjecture,
( ( not @ ( and @ t2 @ t3 ) )
= t4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4) ).
thf(34,negated_conjecture,
( ( not @ ( and @ b @ t1 ) )
= t3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(35,negated_conjecture,
( ( not @ ( and @ a @ t1 ) )
= t2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(36,negated_conjecture,
( ( not @ ( and @ a @ b ) )
= t1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(37,negated_conjecture,
( ( or @ ( and @ cin @ ( or @ a @ b ) ) @ ( and @ ( not @ cin ) @ ( and @ a @ b ) ) )
= carry_def ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',carry_def) ).
thf(38,negated_conjecture,
( ( xor @ ( xor @ a @ b ) @ cin )
= sum_def ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_def) ).
thf(39,plain,
$false = $false,
inference(unfold_def,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( xor @ X @ ( xor @ Y @ Z ) )
= ( xor @ ( xor @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ ( and @ ( not @ X ) @ Y ) @ ( and @ X @ ( not @ Y ) ) )
= ( xor @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( and @ X @ Y ) )
= ( or @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( or @ X @ Y ) )
= ( and @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ( and @ X @ ( or @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ X @ ( and @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( and @ X @ ll0 )
= ll0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( or @ X @ ll1 )
= ll1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(49,plain,
( ( ( not @ ll1 )
= ll0 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(50,plain,
( ( ( not @ ll0 )
= ll1 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(51,plain,
( ( ! [X: $i] :
( ( not @ ( not @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(52,plain,
( ( ! [X: $i] :
( ( and @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( or @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( and @ X @ ( not @ X ) )
= ll0 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( or @ X @ ( not @ X ) )
= ll1 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( or @ X @ ( and @ Y @ Z ) )
= ( and @ ( or @ X @ Y ) @ ( or @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and @ X @ ( or @ Y @ Z ) )
= ( or @ ( and @ X @ Y ) @ ( and @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( and @ X @ ll1 )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(59,plain,
( ( ! [X: $i] :
( ( or @ X @ ll0 )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and @ ( and @ X @ Y ) @ Z )
= ( and @ X @ ( and @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( or @ ( or @ X @ Y ) @ Z )
= ( or @ X @ ( or @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( and @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( or @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(64,plain,
( ( ( sum != sum_def )
| ( carry != carry_def ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(65,plain,
( ( ( not @ ( and @ t1 @ t5 ) )
= carry )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(66,plain,
( ( ( not @ ( and @ t6 @ t7 ) )
= sum )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(67,plain,
( ( ( not @ ( and @ t5 @ cin ) )
= t7 )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(68,plain,
( ( ( not @ ( and @ t4 @ t5 ) )
= t6 )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(69,plain,
( ( ( not @ ( and @ t4 @ cin ) )
= t5 )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(70,plain,
( ( ( not @ ( and @ t2 @ t3 ) )
= t4 )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ( not @ ( and @ b @ t1 ) )
= t3 )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ( not @ ( and @ a @ t1 ) )
= t2 )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(73,plain,
( ( ( not @ ( and @ a @ b ) )
= t1 )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(74,plain,
( ( ( or @ ( and @ cin @ ( or @ a @ b ) ) @ ( and @ ( not @ cin ) @ ( and @ a @ b ) ) )
= carry_def )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(75,plain,
( ( ( xor @ ( xor @ a @ b ) @ cin )
= sum_def )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(76,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(77,plain,
( ( ( sum != sum_def )
| ( carry != carry_def ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(78,plain,
( ( ( xor @ ( xor @ a @ b ) @ cin )
= sum_def )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(79,plain,
( ( ( or @ ( and @ cin @ ( or @ a @ b ) ) @ ( and @ ( not @ cin ) @ ( and @ a @ b ) ) )
= carry_def )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(80,plain,
( ( ( not @ ( and @ a @ b ) )
= t1 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(81,plain,
( ( ( not @ ( and @ a @ t1 ) )
= t2 )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(82,plain,
( ( ( not @ ( and @ b @ t1 ) )
= t3 )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(83,plain,
( ( ( not @ ( and @ t2 @ t3 ) )
= t4 )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(84,plain,
( ( ( not @ ( and @ t4 @ cin ) )
= t5 )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(85,plain,
( ( ( not @ ( and @ t4 @ t5 ) )
= t6 )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(86,plain,
( ( ( not @ ( and @ t5 @ cin ) )
= t7 )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(87,plain,
( ( ( not @ ( and @ t6 @ t7 ) )
= sum )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(88,plain,
( ( ( not @ ( and @ t1 @ t5 ) )
= carry )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(89,plain,
( ( ( sum != sum_def )
| ( carry != carry_def ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(90,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( or @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( and @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( or @ ( or @ X @ Y ) @ Z )
= ( or @ X @ ( or @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(93,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and @ ( and @ X @ Y ) @ Z )
= ( and @ X @ ( and @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(94,plain,
( ( ! [X: $i] :
( ( or @ X @ ll0 )
= X ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(95,plain,
( ( ! [X: $i] :
( ( and @ X @ ll1 )
= X ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and @ X @ ( or @ Y @ Z ) )
= ( or @ ( and @ X @ Y ) @ ( and @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( or @ X @ ( and @ Y @ Z ) )
= ( and @ ( or @ X @ Y ) @ ( or @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(98,plain,
( ( ! [X: $i] :
( ( or @ X @ ( not @ X ) )
= ll1 ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(99,plain,
( ( ! [X: $i] :
( ( and @ X @ ( not @ X ) )
= ll0 ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(100,plain,
( ( ! [X: $i] :
( ( or @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(101,plain,
( ( ! [X: $i] :
( ( and @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(102,plain,
( ( ! [X: $i] :
( ( not @ ( not @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(103,plain,
( ( ( not @ ll0 )
= ll1 )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(104,plain,
( ( ( not @ ll1 )
= ll0 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(105,plain,
( ( ! [X: $i] :
( ( or @ X @ ll1 )
= ll1 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(106,plain,
( ( ! [X: $i] :
( ( and @ X @ ll0 )
= ll0 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(107,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ X @ ( and @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(108,plain,
( ( ! [X: $i,Y: $i] :
( ( and @ X @ ( or @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( or @ X @ Y ) )
= ( and @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(110,plain,
( ( ! [X: $i,Y: $i] :
( ( not @ ( and @ X @ Y ) )
= ( or @ ( not @ X ) @ ( not @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(111,plain,
( ( ! [X: $i,Y: $i] :
( ( or @ ( and @ ( not @ X ) @ Y ) @ ( and @ X @ ( not @ Y ) ) )
= ( xor @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( xor @ X @ ( xor @ Y @ Z ) )
= ( xor @ ( xor @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(114,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(115,plain,
( ( ( ( sum != sum_def ) )
= $true )
| ( ( ( carry != carry_def ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(116,plain,
! [SV1: $i] :
( ( ! [SY40: $i] :
( ( or @ SV1 @ SY40 )
= ( or @ SY40 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(117,plain,
! [SV2: $i] :
( ( ! [SY41: $i] :
( ( and @ SV2 @ SY41 )
= ( and @ SY41 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(118,plain,
! [SV3: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( or @ ( or @ SV3 @ SY42 ) @ SY43 )
= ( or @ SV3 @ ( or @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(119,plain,
! [SV4: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( and @ ( and @ SV4 @ SY44 ) @ SY45 )
= ( and @ SV4 @ ( and @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( or @ SV5 @ ll0 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV6: $i] :
( ( ( and @ SV6 @ ll1 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(122,plain,
! [SV7: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( and @ SV7 @ ( or @ SY46 @ SY47 ) )
= ( or @ ( and @ SV7 @ SY46 ) @ ( and @ SV7 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(123,plain,
! [SV8: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ( or @ SV8 @ ( and @ SY48 @ SY49 ) )
= ( and @ ( or @ SV8 @ SY48 ) @ ( or @ SV8 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(124,plain,
! [SV9: $i] :
( ( ( or @ SV9 @ ( not @ SV9 ) )
= ll1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(125,plain,
! [SV10: $i] :
( ( ( and @ SV10 @ ( not @ SV10 ) )
= ll0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(126,plain,
! [SV11: $i] :
( ( ( or @ SV11 @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(127,plain,
! [SV12: $i] :
( ( ( and @ SV12 @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(128,plain,
! [SV13: $i] :
( ( ( not @ ( not @ SV13 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(129,plain,
! [SV14: $i] :
( ( ( or @ SV14 @ ll1 )
= ll1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV15: $i] :
( ( ( and @ SV15 @ ll0 )
= ll0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
! [SV16: $i] :
( ( ! [SY50: $i] :
( ( or @ SV16 @ ( and @ SV16 @ SY50 ) )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV17: $i] :
( ( ! [SY51: $i] :
( ( and @ SV17 @ ( or @ SV17 @ SY51 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
! [SV18: $i] :
( ( ! [SY52: $i] :
( ( not @ ( or @ SV18 @ SY52 ) )
= ( and @ ( not @ SV18 ) @ ( not @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(134,plain,
! [SV19: $i] :
( ( ! [SY53: $i] :
( ( not @ ( and @ SV19 @ SY53 ) )
= ( or @ ( not @ SV19 ) @ ( not @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV20: $i] :
( ( ! [SY54: $i] :
( ( or @ ( and @ ( not @ SV20 ) @ SY54 ) @ ( and @ SV20 @ ( not @ SY54 ) ) )
= ( xor @ SV20 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(136,plain,
! [SV21: $i] :
( ( ! [SY55: $i] :
( ( xor @ SV21 @ SY55 )
= ( xor @ SY55 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV22: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( xor @ SV22 @ ( xor @ SY56 @ SY57 ) )
= ( xor @ ( xor @ SV22 @ SY56 ) @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(139,plain,
( ( ( sum = sum_def )
= $false )
| ( ( ( carry != carry_def ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(140,plain,
! [SV23: $i,SV1: $i] :
( ( ( or @ SV1 @ SV23 )
= ( or @ SV23 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(141,plain,
! [SV24: $i,SV2: $i] :
( ( ( and @ SV2 @ SV24 )
= ( and @ SV24 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(142,plain,
! [SV25: $i,SV3: $i] :
( ( ! [SY58: $i] :
( ( or @ ( or @ SV3 @ SV25 ) @ SY58 )
= ( or @ SV3 @ ( or @ SV25 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(143,plain,
! [SV26: $i,SV4: $i] :
( ( ! [SY59: $i] :
( ( and @ ( and @ SV4 @ SV26 ) @ SY59 )
= ( and @ SV4 @ ( and @ SV26 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
! [SV27: $i,SV7: $i] :
( ( ! [SY60: $i] :
( ( and @ SV7 @ ( or @ SV27 @ SY60 ) )
= ( or @ ( and @ SV7 @ SV27 ) @ ( and @ SV7 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV28: $i,SV8: $i] :
( ( ! [SY61: $i] :
( ( or @ SV8 @ ( and @ SV28 @ SY61 ) )
= ( and @ ( or @ SV8 @ SV28 ) @ ( or @ SV8 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(146,plain,
! [SV29: $i,SV16: $i] :
( ( ( or @ SV16 @ ( and @ SV16 @ SV29 ) )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV30: $i,SV17: $i] :
( ( ( and @ SV17 @ ( or @ SV17 @ SV30 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV31: $i,SV18: $i] :
( ( ( not @ ( or @ SV18 @ SV31 ) )
= ( and @ ( not @ SV18 ) @ ( not @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV32: $i,SV19: $i] :
( ( ( not @ ( and @ SV19 @ SV32 ) )
= ( or @ ( not @ SV19 ) @ ( not @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV33: $i,SV20: $i] :
( ( ( or @ ( and @ ( not @ SV20 ) @ SV33 ) @ ( and @ SV20 @ ( not @ SV33 ) ) )
= ( xor @ SV20 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(151,plain,
! [SV34: $i,SV21: $i] :
( ( ( xor @ SV21 @ SV34 )
= ( xor @ SV34 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(152,plain,
! [SV35: $i,SV22: $i] :
( ( ! [SY62: $i] :
( ( xor @ SV22 @ ( xor @ SV35 @ SY62 ) )
= ( xor @ ( xor @ SV22 @ SV35 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(153,plain,
( ( ( carry = carry_def )
= $false )
| ( ( sum = sum_def )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV36: $i,SV25: $i,SV3: $i] :
( ( ( or @ ( or @ SV3 @ SV25 ) @ SV36 )
= ( or @ SV3 @ ( or @ SV25 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(155,plain,
! [SV37: $i,SV26: $i,SV4: $i] :
( ( ( and @ ( and @ SV4 @ SV26 ) @ SV37 )
= ( and @ SV4 @ ( and @ SV26 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV38: $i,SV27: $i,SV7: $i] :
( ( ( and @ SV7 @ ( or @ SV27 @ SV38 ) )
= ( or @ ( and @ SV7 @ SV27 ) @ ( and @ SV7 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV39: $i,SV28: $i,SV8: $i] :
( ( ( or @ SV8 @ ( and @ SV28 @ SV39 ) )
= ( and @ ( or @ SV8 @ SV28 ) @ ( or @ SV8 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV40: $i,SV35: $i,SV22: $i] :
( ( ( xor @ SV22 @ ( xor @ SV35 @ SV40 ) )
= ( xor @ ( xor @ SV22 @ SV35 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(159,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,158,157,156,155,154,153,151,150,149,148,147,146,141,140,138,130,129,128,127,126,125,124,121,120,104,103,88,87,86,85,84,83,82,81,80,79]) ).
thf(160,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV003-2 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 17 06:13:49 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 36
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 .
% 0.13/0.36 (rf:0,axioms:36,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:38,loop_count:0,foatp_calls:0,translation:fof_full)......
% 34.31/34.49
% 34.31/34.49 ********************************
% 34.31/34.49 * All subproblems solved! *
% 34.31/34.49 ********************************
% 34.31/34.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,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:159,loop_count:0,foatp_calls:1,translation:fof_full)
% 34.31/34.50
% 34.31/34.50 %**** Beginning of derivation protocol ****
% 34.31/34.50 % SZS output start CNFRefutation
% See solution above
% 34.31/34.50
% 34.31/34.50 %**** End of derivation protocol ****
% 34.31/34.50 %**** no. of clauses in derivation: 160 ****
% 34.31/34.50 %**** clause counter: 159 ****
% 34.31/34.50
% 34.31/34.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:36,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:159,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------