TSTP Solution File: RNG010-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 20:33:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 33
% Syntax : Number of formulae : 151 ( 137 unt; 8 typ; 0 def)
% Number of atoms : 403 ( 274 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1023 ( 42 ~; 18 |; 0 &; 963 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 304 ( 0 ^ 304 !; 0 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_additive_inverse,type,
additive_inverse: $i > $i ).
thf(tp_associator,type,
associator: $i > $i > $i > $i ).
thf(tp_cx,type,
cx: $i ).
thf(tp_cy,type,
cy: $i ).
thf(tp_cz,type,
cz: $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( associator @ Z @ Y @ X )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
thf(2,axiom,
! [Y: $i,X: $i,Z: $i] :
( ( associator @ Y @ X @ Z )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
thf(3,axiom,
! [Y: $i,X: $i] :
( ( multiply @ ( multiply @ Y @ X ) @ Y )
!= ( multiply @ Y @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_law) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( associator @ X @ Y @ Z )
= ( add @ ( multiply @ ( multiply @ X @ Y ) @ Z ) @ ( additive_inverse @ ( multiply @ X @ ( multiply @ Y @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associator) ).
thf(5,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( ( add @ Z @ X )
!= ( add @ Z @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation_for_addition) ).
thf(6,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( ( add @ X @ Z )
!= ( add @ Y @ Z ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation_for_addition) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(9,axiom,
( ( additive_inverse @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_additive_identity) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add2) ).
thf(15,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add1) ).
thf(16,axiom,
! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(17,axiom,
! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_of_inverses) ).
thf(18,axiom,
! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverse) ).
thf(19,axiom,
! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(20,axiom,
! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(21,axiom,
! [X: $i] :
( ( add @ additive_identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ ( multiply @ Y @ X ) ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_moufang) ).
thf(23,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( multiply @ Z @ ( multiply @ X @ ( multiply @ Y @ X ) ) )
= ( multiply @ ( multiply @ ( multiply @ Z @ X ) @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_moufang) ).
thf(24,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(25,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[24]) ).
thf(26,negated_conjecture,
( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_skew_symmetry) ).
thf(27,plain,
$false = $false,
inference(unfold_def,[status(thm)],[25]) ).
thf(28,plain,
( ( ! [Z: $i,Y: $i,X: $i] :
( ( associator @ Z @ Y @ X )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(29,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( associator @ Y @ X @ Z )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(30,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( multiply @ Y @ X ) @ Y )
!= ( multiply @ Y @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( associator @ X @ Y @ Z )
= ( add @ ( multiply @ ( multiply @ X @ Y ) @ Z ) @ ( additive_inverse @ ( multiply @ X @ ( multiply @ Y @ Z ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(32,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( ( add @ Z @ X )
!= ( add @ Z @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(33,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( ( add @ X @ Z )
!= ( add @ Y @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(36,plain,
( ( ( additive_inverse @ additive_identity )
= additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ ( multiply @ Y @ X ) ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( multiply @ Z @ ( multiply @ X @ ( multiply @ Y @ X ) ) )
= ( multiply @ ( multiply @ ( multiply @ Z @ X ) @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(51,plain,
( ( ( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(53,plain,
( ( ! [Z: $i,Y: $i,X: $i] :
( ( associator @ Z @ Y @ X )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(54,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( associator @ Y @ X @ Z )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(55,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( multiply @ Y @ X ) @ Y )
!= ( multiply @ Y @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(56,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( ( add @ Z @ X )
!= ( add @ Z @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(57,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( ( add @ X @ Z )
!= ( add @ Y @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(58,plain,
( ( ( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(59,plain,
( ( ( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
!= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( multiply @ Z @ ( multiply @ X @ ( multiply @ Y @ X ) ) )
= ( multiply @ ( multiply @ ( multiply @ Z @ X ) @ Y ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ ( multiply @ Y @ X ) ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(65,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(74,plain,
( ( ( additive_inverse @ additive_identity )
= additive_identity )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(77,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( ( add @ X @ Z )
!= ( add @ Y @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(78,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( ( add @ Z @ X )
!= ( add @ Z @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( associator @ X @ Y @ Z )
= ( add @ ( multiply @ ( multiply @ X @ Y ) @ Z ) @ ( additive_inverse @ ( multiply @ X @ ( multiply @ Y @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(80,plain,
( ( ! [Y: $i,X: $i] :
( ( multiply @ ( multiply @ Y @ X ) @ Y )
!= ( multiply @ Y @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(81,plain,
( ( ! [Y: $i,X: $i,Z: $i] :
( ( associator @ Y @ X @ Z )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(82,plain,
( ( ! [Z: $i,Y: $i,X: $i] :
( ( associator @ Z @ Y @ X )
!= ( additive_inverse @ ( associator @ X @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(83,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(84,plain,
( ( ( associator @ ( multiply @ cx @ cx ) @ cy @ cz )
= ( add @ ( multiply @ ( associator @ cx @ cy @ cz ) @ cx ) @ ( multiply @ cx @ ( associator @ cx @ cy @ cz ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(85,plain,
! [SV1: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( multiply @ SV1 @ ( multiply @ SY49 @ ( multiply @ SY50 @ SY49 ) ) )
= ( multiply @ ( multiply @ ( multiply @ SV1 @ SY49 ) @ SY50 ) @ SY49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(86,plain,
! [SV2: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( multiply @ ( multiply @ SV2 @ ( multiply @ SY51 @ SV2 ) ) @ SY52 )
= ( multiply @ SV2 @ ( multiply @ SY51 @ ( multiply @ SV2 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(87,plain,
! [SV3: $i] :
( ( ( add @ additive_identity @ SV3 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(88,plain,
! [SV4: $i] :
( ( ( multiply @ additive_identity @ SV4 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(89,plain,
! [SV5: $i] :
( ( ( multiply @ SV5 @ additive_identity )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(90,plain,
! [SV6: $i] :
( ( ( add @ ( additive_inverse @ SV6 ) @ SV6 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(91,plain,
! [SV7: $i] :
( ( ! [SY53: $i] :
( ( additive_inverse @ ( add @ SV7 @ SY53 ) )
= ( add @ ( additive_inverse @ SV7 ) @ ( additive_inverse @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(92,plain,
! [SV8: $i] :
( ( ( additive_inverse @ ( additive_inverse @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(93,plain,
! [SV9: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( multiply @ SV9 @ ( add @ SY54 @ SY55 ) )
= ( add @ ( multiply @ SV9 @ SY54 ) @ ( multiply @ SV9 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV10: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( multiply @ ( add @ SV10 @ SY56 ) @ SY57 )
= ( add @ ( multiply @ SV10 @ SY57 ) @ ( multiply @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(95,plain,
! [SV11: $i] :
( ( ! [SY58: $i] :
( ( multiply @ ( multiply @ SV11 @ SY58 ) @ SY58 )
= ( multiply @ SV11 @ ( multiply @ SY58 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(96,plain,
! [SV12: $i] :
( ( ! [SY59: $i] :
( ( multiply @ ( multiply @ SV12 @ SV12 ) @ SY59 )
= ( multiply @ SV12 @ ( multiply @ SV12 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(97,plain,
! [SV13: $i] :
( ( ! [SY60: $i] :
( ( multiply @ ( additive_inverse @ SV13 ) @ SY60 )
= ( additive_inverse @ ( multiply @ SV13 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(98,plain,
! [SV14: $i] :
( ( ! [SY61: $i] :
( ( multiply @ SV14 @ ( additive_inverse @ SY61 ) )
= ( additive_inverse @ ( multiply @ SV14 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(99,plain,
! [SV15: $i] :
( ( ! [SY62: $i] :
( ( add @ SV15 @ SY62 )
= ( add @ SY62 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(100,plain,
! [SV16: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ( add @ SV16 @ ( add @ SY63 @ SY64 ) )
= ( add @ ( add @ SV16 @ SY63 ) @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(101,plain,
! [SV17: $i] :
( ( ! [SY65: $i,SY66: $i] :
( ( ( add @ SV17 @ SY65 )
!= ( add @ SY66 @ SY65 ) )
| ( SV17 = SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(102,plain,
! [SV18: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ( ( add @ SV18 @ SY67 )
!= ( add @ SV18 @ SY68 ) )
| ( SY67 = SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(103,plain,
! [SV19: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ( associator @ SV19 @ SY69 @ SY70 )
= ( add @ ( multiply @ ( multiply @ SV19 @ SY69 ) @ SY70 ) @ ( additive_inverse @ ( multiply @ SV19 @ ( multiply @ SY69 @ SY70 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(104,plain,
! [SV20: $i] :
( ( ! [SY71: $i] :
( ( multiply @ ( multiply @ SV20 @ SY71 ) @ SV20 )
!= ( multiply @ SV20 @ ( multiply @ SY71 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(105,plain,
! [SV21: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( associator @ SV21 @ SY72 @ SY73 )
!= ( additive_inverse @ ( associator @ SY72 @ SV21 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(106,plain,
! [SV22: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ( associator @ SV22 @ SY74 @ SY75 )
!= ( additive_inverse @ ( associator @ SY75 @ SY74 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(107,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(108,plain,
! [SV23: $i,SV1: $i] :
( ( ! [SY76: $i] :
( ( multiply @ SV1 @ ( multiply @ SV23 @ ( multiply @ SY76 @ SV23 ) ) )
= ( multiply @ ( multiply @ ( multiply @ SV1 @ SV23 ) @ SY76 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(109,plain,
! [SV24: $i,SV2: $i] :
( ( ! [SY77: $i] :
( ( multiply @ ( multiply @ SV2 @ ( multiply @ SV24 @ SV2 ) ) @ SY77 )
= ( multiply @ SV2 @ ( multiply @ SV24 @ ( multiply @ SV2 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(110,plain,
! [SV25: $i,SV7: $i] :
( ( ( additive_inverse @ ( add @ SV7 @ SV25 ) )
= ( add @ ( additive_inverse @ SV7 ) @ ( additive_inverse @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV26: $i,SV9: $i] :
( ( ! [SY78: $i] :
( ( multiply @ SV9 @ ( add @ SV26 @ SY78 ) )
= ( add @ ( multiply @ SV9 @ SV26 ) @ ( multiply @ SV9 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV27: $i,SV10: $i] :
( ( ! [SY79: $i] :
( ( multiply @ ( add @ SV10 @ SV27 ) @ SY79 )
= ( add @ ( multiply @ SV10 @ SY79 ) @ ( multiply @ SV27 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV28: $i,SV11: $i] :
( ( ( multiply @ ( multiply @ SV11 @ SV28 ) @ SV28 )
= ( multiply @ SV11 @ ( multiply @ SV28 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV29: $i,SV12: $i] :
( ( ( multiply @ ( multiply @ SV12 @ SV12 ) @ SV29 )
= ( multiply @ SV12 @ ( multiply @ SV12 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV30: $i,SV13: $i] :
( ( ( multiply @ ( additive_inverse @ SV13 ) @ SV30 )
= ( additive_inverse @ ( multiply @ SV13 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV31: $i,SV14: $i] :
( ( ( multiply @ SV14 @ ( additive_inverse @ SV31 ) )
= ( additive_inverse @ ( multiply @ SV14 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV32: $i,SV15: $i] :
( ( ( add @ SV15 @ SV32 )
= ( add @ SV32 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV33: $i,SV16: $i] :
( ( ! [SY80: $i] :
( ( add @ SV16 @ ( add @ SV33 @ SY80 ) )
= ( add @ ( add @ SV16 @ SV33 ) @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV34: $i,SV17: $i] :
( ( ! [SY81: $i] :
( ( ( add @ SV17 @ SV34 )
!= ( add @ SY81 @ SV34 ) )
| ( SV17 = SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(120,plain,
! [SV35: $i,SV18: $i] :
( ( ! [SY82: $i] :
( ( ( add @ SV18 @ SV35 )
!= ( add @ SV18 @ SY82 ) )
| ( SV35 = SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV36: $i,SV19: $i] :
( ( ! [SY83: $i] :
( ( associator @ SV19 @ SV36 @ SY83 )
= ( add @ ( multiply @ ( multiply @ SV19 @ SV36 ) @ SY83 ) @ ( additive_inverse @ ( multiply @ SV19 @ ( multiply @ SV36 @ SY83 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV37: $i,SV20: $i] :
( ( ( ( multiply @ ( multiply @ SV20 @ SV37 ) @ SV20 )
!= ( multiply @ SV20 @ ( multiply @ SV37 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV38: $i,SV21: $i] :
( ( ! [SY84: $i] :
( ( associator @ SV21 @ SV38 @ SY84 )
!= ( additive_inverse @ ( associator @ SV38 @ SV21 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV39: $i,SV22: $i] :
( ( ! [SY85: $i] :
( ( associator @ SV22 @ SV39 @ SY85 )
!= ( additive_inverse @ ( associator @ SY85 @ SV39 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV40: $i,SV23: $i,SV1: $i] :
( ( ( multiply @ SV1 @ ( multiply @ SV23 @ ( multiply @ SV40 @ SV23 ) ) )
= ( multiply @ ( multiply @ ( multiply @ SV1 @ SV23 ) @ SV40 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV41: $i,SV24: $i,SV2: $i] :
( ( ( multiply @ ( multiply @ SV2 @ ( multiply @ SV24 @ SV2 ) ) @ SV41 )
= ( multiply @ SV2 @ ( multiply @ SV24 @ ( multiply @ SV2 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV42: $i,SV26: $i,SV9: $i] :
( ( ( multiply @ SV9 @ ( add @ SV26 @ SV42 ) )
= ( add @ ( multiply @ SV9 @ SV26 ) @ ( multiply @ SV9 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV43: $i,SV27: $i,SV10: $i] :
( ( ( multiply @ ( add @ SV10 @ SV27 ) @ SV43 )
= ( add @ ( multiply @ SV10 @ SV43 ) @ ( multiply @ SV27 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV44: $i,SV33: $i,SV16: $i] :
( ( ( add @ SV16 @ ( add @ SV33 @ SV44 ) )
= ( add @ ( add @ SV16 @ SV33 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV45: $i,SV34: $i,SV17: $i] :
( ( ( ( add @ SV17 @ SV34 )
!= ( add @ SV45 @ SV34 ) )
| ( SV17 = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV46: $i,SV35: $i,SV18: $i] :
( ( ( ( add @ SV18 @ SV35 )
!= ( add @ SV18 @ SV46 ) )
| ( SV35 = SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV47: $i,SV36: $i,SV19: $i] :
( ( ( associator @ SV19 @ SV36 @ SV47 )
= ( add @ ( multiply @ ( multiply @ SV19 @ SV36 ) @ SV47 ) @ ( additive_inverse @ ( multiply @ SV19 @ ( multiply @ SV36 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV37: $i,SV20: $i] :
( ( ( multiply @ ( multiply @ SV20 @ SV37 ) @ SV20 )
= ( multiply @ SV20 @ ( multiply @ SV37 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV48: $i,SV38: $i,SV21: $i] :
( ( ( ( associator @ SV21 @ SV38 @ SV48 )
!= ( additive_inverse @ ( associator @ SV38 @ SV21 @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV49: $i,SV39: $i,SV22: $i] :
( ( ( ( associator @ SV22 @ SV39 @ SV49 )
!= ( additive_inverse @ ( associator @ SV49 @ SV39 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV45: $i,SV34: $i,SV17: $i] :
( ( ( ( ( add @ SV17 @ SV34 )
!= ( add @ SV45 @ SV34 ) ) )
= $true )
| ( ( SV17 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV46: $i,SV35: $i,SV18: $i] :
( ( ( ( ( add @ SV18 @ SV35 )
!= ( add @ SV18 @ SV46 ) ) )
= $true )
| ( ( SV35 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV48: $i,SV38: $i,SV21: $i] :
( ( ( associator @ SV21 @ SV38 @ SV48 )
= ( additive_inverse @ ( associator @ SV38 @ SV21 @ SV48 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV49: $i,SV39: $i,SV22: $i] :
( ( ( associator @ SV22 @ SV39 @ SV49 )
= ( additive_inverse @ ( associator @ SV49 @ SV39 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV45: $i,SV34: $i,SV17: $i] :
( ( ( ( add @ SV17 @ SV34 )
= ( add @ SV45 @ SV34 ) )
= $false )
| ( ( SV17 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(141,plain,
! [SV46: $i,SV35: $i,SV18: $i] :
( ( ( ( add @ SV18 @ SV35 )
= ( add @ SV18 @ SV46 ) )
= $false )
| ( ( SV35 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(142,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,141,140,139,138,133,132,129,128,127,126,125,117,116,115,114,113,110,107,92,90,89,88,87,84]) ).
thf(143,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 07:07:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 24
% 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:24,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:26,loop_count:0,foatp_calls:0,translation:fof_full).......
% 0.20/0.48
% 0.20/0.48 ********************************
% 0.20/0.48 * All subproblems solved! *
% 0.20/0.48 ********************************
% 0.20/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.49
% 0.20/0.49 %**** Beginning of derivation protocol ****
% 0.20/0.49 % SZS output start CNFRefutation
% See solution above
% 0.20/0.49
% 0.20/0.49 %**** End of derivation protocol ****
% 0.20/0.49 %**** no. of clauses in derivation: 143 ****
% 0.20/0.49 %**** clause counter: 142 ****
% 0.20/0.49
% 0.20/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:24,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------