TSTP Solution File: RNG023-7 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG023-7 : 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 : n025.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 20:33:58 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 132 ( 124 unt; 8 typ; 0 def)
% Number of atoms : 322 ( 215 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 872 ( 6 ~; 0 |; 0 &; 866 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 242 ( 0 ^ 242 !; 0 ?; 242 :)
% 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_commutator,type,
commutator: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ ( additive_inverse @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Z ) ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference4) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( add @ Y @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Y ) ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference3) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ ( additive_inverse @ Y ) ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference2) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ ( additive_inverse @ Z ) ) )
= ( add @ ( multiply @ X @ Y ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference1) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',associator) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_alternative) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_alternative) ).
thf(12,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_for_addition) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_for_addition) ).
thf(14,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
thf(15,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
thf(16,axiom,
! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(17,axiom,
! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(18,axiom,
! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(19,axiom,
! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_zero) ).
thf(20,axiom,
! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_zero) ).
thf(21,axiom,
! [X: $i] :
( ( add @ X @ additive_identity )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_identity) ).
thf(22,axiom,
! [X: $i] :
( ( add @ additive_identity @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_additive_identity) ).
thf(23,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(24,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,negated_conjecture,
( associator @ x @ x @ y )
!= additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_alternative) ).
thf(26,plain,
$false = $false,
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ ( additive_inverse @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Z ) ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( add @ Y @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Y ) ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ ( additive_inverse @ Y ) ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ ( additive_inverse @ Z ) ) )
= ( add @ ( multiply @ X @ Y ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,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)],[9]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,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(41,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(42,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ( ( associator @ x @ x @ y )
!= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ( ( associator @ x @ x @ y )
!= additive_identity ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(52,plain,
( ( ( ( associator @ x @ x @ y )
!= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(58,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(59,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ X @ ( add @ Y @ Z ) )
= ( add @ ( add @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ X ) @ Y )
= ( multiply @ X @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(66,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)],[35]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ ( additive_inverse @ Z ) ) )
= ( add @ ( multiply @ X @ Y ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ ( additive_inverse @ Y ) ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( add @ Y @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Y ) ) @ ( additive_inverse @ ( multiply @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ ( additive_inverse @ Z ) )
= ( add @ ( additive_inverse @ ( multiply @ X @ Z ) ) @ ( additive_inverse @ ( multiply @ Y @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(75,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( ( associator @ x @ x @ y )
= additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(77,plain,
! [SV1: $i] :
( ( ( add @ additive_identity @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( add @ SV2 @ additive_identity )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(79,plain,
! [SV3: $i] :
( ( ( multiply @ additive_identity @ SV3 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(80,plain,
! [SV4: $i] :
( ( ( multiply @ SV4 @ additive_identity )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( add @ ( additive_inverse @ SV5 ) @ SV5 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(82,plain,
! [SV6: $i] :
( ( ( add @ SV6 @ ( additive_inverse @ SV6 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(83,plain,
! [SV7: $i] :
( ( ( additive_inverse @ ( additive_inverse @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( multiply @ SV8 @ ( add @ SY45 @ SY46 ) )
= ( add @ ( multiply @ SV8 @ SY45 ) @ ( multiply @ SV8 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( multiply @ ( add @ SV9 @ SY47 ) @ SY48 )
= ( add @ ( multiply @ SV9 @ SY48 ) @ ( multiply @ SY47 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(86,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ( add @ SV10 @ SY49 )
= ( add @ SY49 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(87,plain,
! [SV11: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( add @ SV11 @ ( add @ SY50 @ SY51 ) )
= ( add @ ( add @ SV11 @ SY50 ) @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(88,plain,
! [SV12: $i] :
( ( ! [SY52: $i] :
( ( multiply @ ( multiply @ SV12 @ SY52 ) @ SY52 )
= ( multiply @ SV12 @ ( multiply @ SY52 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(89,plain,
! [SV13: $i] :
( ( ! [SY53: $i] :
( ( multiply @ ( multiply @ SV13 @ SV13 ) @ SY53 )
= ( multiply @ SV13 @ ( multiply @ SV13 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(90,plain,
! [SV14: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( associator @ SV14 @ SY54 @ SY55 )
= ( add @ ( multiply @ ( multiply @ SV14 @ SY54 ) @ SY55 ) @ ( additive_inverse @ ( multiply @ SV14 @ ( multiply @ SY54 @ SY55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(91,plain,
! [SV15: $i] :
( ( ! [SY56: $i] :
( ( commutator @ SV15 @ SY56 )
= ( add @ ( multiply @ SY56 @ SV15 ) @ ( additive_inverse @ ( multiply @ SV15 @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(92,plain,
! [SV16: $i] :
( ( ! [SY57: $i] :
( ( multiply @ ( additive_inverse @ SV16 ) @ ( additive_inverse @ SY57 ) )
= ( multiply @ SV16 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(93,plain,
! [SV17: $i] :
( ( ! [SY58: $i] :
( ( multiply @ ( additive_inverse @ SV17 ) @ SY58 )
= ( additive_inverse @ ( multiply @ SV17 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(94,plain,
! [SV18: $i] :
( ( ! [SY59: $i] :
( ( multiply @ SV18 @ ( additive_inverse @ SY59 ) )
= ( additive_inverse @ ( multiply @ SV18 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(95,plain,
! [SV19: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ( multiply @ SV19 @ ( add @ SY60 @ ( additive_inverse @ SY61 ) ) )
= ( add @ ( multiply @ SV19 @ SY60 ) @ ( additive_inverse @ ( multiply @ SV19 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(96,plain,
! [SV20: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ( multiply @ ( add @ SV20 @ ( additive_inverse @ SY62 ) ) @ SY63 )
= ( add @ ( multiply @ SV20 @ SY63 ) @ ( additive_inverse @ ( multiply @ SY62 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(97,plain,
! [SV21: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ( multiply @ ( additive_inverse @ SV21 ) @ ( add @ SY64 @ SY65 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV21 @ SY64 ) ) @ ( additive_inverse @ ( multiply @ SV21 @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(98,plain,
! [SV22: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ( multiply @ ( add @ SV22 @ SY66 ) @ ( additive_inverse @ SY67 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV22 @ SY67 ) ) @ ( additive_inverse @ ( multiply @ SY66 @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(99,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(100,plain,
! [SV23: $i,SV8: $i] :
( ( ! [SY68: $i] :
( ( multiply @ SV8 @ ( add @ SV23 @ SY68 ) )
= ( add @ ( multiply @ SV8 @ SV23 ) @ ( multiply @ SV8 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV24: $i,SV9: $i] :
( ( ! [SY69: $i] :
( ( multiply @ ( add @ SV9 @ SV24 ) @ SY69 )
= ( add @ ( multiply @ SV9 @ SY69 ) @ ( multiply @ SV24 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV25: $i,SV10: $i] :
( ( ( add @ SV10 @ SV25 )
= ( add @ SV25 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY70: $i] :
( ( add @ SV11 @ ( add @ SV26 @ SY70 ) )
= ( add @ ( add @ SV11 @ SV26 ) @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV27: $i,SV12: $i] :
( ( ( multiply @ ( multiply @ SV12 @ SV27 ) @ SV27 )
= ( multiply @ SV12 @ ( multiply @ SV27 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV28: $i,SV13: $i] :
( ( ( multiply @ ( multiply @ SV13 @ SV13 ) @ SV28 )
= ( multiply @ SV13 @ ( multiply @ SV13 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV29: $i,SV14: $i] :
( ( ! [SY71: $i] :
( ( associator @ SV14 @ SV29 @ SY71 )
= ( add @ ( multiply @ ( multiply @ SV14 @ SV29 ) @ SY71 ) @ ( additive_inverse @ ( multiply @ SV14 @ ( multiply @ SV29 @ SY71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(107,plain,
! [SV30: $i,SV15: $i] :
( ( ( commutator @ SV15 @ SV30 )
= ( add @ ( multiply @ SV30 @ SV15 ) @ ( additive_inverse @ ( multiply @ SV15 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV31: $i,SV16: $i] :
( ( ( multiply @ ( additive_inverse @ SV16 ) @ ( additive_inverse @ SV31 ) )
= ( multiply @ SV16 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV32: $i,SV17: $i] :
( ( ( multiply @ ( additive_inverse @ SV17 ) @ SV32 )
= ( additive_inverse @ ( multiply @ SV17 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV33: $i,SV18: $i] :
( ( ( multiply @ SV18 @ ( additive_inverse @ SV33 ) )
= ( additive_inverse @ ( multiply @ SV18 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(111,plain,
! [SV34: $i,SV19: $i] :
( ( ! [SY72: $i] :
( ( multiply @ SV19 @ ( add @ SV34 @ ( additive_inverse @ SY72 ) ) )
= ( add @ ( multiply @ SV19 @ SV34 ) @ ( additive_inverse @ ( multiply @ SV19 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV35: $i,SV20: $i] :
( ( ! [SY73: $i] :
( ( multiply @ ( add @ SV20 @ ( additive_inverse @ SV35 ) ) @ SY73 )
= ( add @ ( multiply @ SV20 @ SY73 ) @ ( additive_inverse @ ( multiply @ SV35 @ SY73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV36: $i,SV21: $i] :
( ( ! [SY74: $i] :
( ( multiply @ ( additive_inverse @ SV21 ) @ ( add @ SV36 @ SY74 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV21 @ SV36 ) ) @ ( additive_inverse @ ( multiply @ SV21 @ SY74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV37: $i,SV22: $i] :
( ( ! [SY75: $i] :
( ( multiply @ ( add @ SV22 @ SV37 ) @ ( additive_inverse @ SY75 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV22 @ SY75 ) ) @ ( additive_inverse @ ( multiply @ SV37 @ SY75 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV38: $i,SV23: $i,SV8: $i] :
( ( ( multiply @ SV8 @ ( add @ SV23 @ SV38 ) )
= ( add @ ( multiply @ SV8 @ SV23 ) @ ( multiply @ SV8 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV39: $i,SV24: $i,SV9: $i] :
( ( ( multiply @ ( add @ SV9 @ SV24 ) @ SV39 )
= ( add @ ( multiply @ SV9 @ SV39 ) @ ( multiply @ SV24 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV40: $i,SV26: $i,SV11: $i] :
( ( ( add @ SV11 @ ( add @ SV26 @ SV40 ) )
= ( add @ ( add @ SV11 @ SV26 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(118,plain,
! [SV41: $i,SV29: $i,SV14: $i] :
( ( ( associator @ SV14 @ SV29 @ SV41 )
= ( add @ ( multiply @ ( multiply @ SV14 @ SV29 ) @ SV41 ) @ ( additive_inverse @ ( multiply @ SV14 @ ( multiply @ SV29 @ SV41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV42: $i,SV34: $i,SV19: $i] :
( ( ( multiply @ SV19 @ ( add @ SV34 @ ( additive_inverse @ SV42 ) ) )
= ( add @ ( multiply @ SV19 @ SV34 ) @ ( additive_inverse @ ( multiply @ SV19 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV43: $i,SV35: $i,SV20: $i] :
( ( ( multiply @ ( add @ SV20 @ ( additive_inverse @ SV35 ) ) @ SV43 )
= ( add @ ( multiply @ SV20 @ SV43 ) @ ( additive_inverse @ ( multiply @ SV35 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(121,plain,
! [SV44: $i,SV36: $i,SV21: $i] :
( ( ( multiply @ ( additive_inverse @ SV21 ) @ ( add @ SV36 @ SV44 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV21 @ SV36 ) ) @ ( additive_inverse @ ( multiply @ SV21 @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(122,plain,
! [SV45: $i,SV37: $i,SV22: $i] :
( ( ( multiply @ ( add @ SV22 @ SV37 ) @ ( additive_inverse @ SV45 ) )
= ( add @ ( additive_inverse @ ( multiply @ SV22 @ SV45 ) ) @ ( additive_inverse @ ( multiply @ SV37 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(123,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,122,121,120,119,118,117,116,115,110,109,108,107,105,104,102,99,83,82,81,80,79,78,77]) ).
thf(124,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG023-7 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 22:30:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 23
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.37 .
% 0.13/0.38 (rf:0,axioms:23,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:25,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.20/0.50
% 0.20/0.50 ********************************
% 0.20/0.50 * All subproblems solved! *
% 0.20/0.50 ********************************
% 0.20/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.51
% 0.20/0.51 %**** Beginning of derivation protocol ****
% 0.20/0.51 % SZS output start CNFRefutation
% See solution above
% 0.20/0.51
% 0.20/0.51 %**** End of derivation protocol ****
% 0.20/0.51 %**** no. of clauses in derivation: 124 ****
% 0.20/0.51 %**** clause counter: 123 ****
% 0.20/0.51
% 0.20/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:123,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------