TSTP Solution File: RNG011-5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : RNG011-5 : 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 : n017.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 20:33:57 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 121 ( 113 unt; 8 typ; 0 def)
% Number of atoms : 291 ( 194 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 680 ( 6 ~; 0 |; 0 &; 674 @)
% ( 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 : 190 ( 0 ^ 190 !; 0 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
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_b,type,
b: $i ).
thf(tp_commutator,type,
commutator: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ ( associator @ X @ X @ Y ) @ X ) @ ( associator @ X @ X @ Y ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',middle_associator) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutator) ).
thf(3,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(4,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(5,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',distribute2) ).
thf(6,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',distribute1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverse) ).
thf(10,axiom,
! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id2) ).
thf(11,axiom,
! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id1) ).
thf(12,axiom,
! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
thf(13,axiom,
! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute_additive_inverse) ).
thf(14,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ ( add @ ( additive_inverse @ X ) @ Y ) )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_inverse_and_add) ).
thf(15,axiom,
( ( additive_inverse @ additive_identity )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_identity) ).
thf(16,axiom,
! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
thf(17,axiom,
! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
thf(18,axiom,
! [X: $i] :
( ( add @ additive_identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(19,axiom,
! [X: $i] :
( ( add @ X @ additive_identity )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
thf(20,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
thf(22,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(23,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[22]) ).
thf(24,negated_conjecture,
( multiply @ ( multiply @ ( associator @ a @ a @ b ) @ a ) @ ( associator @ a @ a @ b ) )
!= additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
thf(25,plain,
$false = $false,
inference(unfold_def,[status(thm)],[23]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ ( associator @ X @ X @ Y ) @ X ) @ ( associator @ X @ X @ Y ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(28,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)],[3]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(30,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)],[5]) ).
thf(31,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)],[6]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ ( add @ ( additive_inverse @ X ) @ Y ) )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(40,plain,
( ( ( additive_inverse @ additive_identity )
= additive_identity )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(42,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ( ( multiply @ ( multiply @ ( associator @ a @ a @ b ) @ a ) @ ( associator @ a @ a @ b ) )
!= additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(49,plain,
( ( ( ( multiply @ ( multiply @ ( associator @ a @ a @ b ) @ a ) @ ( associator @ a @ a @ b ) )
!= additive_identity ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(50,plain,
( ( ( ( multiply @ ( multiply @ ( associator @ a @ a @ b ) @ a ) @ ( associator @ a @ a @ b ) )
!= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ Y )
= ( add @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( add @ ( add @ X @ Y ) @ Z )
= ( add @ X @ ( add @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( add @ X @ additive_identity )
= X ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( add @ additive_identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( add @ X @ ( additive_inverse @ X ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( add @ ( additive_inverse @ X ) @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(57,plain,
( ( ( additive_inverse @ additive_identity )
= additive_identity )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( add @ X @ ( add @ ( additive_inverse @ X ) @ Y ) )
= Y ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( additive_inverse @ ( add @ X @ Y ) )
= ( add @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( additive_inverse @ ( additive_inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( multiply @ X @ additive_identity )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(62,plain,
( ( ! [X: $i] :
( ( multiply @ additive_identity @ X )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) )
= ( multiply @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ X @ ( additive_inverse @ Y ) )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( additive_inverse @ X ) @ Y )
= ( additive_inverse @ ( multiply @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( add @ Y @ Z ) )
= ( add @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( add @ X @ Y ) @ Z )
= ( add @ ( multiply @ X @ Z ) @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Y )
= ( multiply @ X @ ( multiply @ Y @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(69,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)],[28]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( commutator @ X @ Y )
= ( add @ ( multiply @ Y @ X ) @ ( additive_inverse @ ( multiply @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ( multiply @ ( multiply @ ( associator @ X @ X @ Y ) @ X ) @ ( associator @ X @ X @ Y ) )
= additive_identity ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(72,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(73,plain,
( ( ( multiply @ ( multiply @ ( associator @ a @ a @ b ) @ a ) @ ( associator @ a @ a @ b ) )
= additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(74,plain,
! [SV1: $i] :
( ( ! [SY37: $i] :
( ( add @ SV1 @ SY37 )
= ( add @ SY37 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(75,plain,
! [SV2: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( add @ ( add @ SV2 @ SY38 ) @ SY39 )
= ( add @ SV2 @ ( add @ SY38 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(76,plain,
! [SV3: $i] :
( ( ( add @ SV3 @ additive_identity )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(77,plain,
! [SV4: $i] :
( ( ( add @ additive_identity @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( add @ SV5 @ ( additive_inverse @ SV5 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(79,plain,
! [SV6: $i] :
( ( ( add @ ( additive_inverse @ SV6 ) @ SV6 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(80,plain,
! [SV7: $i] :
( ( ! [SY40: $i] :
( ( add @ SV7 @ ( add @ ( additive_inverse @ SV7 ) @ SY40 ) )
= SY40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV8: $i] :
( ( ! [SY41: $i] :
( ( additive_inverse @ ( add @ SV8 @ SY41 ) )
= ( add @ ( additive_inverse @ SV8 ) @ ( additive_inverse @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV9: $i] :
( ( ( additive_inverse @ ( additive_inverse @ SV9 ) )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV10: $i] :
( ( ( multiply @ SV10 @ additive_identity )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
! [SV11: $i] :
( ( ( multiply @ additive_identity @ SV11 )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(85,plain,
! [SV12: $i] :
( ( ! [SY42: $i] :
( ( multiply @ ( additive_inverse @ SV12 ) @ ( additive_inverse @ SY42 ) )
= ( multiply @ SV12 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV13: $i] :
( ( ! [SY43: $i] :
( ( multiply @ SV13 @ ( additive_inverse @ SY43 ) )
= ( additive_inverse @ ( multiply @ SV13 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV14: $i] :
( ( ! [SY44: $i] :
( ( multiply @ ( additive_inverse @ SV14 ) @ SY44 )
= ( additive_inverse @ ( multiply @ SV14 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV15: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( multiply @ SV15 @ ( add @ SY45 @ SY46 ) )
= ( add @ ( multiply @ SV15 @ SY45 ) @ ( multiply @ SV15 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV16: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( multiply @ ( add @ SV16 @ SY47 ) @ SY48 )
= ( add @ ( multiply @ SV16 @ SY48 ) @ ( multiply @ SY47 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
! [SV17: $i] :
( ( ! [SY49: $i] :
( ( multiply @ ( multiply @ SV17 @ SY49 ) @ SY49 )
= ( multiply @ SV17 @ ( multiply @ SY49 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV18: $i] :
( ( ! [SY50: $i,SY51: $i] :
( ( associator @ SV18 @ SY50 @ SY51 )
= ( add @ ( multiply @ ( multiply @ SV18 @ SY50 ) @ SY51 ) @ ( additive_inverse @ ( multiply @ SV18 @ ( multiply @ SY50 @ SY51 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(92,plain,
! [SV19: $i] :
( ( ! [SY52: $i] :
( ( commutator @ SV19 @ SY52 )
= ( add @ ( multiply @ SY52 @ SV19 ) @ ( additive_inverse @ ( multiply @ SV19 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(93,plain,
! [SV20: $i] :
( ( ! [SY53: $i] :
( ( multiply @ ( multiply @ ( associator @ SV20 @ SV20 @ SY53 ) @ SV20 ) @ ( associator @ SV20 @ SV20 @ SY53 ) )
= additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(94,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(95,plain,
! [SV21: $i,SV1: $i] :
( ( ( add @ SV1 @ SV21 )
= ( add @ SV21 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV22: $i,SV2: $i] :
( ( ! [SY54: $i] :
( ( add @ ( add @ SV2 @ SV22 ) @ SY54 )
= ( add @ SV2 @ ( add @ SV22 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV23: $i,SV7: $i] :
( ( ( add @ SV7 @ ( add @ ( additive_inverse @ SV7 ) @ SV23 ) )
= SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
! [SV24: $i,SV8: $i] :
( ( ( additive_inverse @ ( add @ SV8 @ SV24 ) )
= ( add @ ( additive_inverse @ SV8 ) @ ( additive_inverse @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(99,plain,
! [SV25: $i,SV12: $i] :
( ( ( multiply @ ( additive_inverse @ SV12 ) @ ( additive_inverse @ SV25 ) )
= ( multiply @ SV12 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV26: $i,SV13: $i] :
( ( ( multiply @ SV13 @ ( additive_inverse @ SV26 ) )
= ( additive_inverse @ ( multiply @ SV13 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
! [SV27: $i,SV14: $i] :
( ( ( multiply @ ( additive_inverse @ SV14 ) @ SV27 )
= ( additive_inverse @ ( multiply @ SV14 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV28: $i,SV15: $i] :
( ( ! [SY55: $i] :
( ( multiply @ SV15 @ ( add @ SV28 @ SY55 ) )
= ( add @ ( multiply @ SV15 @ SV28 ) @ ( multiply @ SV15 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV29: $i,SV16: $i] :
( ( ! [SY56: $i] :
( ( multiply @ ( add @ SV16 @ SV29 ) @ SY56 )
= ( add @ ( multiply @ SV16 @ SY56 ) @ ( multiply @ SV29 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV30: $i,SV17: $i] :
( ( ( multiply @ ( multiply @ SV17 @ SV30 ) @ SV30 )
= ( multiply @ SV17 @ ( multiply @ SV30 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV31: $i,SV18: $i] :
( ( ! [SY57: $i] :
( ( associator @ SV18 @ SV31 @ SY57 )
= ( add @ ( multiply @ ( multiply @ SV18 @ SV31 ) @ SY57 ) @ ( additive_inverse @ ( multiply @ SV18 @ ( multiply @ SV31 @ SY57 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV32: $i,SV19: $i] :
( ( ( commutator @ SV19 @ SV32 )
= ( add @ ( multiply @ SV32 @ SV19 ) @ ( additive_inverse @ ( multiply @ SV19 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV33: $i,SV20: $i] :
( ( ( multiply @ ( multiply @ ( associator @ SV20 @ SV20 @ SV33 ) @ SV20 ) @ ( associator @ SV20 @ SV20 @ SV33 ) )
= additive_identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV34: $i,SV22: $i,SV2: $i] :
( ( ( add @ ( add @ SV2 @ SV22 ) @ SV34 )
= ( add @ SV2 @ ( add @ SV22 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV35: $i,SV28: $i,SV15: $i] :
( ( ( multiply @ SV15 @ ( add @ SV28 @ SV35 ) )
= ( add @ ( multiply @ SV15 @ SV28 ) @ ( multiply @ SV15 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
! [SV36: $i,SV29: $i,SV16: $i] :
( ( ( multiply @ ( add @ SV16 @ SV29 ) @ SV36 )
= ( add @ ( multiply @ SV16 @ SV36 ) @ ( multiply @ SV29 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(111,plain,
! [SV37: $i,SV31: $i,SV18: $i] :
( ( ( associator @ SV18 @ SV31 @ SV37 )
= ( add @ ( multiply @ ( multiply @ SV18 @ SV31 ) @ SV37 ) @ ( additive_inverse @ ( multiply @ SV18 @ ( multiply @ SV31 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(112,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,111,110,109,108,107,106,104,101,100,99,98,97,95,94,84,83,82,79,78,77,76,73]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n017.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 : Mon May 30 19:15:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 22
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 .
% 0.12/0.35 (rf:0,axioms:22,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:24,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.19/0.41
% 0.19/0.41 ********************************
% 0.19/0.41 * All subproblems solved! *
% 0.19/0.41 ********************************
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 113 ****
% 0.19/0.41 %**** clause counter: 112 ****
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:22,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:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------