TSTP Solution File: GRP181-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP181-4 : 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 : n021.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 10:16:47 EDT 2022
% Result : Unsatisfiable 8.88s 9.06s
% Output : CNFRefutation 8.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 127 ( 119 unt; 8 typ; 0 def)
% Number of atoms : 307 ( 205 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 646 ( 6 ~; 0 |; 0 &; 640 @)
% ( 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 : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 216 ( 0 ^ 216 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_greatest_lower_bound,type,
greatest_lower_bound: $i > $i > $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_least_upper_bound,type,
least_upper_bound: $i > $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(1,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
= ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(2,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
= ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(7,axiom,
! [X: $i] :
( ( greatest_lower_bound @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(8,axiom,
! [X: $i] :
( ( least_upper_bound @ X @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ Y )
= ( least_upper_bound @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ Y )
= ( greatest_lower_bound @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(13,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(14,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(15,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ( inverse @ ( least_upper_bound @ X @ Y ) )
= ( greatest_lower_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_7) ).
thf(17,axiom,
! [X: $i,Y: $i] :
( ( inverse @ ( greatest_lower_bound @ X @ Y ) )
= ( least_upper_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_6) ).
thf(18,axiom,
( ( least_upper_bound @ a @ c )
= ( least_upper_bound @ b @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_5) ).
thf(19,axiom,
( ( greatest_lower_bound @ a @ c )
= ( greatest_lower_bound @ b @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_4) ).
thf(20,axiom,
! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_3) ).
thf(21,axiom,
! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_2) ).
thf(22,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12x_1) ).
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,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p12x) ).
thf(26,plain,
$false = $false,
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
= ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
= ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( greatest_lower_bound @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( least_upper_bound @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ Y )
= ( least_upper_bound @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ Y )
= ( greatest_lower_bound @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( least_upper_bound @ X @ Y ) )
= ( greatest_lower_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( greatest_lower_bound @ X @ Y ) )
= ( least_upper_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( ( least_upper_bound @ a @ c )
= ( least_upper_bound @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ( greatest_lower_bound @ a @ c )
= ( greatest_lower_bound @ b @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ( inverse @ identity )
= identity )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( ( a != b ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ( a != b ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(52,plain,
( ( ( a != b ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(53,plain,
( ( ( inverse @ identity )
= identity )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(54,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(56,plain,
( ( ( greatest_lower_bound @ a @ c )
= ( greatest_lower_bound @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(57,plain,
( ( ( least_upper_bound @ a @ c )
= ( least_upper_bound @ b @ c ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( greatest_lower_bound @ X @ Y ) )
= ( least_upper_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( least_upper_bound @ X @ Y ) )
= ( greatest_lower_bound @ ( inverse @ X ) @ ( inverse @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(60,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(61,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ Y )
= ( greatest_lower_bound @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ Y )
= ( least_upper_bound @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( greatest_lower_bound @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( least_upper_bound @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( least_upper_bound @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( least_upper_bound @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(68,plain,
( ( ! [X: $i] :
( ( greatest_lower_bound @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ( least_upper_bound @ X @ ( greatest_lower_bound @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( greatest_lower_bound @ X @ ( least_upper_bound @ X @ Y ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( least_upper_bound @ Y @ Z ) )
= ( least_upper_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( greatest_lower_bound @ Y @ Z ) )
= ( greatest_lower_bound @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(73,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( least_upper_bound @ Y @ Z ) @ X )
= ( least_upper_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(74,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( greatest_lower_bound @ Y @ Z ) @ X )
= ( greatest_lower_bound @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(75,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(76,plain,
( ( a = b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(77,plain,
! [SV1: $i] :
( ( ( inverse @ ( inverse @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(78,plain,
! [SV2: $i] :
( ( ! [SY40: $i] :
( ( inverse @ ( multiply @ SV2 @ SY40 ) )
= ( multiply @ ( inverse @ SY40 ) @ ( inverse @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(79,plain,
! [SV3: $i] :
( ( ! [SY41: $i] :
( ( inverse @ ( greatest_lower_bound @ SV3 @ SY41 ) )
= ( least_upper_bound @ ( inverse @ SV3 ) @ ( inverse @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(80,plain,
! [SV4: $i] :
( ( ! [SY42: $i] :
( ( inverse @ ( least_upper_bound @ SV4 @ SY42 ) )
= ( greatest_lower_bound @ ( inverse @ SV4 ) @ ( inverse @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( multiply @ identity @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV6: $i] :
( ( ( multiply @ ( inverse @ SV6 ) @ SV6 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV7: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( multiply @ ( multiply @ SV7 @ SY43 ) @ SY44 )
= ( multiply @ SV7 @ ( multiply @ SY43 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV8: $i] :
( ( ! [SY45: $i] :
( ( greatest_lower_bound @ SV8 @ SY45 )
= ( greatest_lower_bound @ SY45 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY46: $i] :
( ( least_upper_bound @ SV9 @ SY46 )
= ( least_upper_bound @ SY46 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV10: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( greatest_lower_bound @ SV10 @ ( greatest_lower_bound @ SY47 @ SY48 ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ SV10 @ SY47 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV11: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( least_upper_bound @ SV11 @ ( least_upper_bound @ SY49 @ SY50 ) )
= ( least_upper_bound @ ( least_upper_bound @ SV11 @ SY49 ) @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV12: $i] :
( ( ( least_upper_bound @ SV12 @ SV12 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV13: $i] :
( ( ( greatest_lower_bound @ SV13 @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV14: $i] :
( ( ! [SY51: $i] :
( ( least_upper_bound @ SV14 @ ( greatest_lower_bound @ SV14 @ SY51 ) )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV15: $i] :
( ( ! [SY52: $i] :
( ( greatest_lower_bound @ SV15 @ ( least_upper_bound @ SV15 @ SY52 ) )
= SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV16: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( multiply @ SV16 @ ( least_upper_bound @ SY53 @ SY54 ) )
= ( least_upper_bound @ ( multiply @ SV16 @ SY53 ) @ ( multiply @ SV16 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV17: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( multiply @ SV17 @ ( greatest_lower_bound @ SY55 @ SY56 ) )
= ( greatest_lower_bound @ ( multiply @ SV17 @ SY55 ) @ ( multiply @ SV17 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV18: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ( multiply @ ( least_upper_bound @ SV18 @ SY57 ) @ SY58 )
= ( least_upper_bound @ ( multiply @ SV18 @ SY58 ) @ ( multiply @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV19: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ( multiply @ ( greatest_lower_bound @ SV19 @ SY59 ) @ SY60 )
= ( greatest_lower_bound @ ( multiply @ SV19 @ SY60 ) @ ( multiply @ SY59 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV20: $i,SV2: $i] :
( ( ( inverse @ ( multiply @ SV2 @ SV20 ) )
= ( multiply @ ( inverse @ SV20 ) @ ( inverse @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(98,plain,
! [SV21: $i,SV3: $i] :
( ( ( inverse @ ( greatest_lower_bound @ SV3 @ SV21 ) )
= ( least_upper_bound @ ( inverse @ SV3 ) @ ( inverse @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(99,plain,
! [SV22: $i,SV4: $i] :
( ( ( inverse @ ( least_upper_bound @ SV4 @ SV22 ) )
= ( greatest_lower_bound @ ( inverse @ SV4 ) @ ( inverse @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(100,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY61: $i] :
( ( multiply @ ( multiply @ SV7 @ SV23 ) @ SY61 )
= ( multiply @ SV7 @ ( multiply @ SV23 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV24: $i,SV8: $i] :
( ( ( greatest_lower_bound @ SV8 @ SV24 )
= ( greatest_lower_bound @ SV24 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV25: $i,SV9: $i] :
( ( ( least_upper_bound @ SV9 @ SV25 )
= ( least_upper_bound @ SV25 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY62: $i] :
( ( greatest_lower_bound @ SV10 @ ( greatest_lower_bound @ SV26 @ SY62 ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ SV10 @ SV26 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV27: $i,SV11: $i] :
( ( ! [SY63: $i] :
( ( least_upper_bound @ SV11 @ ( least_upper_bound @ SV27 @ SY63 ) )
= ( least_upper_bound @ ( least_upper_bound @ SV11 @ SV27 ) @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV28: $i,SV14: $i] :
( ( ( least_upper_bound @ SV14 @ ( greatest_lower_bound @ SV14 @ SV28 ) )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV29: $i,SV15: $i] :
( ( ( greatest_lower_bound @ SV15 @ ( least_upper_bound @ SV15 @ SV29 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY64: $i] :
( ( multiply @ SV16 @ ( least_upper_bound @ SV30 @ SY64 ) )
= ( least_upper_bound @ ( multiply @ SV16 @ SV30 ) @ ( multiply @ SV16 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV31: $i,SV17: $i] :
( ( ! [SY65: $i] :
( ( multiply @ SV17 @ ( greatest_lower_bound @ SV31 @ SY65 ) )
= ( greatest_lower_bound @ ( multiply @ SV17 @ SV31 ) @ ( multiply @ SV17 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV32: $i,SV18: $i] :
( ( ! [SY66: $i] :
( ( multiply @ ( least_upper_bound @ SV18 @ SV32 ) @ SY66 )
= ( least_upper_bound @ ( multiply @ SV18 @ SY66 ) @ ( multiply @ SV32 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV33: $i,SV19: $i] :
( ( ! [SY67: $i] :
( ( multiply @ ( greatest_lower_bound @ SV19 @ SV33 ) @ SY67 )
= ( greatest_lower_bound @ ( multiply @ SV19 @ SY67 ) @ ( multiply @ SV33 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV34: $i,SV23: $i,SV7: $i] :
( ( ( multiply @ ( multiply @ SV7 @ SV23 ) @ SV34 )
= ( multiply @ SV7 @ ( multiply @ SV23 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV35: $i,SV26: $i,SV10: $i] :
( ( ( greatest_lower_bound @ SV10 @ ( greatest_lower_bound @ SV26 @ SV35 ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ SV10 @ SV26 ) @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV36: $i,SV27: $i,SV11: $i] :
( ( ( least_upper_bound @ SV11 @ ( least_upper_bound @ SV27 @ SV36 ) )
= ( least_upper_bound @ ( least_upper_bound @ SV11 @ SV27 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV37: $i,SV30: $i,SV16: $i] :
( ( ( multiply @ SV16 @ ( least_upper_bound @ SV30 @ SV37 ) )
= ( least_upper_bound @ ( multiply @ SV16 @ SV30 ) @ ( multiply @ SV16 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(115,plain,
! [SV38: $i,SV31: $i,SV17: $i] :
( ( ( multiply @ SV17 @ ( greatest_lower_bound @ SV31 @ SV38 ) )
= ( greatest_lower_bound @ ( multiply @ SV17 @ SV31 ) @ ( multiply @ SV17 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV39: $i,SV32: $i,SV18: $i] :
( ( ( multiply @ ( least_upper_bound @ SV18 @ SV32 ) @ SV39 )
= ( least_upper_bound @ ( multiply @ SV18 @ SV39 ) @ ( multiply @ SV32 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV40: $i,SV33: $i,SV19: $i] :
( ( ( multiply @ ( greatest_lower_bound @ SV19 @ SV33 ) @ SV40 )
= ( greatest_lower_bound @ ( multiply @ SV19 @ SV40 ) @ ( multiply @ SV33 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(118,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,117,116,115,114,113,112,111,106,105,102,101,99,98,97,96,89,88,82,81,77,76,57,56]) ).
thf(119,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP181-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:24:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 23
% 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 (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)......
% 8.88/9.06
% 8.88/9.06 ********************************
% 8.88/9.06 * All subproblems solved! *
% 8.88/9.06 ********************************
% 8.88/9.06 % 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:118,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.88/9.07
% 8.88/9.07 %**** Beginning of derivation protocol ****
% 8.88/9.07 % SZS output start CNFRefutation
% See solution above
% 8.88/9.07
% 8.88/9.07 %**** End of derivation protocol ****
% 8.88/9.07 %**** no. of clauses in derivation: 119 ****
% 8.88/9.07 %**** clause counter: 118 ****
% 8.88/9.07
% 8.88/9.07 % 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:118,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------