TSTP Solution File: REL050+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : REL050+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n011.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 19:39:24 EDT 2022
% Result : Theorem 56.85s 57.02s
% Output : CNFRefutation 56.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 26
% Syntax : Number of formulae : 100 ( 91 unt; 9 typ; 0 def)
% Number of atoms : 237 ( 162 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 952 ( 2 ~; 0 |; 0 &; 950 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 187 ( 0 ^ 187 !; 0 ?; 187 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_composition,type,
composition: $i > $i > $i ).
thf(tp_converse,type,
converse: $i > $i ).
thf(tp_join,type,
join: $i > $i > $i ).
thf(tp_meet,type,
meet: $i > $i > $i ).
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_top,type,
top: $i ).
thf(tp_zero,type,
zero: $i ).
thf(1,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
= ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_2) ).
thf(2,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
= ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular_law_1) ).
thf(3,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dedekind_law) ).
thf(4,axiom,
! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero) ).
thf(5,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top) ).
thf(6,axiom,
! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(7,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(8,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity) ).
thf(9,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence) ).
thf(10,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity) ).
thf(11,axiom,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity) ).
thf(12,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity) ).
thf(13,axiom,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(14,axiom,
! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(15,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(16,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(17,conjecture,
! [X0: $i] :
( ( complement @ ( composition @ X0 @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(18,negated_conjecture,
( ( ! [X0: $i] :
( ( complement @ ( composition @ X0 @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [X0: $i] :
( ( complement @ ( composition @ X0 @ top ) )
= ( composition @ ( complement @ ( composition @ X0 @ top ) ) @ top ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
= ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
= ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( ( complement @ ( composition @ sK1_X0 @ top ) )
= ( composition @ ( complement @ ( composition @ sK1_X0 @ top ) ) @ top ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(37,plain,
( ( ( ( complement @ ( composition @ sK1_X0 @ top ) )
!= ( composition @ ( complement @ ( composition @ sK1_X0 @ top ) ) @ top ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [X0: $i] :
( zero
= ( meet @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) )
= ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) )
= ( meet @ ( composition @ X0 @ ( meet @ X1 @ ( composition @ ( converse @ X0 ) @ X2 ) ) ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ ( meet @ ( composition @ X0 @ X1 ) @ X2 ) @ ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) )
= ( meet @ ( composition @ ( meet @ X0 @ ( composition @ X2 @ ( converse @ X1 ) ) ) @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ( ( complement @ ( composition @ sK1_X0 @ top ) )
!= ( composition @ ( complement @ ( composition @ sK1_X0 @ top ) ) @ top ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
! [SV1: $i] :
( ( ! [SY35: $i] :
( ( join @ SV1 @ SY35 )
= ( join @ SY35 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(56,plain,
! [SV2: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( join @ SV2 @ ( join @ SY36 @ SY37 ) )
= ( join @ ( join @ SV2 @ SY36 ) @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(57,plain,
! [SV3: $i] :
( ( ! [SY38: $i] :
( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY38 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(58,plain,
! [SV4: $i] :
( ( ! [SY39: $i] :
( ( meet @ SV4 @ SY39 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(59,plain,
! [SV5: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( composition @ SV5 @ ( composition @ SY40 @ SY41 ) )
= ( composition @ ( composition @ SV5 @ SY40 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(60,plain,
! [SV6: $i] :
( ( ( composition @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(61,plain,
! [SV7: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( composition @ ( join @ SV7 @ SY42 ) @ SY43 )
= ( join @ ( composition @ SV7 @ SY43 ) @ ( composition @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(62,plain,
! [SV8: $i] :
( ( ( converse @ ( converse @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV9: $i] :
( ( ! [SY44: $i] :
( ( converse @ ( join @ SV9 @ SY44 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ( converse @ ( composition @ SV10 @ SY45 ) )
= ( composition @ ( converse @ SY45 ) @ ( converse @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV11: $i] :
( ( ! [SY46: $i] :
( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SY46 ) ) ) @ ( complement @ SY46 ) )
= ( complement @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV12: $i] :
( ( top
= ( join @ SV12 @ ( complement @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV13: $i] :
( ( zero
= ( meet @ SV13 @ ( complement @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV14: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( join @ ( meet @ ( composition @ SV14 @ SY47 ) @ SY48 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SY48 @ ( converse @ SY47 ) ) ) @ ( meet @ SY47 @ ( composition @ ( converse @ SV14 ) @ SY48 ) ) ) )
= ( composition @ ( meet @ SV14 @ ( composition @ SY48 @ ( converse @ SY47 ) ) ) @ ( meet @ SY47 @ ( composition @ ( converse @ SV14 ) @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV15: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( join @ ( meet @ ( composition @ SV15 @ SY49 ) @ SY50 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SY49 @ ( composition @ ( converse @ SV15 ) @ SY50 ) ) ) @ SY50 ) )
= ( meet @ ( composition @ SV15 @ ( meet @ SY49 @ ( composition @ ( converse @ SV15 ) @ SY50 ) ) ) @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV16: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( join @ ( meet @ ( composition @ SV16 @ SY51 ) @ SY52 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY52 @ ( converse @ SY51 ) ) ) @ SY51 ) @ SY52 ) )
= ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY52 @ ( converse @ SY51 ) ) ) @ SY51 ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
( ( ( complement @ ( composition @ sK1_X0 @ top ) )
= ( composition @ ( complement @ ( composition @ sK1_X0 @ top ) ) @ top ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV17: $i,SV1: $i] :
( ( ( join @ SV1 @ SV17 )
= ( join @ SV17 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(73,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY53: $i] :
( ( join @ SV2 @ ( join @ SV18 @ SY53 ) )
= ( join @ ( join @ SV2 @ SV18 ) @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(74,plain,
! [SV19: $i,SV3: $i] :
( ( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV19 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(75,plain,
! [SV20: $i,SV4: $i] :
( ( ( meet @ SV4 @ SV20 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(76,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY54: $i] :
( ( composition @ SV5 @ ( composition @ SV21 @ SY54 ) )
= ( composition @ ( composition @ SV5 @ SV21 ) @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(77,plain,
! [SV22: $i,SV7: $i] :
( ( ! [SY55: $i] :
( ( composition @ ( join @ SV7 @ SV22 ) @ SY55 )
= ( join @ ( composition @ SV7 @ SY55 ) @ ( composition @ SV22 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV23: $i,SV9: $i] :
( ( ( converse @ ( join @ SV9 @ SV23 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV24: $i,SV10: $i] :
( ( ( converse @ ( composition @ SV10 @ SV24 ) )
= ( composition @ ( converse @ SV24 ) @ ( converse @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV25: $i,SV11: $i] :
( ( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SV25 ) ) ) @ ( complement @ SV25 ) )
= ( complement @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY56: $i] :
( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SY56 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SY56 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY56 ) ) ) )
= ( composition @ ( meet @ SV14 @ ( composition @ SY56 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY56 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(82,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY57: $i] :
( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SY57 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SY57 ) ) ) @ SY57 ) )
= ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SY57 ) ) ) @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(83,plain,
! [SV28: $i,SV16: $i] :
( ( ! [SY58: $i] :
( ( join @ ( meet @ ( composition @ SV16 @ SV28 ) @ SY58 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY58 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SY58 ) )
= ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SY58 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(84,plain,
! [SV29: $i,SV18: $i,SV2: $i] :
( ( ( join @ SV2 @ ( join @ SV18 @ SV29 ) )
= ( join @ ( join @ SV2 @ SV18 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV30: $i,SV21: $i,SV5: $i] :
( ( ( composition @ SV5 @ ( composition @ SV21 @ SV30 ) )
= ( composition @ ( composition @ SV5 @ SV21 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV31: $i,SV22: $i,SV7: $i] :
( ( ( composition @ ( join @ SV7 @ SV22 ) @ SV31 )
= ( join @ ( composition @ SV7 @ SV31 ) @ ( composition @ SV22 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV32: $i,SV26: $i,SV14: $i] :
( ( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SV32 ) @ ( composition @ ( meet @ SV14 @ ( composition @ SV32 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) )
= ( composition @ ( meet @ SV14 @ ( composition @ SV32 @ ( converse @ SV26 ) ) ) @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV33: $i,SV27: $i,SV15: $i] :
( ( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SV33 ) @ ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SV33 ) ) ) @ SV33 ) )
= ( meet @ ( composition @ SV15 @ ( meet @ SV27 @ ( composition @ ( converse @ SV15 ) @ SV33 ) ) ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV34: $i,SV28: $i,SV16: $i] :
( ( ( join @ ( meet @ ( composition @ SV16 @ SV28 ) @ SV34 ) @ ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SV34 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SV34 ) )
= ( meet @ ( composition @ ( meet @ SV16 @ ( composition @ SV34 @ ( converse @ SV28 ) ) ) @ SV28 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,89,88,87,86,85,84,80,79,78,75,74,72,71,67,66,62]) ).
thf(91,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : REL050+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 8 07:56:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 16
% 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:16,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:18,loop_count:0,foatp_calls:0,translation:fof_full)......
% 56.85/57.02
% 56.85/57.02 ********************************
% 56.85/57.02 * All subproblems solved! *
% 56.85/57.02 ********************************
% 56.85/57.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:16,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
% 56.85/57.03
% 56.85/57.03 %**** Beginning of derivation protocol ****
% 56.85/57.03 % SZS output start CNFRefutation
% See solution above
% 56.85/57.03
% 56.85/57.03 %**** End of derivation protocol ****
% 56.85/57.03 %**** no. of clauses in derivation: 91 ****
% 56.85/57.03 %**** clause counter: 90 ****
% 56.85/57.03
% 56.85/57.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:16,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:90,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------