%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:37:23 AM UTC 2026
% Result : Theorem 8.19s 1.61s
% Output : CNFRefutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 248 ( 171 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 1000 ( 2 ~; 0 |; 0 &; 992 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 192 ( 0 ^; 192 !; 0 ?; 192 :)
% 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_sK2_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',dedekind_law) ).
thf(5,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(7,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(8,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(9,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
thf(11,axiom,
! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
thf(13,axiom,
! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(16,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(17,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ X0 @ ( converse @ X1 ) ) @ X2 )
= X2 )
=> ( ( join @ ( composition @ ( complement @ X2 ) @ X1 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(18,negated_conjecture,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ X0 @ ( converse @ X1 ) ) @ X2 )
= X2 )
=> ( ( join @ ( composition @ ( complement @ X2 ) @ X1 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( join @ ( composition @ X0 @ ( converse @ X1 ) ) @ X2 )
= X2 )
=> ( ( join @ ( composition @ ( complement @ X2 ) @ X1 ) @ ( complement @ X0 ) )
= ( complement @ X0 ) ) ) )
= $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] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,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(25,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,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(29,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,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(31,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,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(33,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(34,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(35,plain,
( ( ! [SY36: $i,SY37: $i] :
( ( ( join @ ( composition @ sK1_X0 @ ( converse @ SY36 ) ) @ SY37 )
= SY37 )
=> ( ( join @ ( composition @ ( complement @ SY37 ) @ SY36 ) @ ( complement @ sK1_X0 ) )
= ( complement @ sK1_X0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [SY38: $i] :
( ( ( join @ ( composition @ sK1_X0 @ ( converse @ sK2_SY36 ) ) @ SY38 )
= SY38 )
=> ( ( join @ ( composition @ ( complement @ SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
= ( complement @ sK1_X0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(37,plain,
( ( ( ( join @ ( composition @ sK1_X0 @ ( converse @ sK2_SY36 ) ) @ sK3_SY38 )
= sK3_SY38 )
=> ( ( join @ ( composition @ ( complement @ sK3_SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
= ( complement @ sK1_X0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(38,plain,
( ( ( join @ ( composition @ sK1_X0 @ ( converse @ sK2_SY36 ) ) @ sK3_SY38 )
= sK3_SY38 )
= $true ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(39,plain,
( ( ( join @ ( composition @ ( complement @ sK3_SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
= ( complement @ sK1_X0 ) )
= $false ),
inference(standard_cnf,[status(thm)],[37]) ).
thf(40,plain,
( ( ( join @ ( composition @ ( complement @ sK3_SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
!= ( complement @ sK1_X0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(42,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(43,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(44,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(45,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ X0 @ ( composition @ X1 @ X2 ) )
= ( composition @ ( composition @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(46,plain,
( ( ! [X0: $i] :
( ( composition @ X0 @ one )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(47,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(48,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(49,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(50,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(52,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(53,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(54,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(55,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(56,plain,
( ( ( join @ ( composition @ sK1_X0 @ ( converse @ sK2_SY36 ) ) @ sK3_SY38 )
= sK3_SY38 )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(57,plain,
( ( ( join @ ( composition @ ( complement @ sK3_SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
!= ( complement @ sK1_X0 ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(58,plain,
! [SV1: $i] :
( ( ! [SY39: $i] :
( ( join @ SV1 @ SY39 )
= ( join @ SY39 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(59,plain,
! [SV2: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( join @ SV2 @ ( join @ SY40 @ SY41 ) )
= ( join @ ( join @ SV2 @ SY40 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(60,plain,
! [SV3: $i] :
( ( ! [SY42: $i] :
( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY42 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY42 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(61,plain,
! [SV4: $i] :
( ( ! [SY43: $i] :
( ( meet @ SV4 @ SY43 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SY43 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(62,plain,
! [SV5: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( composition @ SV5 @ ( composition @ SY44 @ SY45 ) )
= ( composition @ ( composition @ SV5 @ SY44 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV6: $i] :
( ( ( composition @ SV6 @ one )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV7: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( composition @ ( join @ SV7 @ SY46 ) @ SY47 )
= ( join @ ( composition @ SV7 @ SY47 ) @ ( composition @ SY46 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV8: $i] :
( ( ( converse @ ( converse @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV9: $i] :
( ( ! [SY48: $i] :
( ( converse @ ( join @ SV9 @ SY48 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ( converse @ ( composition @ SV10 @ SY49 ) )
= ( composition @ ( converse @ SY49 ) @ ( converse @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV11: $i] :
( ( ! [SY50: $i] :
( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SY50 ) ) ) @ ( complement @ SY50 ) )
= ( complement @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV12: $i] :
( ( top
= ( join @ SV12 @ ( complement @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV13: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( join @ ( meet @ ( composition @ SV13 @ SY51 ) @ SY52 ) @ ( composition @ ( meet @ SV13 @ ( composition @ SY52 @ ( converse @ SY51 ) ) ) @ ( meet @ SY51 @ ( composition @ ( converse @ SV13 ) @ SY52 ) ) ) )
= ( composition @ ( meet @ SV13 @ ( composition @ SY52 @ ( converse @ SY51 ) ) ) @ ( meet @ SY51 @ ( composition @ ( converse @ SV13 ) @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV14: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( join @ ( meet @ ( composition @ SV14 @ SY53 ) @ SY54 ) @ ( meet @ ( composition @ SV14 @ ( meet @ SY53 @ ( composition @ ( converse @ SV14 ) @ SY54 ) ) ) @ SY54 ) )
= ( meet @ ( composition @ SV14 @ ( meet @ SY53 @ ( composition @ ( converse @ SV14 ) @ SY54 ) ) ) @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(72,plain,
! [SV15: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( join @ ( meet @ ( composition @ SV15 @ SY55 ) @ SY56 ) @ ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SY56 @ ( converse @ SY55 ) ) ) @ SY55 ) @ SY56 ) )
= ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SY56 @ ( converse @ SY55 ) ) ) @ SY55 ) @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(73,plain,
( ( ( join @ ( composition @ ( complement @ sK3_SY38 ) @ sK2_SY36 ) @ ( complement @ sK1_X0 ) )
= ( complement @ sK1_X0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV16: $i,SV1: $i] :
( ( ( join @ SV1 @ SV16 )
= ( join @ SV16 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV17: $i,SV2: $i] :
( ( ! [SY57: $i] :
( ( join @ SV2 @ ( join @ SV17 @ SY57 ) )
= ( join @ ( join @ SV2 @ SV17 ) @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV18: $i,SV3: $i] :
( ( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV18 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV19: $i,SV4: $i] :
( ( ( meet @ SV4 @ SV19 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY58: $i] :
( ( composition @ SV5 @ ( composition @ SV20 @ SY58 ) )
= ( composition @ ( composition @ SV5 @ SV20 ) @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY59: $i] :
( ( composition @ ( join @ SV7 @ SV21 ) @ SY59 )
= ( join @ ( composition @ SV7 @ SY59 ) @ ( composition @ SV21 @ SY59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV22: $i,SV9: $i] :
( ( ( converse @ ( join @ SV9 @ SV22 ) )
= ( join @ ( converse @ SV9 ) @ ( converse @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(81,plain,
! [SV23: $i,SV10: $i] :
( ( ( converse @ ( composition @ SV10 @ SV23 ) )
= ( composition @ ( converse @ SV23 ) @ ( converse @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV24: $i,SV11: $i] :
( ( ( join @ ( composition @ ( converse @ SV11 ) @ ( complement @ ( composition @ SV11 @ SV24 ) ) ) @ ( complement @ SV24 ) )
= ( complement @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY60: $i] :
( ( join @ ( meet @ ( composition @ SV13 @ SV25 ) @ SY60 ) @ ( composition @ ( meet @ SV13 @ ( composition @ SY60 @ ( converse @ SV25 ) ) ) @ ( meet @ SV25 @ ( composition @ ( converse @ SV13 ) @ SY60 ) ) ) )
= ( composition @ ( meet @ SV13 @ ( composition @ SY60 @ ( converse @ SV25 ) ) ) @ ( meet @ SV25 @ ( composition @ ( converse @ SV13 ) @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(84,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY61: $i] :
( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SY61 ) @ ( meet @ ( composition @ SV14 @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY61 ) ) ) @ SY61 ) )
= ( meet @ ( composition @ SV14 @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SY61 ) ) ) @ SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(85,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY62: $i] :
( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SY62 ) @ ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SY62 @ ( converse @ SV27 ) ) ) @ SV27 ) @ SY62 ) )
= ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SY62 @ ( converse @ SV27 ) ) ) @ SV27 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV28: $i,SV17: $i,SV2: $i] :
( ( ( join @ SV2 @ ( join @ SV17 @ SV28 ) )
= ( join @ ( join @ SV2 @ SV17 ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV29: $i,SV20: $i,SV5: $i] :
( ( ( composition @ SV5 @ ( composition @ SV20 @ SV29 ) )
= ( composition @ ( composition @ SV5 @ SV20 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV30: $i,SV21: $i,SV7: $i] :
( ( ( composition @ ( join @ SV7 @ SV21 ) @ SV30 )
= ( join @ ( composition @ SV7 @ SV30 ) @ ( composition @ SV21 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV31: $i,SV25: $i,SV13: $i] :
( ( ( join @ ( meet @ ( composition @ SV13 @ SV25 ) @ SV31 ) @ ( composition @ ( meet @ SV13 @ ( composition @ SV31 @ ( converse @ SV25 ) ) ) @ ( meet @ SV25 @ ( composition @ ( converse @ SV13 ) @ SV31 ) ) ) )
= ( composition @ ( meet @ SV13 @ ( composition @ SV31 @ ( converse @ SV25 ) ) ) @ ( meet @ SV25 @ ( composition @ ( converse @ SV13 ) @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV32: $i,SV26: $i,SV14: $i] :
( ( ( join @ ( meet @ ( composition @ SV14 @ SV26 ) @ SV32 ) @ ( meet @ ( composition @ SV14 @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) @ SV32 ) )
= ( meet @ ( composition @ SV14 @ ( meet @ SV26 @ ( composition @ ( converse @ SV14 ) @ SV32 ) ) ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV33: $i,SV27: $i,SV15: $i] :
( ( ( join @ ( meet @ ( composition @ SV15 @ SV27 ) @ SV33 ) @ ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SV33 @ ( converse @ SV27 ) ) ) @ SV27 ) @ SV33 ) )
= ( meet @ ( composition @ ( meet @ SV15 @ ( composition @ SV33 @ ( converse @ SV27 ) ) ) @ SV27 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[56,91,90,89,88,87,86,82,81,80,77,76,74,73,69,65,63]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL043+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n014.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 14:06:11 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.19/1.61
% 8.19/1.61 No.of.Axioms: 15
% 8.19/1.61
% 8.19/1.61 Length.of.Defs: 0
% 8.19/1.61
% 8.19/1.61 Contains.Choice.Funs: false
% 8.19/1.61 ..
% 8.19/1.61
% 8.19/1.61 ********************************
% 8.19/1.61 * All subproblems solved! *
% 8.19/1.61 ********************************
% 8.19/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.19/1.61
% 8.19/1.61 %**** Beginning of derivation protocol ****
% 8.19/1.61 % SZS output start CNFRefutation
% See solution above
% 8.19/1.61
% 8.19/1.61 %**** End of derivation protocol ****
% 8.19/1.61 %**** no. of clauses in derivation: 92 ****
% 8.19/1.61 %**** clause counter: 92 ****
% 8.19/1.61
% 8.19/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------