%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : REL003+1 : 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 10:37:09 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 313 ( 218 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 776 ( 12 ~; 4 |; 5 &; 739 @)
% ( 0 <=>; 16 =>; 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 : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 175 ( 0 ^; 175 !; 0 ?; 175 :)
% 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_SY22,type,
sK2_SY22: $i ).
thf(tp_top,type,
top: $i ).
thf(tp_zero,type,
zero: $i ).
thf(2,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(3,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(4,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(5,axiom,
! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(6,axiom,
! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(7,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(10,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(11,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(12,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(13,axiom,
! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(14,conjecture,
! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(15,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( join @ X0 @ X1 )
= X1 )
=> ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) ) )
& ( ( ( join @ ( converse @ X0 ) @ ( converse @ X1 ) )
= ( converse @ X1 ) )
=> ( ( join @ X0 @ X1 )
= X1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,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)],[7]) ).
thf(23,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(26,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( ! [SY22: $i] :
( ( ( ( join @ sK1_X0 @ SY22 )
= SY22 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ SY22 ) )
= ( converse @ SY22 ) ) )
& ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ SY22 ) )
= ( converse @ SY22 ) )
=> ( ( join @ sK1_X0 @ SY22 )
= SY22 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(28,plain,
( ( ( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) )
& ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
=> ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[28]) ).
thf(30,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
=> ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[28]) ).
thf(31,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
=> ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(33,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(34,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(35,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(37,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(38,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(39,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(40,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(41,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(42,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(43,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
=> ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(44,plain,
( ( ~ ( ( ( join @ sK1_X0 @ sK2_SY22 )
!= sK2_SY22 )
| ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ( join @ SV1 @ SY23 )
= ( join @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( join @ SV2 @ ( join @ SY24 @ SY25 ) )
= ( join @ ( join @ SV2 @ SY24 ) @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY26: $i] :
( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY26 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(48,plain,
! [SV4: $i] :
( ( ! [SY27: $i] :
( ( meet @ SV4 @ SY27 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(49,plain,
! [SV5: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ( composition @ ( join @ SV5 @ SY28 ) @ SY29 )
= ( join @ ( composition @ SV5 @ SY29 ) @ ( composition @ SY28 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(50,plain,
! [SV6: $i] :
( ( ( converse @ ( converse @ SV6 ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(51,plain,
! [SV7: $i] :
( ( ! [SY30: $i] :
( ( converse @ ( join @ SV7 @ SY30 ) )
= ( join @ ( converse @ SV7 ) @ ( converse @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(52,plain,
! [SV8: $i] :
( ( ! [SY31: $i] :
( ( converse @ ( composition @ SV8 @ SY31 ) )
= ( composition @ ( converse @ SY31 ) @ ( converse @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV9: $i] :
( ( ! [SY32: $i] :
( ( join @ ( composition @ ( converse @ SV9 ) @ ( complement @ ( composition @ SV9 @ SY32 ) ) ) @ ( complement @ SY32 ) )
= ( complement @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV10: $i] :
( ( top
= ( join @ SV10 @ ( complement @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
( ( ( ( join @ sK1_X0 @ sK2_SY22 )
!= sK2_SY22 )
| ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV11: $i,SV1: $i] :
( ( ( join @ SV1 @ SV11 )
= ( join @ SV11 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV12: $i,SV2: $i] :
( ( ! [SY33: $i] :
( ( join @ SV2 @ ( join @ SV12 @ SY33 ) )
= ( join @ ( join @ SV2 @ SV12 ) @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV13: $i,SV3: $i] :
( ( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV13 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV14: $i,SV4: $i] :
( ( ( meet @ SV4 @ SV14 )
= ( complement @ ( join @ ( complement @ SV4 ) @ ( complement @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV15: $i,SV5: $i] :
( ( ! [SY34: $i] :
( ( composition @ ( join @ SV5 @ SV15 ) @ SY34 )
= ( join @ ( composition @ SV5 @ SY34 ) @ ( composition @ SV15 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV16: $i,SV7: $i] :
( ( ( converse @ ( join @ SV7 @ SV16 ) )
= ( join @ ( converse @ SV7 ) @ ( converse @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV17: $i,SV8: $i] :
( ( ( converse @ ( composition @ SV8 @ SV17 ) )
= ( composition @ ( converse @ SV17 ) @ ( converse @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV18: $i,SV9: $i] :
( ( ( join @ ( composition @ ( converse @ SV9 ) @ ( complement @ ( composition @ SV9 @ SV18 ) ) ) @ ( complement @ SV18 ) )
= ( complement @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
( ( ( join @ sK1_X0 @ sK2_SY22 )
!= sK2_SY22 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(65,plain,
( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(66,plain,
! [SV19: $i,SV12: $i,SV2: $i] :
( ( ( join @ SV2 @ ( join @ SV12 @ SV19 ) )
= ( join @ ( join @ SV2 @ SV12 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV20: $i,SV15: $i,SV5: $i] :
( ( ( composition @ ( join @ SV5 @ SV15 ) @ SV20 )
= ( join @ ( composition @ SV5 @ SV20 ) @ ( composition @ SV15 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,68,67,66,65,63,62,61,59,58,56,54]) ).
thf(70,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(72,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(73,plain,
( ( ! [X0: $i,X1: $i] :
( ( meet @ X0 @ X1 )
= ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(74,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(75,plain,
( ( ! [X0: $i] :
( ( converse @ ( converse @ X0 ) )
= X0 ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(76,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(77,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( composition @ X0 @ X1 ) )
= ( composition @ ( converse @ X1 ) @ ( converse @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(78,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ ( composition @ ( converse @ X0 ) @ ( complement @ ( composition @ X0 @ X1 ) ) ) @ ( complement @ X1 ) )
= ( complement @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(79,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(80,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
=> ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(81,plain,
( ( ~ ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
!= ( converse @ sK2_SY22 ) )
| ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(82,plain,
! [SV21: $i] :
( ( ! [SY35: $i] :
( ( join @ SV21 @ SY35 )
= ( join @ SY35 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV22: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ( join @ SV22 @ ( join @ SY36 @ SY37 ) )
= ( join @ ( join @ SV22 @ SY36 ) @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV23: $i] :
( ( ! [SY38: $i] :
( SV23
= ( join @ ( complement @ ( join @ ( complement @ SV23 ) @ ( complement @ SY38 ) ) ) @ ( complement @ ( join @ ( complement @ SV23 ) @ SY38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV24: $i] :
( ( ! [SY39: $i] :
( ( meet @ SV24 @ SY39 )
= ( complement @ ( join @ ( complement @ SV24 ) @ ( complement @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV25: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ( composition @ ( join @ SV25 @ SY40 ) @ SY41 )
= ( join @ ( composition @ SV25 @ SY41 ) @ ( composition @ SY40 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV26: $i] :
( ( ( converse @ ( converse @ SV26 ) )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV27: $i] :
( ( ! [SY42: $i] :
( ( converse @ ( join @ SV27 @ SY42 ) )
= ( join @ ( converse @ SV27 ) @ ( converse @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV28: $i] :
( ( ! [SY43: $i] :
( ( converse @ ( composition @ SV28 @ SY43 ) )
= ( composition @ ( converse @ SY43 ) @ ( converse @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(90,plain,
! [SV29: $i] :
( ( ! [SY44: $i] :
( ( join @ ( composition @ ( converse @ SV29 ) @ ( complement @ ( composition @ SV29 @ SY44 ) ) ) @ ( complement @ SY44 ) )
= ( complement @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(91,plain,
! [SV30: $i] :
( ( top
= ( join @ SV30 @ ( complement @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(92,plain,
( ( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
!= ( converse @ sK2_SY22 ) )
| ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV31: $i,SV21: $i] :
( ( ( join @ SV21 @ SV31 )
= ( join @ SV31 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(94,plain,
! [SV32: $i,SV22: $i] :
( ( ! [SY45: $i] :
( ( join @ SV22 @ ( join @ SV32 @ SY45 ) )
= ( join @ ( join @ SV22 @ SV32 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(95,plain,
! [SV33: $i,SV23: $i] :
( ( SV23
= ( join @ ( complement @ ( join @ ( complement @ SV23 ) @ ( complement @ SV33 ) ) ) @ ( complement @ ( join @ ( complement @ SV23 ) @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV34: $i,SV24: $i] :
( ( ( meet @ SV24 @ SV34 )
= ( complement @ ( join @ ( complement @ SV24 ) @ ( complement @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV35: $i,SV25: $i] :
( ( ! [SY46: $i] :
( ( composition @ ( join @ SV25 @ SV35 ) @ SY46 )
= ( join @ ( composition @ SV25 @ SY46 ) @ ( composition @ SV35 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV36: $i,SV27: $i] :
( ( ( converse @ ( join @ SV27 @ SV36 ) )
= ( join @ ( converse @ SV27 ) @ ( converse @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV37: $i,SV28: $i] :
( ( ( converse @ ( composition @ SV28 @ SV37 ) )
= ( composition @ ( converse @ SV37 ) @ ( converse @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV38: $i,SV29: $i] :
( ( ( join @ ( composition @ ( converse @ SV29 ) @ ( complement @ ( composition @ SV29 @ SV38 ) ) ) @ ( complement @ SV38 ) )
= ( complement @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(101,plain,
( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
!= ( converse @ sK2_SY22 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(102,plain,
( ( ( join @ sK1_X0 @ sK2_SY22 )
= sK2_SY22 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(103,plain,
! [SV39: $i,SV32: $i,SV22: $i] :
( ( ( join @ SV22 @ ( join @ SV32 @ SV39 ) )
= ( join @ ( join @ SV22 @ SV32 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV40: $i,SV35: $i,SV25: $i] :
( ( ( composition @ ( join @ SV25 @ SV35 ) @ SV40 )
= ( join @ ( composition @ SV25 @ SV40 ) @ ( composition @ SV35 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
( ( ( join @ ( converse @ sK1_X0 ) @ ( converse @ sK2_SY22 ) )
= ( converse @ sK2_SY22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[87,105,104,103,102,100,99,98,96,95,93,91]) ).
thf(107,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[106,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL003+1 : 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
% 0.09/0.17 % Computer : n014.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:01:56 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 10
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ..
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 104 ****
% 0.09/0.23 %**** clause counter: 106 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,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:106,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------