%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : REL002+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 : n010.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 0.28s 0.32s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 70 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 246 ( 2 ~; 0 |; 0 &; 244 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% 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(2,axiom,
! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
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(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(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] :
( ( join @ X0 @ top )
= top ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(15,negated_conjecture,
( ( ! [X0: $i] :
( ( join @ X0 @ top )
= top ) )
= $false ),
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,plain,
( ( ! [X0: $i] :
( ( join @ X0 @ top )
= top ) )
= $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] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,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(20,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(21,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(22,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(23,plain,
( ( ( join @ sK1_X0 @ top )
= top )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(24,plain,
( ( ( join @ sK1_X0 @ top )
!= top )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [X0: $i,X1: $i] :
( ( join @ X0 @ X1 )
= ( join @ X1 @ X0 ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( join @ X0 @ ( join @ X1 @ X2 ) )
= ( join @ ( join @ X0 @ X1 ) @ X2 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [X0: $i,X1: $i] :
( X0
= ( join @ ( complement @ ( join @ ( complement @ X0 ) @ ( complement @ X1 ) ) ) @ ( complement @ ( join @ ( complement @ X0 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( composition @ ( join @ X0 @ X1 ) @ X2 )
= ( join @ ( composition @ X0 @ X2 ) @ ( composition @ X1 @ X2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(29,plain,
( ( ! [X0: $i,X1: $i] :
( ( converse @ ( join @ X0 @ X1 ) )
= ( join @ ( converse @ X0 ) @ ( converse @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(30,plain,
( ( ! [X0: $i] :
( top
= ( join @ X0 @ ( complement @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(31,plain,
( ( ( join @ sK1_X0 @ top )
!= top )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ( join @ SV1 @ SY14 )
= ( join @ SY14 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ( join @ SV2 @ ( join @ SY15 @ SY16 ) )
= ( join @ ( join @ SV2 @ SY15 ) @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY17: $i] :
( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SY17 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SY17 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV4: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( composition @ ( join @ SV4 @ SY18 ) @ SY19 )
= ( join @ ( composition @ SV4 @ SY19 ) @ ( composition @ SY18 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV5: $i] :
( ( ! [SY20: $i] :
( ( converse @ ( join @ SV5 @ SY20 ) )
= ( join @ ( converse @ SV5 ) @ ( converse @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV6: $i] :
( ( top
= ( join @ SV6 @ ( complement @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
( ( ( join @ sK1_X0 @ top )
= top )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV7: $i,SV1: $i] :
( ( ( join @ SV1 @ SV7 )
= ( join @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY21: $i] :
( ( join @ SV2 @ ( join @ SV8 @ SY21 ) )
= ( join @ ( join @ SV2 @ SV8 ) @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV9: $i,SV3: $i] :
( ( SV3
= ( join @ ( complement @ ( join @ ( complement @ SV3 ) @ ( complement @ SV9 ) ) ) @ ( complement @ ( join @ ( complement @ SV3 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV10: $i,SV4: $i] :
( ( ! [SY22: $i] :
( ( composition @ ( join @ SV4 @ SV10 ) @ SY22 )
= ( join @ ( composition @ SV4 @ SY22 ) @ ( composition @ SV10 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(43,plain,
! [SV11: $i,SV5: $i] :
( ( ( converse @ ( join @ SV5 @ SV11 ) )
= ( join @ ( converse @ SV5 ) @ ( converse @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(44,plain,
! [SV12: $i,SV8: $i,SV2: $i] :
( ( ( join @ SV2 @ ( join @ SV8 @ SV12 ) )
= ( join @ ( join @ SV2 @ SV8 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV13: $i,SV10: $i,SV4: $i] :
( ( ( composition @ ( join @ SV4 @ SV10 ) @ SV13 )
= ( join @ ( composition @ SV4 @ SV13 ) @ ( composition @ SV10 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,45,44,43,41,39,38]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL002+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
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 14:02:26 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/0.32
% 0.28/0.32 No.of.Axioms: 6
% 0.28/0.32
% 0.28/0.32 Length.of.Defs: 0
% 0.28/0.32
% 0.28/0.32 Contains.Choice.Funs: false
% 0.28/0.32 .
% 0.28/0.32
% 0.28/0.32 ********************************
% 0.28/0.32 * All subproblems solved! *
% 0.28/0.32 ********************************
% 0.28/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.28/0.32
% 0.28/0.32 %**** Beginning of derivation protocol ****
% 0.28/0.32 % SZS output start CNFRefutation
% See solution above
% 0.28/0.32
% 0.28/0.32 %**** End of derivation protocol ****
% 0.28/0.32 %**** no. of clauses in derivation: 40 ****
% 0.28/0.32 %**** clause counter: 46 ****
% 0.28/0.32
% 0.28/0.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------