TSTP Solution File: SYO902^8 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO902^8 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n004.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 : Thu Jul 21 17:38:17 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 24
% Syntax : Number of formulae : 69 ( 34 unt; 14 typ; 8 def)
% Number of atoms : 313 ( 75 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 587 ( 231 ~; 83 |; 2 &; 268 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 98 ( 19 ^ 78 !; 1 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_mworld,type,
mworld: $tType ).
thf(tp_mactual,type,
mactual: mworld ).
thf(tp_mand,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mbox,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(tp_mdia,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(tp_mequiv,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mimplies,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mlocal,type,
mlocal: ( mworld > $o ) > $o ).
thf(tp_mnot,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(tp_mor,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(tp_mrel,type,
mrel: mworld > mworld > $o ).
thf(tp_p,type,
p: mworld > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SY3,type,
sK2_SY3: mworld > mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(2,conjecture,
mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(3,negated_conjecture,
( ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,plain,
( ( ~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[1]) ).
thf(6,plain,
( ( ~ ( mlocal @ ( mimplies @ ( mdia @ ( mbox @ ( mdia @ p ) ) ) @ ( mdia @ ( mdia @ p ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( p @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(8,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5]) ).
thf(9,plain,
( ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ( p @ SX2 ) ) ) )
| ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( p @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(11,plain,
( ( ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( p @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ~ ! [SX1: mworld] :
~ ~ ( ~ ( mrel @ SX0 @ SX1 )
| ~ ( p @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [SX0: mworld] :
~ ~ ( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SX1 @ SX2 )
| ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: mworld] :
( ( ~ ~ ( ~ ( mrel @ mactual @ SV2 )
| ~ ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY1 @ SX2 )
| ~ ( p @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(17,plain,
! [SV2: mworld] :
( ( ~ ( ~ ( mrel @ mactual @ SV2 )
| ~ ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY1 @ SX2 )
| ~ ( p @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(19,plain,
! [SV2: mworld] :
( ( ~ ( mrel @ mactual @ SV2 )
| ~ ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY1 @ SX2 )
| ~ ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(21,plain,
! [SV2: mworld] :
( ( ( ~ ( mrel @ mactual @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(23,plain,
( ( ~ ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY1 @ SX2 )
| ~ ( p @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV2: mworld] :
( ( ( mrel @ mactual @ SV2 )
= $false )
| ( ( ~ ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SY1: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY1 )
| ~ ! [SX2: mworld] :
~ ~ ( ~ ( mrel @ SY1 @ SX2 )
| ~ ( p @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: mworld] :
( ( ( ~ ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: mworld] :
( ( ~ ( mrel @ sK1_SX0 @ SV3 )
| ~ ! [SY3: mworld] :
~ ~ ( ~ ( mrel @ SV3 @ SY3 )
| ~ ( p @ SY3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: mworld] :
( ( ( ! [SY0: mworld] :
~ ~ ( ~ ( mrel @ SV2 @ SY0 )
| ~ ( p @ SY0 ) ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(30,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ sK1_SX0 @ SV3 ) )
= $true )
| ( ( ~ ! [SY3: mworld] :
~ ~ ( ~ ( mrel @ SV3 @ SY3 )
| ~ ( p @ SY3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV4: mworld,SV2: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( p @ SV4 ) ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: mworld] :
( ( ( mrel @ sK1_SX0 @ SV3 )
= $false )
| ( ( ~ ! [SY3: mworld] :
~ ~ ( ~ ( mrel @ SV3 @ SY3 )
| ~ ( p @ SY3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV4: mworld,SV2: mworld] :
( ( ( ~ ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( p @ SV4 ) ) )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: mworld] :
( ( ( ! [SY3: mworld] :
~ ~ ( ~ ( mrel @ SV3 @ SY3 )
| ~ ( p @ SY3 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( p @ SV4 ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: mworld] :
( ( ( ~ ~ ( ~ ( mrel @ SV3 @ ( sK2_SY3 @ SV3 ) )
| ~ ( p @ ( sK2_SY3 @ SV3 ) ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(37,plain,
! [SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: mworld] :
( ( ( ~ ( ~ ( mrel @ SV3 @ ( sK2_SY3 @ SV3 ) )
| ~ ( p @ ( sK2_SY3 @ SV3 ) ) ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV4: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( ~ ( p @ SV4 ) )
= $true )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ ( sK2_SY3 @ SV3 ) )
| ~ ( p @ ( sK2_SY3 @ SV3 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV2: mworld,SV4: mworld] :
( ( ( p @ SV4 )
= $false )
| ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( mrel @ mactual @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: mworld] :
( ( ( ~ ( mrel @ SV3 @ ( sK2_SY3 @ SV3 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(43,plain,
! [SV3: mworld] :
( ( ( ~ ( p @ ( sK2_SY3 @ SV3 ) ) )
= $false )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: mworld] :
( ( ( mrel @ SV3 @ ( sK2_SY3 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
! [SV3: mworld] :
( ( ( p @ ( sK2_SY3 @ SV3 ) )
= $true )
| ( ( mrel @ sK1_SX0 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[8,45,44,41,25]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SYO902^8 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 23:43:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 1
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 1246
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:3,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 47 ****
% 0.12/0.38 %**** clause counter: 46 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------