TSTP Solution File: LCL961^11 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL961^11 : 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 : n007.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 : Sun Jul 17 12:27:52 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 76 ( 49 unt; 17 typ; 8 def)
% Number of atoms : 311 ( 66 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 425 ( 75 ~; 73 |; 3 &; 270 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 92 ( 19 ^ 72 !; 1 ?; 92 :)
% 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_q,type,
q: mworld > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: mworld ).
thf(tp_sK2_SX0,type,
sK2_SX0: mworld ).
thf(tp_sK3_SY4,type,
sK3_SY4: mworld ).
thf(tp_sK4_SY6,type,
sK4_SY6: mworld ).
thf(mand,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand) ).
thf(mbox,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox) ).
thf(mdia,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia) ).
thf(mequiv,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv) ).
thf(mimplies,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies) ).
thf(mlocal,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal) ).
thf(mnot,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot) ).
thf(mor,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor) ).
thf(1,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_euclidean) ).
thf(2,axiom,
! [W: mworld] : ( mrel @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(3,conjecture,
mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel16) ).
thf(4,negated_conjecture,
( ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ U )
| ~ ( mrel @ W @ V )
| ( mrel @ U @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1]) ).
thf(7,plain,
( ( ! [W: mworld] : ( mrel @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[2]) ).
thf(8,plain,
( ( ! [W: mworld,V: mworld,U: mworld] :
( ~ ( mrel @ W @ U )
| ~ ( mrel @ W @ V )
| ( mrel @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( mlocal @ ( mor @ ( mbox @ ( mimplies @ ( mbox @ p ) @ ( mbox @ q ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ q ) @ ( mbox @ p ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(10,plain,
( ( ~ ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,mand,mbox,mdia,mequiv,mimplies,mlocal,mnot,mor]) ).
thf(11,plain,
! [SV1: mworld] :
( ( mrel @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[7]) ).
thf(12,plain,
! [SV2: mworld] :
( ( ! [SY0: mworld,SY1: mworld] :
( ~ ( mrel @ SV2 @ SY1 )
| ~ ( mrel @ SV2 @ SY0 )
| ( mrel @ SY1 @ SY0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) ) )
| ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[10]) ).
thf(14,plain,
! [SV3: mworld,SV2: mworld] :
( ( ! [SY2: mworld] :
( ~ ( mrel @ SV2 @ SY2 )
| ~ ( mrel @ SV2 @ SV3 )
| ( mrel @ SY2 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [SX0: mworld] :
( ~ ( mrel @ mactual @ SX0 )
| ~ ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( q @ SX1 ) )
| ! [SX1: mworld] :
( ~ ( mrel @ SX0 @ SX1 )
| ( p @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 )
| ( mrel @ SV4 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 )
| ~ ! [SY3: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY3 )
| ( p @ SY3 ) )
| ! [SY4: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY4 )
| ( q @ SY4 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(19,plain,
( ( ~ ( mrel @ mactual @ sK2_SX0 )
| ~ ! [SY5: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY5 )
| ( q @ SY5 ) )
| ! [SY6: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY6 )
| ( p @ SY6 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 )
| ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ( mrel @ mactual @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SY3: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY3 )
| ( p @ SY3 ) )
| ! [SY4: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY4 )
| ( q @ SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( mrel @ mactual @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ! [SY5: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY5 )
| ( q @ SY5 ) )
| ! [SY6: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY6 )
| ( p @ SY6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(25,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( ~ ( mrel @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( mrel @ mactual @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ! [SY3: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY3 )
| ( p @ SY3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [SY4: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY4 )
| ( q @ SY4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(29,plain,
( ( mrel @ mactual @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[23]) ).
thf(30,plain,
( ( ~ ! [SY5: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY5 )
| ( q @ SY5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(31,plain,
( ( ! [SY6: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY6 )
| ( p @ SY6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(32,plain,
! [SV3: mworld,SV4: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( ~ ( mrel @ SV2 @ SV3 ) )
= $true )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(33,plain,
( ( ! [SY3: mworld] :
( ~ ( mrel @ sK1_SX0 @ SY3 )
| ( p @ SY3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ( mrel @ sK1_SX0 @ sK3_SY4 )
| ( q @ sK3_SY4 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(35,plain,
( ( ! [SY5: mworld] :
( ~ ( mrel @ sK2_SX0 @ SY5 )
| ( q @ SY5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ( mrel @ sK2_SX0 @ sK4_SY6 )
| ( p @ sK4_SY6 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(37,plain,
! [SV4: mworld,SV3: mworld,SV2: mworld] :
( ( ( mrel @ SV2 @ SV3 )
= $false )
| ( ( mrel @ SV2 @ SV4 )
= $false )
| ( ( mrel @ SV4 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: mworld] :
( ( ~ ( mrel @ sK1_SX0 @ SV5 )
| ( p @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( ~ ( mrel @ sK1_SX0 @ sK3_SY4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(40,plain,
( ( q @ sK3_SY4 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(41,plain,
! [SV6: mworld] :
( ( ~ ( mrel @ sK2_SX0 @ SV6 )
| ( q @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( mrel @ sK2_SX0 @ sK4_SY6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
( ( p @ sK4_SY6 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(44,plain,
! [SV5: mworld] :
( ( ( ~ ( mrel @ sK1_SX0 @ SV5 ) )
= $true )
| ( ( p @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( mrel @ sK1_SX0 @ sK3_SY4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV6: mworld] :
( ( ( ~ ( mrel @ sK2_SX0 @ SV6 ) )
= $true )
| ( ( q @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( mrel @ sK2_SX0 @ sK4_SY6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV5: mworld] :
( ( ( mrel @ sK1_SX0 @ SV5 )
= $false )
| ( ( p @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV6: mworld] :
( ( ( mrel @ sK2_SX0 @ SV6 )
= $false )
| ( ( q @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(50,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[11,49,48,47,45,43,40,37,29,26]) ).
thf(51,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL961^11 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 16:24:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 2
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 1238
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:2,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:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.19/0.39
% 0.19/0.39 ********************************
% 0.19/0.39 * All subproblems solved! *
% 0.19/0.39 ********************************
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.39
% 0.19/0.39 %**** Beginning of derivation protocol ****
% 0.19/0.39 % SZS output start CNFRefutation
% See solution above
% 0.19/0.39
% 0.19/0.39 %**** End of derivation protocol ****
% 0.19/0.39 %**** no. of clauses in derivation: 51 ****
% 0.19/0.39 %**** clause counter: 50 ****
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:50,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------