TSTP Solution File: LCL684+1.001 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL684+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n025.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 12:25:46 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 29 unt; 4 typ; 0 def)
% Number of atoms : 265 ( 62 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 423 ( 111 ~; 82 |; 14 &; 214 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 79 ( 0 ^ 75 !; 4 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p101,type,
p101: $i > $o ).
thf(tp_p201,type,
p201: $i > $o ).
thf(tp_r1,type,
r1: $i > $i > $o ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( r1 @ X @ Y )
& ( r1 @ Y @ Z ) )
=> ( r1 @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(2,axiom,
! [X: $i] : ( r1 @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(3,conjecture,
~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ ( r1 @ X @ Y )
| ! [X: $i] :
( ~ ( r1 @ Y @ X )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
thf(4,negated_conjecture,
( ( ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ ( r1 @ X @ Y )
| ! [X: $i] :
( ~ ( r1 @ Y @ X )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,plain,
( ( ~ ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ ( r1 @ X @ Y )
| ! [X: $i] :
( ~ ( r1 @ Y @ X )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( r1 @ X @ Y )
& ( r1 @ Y @ Z ) )
=> ( r1 @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(7,plain,
( ( ! [X: $i] : ( r1 @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(8,plain,
( ( ? [X: $i] :
~ ( ~ ! [Y: $i] :
( ~ ( r1 @ X @ Y )
| ! [X: $i] :
( ~ ( r1 @ Y @ X )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
| ~ ( ( p201 @ X )
& ( p101 @ X ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [SY7: $i] :
( ~ ( r1 @ sK1_X @ SY7 )
| ! [X: $i] :
( ~ ( r1 @ SY7 @ X )
| ~ ( p101 @ X )
| ~ ( p201 @ X ) ) )
& ( p101 @ sK1_X )
& ( p201 @ sK1_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( r1 @ X @ Y )
| ~ ( r1 @ Y @ Z )
| ( r1 @ X @ Z ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [X: $i] : ( r1 @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( r1 @ X @ Y )
| ~ ( r1 @ Y @ Z )
| ( r1 @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY7: $i] :
( ~ ( r1 @ sK1_X @ SY7 )
| ! [X: $i] :
( ~ ( r1 @ SY7 @ X )
| ~ ( p101 @ X )
| ~ ( p201 @ X ) ) )
& ( p101 @ sK1_X )
& ( p201 @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ! [SX1: $i] :
( ~ ( r1 @ SX0 @ SX1 )
| ~ ( p101 @ SX1 )
| ~ ( p201 @ SX1 ) ) )
| ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: $i] :
( ( r1 @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ( r1 @ SV2 @ SY9 )
| ~ ( r1 @ SY9 @ SY10 )
| ( r1 @ SV2 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ! [SX0: $i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ! [SX1: $i] :
( ~ ( r1 @ SX0 @ SX1 )
| ~ ( p101 @ SX1 )
| ~ ( p201 @ SX1 ) ) )
| ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV2: $i] :
( ( ! [SY11: $i] :
( ~ ( r1 @ SV2 @ SV3 )
| ~ ( r1 @ SV3 @ SY11 )
| ( r1 @ SV2 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ! [SX0: $i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ! [SX1: $i] :
( ~ ( r1 @ SX0 @ SX1 )
| ~ ( p101 @ SX1 )
| ~ ( p201 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ~ ( r1 @ SV2 @ SV3 )
| ~ ( r1 @ SV3 @ SV4 )
| ( r1 @ SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ~ ( r1 @ sK1_X @ SX0 )
| ! [SX1: $i] :
( ~ ( r1 @ SX0 @ SX1 )
| ~ ( p101 @ SX1 )
| ~ ( p201 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( r1 @ SV2 @ SV3 )
| ~ ( r1 @ SV3 @ SV4 ) )
= $true )
| ( ( r1 @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV5: $i] :
( ( ~ ( r1 @ sK1_X @ SV5 )
| ! [SY12: $i] :
( ~ ( r1 @ SV5 @ SY12 )
| ~ ( p101 @ SY12 )
| ~ ( p201 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( p101 @ sK1_X )
| ~ ( p201 @ sK1_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( r1 @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( r1 @ SV3 @ SV4 ) )
= $true )
| ( ( r1 @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV5: $i] :
( ( ( ~ ( r1 @ sK1_X @ SV5 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( r1 @ SV5 @ SY12 )
| ~ ( p101 @ SY12 )
| ~ ( p201 @ SY12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ( p101 @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( p201 @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: $i,SV3: $i,SV2: $i] :
( ( ( r1 @ SV2 @ SV3 )
= $false )
| ( ( ~ ( r1 @ SV3 @ SV4 ) )
= $true )
| ( ( r1 @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV5: $i] :
( ( ( r1 @ sK1_X @ SV5 )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( r1 @ SV5 @ SY12 )
| ~ ( p101 @ SY12 )
| ~ ( p201 @ SY12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( p101 @ sK1_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( p201 @ sK1_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(35,plain,
! [SV2: $i,SV4: $i,SV3: $i] :
( ( ( r1 @ SV3 @ SV4 )
= $false )
| ( ( r1 @ SV2 @ SV3 )
= $false )
| ( ( r1 @ SV2 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( r1 @ SV5 @ SV6 )
| ~ ( p101 @ SV6 )
| ~ ( p201 @ SV6 ) )
= $true )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( r1 @ SV5 @ SV6 ) )
= $true )
| ( ( ~ ( p101 @ SV6 )
| ~ ( p201 @ SV6 ) )
= $true )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV6: $i,SV5: $i] :
( ( ( r1 @ SV5 @ SV6 )
= $false )
| ( ( ~ ( p101 @ SV6 )
| ~ ( p201 @ SV6 ) )
= $true )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV5: $i,SV6: $i] :
( ( ( ~ ( p101 @ SV6 ) )
= $true )
| ( ( ~ ( p201 @ SV6 ) )
= $true )
| ( ( r1 @ SV5 @ SV6 )
= $false )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV5: $i,SV6: $i] :
( ( ( p101 @ SV6 )
= $false )
| ( ( ~ ( p201 @ SV6 ) )
= $true )
| ( ( r1 @ SV5 @ SV6 )
= $false )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV5: $i,SV6: $i] :
( ( ( p201 @ SV6 )
= $false )
| ( ( p101 @ SV6 )
= $false )
| ( ( r1 @ SV5 @ SV6 )
= $false )
| ( ( r1 @ sK1_X @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,41,35,34,33]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL684+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n025.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 03:40:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 2
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:4,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 43 ****
% 0.13/0.38 %**** clause counter: 42 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------