TSTP Solution File: NUM635^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM635^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n011.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 : Mon Jul 18 11:53:27 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 30 unt; 5 typ; 0 def)
% Number of atoms : 176 ( 107 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 261 ( 63 ~; 43 |; 4 &; 140 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 0 ^ 67 !; 0 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_one,type,
one: $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_X,type,
sK3_X: ( $i > $o ) > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(1,axiom,
! [M: $i > $o] :
( ( ( M @ one )
& ! [X: $i] :
( ( M @ X )
=> ( M @ ( succ @ X ) ) ) )
=> ! [Y: $i] : ( M @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( ( succ @ X )
= ( succ @ Y ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_injective) ).
thf(3,axiom,
! [X: $i] :
( ( succ @ X )
!= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_is_first) ).
thf(4,conjecture,
! [X: $i,Y: $i] :
( ( X != Y )
=> ( ( succ @ X )
!= ( succ @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz1) ).
thf(5,negated_conjecture,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
=> ( ( succ @ X )
!= ( succ @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[4]) ).
thf(6,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
=> ( ( succ @ X )
!= ( succ @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [M: $i > $o] :
( ( ( M @ one )
& ! [X: $i] :
( ( M @ X )
=> ( M @ ( succ @ X ) ) ) )
=> ! [Y: $i] : ( M @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(8,plain,
( ( ! [X: $i,Y: $i] :
( ( ( succ @ X )
= ( succ @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(9,plain,
( ( ! [X: $i] :
( ( succ @ X )
!= one ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [SY8: $i] :
( ( sK1_X != SY8 )
=> ( ( succ @ sK1_X )
!= ( succ @ SY8 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[6]) ).
thf(11,plain,
( ( ( sK1_X != sK2_SY8 )
=> ( ( succ @ sK1_X )
!= ( succ @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(12,plain,
( ( ( sK1_X != sK2_SY8 ) )
= $true ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(13,plain,
( ( ( ( succ @ sK1_X )
!= ( succ @ sK2_SY8 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ( ( ( succ @ sK1_X )
!= ( succ @ sK2_SY8 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(15,plain,
( ( ( succ @ sK1_X )
= ( succ @ sK2_SY8 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(16,plain,
( ( ( sK1_X != sK2_SY8 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(17,plain,
( ( ! [M: $i > $o] :
( ( ( M @ ( sK3_X @ M ) )
& ~ ( M @ ( succ @ ( sK3_X @ M ) ) ) )
| ~ ( M @ one )
| ! [Y: $i] : ( M @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( ( succ @ X )
!= ( succ @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( succ @ X )
!= one ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( succ @ X )
!= one ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( ( succ @ X )
!= ( succ @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(22,plain,
( ( ! [M: $i > $o] :
( ( ( M @ ( sK3_X @ M ) )
& ~ ( M @ ( succ @ ( sK3_X @ M ) ) ) )
| ~ ( M @ one )
| ! [Y: $i] : ( M @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ( sK1_X != sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ( succ @ sK1_X )
= ( succ @ sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(25,plain,
( ( ! [SX0: $i > $o] :
( ~ ( ~ ( SX0 @ ( sK3_X @ SX0 ) )
| ~ ~ ( SX0 @ ( succ @ ( sK3_X @ SX0 ) ) ) )
| ~ ( SX0 @ one )
| ! [SX1: $i] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( ( succ @ SV1 )
!= one ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY9: $i] :
( ( ( succ @ SV2 )
!= ( succ @ SY9 ) )
| ( SV2 = SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
( ( sK1_X = sK2_SY8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV3: $i > $o] :
( ( ~ ( ~ ( SV3 @ ( sK3_X @ SV3 ) )
| ~ ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) )
| ~ ( SV3 @ one )
| ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i] :
( ( ( succ @ SV1 )
= one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( succ @ SV2 )
!= ( succ @ SV4 ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV3: $i > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK3_X @ SV3 ) )
| ~ ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) )
| ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( ( succ @ SV2 )
!= ( succ @ SV4 ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV3: $i > $o] :
( ( ( ~ ( ~ ( SV3 @ ( sK3_X @ SV3 ) )
| ~ ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) ) )
= $true )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV4: $i,SV2: $i] :
( ( ( ( succ @ SV2 )
= ( succ @ SV4 ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK3_X @ SV3 ) )
| ~ ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( sK3_X @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(38,plain,
! [SV3: $i > $o] :
( ( ( ~ ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) )
= $false )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: $i > $o] :
( ( ( SV3 @ ( sK3_X @ SV3 ) )
= $true )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) ) )
= $true )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
! [SV3: $i > $o] :
( ( ( SV3 @ one )
= $false )
| ( ( SV3 @ ( sK3_X @ SV3 ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(42,plain,
! [SV3: $i > $o] :
( ( ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) )
= $false )
| ( ( ~ ( SV3 @ one ) )
= $true )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(43,plain,
! [SV5: $i,SV3: $i > $o] :
( ( ( SV3 @ SV5 )
= $true )
| ( ( SV3 @ ( sK3_X @ SV3 ) )
= $true )
| ( ( SV3 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV3: $i > $o] :
( ( ( SV3 @ one )
= $false )
| ( ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) )
= $false )
| ( ( ! [SY10: $i] : ( SV3 @ SY10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV6: $i,SV3: $i > $o] :
( ( ( SV3 @ SV6 )
= $true )
| ( ( SV3 @ ( succ @ ( sK3_X @ SV3 ) ) )
= $false )
| ( ( SV3 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,45,43,35,30,28]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM635^2 : TPTP v8.1.0. Released v3.7.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jul 6 13:16:38 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37
% 0.14/0.37 No.of.Axioms: 3
% 0.14/0.37
% 0.14/0.37 Length.of.Defs: 0
% 0.14/0.37
% 0.14/0.37 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:3,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:5,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.14/0.40
% 0.14/0.40 ********************************
% 0.14/0.40 * All subproblems solved! *
% 0.14/0.40 ********************************
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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: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)
% 0.14/0.40
% 0.14/0.40 %**** Beginning of derivation protocol ****
% 0.14/0.40 % SZS output start CNFRefutation
% See solution above
% 0.14/0.40
% 0.14/0.40 %**** End of derivation protocol ****
% 0.14/0.40 %**** no. of clauses in derivation: 47 ****
% 0.14/0.40 %**** clause counter: 46 ****
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:4,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: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)
%------------------------------------------------------------------------------