TSTP Solution File: PUZ104^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : PUZ104^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 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 : Mon Jul 18 18:19:38 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 28 unt; 6 typ; 1 def)
% Number of atoms : 166 ( 60 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 367 ( 78 ~; 52 |; 14 &; 203 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 1 ^ 45 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c1,type,
c1: $i ).
thf(tp_cCKB6_NUM,type,
cCKB6_NUM: $i > $o ).
thf(tp_s,type,
s: $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i > $o ).
thf(tp_sK3_Xw,type,
sK3_Xw: ( $i > $o ) > $i ).
thf(cCKB6_NUM,definition,
( cCKB6_NUM
= ( ^ [Xx: $i] :
! [Xp: $i > $o] :
( ( ( Xp @ c1 )
& ! [Xw: $i] :
( ( Xp @ Xw )
=> ( Xp @ ( s @ Xw ) ) ) )
=> ( Xp @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_NUM) ).
thf(1,conjecture,
! [Xx: $i] :
( ( cCKB6_NUM @ Xx )
=> ( cCKB6_NUM @ ( s @ ( s @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB6_L4000) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i] :
( ( cCKB6_NUM @ Xx )
=> ( cCKB6_NUM @ ( s @ ( s @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i] :
( ! [SY1: $i > $o] :
( ( ( SY1 @ c1 )
& ! [Xw: $i] :
( ( SY1 @ Xw )
=> ( SY1 @ ( s @ Xw ) ) ) )
=> ( SY1 @ SY0 ) )
=> ! [SY3: $i > $o] :
( ( ( SY3 @ c1 )
& ! [Xw: $i] :
( ( SY3 @ Xw )
=> ( SY3 @ ( s @ Xw ) ) ) )
=> ( SY3 @ ( s @ ( s @ SY0 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cCKB6_NUM]) ).
thf(4,plain,
( ( ! [SY10: $i > $o] :
( ( ( SY10 @ c1 )
& ! [Xw: $i] :
( ( SY10 @ Xw )
=> ( SY10 @ ( s @ Xw ) ) ) )
=> ( SY10 @ sK1_SY0 ) )
=> ! [SY12: $i > $o] :
( ( ( SY12 @ c1 )
& ! [Xw: $i] :
( ( SY12 @ Xw )
=> ( SY12 @ ( s @ Xw ) ) ) )
=> ( SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY10: $i > $o] :
( ( ( SY10 @ c1 )
& ! [Xw: $i] :
( ( SY10 @ Xw )
=> ( SY10 @ ( s @ Xw ) ) ) )
=> ( SY10 @ sK1_SY0 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(6,plain,
( ( ! [SY12: $i > $o] :
( ( ( SY12 @ c1 )
& ! [Xw: $i] :
( ( SY12 @ Xw )
=> ( SY12 @ ( s @ Xw ) ) ) )
=> ( SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ! [SY12: $i > $o] :
( ( ( SY12 @ c1 )
& ! [Xw: $i] :
( ( SY12 @ Xw )
=> ( SY12 @ ( s @ Xw ) ) ) )
=> ( SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [SY14: $i] :
( ~ ( sK2_SY12 @ SY14 )
| ( sK2_SY12 @ ( s @ SY14 ) ) )
& ( sK2_SY12 @ c1 )
& ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [SY10: $i > $o] :
( ( ( SY10 @ ( sK3_Xw @ SY10 ) )
& ~ ( SY10 @ ( s @ ( sK3_Xw @ SY10 ) ) ) )
| ~ ( SY10 @ c1 )
| ( SY10 @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [SY10: $i > $o] :
( ( ( SY10 @ ( sK3_Xw @ SY10 ) )
& ~ ( SY10 @ ( s @ ( sK3_Xw @ SY10 ) ) ) )
| ~ ( SY10 @ c1 )
| ( SY10 @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [SY14: $i] :
( ~ ( sK2_SY12 @ SY14 )
| ( sK2_SY12 @ ( s @ SY14 ) ) )
& ( sK2_SY12 @ c1 )
& ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) )
| ~ ( sK2_SY12 @ c1 ) )
| ~ ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,cCKB6_NUM]) ).
thf(13,plain,
( ( ! [SX0: $i > $o] :
( ~ ( ~ ( SX0 @ ( sK3_Xw @ SX0 ) )
| ~ ~ ( SX0 @ ( s @ ( sK3_Xw @ SX0 ) ) ) )
| ~ ( SX0 @ c1 )
| ( SX0 @ sK1_SY0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,cCKB6_NUM]) ).
thf(14,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) )
| ~ ( sK2_SY12 @ c1 ) )
| ~ ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i > $o] :
( ( ~ ( ~ ( SV1 @ ( sK3_Xw @ SV1 ) )
| ~ ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) )
| ~ ( SV1 @ c1 )
| ( SV1 @ sK1_SY0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) )
| ~ ( sK2_SY12 @ c1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xw @ SV1 ) )
| ~ ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) )
| ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) )
| ~ ( sK2_SY12 @ c1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i > $o] :
( ( ( ~ ( ~ ( SV1 @ ( sK3_Xw @ SV1 ) )
| ~ ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) ) )
= $true )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) )
| ~ ( sK2_SY12 @ c1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( sK2_SY12 @ ( s @ ( s @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xw @ SV1 ) )
| ~ ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) )
= $false )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ( sK2_SY12 @ c1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( sK3_Xw @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i > $o] :
( ( ( ~ ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) )
= $false )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: $i] :
( ~ ( sK2_SY12 @ SX0 )
| ( sK2_SY12 @ ( s @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( sK2_SY12 @ c1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( sK3_Xw @ SV1 ) )
= $true )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i > $o] :
( ( ( ~ ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) ) )
= $true )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ~ ( sK2_SY12 @ SV2 )
| ( sK2_SY12 @ ( s @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ c1 )
= $false )
| ( ( SV1 @ ( sK3_Xw @ SV1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) )
= $false )
| ( ( ~ ( SV1 @ c1 ) )
= $true )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( ~ ( sK2_SY12 @ SV2 ) )
= $true )
| ( ( sK2_SY12 @ ( s @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV1: $i > $o] :
( ( ( SV1 @ c1 )
= $false )
| ( ( SV1 @ ( s @ ( sK3_Xw @ SV1 ) ) )
= $false )
| ( ( SV1 @ sK1_SY0 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV2: $i] :
( ( ( sK2_SY12 @ SV2 )
= $false )
| ( ( sK2_SY12 @ ( s @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[23,38,37,34,30]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ104^5 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat May 28 23:11:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 201
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:0,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:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.19/0.37
% 0.19/0.37 ********************************
% 0.19/0.37 * All subproblems solved! *
% 0.19/0.37 ********************************
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:39,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.37
% 0.19/0.37 %**** Beginning of derivation protocol ****
% 0.19/0.37 % SZS output start CNFRefutation
% See solution above
% 0.19/0.37
% 0.19/0.37 %**** End of derivation protocol ****
% 0.19/0.37 %**** no. of clauses in derivation: 40 ****
% 0.19/0.37 %**** clause counter: 39 ****
% 0.19/0.37
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:39,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------