TSTP Solution File: SYN057^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN057^5 : 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 : n003.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 08:23:06 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 35 unt; 7 typ; 0 def)
% Number of atoms : 300 ( 74 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 327 ( 75 ~; 53 |; 25 &; 150 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 0 ^ 49 !; 8 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cF,type,
cF: $i > $o ).
thf(tp_cG,type,
cG: $i > $o ).
thf(tp_cH,type,
cH: $i > $o ).
thf(tp_cI,type,
cI: $i > $o ).
thf(tp_cJ,type,
cJ: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i ).
thf(1,conjecture,
( ( ? [Xx: $i] :
( ( cF @ Xx )
& ~ ( cG @ Xx ) )
& ! [Xx: $i] :
( ( cF @ Xx )
=> ( cH @ Xx ) )
& ! [Xx: $i] :
( ( ( cJ @ Xx )
& ( cI @ Xx ) )
=> ( cF @ Xx ) )
& ( ? [Xx: $i] :
( ( cH @ Xx )
& ~ ( cG @ Xx ) )
=> ! [Xx: $i] :
( ( cI @ Xx )
=> ~ ( cH @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( cJ @ Xx )
=> ~ ( cI @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL27) ).
thf(2,negated_conjecture,
( ( ( ? [Xx: $i] :
( ( cF @ Xx )
& ~ ( cG @ Xx ) )
& ! [Xx: $i] :
( ( cF @ Xx )
=> ( cH @ Xx ) )
& ! [Xx: $i] :
( ( ( cJ @ Xx )
& ( cI @ Xx ) )
=> ( cF @ Xx ) )
& ( ? [Xx: $i] :
( ( cH @ Xx )
& ~ ( cG @ Xx ) )
=> ! [Xx: $i] :
( ( cI @ Xx )
=> ~ ( cH @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( cJ @ Xx )
=> ~ ( cI @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ? [Xx: $i] :
( ( cF @ Xx )
& ~ ( cG @ Xx ) )
& ! [Xx: $i] :
( ( cF @ Xx )
=> ( cH @ Xx ) )
& ! [Xx: $i] :
( ( ( cJ @ Xx )
& ( cI @ Xx ) )
=> ( cF @ Xx ) )
& ( ? [Xx: $i] :
( ( cH @ Xx )
& ~ ( cG @ Xx ) )
=> ! [Xx: $i] :
( ( cI @ Xx )
=> ~ ( cH @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( cJ @ Xx )
=> ~ ( cI @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ? [Xx: $i] :
( ( cF @ Xx )
& ~ ( cG @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( ( cF @ Xx )
=> ( cH @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i] :
( ( ( cJ @ Xx )
& ( cI @ Xx ) )
=> ( cF @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ? [Xx: $i] :
( ( cH @ Xx )
& ~ ( cG @ Xx ) )
=> ! [Xx: $i] :
( ( cI @ Xx )
=> ~ ( cH @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: $i] :
( ( cJ @ Xx )
=> ~ ( cI @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [Xx: $i] :
( ( cJ @ Xx )
=> ~ ( cI @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( cJ @ sK1_Xx )
& ( cI @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ( cF @ sK2_Xx )
& ~ ( cG @ sK2_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cH @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cJ @ Xx )
| ( cF @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [Xx: $i] :
( ~ ( cH @ Xx )
| ( cG @ Xx ) )
| ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [Xx: $i] :
( ~ ( cH @ Xx )
| ( cG @ Xx ) )
| ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(16,plain,
( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cJ @ Xx )
| ( cF @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cH @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(18,plain,
( ( ( cF @ sK2_Xx )
& ~ ( cG @ sK2_Xx ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(19,plain,
( ( ( cJ @ sK1_Xx )
& ( cI @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ ( ~ ( cF @ sK2_Xx )
| ~ ~ ( cG @ sK2_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( ~ ( cJ @ sK1_Xx )
| ~ ( cI @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(22,plain,
( ( ( ! [Xx: $i] :
( ~ ( cH @ Xx )
| ( cG @ Xx ) ) )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV1: $i] :
( ( ~ ( cI @ SV1 )
| ~ ( cJ @ SV1 )
| ( cF @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV2: $i] :
( ( ~ ( cF @ SV2 )
| ( cH @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
( ( ~ ( cF @ sK2_Xx )
| ~ ~ ( cG @ sK2_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ( cJ @ sK1_Xx )
| ~ ( cI @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i] :
( ( ( ~ ( cH @ SV3 )
| ( cG @ SV3 ) )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( ~ ( cI @ SV1 )
| ~ ( cJ @ SV1 ) )
= $true )
| ( ( cF @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i] :
( ( ( ~ ( cF @ SV2 ) )
= $true )
| ( ( cH @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( cF @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ~ ( cG @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ ( cJ @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( ~ ( cI @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(34,plain,
! [SV3: $i] :
( ( ( ~ ( cH @ SV3 ) )
= $true )
| ( ( cG @ SV3 )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV1: $i] :
( ( ( ~ ( cI @ SV1 ) )
= $true )
| ( ( ~ ( cJ @ SV1 ) )
= $true )
| ( ( cF @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( cF @ SV2 )
= $false )
| ( ( cH @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(37,plain,
( ( cF @ sK2_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(38,plain,
( ( ~ ( cG @ sK2_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(39,plain,
( ( cJ @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(40,plain,
( ( cI @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( cH @ SV3 )
= $false )
| ( ( cG @ SV3 )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cI @ Xx )
| ~ ( cH @ Xx ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(42,plain,
! [SV1: $i] :
( ( ( cI @ SV1 )
= $false )
| ( ( ~ ( cJ @ SV1 ) )
= $true )
| ( ( cF @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(43,plain,
( ( cG @ sK2_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV3: $i,SV4: $i] :
( ( ( ~ ( cI @ SV4 )
| ~ ( cH @ SV4 ) )
= $true )
| ( ( cG @ SV3 )
= $true )
| ( ( cH @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: $i] :
( ( ( cJ @ SV1 )
= $false )
| ( ( cI @ SV1 )
= $false )
| ( ( cF @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV4: $i] :
( ( ( ~ ( cI @ SV4 ) )
= $true )
| ( ( ~ ( cH @ SV4 ) )
= $true )
| ( ( cG @ SV3 )
= $true )
| ( ( cH @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(47,plain,
! [SV3: $i,SV4: $i] :
( ( ( cI @ SV4 )
= $false )
| ( ( ~ ( cH @ SV4 ) )
= $true )
| ( ( cG @ SV3 )
= $true )
| ( ( cH @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(48,plain,
! [SV3: $i,SV4: $i] :
( ( ( cH @ SV4 )
= $false )
| ( ( cI @ SV4 )
= $false )
| ( ( cG @ SV3 )
= $true )
| ( ( cH @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(49,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,48,45,43,40,39,37]) ).
thf(50,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN057^5 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n003.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 : Tue Jul 12 06:00:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (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).
% 0.13/0.38
% 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/sandbox2/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:49,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: 50 ****
% 0.13/0.38 %**** clause counter: 49 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox2/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:49,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------