TSTP Solution File: SYN058^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN058^5 : 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 : 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 : Thu Jul 21 08:23:07 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 35 unt; 10 typ; 0 def)
% Number of atoms : 357 ( 86 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 400 ( 120 ~; 73 |; 25 &; 156 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 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_cP,type,
cP: $i > $o ).
thf(tp_cQ,type,
cQ: $i > $o ).
thf(tp_cR,type,
cR: $i > $o ).
thf(tp_cS,type,
cS: $i > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i ).
thf(tp_sK3_Xx,type,
sK3_Xx: $i ).
thf(tp_sK4_REN,type,
sK4_REN: $o ).
thf(1,conjecture,
( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ! [Xx0: $i] : ( cQ @ Xx0 ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
| ( cR @ Xx ) )
=> ? [Xx: $i] :
( ( cQ @ Xx )
& ( cS @ Xx ) ) )
& ( ? [Xx: $i] : ( cS @ Xx )
=> ! [Xx: $i] :
( ( cF @ Xx )
=> ( cG @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( ( cP @ Xx )
& ( cF @ Xx ) )
=> ( cG @ Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPELL28) ).
thf(2,negated_conjecture,
( ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ! [Xx0: $i] : ( cQ @ Xx0 ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
| ( cR @ Xx ) )
=> ? [Xx: $i] :
( ( cQ @ Xx )
& ( cS @ Xx ) ) )
& ( ? [Xx: $i] : ( cS @ Xx )
=> ! [Xx: $i] :
( ( cF @ Xx )
=> ( cG @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( ( cP @ Xx )
& ( cF @ Xx ) )
=> ( cG @ Xx ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ! [Xx0: $i] : ( cQ @ Xx0 ) )
& ( ! [Xx: $i] :
( ( cQ @ Xx )
| ( cR @ Xx ) )
=> ? [Xx: $i] :
( ( cQ @ Xx )
& ( cS @ Xx ) ) )
& ( ? [Xx: $i] : ( cS @ Xx )
=> ! [Xx: $i] :
( ( cF @ Xx )
=> ( cG @ Xx ) ) ) )
=> ! [Xx: $i] :
( ( ( cP @ Xx )
& ( cF @ Xx ) )
=> ( cG @ Xx ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( cP @ Xx )
=> ! [Xx0: $i] : ( cQ @ Xx0 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
( ( cQ @ Xx )
| ( cR @ Xx ) )
=> ? [Xx: $i] :
( ( cQ @ Xx )
& ( cS @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ? [Xx: $i] : ( cS @ Xx )
=> ! [Xx: $i] :
( ( cF @ Xx )
=> ( cG @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i] :
( ( ( cP @ Xx )
& ( cF @ Xx ) )
=> ( cG @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [Xx: $i] :
( ( ( cP @ Xx )
& ( cF @ Xx ) )
=> ( cG @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( cF @ sK1_Xx )
& ( cP @ sK1_Xx )
& ~ ( cG @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Xx: $i] :
~ ( cP @ Xx )
| ! [Xx0: $i] : ( cQ @ Xx0 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ( sK4_REN
| ( ( cQ @ sK2_Xx )
& ( cS @ sK2_Xx ) ) )
& ( sK4_REN
=> ( ~ ( cQ @ sK3_Xx )
& ~ ( cR @ sK3_Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [Xx: $i] :
~ ( cS @ Xx )
| ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [Xx: $i] :
~ ( cS @ Xx )
| ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ( sK4_REN
| ( ( cQ @ sK2_Xx )
& ( cS @ sK2_Xx ) ) )
& ( sK4_REN
=> ( ~ ( cQ @ sK3_Xx )
& ~ ( cR @ sK3_Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [Xx: $i] :
~ ( cP @ Xx )
| ! [Xx0: $i] : ( cQ @ Xx0 ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( cF @ sK1_Xx )
& ( cP @ sK1_Xx )
& ~ ( cG @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ~ ( ~ ( sK4_REN
| ~ ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(18,plain,
( ( ~ ( ~ ~ ( ~ ( cF @ sK1_Xx )
| ~ ( cP @ sK1_Xx ) )
| ~ ~ ( cG @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(19,plain,
( ( ( ! [Xx: $i] :
~ ( cS @ Xx ) )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(20,plain,
( ( ( ! [Xx: $i] :
~ ( cP @ Xx ) )
= $true )
| ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(21,plain,
( ( ~ ( sK4_REN
| ~ ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) ) )
| ~ ( ~ sK4_REN
| ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ~ ( ~ ( cF @ sK1_Xx )
| ~ ( cP @ sK1_Xx ) )
| ~ ~ ( cG @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( ~ ( cS @ SV1 ) )
= $true )
| ( ( ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i] :
( ( ( ~ ( cP @ SV2 ) )
= $true )
| ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( sK4_REN
| ~ ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ~ sK4_REN
| ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ~ ( ~ ( cF @ sK1_Xx )
| ~ ( cP @ sK1_Xx ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(28,plain,
( ( ~ ~ ( cG @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( cS @ SV1 )
= $false )
| ( ( ! [Xx: $i] :
( ~ ( cF @ Xx )
| ( cG @ Xx ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( cP @ SV2 )
= $false )
| ( ( ! [Xx0: $i] : ( cQ @ Xx0 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( sK4_REN
| ~ ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(32,plain,
( ( ~ sK4_REN
| ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(33,plain,
( ( ~ ( ~ ( cF @ sK1_Xx )
| ~ ( cP @ sK1_Xx ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
( ( ~ ( cG @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(35,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( cF @ SV3 )
| ( cG @ SV3 ) )
= $true )
| ( ( cS @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV2: $i,SV4: $i] :
( ( ( cQ @ SV4 )
= $true )
| ( ( cP @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( sK4_REN = $true )
| ( ( ~ ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ( ~ sK4_REN )
= $true )
| ( ( ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ( cF @ sK1_Xx )
| ~ ( cP @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( cG @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( cF @ SV3 ) )
= $true )
| ( ( cG @ SV3 )
= $true )
| ( ( cS @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(42,plain,
( ( ( ~ ( cQ @ sK2_Xx )
| ~ ( cS @ sK2_Xx ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
( ( sK4_REN = $false )
| ( ( ~ ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( ~ ( cF @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( cP @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV1: $i,SV3: $i] :
( ( ( cF @ SV3 )
= $false )
| ( ( cG @ SV3 )
= $true )
| ( ( cS @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(47,plain,
( ( ( ~ ( cQ @ sK2_Xx ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(48,plain,
( ( ( ~ ( cS @ sK2_Xx ) )
= $false )
| ( sK4_REN = $true ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(49,plain,
( ( ( ~ ~ ( cQ @ sK3_Xx )
| ~ ~ ( cR @ sK3_Xx ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( cF @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
( ( cP @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
( ( ( cQ @ sK2_Xx )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
( ( ( cS @ sK2_Xx )
= $true )
| ( sK4_REN = $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(54,plain,
( ( ( ~ ~ ( cQ @ sK3_Xx ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(55,plain,
( ( ( ~ ~ ( cR @ sK3_Xx ) )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(56,plain,
( ( ( ~ ( cQ @ sK3_Xx ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(57,plain,
( ( ( ~ ( cR @ sK3_Xx ) )
= $true )
| ( sK4_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ( cQ @ sK3_Xx )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(59,plain,
( ( ( cR @ sK3_Xx )
= $false )
| ( sK4_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,59,58,53,52,51,50,46,40]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SYN058^5 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 12 07:54:43 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 0
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 0
% 0.14/0.36
% 0.14/0.36 Contains.Choice.Funs: false
% 0.14/0.36 (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)..
% 0.14/0.39
% 0.14/0.39 ********************************
% 0.14/0.39 * All subproblems solved! *
% 0.14/0.39 ********************************
% 0.14/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:60,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: 61 ****
% 0.14/0.40 %**** clause counter: 60 ****
% 0.14/0.40
% 0.14/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------