TSTP Solution File: SEU511^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU511^2 : 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 : n026.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 : Tue Jul 19 12:12:28 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 19 unt; 6 typ; 2 def)
% Number of atoms : 100 ( 40 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 85 ( 16 ~; 10 |; 2 &; 46 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 1 ^ 25 !; 5 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY6,type,
sK2_SY6: $i ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(1,conjecture,
( emptysetE
=> ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(2,negated_conjecture,
( ( emptysetE
=> ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ! [SY0: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY0 )
=> ( SY0 != emptyset ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,emptysetE,nonempty]) ).
thf(4,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY0 )
=> ( SY0 != emptyset ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY0 )
=> ( SY0 != emptyset ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( in @ sK2_SY6 @ sK1_SY0 )
& ( sK1_SY0 = emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK2_SY6 @ sK1_SY0 )
& ( sK1_SY0 = emptyset ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ ( in @ sK2_SY6 @ sK1_SY0 )
| ( sK1_SY0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,emptysetE,nonempty]) ).
thf(12,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ ( in @ sK2_SY6 @ sK1_SY0 )
| ( sK1_SY0 != emptyset ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(14,plain,
! [SV1: $i] :
( ( ( ~ ( in @ SV1 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( in @ sK2_SY6 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ( sK1_SY0 != emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( in @ sK2_SY6 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[15]) ).
thf(19,plain,
( ( sK1_SY0 = emptyset )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV1: $i,SV2: $o] :
( ( SV2 = $true )
| ( ( in @ SV1 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV1: $i] :
( ( $true = $true )
| ( ( in @ SV1 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( $false = $true )
| ( ( in @ SV1 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[17]) ).
thf(23,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,22,21,20,19]) ).
thf(24,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU511^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 05:16:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 0
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 303
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.35 (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)
% 0.12/0.37 ********************************
% 0.12/0.37 * All subproblems solved! *
% 0.12/0.37 ********************************
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/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:23,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 24 ****
% 0.12/0.37 %**** clause counter: 23 ****
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/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:23,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------