TSTP Solution File: SEU541^2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU541^2 : 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 : n013.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 12:12:44 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 23 unt; 6 typ; 2 def)
% Number of atoms : 124 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 126 ( 22 ~; 13 |; 2 &; 78 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 1 ^ 13 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_sK1_SY0,type,
sK1_SY0: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(set2prop,definition,
( set2prop
= ( ^ [A: $i] : ( in @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set2prop) ).
thf(1,conjecture,
( prop2setI
=> ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(2,negated_conjecture,
( ( prop2setI
=> ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ! [SY0: $o] :
( SY0
=> ( in @ emptyset @ ( prop2set @ SY0 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,prop2setI,set2prop]) ).
thf(4,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $o] :
( SY0
=> ( in @ emptyset @ ( prop2set @ SY0 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $o] :
( SY0
=> ( in @ emptyset @ ( prop2set @ SY0 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( sK1_SY0
& ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( sK1_SY0
& ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( ~ sK1_SY0
| ~ ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,prop2setI,set2prop]) ).
thf(12,plain,
! [SV1: $o] :
( ( ~ SV1
| ( in @ emptyset @ ( prop2set @ SV1 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(14,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ sK1_SY0
| ~ ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV1: $o] :
( ( ( ~ SV1 )
= $true )
| ( ( in @ emptyset @ ( prop2set @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ( ~ $true )
= $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ( ~ $false )
= $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(19,plain,
( ( ~ sK1_SY0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(21,plain,
! [SV1: $o] :
( ( SV1 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(22,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(23,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(24,plain,
sK1_SY0 = $true,
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ( in @ emptyset @ ( prop2set @ sK1_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(26,plain,
( ( in @ emptyset @ ( prop2set @ sK1_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(27,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,26,24,23,22]) ).
thf(28,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU541^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n013.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 : Mon Jun 20 06:16:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 302
% 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)
% 0.13/0.36 ********************************
% 0.13/0.36 * All subproblems solved! *
% 0.13/0.36 ********************************
% 0.13/0.36 % 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:27,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.36
% 0.13/0.36 %**** Beginning of derivation protocol ****
% 0.13/0.36 % SZS output start CNFRefutation
% See solution above
% 0.13/0.36
% 0.13/0.36 %**** End of derivation protocol ****
% 0.13/0.36 %**** no. of clauses in derivation: 28 ****
% 0.13/0.36 %**** clause counter: 27 ****
% 0.13/0.36
% 0.13/0.36 % 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:27,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------