TSTP Solution File: SEU623^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU623^2 : 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 : n032.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 12:13:26 EDT 2022
% Result : Theorem 0.16s 0.35s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 61 ( 38 unt; 13 typ; 4 def)
% Number of atoms : 225 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 419 ( 37 ~; 32 |; 2 &; 319 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 99 ( 0 ^ 99 !; 0 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(1,conjecture,
( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(2,negated_conjecture,
( ( subsetE
=> ( powersetsubset
=> ( binunionLsub
=> ( singletoninpowerset
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binunionLsub,powersetsubset,singletoninpowerset,subsetE]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( ( in @ sK3_SY17 @ sK1_A )
& ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(13,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(14,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ( in @ sK3_SY17 @ sK1_A )
& ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ~ ( ~ ( in @ sK3_SY17 @ sK1_A )
| ~ ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18,binunionLsub,powersetsubset,singletoninpowerset,subsetE]) ).
thf(20,plain,
! [SV1: $i] :
( ( ! [SY18: $i] :
( ~ ( in @ SY18 @ SV1 )
| ( in @ ( setadjoin @ SY18 @ emptyset ) @ ( powerset @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY19: $i] : ( subset @ SV2 @ ( binunion @ SV2 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ~ ( subset @ SV3 @ SY20 )
| ( subset @ ( powerset @ SV3 ) @ ( powerset @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV4: $i] :
( ( ! [SY21: $i] :
( ~ ( subset @ SV4 @ SY21 )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ SV4 )
| ( in @ SY22 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_A )
| ~ ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV1 )
| ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
! [SV6: $i,SV2: $i] :
( ( subset @ SV2 @ ( binunion @ SV2 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(27,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV7 )
| ( subset @ ( powerset @ SV3 ) @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV8 )
| ! [SY23: $i] :
( ~ ( in @ SY23 @ SV4 )
| ( in @ SY23 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(31,plain,
! [SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV1 ) )
= $true )
| ( ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 ) )
= $true )
| ( ( subset @ ( powerset @ SV3 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV8 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV4 )
| ( in @ SY23 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( in @ sK3_SY17 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ SV1 )
= $false )
| ( ( in @ ( setadjoin @ SV5 @ emptyset ) @ ( powerset @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $false )
| ( ( subset @ ( powerset @ SV3 ) @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV8: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV8 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ SV4 )
| ( in @ SY23 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
( ( in @ ( setadjoin @ sK3_SY17 @ emptyset ) @ ( powerset @ ( binunion @ sK1_A @ sK2_SY15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV4 )
| ( in @ SV9 @ SV8 ) )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV4 ) )
= $true )
| ( ( in @ SV9 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV8: $i,SV4: $i,SV9: $i] :
( ( ( in @ SV9 @ SV4 )
= $false )
| ( ( in @ SV9 @ SV8 )
= $true )
| ( ( subset @ SV4 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,42,39,37,36,34]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU623^2 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sun Jun 19 06:45:47 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.16/0.31
% 0.16/0.31 No.of.Axioms: 0
% 0.16/0.31
% 0.16/0.31 Length.of.Defs: 758
% 0.16/0.31
% 0.16/0.31 Contains.Choice.Funs: false
% 0.16/0.31 (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)..
% 0.16/0.35
% 0.16/0.35 ********************************
% 0.16/0.35 * All subproblems solved! *
% 0.16/0.35 ********************************
% 0.16/0.35 % SZS status Theorem for /export/starexec/sandbox/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:43,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.16/0.35
% 0.16/0.35 %**** Beginning of derivation protocol ****
% 0.16/0.35 % SZS output start CNFRefutation
% See solution above
% 0.16/0.35
% 0.16/0.35 %**** End of derivation protocol ****
% 0.16/0.35 %**** no. of clauses in derivation: 44 ****
% 0.16/0.35 %**** clause counter: 43 ****
% 0.16/0.35
% 0.16/0.35 % SZS status Theorem for /export/starexec/sandbox/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:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------