TSTP Solution File: SEU718^2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU718^2 : 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 : n028.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 12:14:10 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 64 ( 47 unt; 9 typ; 2 def)
% Number of atoms : 293 ( 62 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 656 ( 162 ~; 64 |; 10 &; 380 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 74 ( 0 ^ 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY16,type,
sK3_SY16: $i ).
thf(tp_sK4_SY18,type,
sK4_SY18: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
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
=> ( powersetE1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(2,negated_conjecture,
( ( subsetE
=> ( powersetE1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) )
= $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] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,powersetE1,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] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY18 @ sK1_A )
& ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
& ( in @ sK4_SY18 @ sK2_SY13 )
& ~ ( in @ sK4_SY18 @ sK3_SY16 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY18 @ sK1_A )
& ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
& ( in @ sK4_SY18 @ sK2_SY13 )
& ~ ( in @ sK4_SY18 @ sK3_SY16 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,powersetE1,subsetE]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ ( powerset @ SV1 ) )
| ( subset @ SY19 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ~ ( subset @ SV2 @ SY20 )
| ! [SY21: $i] :
( ~ ( in @ SY21 @ SV2 )
| ( in @ SY21 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ ( powerset @ SV1 ) )
| ( subset @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( subset @ SV2 @ SV4 )
| ! [SY22: $i] :
( ~ ( in @ SY22 @ SV2 )
| ( in @ SY22 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ ( powerset @ SV1 ) ) )
= $true )
| ( ( subset @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( subset @ SV2 @ SV4 ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ SV2 )
| ( in @ SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK2_SY13 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i,SV3: $i] :
( ( ( in @ SV3 @ ( powerset @ SV1 ) )
= $false )
| ( ( subset @ SV3 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: $i,SV2: $i] :
( ( ( subset @ SV2 @ SV4 )
= $false )
| ( ( ! [SY22: $i] :
( ~ ( in @ SY22 @ SV2 )
| ( in @ SY22 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 )
| ( in @ SV5 @ SV4 ) )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ( in @ sK3_SY16 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(31,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV2 ) )
= $true )
| ( ( in @ SV5 @ SV4 )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( in @ sK3_SY16 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(35,plain,
! [SV4: $i,SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ SV2 )
= $false )
| ( ( in @ SV5 @ SV4 )
= $true )
| ( ( subset @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
( ( ~ ( in @ sK4_SY18 @ sK1_A )
| ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ( in @ sK4_SY18 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(38,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(39,plain,
( ( in @ sK4_SY18 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( ~ ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
| ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
( ( ~ ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(43,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(44,plain,
( ( in @ sK2_SY13 @ ( powerset @ sK3_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(45,plain,
( ( ~ ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(46,plain,
( ( ~ ( in @ sK4_SY18 @ sK2_SY13 )
| ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(47,plain,
( ( ~ ( in @ sK4_SY18 @ sK2_SY13 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(48,plain,
( ( ~ ~ ( in @ sK4_SY18 @ sK3_SY16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( in @ sK4_SY18 @ sK2_SY13 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ( in @ sK4_SY18 @ sK3_SY16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(51,plain,
( ( in @ sK4_SY18 @ sK3_SY16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(52,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,51,49,44,39,35,33,26]) ).
thf(53,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU718^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 03:05:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33
% 0.12/0.33 No.of.Axioms: 0
% 0.12/0.33
% 0.12/0.33 Length.of.Defs: 346
% 0.12/0.33
% 0.12/0.33 Contains.Choice.Funs: false
% 0.12/0.34 (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)..
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:52,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 53 ****
% 0.12/0.38 %**** clause counter: 52 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:52,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------