TSTP Solution File: SEU713^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU713^2 : 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 12:14:08 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 40 unt; 10 typ; 3 def)
% Number of atoms : 282 ( 69 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 593 ( 77 ~; 49 |; 6 &; 427 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 114 ( 0 ^ 114 !; 0 ?; 114 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetI,type,
powersetI: $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_sK4_Xx,type,
sK4_Xx: $i > $i > $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(1,conjecture,
( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem) ).
thf(2,negated_conjecture,
( ( powersetI
=> ( powersetE
=> ( setminusEL
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,powersetE,powersetI,setminusEL]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK4_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK4_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
& ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,powersetE,powersetI,setminusEL]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK4_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,powersetE,powersetI,setminusEL]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( in @ SY19 @ ( setminus @ SV1 @ SY18 ) )
| ( in @ SY19 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ ( powerset @ SV2 ) )
| ! [SY21: $i] :
( ~ ( in @ SY21 @ SY20 )
| ( in @ SY21 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ~ ( ~ ( in @ ( sK4_Xx @ SY22 @ SV3 ) @ SY22 )
| ~ ~ ( in @ ( sK4_Xx @ SY22 @ SV3 ) @ SV3 ) )
| ( in @ SY22 @ ( powerset @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SY23 @ ( setminus @ SV1 @ SV4 ) )
| ( in @ SY23 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) )
| ! [SY24: $i] :
( ~ ( in @ SY24 @ SV5 )
| ( in @ SY24 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK2_SY15 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
| ( in @ SV6 @ ( powerset @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ SV4 ) )
| ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( powerset @ SV2 ) ) )
= $true )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV5 )
| ( in @ SY24 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( in @ sK2_SY15 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ ( setminus @ SV1 @ SV4 ) ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false )
| ( ( ! [SY24: $i] :
( ~ ( in @ SY24 @ SV5 )
| ( in @ SY24 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
| ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
| ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ ( setminus @ SV1 @ SV4 ) )
= $false )
| ( ( in @ SV7 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV5 )
| ( in @ SV8 @ SV2 ) )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ( in @ sK3_SY17 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV5 ) )
= $true )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
( ( in @ sK3_SY17 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(45,plain,
( ( ~ ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV6 )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( in @ SV8 @ SV5 )
= $false )
| ( ( in @ SV8 @ SV2 )
= $true )
| ( ( in @ SV5 @ ( powerset @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
( ( in @ ( setminus @ sK2_SY15 @ sK3_SY17 ) @ ( powerset @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ ( sK4_Xx @ SV6 @ SV3 ) @ SV3 )
= $false )
| ( ( in @ SV6 @ ( powerset @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,50,49,48,46,44,37]) ).
thf(52,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU713^2 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n013.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 : Sun Jun 19 20:57:59 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36
% 0.14/0.36 No.of.Axioms: 0
% 0.14/0.36
% 0.14/0.36 Length.of.Defs: 564
% 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)..
% 0.14/0.40
% 0.14/0.40 ********************************
% 0.14/0.40 * All subproblems solved! *
% 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:51,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: 52 ****
% 0.14/0.40 %**** clause counter: 51 ****
% 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:51,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------