TSTP Solution File: SEU727^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU727^2 : 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 : n027.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 12:14:14 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 39 unt; 8 typ; 2 def)
% Number of atoms : 223 ( 51 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 518 ( 86 ~; 39 |; 6 &; 357 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 81 ( 0 ^ 81 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SY14,type,
sK3_SY14: $i ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(1,conjecture,
( setminusI
=> ( setminusER
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(2,negated_conjecture,
( ( setminusI
=> ( setminusER
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setminusER,setminusI]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK2_SY12 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY14 @ sK1_A )
& ( in @ sK3_SY14 @ sK2_SY12 )
& ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(13,plain,
( ( ( in @ sK2_SY12 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY14 @ sK1_A )
& ( in @ sK3_SY14 @ sK2_SY12 )
& ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( ~ ( in @ sK2_SY12 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,setminusER,setminusI]) ).
thf(15,plain,
! [SV1: $i] :
( ( ! [SY15: $i,SY16: $i] :
( ~ ( in @ SY16 @ ( setminus @ SV1 @ SY15 ) )
| ~ ( in @ SY16 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( in @ SY18 @ SV2 )
| ( in @ SY18 @ SY17 )
| ( in @ SY18 @ ( setminus @ SV2 @ SY17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( in @ sK2_SY12 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY19: $i] :
( ~ ( in @ SY19 @ ( setminus @ SV1 @ SV3 ) )
| ~ ( in @ SY19 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY20: $i] :
( ~ ( in @ SY20 @ SV2 )
| ( in @ SY20 @ SV4 )
| ( in @ SY20 @ ( setminus @ SV2 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( in @ sK2_SY12 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( setminus @ SV1 @ SV3 ) )
| ~ ( in @ SV5 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV2 )
| ( in @ SV6 @ SV4 )
| ( in @ SV6 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( in @ sK2_SY12 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( setminus @ SV1 @ SV3 ) ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV2 ) )
= $true )
| ( ( ( in @ SV6 @ SV4 )
| ( in @ SV6 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV3: $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5 @ ( setminus @ SV1 @ SV3 ) )
= $false )
| ( ( ~ ( in @ SV5 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i,SV2: $i,SV6: $i] :
( ( ( in @ SV6 @ SV2 )
= $false )
| ( ( ( in @ SV6 @ SV4 )
| ( in @ SV6 @ ( setminus @ SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( in @ sK3_SY14 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(32,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i,SV3: $i,SV5: $i] :
( ( ( in @ SV5 @ SV3 )
= $false )
| ( ( in @ SV5 @ ( setminus @ SV1 @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i,SV4: $i,SV6: $i] :
( ( ( in @ SV6 @ SV4 )
= $true )
| ( ( in @ SV6 @ ( setminus @ SV2 @ SV4 ) )
= $true )
| ( ( in @ SV6 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( in @ sK3_SY14 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY12 )
| ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(38,plain,
( ( ~ ( in @ sK3_SY14 @ sK2_SY12 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(39,plain,
( ( ~ ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(40,plain,
( ( in @ sK3_SY14 @ sK2_SY12 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ~ ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(42,plain,
( ( in @ sK3_SY14 @ ( setminus @ sK1_A @ ( setminus @ sK1_A @ sK2_SY12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,42,40,35,34,33]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU727^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.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 : Mon Jun 20 09:23:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 382
% 0.12/0.34
% 0.12/0.34 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).
% 0.12/0.37
% 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: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:43,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: 44 ****
% 0.12/0.38 %**** clause counter: 43 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox2/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:43,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------