TSTP Solution File: SEU634^2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU634^2 : 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 12:13:32 EDT 2022
% Result : Theorem 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 29 unt; 11 typ; 3 def)
% Number of atoms : 235 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 458 ( 58 ~; 41 |; 7 &; 331 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 89 ( 0 ^ 86 !; 3 ?; 89 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_Xx,type,
sK2_Xx: $i > $i > $i ).
thf(tp_sK3_X,type,
sK3_X: $i > $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(2,negated_conjecture,
( ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,setunionE2,subsetI2,uniqinunit]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ( subset @ ( setunion @ ( setadjoin @ sK1_A @ emptyset ) ) @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK2_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK3_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK3_X @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK3_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK3_X @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK2_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK2_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ~ ( subset @ ( setunion @ ( setadjoin @ sK1_A @ emptyset ) ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK2_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,setunionE2,subsetI2,uniqinunit]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ ( sK3_X @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ SX1 @ ( sK3_X @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,setunionE2,subsetI2,uniqinunit]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ~ ( in @ SV1 @ ( setadjoin @ SY10 @ emptyset ) )
| ( SV1 = SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
( ( subset @ ( setunion @ ( setadjoin @ sK1_A @ emptyset ) ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(21,plain,
! [SV2: $i] :
( ( ! [SY11: $i] :
( ~ ( ~ ( in @ ( sK2_Xx @ SY11 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK2_Xx @ SY11 @ SV2 ) @ SY11 ) )
| ( subset @ SV2 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY12: $i] :
( ~ ( in @ SY12 @ ( setunion @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_X @ SY12 @ SV3 ) @ SV3 )
| ~ ( in @ SY12 @ ( sK3_X @ SY12 @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ ( setadjoin @ SV4 @ emptyset ) )
| ( SV1 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 ) )
| ( subset @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ ( setunion @ SV3 ) )
| ~ ( ~ ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ ( setadjoin @ SV4 @ emptyset ) ) )
= $true )
| ( ( SV1 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 ) ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( setunion @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV1: $i] :
( ( ( in @ SV1 @ ( setadjoin @ SV4 @ emptyset ) )
= $false )
| ( ( SV1 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV2 )
| ~ ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV2 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 ) )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 )
| ~ ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) ) )
= $false )
| ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV2 )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 ) )
= $true )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) ) )
= $false )
| ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV2: $i,SV5: $i] :
( ( ( in @ ( sK2_Xx @ SV5 @ SV2 ) @ SV5 )
= $false )
| ( ( subset @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_X @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ ( sK3_X @ SV6 @ SV3 ) )
= $true )
| ( ( in @ SV6 @ ( setunion @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,41,40,39,35,29]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU634^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n028.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 20:57:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 565
% 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)..
% 0.19/0.42
% 0.19/0.42 ********************************
% 0.19/0.42 * All subproblems solved! *
% 0.19/0.42 ********************************
% 0.19/0.42 % 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.42
% 0.19/0.42 %**** Beginning of derivation protocol ****
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
% 0.19/0.42
% 0.19/0.42 %**** End of derivation protocol ****
% 0.19/0.42 %**** no. of clauses in derivation: 43 ****
% 0.19/0.42 %**** clause counter: 42 ****
% 0.19/0.42
% 0.19/0.42 % 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------