TSTP Solution File: SET899+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n003.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 03:06:04 EDT 2022
% Result : Theorem 0.06s 0.27s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 45 unt; 10 typ; 0 def)
% Number of atoms : 214 ( 56 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 355 ( 42 ~; 35 |; 2 &; 266 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 71 ( 0 ^ 67 !; 4 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
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_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(5,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(6,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_zfmisc_1) ).
thf(7,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [SY12: $i,SY13: $i] :
( ( subset @ sK1_A @ SY12 )
=> ( ( in @ SY13 @ sK1_A )
| ( subset @ sK1_A @ ( set_difference @ SY12 @ ( singleton @ SY13 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ! [SY14: $i] :
( ( subset @ sK1_A @ sK2_SY12 )
=> ( ( in @ SY14 @ sK1_A )
| ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ SY14 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( subset @ sK1_A @ sK2_SY12 )
=> ( ( in @ sK3_SY14 @ sK1_A )
| ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( subset @ sK1_A @ sK2_SY12 )
= $true ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(18,plain,
( ( ( in @ sK3_SY14 @ sK1_A )
| ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ( in @ sK3_SY14 @ sK1_A )
| ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( ~ ( in @ sK3_SY14 @ sK1_A )
& ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(22,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(23,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(25,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(26,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(28,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(31,plain,
( ( subset @ sK1_A @ sK2_SY12 )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ~ ( in @ sK3_SY14 @ sK1_A )
& ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(33,plain,
( ( ~ ( ~ ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SV2 @ SY15 )
| ~ ( in @ SY15 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY16: $i] :
( ~ ( subset @ SV3 @ SY16 )
| ! [SY17: $i] :
( ( in @ SY17 @ SV3 )
| ( subset @ SV3 @ ( set_difference @ SY16 @ ( singleton @ SY17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
( ( ~ ~ ( in @ sK3_SY14 @ sK1_A )
| ~ ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV4: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV4 )
| ~ ( in @ SV4 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV5 )
| ! [SY18: $i] :
( ( in @ SY18 @ SV3 )
| ( subset @ SV3 @ ( set_difference @ SV5 @ ( singleton @ SY18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
( ( ~ ~ ( in @ sK3_SY14 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
( ( ~ ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV4: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV4 ) )
= $true )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV5 ) )
= $true )
| ( ( ! [SY18: $i] :
( ( in @ SY18 @ SV3 )
| ( subset @ SV3 @ ( set_difference @ SV5 @ ( singleton @ SY18 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ( in @ sK3_SY14 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(46,plain,
( ( ~ ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV4: $i,SV2: $i] :
( ( ( in @ SV2 @ SV4 )
= $false )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV5 )
= $false )
| ( ( ! [SY18: $i] :
( ( in @ SY18 @ SV3 )
| ( subset @ SV3 @ ( set_difference @ SV5 @ ( singleton @ SY18 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( in @ sK3_SY14 @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( subset @ sK1_A @ ( set_difference @ sK2_SY12 @ ( singleton @ sK3_SY14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV2: $i,SV4: $i] :
( ( ( in @ SV4 @ SV2 )
= $false )
| ( ( in @ SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: $i,SV3: $i,SV6: $i] :
( ( ( ( in @ SV6 @ SV3 )
| ( subset @ SV3 @ ( set_difference @ SV5 @ ( singleton @ SV6 ) ) ) )
= $true )
| ( ( subset @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV5: $i,SV3: $i,SV6: $i] :
( ( ( in @ SV6 @ SV3 )
= $true )
| ( ( subset @ SV3 @ ( set_difference @ SV5 @ ( singleton @ SV6 ) ) )
= $true )
| ( ( subset @ SV3 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(54,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,53,51,50,49,36,34,31]) ).
thf(55,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SET899+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.07 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.06/0.25 % Computer : n003.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Sat Jul 9 23:42:14 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.06/0.25
% 0.06/0.25 No.of.Axioms: 5
% 0.06/0.25
% 0.06/0.25 Length.of.Defs: 0
% 0.06/0.25
% 0.06/0.25 Contains.Choice.Funs: false
% 0.06/0.25 (rf:0,axioms:5,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:7,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.06/0.27
% 0.06/0.27 ********************************
% 0.06/0.27 * All subproblems solved! *
% 0.06/0.27 ********************************
% 0.06/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:54,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.27
% 0.06/0.27 %**** Beginning of derivation protocol ****
% 0.06/0.27 % SZS output start CNFRefutation
% See solution above
% 0.06/0.27
% 0.06/0.27 %**** End of derivation protocol ****
% 0.06/0.27 %**** no. of clauses in derivation: 55 ****
% 0.06/0.27 %**** clause counter: 54 ****
% 0.06/0.27
% 0.06/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:54,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------