TSTP Solution File: SET886+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET886+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 : n010.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 03:05:59 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 55 ( 42 unt; 9 typ; 0 def)
% Number of atoms : 141 ( 68 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 193 ( 12 ~; 7 |; 0 &; 166 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 64 ( 0 ^ 60 !; 4 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(tp_sK3_SY15,type,
sK3_SY15: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(4,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_zfmisc_1) ).
thf(8,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
=> ( ( unordered_pair @ A @ B )
= ( singleton @ C ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
=> ( A = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(16,plain,
( ( ! [SY13: $i,SY14: $i] :
( ( subset @ ( unordered_pair @ sK1_A @ SY13 ) @ ( singleton @ SY14 ) )
=> ( ( unordered_pair @ sK1_A @ SY13 )
= ( singleton @ SY14 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(17,plain,
( ( ! [SY15: $i] :
( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY13 ) @ ( singleton @ SY15 ) )
=> ( ( unordered_pair @ sK1_A @ sK2_SY13 )
= ( singleton @ SY15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(18,plain,
( ( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY13 ) @ ( singleton @ sK3_SY15 ) )
=> ( ( unordered_pair @ sK1_A @ sK2_SY13 )
= ( singleton @ sK3_SY15 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(19,plain,
( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY13 ) @ ( singleton @ sK3_SY15 ) )
= $true ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(20,plain,
( ( ( unordered_pair @ sK1_A @ sK2_SY13 )
= ( singleton @ sK3_SY15 ) )
= $false ),
inference(standard_cnf,[status(thm)],[18]) ).
thf(21,plain,
( ( ( ( unordered_pair @ sK1_A @ sK2_SY13 )
!= ( singleton @ sK3_SY15 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
| ( A = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(23,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(24,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(25,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(27,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
| ( A = C ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(32,plain,
( ( subset @ ( unordered_pair @ sK1_A @ sK2_SY13 ) @ ( singleton @ sK3_SY15 ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(33,plain,
( ( ( ( unordered_pair @ sK1_A @ sK2_SY13 )
!= ( singleton @ sK3_SY15 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ( unordered_pair @ SV1 @ SY16 )
= ( unordered_pair @ SY16 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(35,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ~ ( subset @ ( unordered_pair @ SV3 @ SY17 ) @ ( singleton @ SY18 ) )
| ( SV3 = SY18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV4 )
= ( singleton @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
( ( ( unordered_pair @ sK1_A @ sK2_SY13 )
= ( singleton @ sK3_SY15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV5: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV5 )
= ( unordered_pair @ SV5 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY19: $i] :
( ~ ( subset @ ( unordered_pair @ SV3 @ SV6 ) @ ( singleton @ SY19 ) )
| ( SV3 = SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV3 @ SV6 ) @ ( singleton @ SV7 ) )
| ( SV3 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV3 @ SV6 ) @ ( singleton @ SV7 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV7: $i,SV6: $i,SV3: $i] :
( ( ( subset @ ( unordered_pair @ SV3 @ SV6 ) @ ( singleton @ SV7 ) )
= $false )
| ( ( SV3 = SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,44,40,39,38,36,35,32]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 11 08:35:45 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35
% 0.14/0.35 No.of.Axioms: 6
% 0.14/0.35
% 0.14/0.35 Length.of.Defs: 0
% 0.14/0.35
% 0.14/0.35 Contains.Choice.Funs: false
% 0.14/0.35 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.21/0.39
% 0.21/0.39 ********************************
% 0.21/0.39 * All subproblems solved! *
% 0.21/0.39 ********************************
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.39
% 0.21/0.39 %**** Beginning of derivation protocol ****
% 0.21/0.39 % SZS output start CNFRefutation
% See solution above
% 0.21/0.39
% 0.21/0.39 %**** End of derivation protocol ****
% 0.21/0.39 %**** no. of clauses in derivation: 46 ****
% 0.21/0.39 %**** clause counter: 45 ****
% 0.21/0.39
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------