TSTP Solution File: SEU150+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 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 12:07:10 EDT 2022
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 29 unt; 5 typ; 0 def)
% Number of atoms : 111 ( 72 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 94 ( 8 ~; 7 |; 0 &; 71 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 ^ 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_SY10,type,
sK3_SY10: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(2,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(5,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(6,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $false ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(9,plain,
$true = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(10,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [SY8: $i,SY9: $i] :
( ( ( singleton @ sK1_A )
= ( unordered_pair @ SY8 @ SY9 ) )
=> ( SY8 = SY9 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).
thf(13,plain,
( ( ! [SY10: $i] :
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ SY10 ) )
=> ( sK2_SY8 = SY10 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(14,plain,
( ( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
=> ( sK2_SY8 = sK3_SY10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( sK2_SY8 = sK3_SY10 )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ( sK2_SY8 != sK3_SY10 ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(20,plain,
$true = $true,
inference(copy,[status(thm)],[10]) ).
thf(21,plain,
$true = $true,
inference(copy,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ( singleton @ sK1_A )
= ( unordered_pair @ sK2_SY8 @ sK3_SY10 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(24,plain,
( ( ( sK2_SY8 != sK3_SY10 ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( unordered_pair @ SV1 @ SY11 )
= ( unordered_pair @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ! [SY13: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SY12 @ SY13 ) )
| ( SV2 = SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( sK2_SY8 = sK3_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV3: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV3 )
= ( unordered_pair @ SV3 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(29,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY14: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SY14 ) )
| ( SV2 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
! [SV4: $i,SV2: $i] :
( ( ( ! [SY14: $i] :
( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SY14 ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(31,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ( ( singleton @ SV2 )
!= ( unordered_pair @ SV4 @ SV5 ) ) )
= $true )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(32,plain,
! [SV5: $i,SV4: $i,SV2: $i] :
( ( ( ( singleton @ SV2 )
= ( unordered_pair @ SV4 @ SV5 ) )
= $false )
| ( ( SV2 = SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,32,28,27,23,21]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU150+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % 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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 11:53:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 4
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:4,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:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.13/0.37
% 0.13/0.37 ********************************
% 0.13/0.37 * All subproblems solved! *
% 0.13/0.37 ********************************
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.37
% 0.13/0.37 %**** Beginning of derivation protocol ****
% 0.13/0.37 % SZS output start CNFRefutation
% See solution above
% 0.13/0.37
% 0.13/0.37 %**** End of derivation protocol ****
% 0.13/0.37 %**** no. of clauses in derivation: 34 ****
% 0.13/0.37 %**** clause counter: 33 ****
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------