TSTP Solution File: SEU844^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU844^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n009.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 12:15:21 EDT 2022
% Result : Theorem 0.17s 0.35s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 45 unt; 5 typ; 0 def)
% Number of atoms : 271 ( 118 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 297 ( 78 ~; 54 |; 8 &; 142 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 136 ( 0 ^ 136 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_cS,type,
cS: a > $o ).
thf(tp_cT,type,
cT: a > $o ).
thf(tp_sK1_Xx,type,
sK1_Xx: a ).
thf(tp_sK2_Xx,type,
sK2_Xx: a ).
thf(1,conjecture,
( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
=> ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) )
& ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM8_pme) ).
thf(2,negated_conjecture,
( ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
=> ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) )
& ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
=> ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) )
& ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) )
& ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ! [Xx: a] :
( ( cS @ Xx )
=> ( cT @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [Xx: a] :
( ( cT @ Xx )
=> ( cS @ Xx ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ( cS @ sK1_Xx )
& ~ ( cT @ sK1_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ( cT @ sK2_Xx )
& ~ ( cS @ sK2_Xx ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(13,plain,
( ( ( cS @ sK1_Xx )
& ~ ( cT @ sK1_Xx ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ( ~ ( cS @ sK1_Xx )
| ~ ~ ( cT @ sK1_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
! [SV1: a > $o] :
( ( ! [SY4: a > $o] : ( SV1 = SY4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ~ ( cS @ sK1_Xx )
| ~ ~ ( cT @ sK1_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(17,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( SV1 = SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ( cS @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ~ ( cT @ sK1_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( ! [SV3: a] :
( ( SV1 @ SV3 )
= ( SV2 @ SV3 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: a > $o,SV1: a > $o] :
( ( SV1 = SV2 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( cS @ sK1_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( cT @ sK1_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= ( SV2 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( cT @ sK1_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ~ ( ( SV1 @ SV4 )
| ( SV2 @ SV4 ) )
| ~ ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(27,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= ( SV2 @ SV4 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( ~ ( ( SV1 @ SV4 )
| ( SV2 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( ( SV1 @ SV4 )
| ( SV2 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(30,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= $false )
| ( ( ~ ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(31,plain,
! [SV1: a > $o,SV4: a,SV2: a > $o] :
( ( ( SV2 @ SV4 )
= $false )
| ( ( ~ ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) )
= $false )
| ( ( SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 )
| ~ ( SV2 @ SV4 ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 ) )
= $false )
| ( ( SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV1: a > $o,SV4: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV4 ) )
= $false )
| ( ( SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( ~ ( SV1 @ SV4 ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV4: a,SV2: a > $o] :
( ( ( ~ ( SV2 @ SV4 ) )
= $false )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(38,plain,
! [SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
! [SV1: a > $o,SV4: a,SV2: a > $o] :
( ( ( SV2 @ SV4 )
= $true )
| ( ( SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: a > $o,SV4: a,SV1: a > $o] :
( ( ( SV1 @ SV4 )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV4: a,SV2: a > $o] :
( ( ( SV2 @ SV4 )
= $true )
| ( ( SV2 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,41,40,39,38,27,25,22]) ).
thf(43,plain,
( ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(44,plain,
( ( ( cT @ sK2_Xx )
& ~ ( cS @ sK2_Xx ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(45,plain,
( ( ~ ( ~ ( cT @ sK2_Xx )
| ~ ~ ( cS @ sK2_Xx ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(46,plain,
! [SV5: a > $o] :
( ( ! [SY5: a > $o] : ( SV5 = SY5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(47,plain,
( ( ~ ( cT @ sK2_Xx )
| ~ ~ ( cS @ sK2_Xx ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV6: a > $o,SV5: a > $o] :
( ( SV5 = SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(49,plain,
( ( ~ ( cT @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(50,plain,
( ( ~ ~ ( cS @ sK2_Xx ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV6: a > $o,SV5: a > $o] :
( ( ! [SV7: a] :
( ( SV5 @ SV7 )
= ( SV6 @ SV7 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[48]) ).
thf(52,plain,
! [SV6: a > $o,SV5: a > $o] :
( ( SV5 = SV6 )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( cT @ sK2_Xx )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ( cS @ sK2_Xx ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( SV5 @ SV8 )
= ( SV6 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(56,plain,
( ( cS @ sK2_Xx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ~ ( ( SV5 @ SV8 )
| ( SV6 @ SV8 ) )
| ~ ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(58,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( SV5 @ SV8 )
= ( SV6 @ SV8 ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( ~ ( ( SV5 @ SV8 )
| ( SV6 @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(60,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( ( SV5 @ SV8 )
| ( SV6 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(61,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( SV5 @ SV8 )
= $false )
| ( ( ~ ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(62,plain,
! [SV5: a > $o,SV8: a,SV6: a > $o] :
( ( ( SV6 @ SV8 )
= $false )
| ( ( ~ ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(63,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) )
= $false )
| ( ( SV5 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( ~ ( SV5 @ SV8 )
| ~ ( SV6 @ SV8 ) )
= $false )
| ( ( SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV8: a,SV5: a > $o] :
( ( ( ~ ( SV5 @ SV8 ) )
= $false )
| ( ( SV5 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(66,plain,
! [SV5: a > $o,SV8: a,SV6: a > $o] :
( ( ( ~ ( SV6 @ SV8 ) )
= $false )
| ( ( SV5 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( ~ ( SV5 @ SV8 ) )
= $false )
| ( ( SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV8: a,SV6: a > $o] :
( ( ( ~ ( SV6 @ SV8 ) )
= $false )
| ( ( SV6 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV8: a,SV5: a > $o] :
( ( ( SV5 @ SV8 )
= $true )
| ( ( SV5 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV5: a > $o,SV8: a,SV6: a > $o] :
( ( ( SV6 @ SV8 )
= $true )
| ( ( SV5 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV6: a > $o,SV8: a,SV5: a > $o] :
( ( ( SV5 @ SV8 )
= $true )
| ( ( SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV8: a,SV6: a > $o] :
( ( ( SV6 @ SV8 )
= $true )
| ( ( SV6 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,72,71,70,69,58,56,53]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU844^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jun 20 02:22:52 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32
% 0.10/0.32 No.of.Axioms: 0
% 0.10/0.32
% 0.10/0.32 Length.of.Defs: 0
% 0.10/0.32
% 0.10/0.32 Contains.Choice.Funs: false
% 0.10/0.32 (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).
% 0.17/0.35
% 0.17/0.35 ********************************
% 0.17/0.35 * All subproblems solved! *
% 0.17/0.35 ********************************
% 0.17/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.17/0.35
% 0.17/0.35 %**** Beginning of derivation protocol ****
% 0.17/0.35 % SZS output start CNFRefutation
% See solution above
% 0.17/0.35
% 0.17/0.35 %**** End of derivation protocol ****
% 0.17/0.35 %**** no. of clauses in derivation: 74 ****
% 0.17/0.35 %**** clause counter: 73 ****
% 0.17/0.35
% 0.17/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------