TSTP Solution File: SYO374^5 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO374^5 : 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 : 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 : Thu Jul 21 17:33:39 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 54 unt; 6 typ; 0 def)
% Number of atoms : 181 ( 83 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 316 ( 64 ~; 36 |; 7 &; 194 @)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 0 ^ 76 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cM,type,
cM: $i > $i ).
thf(tp_cN,type,
cN: $i > $i ).
thf(tp_sK1_Xq,type,
sK1_Xq: ( $i > $i ) > $o ).
thf(tp_sK2_Xq,type,
sK2_Xq: ( $i > $i ) > $o ).
thf(tp_sK3_E,type,
sK3_E: $i ).
thf(tp_sK4_E,type,
sK4_E: $i ).
thf(1,conjecture,
( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT_A_LEIB2) ).
thf(2,negated_conjecture,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) )
=> ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ( Xp @ ( cM @ Xx ) )
<=> ( Xp @ ( cN @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
<=> ( Xq @ cN ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
=> ( Xq @ cN ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(7,plain,
( ( ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cN )
=> ( Xq @ cM ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[5]) ).
thf(8,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cM )
=> ( Xq @ cN ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [Xq: ( $i > $i ) > $o] :
( ( Xq @ cN )
=> ( Xq @ cM ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(10,plain,
( ( ( sK1_Xq @ cM )
& ~ ( sK1_Xq @ cN ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(11,plain,
( ( ( sK2_Xq @ cN )
& ~ ( sK2_Xq @ cM ) )
= $true ),
inference(extcnf_combined,[status(esa)],[9]) ).
thf(12,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cM @ Xx ) )
| ( Xp @ ( cN @ Xx ) ) )
& ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cN @ Xx ) )
| ( Xp @ ( cM @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(13,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cM @ Xx ) )
| ( Xp @ ( cN @ Xx ) ) )
& ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cN @ Xx ) )
| ( Xp @ ( cM @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ( sK1_Xq @ cM )
& ~ ( sK1_Xq @ cN ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(15,plain,
( ( ~ ( ~ ( sK1_Xq @ cM )
| ~ ~ ( sK1_Xq @ cN ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(16,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( sK1_Xq @ cM )
| ~ ~ ( sK1_Xq @ cN ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( sK1_Xq @ cM ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ~ ( sK1_Xq @ cN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( sK1_Xq @ cM )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( sK1_Xq @ cN ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( sK1_Xq @ cN )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV1: $i] :
( ( ! [SY3: $i > $o] :
( ~ ( SY3 @ ( cM @ SV1 ) )
| ( SY3 @ ( cN @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV1: $i,SV3: $i > $o] :
( ( ~ ( SV3 @ ( cM @ SV1 ) )
| ( SV3 @ ( cN @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i,SV3: $i > $o] :
( ( ( ~ ( SV3 @ ( cM @ SV1 ) ) )
= $true )
| ( ( SV3 @ ( cN @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV1: $i,SV3: $i > $o] :
( ( ( SV3 @ ( cM @ SV1 ) )
= $false )
| ( ( SV3 @ ( cN @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV1: $i] :
( ( ( ( cM @ SV1 )
= ( cM @ SV1 ) )
= $false )
| ( ( ( cN @ SV1 )
= ( cM @ SV1 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[34:[bind(SV3,$thf( ^ [SV5: $i] : ( SV5 = ( cM @ SV1 ) ) ))]]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( cN @ SV1 )
= ( cM @ SV1 ) )
= $true ),
inference(sim,[status(thm)],[36]) ).
thf(40,plain,
( ( ( sK1_Xq @ cN )
= ( sK1_Xq @ cM ) )
= $false ),
inference(res,[status(thm)],[27,23]) ).
thf(41,plain,
( ( ( cN @ sK3_E )
= ( cM @ sK3_E ) )
= $false ),
inference(extuni,[status(esa)],[40]) ).
thf(42,plain,
! [SV7: $i] :
( ( ( cN @ SV7 )
= ( cM @ SV7 ) )
= $true ),
inference(rename,[status(thm)],[37]) ).
thf(47,plain,
! [SV7: $i] :
( ( ( ( cN @ sK3_E )
= ( cM @ sK3_E ) )
= ( ( cN @ SV7 )
= ( cM @ SV7 ) ) )
= $false ),
inference(res,[status(thm)],[41,42]) ).
thf(50,plain,
$false = $true,
inference(extuni,[status(esa)],[47:[bind(SV7,$thf( sK3_E ))]]) ).
thf(51,plain,
( ( ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cM @ Xx ) )
| ( Xp @ ( cN @ Xx ) ) )
& ! [Xx: $i,Xp: $i > $o] :
( ~ ( Xp @ ( cN @ Xx ) )
| ( Xp @ ( cM @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(52,plain,
( ( ( sK2_Xq @ cN )
& ~ ( sK2_Xq @ cM ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(53,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(54,plain,
( ( ~ ( ~ ( sK2_Xq @ cN )
| ~ ~ ( sK2_Xq @ cM ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(55,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cN @ SX0 ) )
| ( SX1 @ ( cM @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(56,plain,
( ( ~ ( sK2_Xq @ cN )
| ~ ~ ( sK2_Xq @ cM ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
( ( ~ ( sK2_Xq @ cN ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(60,plain,
( ( ~ ~ ( sK2_Xq @ cM ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( SX1 @ ( cM @ SX0 ) )
| ( SX1 @ ( cN @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(63,plain,
( ( sK2_Xq @ cN )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(64,plain,
( ( ~ ( sK2_Xq @ cM ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV9: $i] :
( ( ! [SY5: $i > $o] :
( ~ ( SY5 @ ( cM @ SV9 ) )
| ( SY5 @ ( cN @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(67,plain,
( ( sK2_Xq @ cM )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV9: $i,SV11: $i > $o] :
( ( ~ ( SV11 @ ( cM @ SV9 ) )
| ( SV11 @ ( cN @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV9: $i,SV11: $i > $o] :
( ( ( ~ ( SV11 @ ( cM @ SV9 ) ) )
= $true )
| ( ( SV11 @ ( cN @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV9: $i,SV11: $i > $o] :
( ( ( SV11 @ ( cM @ SV9 ) )
= $false )
| ( ( SV11 @ ( cN @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(74,plain,
! [SV9: $i] :
( ( ( ( cM @ SV9 )
= ( cM @ SV9 ) )
= $false )
| ( ( ( cN @ SV9 )
= ( cM @ SV9 ) )
= $true ) ),
inference(replace_leibnizEQ,[status(thm)],[72:[bind(SV11,$thf( ^ [SV13: $i] : ( SV13 = ( cM @ SV9 ) ) ))]]) ).
thf(75,plain,
! [SV9: $i] :
( ( ( cN @ SV9 )
= ( cM @ SV9 ) )
= $true ),
inference(sim,[status(thm)],[74]) ).
thf(78,plain,
( ( ( sK2_Xq @ cM )
= ( sK2_Xq @ cN ) )
= $false ),
inference(res,[status(thm)],[67,63]) ).
thf(79,plain,
( ( ( cM @ sK4_E )
= ( cN @ sK4_E ) )
= $false ),
inference(extuni,[status(esa)],[78]) ).
thf(80,plain,
! [SV15: $i] :
( ( ( cN @ SV15 )
= ( cM @ SV15 ) )
= $true ),
inference(rename,[status(thm)],[75]) ).
thf(85,plain,
! [SV15: $i] :
( ( ( ( cM @ sK4_E )
= ( cN @ sK4_E ) )
= ( ( cN @ SV15 )
= ( cM @ SV15 ) ) )
= $false ),
inference(res,[status(thm)],[79,80]) ).
thf(87,plain,
$false = $true,
inference(extuni,[status(esa)],[85:[bind(SV15,$thf( sK4_E ))]]) ).
thf(88,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[87,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO374^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 00:07:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 0
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.34 (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)...
% 0.19/0.45
% 0.19/0.45 ********************************
% 0.19/0.45 * All subproblems solved! *
% 0.19/0.45 ********************************
% 0.19/0.45 % 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:87,loop_count:5,foatp_calls:2,translation:fof_full)
% 0.19/0.45
% 0.19/0.45 %**** Beginning of derivation protocol ****
% 0.19/0.45 % SZS output start CNFRefutation
% See solution above
% 0.19/0.45
% 0.19/0.45 %**** End of derivation protocol ****
% 0.19/0.45 %**** no. of clauses in derivation: 61 ****
% 0.19/0.45 %**** clause counter: 87 ****
% 0.19/0.45
% 0.19/0.45 % 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:87,loop_count:5,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------