TSTP Solution File: SET638^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET638^5 : 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 : 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 03:03:51 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 67 ( 31 unt; 5 typ; 0 def)
% Number of atoms : 412 ( 118 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 453 ( 140 ~; 104 |; 16 &; 172 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 20 ^ 63 !; 0 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $tType ).
thf(tp_sK1_X,type,
sK1_X: a > $o ).
thf(tp_sK2_SY7,type,
sK2_SY7: a > $o ).
thf(tp_sK3_SY13,type,
sK3_SY13: a > $o ).
thf(tp_sK4_SY17,type,
sK4_SY17: a ).
thf(1,conjecture,
! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( ( Y @ Xx )
| ( Z @ Xx ) ) )
& ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Z @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_120_pme) ).
thf(2,negated_conjecture,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( ( Y @ Xx )
| ( Z @ Xx ) ) )
& ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Z @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: a > $o,Y: a > $o,Z: a > $o] :
( ( ! [Xx: a] :
( ( X @ Xx )
=> ( ( Y @ Xx )
| ( Z @ Xx ) ) )
& ( ( ^ [Xx: a] :
( ( X @ Xx )
& ( Z @ Xx ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [Xx: a] :
( ( X @ Xx )
=> ( Y @ Xx ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [SY7: a > $o,SY8: a > $o] :
( ( ! [SY9: a] :
( ( sK1_X @ SY9 )
=> ( ( SY7 @ SY9 )
| ( SY8 @ SY9 ) ) )
& ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( SY8 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [SY12: a] :
( ( sK1_X @ SY12 )
=> ( SY7 @ SY12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY13: a > $o] :
( ( ! [SY14: a] :
( ( sK1_X @ SY14 )
=> ( ( sK2_SY7 @ SY14 )
| ( SY13 @ SY14 ) ) )
& ( ( ^ [SY10: a] :
( ( sK1_X @ SY10 )
& ( SY13 @ SY10 ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [SY17: a] :
( ( sK1_X @ SY17 )
=> ( sK2_SY7 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ! [SY18: a] :
( ( sK1_X @ SY18 )
=> ( ( sK2_SY7 @ SY18 )
| ( sK3_SY13 @ SY18 ) ) )
& ( ( ^ [SY19: a] :
( ( sK1_X @ SY19 )
& ( sK3_SY13 @ SY19 ) ) )
= ( ^ [Xx: a] : $false ) ) )
=> ! [SY17: a] :
( ( sK1_X @ SY17 )
=> ( sK2_SY7 @ SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [SY18: a] :
( ( sK1_X @ SY18 )
=> ( ( sK2_SY7 @ SY18 )
| ( sK3_SY13 @ SY18 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ^ [SY19: a] :
( ( sK1_X @ SY19 )
& ( sK3_SY13 @ SY19 ) ) )
= ( ^ [Xx: a] : $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY17: a] :
( ( sK1_X @ SY17 )
=> ( sK2_SY7 @ SY17 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY17: a] :
( ( sK1_X @ SY17 )
=> ( sK2_SY7 @ SY17 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ( sK1_X @ sK4_SY17 )
& ~ ( sK2_SY7 @ sK4_SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY18: a] :
( ~ ( sK1_X @ SY18 )
| ( sK2_SY7 @ SY18 )
| ( sK3_SY13 @ SY18 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(13,plain,
( ( ( ^ [SY19: a] :
( ( sK1_X @ SY19 )
& ( sK3_SY13 @ SY19 ) ) )
= ( ^ [Xx: a] : $false ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(14,plain,
( ( ! [SY18: a] :
( ~ ( sK1_X @ SY18 )
| ( sK2_SY7 @ SY18 )
| ( sK3_SY13 @ SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( ( sK1_X @ sK4_SY17 )
& ~ ( sK2_SY7 @ sK4_SY17 ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK3_SY13 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( ~ ( sK1_X @ sK4_SY17 )
| ~ ~ ( sK2_SY7 @ sK4_SY17 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
! [SV1: a] :
( ( ~ ( sK1_X @ SV1 )
| ( sK2_SY7 @ SV1 )
| ( sK3_SY13 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [SV2: a] :
( ( ~ ( ~ ( sK1_X @ SV2 )
| ~ ( sK3_SY13 @ SV2 ) ) )
= $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ( ^ [SX0: a] :
~ ( ~ ( sK1_X @ SX0 )
| ~ ( sK3_SY13 @ SX0 ) ) )
= ( ^ [SX0: a] : $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( sK1_X @ sK4_SY17 )
| ~ ~ ( sK2_SY7 @ sK4_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: a] :
( ( ( ~ ( sK1_X @ SV1 ) )
= $true )
| ( ( ( sK2_SY7 @ SV1 )
| ( sK3_SY13 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( sK1_X @ sK4_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ~ ( sK2_SY7 @ sK4_SY17 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: a] :
( ( ( sK1_X @ SV1 )
= $false )
| ( ( ( sK2_SY7 @ SV1 )
| ( sK3_SY13 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: a] :
( ( ~ ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| $false )
| ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $false )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( sK1_X @ sK4_SY17 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[24]) ).
thf(30,plain,
( ( ~ ( sK2_SY7 @ sK4_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
! [SV1: a] :
( ( ( sK2_SY7 @ SV1 )
= $true )
| ( ( sK3_SY13 @ SV1 )
= $true )
| ( ( sK1_X @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(33,plain,
( ( sK2_SY7 @ sK4_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(36,plain,
! [SV3: a] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 ) )
= $true )
| ( ( ~ ( sK3_SY13 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(41,plain,
( ( ( ~ $false )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: a] :
( ( ( sK1_X @ SV3 )
= $false )
| ( ( ~ ( sK3_SY13 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(44,plain,
( ( $false = $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: a] :
( ( ( sK3_SY13 @ SV3 )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
| ~ $false )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(48,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(49,plain,
! [SV3: a] :
( ( ( ~ ( sK3_SY13 @ SV3 ) )
= $false )
| ( $false = $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV3: a] :
( ( ( ~ ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV3: a] :
( ( ( ~ $false )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(52,plain,
! [SV3: a] :
( ( ( sK1_X @ SV3 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(53,plain,
! [SV3: a] :
( ( ( sK3_SY13 @ SV3 )
= $true )
| ( $false = $false ) ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
! [SV3: a] :
( ( ( ~ ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) ) )
= $true )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV3: a] :
( ( $false = $true )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 )
| ~ ( sK3_SY13 @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(57,plain,
! [SV3: a] :
( ( ( ~ ( sK1_X @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(58,plain,
! [SV3: a] :
( ( ( ~ ( sK3_SY13 @ SV3 ) )
= $false )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(59,plain,
! [SV3: a] :
( ( ( sK1_X @ SV3 )
= $true )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV3: a] :
( ( ( sK3_SY13 @ SV3 )
= $true )
| ( ( sK1_X @ SV3 )
= $false )
| ( ( sK3_SY13 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(61,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,60,59,55,53,52,44,33,31,29,28]) ).
thf(62,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET638^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n010.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
% 0.12/0.34 % DateTime : Sat Jul 9 18:48:45 EDT 2022
% 0.12/0.34 % 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).
% 0.12/0.38
% 0.12/0.38 ********************************
% 0.12/0.38 * All subproblems solved! *
% 0.12/0.38 ********************************
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.38
% 0.12/0.38 %**** Beginning of derivation protocol ****
% 0.12/0.38 % SZS output start CNFRefutation
% See solution above
% 0.12/0.38
% 0.12/0.38 %**** End of derivation protocol ****
% 0.12/0.38 %**** no. of clauses in derivation: 62 ****
% 0.12/0.38 %**** clause counter: 61 ****
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:61,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------