TSTP Solution File: SYO504^1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO504^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.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 17:35:13 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 96 ( 23 unt; 6 typ; 0 def)
% Number of atoms : 888 ( 189 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 595 ( 175 ~; 172 |; 14 &; 231 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $o ).
thf(tp_b,type,
b: $o ).
thf(tp_f,type,
f: ( ( $o > $o > $o ) > $o ) > $o ).
thf(tp_g,type,
g: ( $o > $o > $o ) > $o ).
thf(tp_h,type,
h: $o > $o > $o ).
thf(tp_i,type,
i: $o > $o > $o ).
thf(1,conjecture,
( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',claim) ).
thf(2,negated_conjecture,
( ( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( ( ( h @ a @ b )
= ( a
& b ) )
& ( ( i @ a @ b )
= ( a
| b ) )
& ( ( f @ g )
= ( i @ a @ b ) )
& ( h @ a @ b ) )
=> ( f @ g ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( h @ a @ b )
= ( a
& b ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ( i @ a @ b )
= ( a
| b ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ( f @ g )
= ( i @ a @ b ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( h @ a @ b )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( f @ g )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ~ ( f @ g ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(10,plain,
( ( h @ a @ b )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ( f @ g )
= ( i @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(12,plain,
( ( ( i @ a @ b )
= ( a
| b ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ( h @ a @ b )
= ( a
& b ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(14,plain,
( ( ~ ( f @ g ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ( h @ a @ b )
= ( ~ ( ~ a
| ~ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ( f @ g )
| ( i @ a @ b ) )
| ~ ( ~ ( f @ g )
| ~ ( i @ a @ b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[11]) ).
thf(17,plain,
( ( ( f @ g )
= ( i @ a @ b ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[11]) ).
thf(18,plain,
( ( ~ ( ( i @ a @ b )
| a
| b )
| ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[12]) ).
thf(19,plain,
( ( ( i @ a @ b )
= ( a
| b ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[12]) ).
thf(20,plain,
( ( f @ g )
= $false ),
inference(extcnf_not_pos,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ( ( h @ a @ b )
| ~ ( ~ a
| ~ b ) )
| ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(22,plain,
( ( ( h @ a @ b )
= ( ~ ( ~ a
| ~ b ) ) )
= $true ),
inference(extcnf_equal_pos,[status(thm)],[15]) ).
thf(23,plain,
( ( ( ~ ( ( f @ g )
| ( i @ a @ b ) ) )
= $true )
| ( ( ~ ( ~ ( f @ g )
| ~ ( i @ a @ b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[16]) ).
thf(24,plain,
( ( ( ~ ( ( i @ a @ b )
| a
| b ) )
= $true )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(25,plain,
( ( ( ~ ( ( h @ a @ b )
| ~ ( ~ a
| ~ b ) ) )
= $true )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(26,plain,
( ( ( ( f @ g )
| ( i @ a @ b ) )
= $false )
| ( ( ~ ( ~ ( f @ g )
| ~ ( i @ a @ b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ( ( i @ a @ b )
| a
| b )
= $false )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ( ( h @ a @ b )
| ~ ( ~ a
| ~ b ) )
= $false )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ( f @ g )
= $false )
| ( ( ~ ( ~ ( f @ g )
| ~ ( i @ a @ b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ( i @ a @ b )
= $false )
| ( ( ~ ( ~ ( f @ g )
| ~ ( i @ a @ b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ( i @ a @ b )
= $false )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ( a
| b )
= $false )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
( ( ( h @ a @ b )
= $false )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(34,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $false )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[28]) ).
thf(35,plain,
( ( ( ~ ( f @ g )
| ~ ( i @ a @ b ) )
= $false )
| ( ( f @ g )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(36,plain,
( ( ( ~ ( f @ g )
| ~ ( i @ a @ b ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(37,plain,
( ( ( ~ ( i @ a @ b )
| ~ ( a
| b ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( a = $false )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(39,plain,
( ( b = $false )
| ( ( ~ ( ~ ( i @ a @ b )
| ~ ( a
| b ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(40,plain,
( ( ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(41,plain,
( ( ( ~ a
| ~ b )
= $true )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(42,plain,
( ( ( ~ ( f @ g ) )
= $false )
| ( ( f @ g )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(43,plain,
( ( ( ~ ( i @ a @ b ) )
= $false )
| ( ( f @ g )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(44,plain,
( ( ( ~ ( f @ g ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(45,plain,
( ( ( ~ ( i @ a @ b ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(46,plain,
( ( ( ~ ( i @ a @ b ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(47,plain,
( ( ( ~ ( a
| b ) )
= $false )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(48,plain,
( ( ( ~ ( i @ a @ b )
| ~ ( a
| b ) )
= $false )
| ( a = $false ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(49,plain,
( ( ( ~ ( i @ a @ b )
| ~ ( a
| b ) )
= $false )
| ( b = $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(50,plain,
( ( ( ~ ( h @ a @ b ) )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(51,plain,
( ( ( ~ ~ ( ~ a
| ~ b ) )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(52,plain,
( ( ( ~ a )
= $true )
| ( ( ~ b )
= $true )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(53,plain,
( ( ( f @ g )
= $true )
| ( ( f @ g )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(54,plain,
( ( ( i @ a @ b )
= $true )
| ( ( f @ g )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[43]) ).
thf(55,plain,
( ( ( f @ g )
= $true )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(56,plain,
( ( ( i @ a @ b )
= $true )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(57,plain,
( ( ( i @ a @ b )
= $true )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(58,plain,
( ( ( a
| b )
= $true )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(59,plain,
( ( ( ~ ( i @ a @ b ) )
= $false )
| ( a = $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(60,plain,
( ( ( ~ ( a
| b ) )
= $false )
| ( a = $false ) ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(61,plain,
( ( ( ~ ( i @ a @ b ) )
= $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(62,plain,
( ( ( ~ ( a
| b ) )
= $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(63,plain,
( ( ( h @ a @ b )
= $true )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(64,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $true )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(65,plain,
( ( a = $false )
| ( ( ~ b )
= $true )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(66,plain,
( ( a = $true )
| ( b = $true )
| ( ( i @ a @ b )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(67,plain,
( ( ( i @ a @ b )
= $true )
| ( a = $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(68,plain,
( ( ( a
| b )
= $true )
| ( a = $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(69,plain,
( ( ( i @ a @ b )
= $true )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(70,plain,
( ( ( a
| b )
= $true )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ( ~ a
| ~ b )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(72,plain,
( ( b = $false )
| ( a = $false )
| ( ( ~ ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(73,plain,
( ( a = $true )
| ( b = $true )
| ( a = $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
( ( a = $true )
| ( b = $true )
| ( b = $false ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
( ( ( ~ a )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(76,plain,
( ( ( ~ b )
= $false )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[71]) ).
thf(77,plain,
( ( ( ~ ( h @ a @ b )
| ~ ~ ( ~ a
| ~ b ) )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
( ( a = $true )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
( ( b = $true )
| ( ( h @ a @ b )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(80,plain,
( ( ( ~ ( h @ a @ b ) )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(81,plain,
( ( ( ~ ~ ( ~ a
| ~ b ) )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(82,plain,
( ( ( h @ a @ b )
= $true )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(83,plain,
( ( ( ~ ( ~ a
| ~ b ) )
= $true )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(84,plain,
( ( ( ~ a
| ~ b )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(85,plain,
( ( ( ~ a )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(86,plain,
( ( ( ~ b )
= $false )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(87,plain,
( ( a = $true )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(88,plain,
( ( b = $true )
| ( a = $false )
| ( b = $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(89,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[10,88,87,82,79,78,74,73,69,67,66,63,57,56,55,54,53,22,20,19,17]) ).
thf(90,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO504^1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n022.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 13:57:40 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).
% 0.12/0.36
% 0.12/0.36 ********************************
% 0.12/0.36 * All subproblems solved! *
% 0.12/0.36 ********************************
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.12/0.37
% 0.12/0.37 %**** Beginning of derivation protocol ****
% 0.12/0.37 % SZS output start CNFRefutation
% See solution above
% 0.12/0.37
% 0.12/0.37 %**** End of derivation protocol ****
% 0.12/0.37 %**** no. of clauses in derivation: 90 ****
% 0.12/0.37 %**** clause counter: 89 ****
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------