TSTP Solution File: SYN045+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN045+1 : TPTP v8.1.0. Released v2.0.0.
% 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 08:22:52 EDT 2022
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 79 ( 56 unt; 3 typ; 0 def)
% Number of atoms : 472 ( 93 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 478 ( 268 ~; 173 |; 30 &; 0 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_p,type,
p: $o ).
thf(tp_q,type,
q: $o ).
thf(tp_r,type,
r: $o ).
thf(1,conjecture,
( ( p
| ( q
& r ) )
<=> ( ( p
| q )
& ( p
| r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel13) ).
thf(2,negated_conjecture,
( ( ( p
| ( q
& r ) )
<=> ( ( p
| q )
& ( p
| r ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ( p
| ( q
& r ) )
<=> ( ( p
| q )
& ( p
| r ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ( p
| ( q
& r ) )
=> ( ( p
| q )
& ( p
| r ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ( ( p
| q )
& ( p
| r ) )
=> ( p
| ( q
& r ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ( p
| ( q
& r ) )
=> ( ( p
| q )
& ( p
| r ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ( ( p
| q )
& ( p
| r ) )
=> ( p
| ( q
& r ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ( q
| p )
& ( r
| p )
& ( ~ p
| ~ p )
& ( ~ p
| ~ r )
& ( ~ q
| ~ p )
& ( ~ q
| ~ r ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ( p
| q )
& ( p
| r )
& ( ~ q
| ~ r )
& ~ p )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( q
| p )
& ( r
| p )
& ( ~ p
| ~ p )
& ( ~ p
| ~ r )
& ( ~ q
| ~ p )
& ( ~ q
| ~ r ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ( q
| p )
| ~ ( r
| p ) )
| ~ ~ ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
| ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( ~ ( q
| p )
| ~ ( r
| p ) )
| ~ ~ ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
| ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ( q
| p )
| ~ ( r
| p ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
| ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ( q
| p )
| ~ ( r
| p ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
| ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( q
| p )
| ~ ( r
| p ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
| ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( q
| p ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( r
| p ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( q
| p )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( r
| p )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( q = $true )
| ( p = $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( r = $true )
| ( p = $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( ~ p
| ~ p )
| ~ ( ~ p
| ~ r ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ( ~ q
| ~ p )
| ~ ( ~ q
| ~ r ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ( ~ p
| ~ p ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( ~ p
| ~ r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ( ~ q
| ~ p ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( ~ ( ~ q
| ~ r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ p
| ~ p )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ p
| ~ r )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(37,plain,
( ( ~ q
| ~ p )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(38,plain,
( ( ~ q
| ~ r )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ( ~ p )
= $true )
| ( ( ~ p )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
( ( ( ~ p )
= $true )
| ( ( ~ r )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(41,plain,
( ( ( ~ q )
= $true )
| ( ( ~ p )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
( ( ( ~ q )
= $true )
| ( ( ~ r )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( p = $false )
| ( ( ~ p )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( p = $false )
| ( ( ~ r )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(45,plain,
( ( q = $false )
| ( ( ~ p )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
( ( q = $false )
| ( ( ~ r )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
( ( p = $false )
| ( p = $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( r = $false )
| ( p = $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
( ( p = $false )
| ( q = $false ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( r = $false )
| ( q = $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,50,49,48,47,28]) ).
thf(52,plain,
( ( ( p
| q )
& ( p
| r )
& ( ~ q
| ~ r )
& ~ p )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(53,plain,
( ( ~ ( ~ ~ ( ~ ( p
| q )
| ~ ( p
| r ) )
| ~ ~ ( ~ ( ~ q
| ~ r )
| ~ ~ p ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(54,plain,
( ( ~ ~ ( ~ ( p
| q )
| ~ ( p
| r ) )
| ~ ~ ( ~ ( ~ q
| ~ r )
| ~ ~ p ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(55,plain,
( ( ~ ~ ( ~ ( p
| q )
| ~ ( p
| r ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( ~ q
| ~ r )
| ~ ~ p ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[54]) ).
thf(57,plain,
( ( ~ ( ~ ( p
| q )
| ~ ( p
| r ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(58,plain,
( ( ~ ( ~ ( ~ q
| ~ r )
| ~ ~ p ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(59,plain,
( ( ~ ( p
| q )
| ~ ( p
| r ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( ~ q
| ~ r )
| ~ ~ p )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(61,plain,
( ( ~ ( p
| q ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(62,plain,
( ( ~ ( p
| r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[59]) ).
thf(63,plain,
( ( ~ ( ~ q
| ~ r ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
( ( ~ ~ p )
= $false ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
( ( p
| q )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
( ( p
| r )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ q
| ~ r )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
( ( ~ p )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
( ( p = $true )
| ( q = $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
( ( p = $true )
| ( r = $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(71,plain,
( ( ( ~ q )
= $true )
| ( ( ~ r )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(72,plain,
p = $false,
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(73,plain,
( ( q = $false )
| ( ( ~ r )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(74,plain,
( ( r = $false )
| ( q = $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,74,72,70]) ).
thf(76,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[75,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SYN045+1 : TPTP v8.1.0. Released v2.0.0.
% 0.05/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.33 % Computer : n003.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 600
% 0.09/0.33 % DateTime : Mon Jul 11 20:23:00 EDT 2022
% 0.09/0.33 % CPUTime :
% 0.09/0.34
% 0.09/0.34 No.of.Axioms: 0
% 0.09/0.34
% 0.09/0.34 Length.of.Defs: 0
% 0.09/0.34
% 0.09/0.34 Contains.Choice.Funs: false
% 0.09/0.34 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.09/0.39
% 0.09/0.39 ********************************
% 0.09/0.39 * All subproblems solved! *
% 0.09/0.39 ********************************
% 0.09/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.39
% 0.09/0.39 %**** Beginning of derivation protocol ****
% 0.09/0.39 % SZS output start CNFRefutation
% See solution above
% 0.09/0.39
% 0.09/0.39 %**** End of derivation protocol ****
% 0.09/0.39 %**** no. of clauses in derivation: 76 ****
% 0.09/0.39 %**** clause counter: 75 ****
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:75,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------