TSTP Solution File: SYN063+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYN063+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 : n005.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 08:23:11 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 129 ( 86 unt; 6 typ; 0 def)
% Number of atoms : 941 ( 169 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1681 ( 601 ~; 417 |; 42 &; 600 @)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 40 ( 0 ^ 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_big_p,type,
big_p: $i > $o ).
thf(tp_c,type,
c: $i ).
thf(tp_sK1_X1,type,
sK1_X1: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(1,conjecture,
( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel33) ).
thf(2,negated_conjecture,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) )
<=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) )
=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(5,plain,
( ( ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) )
=> ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[3]) ).
thf(6,plain,
( ( ~ ( ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) )
=> ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(7,plain,
( ( ~ ( ! [X1: $i] :
( ( ~ ( big_p @ a )
| ( big_p @ X1 )
| ( big_p @ c ) )
& ( ~ ( big_p @ a )
| ~ ( big_p @ b )
| ( big_p @ c ) ) )
=> ! [X: $i] :
( ( ( big_p @ a )
& ( ( big_p @ X )
=> ( big_p @ b ) ) )
=> ( big_p @ c ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ! [X: $i] : ( big_p @ X )
| ~ ( big_p @ a )
| ( big_p @ c ) )
& ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) )
& ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
& ( ~ ( big_p @ c )
| ( big_p @ a ) )
& ( ~ ( big_p @ c )
| ( big_p @ b ) )
& ( ( big_p @ a )
| ~ ( big_p @ c ) )
& ( ( big_p @ a )
| ( big_p @ a ) )
& ( ( big_p @ a )
| ( big_p @ b ) )
& ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(9,plain,
( ( ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [X1: $i] : ( big_p @ X1 ) )
& ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) )
& ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
& ( big_p @ a )
& ~ ( big_p @ c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(10,plain,
( ( ( ! [X: $i] : ( big_p @ X )
| ~ ( big_p @ a )
| ( big_p @ c ) )
& ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) )
& ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
& ( ~ ( big_p @ c )
| ( big_p @ a ) )
& ( ~ ( big_p @ c )
| ( big_p @ b ) )
& ( ( big_p @ a )
| ~ ( big_p @ c ) )
& ( ( big_p @ a )
| ( big_p @ a ) )
& ( ( big_p @ a )
| ( big_p @ b ) )
& ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
& ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ( ~ ~ ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
| ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(12,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
| ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[11]) ).
thf(13,plain,
( ( ~ ~ ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
| ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(14,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
| ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
| ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(18,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(21,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(23,plain,
( ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a )
| ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ~ ( big_p @ b )
| ~ ( big_p @ a )
| ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(27,plain,
( ( ( ! [SX0: $i] : ( big_p @ SX0 )
| ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( ~ ( big_p @ b )
| ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ( ! [SX0: $i] : ( big_p @ SX0 ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( ( ~ ( big_p @ b ) )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ~ ( ~ ( big_p @ c )
| ~ ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( big_p @ SV1 )
= $true )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
( ( ( big_p @ b )
= $false )
| ( ( ~ ( big_p @ a ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(39,plain,
( ( ~ ( big_p @ c )
| ~ ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV1: $i] :
( ( ( big_p @ a )
= $false )
| ( ( big_p @ SV1 )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(44,plain,
( ( ( big_p @ a )
= $false )
| ( ( big_p @ b )
= $false )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
( ( ( ~ ( big_p @ c ) )
= $true )
| ( ( ~ ( big_p @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(48,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
| ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(49,plain,
( ( ( big_p @ c )
= $false )
| ( ( ~ ( big_p @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ( ~ ( big_p @ c )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(51,plain,
( ( ~ ( ~ ( big_p @ c )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
( ( ~ ( ( big_p @ a )
| ~ ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(53,plain,
( ( ~ ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[47]) ).
thf(54,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(55,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[48]) ).
thf(56,plain,
( ( ( big_p @ c )
= $false )
| ( ( big_p @ c )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(57,plain,
( ( ~ ( big_p @ c )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(58,plain,
( ( ~ ( big_p @ c )
| ( big_p @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(59,plain,
( ( ( big_p @ a )
| ~ ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(60,plain,
( ( ~ ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(61,plain,
( ( ~ ( big_p @ sK1_X1 )
| ~ ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(62,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(63,plain,
( ( ( ~ ( big_p @ c ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(64,plain,
( ( ( ~ ( big_p @ c ) )
= $true )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(65,plain,
( ( ( big_p @ a )
= $true )
| ( ( ~ ( big_p @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(66,plain,
( ( ~ ( ( big_p @ a )
| ( big_p @ a ) )
| ~ ( ( big_p @ a )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( ( ~ ( big_p @ c ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(68,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
| ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(69,plain,
( ( ( big_p @ c )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(70,plain,
( ( ( big_p @ c )
= $false )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
( ( ( big_p @ c )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
( ( ~ ( ( big_p @ a )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
( ( ~ ( ( big_p @ a )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(74,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( ( ~ ( big_p @ c ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(75,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(76,plain,
( ( ~ ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
( ( ( big_p @ a )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(78,plain,
( ( ( big_p @ a )
| ( big_p @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(79,plain,
( ( ( big_p @ c )
= $false )
| ( ( big_p @ sK1_X1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
( ( ~ ( big_p @ sK1_X1 )
| ( big_p @ a ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(81,plain,
( ( ~ ( big_p @ sK1_X1 )
| ( big_p @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(82,plain,
( ( ( big_p @ a )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(83,plain,
( ( ( big_p @ a )
= $true )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(84,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(85,plain,
( ( ( ~ ( big_p @ sK1_X1 ) )
= $true )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( ( big_p @ a )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(87,plain,
( ( ( big_p @ sK1_X1 )
= $false )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,87,86,83,82,79,71,70,69,56,44]) ).
thf(89,plain,
( ( ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [X1: $i] : ( big_p @ X1 ) )
& ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) )
& ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
& ( big_p @ a )
& ~ ( big_p @ c ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(90,plain,
( ( ~ ( ~ ~ ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
| ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
| ~ ~ ( big_p @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(91,plain,
( ( ~ ~ ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
| ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
| ~ ~ ( big_p @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(92,plain,
( ( ~ ~ ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
| ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(93,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
| ~ ~ ( big_p @ c ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(94,plain,
( ( ~ ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
| ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(95,plain,
( ( ~ ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
| ~ ~ ( big_p @ c ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(96,plain,
( ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
| ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
| ~ ~ ( big_p @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(98,plain,
( ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(99,plain,
( ( ~ ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(100,plain,
( ( ~ ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(101,plain,
( ( ~ ~ ( big_p @ c ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(102,plain,
( ( ( big_p @ c )
| ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(103,plain,
( ( ( big_p @ c )
| ~ ( big_p @ a )
| ~ ( big_p @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(104,plain,
( ( ~ ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(105,plain,
( ( ~ ( big_p @ c ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
( ( ( big_p @ c )
= $true )
| ( ( ~ ( big_p @ a )
| ! [SX0: $i] : ( big_p @ SX0 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
( ( ( big_p @ c )
= $true )
| ( ( ~ ( big_p @ a )
| ~ ( big_p @ b ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
( ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
| ~ ( big_p @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
( ( big_p @ c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ! [SX0: $i] : ( big_p @ SX0 ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(111,plain,
( ( ( ~ ( big_p @ a ) )
= $true )
| ( ( ~ ( big_p @ b ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(112,plain,
( ( ~ ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(113,plain,
( ( ~ ( big_p @ a ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(114,plain,
( ( ( big_p @ a )
= $false )
| ( ( ! [SX0: $i] : ( big_p @ SX0 ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
( ( ( big_p @ a )
= $false )
| ( ( ~ ( big_p @ b ) )
= $true )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
( ( ~ ( big_p @ sK2_X )
| ( big_p @ b ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(117,plain,
( ( big_p @ a )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(118,plain,
! [SV2: $i] :
( ( ( big_p @ SV2 )
= $true )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
( ( ( big_p @ b )
= $false )
| ( ( big_p @ a )
= $false )
| ( ( big_p @ c )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(120,plain,
( ( ( ~ ( big_p @ sK2_X ) )
= $true )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(121,plain,
( ( ( big_p @ sK2_X )
= $false )
| ( ( big_p @ b )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(122,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[109,121,119,118,117]) ).
thf(123,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[122,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% 0.04/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 03:15:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (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)...
% 0.19/0.40
% 0.19/0.40 ********************************
% 0.19/0.40 * All subproblems solved! *
% 0.19/0.40 ********************************
% 0.19/0.40 % 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:122,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.41
% 0.19/0.41 %**** Beginning of derivation protocol ****
% 0.19/0.41 % SZS output start CNFRefutation
% See solution above
% 0.19/0.41
% 0.19/0.41 %**** End of derivation protocol ****
% 0.19/0.41 %**** no. of clauses in derivation: 123 ****
% 0.19/0.41 %**** clause counter: 122 ****
% 0.19/0.41
% 0.19/0.41 % 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:122,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------