TSTP Solution File: SYO040^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO040^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n004.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 : 300s
% DateTime : Tue May 21 08:44:21 EDT 2024
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 7 unt; 9 typ; 0 def)
% Number of atoms : 1483 ( 33 equ; 0 cnn)
% Maximal formula atoms : 168 ( 23 avg)
% Number of connectives : 1851 ( 430 ~; 723 |; 203 &; 483 @)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 ^ 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
f: $o > $o ).
thf(decl_23,type,
h: $o > $i ).
thf(decl_24,type,
x: $o ).
thf(decl_25,type,
epred1_0: $o ).
thf(decl_26,type,
epred2_0: $o ).
thf(decl_27,type,
epred3_0: $o ).
thf(decl_28,type,
epred4_0: $o ).
thf(decl_29,type,
epred5_0: $o ).
thf(decl_30,type,
epred6_0: $o ).
thf(2,axiom,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',2) ).
thf(c_0_1,plain,
( epred3_0
<=> ( ( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( ( h @ $true )
= ( h @ $true ) ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( ( h @ $true )
= ( h @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_2,plain,
( epred1_0
<=> ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) ) ),
introduced(definition) ).
thf(c_0_3,plain,
( epred2_0
<=> ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) ),
introduced(definition) ).
thf(c_0_4,plain,
( ( ( epred1_0
& epred2_0 )
| ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( ( h @ $true )
= ( h @ $true ) ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( ( h @ $true )
= ( h @ $false ) ) ) ) )
=> epred3_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_1]),c_0_2]),c_0_3]) ).
thf(c_0_5,plain,
( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ~ ( f @ $false ) )
=> epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
thf(c_0_6,plain,
( ( ~ epred1_0
| ~ epred2_0
| epred3_0 )
& ( ~ x
| x
| ~ x
| x
| epred3_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred3_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred3_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred3_0 )
& ( ( ( h @ $true )
!= ( h @ $false ) )
| ~ x
| x
| epred3_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred3_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred3_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred3_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred3_0 )
& ( ( ( h @ $true )
!= ( h @ $false ) )
| ( f @ $false )
| x
| epred3_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred3_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred3_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred3_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred3_0 )
& ( ( ( h @ $true )
!= ( h @ $false ) )
| ~ x
| ( f @ $true )
| epred3_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred3_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred3_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred3_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred3_0 )
& ( ( ( h @ $true )
!= ( h @ $false ) )
| ( f @ $false )
| ( f @ $true )
| epred3_0 )
& ( ~ x
| x
| ( ( h @ $true )
!= ( h @ $true ) )
| epred3_0 )
& ( ~ ( f @ $false )
| x
| ( ( h @ $true )
!= ( h @ $true ) )
| epred3_0 )
& ( ~ x
| ~ ( f @ $true )
| ( ( h @ $true )
!= ( h @ $true ) )
| epred3_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( ( h @ $true )
!= ( h @ $true ) )
| epred3_0 )
& ( ( ( h @ $true )
!= ( h @ $false ) )
| ( ( h @ $true )
!= ( h @ $true ) )
| epred3_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
thf(c_0_7,plain,
( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
thf(c_0_8,plain,
( ( ~ x
| x
| ~ x
| x
| epred2_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred2_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred2_0 )
& ( ~ ( f @ $false )
| ~ x
| x
| epred2_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred2_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred2_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred2_0 )
& ( ~ ( f @ $false )
| ( f @ $false )
| x
| epred2_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ~ x
| ( f @ $true )
| epred2_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ( f @ $false )
| ( f @ $true )
| epred2_0 )
& ( ~ x
| x
| ~ ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| x
| ~ ( f @ $true )
| epred2_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ ( f @ $true )
| epred2_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| epred2_0 )
& ( ( f @ $false )
| epred2_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
thf(c_0_9,plain,
( epred4_0
<=> ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ( f @ $true ) ) ),
introduced(definition) ).
thf(c_0_10,plain,
( epred3_0
| ~ x
| ~ ( f @ $true )
| ( ( h @ $true )
!= ( h @ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_11,plain,
( ( ~ x
| x
| ~ x
| x
| epred1_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred1_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred1_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred1_0 )
& ( ( f @ $false )
| ~ x
| x
| epred1_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred1_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred1_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred1_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred1_0 )
& ( ( f @ $false )
| ( f @ $false )
| x
| epred1_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred1_0 )
& ( ( f @ $false )
| ~ x
| ( f @ $true )
| epred1_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ( f @ $false )
| ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ~ x
| x
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $true )
| epred1_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $true )
| epred1_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $true )
| epred1_0 )
& ( ( f @ $false )
| ( f @ $true )
| epred1_0 )
& ( ( f @ $true )
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
thf(c_0_12,plain,
( epred2_0
| ~ ( f @ ~ $true )
| ~ ( f @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_13,plain,
( ( f @ ~ $true )
| epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_14,plain,
( epred6_0
<=> ( ( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( ( h @ $false )
= ( h @ $true ) ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( ( h @ $false )
= ( h @ $false ) ) ) ) ) ),
introduced(definition) ).
thf(c_0_15,plain,
( epred5_0
<=> ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ( f @ $false ) ) ),
introduced(definition) ).
thf(c_0_16,plain,
( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ~ ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
=> epred4_0 ),
inference(split_equiv,[status(thm)],[c_0_9]) ).
thf(c_0_17,plain,
( epred3_0
| ~ x
| ~ ( f @ $true ) ),
inference(cn,[status(thm)],[c_0_10]) ).
thf(c_0_18,plain,
( ( f @ $true )
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_19,plain,
( ( f @ $true )
| epred2_0
| ~ ( f @ ~ $true )
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_20,plain,
( epred2_0
| ~ ( f @ $true ) ),
inference(csr,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_21,plain,
( ( ( epred4_0
& epred5_0 )
| ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( ( h @ $false )
= ( h @ $true ) ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( ( h @ $false )
= ( h @ $false ) ) ) ) )
=> epred6_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(split_equiv,[status(thm)],[c_0_14]),c_0_9]),c_0_15]) ).
thf(c_0_22,plain,
( ( ~ x
| x
| ~ x
| x
| epred4_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred4_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred4_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred4_0 )
& ( ( f @ $false )
| ~ x
| x
| epred4_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred4_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred4_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred4_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred4_0 )
& ( ( f @ $false )
| ( f @ $false )
| x
| epred4_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred4_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred4_0 )
& ( ( f @ $false )
| ~ x
| ( f @ $true )
| epred4_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ( f @ $false )
| ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ~ x
| x
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $true )
| epred4_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $true )
| epred4_0 )
& ( ( f @ $false )
| ( f @ $true )
| epred4_0 )
& ( ~ ( f @ $true )
| epred4_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
thf(c_0_23,plain,
( x
| epred3_0
| ~ ( f @ ~ $true )
| ( ( h @ $true )
!= ( h @ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_24,plain,
( ( f @ ~ $true )
| ( f @ ~ $true )
| x
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_25,plain,
( epred3_0
| ~ epred1_0
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_26,plain,
( epred1_0
| epred3_0
| ~ x ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
thf(c_0_27,plain,
( epred2_0
| ~ x ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_19,c_0_13]),c_0_20]) ).
thf(c_0_28,plain,
( ( ~ epred4_0
| ~ epred5_0
| epred6_0 )
& ( ~ x
| x
| ~ x
| x
| epred6_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred6_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred6_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred6_0 )
& ( ( ( h @ $false )
!= ( h @ $false ) )
| ~ x
| x
| epred6_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred6_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred6_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred6_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred6_0 )
& ( ( ( h @ $false )
!= ( h @ $false ) )
| ( f @ $false )
| x
| epred6_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred6_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred6_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred6_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred6_0 )
& ( ( ( h @ $false )
!= ( h @ $false ) )
| ~ x
| ( f @ $true )
| epred6_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred6_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred6_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred6_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred6_0 )
& ( ( ( h @ $false )
!= ( h @ $false ) )
| ( f @ $false )
| ( f @ $true )
| epred6_0 )
& ( ~ x
| x
| ( ( h @ $false )
!= ( h @ $true ) )
| epred6_0 )
& ( ~ ( f @ $false )
| x
| ( ( h @ $false )
!= ( h @ $true ) )
| epred6_0 )
& ( ~ x
| ~ ( f @ $true )
| ( ( h @ $false )
!= ( h @ $true ) )
| epred6_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( ( h @ $false )
!= ( h @ $true ) )
| epred6_0 )
& ( ( ( h @ $false )
!= ( h @ $false ) )
| ( ( h @ $false )
!= ( h @ $true ) )
| epred6_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
thf(c_0_29,plain,
( ( f @ ~ $true )
| ( f @ $true )
| epred4_0 ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_30,plain,
( epred4_0
| ~ ( f @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_31,axiom,
~ ( epred3_0
& epred6_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[2]),c_0_1]),c_0_14]) ).
thf(c_0_32,plain,
( x
| epred3_0
| ~ ( f @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_23]) ).
thf(c_0_33,plain,
( x
| epred1_0
| ( f @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_24]) ).
thf(c_0_34,plain,
( epred3_0
| ~ x ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
thf(c_0_35,plain,
( ( f @ $true )
| epred6_0
| ( ( h @ ~ $true )
!= ( h @ ~ $true ) )
| ~ x ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_36,plain,
( x
| ( f @ $true )
| epred4_0
| ~ ( f @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_37,plain,
( ( f @ ~ $true )
| epred4_0 ),
inference(csr,[status(thm)],[c_0_29,c_0_30]) ).
thf(c_0_38,plain,
( ~ epred3_0
| ~ epred6_0 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])]) ).
thf(c_0_39,plain,
( epred1_0
| epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
thf(c_0_40,plain,
( epred2_0
| epred3_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_13]),c_0_34]) ).
thf(c_0_41,plain,
( ( ( ( ( ( ~ x
| ~ ( f @ $true ) )
& ( x
| ~ ( f @ $false ) ) )
| ( f @ $true ) )
& ( ( ( ~ x
| ( f @ $true ) )
& ( x
| ( f @ $false ) ) )
| ( f @ $false ) ) )
| ( f @ $false ) )
=> epred5_0 ),
inference(split_equiv,[status(thm)],[c_0_15]) ).
thf(c_0_42,plain,
( epred6_0
| ( f @ $true )
| ~ x ),
inference(cn,[status(thm)],[c_0_35]) ).
thf(c_0_43,plain,
( epred4_0
| x ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_36,c_0_37]),c_0_30]) ).
thf(c_0_44,plain,
( ~ epred3_0
| ~ epred6_0 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
thf(c_0_45,plain,
epred3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_39]),c_0_40]) ).
thf(c_0_46,plain,
( ( ~ x
| x
| ~ x
| x
| epred5_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| x
| epred5_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| x
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| x
| epred5_0 )
& ( ~ ( f @ $false )
| ~ x
| x
| epred5_0 )
& ( ~ x
| x
| ( f @ $false )
| x
| epred5_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| x
| epred5_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| x
| epred5_0 )
& ( ~ ( f @ $false )
| ( f @ $false )
| x
| epred5_0 )
& ( ~ x
| x
| ~ x
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| x
| ~ x
| ( f @ $true )
| epred5_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ x
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ~ x
| ( f @ $true )
| epred5_0 )
& ( ~ x
| x
| ( f @ $false )
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| x
| ( f @ $false )
| ( f @ $true )
| epred5_0 )
& ( ~ x
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ( f @ $false )
| ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ( f @ $false )
| ( f @ $true )
| epred5_0 )
& ( ~ x
| x
| ~ ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| x
| ~ ( f @ $true )
| epred5_0 )
& ( ~ x
| ~ ( f @ $true )
| ~ ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| ~ ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| ~ ( f @ $true )
| epred5_0 )
& ( ~ ( f @ $false )
| epred5_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
thf(c_0_47,plain,
( ( f @ ~ $true )
| x
| epred6_0
| ( ( h @ ~ $true )
!= ( h @ ~ $true ) ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_48,plain,
( epred6_0
| epred4_0 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_43]) ).
thf(c_0_49,plain,
~ epred6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]) ).
thf(c_0_50,plain,
( epred5_0
| ~ x
| ~ ( f @ $true )
| ~ ( f @ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_51,plain,
( x
| epred6_0
| ( f @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_52,plain,
( epred6_0
| ~ epred4_0
| ~ epred5_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
thf(c_0_53,plain,
epred4_0,
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_54,plain,
( epred5_0
| ~ x
| ~ ( f @ $true ) ),
inference(cn,[status(thm)],[c_0_50]) ).
thf(c_0_55,plain,
( ~ epred6_0
| ~ x ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
thf(c_0_56,plain,
( epred5_0
| ~ ( f @ ~ $true ) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
thf(c_0_57,plain,
( ( f @ ~ $true )
| x ),
inference(sr,[status(thm)],[c_0_51,c_0_49]) ).
thf(c_0_58,plain,
~ epred5_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53])]),c_0_49]) ).
thf(c_0_59,plain,
( epred5_0
| ~ x ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_42]),c_0_55]) ).
thf(c_0_60,plain,
x,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
thf(c_0_61,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO040^1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 10:56:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 # Version: 3.1.0-ho
% 0.19/0.49 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49 # Starting ho_unfolding_6 with 300s (1) cores
% 0.19/0.49 # Starting sh4l with 300s (1) cores
% 0.19/0.49 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.19/0.49 # ho_unfolding_6 with pid 19155 completed with status 0
% 0.19/0.49 # Result found by ho_unfolding_6
% 0.19/0.49 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49 # Starting ho_unfolding_6 with 300s (1) cores
% 0.19/0.49 # No SInE strategy applied
% 0.19/0.49 # Search class: HGHSF-FFMM11-SFFFFFNN
% 0.19/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.49 # new_ho_10 with pid 19162 completed with status 0
% 0.19/0.49 # Result found by new_ho_10
% 0.19/0.49 # Preprocessing class: HSSSSMSSSSSNFFN.
% 0.19/0.49 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.49 # Starting new_ho_10 with 1500s (5) cores
% 0.19/0.49 # Starting ho_unfolding_6 with 300s (1) cores
% 0.19/0.49 # No SInE strategy applied
% 0.19/0.49 # Search class: HGHSF-FFMM11-SFFFFFNN
% 0.19/0.49 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.49 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.49 # Preprocessing time : 0.001 s
% 0.19/0.49 # Presaturation interreduction done
% 0.19/0.49
% 0.19/0.49 # Proof found!
% 0.19/0.49 # SZS status Unsatisfiable
% 0.19/0.49 # SZS output start CNFRefutation
% See solution above
% 0.19/0.49 # Parsed axioms : 4
% 0.19/0.49 # Removed by relevancy pruning/SinE : 0
% 0.19/0.49 # Initial clauses : 160
% 0.19/0.49 # Removed in clause preprocessing : 119
% 0.19/0.49 # Initial clauses in saturation : 41
% 0.19/0.49 # Processed clauses : 90
% 0.19/0.49 # ...of these trivial : 0
% 0.19/0.49 # ...subsumed : 22
% 0.19/0.49 # ...remaining for further processing : 68
% 0.19/0.49 # Other redundant clauses eliminated : 0
% 0.19/0.49 # Clauses deleted for lack of memory : 0
% 0.19/0.49 # Backward-subsumed : 13
% 0.19/0.49 # Backward-rewritten : 19
% 0.19/0.49 # Generated clauses : 42
% 0.19/0.49 # ...of the previous two non-redundant : 42
% 0.19/0.49 # ...aggressively subsumed : 0
% 0.19/0.49 # Contextual simplify-reflections : 14
% 0.19/0.49 # Paramodulations : 37
% 0.19/0.49 # Factorizations : 0
% 0.19/0.49 # NegExts : 0
% 0.19/0.49 # Equation resolutions : 0
% 0.19/0.49 # Disequality decompositions : 0
% 0.19/0.49 # Total rewrite steps : 18
% 0.19/0.49 # ...of those cached : 13
% 0.19/0.49 # Propositional unsat checks : 0
% 0.19/0.49 # Propositional check models : 0
% 0.19/0.49 # Propositional check unsatisfiable : 0
% 0.19/0.49 # Propositional clauses : 0
% 0.19/0.49 # Propositional clauses after purity: 0
% 0.19/0.49 # Propositional unsat core size : 0
% 0.19/0.49 # Propositional preprocessing time : 0.000
% 0.19/0.49 # Propositional encoding time : 0.000
% 0.19/0.49 # Propositional solver time : 0.000
% 0.19/0.49 # Success case prop preproc time : 0.000
% 0.19/0.49 # Success case prop encoding time : 0.000
% 0.19/0.49 # Success case prop solver time : 0.000
% 0.19/0.49 # Current number of processed clauses : 10
% 0.19/0.49 # Positive orientable unit clauses : 5
% 0.19/0.49 # Positive unorientable unit clauses: 0
% 0.19/0.49 # Negative unit clauses : 2
% 0.19/0.49 # Non-unit-clauses : 3
% 0.19/0.49 # Current number of unprocessed clauses: 12
% 0.19/0.49 # ...number of literals in the above : 36
% 0.19/0.49 # Current number of archived formulas : 0
% 0.19/0.49 # Current number of archived clauses : 58
% 0.19/0.49 # Clause-clause subsumption calls (NU) : 130
% 0.19/0.49 # Rec. Clause-clause subsumption calls : 113
% 0.19/0.49 # Non-unit clause-clause subsumptions : 44
% 0.19/0.49 # Unit Clause-clause subsumption calls : 18
% 0.19/0.49 # Rewrite failures with RHS unbound : 0
% 0.19/0.49 # BW rewrite match attempts : 5
% 0.19/0.49 # BW rewrite match successes : 5
% 0.19/0.49 # Condensation attempts : 90
% 0.19/0.49 # Condensation successes : 0
% 0.19/0.49 # Termbank termtop insertions : 5133
% 0.19/0.49 # Search garbage collected termcells : 1026
% 0.19/0.49
% 0.19/0.49 # -------------------------------------------------
% 0.19/0.49 # User time : 0.010 s
% 0.19/0.49 # System time : 0.003 s
% 0.19/0.49 # Total time : 0.013 s
% 0.19/0.49 # Maximum resident set size: 1928 pages
% 0.19/0.49
% 0.19/0.49 # -------------------------------------------------
% 0.19/0.50 # User time : 0.010 s
% 0.19/0.50 # System time : 0.006 s
% 0.19/0.50 # Total time : 0.017 s
% 0.19/0.50 # Maximum resident set size: 1696 pages
% 0.19/0.50 % E---3.1 exiting
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------