TSTP Solution File: NUM730_8 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 01:15:51 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 9 unt; 14 typ; 0 def)
% Number of atoms : 938 ( 36 equ)
% Maximal formula atoms : 117 ( 15 avg)
% Number of connectives : 669 ( 242 ~; 346 |; 77 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 5 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 450 ( 450 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
frac: $tType ).
tff(decl_sort2,type,
nat: $tType ).
tff(decl_22,type,
x: frac ).
tff(decl_23,type,
y: frac ).
tff(decl_24,type,
orec3: ( $o * $o * $o ) > $o ).
tff(decl_25,type,
ts: ( nat * nat ) > nat ).
tff(decl_26,type,
c1x: frac > nat ).
tff(decl_27,type,
c2y: frac > nat ).
tff(decl_28,type,
c1y: frac > nat ).
tff(decl_29,type,
c2x: frac > nat ).
tff(decl_30,type,
more: ( nat * nat ) > $o ).
tff(decl_31,type,
less: ( nat * nat ) > $o ).
tff(decl_32,type,
epred1_0: $o ).
tff(decl_33,type,
epred2_0: $o ).
tff(satz41,conjecture,
orec3(ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)),more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))),less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz41) ).
tff(satz10,axiom,
! [X1: nat,X2: nat] : orec3(X1 = X2,more(X1,X2),less(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10) ).
tff(c_0_2,plain,
( epred1_0
<=> ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$true,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$true,$false) ) ) )
& ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$false,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$false,$false) ) ) ) ) ) ),
introduced(definition) ).
tff(c_0_3,plain,
( epred2_0
<=> ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$true,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$true,$false) ) ) )
& ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$false,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$false,$false) ) ) ) ) ) ),
introduced(definition) ).
fof(c_0_4,negated_conjecture,
~ ( epred1_0
& epred2_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(assume_negation,[status(cth)],[satz41])]),c_0_2]),c_0_3]) ).
tff(c_0_5,plain,
( ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$true,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$true,$false) ) ) )
& ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$false,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($false,$false,$false) ) ) ) ) )
=> epred2_0 ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_6,negated_conjecture,
( ~ epred1_0
| ~ epred2_0 ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
tff(c_0_7,plain,
( ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| epred2_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| ~ orec3($false,$false,$true)
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| ~ orec3($false,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| ~ orec3($false,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| ~ orec3($false,$false,$true)
| ~ orec3($false,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| ~ orec3($false,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false)
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| ~ orec3($false,$true,$false)
| ~ orec3($false,$true,$true)
| epred2_0 )
& ( ~ orec3($false,$false,$false)
| ~ orec3($false,$false,$true)
| ~ orec3($false,$true,$false)
| ~ orec3($false,$true,$true)
| epred2_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
tff(c_0_8,plain,
( ( ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) )
| ( ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$true,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$true,$false) ) ) )
& ( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$false,$true) )
& ( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| orec3($true,$false,$false) ) ) ) ) )
=> epred1_0 ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
tff(c_0_9,axiom,
! [X1: nat,X2: nat] :
( ( ( X1 != X2 )
| ( ( ~ more(X1,X2)
| ( ( ~ less(X1,X2)
| orec3($true,$true,$true) )
& ( less(X1,X2)
| orec3($true,$true,$false) ) ) )
& ( more(X1,X2)
| ( ( ~ less(X1,X2)
| orec3($true,$false,$true) )
& ( less(X1,X2)
| orec3($true,$false,$false) ) ) ) ) )
& ( ( X1 = X2 )
| ( ( ~ more(X1,X2)
| ( ( ~ less(X1,X2)
| orec3($false,$true,$true) )
& ( less(X1,X2)
| orec3($false,$true,$false) ) ) )
& ( more(X1,X2)
| ( ( ~ less(X1,X2)
| orec3($false,$false,$true) )
& ( less(X1,X2)
| orec3($false,$false,$false) ) ) ) ) ) ),
inference(fool_unroll,[status(thm)],[satz10]) ).
cnf(c_0_10,negated_conjecture,
( ~ epred1_0
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
tcf(c_0_11,plain,
( epred2_0
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tff(c_0_12,plain,
( ( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| epred1_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true)
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true)
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true)
| ~ orec3($true,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true)
| ~ orec3($true,$true,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false)
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true)
| ~ orec3($true,$true,$false)
| ~ orec3($true,$true,$true)
| epred1_0 )
& ( ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true)
| ~ orec3($true,$true,$false)
| ~ orec3($true,$true,$true)
| epred1_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
tff(c_0_13,plain,
! [X3: nat,X4: nat] :
( ( ~ less(X3,X4)
| orec3($true,$true,$true)
| ~ more(X3,X4)
| ( X3 != X4 ) )
& ( less(X3,X4)
| orec3($true,$true,$false)
| ~ more(X3,X4)
| ( X3 != X4 ) )
& ( ~ less(X3,X4)
| orec3($true,$false,$true)
| more(X3,X4)
| ( X3 != X4 ) )
& ( less(X3,X4)
| orec3($true,$false,$false)
| more(X3,X4)
| ( X3 != X4 ) )
& ( ~ less(X3,X4)
| orec3($false,$true,$true)
| ~ more(X3,X4)
| ( X3 = X4 ) )
& ( less(X3,X4)
| orec3($false,$true,$false)
| ~ more(X3,X4)
| ( X3 = X4 ) )
& ( ~ less(X3,X4)
| orec3($false,$false,$true)
| more(X3,X4)
| ( X3 = X4 ) )
& ( less(X3,X4)
| orec3($false,$false,$false)
| more(X3,X4)
| ( X3 = X4 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
tcf(c_0_14,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_15,negated_conjecture,
( ~ epred1_0
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$true) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
tcf(c_0_16,plain,
( ( ts(c1x(x),c2y(y)) = ts(c1y(y),c2x(x)) )
| epred1_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_17,plain,
! [X1: nat,X2: nat] :
( orec3($false,$true,$true)
| ( X1 = X2 )
| ~ less(X1,X2)
| ~ more(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_18,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_19,negated_conjecture,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ epred1_0
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$true,$false) ),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
tcf(c_0_20,plain,
! [X1: nat,X2: nat] :
( less(X1,X2)
| orec3($false,$true,$false)
| ( X1 = X2 )
| ~ more(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_21,plain,
( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
tcf(c_0_22,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred2_0
| ~ orec3($false,$false,$false) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_23,negated_conjecture,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ epred1_0
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true) ),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
tcf(c_0_24,plain,
! [X1: nat,X2: nat] :
( orec3($false,$false,$true)
| more(X1,X2)
| ( X1 = X2 )
| ~ less(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_25,plain,
( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_20]),c_0_21]) ).
tcf(c_0_26,plain,
( epred2_0
| ( ts(c1x(x),c2y(y)) != ts(c1y(y),c2x(x)) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_27,negated_conjecture,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ epred1_0
| ~ orec3($false,$false,$false) ),
inference(spm,[status(thm)],[c_0_10,c_0_22]) ).
tcf(c_0_28,plain,
! [X1: nat,X2: nat] :
( less(X1,X2)
| orec3($false,$false,$false)
| more(X1,X2)
| ( X1 = X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_29,plain,
( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_24]),c_0_25]) ).
tcf(c_0_30,negated_conjecture,
( ( ts(c1y(y),c2x(x)) != ts(c1x(x),c2y(y)) )
| ~ epred1_0 ),
inference(spm,[status(thm)],[c_0_10,c_0_26]) ).
tcf(c_0_31,plain,
ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_28]),c_0_25]),c_0_29]) ).
tcf(c_0_32,plain,
! [X1: nat,X2: nat] :
( orec3($true,$true,$true)
| ~ less(X1,X2)
| ~ more(X1,X2)
| ( X1 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_33,plain,
( epred1_0
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$true) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31])]) ).
tcf(c_0_35,plain,
! [X1: nat] :
( orec3($true,$true,$true)
| ~ less(X1,X1)
| ~ more(X1,X1) ),
inference(er,[status(thm)],[c_0_32]) ).
tcf(c_0_36,plain,
! [X1: nat,X2: nat] :
( orec3($true,$false,$true)
| more(X1,X2)
| ~ less(X1,X2)
| ( X1 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_37,plain,
! [X1: nat,X2: nat] :
( less(X1,X2)
| orec3($true,$true,$false)
| ~ more(X1,X2)
| ( X1 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_38,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0
| ~ orec3($true,$false,$false)
| ~ orec3($true,$false,$true) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_39,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_31]),c_0_31]),c_0_34]),c_0_35]) ).
tcf(c_0_40,plain,
! [X1: nat] :
( more(X1,X1)
| orec3($true,$false,$true)
| ~ less(X1,X1) ),
inference(er,[status(thm)],[c_0_36]) ).
tcf(c_0_41,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0
| ~ orec3($true,$false,$false) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_42,plain,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0
| ~ more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$true,$false) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_43,plain,
! [X1: nat] :
( less(X1,X1)
| orec3($true,$true,$false)
| ~ more(X1,X1) ),
inference(er,[status(thm)],[c_0_37]) ).
tcf(c_0_44,plain,
( more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ orec3($true,$false,$true)
| ~ orec3($true,$false,$false) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_31]),c_0_34]) ).
tcf(c_0_45,plain,
( orec3($true,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
tcf(c_0_46,plain,
! [X1: nat,X2: nat] :
( less(X1,X2)
| orec3($true,$false,$false)
| more(X1,X2)
| ( X1 != X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_47,negated_conjecture,
( less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ( ts(c1y(y),c2x(x)) != ts(c1x(x),c2y(y)) )
| ~ orec3($true,$false,$false) ),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
tcf(c_0_48,plain,
~ more(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_31]),c_0_31]),c_0_34]),c_0_43]),c_0_39]) ).
tcf(c_0_49,plain,
( ~ less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y)))
| ~ orec3($true,$false,$false) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_44]),c_0_45]) ).
tcf(c_0_50,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| epred1_0
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_51,plain,
! [X1: nat] :
( less(X1,X1)
| more(X1,X1)
| orec3($true,$false,$false) ),
inference(er,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
~ orec3($true,$false,$false),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_31]),c_0_31]),c_0_31])]),c_0_48]),c_0_49]) ).
tcf(c_0_53,plain,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($false,$false,$true)
| ~ orec3($true,$false,$true) ),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
tcf(c_0_54,plain,
( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
| orec3($false,$false,$true)
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x))) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
tcf(c_0_55,plain,
! [X1: nat] :
( less(X1,X1)
| more(X1,X1) ),
inference(sr,[status(thm)],[c_0_51,c_0_52]) ).
tcf(c_0_56,plain,
( ( ts(c1y(y),c2x(x)) = ts(c1x(x),c2y(y)) )
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_53]),c_0_54]) ).
tcf(c_0_57,plain,
less(ts(c1x(x),c2y(y)),ts(c1x(x),c2y(y))),
inference(spm,[status(thm)],[c_0_48,c_0_55]) ).
tcf(c_0_58,negated_conjecture,
( more(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ less(ts(c1x(x),c2y(y)),ts(c1y(y),c2x(x)))
| ~ orec3($true,$false,$true) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_50]),c_0_56]) ).
cnf(c_0_59,plain,
orec3($true,$false,$true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_57])]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_31]),c_0_31]),c_0_57]),c_0_59])]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM730_8 : TPTP v8.2.0. Released v8.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 04:52:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/eprover --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
% 0.21/0.52 # Version: 3.1.0
% 0.21/0.52 # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52 # Starting new_bool_1 with 300s (1) cores
% 0.21/0.52 # Starting sh5l with 300s (1) cores
% 0.21/0.52 # new_bool_3 with pid 19593 completed with status 0
% 0.21/0.52 # Result found by new_bool_3
% 0.21/0.52 # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52 # Search class: FGHSF-FFMF21-SFFFFFNN
% 0.21/0.52 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 181s (1) cores
% 0.21/0.52 # 208_C09_12_F1_SE_CS_SP_PS_S070I with pid 19601 completed with status 0
% 0.21/0.52 # Result found by 208_C09_12_F1_SE_CS_SP_PS_S070I
% 0.21/0.52 # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.21/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.21/0.52 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.21/0.52 # Starting new_bool_3 with 300s (1) cores
% 0.21/0.52 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.21/0.52 # Search class: FGHSF-FFMF21-SFFFFFNN
% 0.21/0.52 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.21/0.52 # Starting 208_C09_12_F1_SE_CS_SP_PS_S070I with 181s (1) cores
% 0.21/0.52 # Preprocessing time : 0.002 s
% 0.21/0.52 # Presaturation interreduction done
% 0.21/0.52
% 0.21/0.52 # Proof found!
% 0.21/0.52 # SZS status Theorem
% 0.21/0.52 # SZS output start CNFRefutation
% See solution above
% 0.21/0.52 # Parsed axioms : 14
% 0.21/0.52 # Removed by relevancy pruning/SinE : 12
% 0.21/0.52 # Initial clauses : 61
% 0.21/0.52 # Removed in clause preprocessing : 24
% 0.21/0.52 # Initial clauses in saturation : 37
% 0.21/0.52 # Processed clauses : 358
% 0.21/0.52 # ...of these trivial : 5
% 0.21/0.52 # ...subsumed : 162
% 0.21/0.52 # ...remaining for further processing : 190
% 0.21/0.52 # Other redundant clauses eliminated : 4
% 0.21/0.52 # Clauses deleted for lack of memory : 0
% 0.21/0.52 # Backward-subsumed : 78
% 0.21/0.52 # Backward-rewritten : 56
% 0.21/0.52 # Generated clauses : 432
% 0.21/0.52 # ...of the previous two non-redundant : 324
% 0.21/0.52 # ...aggressively subsumed : 0
% 0.21/0.52 # Contextual simplify-reflections : 30
% 0.21/0.52 # Paramodulations : 425
% 0.21/0.52 # Factorizations : 0
% 0.21/0.52 # NegExts : 0
% 0.21/0.52 # Equation resolutions : 4
% 0.21/0.52 # Disequality decompositions : 0
% 0.21/0.52 # Total rewrite steps : 95
% 0.21/0.52 # ...of those cached : 91
% 0.21/0.52 # Propositional unsat checks : 0
% 0.21/0.52 # Propositional check models : 0
% 0.21/0.52 # Propositional check unsatisfiable : 0
% 0.21/0.52 # Propositional clauses : 0
% 0.21/0.52 # Propositional clauses after purity: 0
% 0.21/0.52 # Propositional unsat core size : 0
% 0.21/0.52 # Propositional preprocessing time : 0.000
% 0.21/0.52 # Propositional encoding time : 0.000
% 0.21/0.52 # Propositional solver time : 0.000
% 0.21/0.52 # Success case prop preproc time : 0.000
% 0.21/0.52 # Success case prop encoding time : 0.000
% 0.21/0.52 # Success case prop solver time : 0.000
% 0.21/0.52 # Current number of processed clauses : 20
% 0.21/0.52 # Positive orientable unit clauses : 4
% 0.21/0.52 # Positive unorientable unit clauses: 0
% 0.21/0.52 # Negative unit clauses : 4
% 0.21/0.52 # Non-unit-clauses : 12
% 0.21/0.52 # Current number of unprocessed clauses: 13
% 0.21/0.52 # ...number of literals in the above : 55
% 0.21/0.52 # Current number of archived formulas : 0
% 0.21/0.52 # Current number of archived clauses : 166
% 0.21/0.52 # Clause-clause subsumption calls (NU) : 4270
% 0.21/0.52 # Rec. Clause-clause subsumption calls : 1234
% 0.21/0.52 # Non-unit clause-clause subsumptions : 249
% 0.21/0.52 # Unit Clause-clause subsumption calls : 54
% 0.21/0.52 # Rewrite failures with RHS unbound : 0
% 0.21/0.52 # BW rewrite match attempts : 5
% 0.21/0.52 # BW rewrite match successes : 4
% 0.21/0.52 # Condensation attempts : 0
% 0.21/0.52 # Condensation successes : 0
% 0.21/0.52 # Termbank termtop insertions : 14306
% 0.21/0.52 # Search garbage collected termcells : 428
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.027 s
% 0.21/0.52 # System time : 0.002 s
% 0.21/0.52 # Total time : 0.028 s
% 0.21/0.52 # Maximum resident set size: 1760 pages
% 0.21/0.52
% 0.21/0.52 # -------------------------------------------------
% 0.21/0.52 # User time : 0.029 s
% 0.21/0.52 # System time : 0.003 s
% 0.21/0.52 # Total time : 0.032 s
% 0.21/0.52 # Maximum resident set size: 1712 pages
% 0.21/0.52 % E---3.1 exiting
% 0.21/0.53 % E exiting
%------------------------------------------------------------------------------