%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM395+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : 300s
% DateTime : Sat Jun 21 05:20:53 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 148 ( 70 ~; 27 |; 11 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 12 ( 12 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 14 ( 12 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(ordinal_type,type,
ordinal: $i > $o ).
tff(empty_set_type,type,
empty_set: $i ).
tff(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
tff(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
tff(1,plain,
( epsilon_connected(empty_set)
<=> epsilon_connected(empty_set) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( epsilon_transitive(empty_set)
& epsilon_connected(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l18_ordinal1) ).
tff(3,plain,
epsilon_connected(empty_set),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
epsilon_connected(empty_set),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( epsilon_transitive(empty_set)
<=> epsilon_transitive(empty_set) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
epsilon_transitive(empty_set),
inference(and_elim,[status(thm)],[2]) ).
tff(7,plain,
epsilon_transitive(empty_set),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ~ ( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) )
| ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) ),
inference(tautology,[status(thm)],[]) ).
tff(9,plain,
~ ( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) ),
inference(unit_resolution,[status(thm)],[8,7,4]) ).
tff(10,plain,
( ~ ordinal(empty_set)
<=> ~ ordinal(empty_set) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ ordinal(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_ordinal1) ).
tff(12,plain,
~ ordinal(empty_set),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( ( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) )
<=> ordinal(empty_set) )
| ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set)
| ordinal(empty_set) ),
inference(tautology,[status(thm)],[]) ).
tff(14,plain,
( ( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) )
<=> ordinal(empty_set) ),
inference(unit_resolution,[status(thm)],[13,12,9]) ).
tff(15,plain,
^ [A: $i] :
refl(( ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) )
<=> ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) )
<=> ! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [A: $i] :
trans(trans(monotonicity(rewrite(( ( epsilon_transitive(A)
& epsilon_connected(A) )
<=> ~ ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) ) )),
( ( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) )
<=> ( ordinal(A)
<=> ~ ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) ) ) )),
rewrite(( ( ordinal(A)
<=> ~ ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) ) )
<=> ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) )),
( ( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) )
<=> ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) )),
rewrite(( ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) )
<=> ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) )),
( ( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) )
<=> ~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) )
<=> ! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) )
<=> ! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
tff(21,plain,
! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [A: $i] :
( ordinal(A)
<=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ~ ! [A: $i] :
~ ( ( ~ epsilon_transitive(A)
| ~ epsilon_connected(A) )
<=> ordinal(A) )
| ~ ( ( ~ epsilon_transitive(empty_set)
| ~ epsilon_connected(empty_set) )
<=> ordinal(empty_set) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,24,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : NUM395+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:02:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------