%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV077+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:31:27 AM UTC 2025
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 25 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 145 ( 55 ~; 36 |; 39 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pv40_type,type,
pv40: $i ).
tff(n0_type,type,
n0: $i ).
tff(true_type,type,
true: $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n5_type,type,
n5: $i ).
tff(pv31_type,type,
pv31: $i ).
tff(1,plain,
( true
<=> true ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
true,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',ttrue) ).
tff(3,plain,
true,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( true
| ( n0 != pv40 )
| ~ true ),
inference(tautology,[status(thm)],[]) ).
tff(5,plain,
( true
| ( n0 != pv40 ) ),
inference(unit_resolution,[status(thm)],[4,3]) ).
tff(6,plain,
( leq(pv31,minus(n5,n1))
<=> leq(pv31,minus(n5,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ~ ( ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) )
=> ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 != pv40 )
=> ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( ( n0 = pv40 )
=> true ) ) )
<=> ~ ( ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 = pv40 )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( true
| ( n0 != pv40 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ ( ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) )
=> ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 != pv40 )
=> ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( ( n0 = pv40 )
=> true ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_array_0018) ).
tff(9,plain,
~ ( ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 = pv40 )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( true
| ( n0 != pv40 ) ) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[9]) ).
tff(11,plain,
leq(pv31,minus(n5,n1)),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
leq(pv31,minus(n5,n1)),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
( leq(n0,pv31)
<=> leq(n0,pv31) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
leq(n0,pv31),
inference(and_elim,[status(thm)],[10]) ).
tff(15,plain,
leq(n0,pv31),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ~ ( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) )
<=> ( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( true
| ( n0 != pv40 ) ) )
<=> ~ ( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( true
| ( n0 != pv40 ) ) )
<=> ~ ~ ( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( true
| ( n0 != pv40 ) ) )
<=> ( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) ) ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,plain,
( ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 = pv40 )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( true
| ( n0 != pv40 ) ) )
<=> ~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( true
| ( n0 != pv40 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( ( n0 = pv40 )
| ( leq(n0,pv31)
& leq(pv31,minus(n5,n1)) ) )
& ( true
| ( n0 != pv40 ) ) ),
inference(or_elim,[status(thm)],[9]) ).
tff(22,plain,
~ ( leq(n0,pv31)
& leq(pv31,minus(n5,n1))
& ( true
| ( n0 != pv40 ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ leq(n0,pv31)
| ~ leq(pv31,minus(n5,n1))
| ~ ( true
| ( n0 != pv40 ) ) ),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,15,12,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV077+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:27:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------