%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV067+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:31:26 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 61 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 251 ( 4 equ)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 285 ( 99 ~; 77 |; 72 &)
% ( 25 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(pv63_type,type,
pv63: $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(n5_type,type,
n5: $i ).
tff(n135300_type,type,
n135300: $i ).
tff(pv10_type,type,
pv10: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(pv78_type,type,
pv78: $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(q_type,type,
q: $i ).
tff(1,plain,
( ( succ(n0) = n1 )
<=> ( succ(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
tff(3,plain,
succ(n0) = n1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( leq(succ(n0),pv63)
<=> leq(n1,pv63) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( leq(n1,pv63)
<=> leq(succ(n0),pv63) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( leq(n1,pv63)
<=> leq(n1,pv63) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
=> ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ) )
<=> ~ ( ~ ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
| ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ ( ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
=> ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( gt(a_select3(q,pv10,pv63),pv78)
=> ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_array_0008) ).
tff(9,plain,
~ ( ~ ( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
| ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( leq(n0,pv10)
& leq(n1,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) ),
inference(or_elim,[status(thm)],[9]) ).
tff(11,plain,
leq(n1,pv63),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
leq(n1,pv63),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
leq(succ(n0),pv63),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( leq(pv63,minus(n5,n1))
<=> leq(pv63,minus(n5,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
leq(pv63,minus(n5,n1)),
inference(and_elim,[status(thm)],[10]) ).
tff(16,plain,
leq(pv63,minus(n5,n1)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( leq(pv10,minus(n135300,n1))
<=> leq(pv10,minus(n135300,n1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
leq(pv10,minus(n135300,n1)),
inference(and_elim,[status(thm)],[10]) ).
tff(19,plain,
leq(pv10,minus(n135300,n1)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( leq(n0,pv10)
<=> leq(n0,pv10) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
leq(n0,pv10),
inference(and_elim,[status(thm)],[10]) ).
tff(22,plain,
leq(n0,pv10),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ ~ ( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) )
<=> ( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
<=> ~ ( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
<=> ~ ~ ( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) )
<=> ( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) )
<=> ~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1))
& ( gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) )
& ( ~ gt(a_select3(q,pv10,pv63),pv78)
| ( leq(n0,pv10)
& leq(pv10,minus(n135300,n1)) ) ) ),
inference(or_elim,[status(thm)],[9]) ).
tff(29,plain,
~ ( leq(n0,pv10)
& leq(n0,pv63)
& leq(pv10,minus(n135300,n1))
& leq(pv63,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ leq(n0,pv10)
| ~ leq(n0,pv63)
| ~ leq(pv10,minus(n135300,n1))
| ~ leq(pv63,minus(n5,n1)) ),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
~ leq(n0,pv63),
inference(unit_resolution,[status(thm)],[30,22,19,16]) ).
tff(32,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ gt(Y,X)
| leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X: $i,Y: $i] :
rewrite(( ( gt(Y,X)
=> leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
tff(38,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(pv63,n0)
| leq(n0,pv63) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(pv63,n0)
| leq(n0,pv63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(pv63,n0)
| leq(n0,pv63) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(pv63,n0)
| leq(n0,pv63) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ gt(pv63,n0),
inference(unit_resolution,[status(thm)],[44,41,31]) ).
tff(46,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ( ~ leq(succ(X),Y)
| gt(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [X: $i,Y: $i] :
rewrite(( ( leq(succ(X),Y)
=> gt(Y,X) )
<=> ( ~ leq(succ(X),Y)
| gt(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i,Y: $i] :
( leq(succ(X),Y)
=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X: $i,Y: $i] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
tff(52,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),pv63)
| gt(pv63,n0) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),pv63)
| gt(pv63,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),pv63)
| gt(pv63,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),pv63)
| gt(pv63,n0) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( ~ leq(succ(n0),pv63)
| gt(pv63,n0) ),
inference(unit_resolution,[status(thm)],[58,55]) ).
tff(60,plain,
~ leq(succ(n0),pv63),
inference(unit_resolution,[status(thm)],[59,45]) ).
tff(61,plain,
$false,
inference(unit_resolution,[status(thm)],[60,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV067+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:26:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------