%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV138+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:31:34 AM UTC 2025
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 255 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 300 ( 109 ~; 87 |; 56 &)
% ( 43 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 94 ( 86 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(pv1325_type,type,
pv1325: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(s_best7_type,type,
s_best7: $i ).
tff(s_values7_type,type,
s_values7: $i ).
tff(n3_type,type,
n3: $i ).
tff(s_worst7_type,type,
s_worst7: $i ).
tff(s_sworst7_type,type,
s_sworst7: $i ).
tff(n2_type,type,
n2: $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ( leq(X,Y)
<=> gt(succ(Y),X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
tff(5,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
| ( leq(n0,pv1325)
<=> gt(succ(pv1325),n0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( leq(n0,pv1325)
<=> gt(succ(pv1325),n0) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ leq(n0,pv1325)
<=> ~ leq(n0,pv1325) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ~ ( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& gt(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7)) )
=> leq(n0,pv1325) )
<=> ~ ( ~ ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& gt(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7)) )
| leq(n0,pv1325) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ ( ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& gt(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7)) )
=> leq(n0,pv1325) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gauss_array_0008) ).
tff(13,plain,
~ ( ~ ( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& gt(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7)) )
| leq(n0,pv1325) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ leq(n0,pv1325),
inference(or_elim,[status(thm)],[13]) ).
tff(15,plain,
~ leq(n0,pv1325),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ( leq(n0,pv1325)
<=> gt(succ(pv1325),n0) )
| leq(n0,pv1325)
| ~ gt(succ(pv1325),n0) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ ( leq(n0,pv1325)
<=> gt(succ(pv1325),n0) )
| ~ gt(succ(pv1325),n0) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
~ gt(succ(pv1325),n0),
inference(unit_resolution,[status(thm)],[17,9]) ).
tff(19,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
| ( leq(n2,pv1325)
<=> gt(succ(pv1325),n2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( leq(n2,pv1325)
<=> gt(succ(pv1325),n2) ),
inference(unit_resolution,[status(thm)],[19,7]) ).
tff(21,plain,
( leq(n2,pv1325)
<=> leq(n2,pv1325) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( leq(n0,s_best7)
& leq(n0,s_sworst7)
& leq(n0,s_worst7)
& leq(n2,pv1325)
& leq(s_best7,n3)
& leq(s_sworst7,n3)
& leq(s_worst7,n3)
& leq(pv1325,n3)
& gt(a_select2(s_values7,pv1325),a_select2(s_values7,s_best7)) ),
inference(or_elim,[status(thm)],[13]) ).
tff(23,plain,
leq(n2,pv1325),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
leq(n2,pv1325),
inference(modus_ponens,[status(thm)],[23,21]) ).
tff(25,plain,
( ~ ( leq(n2,pv1325)
<=> gt(succ(pv1325),n2) )
| ~ leq(n2,pv1325)
| gt(succ(pv1325),n2) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ ( leq(n2,pv1325)
<=> gt(succ(pv1325),n2) )
| gt(succ(pv1325),n2) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
gt(succ(pv1325),n2),
inference(unit_resolution,[status(thm)],[26,20]) ).
tff(28,plain,
( gt(n2,n0)
<=> gt(n2,n0) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
gt(n2,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
tff(30,plain,
gt(n2,n0),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( gt(X,Y)
& gt(Y,Z) )
<=> ~ ( ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
( ~ ( gt(X,Y)
& gt(Y,Z) )
<=> ~ ~ ( ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
rewrite(( ~ ~ ( ~ gt(X,Y)
| ~ gt(Y,Z) )
<=> ( ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
( ~ ( gt(X,Y)
& gt(Y,Z) )
<=> ( ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
( ( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) )
<=> ( ~ gt(X,Y)
| ~ gt(Y,Z)
| gt(X,Z) ) )),
rewrite(( ( ~ gt(X,Y)
| ~ gt(Y,Z)
| gt(X,Z) )
<=> ( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
( ( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) )
<=> ( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( gt(X,Y)
& gt(Y,Z) )
=> gt(X,Z) )
<=> ( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( gt(X,Y)
& gt(Y,Z) )
=> gt(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( gt(X,Y)
& gt(Y,Z) )
=> gt(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_gt) ).
tff(38,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( gt(X,Y)
& gt(Y,Z) )
| gt(X,Z) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) ),
inference(modus_ponens,[status(thm)],[41,31]) ).
tff(43,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( gt(succ(pv1325),n0)
| ~ gt(succ(pv1325),n2)
| ~ gt(n2,n0) )
<=> ( ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| gt(succ(pv1325),n0)
| ~ gt(succ(pv1325),n2)
| ~ gt(n2,n0) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| gt(succ(pv1325),n0)
| ~ gt(succ(pv1325),n2)
| ~ gt(n2,n0) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| gt(succ(pv1325),n0)
| ~ gt(succ(pv1325),n2)
| ~ gt(n2,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( gt(X,Z)
| ~ gt(X,Y)
| ~ gt(Y,Z) )
| ~ gt(n2,n0)
| ~ gt(succ(pv1325),n2)
| gt(succ(pv1325),n0) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,42,30,27,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV138+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.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 09:31:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------