%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV142+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 05:31:35 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 35 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 210 ( 4 equ)
% Maximal formula atoms : 54 ( 6 avg)
% Number of connectives : 243 ( 70 ~; 66 |; 65 &)
% ( 13 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 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 : 10 ( 10 usr; 9 con; 0-1 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(n3_type,type,
n3: $i ).
tff(s_worst7_type,type,
s_worst7: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(s_sworst7_type,type,
s_sworst7: $i ).
tff(s_best7_type,type,
s_best7: $i ).
tff(pv1341_type,type,
pv1341: $i ).
tff(tptp_float_0_001_type,type,
tptp_float_0_001: $i ).
tff(1,plain,
( ( succ(n0) = n1 )
<=> ( succ(n0) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
tff(3,plain,
succ(n0) = n1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( leq(succ(n0),loopcounter)
<=> leq(n1,loopcounter) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( leq(n1,loopcounter)
<=> leq(succ(n0),loopcounter) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( leq(n1,loopcounter)
<=> leq(n1,loopcounter) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ~ ( ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) )
<=> ~ ( ~ ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_best7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) )
| leq(s_best7,n3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
~ ( ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_best7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_sworst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(n0,s_worst7) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_best7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_sworst7,n3) )
& ( ~ leq(tptp_float_0_001,pv1341)
=> leq(s_worst7,n3) )
& ( gt(loopcounter,n0)
=> leq(n0,s_best7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_sworst7) )
& ( gt(loopcounter,n0)
=> leq(n0,s_worst7) )
& ( gt(loopcounter,n0)
=> leq(s_best7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_sworst7,n3) )
& ( gt(loopcounter,n0)
=> leq(s_worst7,n3) ) )
=> leq(s_best7,n3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gauss_array_0012) ).
tff(9,plain,
~ ( ~ ( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_best7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) )
| leq(s_best7,n3) ),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( leq(tptp_float_0_001,pv1341)
& leq(n1,loopcounter)
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_best7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_sworst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(n0,s_worst7) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_best7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_sworst7,n3) )
& ( leq(tptp_float_0_001,pv1341)
| leq(s_worst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_best7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_sworst7) )
& ( ~ gt(loopcounter,n0)
| leq(n0,s_worst7) )
& ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_sworst7,n3) )
& ( ~ gt(loopcounter,n0)
| leq(s_worst7,n3) ) ),
inference(or_elim,[status(thm)],[9]) ).
tff(11,plain,
leq(n1,loopcounter),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
leq(n1,loopcounter),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
leq(succ(n0),loopcounter),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ leq(s_best7,n3)
<=> ~ leq(s_best7,n3) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
~ leq(s_best7,n3),
inference(or_elim,[status(thm)],[9]) ).
tff(16,plain,
~ leq(s_best7,n3),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
<=> ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ gt(loopcounter,n0)
| leq(s_best7,n3) ),
inference(and_elim,[status(thm)],[10]) ).
tff(19,plain,
( ~ gt(loopcounter,n0)
| leq(s_best7,n3) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ gt(loopcounter,n0),
inference(unit_resolution,[status(thm)],[19,16]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,axiom,
! [X: $i,Y: $i] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
tff(27,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),loopcounter)
| gt(loopcounter,n0) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),loopcounter)
| gt(loopcounter,n0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),loopcounter)
| gt(loopcounter,n0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(n0),loopcounter)
| gt(loopcounter,n0) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ leq(succ(n0),loopcounter),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV142+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:31:20 EDT 2025
% 0.12/0.33 % 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
%------------------------------------------------------------------------------