TSTP Solution File: SWV142+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Thu Sep 29 15:10:07 EDT 2022
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 47 ( 10 unt; 13 typ; 0 def)
% Number of atoms : 212 ( 0 equ)
% Maximal formula atoms : 54 ( 6 avg)
% Number of connectives : 251 ( 75 ~; 67 |; 65 &)
% ( 15 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-1 aty)
% Number of variables : 34 ( 30 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(n0_type,type,
n0: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i ).
tff(s_best7_type,type,
s_best7: $i ).
tff(s_worst7_type,type,
s_worst7: $i ).
tff(s_sworst7_type,type,
s_sworst7: $i ).
tff(pv1341_type,type,
pv1341: $i ).
tff(tptp_float_0_001_type,type,
tptp_float_0_001: $i ).
tff(n1_type,type,
n1: $i ).
tff(1,plain,
( ~ gt(loopcounter,n0)
<=> ~ gt(loopcounter,succ(tptp_minus_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ gt(loopcounter,n0)
<=> ~ gt(loopcounter,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( ~ gt(loopcounter,n0)
| $false )
<=> ~ gt(loopcounter,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,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(5,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(6,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)],[5,4]) ).
tff(7,plain,
~ leq(s_best7,n3),
inference(or_elim,[status(thm)],[6]) ).
tff(8,plain,
( leq(s_best7,n3)
<=> $false ),
inference(iff_false,[status(thm)],[7]) ).
tff(9,plain,
( ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
<=> ( ~ gt(loopcounter,n0)
| $false ) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ( ~ gt(loopcounter,n0)
| leq(s_best7,n3) )
<=> ~ gt(loopcounter,n0) ),
inference(transitivity,[status(thm)],[9,3]) ).
tff(11,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)],[6]) ).
tff(12,plain,
( ~ gt(loopcounter,n0)
| leq(s_best7,n3) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
~ gt(loopcounter,n0),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
~ gt(loopcounter,n0),
inference(modus_ponens,[status(thm)],[13,2]) ).
tff(15,plain,
~ gt(loopcounter,succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[14,1]) ).
tff(16,plain,
( leq(n1,loopcounter)
<=> leq(succ(succ(tptp_minus_1)),loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( leq(n1,loopcounter)
<=> leq(n1,loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
leq(n1,loopcounter),
inference(and_elim,[status(thm)],[11]) ).
tff(19,plain,
leq(n1,loopcounter),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
leq(succ(succ(tptp_minus_1)),loopcounter),
inference(modus_ponens,[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(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,20,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV142+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 01:49:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------