TSTP Solution File: ARI609_1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ARI609_1 : TPTP v8.1.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n002.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 : Wed Aug 31 15:48:42 EDT 2022
% Result : Theorem 0.16s 0.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 20 unt; 3 typ; 0 def)
% Number of atoms : 48 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 18 ~; 4 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 168 ( 39 atm; 71 fun; 27 num; 31 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
b: $int ).
tff(f153,plain,
$false,
inference(subsumption_resolution,[],[f148,f21]) ).
tff(f21,plain,
~ $less($sum(a,$uminus(b)),0),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ~ $less($sum(a,$uminus(b)),0)
& $less($sum(f(a),$uminus(f(b))),0)
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ) ),
inference(flattening,[],[f17]) ).
tff(f17,plain,
( $less($sum(f(a),$uminus(f(b))),0)
& ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ $less(f(X0),f(X1)) ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f16,plain,
~ ( ( ~ $less($sum(a,$uminus(b)),0)
& ! [X1: $int,X0: $int] :
( ~ $less(X0,X1)
=> ~ $less(f(X0),f(X1)) ) )
=> ~ $less($sum(f(a),$uminus(f(b))),0) ),
inference(rectify,[],[f3]) ).
tff(f3,plain,
~ ( ( ~ $less($sum(a,$uminus(b)),0)
& ! [X1: $int,X0: $int] :
( ~ $less(X1,X0)
=> ~ $less(f(X1),f(X0)) ) )
=> ~ $less($sum(f(a),$uminus(f(b))),0) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ( ( $lesseq(0,$sum(a,$uminus(b)))
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
( ( $lesseq(0,$sum(a,$uminus(b)))
& ! [X1: $int,X0: $int] :
( $lesseq(X0,X1)
=> $lesseq(f(X0),f(X1)) ) )
=> $lesseq(0,$sum(f(a),$uminus(f(b)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_mon_implies_f_a_b_1) ).
tff(f148,plain,
$less($sum(a,$uminus(b)),0),
inference(superposition,[],[f105,f8]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_145,[]) ).
tff(f105,plain,
! [X0: $int] : $less($sum(a,X0),$sum(b,X0)),
inference(resolution,[],[f102,f12]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f102,plain,
$less(a,b),
inference(resolution,[],[f101,f19]) ).
tff(f19,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X0),f(X1))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tff(f101,plain,
$less(f(a),f(b)),
inference(backward_demodulation,[],[f87,f92]) ).
tff(f92,plain,
! [X0: $int] : ( $sum(0,X0) = X0 ),
inference(superposition,[],[f50,f14]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_153,[]) ).
tff(f50,plain,
! [X0: $int] : ( $sum(0,$uminus(X0)) = $uminus(X0) ),
inference(evaluation,[],[f46]) ).
tff(f46,plain,
! [X0: $int] : ( $sum($uminus(0),$uminus(X0)) = $uminus(X0) ),
inference(superposition,[],[f7,f6]) ).
tff(f6,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_142,[]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_144,[]) ).
tff(f87,plain,
$less(f(a),$sum(0,f(b))),
inference(forward_demodulation,[],[f84,f6]) ).
tff(f84,plain,
$less($sum(f(a),0),$sum(0,f(b))),
inference(evaluation,[],[f80]) ).
tff(f80,plain,
$less($sum(f(a),0),$sum(0,$uminus($uminus(f(b))))),
inference(superposition,[],[f76,f8]) ).
tff(f76,plain,
! [X0: $int] : $less($sum(f(a),$sum($uminus(f(b)),X0)),$sum(0,X0)),
inference(forward_demodulation,[],[f71,f5]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_141,[]) ).
tff(f71,plain,
! [X0: $int] : $less($sum($sum(f(a),$uminus(f(b))),X0),$sum(0,X0)),
inference(resolution,[],[f12,f20]) ).
tff(f20,plain,
$less($sum(f(a),$uminus(f(b))),0),
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ARI609=1 : TPTP v8.1.0. Released v5.1.0.
% 0.06/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.31 % Computer : n002.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Aug 29 16:03:43 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.47 % (5539)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 0.16/0.48 % (5557)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.16/0.48 % (5548)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.16/0.48 % (5556)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.16/0.49 % (5549)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.16/0.49 % (5543)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.16/0.49 % (5542)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.50 % (5536)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.16/0.50 % (5541)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.16/0.50 % (5535)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.16/0.50 % (5557)First to succeed.
% 0.16/0.50 % (5537)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.16/0.50 % (5538)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.16/0.50 % (5534)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/191324Mi)
% 0.16/0.50 % (5534)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.50 % (5534)Terminated due to inappropriate strategy.
% 0.16/0.50 % (5534)------------------------------
% 0.16/0.50 % (5534)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50 % (5534)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50 % (5534)Termination reason: Inappropriate
% 0.16/0.50
% 0.16/0.50 % (5534)Memory used [KB]: 895
% 0.16/0.50 % (5534)Time elapsed: 0.002 s
% 0.16/0.50 % (5534)Instructions burned: 2 (million)
% 0.16/0.50 % (5534)------------------------------
% 0.16/0.50 % (5534)------------------------------
% 0.16/0.51 % (5557)Refutation found. Thanks to Tanya!
% 0.16/0.51 % SZS status Theorem for theBenchmark
% 0.16/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51 % (5557)------------------------------
% 0.16/0.51 % (5557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51 % (5557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51 % (5557)Termination reason: Refutation
% 0.16/0.51
% 0.16/0.51 % (5557)Memory used [KB]: 5500
% 0.16/0.51 % (5557)Time elapsed: 0.077 s
% 0.16/0.51 % (5557)Instructions burned: 8 (million)
% 0.16/0.51 % (5557)------------------------------
% 0.16/0.51 % (5557)------------------------------
% 0.16/0.51 % (5533)Success in time 0.188 s
%------------------------------------------------------------------------------