TSTP Solution File: ARI609_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI609_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Tue Apr 30 10:35:41 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 13 unt; 3 typ; 0 def)
% Number of atoms : 37 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 4 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 122 ( 34 atm; 49 fun; 16 num; 23 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 : 23 ( 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_1,type,
a: $int ).
tff(func_def_2,type,
b: $int ).
tff(f684,plain,
$false,
inference(subsumption_resolution,[],[f675,f19]) ).
tff(f19,plain,
~ $less($sum(a,$uminus(b)),0),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( $less($sum(f(a),$uminus(f(b))),0)
& ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $int] :
( ~ $less(f(X1),f(X0))
| $less(X1,X0) ) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
( $less($sum(f(a),$uminus(f(b))),0)
& ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $int] :
( ~ $less(f(X1),f(X0))
| $less(X1,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ( ( ~ $less($sum(a,$uminus(b)),0)
& ! [X0: $int,X1: $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)))
& ! [X0: $int,X1: $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)))
& ! [X0: $int,X1: $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(f675,plain,
$less($sum(a,$uminus(b)),0),
inference(superposition,[],[f637,f8]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f637,plain,
! [X0: $int] : $less($sum(a,X0),$sum(b,X0)),
inference(resolution,[],[f634,f12]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f634,plain,
$less(a,b),
inference(resolution,[],[f629,f18]) ).
tff(f18,plain,
! [X0: $int,X1: $int] :
( ~ $less(f(X1),f(X0))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f629,plain,
$less(f(a),f(b)),
inference(evaluation,[],[f626]) ).
tff(f626,plain,
$less($sum(f(a),0),$uminus($uminus(f(b)))),
inference(superposition,[],[f585,f8]) ).
tff(f585,plain,
! [X0: $int] : $less($sum(f(a),$sum($uminus(f(b)),X0)),X0),
inference(backward_demodulation,[],[f434,f5]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f434,plain,
! [X0: $int] : $less($sum($sum(f(a),$uminus(f(b))),X0),X0),
inference(evaluation,[],[f413]) ).
tff(f413,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,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI609_1 : TPTP v8.1.2. Released v5.1.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 05:23:11 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (15850)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (15856)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.36 % (15854)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.36 % (15855)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.36 % (15854)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (15854)Terminated due to inappropriate strategy.
% 0.13/0.36 % (15854)------------------------------
% 0.13/0.36 % (15854)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36 % (15854)Termination reason: Inappropriate
% 0.13/0.36
% 0.13/0.36 % (15854)Memory used [KB]: 718
% 0.13/0.36 % (15854)Time elapsed: 0.002 s
% 0.13/0.36 % (15854)Instructions burned: 2 (million)
% 0.13/0.36 % (15854)------------------------------
% 0.13/0.36 % (15854)------------------------------
% 0.13/0.36 % (15852)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (15853)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.36 % (15851)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (15852)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37 % (15852)Terminated due to inappropriate strategy.
% 0.13/0.37 % (15852)------------------------------
% 0.13/0.37 % (15852)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (15857)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37 % (15852)Termination reason: Inappropriate
% 0.13/0.37
% 0.13/0.37 % (15852)Memory used [KB]: 718
% 0.13/0.37 % (15852)Time elapsed: 0.003 s
% 0.13/0.37 % (15852)Instructions burned: 2 (million)
% 0.13/0.37 % (15852)------------------------------
% 0.13/0.37 % (15852)------------------------------
% 0.13/0.37 % (15851)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37 % (15851)Terminated due to inappropriate strategy.
% 0.13/0.37 % (15851)------------------------------
% 0.13/0.37 % (15851)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (15851)Termination reason: Inappropriate
% 0.13/0.37
% 0.13/0.37 % (15851)Memory used [KB]: 718
% 0.13/0.37 % (15851)Time elapsed: 0.002 s
% 0.13/0.37 % (15851)Instructions burned: 2 (million)
% 0.13/0.37 % (15851)------------------------------
% 0.13/0.37 % (15851)------------------------------
% 0.13/0.37 % (15857)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37 % (15857)Terminated due to inappropriate strategy.
% 0.13/0.37 % (15857)------------------------------
% 0.13/0.37 % (15857)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (15857)Termination reason: Inappropriate
% 0.13/0.37
% 0.13/0.37 % (15857)Memory used [KB]: 718
% 0.13/0.37 % (15857)Time elapsed: 0.002 s
% 0.13/0.37 % (15857)Instructions burned: 2 (million)
% 0.13/0.37 % (15857)------------------------------
% 0.13/0.37 % (15857)------------------------------
% 0.13/0.38 % (15858)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.38 % (15858)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38 % (15858)Terminated due to inappropriate strategy.
% 0.13/0.38 % (15858)------------------------------
% 0.13/0.38 % (15858)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38 % (15858)Termination reason: Inappropriate
% 0.13/0.38
% 0.13/0.38 % (15858)Memory used [KB]: 718
% 0.13/0.38 % (15858)Time elapsed: 0.002 s
% 0.13/0.38 % (15858)Instructions burned: 2 (million)
% 0.13/0.38 % (15858)------------------------------
% 0.13/0.38 % (15858)------------------------------
% 0.13/0.38 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.13/0.38 % (15859)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.38 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.13/0.38 % (15860)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.38 % (15861)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.38 % (15860)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38 % (15860)Terminated due to inappropriate strategy.
% 0.13/0.38 % (15860)------------------------------
% 0.13/0.38 % (15860)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38 % (15860)Termination reason: Inappropriate
% 0.13/0.38
% 0.13/0.38 % (15860)Memory used [KB]: 718
% 0.13/0.38 % (15860)Time elapsed: 0.002 s
% 0.13/0.38 % (15860)Instructions burned: 2 (million)
% 0.13/0.38 % (15860)------------------------------
% 0.13/0.38 % (15860)------------------------------
% 0.13/0.38 % (15855)First to succeed.
% 0.13/0.38 % (15855)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38 % (15855)------------------------------
% 0.13/0.38 % (15855)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38 % (15855)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (15855)Memory used [KB]: 952
% 0.13/0.38 % (15855)Time elapsed: 0.021 s
% 0.13/0.38 % (15855)Instructions burned: 39 (million)
% 0.13/0.38 % (15855)------------------------------
% 0.13/0.38 % (15855)------------------------------
% 0.13/0.38 % (15850)Success in time 0.033 s
%------------------------------------------------------------------------------