TSTP Solution File: NUM877_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM877_1 : TPTP v8.2.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.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 May 21 02:14:08 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 36
% Syntax : Number of formulae : 82 ( 24 unt; 2 typ; 0 def)
% Number of atoms : 174 ( 42 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 167 ( 73 ~; 66 |; 4 &)
% ( 20 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 270 ( 49 atm; 100 fun; 33 num; 88 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 84 !; 4 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sK1: $int ).
tff(f179,plain,
$false,
inference(avatar_sat_refutation,[],[f25,f30,f34,f38,f42,f46,f50,f54,f58,f68,f72,f84,f88,f102,f119,f143,f158,f163,f173,f177,f178]) ).
tff(f178,plain,
( spl2_1
| ~ spl2_6
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f151,f141,f44,f22]) ).
tff(f22,plain,
( spl2_1
<=> ( sK0 = sK1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
tff(f44,plain,
( spl2_6
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
tff(f141,plain,
( spl2_16
<=> ! [X0: $int] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
tff(f151,plain,
( ( sK0 = sK1 )
| ~ spl2_6
| ~ spl2_16 ),
inference(evaluation,[],[f147]) ).
tff(f147,plain,
( ( $uminus($uminus(sK1)) = $sum(sK0,0) )
| ~ spl2_6
| ~ spl2_16 ),
inference(superposition,[],[f142,f45]) ).
tff(f45,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f142,plain,
( ! [X0: $int] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f141]) ).
tff(f177,plain,
( spl2_20
| ~ spl2_7
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f63,f56,f48,f175]) ).
tff(f175,plain,
( spl2_20
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
tff(f48,plain,
( spl2_7
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
tff(f56,plain,
( spl2_9
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
tff(f63,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl2_7
| ~ spl2_9 ),
inference(superposition,[],[f57,f49]) ).
tff(f49,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f48]) ).
tff(f57,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f173,plain,
( spl2_19
| ~ spl2_7
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f60,f52,f48,f171]) ).
tff(f171,plain,
( spl2_19
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
tff(f52,plain,
( spl2_8
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
tff(f60,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl2_7
| ~ spl2_8 ),
inference(superposition,[],[f53,f49]) ).
tff(f53,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f52]) ).
tff(f163,plain,
( spl2_18
| ~ spl2_2
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f111,f86,f27,f161]) ).
tff(f161,plain,
( spl2_18
<=> ! [X0: $int] :
( $less($sum(X0,$uminus(sK1)),0)
| ~ $less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
tff(f27,plain,
( spl2_2
<=> ( 0 = $sum(sK0,$uminus(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
tff(f86,plain,
( spl2_13
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
tff(f111,plain,
( ! [X0: $int] :
( $less($sum(X0,$uminus(sK1)),0)
| ~ $less(X0,sK0) )
| ~ spl2_2
| ~ spl2_13 ),
inference(superposition,[],[f87,f29]) ).
tff(f29,plain,
( ( 0 = $sum(sK0,$uminus(sK1)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f27]) ).
tff(f87,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f86]) ).
tff(f158,plain,
( spl2_17
| ~ spl2_2
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f106,f86,f27,f156]) ).
tff(f156,plain,
( spl2_17
<=> ! [X0: $int] :
( $less(0,$sum(X0,$uminus(sK1)))
| ~ $less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
tff(f106,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,$uminus(sK1)))
| ~ $less(sK0,X0) )
| ~ spl2_2
| ~ spl2_13 ),
inference(superposition,[],[f87,f29]) ).
tff(f143,plain,
( spl2_16
| ~ spl2_2
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f137,f117,f27,f141]) ).
tff(f117,plain,
( spl2_15
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
tff(f137,plain,
( ! [X0: $int] : ( $sum(sK0,$sum($uminus(sK1),X0)) = X0 )
| ~ spl2_2
| ~ spl2_15 ),
inference(evaluation,[],[f120]) ).
tff(f120,plain,
( ! [X0: $int] : ( $sum(sK0,$sum($uminus(sK1),X0)) = $sum(0,X0) )
| ~ spl2_2
| ~ spl2_15 ),
inference(superposition,[],[f118,f29]) ).
tff(f118,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f117]) ).
tff(f119,plain,
spl2_15,
inference(avatar_split_clause,[],[f5,f117]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f102,plain,
( spl2_14
| ~ spl2_3
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f59,f52,f32,f100]) ).
tff(f100,plain,
( spl2_14
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
tff(f32,plain,
( spl2_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
tff(f59,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl2_3
| ~ spl2_8 ),
inference(resolution,[],[f53,f33]) ).
tff(f33,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f88,plain,
spl2_13,
inference(avatar_split_clause,[],[f12,f86]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f84,plain,
spl2_12,
inference(avatar_split_clause,[],[f7,f82]) ).
tff(f82,plain,
( spl2_12
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f72,plain,
spl2_11,
inference(avatar_split_clause,[],[f11,f70]) ).
tff(f70,plain,
( spl2_11
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f68,plain,
spl2_10,
inference(avatar_split_clause,[],[f10,f66]) ).
tff(f66,plain,
( spl2_10
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f58,plain,
spl2_9,
inference(avatar_split_clause,[],[f15,f56]) ).
tff(f15,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f54,plain,
spl2_8,
inference(avatar_split_clause,[],[f13,f52]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f50,plain,
spl2_7,
inference(avatar_split_clause,[],[f4,f48]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f46,plain,
spl2_6,
inference(avatar_split_clause,[],[f8,f44]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f42,plain,
spl2_5,
inference(avatar_split_clause,[],[f14,f40]) ).
tff(f40,plain,
( spl2_5
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f38,plain,
spl2_4,
inference(avatar_split_clause,[],[f6,f36]) ).
tff(f36,plain,
( spl2_4
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
tff(f6,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f34,plain,
spl2_3,
inference(avatar_split_clause,[],[f9,f32]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f30,plain,
spl2_2,
inference(avatar_split_clause,[],[f19,f27]) ).
tff(f19,plain,
0 = $sum(sK0,$uminus(sK1)),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ( sK0 != sK1 )
& ( 0 = $sum(sK0,$uminus(sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).
tff(f17,plain,
( ? [X0: $int,X1: $int] :
( ( X0 != X1 )
& ( 0 = $sum(X0,$uminus(X1)) ) )
=> ( ( sK0 != sK1 )
& ( 0 = $sum(sK0,$uminus(sK1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
( ( X0 != X1 )
& ( 0 = $sum(X0,$uminus(X1)) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ! [X0: $int,X1: $int] :
( ( 0 = $sum(X0,$uminus(X1)) )
=> ( X0 = X1 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( ( $difference(X0,X1) = 0 )
=> ( X0 = X1 ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( ( $difference(X0,X1) = 0 )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diff_identity) ).
tff(f25,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f20,f22]) ).
tff(f20,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM877_1 : TPTP v8.2.0. Released v5.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n008.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 : Mon May 20 05:00:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (22681)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (22684)WARNING: value z3 for option sas not known
% 0.13/0.36 % (22685)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (22683)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (22682)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (22686)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36 % (22687)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36 % (22684)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (22688)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36 % (22685)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (22682)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (22683)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (22682)Terminated due to inappropriate strategy.
% 0.13/0.36 % (22682)------------------------------
% 0.13/0.36 % (22682)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36 % (22685)Terminated due to inappropriate strategy.
% 0.13/0.36 % (22685)------------------------------
% 0.13/0.36 % (22685)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36 % (22683)Terminated due to inappropriate strategy.
% 0.13/0.36 % (22683)------------------------------
% 0.13/0.36 % (22683)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.36 % (22685)Termination reason: Inappropriate
% 0.13/0.36 % (22683)Termination reason: Inappropriate
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % (22685)Memory used [KB]: 723
% 0.13/0.36 % (22683)Memory used [KB]: 723
% 0.13/0.36 % (22685)Time elapsed: 0.002 s
% 0.13/0.36 % (22683)Time elapsed: 0.002 s
% 0.13/0.36 % (22685)Instructions burned: 2 (million)
% 0.13/0.36 % (22683)Instructions burned: 2 (million)
% 0.13/0.36 % (22682)Termination reason: Inappropriate
% 0.13/0.36
% 0.13/0.36 % (22682)Memory used [KB]: 723
% 0.13/0.36 % (22682)Time elapsed: 0.002 s
% 0.13/0.36 % (22682)Instructions burned: 2 (million)
% 0.13/0.37 % (22685)------------------------------
% 0.13/0.37 % (22685)------------------------------
% 0.13/0.37 % (22683)------------------------------
% 0.13/0.37 % (22683)------------------------------
% 0.13/0.37 % (22682)------------------------------
% 0.13/0.37 % (22682)------------------------------
% 0.13/0.37 % (22686)First to succeed.
% 0.13/0.37 % (22686)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22681"
% 0.13/0.37 % (22686)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37 % (22686)------------------------------
% 0.13/0.37 % (22686)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37 % (22686)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (22686)Memory used [KB]: 868
% 0.13/0.37 % (22686)Time elapsed: 0.008 s
% 0.13/0.37 % (22686)Instructions burned: 10 (million)
% 0.13/0.37 % (22681)Success in time 0.012 s
%------------------------------------------------------------------------------