TSTP Solution File: NUM921_1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM921_1 : TPTP v8.1.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n015.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 18:02:52 EDT 2022
% Result : Theorem 1.91s 0.60s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 87 ( 28 unt; 5 typ; 0 def)
% Number of atoms : 159 ( 24 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 143 ( 66 ~; 59 |; 1 &)
% ( 14 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 164 ( 55 atm; 39 fun; 35 num; 35 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 5 usr; 7 con; 0-2 aty)
% Number of variables : 35 ( 34 !; 1 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(f275,plain,
$false,
inference(avatar_smt_refutation,[],[f26,f30,f34,f40,f46,f57,f66,f87,f94,f148,f182,f197,f212,f270,f274]) ).
tff(f274,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f273]) ).
tff(f273,plain,
( $false
| spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_6 ),
inference(subsumption_resolution,[],[f272,f45]) ).
tff(f45,plain,
( $less(sK0,sF1)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f44,plain,
( spl4_5
<=> $less(sK0,sF1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f272,plain,
( ~ $less(sK0,sF1)
| spl4_1
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_demodulation,[],[f271,f56]) ).
tff(f56,plain,
( ( $uminus(sF2) = sF1 )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f55,plain,
( spl4_6
<=> ( $uminus(sF2) = sF1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f271,plain,
( ~ $less(sK0,$uminus(sF2))
| spl4_1
| ~ spl4_4 ),
inference(subsumption_resolution,[],[f265,f25]) ).
tff(f25,plain,
( ~ $less(sF3,0)
| spl4_1 ),
inference(avatar_component_clause,[],[f24]) ).
tff(f24,plain,
( spl4_1
<=> $less(sF3,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f265,plain,
( $less(sF3,0)
| ~ $less(sK0,$uminus(sF2))
| ~ spl4_4 ),
inference(superposition,[],[f131,f42]) ).
tff(f42,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f8,f14]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_153,[]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_145,[]) ).
tff(f131,plain,
( ! [X15: $int] :
( $less(sF3,$sum(X15,sF2))
| ~ $less(sK0,X15) )
| ~ spl4_4 ),
inference(superposition,[],[f12,f39]) ).
tff(f39,plain,
( ( $sum(sK0,sF2) = sF3 )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f38,plain,
( spl4_4
<=> ( $sum(sK0,sF2) = sF3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_150,[]) ).
tff(f270,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f269]) ).
tff(f269,plain,
( $false
| spl4_1
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f268,f25]) ).
tff(f268,plain,
( $less(sF3,0)
| ~ spl4_4
| ~ spl4_5
| ~ spl4_7 ),
inference(subsumption_resolution,[],[f267,f45]) ).
tff(f267,plain,
( ~ $less(sK0,sF1)
| $less(sF3,0)
| ~ spl4_4
| ~ spl4_7 ),
inference(superposition,[],[f131,f65]) ).
tff(f65,plain,
( ( 0 = $sum(sF1,sF2) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f64,plain,
( spl4_7
<=> ( 0 = $sum(sF1,sF2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f212,plain,
spl4_14,
inference(avatar_split_clause,[],[f208,f210]) ).
tff(f210,plain,
( spl4_14
<=> $less(-1,f(0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
tff(f208,plain,
$less(-1,f(0)),
inference(evaluation,[],[f205]) ).
tff(f205,plain,
$less($uminus(1),f(0)),
inference(superposition,[],[f175,f8]) ).
tff(f175,plain,
! [X0: $int] : $less(X0,f($sum(1,X0))),
inference(superposition,[],[f82,f4]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_140,[]) ).
tff(f82,plain,
! [X1: $int] : $less(X1,f($sum(X1,1))),
inference(resolution,[],[f78,f13]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_152,[]) ).
tff(f78,plain,
! [X0: $int] : ~ $less(f(X0),X0),
inference(resolution,[],[f75,f9]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_147,[]) ).
tff(f75,plain,
! [X0: $int,X1: $int] :
( $less(X0,f(X1))
| ~ $less(X0,X1) ),
inference(resolution,[],[f10,f17]) ).
tff(f17,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f16]) ).
tff(f16,plain,
( ? [X1: $int] : ~ $less($sum(X1,$uminus(f(X1))),0)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X1: $int] : $less($sum(X1,$uminus(f(X1))),0) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X1: $int] : $less($difference(X1,f(X1)),0) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X1: $int] : $less($difference(X1,f(X1)),0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_148,[]) ).
tff(f197,plain,
( ~ spl4_13
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f193,f28,f195]) ).
tff(f195,plain,
( spl4_13
<=> $less(f(f(sF1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
tff(f28,plain,
( spl4_2
<=> ( f(sK0) = sF1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f193,plain,
( ~ $less(f(f(sF1)),sK0)
| ~ spl4_2 ),
inference(superposition,[],[f88,f29]) ).
tff(f29,plain,
( ( f(sK0) = sF1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f28]) ).
tff(f88,plain,
! [X0: $int] : ~ $less(f(f(f(X0))),X0),
inference(resolution,[],[f81,f75]) ).
tff(f81,plain,
! [X0: $int] : ~ $less(f(f(X0)),X0),
inference(resolution,[],[f78,f75]) ).
tff(f182,plain,
spl4_12,
inference(avatar_split_clause,[],[f177,f180]) ).
tff(f180,plain,
( spl4_12
<=> $less(0,f(1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
tff(f177,plain,
$less(0,f(1)),
inference(superposition,[],[f82,f47]) ).
tff(f47,plain,
! [X0: $int] : ( $sum(0,X0) = X0 ),
inference(superposition,[],[f4,f6]) ).
tff(f6,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_142,[]) ).
tff(f148,plain,
( spl4_10
| spl4_11
| spl4_1 ),
inference(avatar_split_clause,[],[f102,f24,f146,f143]) ).
tff(f143,plain,
( spl4_10
<=> $less(0,sF3) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f146,plain,
( spl4_11
<=> ( 0 = sF3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f102,plain,
( ( 0 = sF3 )
| $less(0,sF3)
| spl4_1 ),
inference(resolution,[],[f11,f25]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_149,[]) ).
tff(f94,plain,
( ~ spl4_9
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f90,f28,f92]) ).
tff(f92,plain,
( spl4_9
<=> $less(f(sF1),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f90,plain,
( ~ $less(f(sF1),sK0)
| ~ spl4_2 ),
inference(superposition,[],[f81,f29]) ).
tff(f87,plain,
( ~ spl4_8
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f83,f28,f85]) ).
tff(f85,plain,
( spl4_8
<=> $less(sF1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f83,plain,
( ~ $less(sF1,sK0)
| ~ spl4_2 ),
inference(superposition,[],[f78,f29]) ).
tff(f66,plain,
( spl4_7
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f41,f32,f64]) ).
tff(f32,plain,
( spl4_3
<=> ( sF2 = $uminus(sF1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f41,plain,
( ( 0 = $sum(sF1,sF2) )
| ~ spl4_3 ),
inference(superposition,[],[f8,f33]) ).
tff(f33,plain,
( ( sF2 = $uminus(sF1) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f57,plain,
( spl4_6
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f36,f32,f55]) ).
tff(f36,plain,
( ( $uminus(sF2) = sF1 )
| ~ spl4_3 ),
inference(superposition,[],[f14,f33]) ).
tff(f46,plain,
( spl4_5
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f35,f28,f44]) ).
tff(f35,plain,
( $less(sK0,sF1)
| ~ spl4_2 ),
inference(superposition,[],[f17,f29]) ).
tff(f40,plain,
spl4_4,
inference(avatar_split_clause,[],[f21,f38]) ).
tff(f21,plain,
$sum(sK0,sF2) = sF3,
introduced(function_definition,[]) ).
tff(f34,plain,
spl4_3,
inference(avatar_split_clause,[],[f20,f32]) ).
tff(f20,plain,
sF2 = $uminus(sF1),
introduced(function_definition,[]) ).
tff(f30,plain,
spl4_2,
inference(avatar_split_clause,[],[f19,f28]) ).
tff(f19,plain,
f(sK0) = sF1,
introduced(function_definition,[]) ).
tff(f26,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f22,f24]) ).
tff(f22,plain,
~ $less(sF3,0),
inference(definition_folding,[],[f18,f21,f20,f19]) ).
tff(f18,plain,
~ $less($sum(sK0,$uminus(f(sK0))),0),
inference(cnf_transformation,[],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM921=1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n015.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 Aug 30 09:27:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.41 % (30703)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.20/0.42 % (30718)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.44 % (30718)Instruction limit reached!
% 0.20/0.44 % (30718)------------------------------
% 0.20/0.44 % (30718)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.44 % (30718)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.44 % (30718)Termination reason: Unknown
% 0.20/0.44 % (30718)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (30718)Memory used [KB]: 5373
% 0.20/0.44 % (30718)Time elapsed: 0.004 s
% 0.20/0.44 % (30718)Instructions burned: 2 (million)
% 0.20/0.44 % (30718)------------------------------
% 0.20/0.44 % (30718)------------------------------
% 0.20/0.52 % (30711)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 0.20/0.57 % (30711)Instruction limit reached!
% 0.20/0.57 % (30711)------------------------------
% 0.20/0.57 % (30711)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57 % (30711)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.57 % (30711)Termination reason: Unknown
% 0.20/0.57 % (30711)Termination phase: Saturation
% 0.20/0.57
% 0.20/0.57 % (30711)Memory used [KB]: 5756
% 0.20/0.57 % (30711)Time elapsed: 0.121 s
% 0.20/0.57 % (30711)Instructions burned: 26 (million)
% 0.20/0.57 % (30711)------------------------------
% 0.20/0.57 % (30711)------------------------------
% 0.20/0.58 % (30709)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.20/0.58 % (30704)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.20/0.58 % (30708)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.59 % (30726)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.59 % (30703)First to succeed.
% 0.20/0.60 % (30707)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.60 % (30719)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.91/0.60 % (30728)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 1.91/0.60 % (30703)Refutation found. Thanks to Tanya!
% 1.91/0.60 % SZS status Theorem for theBenchmark
% 1.91/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.91/0.60 % (30703)------------------------------
% 1.91/0.60 % (30703)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.91/0.60 % (30703)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.91/0.60 % (30703)Termination reason: Refutation
% 1.91/0.60
% 1.91/0.60 % (30703)Memory used [KB]: 1151
% 1.91/0.60 % (30703)Time elapsed: 0.185 s
% 1.91/0.60 % (30703)Instructions burned: 111 (million)
% 1.91/0.60 % (30703)------------------------------
% 1.91/0.60 % (30703)------------------------------
% 1.91/0.60 % (30702)Success in time 0.25 s
%------------------------------------------------------------------------------