TSTP Solution File: ANA003-4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 10:30:39 EDT 2024
% Result : Unsatisfiable 0.17s 0.36s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 46 ( 3 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 121 ( 51 ~; 65 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f270,plain,
$false,
inference(avatar_sat_refutation,[],[f100,f162,f170,f241,f249,f269]) ).
fof(f269,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f267,plain,
( $false
| spl0_1
| ~ spl0_6 ),
inference(resolution,[],[f266,f95]) ).
fof(f95,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| spl0_1 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f94,plain,
( spl0_1
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f266,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_6 ),
inference(resolution,[],[f240,f6]) ).
fof(f6,axiom,
! [X3] :
( ~ less_or_equal(delta_1(X3),n0)
| less_or_equal(X3,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f240,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f238,plain,
( spl0_6
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f249,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f247,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f246,f95]) ).
fof(f246,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_4 ),
inference(resolution,[],[f204,f7]) ).
fof(f7,axiom,
! [X3] :
( ~ less_or_equal(delta_2(X3),n0)
| less_or_equal(X3,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f204,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f202,plain,
( spl0_4
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f241,plain,
( spl0_6
| spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f232,f160,f202,f238]) ).
fof(f160,plain,
( spl0_3
<=> ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(X0,n0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f232,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_3 ),
inference(resolution,[],[f231,f3]) ).
fof(f3,axiom,
! [X2,X1] :
( ~ less_or_equal(minimum(X1,X2),n0)
| less_or_equal(X2,n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
fof(f231,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f218,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_3 ),
inference(resolution,[],[f196,f14]) ).
fof(f14,plain,
! [X0,X1] :
( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)
| less_or_equal(minimum(X0,X1),n0) ),
inference(resolution,[],[f11,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum3) ).
fof(f11,axiom,
! [X4] :
( less_or_equal(absolute(add(xs(X4),negate(a_real_number))),X4)
| less_or_equal(X4,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f196,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0) )
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f175,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(minimum(X0,delta_2(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)
| less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0) )
| ~ spl0_3 ),
inference(resolution,[],[f161,f13]) ).
fof(f13,plain,
! [X0,X1] :
( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)
| less_or_equal(minimum(X0,X1),n0) ),
inference(resolution,[],[f11,f2]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum7) ).
fof(f161,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(X0,n0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f170,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f169]) ).
fof(f169,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f163,f10]) ).
fof(f10,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f163,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl0_1 ),
inference(resolution,[],[f96,f5]) ).
fof(f5,axiom,
! [X1] :
( ~ less_or_equal(half(X1),n0)
| less_or_equal(X1,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
fof(f96,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f162,plain,
( spl0_1
| spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f101,f98,f160,f94]) ).
fof(f98,plain,
( spl0_2
<=> ! [X0] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f101,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) )
| ~ spl0_2 ),
inference(resolution,[],[f99,f8]) ).
fof(f8,axiom,
! [X3,X0] :
( less_or_equal(absolute(add(f(X0),negate(f(a_real_number)))),X3)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_1(X3))
| less_or_equal(X3,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f99,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(X0,n0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f100,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f36,f98,f94]) ).
fof(f36,plain,
! [X0] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[],[f21,f9]) ).
fof(f9,axiom,
! [X3,X0] :
( less_or_equal(absolute(add(g(X0),negate(g(a_real_number)))),X3)
| ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_2(X3))
| less_or_equal(X3,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f21,plain,
! [X0] :
( ~ less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(resolution,[],[f12,f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X1,X2),X0)
| ~ less_or_equal(X2,half(X0))
| ~ less_or_equal(X1,half(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f12,axiom,
! [X4] :
( ~ less_or_equal(add(absolute(add(f(xs(X4)),negate(f(a_real_number)))),absolute(add(g(xs(X4)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X4,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ANA003-4 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Apr 30 00:37:02 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (21735)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (21738)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 % (21736)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35 % (21740)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35 % (21741)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.35 % (21742)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35 % (21743)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)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 % (21739)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)
% 0.12/0.36 % (21739)First to succeed.
% 0.17/0.36 % (21739)Refutation found. Thanks to Tanya!
% 0.17/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.36 % (21739)------------------------------
% 0.17/0.36 % (21739)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.36 % (21739)Termination reason: Refutation
% 0.17/0.36
% 0.17/0.36 % (21739)Memory used [KB]: 889
% 0.17/0.36 % (21739)Time elapsed: 0.007 s
% 0.17/0.36 % (21739)Instructions burned: 11 (million)
% 0.17/0.36 % (21739)------------------------------
% 0.17/0.36 % (21739)------------------------------
% 0.17/0.36 % (21735)Success in time 0.017 s
%------------------------------------------------------------------------------