%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA003-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:30:49 AM UTC 2026
% Result : Unsatisfiable 1.66s 1.04s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 69 ( 12 unt; 8 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 169 ( 72 ~; 89 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X2,X0,X1] :
( less_or_equal(add(X0,X2),X1)
| ~ less_or_equal(X2,half(X1))
| ~ less_or_equal(X0,half(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f16,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
fof(f19,axiom,
! [X0,X1] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_less_or_equal) ).
fof(f20,axiom,
! [X2,X0,X1] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_or_equal) ).
fof(f27,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f28,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f29,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(f(X1),negate(f(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_1(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f30,axiom,
! [X0,X1] :
( less_or_equal(absolute(add(g(X1),negate(g(a_real_number)))),X0)
| ~ less_or_equal(absolute(add(X1,negate(a_real_number))),delta_2(X0))
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f31,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f32,axiom,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f33,negated_conjecture,
! [X0] :
( ~ less_or_equal(add(absolute(add(f(xs(X0)),negate(f(a_real_number)))),absolute(add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_2) ).
fof(f123,plain,
! [X0] :
( ~ less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0) ),
inference(resolution,[],[f15,f33]) ).
fof(f143,definition,
( spl1_1
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f144,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f149,plain,
! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0) ),
inference(resolution,[],[f30,f123]) ).
fof(f153,definition,
( spl1_3
<=> ! [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(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0)) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f154,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
| less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0))) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( spl1_1
| spl1_3 ),
inference(avatar_split_clause,[],[f149,f153,f143]) ).
fof(f156,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl1_1 ),
inference(resolution,[],[f144,f16]) ).
fof(f157,plain,
( $false
| ~ spl1_1 ),
inference(resolution,[],[f156,f31]) ).
fof(f158,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f157]) ).
fof(f159,plain,
( ! [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(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0) )
| ~ spl1_3 ),
inference(resolution,[],[f154,f29]) ).
fof(f163,definition,
( spl1_4
<=> ! [X0] :
( less_or_equal(X0,n0)
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_2(half(epsilon_0))) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f164,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) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( spl1_1
| spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f159,f153,f163,f143]) ).
fof(f166,plain,
( ~ less_or_equal(absolute(add(xs(delta_2(half(epsilon_0))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl1_4 ),
inference(resolution,[],[f164,f32]) ).
fof(f168,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(X0),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(X0,n0)
| less_or_equal(delta_2(half(epsilon_0)),absolute(add(xs(X0),negate(a_real_number)))) )
| ~ spl1_4 ),
inference(resolution,[],[f164,f19]) ).
fof(f169,plain,
( ~ less_or_equal(absolute(add(xs(delta_2(half(epsilon_0))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl1_4 ),
inference(duplicate_literal_removal,[],[f166]) ).
fof(f171,definition,
( spl1_5
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f172,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f174,definition,
( spl1_6
<=> less_or_equal(absolute(add(xs(delta_2(half(epsilon_0))),negate(a_real_number))),delta_1(half(epsilon_0))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f175,plain,
( ~ less_or_equal(absolute(add(xs(delta_2(half(epsilon_0))),negate(a_real_number))),delta_1(half(epsilon_0)))
| spl1_6 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f176,plain,
( spl1_5
| ~ spl1_6
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f169,f163,f174,f171]) ).
fof(f177,plain,
( ! [X0] :
( ~ less_or_equal(absolute(add(xs(delta_2(half(epsilon_0))),negate(a_real_number))),X0)
| ~ less_or_equal(X0,delta_1(half(epsilon_0))) )
| spl1_6 ),
inference(resolution,[],[f175,f20]) ).
fof(f200,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(delta_2(half(epsilon_0)),absolute(add(xs(delta_1(half(epsilon_0))),negate(a_real_number))))
| less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl1_4 ),
inference(resolution,[],[f168,f32]) ).
fof(f203,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(delta_2(half(epsilon_0)),absolute(add(xs(delta_1(half(epsilon_0))),negate(a_real_number))))
| ~ spl1_4 ),
inference(duplicate_literal_removal,[],[f200]) ).
fof(f205,definition,
( spl1_10
<=> less_or_equal(delta_2(half(epsilon_0)),absolute(add(xs(delta_1(half(epsilon_0))),negate(a_real_number)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f208,definition,
( spl1_11
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f209,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f210,plain,
( spl1_10
| spl1_11
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f203,f163,f208,f205]) ).
fof(f462,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))
| less_or_equal(delta_2(half(epsilon_0)),n0)
| spl1_6 ),
inference(resolution,[],[f177,f32]) ).
fof(f516,definition,
( spl1_58
<=> less_or_equal(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))) ),
introduced(definition,[new_symbols(definition,[spl1_58])],[avatar_definition]) ).
fof(f517,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))
| spl1_58 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f518,plain,
( spl1_5
| ~ spl1_58
| spl1_6 ),
inference(avatar_split_clause,[],[f462,f174,f516,f171]) ).
fof(f537,plain,
( ! [X0] :
( ~ less_or_equal(X0,delta_1(half(epsilon_0)))
| ~ less_or_equal(delta_2(half(epsilon_0)),X0) )
| spl1_58 ),
inference(resolution,[],[f517,f20]) ).
fof(f811,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),absolute(add(xs(delta_1(half(epsilon_0))),negate(a_real_number))))
| less_or_equal(delta_1(half(epsilon_0)),n0)
| spl1_58 ),
inference(resolution,[],[f537,f32]) ).
fof(f853,plain,
( spl1_11
| ~ spl1_10
| spl1_58 ),
inference(avatar_split_clause,[],[f811,f516,f205,f208]) ).
fof(f854,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl1_5 ),
inference(resolution,[],[f172,f28]) ).
fof(f857,plain,
( spl1_1
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f854,f171,f143]) ).
fof(f858,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl1_11 ),
inference(resolution,[],[f209,f27]) ).
fof(f860,plain,
( spl1_1
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f858,f208,f143]) ).
cnf(s2,plain,
( spl1_1
| spl1_3 ),
inference(sat_conversion,[],[f155]) ).
cnf(s3,plain,
~ spl1_1,
inference(sat_conversion,[],[f158]) ).
cnf(s4,plain,
( spl1_1
| ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f165]) ).
cnf(s5,plain,
( ~ spl1_4
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f176]) ).
cnf(s8,plain,
( ~ spl1_4
| spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f210]) ).
cnf(s45,plain,
( spl1_5
| spl1_6
| ~ spl1_58 ),
inference(sat_conversion,[],[f518]) ).
cnf(s93,plain,
( ~ spl1_10
| spl1_11
| spl1_58 ),
inference(sat_conversion,[],[f853]) ).
cnf(s95,plain,
( spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f857]) ).
cnf(s96,plain,
( spl1_1
| ~ spl1_11 ),
inference(sat_conversion,[],[f860]) ).
cnf(s104,plain,
~ spl1_11,
inference(rat,[],[s96,s3]) ).
cnf(s105,plain,
~ spl1_5,
inference(rat,[],[s95,s3]) ).
cnf(s109,plain,
spl1_3,
inference(rat,[],[s2,s3]) ).
cnf(s115,plain,
spl1_4,
inference(rat,[],[s4,s3,s109]) ).
cnf(s119,plain,
spl1_10,
inference(rat,[],[s8,s104,s115]) ).
cnf(s120,plain,
~ spl1_6,
inference(rat,[],[s5,s105,s115]) ).
cnf(s121,plain,
spl1_58,
inference(rat,[],[s93,s104,s119]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s45,s105,s121,s120]) ).
fof(f861,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:23:26 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.66/1.04 % (2761834)Input is clausal, will run a generic CNF schedule.
% 1.66/1.04 % (2761866)dis-21_1_sil=8000:lcm=predicate:random_seed=3405658690:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.66/1.04 % (2761866)First to succeed.
% 1.66/1.04 % (2761866)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2761834"
% 1.66/1.04 % (2761859)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4226430300:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.66/1.04 % (2761858)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=66347678:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.66/1.04 % (2761864)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=378577209:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.66/1.04 % (2761860)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3829685383:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.66/1.04 % (2761861)lrs+10_1_sil=8000:sp=occurrence:random_seed=3163493234:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.66/1.04 % (2761865)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2376400329:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.66/1.04 % (2761861)Instruction limit reached!
% 1.66/1.04 % (2761861)------------------------------
% 1.66/1.04 % (2761861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.04 % (2761861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.04 % (2761861)CaDiCaL version: 2.1.3
% 1.66/1.04 % (2761861)Termination reason: Instruction limit
% 1.66/1.04 % (2761861)Termination phase: Saturation
% 1.66/1.04 % (2761861)Time elapsed: 0.064 s
% 1.66/1.04 % (2761861)Peak memory usage: 88 MB
% 1.66/1.04 % (2761861)Instructions burned: 108 (million)
% 1.66/1.04 % (2761864)Instruction limit reached!
% 1.66/1.04 % (2761864)------------------------------
% 1.66/1.04 % (2761864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.66/1.04 % (2761864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.66/1.04 % (2761864)CaDiCaL version: 2.1.3
% 1.66/1.04 % (2761864)Termination reason: Instruction limit
% 1.66/1.04 % (2761864)Termination phase: Saturation
% 1.66/1.04 % (2761864)Time elapsed: 0.074 s
% 1.66/1.04 % (2761864)Peak memory usage: 89 MB
% 1.66/1.04 % (2761864)Instructions burned: 115 (million)
% 1.66/1.04 % (2761866)Refutation found. Thanks to Tanya!
% 1.66/1.04 % SZS status Unsatisfiable for theBenchmark
% 1.66/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.14 % (2761866)------------------------------
% 0.20/1.14 % (2761866)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.14 % (2761866)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.14 % (2761866)CaDiCaL version: 2.1.3
% 0.20/1.14 % (2761866)Termination reason: Refutation
% 0.20/1.14 % (2761866)Time elapsed: 0.009 s
% 0.20/1.14 % (2761866)Peak memory usage: 89 MB
% 0.20/1.14 % (2761866)Instructions burned: 23 (million)
% 0.20/1.14 % (2761866)------------------------------
% 0.20/1.14 % (2761866)------------------------------
% 0.20/1.14 % (2761834)Success in time 0.271 s
% 0.20/1.14 % Vampire exiting
%------------------------------------------------------------------------------