%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 09:31:14 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 57 ( 9 unt; 5 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 137 ( 60 ~; 72 |; 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 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).
fof(f3,axiom,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).
fof(f4,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(f5,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f8,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(f9,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(f10,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f11,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(f12,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(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(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(f15,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,[],[f4,f12]) ).
fof(f22,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,[],[f9,f15]) ).
fof(f26,definition,
( spl0_1
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f27,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f28,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f30,definition,
( spl0_2
<=> ! [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,[spl0_2])],[avatar_definition]) ).
fof(f31,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))) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f22,f30,f26]) ).
fof(f33,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) )
| ~ spl0_2 ),
inference(resolution,[],[f31,f8]) ).
fof(f35,definition,
( spl0_3
<=> ! [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,[spl0_3])],[avatar_definition]) ).
fof(f36,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,[],[f35]) ).
fof(f37,plain,
( spl0_1
| spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f33,f30,f35,f26]) ).
fof(f40,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl0_1 ),
inference(resolution,[],[f28,f5]) ).
fof(f41,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f40,f10]) ).
fof(f42,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f41]) ).
fof(f87,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,[],[f36,f13]) ).
fof(f88,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,[],[f87]) ).
fof(f92,definition,
( spl0_4
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f94,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f108,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,[],[f88,f14]) ).
fof(f109,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| ~ spl0_3 ),
inference(duplicate_literal_removal,[],[f108]) ).
fof(f114,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_3 ),
inference(resolution,[],[f109,f3]) ).
fof(f116,definition,
( spl0_6
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f118,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( spl0_6
| spl0_4
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f114,f35,f92,f116]) ).
fof(f124,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_4 ),
inference(resolution,[],[f94,f7]) ).
fof(f125,plain,
( $false
| spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f124,f27]) ).
fof(f126,plain,
( spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f129,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_6 ),
inference(resolution,[],[f118,f6]) ).
fof(f130,plain,
( $false
| spl0_1
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f129,f27]) ).
fof(f131,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f130]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f42]) ).
cnf(s5,plain,
( ~ spl0_3
| spl0_4
| spl0_6 ),
inference(sat_conversion,[],[f119]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f131]) ).
cnf(s8,plain,
~ spl0_6,
inference(rat,[],[s7,s3]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s6,s3]) ).
cnf(s10,plain,
~ spl0_3,
inference(rat,[],[s5,s8,s9]) ).
cnf(s11,plain,
~ spl0_2,
inference(rat,[],[s2,s10,s3]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s3]) ).
fof(f132,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n013.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 20:24:51 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24 % (1516731)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (1516740)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1008851798:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.24 % (1516740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1516731-1516740"...
% 0.07/0.24 % (1516740)...printing done.
% 0.07/0.24 % (1516740)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (1516740)------------------------------
% 0.07/0.25 % (1516740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (1516740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (1516740)CaDiCaL version: 2.1.3
% 0.07/0.25 % (1516740)Termination reason: Refutation
% 0.07/0.25 % (1516740)Time elapsed: 0.003 s
% 0.07/0.25 % (1516740)Peak memory usage: 12 MB
% 0.07/0.25 % (1516740)Instructions burned: 7 (million)
% 0.07/0.25 % (1516731)Success in time 0.029 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------