%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 09:31:15 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 55 ( 8 unt; 4 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 139 ( 58 ~; 77 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(add(absolute(X0),absolute(X1)),X2)
| less_or_equal(absolute(add(X0,X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absolute_sum_less_or_equal_sum_of_absolutes2) ).
fof(f2,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(f3,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(f4,axiom,
! [X0,X1] :
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X1,n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minimum9) ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).
fof(f6,axiom,
! [X0] :
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_and_half) ).
fof(f7,axiom,
! [X0] :
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f8,axiom,
! [X0] :
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f11,axiom,
~ less_or_equal(epsilon_0,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
fof(f12,axiom,
! [X0] :
( less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
fof(f13,negated_conjecture,
! [X0] :
( ~ less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7_1) ).
fof(f14,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,[],[f12,f3]) ).
fof(f15,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,[],[f12,f2]) ).
fof(f16,plain,
! [X2,X0,X1] :
( less_or_equal(absolute(add(X2,X0)),X1)
| ~ less_or_equal(absolute(X2),half(X1))
| ~ less_or_equal(absolute(X0),half(X1)) ),
inference(resolution,[],[f5,f1]) ).
fof(f27,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,[],[f16,f13]) ).
fof(f30,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)))
| less_or_equal(half(epsilon_0),n0) ),
inference(resolution,[],[f27,f10]) ).
fof(f41,definition,
( spl0_3
<=> less_or_equal(half(epsilon_0),n0) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f42,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| spl0_3 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f43,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f45,definition,
( spl0_4
<=> ! [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) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f46,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_4 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f30,f45,f41]) ).
fof(f55,plain,
( less_or_equal(epsilon_0,n0)
| ~ spl0_3 ),
inference(resolution,[],[f43,f6]) ).
fof(f56,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f55,f11]) ).
fof(f57,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f56]) ).
fof(f75,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_4 ),
inference(resolution,[],[f46,f9]) ).
fof(f85,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))) )
| spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f75,f42]) ).
fof(f98,plain,
( ! [X0] :
( less_or_equal(minimum(X0,delta_2(half(epsilon_0))),n0)
| ~ 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
| ~ spl0_4 ),
inference(resolution,[],[f85,f14]) ).
fof(f100,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
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f98]) ).
fof(f116,definition,
( spl0_10
<=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f118,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f232,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
| ~ spl0_4 ),
inference(resolution,[],[f100,f15]) ).
fof(f238,plain,
( less_or_equal(minimum(delta_1(half(epsilon_0)),delta_2(half(epsilon_0))),n0)
| spl0_3
| ~ spl0_4 ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f244,plain,
( less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0)
| spl0_3
| ~ spl0_4 ),
inference(resolution,[],[f238,f4]) ).
fof(f246,definition,
( spl0_13
<=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f248,plain,
( less_or_equal(delta_1(half(epsilon_0)),n0)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
( spl0_13
| spl0_10
| spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f244,f45,f41,f116,f246]) ).
fof(f255,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_10 ),
inference(resolution,[],[f118,f8]) ).
fof(f256,plain,
( $false
| spl0_3
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f255,f42]) ).
fof(f257,plain,
( spl0_3
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f292,plain,
( less_or_equal(half(epsilon_0),n0)
| ~ spl0_13 ),
inference(resolution,[],[f248,f7]) ).
fof(f293,plain,
( $false
| spl0_3
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f292,f42]) ).
fof(f294,plain,
( spl0_3
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f293]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f57]) ).
cnf(s8,plain,
( spl0_3
| ~ spl0_4
| spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f249]) ).
cnf(s9,plain,
( spl0_3
| ~ spl0_10 ),
inference(sat_conversion,[],[f257]) ).
cnf(s10,plain,
( spl0_3
| ~ spl0_13 ),
inference(sat_conversion,[],[f294]) ).
cnf(s11,plain,
~ spl0_13,
inference(rat,[],[s10,s3]) ).
cnf(s12,plain,
~ spl0_10,
inference(rat,[],[s9,s3]) ).
cnf(s13,plain,
~ spl0_4,
inference(rat,[],[s8,s11,s12,s3]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s13,s3]) ).
fof(f295,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 20:32:04 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.27 % (685543)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (685551)dis+10_1_sil=32000:sp=arity:random_seed=3669926508:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.27 % (685549)% WARNING: option uhcvi not known.
% 0.18/0.27 % (685551) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-685543-685551"...
% 0.18/0.27 % (685551)...printing done.
% 0.18/0.27 % (685551)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (685551)------------------------------
% 0.18/0.27 % (685551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (685551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (685551)CaDiCaL version: 2.1.3
% 0.18/0.27 % (685551)Termination reason: Refutation
% 0.18/0.27 % (685551)Time elapsed: 0.005 s
% 0.18/0.27 % (685551)Peak memory usage: 11 MB
% 0.18/0.27 % (685551)Instructions burned: 11 (million)
% 0.18/0.27 % (685543)Success in time 0.034 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------