%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:30:48 AM UTC 2026
% Result : Unsatisfiable 2.99s 1.10s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 118 ( 16 unt; 13 def)
% Number of atoms : 349 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 412 ( 181 ~; 218 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : less_than_or_equal(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_less) ).
fof(f2,axiom,
! [X0,X1] :
( less_than_or_equal(X0,X1)
| less_than_or_equal(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_less) ).
fof(f3,axiom,
! [X2,X0,X1] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,X2)
| ~ less_than_or_equal(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f4,axiom,
! [X0,X1] :
( less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,q(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation1) ).
fof(f5,axiom,
! [X0,X1] :
( less_than_or_equal(X1,X0)
| ~ less_than_or_equal(q(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interpolation2) ).
fof(f6,axiom,
! [X0] :
( less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(X0))
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
fof(f7,axiom,
! [X0,X1] :
( less_than_or_equal(X1,h(X0))
| ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(f(X1),n0)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
fof(f8,axiom,
! [X0] :
( less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(k(X0),X0)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity3) ).
fof(f9,axiom,
! [X0,X1] :
( less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(X0,X1)
| ~ less_than_or_equal(n0,f(X1))
| less_than_or_equal(k(X0),X1)
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity4) ).
fof(f10,axiom,
! [X0] :
( less_than_or_equal(X0,l)
| ~ less_than_or_equal(X0,upper_bound)
| ~ less_than_or_equal(f(X0),n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover1) ).
fof(f11,axiom,
! [X0] :
( less_than_or_equal(g(X0),upper_bound)
| less_than_or_equal(l,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
fof(f12,axiom,
! [X0] :
( less_than_or_equal(f(g(X0)),n0)
| less_than_or_equal(l,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
fof(f13,axiom,
! [X0] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(g(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
fof(f14,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_interval) ).
fof(f15,axiom,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_mapping) ).
fof(f16,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_mapping) ).
fof(f17,negated_conjecture,
( ~ less_than_or_equal(f(l),n0)
| ~ less_than_or_equal(n0,f(l)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
fof(f19,definition,
( spl0_1
<=> less_than_or_equal(n0,f(l)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f21,plain,
( ~ less_than_or_equal(n0,f(l))
| spl0_1 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f23,definition,
( spl0_2
<=> less_than_or_equal(f(l),n0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f25,plain,
( ~ less_than_or_equal(f(l),n0)
| spl0_2 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f17,f23,f19]) ).
fof(f35,plain,
( ! [X0] :
( ~ less_than_or_equal(f(l),X0)
| ~ less_than_or_equal(X0,n0) )
| spl0_2 ),
inference(resolution,[],[f3,f25]) ).
fof(f61,plain,
( ~ less_than_or_equal(l,h(l))
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(n0,n0)
| spl0_2 ),
inference(resolution,[],[f6,f35]) ).
fof(f62,plain,
( ~ less_than_or_equal(l,h(l))
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f61,f1]) ).
fof(f64,definition,
( spl0_6
<=> less_than_or_equal(l,upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f65,plain,
( less_than_or_equal(l,upper_bound)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( ~ less_than_or_equal(l,upper_bound)
| spl0_6 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_7
<=> less_than_or_equal(lower_bound,l) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f69,plain,
( less_than_or_equal(lower_bound,l)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f70,plain,
( ~ less_than_or_equal(lower_bound,l)
| spl0_7 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f72,definition,
( spl0_8
<=> less_than_or_equal(l,h(l)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f74,plain,
( ~ less_than_or_equal(l,h(l))
| spl0_8 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| spl0_2 ),
inference(avatar_split_clause,[],[f62,f23,f72,f68,f64]) ).
fof(f77,plain,
( ~ less_than_or_equal(g(upper_bound),upper_bound)
| spl0_6 ),
inference(resolution,[],[f66,f13]) ).
fof(f87,plain,
( less_than_or_equal(l,upper_bound)
| spl0_6 ),
inference(resolution,[],[f77,f11]) ).
fof(f92,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f87,f66]) ).
fof(f93,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f92]) ).
fof(f94,plain,
( ~ less_than_or_equal(lower_bound,upper_bound)
| ~ less_than_or_equal(f(lower_bound),n0)
| spl0_7 ),
inference(resolution,[],[f70,f10]) ).
fof(f99,plain,
( ~ less_than_or_equal(f(lower_bound),n0)
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f94,f14]) ).
fof(f100,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f99,f15]) ).
fof(f101,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f102,plain,
( ~ less_than_or_equal(g(h(l)),h(l))
| spl0_8 ),
inference(resolution,[],[f74,f13]) ).
fof(f126,plain,
( ~ less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(f(g(h(l))),n0)
| less_than_or_equal(f(l),n0)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound)
| spl0_8 ),
inference(resolution,[],[f102,f7]) ).
fof(f131,plain,
( ~ less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(f(g(h(l))),n0)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound)
| spl0_2
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f126,f25]) ).
fof(f132,plain,
( ~ less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(f(g(h(l))),n0)
| ~ less_than_or_equal(l,upper_bound)
| spl0_2
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f131,f69]) ).
fof(f133,plain,
( ~ less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(f(g(h(l))),n0)
| spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f132,f65]) ).
fof(f135,definition,
( spl0_12
<=> less_than_or_equal(f(g(h(l))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f137,plain,
( ~ less_than_or_equal(f(g(h(l))),n0)
| spl0_12 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f139,definition,
( spl0_13
<=> less_than_or_equal(g(h(l)),l) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f141,plain,
( ~ less_than_or_equal(g(h(l)),l)
| spl0_13 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f133,f72,f68,f64,f23,f139,f135]) ).
fof(f164,plain,
( less_than_or_equal(l,h(l))
| spl0_12 ),
inference(resolution,[],[f137,f12]) ).
fof(f171,definition,
( spl0_14
<=> less_than_or_equal(g(h(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f173,plain,
( ~ less_than_or_equal(g(h(l)),upper_bound)
| spl0_14 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f183,plain,
( $false
| spl0_8
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f164,f74]) ).
fof(f184,plain,
( spl0_8
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f183]) ).
fof(f202,plain,
( ~ less_than_or_equal(g(h(l)),upper_bound)
| ~ less_than_or_equal(f(g(h(l))),n0)
| spl0_13 ),
inference(resolution,[],[f141,f10]) ).
fof(f207,plain,
( ~ spl0_12
| ~ spl0_14
| spl0_13 ),
inference(avatar_split_clause,[],[f202,f139,f171,f135]) ).
fof(f212,plain,
( less_than_or_equal(l,h(l))
| spl0_14 ),
inference(resolution,[],[f173,f11]) ).
fof(f219,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f212,f171,f72]) ).
fof(f220,plain,
( ! [X0] :
( ~ less_than_or_equal(l,X0)
| ~ less_than_or_equal(n0,f(X0))
| less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound) )
| spl0_1 ),
inference(resolution,[],[f21,f9]) ).
fof(f221,plain,
( ~ less_than_or_equal(k(l),l)
| ~ less_than_or_equal(lower_bound,l)
| ~ less_than_or_equal(l,upper_bound)
| spl0_1 ),
inference(resolution,[],[f21,f8]) ).
fof(f226,plain,
( ~ less_than_or_equal(k(l),l)
| ~ less_than_or_equal(l,upper_bound)
| spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f221,f69]) ).
fof(f227,plain,
( ! [X0] :
( ~ less_than_or_equal(l,X0)
| ~ less_than_or_equal(n0,f(X0))
| less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(l,upper_bound) )
| spl0_1
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f220,f69]) ).
fof(f228,plain,
( ~ less_than_or_equal(k(l),l)
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f226,f65]) ).
fof(f229,plain,
( ! [X0] :
( less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(l,X0) )
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f227,f65]) ).
fof(f232,plain,
( ~ less_than_or_equal(q(l,k(l)),l)
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f228,f5]) ).
fof(f233,plain,
( ~ less_than_or_equal(k(l),q(l,k(l)))
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f228,f4]) ).
fof(f240,definition,
( spl0_20
<=> less_than_or_equal(k(l),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f241,plain,
( less_than_or_equal(k(l),upper_bound)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| spl0_20 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f307,plain,
( ~ less_than_or_equal(n0,f(upper_bound))
| ~ less_than_or_equal(l,upper_bound)
| spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(resolution,[],[f242,f229]) ).
fof(f312,plain,
( ~ less_than_or_equal(l,upper_bound)
| spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f307,f16]) ).
fof(f313,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f312,f65]) ).
fof(f314,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f315,plain,
( ~ less_than_or_equal(q(l,k(l)),upper_bound)
| ~ less_than_or_equal(f(q(l,k(l))),n0)
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f232,f10]) ).
fof(f319,plain,
( less_than_or_equal(l,q(l,k(l)))
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f232,f2]) ).
fof(f321,definition,
( spl0_27
<=> less_than_or_equal(f(q(l,k(l))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f323,plain,
( ~ less_than_or_equal(f(q(l,k(l))),n0)
| spl0_27 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f325,definition,
( spl0_28
<=> less_than_or_equal(q(l,k(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f327,plain,
( ~ less_than_or_equal(q(l,k(l)),upper_bound)
| spl0_28 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f328,plain,
( ~ spl0_27
| ~ spl0_28
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f315,f68,f64,f19,f325,f321]) ).
fof(f357,plain,
( ~ less_than_or_equal(n0,f(q(l,k(l))))
| ~ less_than_or_equal(l,q(l,k(l)))
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f233,f229]) ).
fof(f358,plain,
( ! [X0] :
( ~ less_than_or_equal(k(l),X0)
| ~ less_than_or_equal(X0,q(l,k(l))) )
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(resolution,[],[f233,f3]) ).
fof(f363,definition,
( spl0_31
<=> less_than_or_equal(l,q(l,k(l))) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f367,definition,
( spl0_32
<=> less_than_or_equal(n0,f(q(l,k(l)))) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f370,plain,
( ~ spl0_31
| ~ spl0_32
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f357,f68,f64,f19,f367,f363]) ).
fof(f536,plain,
( spl0_31
| spl0_1
| ~ spl0_6
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f319,f68,f64,f19,f363]) ).
fof(f708,plain,
( less_than_or_equal(n0,f(q(l,k(l))))
| spl0_27 ),
inference(resolution,[],[f323,f2]) ).
fof(f709,plain,
( spl0_32
| spl0_27 ),
inference(avatar_split_clause,[],[f708,f321,f367]) ).
fof(f727,plain,
( less_than_or_equal(upper_bound,q(l,k(l)))
| spl0_28 ),
inference(resolution,[],[f327,f2]) ).
fof(f1020,plain,
( ~ less_than_or_equal(upper_bound,q(l,k(l)))
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20 ),
inference(resolution,[],[f358,f241]) ).
fof(f1733,plain,
( $false
| spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1020,f727]) ).
fof(f1734,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| spl0_28 ),
inference(avatar_contradiction_clause,[],[f1733]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f26]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f76]) ).
cnf(s7,plain,
spl0_6,
inference(sat_conversion,[],[f93]) ).
cnf(s8,plain,
spl0_7,
inference(sat_conversion,[],[f101]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_7
| spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f142]) ).
cnf(s12,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f184]) ).
cnf(s14,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f207]) ).
cnf(s17,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f219]) ).
cnf(s23,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_20 ),
inference(sat_conversion,[],[f314]) ).
cnf(s24,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_27
| ~ spl0_28 ),
inference(sat_conversion,[],[f328]) ).
cnf(s27,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_31
| ~ spl0_32 ),
inference(sat_conversion,[],[f370]) ).
cnf(s36,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| spl0_31 ),
inference(sat_conversion,[],[f536]) ).
cnf(s48,plain,
( spl0_27
| spl0_32 ),
inference(sat_conversion,[],[f709]) ).
cnf(s109,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_20
| spl0_28 ),
inference(sat_conversion,[],[f1734]) ).
cnf(s110,plain,
( spl0_2
| ~ spl0_8 ),
inference(rat,[],[s5,s8,s7]) ).
cnf(s112,plain,
spl0_1,
inference(rat,[],[s24,s48,s109,s27,s23,s36,s8,s7]) ).
cnf(s113,plain,
~ spl0_2,
inference(rat,[],[s1,s112]) ).
cnf(s114,plain,
~ spl0_8,
inference(rat,[],[s110,s113]) ).
cnf(s115,plain,
spl0_14,
inference(rat,[],[s17,s114]) ).
cnf(s116,plain,
spl0_12,
inference(rat,[],[s12,s114]) ).
cnf(s117,plain,
spl0_13,
inference(rat,[],[s14,s115,s116]) ).
cnf(s118,plain,
$false,
inference(rat,[],[s10,s114,s113,s7,s8,s117,s116]) ).
fof(f1735,plain,
$false,
inference(avatar_sat_refutation,[],[s118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:24:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.23 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
% 2.99/1.10 % (1516309)Input is clausal, will run a generic CNF schedule.
% 2.99/1.10 % (1516318)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3965609005:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.99/1.10 % (1516318)Instruction limit reached!
% 2.99/1.10 % (1516318)------------------------------
% 2.99/1.10 % (1516318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.10 % (1516318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.10 % (1516318)CaDiCaL version: 2.1.3
% 2.99/1.10 % (1516318)Termination reason: Instruction limit
% 2.99/1.10 % (1516318)Termination phase: Saturation
% 2.99/1.10 % (1516318)Time elapsed: 0.026 s
% 2.99/1.10 % (1516318)Peak memory usage: 88 MB
% 2.99/1.10 % (1516318)Instructions burned: 119 (million)
% 2.99/1.10 % (1516319)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2502836706:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.99/1.10 % (1516320)dis-21_1_sil=8000:lcm=predicate:random_seed=497565305: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)
% 2.99/1.10 % (1516315)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1152445823:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.99/1.10 % (1516316)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2755927450:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.99/1.10 % (1516314)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=2884418742:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.99/1.10 % (1516317)lrs+10_1_sil=8000:sp=occurrence:random_seed=4013961280:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.99/1.10 % (1516319)First to succeed.
% 2.99/1.10 % (1516319)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1516309"
% 2.99/1.10 % (1516317)Instruction limit reached!
% 2.99/1.10 % (1516317)------------------------------
% 2.99/1.10 % (1516317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.10 % (1516317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.10 % (1516317)CaDiCaL version: 2.1.3
% 2.99/1.10 % (1516317)Termination reason: Instruction limit
% 2.99/1.10 % (1516317)Termination phase: Saturation
% 2.99/1.10 % (1516317)Time elapsed: 0.067 s
% 2.99/1.10 % (1516317)Peak memory usage: 88 MB
% 2.99/1.10 % (1516317)Instructions burned: 108 (million)
% 2.99/1.10 % (1516320)Instruction limit reached!
% 2.99/1.10 % (1516320)------------------------------
% 2.99/1.10 % (1516320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.10 % (1516320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.10 % (1516320)CaDiCaL version: 2.1.3
% 2.99/1.10 % (1516320)Termination reason: Instruction limit
% 2.99/1.10 % (1516320)Termination phase: Saturation
% 2.99/1.10 % (1516320)Time elapsed: 0.076 s
% 2.99/1.10 % (1516320)Peak memory usage: 89 MB
% 2.99/1.10 % (1516320)Instructions burned: 117 (million)
% 2.99/1.10 % (1516328)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2648087276:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.99/1.10 % (1516328)Instruction limit reached!
% 2.99/1.10 % (1516328)------------------------------
% 2.99/1.10 % (1516328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.10 % (1516328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.10 % (1516328)CaDiCaL version: 2.1.3
% 2.99/1.10 % (1516328)Termination reason: Instruction limit
% 2.99/1.10 % (1516328)Termination phase: Saturation
% 2.99/1.10 % (1516328)Time elapsed: 0.047 s
% 2.99/1.10 % (1516328)Peak memory usage: 89 MB
% 2.99/1.10 % (1516328)Instructions burned: 147 (million)
% 2.99/1.10 % (1516329)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2661689566:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 2.99/1.10 % (1516330)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2956749916:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.99/1.10 % (1516332)lrs+10_64_to=lpo:sil=8000:random_seed=3142014487:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 2.99/1.10 % (1516332)Instruction limit reached!
% 2.99/1.10 % (1516332)------------------------------
% 2.99/1.10 % (1516332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.10 % (1516332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.10 % (1516332)CaDiCaL version: 2.1.3
% 2.99/1.10 % (1516332)Termination reason: Instruction limit
% 2.99/1.10 % (1516332)Termination phase: Saturation
% 2.99/1.10 % (1516332)Time elapsed: 0.038 s
% 2.99/1.10 % (1516332)Peak memory usage: 88 MB
% 2.99/1.10 % (1516332)Instructions burned: 129 (million)
% 2.99/1.10 % (1516319)Refutation found. Thanks to Tanya!
% 2.99/1.10 % SZS status Unsatisfiable for theBenchmark
% 2.99/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.19 % (1516319)------------------------------
% 3.56/1.19 % (1516319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.19 % (1516319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.19 % (1516319)CaDiCaL version: 2.1.3
% 3.56/1.19 % (1516319)Termination reason: Refutation
% 3.56/1.19 % (1516319)Time elapsed: 0.027 s
% 3.56/1.19 % (1516319)Peak memory usage: 89 MB
% 3.56/1.19 % (1516319)Instructions burned: 35 (million)
% 3.56/1.19 % (1516319)------------------------------
% 3.56/1.19 % (1516319)------------------------------
% 3.56/1.19 % (1516309)Success in time 0.427 s
% 3.56/1.19 % Vampire exiting
%------------------------------------------------------------------------------