%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA002-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 09:31:13 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 33
% Syntax : Number of formulae : 150 ( 23 unt; 15 def)
% Number of atoms : 374 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 412 ( 188 ~; 209 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 16 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( in_interval(X0,X1,X2)
| ~ less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_interval) ).
fof(f2,axiom,
! [X0] : less_than_or_equal(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_less) ).
fof(f3,axiom,
! [X0,X1] :
( less_than_or_equal(X0,X1)
| less_than_or_equal(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_less) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f5,axiom,
! [X0,X1] :
( ~ less_than_or_equal(X0,q(X1,X0))
| less_than_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation1) ).
fof(f6,axiom,
! [X0,X1] :
( ~ less_than_or_equal(q(X0,X1),X0)
| less_than_or_equal(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interpolation2) ).
fof(f7,axiom,
! [X0] :
( less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(X0))
| ~ in_interval(lower_bound,X0,upper_bound) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
fof(f8,axiom,
! [X0,X1] :
( less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(f(X1),n0)
| less_than_or_equal(X1,h(X0))
| ~ in_interval(lower_bound,X0,upper_bound) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
fof(f9,axiom,
! [X0] :
( less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(k(X0),X0)
| ~ in_interval(lower_bound,X0,upper_bound) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity3) ).
fof(f10,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)
| ~ in_interval(lower_bound,X0,upper_bound) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity4) ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p',crossover1) ).
fof(f12,axiom,
! [X0] :
( less_than_or_equal(g(X0),upper_bound)
| less_than_or_equal(l,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover2_and_g_function1) ).
fof(f13,axiom,
! [X0] :
( less_than_or_equal(f(g(X0)),n0)
| less_than_or_equal(l,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
fof(f14,axiom,
! [X0] :
( ~ less_than_or_equal(g(X0),X0)
| less_than_or_equal(l,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',crossover4_and_g_function3) ).
fof(f15,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_interval) ).
fof(f16,axiom,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_mapping) ).
fof(f17,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_mapping) ).
fof(f18,negated_conjecture,
~ in_interval(f(l),n0,f(l)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
fof(f19,plain,
! [X2,X0,X1] :
( in_interval(X0,X1,X2)
| less_than_or_equal(X0,X1)
| less_than_or_equal(X1,X2) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f20,plain,
! [X0] : ~ less_than_or_equal(X0,X0),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(X0,X1) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ less_than_or_equal(X0,X1)
| less_than_or_equal(X0,X2)
| less_than_or_equal(X2,X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( less_than_or_equal(X0,q(X1,X0))
| ~ less_than_or_equal(X0,X1) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( less_than_or_equal(q(X0,X1),X0)
| ~ less_than_or_equal(X1,X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f25,plain,
! [X0] :
( ~ less_than_or_equal(f(X0),n0)
| less_than_or_equal(X0,h(X0))
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( ~ less_than_or_equal(f(X0),n0)
| less_than_or_equal(X1,X0)
| less_than_or_equal(f(X1),n0)
| ~ less_than_or_equal(X1,h(X0))
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f27,plain,
! [X0] :
( ~ less_than_or_equal(n0,f(X0))
| less_than_or_equal(k(X0),X0)
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f28,plain,
! [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)
| ~ in_interval(lower_bound,X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f29,plain,
! [X0] :
( ~ less_than_or_equal(X0,l)
| less_than_or_equal(X0,upper_bound)
| less_than_or_equal(f(X0),n0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f30,plain,
! [X0] :
( ~ less_than_or_equal(g(X0),upper_bound)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f31,plain,
! [X0] :
( ~ less_than_or_equal(f(g(X0)),n0)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f32,plain,
! [X0] :
( less_than_or_equal(g(X0),X0)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f33,plain,
~ less_than_or_equal(lower_bound,upper_bound),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f34,plain,
~ less_than_or_equal(f(lower_bound),n0),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f35,plain,
~ less_than_or_equal(n0,f(upper_bound)),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f36,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(l,upper_bound) ),
inference(resolution,[],[f32,f30]) ).
fof(f38,plain,
~ less_than_or_equal(l,upper_bound),
inference(duplicate_literal_removal,[],[f36]) ).
fof(f40,plain,
! [X0,X1] :
( ~ less_than_or_equal(X1,q(X1,X0))
| ~ less_than_or_equal(X0,X1) ),
inference(resolution,[],[f24,f21]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ less_than_or_equal(X0,X2)
| less_than_or_equal(X1,q(X2,X0))
| less_than_or_equal(X0,X1) ),
inference(resolution,[],[f22,f23]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ less_than_or_equal(X1,X0)
| less_than_or_equal(X2,X0)
| less_than_or_equal(q(X0,X1),X2) ),
inference(resolution,[],[f22,f24]) ).
fof(f44,plain,
( less_than_or_equal(f(l),n0)
| less_than_or_equal(n0,f(l)) ),
inference(resolution,[],[f19,f18]) ).
fof(f46,definition,
( spl0_1
<=> less_than_or_equal(n0,f(l)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f48,plain,
( less_than_or_equal(n0,f(l))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f50,definition,
( spl0_2
<=> less_than_or_equal(f(l),n0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f52,plain,
( less_than_or_equal(f(l),n0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f44,f50,f46]) ).
fof(f56,plain,
( ! [X0] :
( less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(l))
| ~ in_interval(lower_bound,l,upper_bound) )
| ~ spl0_2 ),
inference(resolution,[],[f52,f26]) ).
fof(f57,plain,
( less_than_or_equal(l,h(l))
| ~ in_interval(lower_bound,l,upper_bound)
| ~ spl0_2 ),
inference(resolution,[],[f52,f25]) ).
fof(f62,definition,
( spl0_3
<=> in_interval(lower_bound,l,upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f63,plain,
( in_interval(lower_bound,l,upper_bound)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f64,plain,
( ~ in_interval(lower_bound,l,upper_bound)
| spl0_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl0_4
<=> less_than_or_equal(l,h(l)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f68,plain,
( less_than_or_equal(l,h(l))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f71,definition,
( spl0_5
<=> ! [X0] :
( less_than_or_equal(X0,l)
| ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(f(X0),n0) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f72,plain,
( ! [X0] :
( ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f89,plain,
( less_than_or_equal(lower_bound,l)
| less_than_or_equal(l,upper_bound)
| spl0_3 ),
inference(resolution,[],[f64,f19]) ).
fof(f90,plain,
( less_than_or_equal(lower_bound,l)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f89,f38]) ).
fof(f134,plain,
( less_than_or_equal(k(l),l)
| ~ in_interval(lower_bound,l,upper_bound)
| ~ spl0_1 ),
inference(resolution,[],[f48,f27]) ).
fof(f137,plain,
( ! [X0] :
( less_than_or_equal(X0,f(l))
| less_than_or_equal(n0,X0) )
| ~ spl0_1 ),
inference(resolution,[],[f48,f22]) ).
fof(f140,plain,
( less_than_or_equal(lower_bound,upper_bound)
| less_than_or_equal(f(lower_bound),n0)
| spl0_3 ),
inference(resolution,[],[f90,f29]) ).
fof(f145,plain,
( less_than_or_equal(f(lower_bound),n0)
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f140,f33]) ).
fof(f155,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f145,f34]) ).
fof(f156,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f158,definition,
( spl0_15
<=> less_than_or_equal(k(l),l) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f160,plain,
( less_than_or_equal(k(l),l)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( ~ spl0_3
| spl0_15
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f134,f46,f158,f62]) ).
fof(f163,definition,
( spl0_16
<=> ! [X0] :
( less_than_or_equal(l,X0)
| ~ less_than_or_equal(k(l),X0)
| less_than_or_equal(n0,f(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f164,plain,
( ! [X0] :
( ~ less_than_or_equal(k(l),X0)
| less_than_or_equal(l,X0)
| less_than_or_equal(n0,f(X0)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f168,plain,
( ! [X0] :
( less_than_or_equal(q(l,k(l)),X0)
| less_than_or_equal(X0,l) )
| ~ spl0_15 ),
inference(resolution,[],[f160,f43]) ).
fof(f169,plain,
( ! [X0] :
( less_than_or_equal(X0,q(l,k(l)))
| less_than_or_equal(k(l),X0) )
| ~ spl0_15 ),
inference(resolution,[],[f160,f42]) ).
fof(f177,definition,
( spl0_18
<=> less_than_or_equal(k(l),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f179,plain,
( less_than_or_equal(k(l),upper_bound)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f182,definition,
( spl0_19
<=> less_than_or_equal(q(l,k(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f184,plain,
( less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f186,definition,
( spl0_20
<=> less_than_or_equal(f(q(l,k(l))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f188,plain,
( less_than_or_equal(f(q(l,k(l))),n0)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f196,plain,
( ! [X0] :
( less_than_or_equal(n0,n0)
| less_than_or_equal(l,X0)
| less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(k(l),X0)
| ~ in_interval(lower_bound,l,upper_bound) )
| ~ spl0_1 ),
inference(resolution,[],[f137,f28]) ).
fof(f207,plain,
( ! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(k(l),X0)
| ~ in_interval(lower_bound,l,upper_bound) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f196,f20]) ).
fof(f208,plain,
( ! [X0] :
( less_than_or_equal(l,X0)
| less_than_or_equal(n0,f(X0))
| ~ less_than_or_equal(k(l),X0) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f207,f63]) ).
fof(f209,plain,
( spl0_16
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f208,f62,f46,f163]) ).
fof(f210,plain,
( ! [X0] :
( less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(l)) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f56,f63]) ).
fof(f211,plain,
( less_than_or_equal(l,h(l))
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f57,f63]) ).
fof(f217,plain,
( spl0_5
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f210,f62,f50,f71]) ).
fof(f218,plain,
( spl0_4
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f211,f62,f50,f66]) ).
fof(f464,plain,
( less_than_or_equal(g(h(l)),l)
| less_than_or_equal(f(g(h(l))),n0)
| ~ less_than_or_equal(l,h(l))
| ~ spl0_5 ),
inference(resolution,[],[f72,f32]) ).
fof(f465,plain,
( less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(l,h(l))
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f464,f31]) ).
fof(f475,plain,
( less_than_or_equal(g(h(l)),l)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f465,f68]) ).
fof(f488,definition,
( spl0_41
<=> less_than_or_equal(g(h(l)),l) ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f490,plain,
( less_than_or_equal(g(h(l)),l)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f719,plain,
( ~ less_than_or_equal(upper_bound,q(l,k(l)))
| ~ spl0_19 ),
inference(resolution,[],[f184,f21]) ).
fof(f777,plain,
( less_than_or_equal(l,l)
| less_than_or_equal(q(l,k(l)),upper_bound)
| less_than_or_equal(f(q(l,k(l))),n0)
| ~ spl0_15 ),
inference(resolution,[],[f168,f29]) ).
fof(f780,definition,
( spl0_61
<=> less_than_or_equal(l,q(l,k(l))) ),
introduced(definition,[new_symbols(definition,[spl0_61])],[avatar_definition]) ).
fof(f781,plain,
( less_than_or_equal(l,q(l,k(l)))
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f897,plain,
( less_than_or_equal(k(l),k(l))
| less_than_or_equal(l,q(l,k(l)))
| less_than_or_equal(n0,f(q(l,k(l))))
| ~ spl0_15
| ~ spl0_16 ),
inference(resolution,[],[f169,f164]) ).
fof(f902,plain,
( less_than_or_equal(l,q(l,k(l)))
| less_than_or_equal(n0,f(q(l,k(l))))
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f897,f20]) ).
fof(f918,definition,
( spl0_80
<=> less_than_or_equal(n0,f(q(l,k(l)))) ),
introduced(definition,[new_symbols(definition,[spl0_80])],[avatar_definition]) ).
fof(f921,plain,
( spl0_80
| spl0_61
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f902,f163,f158,f780,f918]) ).
fof(f1491,plain,
( less_than_or_equal(k(l),upper_bound)
| ~ spl0_15
| ~ spl0_19 ),
inference(resolution,[],[f719,f169]) ).
fof(f1492,plain,
( spl0_18
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f1491,f182,f158,f177]) ).
fof(f1493,plain,
( less_than_or_equal(l,upper_bound)
| less_than_or_equal(n0,f(upper_bound))
| ~ spl0_16
| ~ spl0_18 ),
inference(resolution,[],[f179,f164]) ).
fof(f1498,plain,
( less_than_or_equal(n0,f(upper_bound))
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1493,f38]) ).
fof(f1499,plain,
( $false
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1498,f35]) ).
fof(f1500,plain,
( ~ spl0_16
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1499]) ).
fof(f1502,plain,
( less_than_or_equal(q(l,k(l)),upper_bound)
| less_than_or_equal(f(q(l,k(l))),n0)
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f777,f20]) ).
fof(f1504,plain,
( spl0_20
| spl0_19
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f1502,f158,f182,f186]) ).
fof(f1555,plain,
( ~ less_than_or_equal(n0,f(q(l,k(l))))
| ~ spl0_20 ),
inference(resolution,[],[f188,f21]) ).
fof(f1556,plain,
( ~ spl0_80
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1555,f186,f918]) ).
fof(f1934,plain,
( ~ less_than_or_equal(k(l),l)
| ~ spl0_61 ),
inference(resolution,[],[f781,f40]) ).
fof(f1942,plain,
( $false
| ~ spl0_15
| ~ spl0_61 ),
inference(forward_subsumption_resolution,[],[f1934,f160]) ).
fof(f1943,plain,
( ~ spl0_15
| ~ spl0_61 ),
inference(avatar_contradiction_clause,[],[f1942]) ).
fof(f1963,plain,
( spl0_41
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f475,f71,f66,f488]) ).
fof(f2091,plain,
( less_than_or_equal(g(h(l)),upper_bound)
| less_than_or_equal(f(g(h(l))),n0)
| ~ spl0_41 ),
inference(resolution,[],[f490,f29]) ).
fof(f2099,definition,
( spl0_134
<=> less_than_or_equal(f(g(h(l))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_134])],[avatar_definition]) ).
fof(f2101,plain,
( less_than_or_equal(f(g(h(l))),n0)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f2099]) ).
fof(f2103,definition,
( spl0_135
<=> less_than_or_equal(g(h(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_135])],[avatar_definition]) ).
fof(f2105,plain,
( less_than_or_equal(g(h(l)),upper_bound)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f2103]) ).
fof(f2106,plain,
( spl0_134
| spl0_135
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f2091,f488,f2103,f2099]) ).
fof(f2538,plain,
( ~ less_than_or_equal(l,h(l))
| ~ spl0_134 ),
inference(resolution,[],[f2101,f31]) ).
fof(f2560,plain,
( $false
| ~ spl0_4
| ~ spl0_134 ),
inference(forward_subsumption_resolution,[],[f2538,f68]) ).
fof(f2561,plain,
( ~ spl0_4
| ~ spl0_134 ),
inference(avatar_contradiction_clause,[],[f2560]) ).
fof(f2581,plain,
( ~ less_than_or_equal(l,h(l))
| ~ spl0_135 ),
inference(resolution,[],[f2105,f30]) ).
fof(f2588,plain,
( $false
| ~ spl0_4
| ~ spl0_135 ),
inference(forward_subsumption_resolution,[],[f2581,f68]) ).
fof(f2589,plain,
( ~ spl0_4
| ~ spl0_135 ),
inference(avatar_contradiction_clause,[],[f2588]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f53]) ).
cnf(s10,plain,
spl0_3,
inference(sat_conversion,[],[f156]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s16,plain,
( ~ spl0_1
| ~ spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f209]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f217]) ).
cnf(s22,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f218]) ).
cnf(s133,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_61
| spl0_80 ),
inference(sat_conversion,[],[f921]) ).
cnf(s186,plain,
( ~ spl0_15
| spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f1492]) ).
cnf(s187,plain,
( ~ spl0_16
| ~ spl0_18 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s189,plain,
( ~ spl0_15
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f1504]) ).
cnf(s195,plain,
( ~ spl0_20
| ~ spl0_80 ),
inference(sat_conversion,[],[f1556]) ).
cnf(s201,plain,
( ~ spl0_15
| ~ spl0_61 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s218,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_41 ),
inference(sat_conversion,[],[f1963]) ).
cnf(s246,plain,
( ~ spl0_41
| spl0_134
| spl0_135 ),
inference(sat_conversion,[],[f2106]) ).
cnf(s273,plain,
( ~ spl0_4
| ~ spl0_134 ),
inference(sat_conversion,[],[f2561]) ).
cnf(s274,plain,
( ~ spl0_4
| ~ spl0_135 ),
inference(sat_conversion,[],[f2589]) ).
cnf(s279,plain,
~ spl0_2,
inference(rat,[],[s246,s218,s273,s274,s21,s22,s10]) ).
cnf(s280,plain,
spl0_1,
inference(rat,[],[s1,s279]) ).
cnf(s281,plain,
spl0_16,
inference(rat,[],[s16,s10,s280]) ).
cnf(s282,plain,
spl0_15,
inference(rat,[],[s11,s10,s280]) ).
cnf(s283,plain,
~ spl0_18,
inference(rat,[],[s187,s281]) ).
cnf(s284,plain,
~ spl0_61,
inference(rat,[],[s201,s282]) ).
cnf(s291,plain,
~ spl0_19,
inference(rat,[],[s186,s282,s283]) ).
cnf(s293,plain,
spl0_80,
inference(rat,[],[s133,s282,s281,s284]) ).
cnf(s295,plain,
spl0_20,
inference(rat,[],[s189,s282,s291]) ).
cnf(s298,plain,
$false,
inference(rat,[],[s195,s293,s295]) ).
fof(f2590,plain,
$false,
inference(avatar_sat_refutation,[],[s298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA002-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.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 20:25:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.21/0.32 % (3419979)Will run a generic schedule for satisfiability detection.
% 0.21/0.32 % (3419987)dis+10_1_sil=32000:sp=arity:random_seed=1088850989:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.32 % (3419985)% WARNING: option uhcvi not known.
% 0.21/0.32 % (3419986)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=278465306:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.32 % (3419988)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4253652407:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.32 % (3419984)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3671614314_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.32 % (3419985)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1233516241:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.32 % (3419989)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=316845902:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.32 % (3419990)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2988666359:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.32 % TRYING [1]
% 0.21/0.32 % TRYING [2]
% 0.21/0.32 % TRYING [3]
% 0.21/0.32 % TRYING [4]
% 0.21/0.32 % TRYING [5]
% 0.21/0.32 % TRYING [6]
% 0.21/0.32 % (3419987)Instruction limit reached!
% 0.21/0.32 % (3419987)------------------------------
% 0.21/0.32 % (3419987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419987)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419987)Termination reason: Instruction limit
% 0.21/0.32 % (3419987)Termination phase: Saturation
% 0.21/0.32 % (3419987)Time elapsed: 0.037 s
% 0.21/0.32 % (3419987)Peak memory usage: 12 MB
% 0.21/0.32 % (3419987)Instructions burned: 107 (million)
% 0.21/0.32 % TRYING [7]
% 0.21/0.32 % (3419998)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1437292354:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.32 % TRYING [1]
% 0.21/0.32 % TRYING [2]
% 0.21/0.32 % TRYING [3]
% 0.21/0.32 % TRYING [4]
% 0.21/0.32 % TRYING [5]
% 0.21/0.32 % TRYING [6]
% 0.21/0.32 % (3419985) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3419979-3419985"...
% 0.21/0.32 % (3419985)...printing done.
% 0.21/0.32 % (3419985)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (3419985)------------------------------
% 0.21/0.32 % (3419985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419985)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419985)Termination reason: Refutation
% 0.21/0.32 % (3419985)Time elapsed: 0.053 s
% 0.21/0.32 % (3419985)Peak memory usage: 13 MB
% 0.21/0.32 % (3419985)Instructions burned: 76 (million)
% 0.21/0.32 % (3419979)Success in time 0.088 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------