%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 27
% Syntax : Number of formulae : 128 ( 18 unt; 10 def)
% Number of atoms : 361 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 400 ( 167 ~; 223 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : less_than_or_equal(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f4,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(f5,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(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/sandbox2/benchmark/theBenchmark.p',continuity1) ).
fof(f7,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))
| ~ less_than_or_equal(lower_bound,X0)
| ~ less_than_or_equal(X0,upper_bound) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',crossover3_and_g_function2) ).
fof(f13,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(f14,axiom,
less_than_or_equal(lower_bound,upper_bound),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_interval) ).
fof(f15,axiom,
less_than_or_equal(f(lower_bound),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_mapping) ).
fof(f16,axiom,
less_than_or_equal(n0,f(upper_bound)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_there_is_x_which_crosses) ).
fof(f18,plain,
! [X0] : ~ less_than_or_equal(X0,X0),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( ~ less_than_or_equal(X1,X0)
| ~ less_than_or_equal(X0,X1) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f20,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,[],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( less_than_or_equal(X0,q(X1,X0))
| ~ less_than_or_equal(X0,X1) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f22,plain,
! [X0,X1] :
( less_than_or_equal(q(X0,X1),X0)
| ~ less_than_or_equal(X1,X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f23,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f24,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))
| less_than_or_equal(lower_bound,X0)
| less_than_or_equal(X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f25,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f26,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)
| less_than_or_equal(lower_bound,X0)
| less_than_or_equal(X0,upper_bound) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f27,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,[],[f10]) ).
fof(f28,plain,
! [X0] :
( ~ less_than_or_equal(g(X0),upper_bound)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f29,plain,
! [X0] :
( ~ less_than_or_equal(f(g(X0)),n0)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f30,plain,
! [X0] :
( less_than_or_equal(g(X0),X0)
| ~ less_than_or_equal(l,X0) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f31,plain,
~ less_than_or_equal(lower_bound,upper_bound),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f32,plain,
~ less_than_or_equal(f(lower_bound),n0),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f33,plain,
~ less_than_or_equal(n0,f(upper_bound)),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f34,plain,
( less_than_or_equal(f(l),n0)
| less_than_or_equal(n0,f(l)) ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f36,definition,
( spl0_1
<=> less_than_or_equal(n0,f(l)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f38,plain,
( less_than_or_equal(n0,f(l))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f40,definition,
( spl0_2
<=> less_than_or_equal(f(l),n0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f42,plain,
( less_than_or_equal(f(l),n0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f34,f40,f36]) ).
fof(f46,plain,
( ~ less_than_or_equal(l,upper_bound)
| ~ less_than_or_equal(l,upper_bound) ),
inference(resolution,[],[f30,f28]) ).
fof(f48,plain,
~ less_than_or_equal(l,upper_bound),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f50,plain,
! [X0,X1] :
( ~ less_than_or_equal(X1,q(X1,X0))
| ~ less_than_or_equal(X0,X1) ),
inference(resolution,[],[f22,f19]) ).
fof(f51,plain,
! [X2,X0,X1] :
( less_than_or_equal(X1,q(X2,X0))
| less_than_or_equal(X0,X1)
| ~ less_than_or_equal(X0,X2) ),
inference(resolution,[],[f20,f21]) ).
fof(f53,plain,
( ! [X0] :
( less_than_or_equal(f(l),X0)
| less_than_or_equal(X0,n0) )
| ~ spl0_2 ),
inference(resolution,[],[f20,f42]) ).
fof(f58,plain,
! [X0] :
( less_than_or_equal(f(q(l,X0)),n0)
| less_than_or_equal(q(l,X0),upper_bound)
| ~ less_than_or_equal(X0,l) ),
inference(resolution,[],[f27,f22]) ).
fof(f80,definition,
( spl0_6
<=> less_than_or_equal(lower_bound,l) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f81,plain,
( ~ less_than_or_equal(lower_bound,l)
| spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f82,plain,
( less_than_or_equal(lower_bound,l)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f84,definition,
( spl0_7
<=> less_than_or_equal(l,h(l)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f86,plain,
( less_than_or_equal(l,h(l))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f93,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,[],[f25,f38]) ).
fof(f94,plain,
( less_than_or_equal(k(l),l)
| less_than_or_equal(lower_bound,l)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f93,f48]) ).
fof(f96,definition,
( spl0_8
<=> less_than_or_equal(k(l),l) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f98,plain,
( less_than_or_equal(k(l),l)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f102,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(resolution,[],[f42,f23]) ).
fof(f105,plain,
( less_than_or_equal(l,h(l))
| less_than_or_equal(lower_bound,l)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f102,f48]) ).
fof(f106,plain,
( spl0_6
| spl0_7
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f105,f40,f84,f80]) ).
fof(f110,definition,
( spl0_9
<=> ! [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_9])],[avatar_definition]) ).
fof(f111,plain,
( ! [X0] :
( ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f113,plain,
( less_than_or_equal(lower_bound,upper_bound)
| less_than_or_equal(f(lower_bound),n0)
| ~ spl0_6 ),
inference(resolution,[],[f82,f27]) ).
fof(f116,plain,
( less_than_or_equal(f(lower_bound),n0)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f113,f31]) ).
fof(f117,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f116,f32]) ).
fof(f118,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f117]) ).
fof(f121,plain,
( ! [X0] :
( less_than_or_equal(n0,n0)
| less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(lower_bound,l)
| less_than_or_equal(l,upper_bound) )
| ~ spl0_2 ),
inference(resolution,[],[f53,f24]) ).
fof(f127,plain,
( ! [X0] :
( less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(lower_bound,l)
| less_than_or_equal(l,upper_bound) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f121,f18]) ).
fof(f128,plain,
( ! [X0] :
( less_than_or_equal(X0,l)
| less_than_or_equal(f(X0),n0)
| ~ less_than_or_equal(X0,h(l))
| less_than_or_equal(l,upper_bound) )
| ~ spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f127,f81]) ).
fof(f129,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_6 ),
inference(forward_subsumption_resolution,[],[f128,f48]) ).
fof(f130,plain,
( spl0_9
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f129,f80,f40,f110]) ).
fof(f134,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_9 ),
inference(resolution,[],[f111,f30]) ).
fof(f135,plain,
( less_than_or_equal(g(h(l)),l)
| ~ less_than_or_equal(l,h(l))
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f134,f29]) ).
fof(f145,plain,
( less_than_or_equal(g(h(l)),l)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f135,f86]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ less_than_or_equal(q(X2,X0),X1)
| ~ less_than_or_equal(X0,X2)
| less_than_or_equal(X0,X1) ),
inference(resolution,[],[f51,f19]) ).
fof(f190,plain,
! [X0] :
( ~ less_than_or_equal(n0,f(q(l,X0)))
| ~ less_than_or_equal(X0,l)
| less_than_or_equal(q(l,X0),upper_bound) ),
inference(resolution,[],[f58,f19]) ).
fof(f193,plain,
( less_than_or_equal(g(h(l)),upper_bound)
| less_than_or_equal(f(g(h(l))),n0)
| ~ spl0_7
| ~ spl0_9 ),
inference(resolution,[],[f145,f27]) ).
fof(f197,definition,
( spl0_14
<=> less_than_or_equal(f(g(h(l))),n0) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f199,plain,
( less_than_or_equal(f(g(h(l))),n0)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl0_15
<=> less_than_or_equal(g(h(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f203,plain,
( less_than_or_equal(g(h(l)),upper_bound)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( spl0_14
| spl0_15
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f193,f110,f84,f201,f197]) ).
fof(f494,plain,
( ~ less_than_or_equal(l,h(l))
| ~ spl0_14 ),
inference(resolution,[],[f199,f29]) ).
fof(f514,plain,
( $false
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f494,f86]) ).
fof(f515,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f516,plain,
( ~ less_than_or_equal(l,h(l))
| ~ spl0_15 ),
inference(resolution,[],[f203,f28]) ).
fof(f521,plain,
( $false
| ~ spl0_7
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f516,f86]) ).
fof(f522,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f521]) ).
fof(f523,plain,
( less_than_or_equal(k(l),l)
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f94,f81]) ).
fof(f533,plain,
( spl0_8
| ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f523,f80,f36,f96]) ).
fof(f534,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,[],[f38,f26]) ).
fof(f541,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_6 ),
inference(forward_subsumption_resolution,[],[f534,f81]) ).
fof(f543,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 ),
inference(forward_subsumption_resolution,[],[f541,f48]) ).
fof(f555,definition,
( spl0_35
<=> less_than_or_equal(k(l),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f556,plain,
( ~ less_than_or_equal(k(l),upper_bound)
| spl0_35 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f557,plain,
( less_than_or_equal(k(l),upper_bound)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f563,definition,
( spl0_37
<=> less_than_or_equal(q(l,k(l)),upper_bound) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f565,plain,
( less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f626,plain,
( ! [X0] :
( less_than_or_equal(n0,f(q(X0,k(l))))
| less_than_or_equal(l,q(X0,k(l)))
| ~ less_than_or_equal(k(l),X0) )
| ~ spl0_1
| spl0_6 ),
inference(resolution,[],[f543,f21]) ).
fof(f640,plain,
( less_than_or_equal(n0,f(upper_bound))
| less_than_or_equal(l,upper_bound)
| ~ spl0_1
| spl0_6
| ~ spl0_35 ),
inference(resolution,[],[f557,f543]) ).
fof(f645,plain,
( less_than_or_equal(l,upper_bound)
| ~ spl0_1
| spl0_6
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f640,f33]) ).
fof(f646,plain,
( $false
| ~ spl0_1
| spl0_6
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f645,f48]) ).
fof(f647,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f646]) ).
fof(f848,plain,
( less_than_or_equal(l,q(l,k(l)))
| ~ less_than_or_equal(k(l),l)
| ~ less_than_or_equal(k(l),l)
| less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_1
| spl0_6 ),
inference(resolution,[],[f626,f190]) ).
fof(f855,plain,
( less_than_or_equal(l,q(l,k(l)))
| ~ less_than_or_equal(k(l),l)
| less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_1
| spl0_6 ),
inference(duplicate_literal_removal,[],[f848]) ).
fof(f856,plain,
( ~ less_than_or_equal(k(l),l)
| less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_1
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f855,f50]) ).
fof(f857,plain,
( less_than_or_equal(q(l,k(l)),upper_bound)
| ~ spl0_1
| spl0_6
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f856,f98]) ).
fof(f858,plain,
( spl0_37
| ~ spl0_1
| spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f857,f96,f80,f36,f563]) ).
fof(f892,plain,
( ~ less_than_or_equal(k(l),l)
| less_than_or_equal(k(l),upper_bound)
| ~ spl0_37 ),
inference(resolution,[],[f565,f174]) ).
fof(f897,plain,
( less_than_or_equal(k(l),upper_bound)
| ~ spl0_8
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f892,f98]) ).
fof(f899,plain,
( $false
| ~ spl0_8
| spl0_35
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f897,f556]) ).
fof(f900,plain,
( ~ spl0_8
| spl0_35
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f899]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s11,plain,
( ~ spl0_2
| spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f106]) ).
cnf(s13,plain,
~ spl0_6,
inference(sat_conversion,[],[f118]) ).
cnf(s14,plain,
( ~ spl0_2
| spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f130]) ).
cnf(s19,plain,
( ~ spl0_7
| ~ spl0_9
| spl0_14
| spl0_15 ),
inference(sat_conversion,[],[f204]) ).
cnf(s33,plain,
( ~ spl0_7
| ~ spl0_14 ),
inference(sat_conversion,[],[f515]) ).
cnf(s34,plain,
( ~ spl0_7
| ~ spl0_15 ),
inference(sat_conversion,[],[f522]) ).
cnf(s37,plain,
( ~ spl0_1
| spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f533]) ).
cnf(s48,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_35 ),
inference(sat_conversion,[],[f647]) ).
cnf(s74,plain,
( ~ spl0_1
| spl0_6
| ~ spl0_8
| spl0_37 ),
inference(sat_conversion,[],[f858]) ).
cnf(s80,plain,
( ~ spl0_8
| spl0_35
| ~ spl0_37 ),
inference(sat_conversion,[],[f900]) ).
cnf(s82,plain,
( ~ spl0_2
| spl0_7 ),
inference(rat,[],[s11,s13]) ).
cnf(s88,plain,
~ spl0_2,
inference(rat,[],[s19,s33,s34,s82,s14,s13]) ).
cnf(s89,plain,
spl0_1,
inference(rat,[],[s1,s88]) ).
cnf(s90,plain,
~ spl0_35,
inference(rat,[],[s48,s13,s89]) ).
cnf(s91,plain,
spl0_8,
inference(rat,[],[s37,s13,s89]) ).
cnf(s92,plain,
~ spl0_37,
inference(rat,[],[s80,s90,s91]) ).
cnf(s97,plain,
$false,
inference(rat,[],[s74,s89,s13,s92,s91]) ).
fof(f901,plain,
$false,
inference(avatar_sat_refutation,[],[s97]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n016.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 20:30:04 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.20/0.27 % (3953219)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (3953227)dis+10_1_sil=32000:sp=arity:random_seed=2074766731:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (3953225)% WARNING: option uhcvi not known.
% 0.20/0.27 % (3953224)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4169426139_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (3953226)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3869766149:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (3953225)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4210300697:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (3953228)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3469523657:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (3953230)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1302085383:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (3953229)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=276288576:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % TRYING [1]
% 0.20/0.27 % TRYING [2]
% 0.20/0.27 % TRYING [3]
% 0.20/0.27 % TRYING [4]
% 0.20/0.27 % TRYING [5]
% 0.20/0.27 % TRYING [6]
% 0.20/0.27 % TRYING [7]
% 0.20/0.27 % (3953225) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3953219-3953225"...
% 0.20/0.27 % (3953225)...printing done.
% 0.20/0.27 % (3953225)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (3953225)------------------------------
% 0.20/0.28 % (3953225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (3953225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (3953225)CaDiCaL version: 2.1.3
% 0.20/0.28 % (3953225)Termination reason: Refutation
% 0.20/0.28 % (3953225)Time elapsed: 0.021 s
% 0.20/0.28 % (3953225)Peak memory usage: 12 MB
% 0.20/0.28 % (3953225)Instructions burned: 27 (million)
% 0.20/0.28 % (3953219)Success in time 0.055 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------