%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 11:58:51 AM UTC 2026
% Result : Theorem 0.98s 0.59s
% Output : Refutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 36
% Syntax : Number of formulae : 165 ( 54 unt; 18 def)
% Number of atoms : 411 ( 25 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 463 ( 217 ~; 210 |; 2 &)
% ( 23 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 28 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn 147 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f43,conjecture,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(f44,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ r1,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
=> r1 ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f47,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f48,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(X0)
& is_a_theorem(implies(X0,X1)) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f52,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f51]) ).
fof(f53,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) )
| ~ modus_ponens ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f56,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f48]) ).
fof(f57,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f47]) ).
fof(f58,plain,
( r1
| ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f59,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f61,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f66,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f67,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f57]) ).
fof(f69,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| r1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f70,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f74,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f75,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f76,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f77,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f78,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f79,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f80,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f81,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f83,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f86,plain,
~ r1,
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X0,X1] :
( modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(consistent_polarity_flipping,[],[f64]) ).
fof(f88,plain,
! [X0] :
( kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(consistent_polarity_flipping,[],[f66]) ).
fof(f89,plain,
! [X2,X0,X1] :
( kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(consistent_polarity_flipping,[],[f68]) ).
fof(f90,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| ~ r1 ),
inference(consistent_polarity_flipping,[],[f69]) ).
fof(f91,plain,
! [X0,X1] :
( op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f74]) ).
fof(f92,plain,
~ op_equiv,
inference(consistent_polarity_flipping,[],[f77]) ).
fof(f93,plain,
~ modus_ponens,
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f94,plain,
~ kn1,
inference(consistent_polarity_flipping,[],[f79]) ).
fof(f95,plain,
~ kn3,
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f97,plain,
r1,
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f99,definition,
( spl1_1
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f100,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,definition,
( spl1_2
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f105,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f91,f102,f99]) ).
fof(f107,definition,
( spl1_3
<=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,definition,
( spl1_4
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f113,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f73,f110,f107]) ).
fof(f115,definition,
( spl1_5
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f116,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl1_6
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f121,plain,
( spl1_5
| ~ spl1_6 ),
inference(avatar_split_clause,[],[f72,f118,f115]) ).
fof(f131,definition,
( spl1_9
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f132,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,definition,
( spl1_10
<=> op_or ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f137,plain,
( spl1_9
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f70,f134,f131]) ).
fof(f139,definition,
( spl1_11
<=> r1 ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f143,definition,
( spl1_12
<=> is_a_theorem(implies(or(sK0,sK0),sK0)) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f145,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| spl1_12 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f146,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f90,f143,f139]) ).
fof(f148,definition,
( spl1_13
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
introduced(definition,[new_symbols(definition,[spl1_13])],[avatar_definition]) ).
fof(f149,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,definition,
( spl1_14
<=> kn3 ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f154,plain,
( spl1_13
| spl1_14 ),
inference(avatar_split_clause,[],[f89,f151,f148]) ).
fof(f156,definition,
( spl1_15
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[spl1_15])],[avatar_definition]) ).
fof(f157,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,definition,
( spl1_16
<=> kn2 ),
introduced(definition,[new_symbols(definition,[spl1_16])],[avatar_definition]) ).
fof(f162,plain,
( spl1_15
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f67,f159,f156]) ).
fof(f164,definition,
( spl1_17
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[spl1_17])],[avatar_definition]) ).
fof(f165,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl1_17 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,definition,
( spl1_18
<=> kn1 ),
introduced(definition,[new_symbols(definition,[spl1_18])],[avatar_definition]) ).
fof(f170,plain,
( spl1_17
| spl1_18 ),
inference(avatar_split_clause,[],[f88,f167,f164]) ).
fof(f180,definition,
( spl1_21
<=> ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl1_21])],[avatar_definition]) ).
fof(f181,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ spl1_21 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,definition,
( spl1_22
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[spl1_22])],[avatar_definition]) ).
fof(f186,plain,
( spl1_21
| spl1_22 ),
inference(avatar_split_clause,[],[f87,f183,f180]) ).
fof(f187,plain,
spl1_11,
inference(avatar_split_clause,[],[f97,f139]) ).
fof(f188,plain,
spl1_10,
inference(avatar_split_clause,[],[f75,f134]) ).
fof(f189,plain,
spl1_6,
inference(avatar_split_clause,[],[f76,f118]) ).
fof(f190,plain,
spl1_16,
inference(avatar_split_clause,[],[f80,f159]) ).
fof(f192,plain,
spl1_4,
inference(avatar_split_clause,[],[f83,f110]) ).
fof(f194,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f92,f102]) ).
fof(f195,plain,
~ spl1_22,
inference(avatar_split_clause,[],[f93,f183]) ).
fof(f196,plain,
~ spl1_18,
inference(avatar_split_clause,[],[f94,f167]) ).
fof(f197,plain,
~ spl1_14,
inference(avatar_split_clause,[],[f95,f151]) ).
fof(f199,plain,
( ! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) )
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f181,f165]) ).
fof(f201,plain,
( ! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2)
| ~ spl1_3
| ~ spl1_5 ),
inference(superposition,[],[f108,f116]) ).
fof(f208,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2)))
| ~ spl1_5
| ~ spl1_9 ),
inference(superposition,[],[f132,f116]) ).
fof(f214,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl1_5
| ~ spl1_9 ),
inference(superposition,[],[f132,f116]) ).
fof(f221,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2)
| ~ spl1_5
| ~ spl1_9 ),
inference(forward_demodulation,[],[f208,f116]) ).
fof(f231,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ spl1_1
| ~ spl1_15 ),
inference(superposition,[],[f157,f100]) ).
fof(f232,plain,
( ! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) )
| ~ spl1_1
| ~ spl1_17
| ~ spl1_21 ),
inference(superposition,[],[f199,f100]) ).
fof(f234,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13 ),
inference(forward_demodulation,[],[f149,f214]) ).
fof(f235,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(or(and(X0,X1),not(and(X1,X2)))) )
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_21 ),
inference(resolution,[],[f234,f181]) ).
fof(f245,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1)))
| ~ spl1_1
| ~ spl1_5
| ~ spl1_9
| ~ spl1_15 ),
inference(superposition,[],[f231,f214]) ).
fof(f255,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_15 ),
inference(superposition,[],[f157,f201]) ).
fof(f305,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0)))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_15 ),
inference(superposition,[],[f255,f214]) ).
fof(f477,plain,
( ! [X0,X1] : is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0))))
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f235,f165]) ).
fof(f938,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) )
| ~ spl1_1
| ~ spl1_5
| ~ spl1_9
| ~ spl1_15
| ~ spl1_21 ),
inference(resolution,[],[f245,f181]) ).
fof(f1160,plain,
( ! [X0,X1] : is_a_theorem(or(and(and(not(X1),not(X1)),not(X0)),or(X0,X1)))
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(superposition,[],[f477,f132]) ).
fof(f1168,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(and(not(X1),not(X1)),X0),or(X0,X1)))
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(forward_demodulation,[],[f1160,f221]) ).
fof(f1179,plain,
( ! [X0,X1] : is_a_theorem(implies(or(implies(not(X1),X1),X0),or(X0,X1)))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(forward_demodulation,[],[f1168,f201]) ).
fof(f1186,plain,
( ! [X0,X1] : is_a_theorem(implies(or(or(X1,X1),X0),or(X0,X1)))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(forward_demodulation,[],[f1179,f214]) ).
fof(f2286,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(or(X1,X1),X0))
| is_a_theorem(or(X0,X1)) )
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f1186,f181]) ).
fof(f4634,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f2286,f305]) ).
fof(f4663,plain,
( ! [X0] : is_a_theorem(implies(X0,X0))
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(forward_demodulation,[],[f4634,f108]) ).
fof(f4683,plain,
( ! [X0] : is_a_theorem(equiv(X0,X0))
| ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(backward_subsumption_resolution,[],[f232,f4663]) ).
fof(f4698,plain,
( ! [X0] : is_a_theorem(or(X0,not(X0)))
| ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f4683,f938]) ).
fof(f5375,plain,
( ! [X0] : is_a_theorem(or(not(or(X0,X0)),X0))
| ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(resolution,[],[f4698,f2286]) ).
fof(f5412,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(forward_demodulation,[],[f5375,f108]) ).
fof(f5833,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| spl1_12
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(backward_subsumption_resolution,[],[f145,f5412]) ).
fof(f5850,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| spl1_12
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(avatar_contradiction_clause,[],[f5833]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f105]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s3,plain,
( spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f121]) ).
cnf(s5,plain,
( spl1_9
| ~ spl1_10 ),
inference(sat_conversion,[],[f137]) ).
cnf(s6,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(sat_conversion,[],[f146]) ).
cnf(s7,plain,
( spl1_13
| spl1_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s8,plain,
( spl1_15
| ~ spl1_16 ),
inference(sat_conversion,[],[f162]) ).
cnf(s9,plain,
( spl1_17
| spl1_18 ),
inference(sat_conversion,[],[f170]) ).
cnf(s11,plain,
( spl1_21
| spl1_22 ),
inference(sat_conversion,[],[f186]) ).
cnf(s12,plain,
spl1_11,
inference(sat_conversion,[],[f187]) ).
cnf(s13,plain,
spl1_10,
inference(sat_conversion,[],[f188]) ).
cnf(s14,plain,
spl1_6,
inference(sat_conversion,[],[f189]) ).
cnf(s15,plain,
spl1_16,
inference(sat_conversion,[],[f190]) ).
cnf(s17,plain,
spl1_4,
inference(sat_conversion,[],[f192]) ).
cnf(s19,plain,
~ spl1_2,
inference(sat_conversion,[],[f194]) ).
cnf(s20,plain,
~ spl1_22,
inference(sat_conversion,[],[f195]) ).
cnf(s21,plain,
~ spl1_18,
inference(sat_conversion,[],[f196]) ).
cnf(s22,plain,
~ spl1_14,
inference(sat_conversion,[],[f197]) ).
cnf(s24,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_5
| ~ spl1_9
| spl1_12
| ~ spl1_13
| ~ spl1_15
| ~ spl1_17
| ~ spl1_21 ),
inference(sat_conversion,[],[f5850]) ).
cnf(s25,plain,
spl1_21,
inference(rat,[],[s11,s20]) ).
cnf(s27,plain,
spl1_17,
inference(rat,[],[s9,s21]) ).
cnf(s28,plain,
spl1_15,
inference(rat,[],[s8,s15]) ).
cnf(s29,plain,
spl1_13,
inference(rat,[],[s7,s22]) ).
cnf(s30,plain,
~ spl1_12,
inference(rat,[],[s6,s12]) ).
cnf(s31,plain,
spl1_9,
inference(rat,[],[s5,s13]) ).
cnf(s33,plain,
spl1_5,
inference(rat,[],[s3,s14]) ).
cnf(s34,plain,
spl1_3,
inference(rat,[],[s2,s17]) ).
cnf(s35,plain,
~ spl1_1,
inference(rat,[],[s24,s25,s27,s28,s29,s30,s31,s33,s34]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s1,s19,s35]) ).
fof(f5880,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:58:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.98/0.59 % (3704225)Will run a generic schedule for satisfiability detection.
% 0.98/0.59 % (3704234)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4293711809:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.98/0.59 % (3704231)% WARNING: option uhcvi not known.
% 0.98/0.59 % (3704230)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=866075104_2999 on theBenchmark for (2999ds/0Mi)
% 0.98/0.59 % (3704231)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=543561687:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.98/0.59 % (3704232)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3601896280:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.98/0.59 % (3704233)dis+10_1_sil=32000:sp=arity:random_seed=3115868081:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.98/0.59 % (3704235)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1430613965:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.59 % (3704236)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=425560797:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.98/0.59 % TRYING [1]
% 0.98/0.59 % TRYING [2]
% 0.98/0.59 % TRYING [3]
% 0.98/0.59 % TRYING [4]
% 0.98/0.59 % (3704234)Instruction limit reached!
% 0.98/0.59 % (3704234)------------------------------
% 0.98/0.59 % (3704234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3704234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3704234)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3704234)Termination reason: Instruction limit
% 0.98/0.59 % (3704234)Termination phase: Saturation
% 0.98/0.59 % (3704234)Time elapsed: 0.041 s
% 0.98/0.59 % (3704234)Peak memory usage: 13 MB
% 0.98/0.59 % (3704234)Instructions burned: 116 (million)
% 0.98/0.59 % (3704244)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=26442927:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.98/0.59 % TRYING [1]
% 0.98/0.59 % TRYING [2]
% 0.98/0.59 % TRYING [3]
% 0.98/0.59 % TRYING [4]
% 0.98/0.59 % (3704233)Instruction limit reached!
% 0.98/0.59 % (3704233)------------------------------
% 0.98/0.59 % (3704233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3704233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3704233)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3704233)Termination reason: Instruction limit
% 0.98/0.59 % (3704233)Termination phase: Saturation
% 0.98/0.59 % (3704233)Time elapsed: 0.064 s
% 0.98/0.59 % (3704233)Peak memory usage: 13 MB
% 0.98/0.59 % (3704233)Instructions burned: 104 (million)
% 0.98/0.59 % (3704235)Instruction limit reached!
% 0.98/0.59 % (3704235)------------------------------
% 0.98/0.59 % (3704235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3704235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3704235)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3704235)Termination reason: Instruction limit
% 0.98/0.59 % (3704235)Termination phase: Saturation
% 0.98/0.59 % (3704235)Time elapsed: 0.083 s
% 0.98/0.59 % (3704235)Peak memory usage: 14 MB
% 0.98/0.59 % (3704235)Instructions burned: 132 (million)
% 0.98/0.59 % (3704246)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=741701441:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.98/0.59 % TRYING [5]
% 0.98/0.59 % (3704248)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3528716715:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.98/0.59 % (3704236)Instruction limit reached!
% 0.98/0.59 % (3704236)------------------------------
% 0.98/0.59 % (3704236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3704236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3704236)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3704236)Termination reason: Instruction limit
% 0.98/0.59 % (3704236)Termination phase: Saturation
% 0.98/0.59 % (3704236)Time elapsed: 0.105 s
% 0.98/0.59 % (3704236)Peak memory usage: 14 MB
% 0.98/0.59 % (3704236)Instructions burned: 159 (million)
% 0.98/0.59 % TRYING [5]
% 0.98/0.59 % (3704250)ott-21_1_sil=16000:fs=off:random_seed=3815286645:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.98/0.59 % (3704231) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3704225-3704231"...
% 0.98/0.59 % (3704231)...printing done.
% 0.98/0.59 % (3704231)Refutation found. Thanks to Tanya!
% 0.98/0.59 % SZS status Theorem for theBenchmark
% 0.98/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.98/0.59 % (3704231)------------------------------
% 0.98/0.59 % (3704231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.98/0.59 % (3704231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.98/0.59 % (3704231)CaDiCaL version: 2.1.3
% 0.98/0.59 % (3704231)Termination reason: Refutation
% 0.98/0.59 % (3704231)Time elapsed: 0.128 s
% 0.98/0.59 % (3704231)Peak memory usage: 16 MB
% 0.98/0.59 % (3704231)Instructions burned: 217 (million)
% 0.98/0.59 % (3704225)Success in time 0.165 s
% 0.98/0.59 % Vampire exiting
%------------------------------------------------------------------------------