%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL345-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 11:52:02 AM UTC 2026
% Result : Unsatisfiable 9.40s 2.20s
% Output : Refutation 10.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 34
% Syntax : Number of formulae : 149 ( 83 unt; 23 def)
% Number of atoms : 247 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 195 ( 97 ~; 92 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 115 ( 0 sgn 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f6,axiom,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f7,axiom,
! [X0] :
( ~ axiom(X0)
| theorem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f8,axiom,
! [X0,X1] :
( theorem(X0)
| ~ theorem(implies(X1,X0))
| ~ theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f9,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
fof(f10,axiom,
! [X0,X1] : equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,negated_conjecture,
~ theorem(or(equivalent(or(p,q),p),equivalent(or(p,q),q))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f12,plain,
! [X0,X1] : equivalent(X0,X1) = not(or(not(or(not(X0),X1)),not(or(not(X1),X0)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f13,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f14,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f15,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f16,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f17,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f18,plain,
! [X0,X1] :
( ~ theorem(or(not(X1),X0))
| theorem(X0)
| ~ theorem(X1) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f19,plain,
~ theorem(or(not(or(not(or(not(or(p,q)),p)),not(or(not(p),or(p,q))))),not(or(not(or(not(or(p,q)),q)),not(or(not(q),or(p,q))))))),
inference(definition_unfolding,[],[f11,f12,f12]) ).
fof(f20,definition,
sF0 = or(p,q),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f21,plain,
or(p,q) = sF0,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF1 = not(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f23,plain,
not(sF0) = sF1,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF2 = or(sF1,p),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f25,plain,
or(sF1,p) = sF2,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF3 = not(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f27,plain,
not(sF2) = sF3,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF4 = not(p),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f29,plain,
not(p) = sF4,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF5 = or(sF4,sF0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f31,plain,
or(sF4,sF0) = sF5,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF6 = not(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f33,plain,
not(sF5) = sF6,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF7 = or(sF3,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f35,plain,
or(sF3,sF6) = sF7,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF8 = not(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f37,plain,
not(sF7) = sF8,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF9 = or(sF1,q),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f39,plain,
or(sF1,q) = sF9,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF10 = not(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f41,plain,
not(sF9) = sF10,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF11 = not(q),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f43,plain,
not(q) = sF11,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF12 = or(sF11,sF0),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f45,plain,
or(sF11,sF0) = sF12,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF13 = not(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f47,plain,
not(sF12) = sF13,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF14 = or(sF10,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f49,plain,
or(sF10,sF13) = sF14,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF15 = not(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f51,plain,
not(sF14) = sF15,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF16 = or(sF8,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f53,plain,
or(sF8,sF15) = sF16,
inference(reorient_equations,[],[f52]) ).
fof(f54,plain,
~ theorem(sF16),
inference(definition_folding,[],[f19,f53,f51,f49,f47,f45,f21,f43,f41,f39,f23,f21,f37,f35,f33,f31,f21,f29,f27,f25,f23,f21]) ).
fof(f59,plain,
! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(resolution,[],[f7,f17]) ).
fof(f60,plain,
! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(resolution,[],[f7,f16]) ).
fof(f62,plain,
! [X0] : theorem(or(not(or(sF8,or(X0,sF15))),or(X0,sF16))),
inference(superposition,[],[f60,f53]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f18,f60]) ).
fof(f74,plain,
! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ),
inference(resolution,[],[f18,f59]) ).
fof(f114,plain,
! [X0] :
( ~ theorem(or(sF6,X0))
| theorem(X0)
| ~ theorem(sF5) ),
inference(superposition,[],[f18,f33]) ).
fof(f118,definition,
( spl17_9
<=> theorem(sF5) ),
introduced(definition,[new_symbols(definition,[spl17_9])],[avatar_definition]) ).
fof(f120,plain,
( ~ theorem(sF5)
| spl17_9 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f122,definition,
( spl17_10
<=> ! [X0] :
( ~ theorem(or(sF6,X0))
| theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition]) ).
fof(f123,plain,
( ! [X0] :
( ~ theorem(or(sF6,X0))
| theorem(X0) )
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f124,plain,
( ~ spl17_9
| spl17_10 ),
inference(avatar_split_clause,[],[f114,f122,f118]) ).
fof(f125,plain,
! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0)
| ~ theorem(sF12) ),
inference(superposition,[],[f18,f47]) ).
fof(f129,definition,
( spl17_11
<=> theorem(sF12) ),
introduced(definition,[new_symbols(definition,[spl17_11])],[avatar_definition]) ).
fof(f131,plain,
( ~ theorem(sF12)
| spl17_11 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl17_12
<=> ! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[spl17_12])],[avatar_definition]) ).
fof(f134,plain,
( ! [X0] :
( ~ theorem(or(sF13,X0))
| theorem(X0) )
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f135,plain,
( ~ spl17_11
| spl17_12 ),
inference(avatar_split_clause,[],[f125,f133,f129]) ).
fof(f182,plain,
! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(resolution,[],[f15,f7]) ).
fof(f188,plain,
! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f182,f18]) ).
fof(f264,plain,
theorem(or(not(sF7),or(sF6,sF3))),
inference(superposition,[],[f182,f35]) ).
fof(f265,plain,
theorem(or(sF8,or(sF6,sF3))),
inference(forward_demodulation,[],[f264,f37]) ).
fof(f305,plain,
! [X0,X1] : theorem(or(not(X0),or(X1,X0))),
inference(resolution,[],[f14,f7]) ).
fof(f340,plain,
theorem(or(not(q),sF0)),
inference(superposition,[],[f305,f21]) ).
fof(f341,plain,
theorem(or(not(p),sF2)),
inference(superposition,[],[f305,f25]) ).
fof(f351,plain,
theorem(or(sF4,sF2)),
inference(forward_demodulation,[],[f341,f29]) ).
fof(f352,plain,
theorem(or(sF11,sF0)),
inference(forward_demodulation,[],[f340,f43]) ).
fof(f353,plain,
theorem(sF12),
inference(forward_demodulation,[],[f352,f45]) ).
fof(f354,plain,
( $false
| spl17_11 ),
inference(forward_subsumption_resolution,[],[f353,f131]) ).
fof(f355,plain,
spl17_11,
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ),
inference(resolution,[],[f74,f18]) ).
fof(f378,plain,
! [X0] :
( theorem(or(not(sF14),or(sF10,X0)))
| ~ theorem(or(not(sF13),X0)) ),
inference(superposition,[],[f74,f49]) ).
fof(f389,plain,
! [X0] :
( theorem(or(sF15,or(sF10,X0)))
| ~ theorem(or(not(sF13),X0)) ),
inference(forward_demodulation,[],[f378,f51]) ).
fof(f402,plain,
! [X2,X0,X1] :
( ~ theorem(or(X0,or(X2,X1)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[],[f369,f182]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( ~ theorem(or(X0,or(X1,X3)))
| theorem(or(X0,or(X1,X2)))
| ~ theorem(or(not(X3),X2)) ),
inference(resolution,[],[f369,f74]) ).
fof(f404,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ),
inference(resolution,[],[f369,f305]) ).
fof(f405,plain,
! [X0,X1] :
( ~ theorem(or(sF4,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,p)) ),
inference(superposition,[],[f369,f29]) ).
fof(f408,plain,
! [X0,X1] :
( ~ theorem(or(sF3,X0))
| theorem(or(X1,X0))
| ~ theorem(or(X1,sF2)) ),
inference(superposition,[],[f369,f27]) ).
fof(f418,plain,
! [X0,X1] : theorem(or(not(X0),or(X0,X1))),
inference(resolution,[],[f402,f305]) ).
fof(f427,plain,
! [X0] : theorem(or(not(or(X0,X0)),X0)),
inference(resolution,[],[f13,f7]) ).
fof(f428,plain,
! [X0,X1] :
( ~ theorem(or(X0,or(X1,X1)))
| theorem(or(X0,X1)) ),
inference(resolution,[],[f427,f369]) ).
fof(f429,plain,
! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[],[f427,f18]) ).
fof(f436,plain,
! [X0] : theorem(or(not(X0),X0)),
inference(resolution,[],[f428,f305]) ).
fof(f439,plain,
! [X0] :
( ~ theorem(or(sF8,or(X0,sF15)))
| theorem(or(X0,sF16)) ),
inference(resolution,[],[f62,f18]) ).
fof(f489,plain,
! [X2,X3,X0,X1] :
( theorem(or(not(or(X0,or(X1,X2))),or(X1,X3)))
| ~ theorem(or(not(or(X0,X2)),X3)) ),
inference(resolution,[],[f403,f60]) ).
fof(f535,plain,
! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[],[f404,f402]) ).
fof(f545,plain,
! [X0] :
( ~ theorem(or(X0,sF15))
| theorem(or(X0,sF16)) ),
inference(superposition,[],[f404,f53]) ).
fof(f622,definition,
( spl17_20
<=> theorem(or(sF1,sF0)) ),
introduced(definition,[new_symbols(definition,[spl17_20])],[avatar_definition]) ).
fof(f624,plain,
( theorem(or(sF1,sF0))
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f629,plain,
! [X2,X3,X0,X1] :
( ~ theorem(or(not(or(X0,X1)),X2))
| theorem(or(X3,X2))
| ~ theorem(or(X0,or(X3,X1))) ),
inference(resolution,[],[f489,f18]) ).
fof(f659,plain,
! [X0] : theorem(or(X0,not(X0))),
inference(resolution,[],[f436,f188]) ).
fof(f662,plain,
theorem(or(sF1,sF0)),
inference(superposition,[],[f436,f23]) ).
fof(f669,plain,
spl17_20,
inference(avatar_split_clause,[],[f662,f622]) ).
fof(f695,plain,
! [X0] :
( ~ theorem(or(sF8,X0))
| theorem(or(X0,sF16)) ),
inference(resolution,[],[f535,f439]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ theorem(or(sF13,X0))
| theorem(or(X0,X1)) )
| ~ spl17_12 ),
inference(resolution,[],[f535,f134]) ).
fof(f757,plain,
theorem(or(sF6,or(sF8,sF3))),
inference(resolution,[],[f265,f73]) ).
fof(f1045,plain,
theorem(or(not(p),sF0)),
inference(superposition,[],[f418,f21]) ).
fof(f1053,plain,
theorem(or(sF4,sF0)),
inference(forward_demodulation,[],[f1045,f29]) ).
fof(f1054,plain,
theorem(sF5),
inference(forward_demodulation,[],[f1053,f31]) ).
fof(f1055,plain,
( $false
| spl17_9 ),
inference(forward_subsumption_resolution,[],[f1054,f120]) ).
fof(f1056,plain,
spl17_9,
inference(avatar_contradiction_clause,[],[f1055]) ).
fof(f1060,plain,
( theorem(or(sF8,sF3))
| ~ spl17_10 ),
inference(resolution,[],[f123,f757]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ theorem(or(not(sF9),X0))
| theorem(or(X1,X0))
| ~ theorem(or(sF1,or(X1,q))) ),
inference(superposition,[],[f629,f39]) ).
fof(f1133,plain,
! [X0,X1] :
( ~ theorem(or(sF1,or(X1,q)))
| theorem(or(X1,X0))
| ~ theorem(or(sF10,X0)) ),
inference(forward_demodulation,[],[f1123,f41]) ).
fof(f1254,plain,
( ! [X0] : theorem(or(not(sF13),X0))
| ~ spl17_12 ),
inference(resolution,[],[f696,f659]) ).
fof(f1319,plain,
! [X0] :
( ~ theorem(or(not(sF13),X0))
| theorem(or(sF10,or(sF15,X0))) ),
inference(resolution,[],[f389,f73]) ).
fof(f1326,plain,
( ! [X0] : theorem(or(sF10,or(sF15,X0)))
| ~ spl17_12 ),
inference(forward_subsumption_resolution,[],[f1319,f1254]) ).
fof(f1383,definition,
( spl17_45
<=> theorem(or(sF3,sF16)) ),
introduced(definition,[new_symbols(definition,[spl17_45])],[avatar_definition]) ).
fof(f1385,plain,
( theorem(or(sF3,sF16))
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f1462,plain,
( theorem(or(sF3,sF16))
| ~ spl17_10 ),
inference(resolution,[],[f1060,f695]) ).
fof(f1464,plain,
( spl17_45
| ~ spl17_10 ),
inference(avatar_split_clause,[],[f1462,f122,f1383]) ).
fof(f1466,plain,
( ! [X0] :
( ~ theorem(or(X0,sF2))
| theorem(or(X0,sF16)) )
| ~ spl17_45 ),
inference(resolution,[],[f1385,f408]) ).
fof(f1473,plain,
( theorem(or(sF4,sF16))
| ~ spl17_45 ),
inference(resolution,[],[f1466,f351]) ).
fof(f1617,plain,
! [X0] :
( ~ theorem(or(sF1,sF0))
| theorem(or(p,X0))
| ~ theorem(or(sF10,X0)) ),
inference(superposition,[],[f1133,f21]) ).
fof(f1619,plain,
( ! [X0] :
( ~ theorem(or(sF10,X0))
| theorem(or(p,X0)) )
| ~ spl17_20 ),
inference(forward_subsumption_resolution,[],[f1617,f624]) ).
fof(f1624,plain,
( ! [X0] :
( ~ theorem(or(X0,p))
| theorem(or(X0,sF16)) )
| ~ spl17_45 ),
inference(resolution,[],[f405,f1473]) ).
fof(f1639,plain,
( ! [X0] : theorem(or(p,or(sF15,X0)))
| ~ spl17_12
| ~ spl17_20 ),
inference(resolution,[],[f1619,f1326]) ).
fof(f1651,plain,
( theorem(or(p,sF15))
| ~ spl17_12
| ~ spl17_20 ),
inference(resolution,[],[f1639,f428]) ).
fof(f1668,plain,
( theorem(or(p,sF16))
| ~ spl17_12
| ~ spl17_20 ),
inference(resolution,[],[f1651,f545]) ).
fof(f1670,plain,
( theorem(or(sF16,p))
| ~ spl17_12
| ~ spl17_20 ),
inference(resolution,[],[f1668,f188]) ).
fof(f1671,plain,
( theorem(or(sF16,sF16))
| ~ spl17_12
| ~ spl17_20
| ~ spl17_45 ),
inference(resolution,[],[f1670,f1624]) ).
fof(f1673,plain,
( theorem(sF16)
| ~ spl17_12
| ~ spl17_20
| ~ spl17_45 ),
inference(resolution,[],[f1671,f429]) ).
fof(f1675,plain,
( $false
| ~ spl17_12
| ~ spl17_20
| ~ spl17_45 ),
inference(forward_subsumption_resolution,[],[f1673,f54]) ).
fof(f1676,plain,
( ~ spl17_12
| ~ spl17_20
| ~ spl17_45 ),
inference(avatar_contradiction_clause,[],[f1675]) ).
cnf(s5,plain,
( ~ spl17_9
| spl17_10 ),
inference(sat_conversion,[],[f124]) ).
cnf(s6,plain,
( ~ spl17_11
| spl17_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s10,plain,
spl17_11,
inference(sat_conversion,[],[f355]) ).
cnf(s12,plain,
spl17_20,
inference(sat_conversion,[],[f669]) ).
cnf(s26,plain,
spl17_9,
inference(sat_conversion,[],[f1056]) ).
cnf(s28,plain,
( ~ spl17_10
| spl17_45 ),
inference(sat_conversion,[],[f1464]) ).
cnf(s29,plain,
( ~ spl17_12
| ~ spl17_20
| ~ spl17_45 ),
inference(sat_conversion,[],[f1676]) ).
cnf(s30,plain,
spl17_12,
inference(rat,[],[s6,s10]) ).
cnf(s31,plain,
~ spl17_45,
inference(rat,[],[s29,s12,s30]) ).
cnf(s32,plain,
~ spl17_10,
inference(rat,[],[s28,s31]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s5,s32,s26]) ).
fof(f1677,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL345-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 15:36:20 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 9.40/2.20 % (3550321)Input is clausal, will run a generic CNF schedule.
% 9.40/2.20 % (3550330)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4179024503:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.40/2.20 % (3550327)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3188196799:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.40/2.20 % (3550328)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=844128787:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.40/2.20 % (3550331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2958135945:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.40/2.20 % (3550329)lrs+10_1_sil=8000:sp=occurrence:random_seed=3837138779:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.40/2.20 % (3550332)dis-21_1_sil=8000:lcm=predicate:random_seed=2610677173: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)
% 9.40/2.20 % (3550326)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=2894992632:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.40/2.20 % (3550330)Instruction limit reached!
% 9.40/2.20 % (3550330)------------------------------
% 9.40/2.20 % (3550330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550330)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550330)Termination reason: Instruction limit
% 9.40/2.20 % (3550330)Termination phase: Saturation
% 9.40/2.20 % (3550330)Time elapsed: 0.039 s
% 9.40/2.20 % (3550330)Peak memory usage: 89 MB
% 9.40/2.20 % (3550330)Instructions burned: 115 (million)
% 9.40/2.20 % (3550332)Instruction limit reached!
% 9.40/2.20 % (3550332)------------------------------
% 9.40/2.20 % (3550332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550332)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550332)Termination reason: Instruction limit
% 9.40/2.20 % (3550332)Termination phase: Saturation
% 9.40/2.20 % (3550332)Time elapsed: 0.057 s
% 9.40/2.20 % (3550332)Peak memory usage: 87 MB
% 9.40/2.20 % (3550332)Instructions burned: 117 (million)
% 9.40/2.20 % (3550329)Instruction limit reached!
% 9.40/2.20 % (3550329)------------------------------
% 9.40/2.20 % (3550329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550329)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550329)Termination reason: Instruction limit
% 9.40/2.20 % (3550329)Termination phase: Saturation
% 9.40/2.20 % (3550329)Time elapsed: 0.070 s
% 9.40/2.20 % (3550329)Peak memory usage: 89 MB
% 9.40/2.20 % (3550329)Instructions burned: 107 (million)
% 9.40/2.20 % (3550331)Instruction limit reached!
% 9.40/2.20 % (3550331)------------------------------
% 9.40/2.20 % (3550331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550331)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550331)Termination reason: Instruction limit
% 9.40/2.20 % (3550331)Termination phase: Saturation
% 9.40/2.20 % (3550331)Time elapsed: 0.115 s
% 9.40/2.20 % (3550331)Peak memory usage: 89 MB
% 9.40/2.20 % (3550331)Instructions burned: 181 (million)
% 9.40/2.20 % (3550340)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=1464732438:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 9.40/2.20 % (3550340)Refutation not found, incomplete strategy
% 9.40/2.20 % (3550340)------------------------------
% 9.40/2.20 % (3550340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550340)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550340)Termination reason: Refutation not found, incomplete strategy
% 9.40/2.20 % (3550340)Time elapsed: 0.001 s
% 9.40/2.20 % (3550340)Peak memory usage: 88 MB
% 9.40/2.20 % (3550341)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3513671579: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)
% 9.40/2.20 % (3550341)Refutation not found, incomplete strategy
% 9.40/2.20 % (3550341)------------------------------
% 9.40/2.20 % (3550341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550341)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550341)Termination reason: Refutation not found, incomplete strategy
% 9.40/2.20 % (3550341)Time elapsed: 0.001 s
% 9.40/2.20 % (3550341)Peak memory usage: 87 MB
% 9.40/2.20 % (3550342)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=175541131:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 9.40/2.20 % (3550342)Refutation not found, incomplete strategy
% 9.40/2.20 % (3550342)------------------------------
% 9.40/2.20 % (3550342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550342)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550342)Termination reason: Refutation not found, incomplete strategy
% 9.40/2.20 % (3550342)Time elapsed: 0.001 s
% 9.40/2.20 % (3550342)Peak memory usage: 88 MB
% 9.40/2.20 % (3550340)------------------------------
% 9.40/2.20 % (3550340)------------------------------
% 9.40/2.20 % (3550343)lrs+10_64_to=lpo:sil=8000:random_seed=3460532636:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 9.40/2.20 % (3550343)Instruction limit reached!
% 9.40/2.20 % (3550343)------------------------------
% 9.40/2.20 % (3550343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550343)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550343)Termination reason: Instruction limit
% 9.40/2.20 % (3550343)Termination phase: Saturation
% 9.40/2.20 % (3550343)Time elapsed: 0.073 s
% 9.40/2.20 % (3550343)Peak memory usage: 89 MB
% 9.40/2.20 % (3550343)Instructions burned: 126 (million)
% 9.40/2.20 % (3550347)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2478168556:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 9.40/2.20 % (3550341)------------------------------
% 9.40/2.20 % (3550341)------------------------------
% 9.40/2.20 % (3550347)Instruction limit reached!
% 9.40/2.20 % (3550347)------------------------------
% 9.40/2.20 % (3550347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550347)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550347)Termination reason: Instruction limit
% 9.40/2.20 % (3550347)Termination phase: Saturation
% 9.40/2.20 % (3550347)Time elapsed: 0.068 s
% 9.40/2.20 % (3550347)Peak memory usage: 90 MB
% 9.40/2.20 % (3550347)Instructions burned: 194 (million)
% 9.40/2.20 % (3550342)------------------------------
% 9.40/2.20 % (3550342)------------------------------
% 9.40/2.20 % (3550349)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=742164776:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 9.40/2.20 % (3550351)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3155623734:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 9.40/2.20 % (3550352)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=33753436:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 9.40/2.20 % (3550349)Instruction limit reached!
% 9.40/2.20 % (3550349)------------------------------
% 9.40/2.20 % (3550349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550349)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550349)Termination reason: Instruction limit
% 9.40/2.20 % (3550349)Termination phase: Saturation
% 9.40/2.20 % (3550349)Time elapsed: 0.103 s
% 9.40/2.20 % (3550349)Peak memory usage: 91 MB
% 9.40/2.20 % (3550349)Instructions burned: 158 (million)
% 9.40/2.20 % (3550353)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1270744288:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 9.40/2.20 % (3550353)Refutation not found, incomplete strategy
% 9.40/2.20 % (3550353)------------------------------
% 9.40/2.20 % (3550353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550353)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550353)Termination reason: Refutation not found, incomplete strategy
% 9.40/2.20 % (3550353)Time elapsed: 0.001 s
% 9.40/2.20 % (3550353)Peak memory usage: 87 MB
% 9.40/2.20 % (3550352)Instruction limit reached!
% 9.40/2.20 % (3550352)------------------------------
% 9.40/2.20 % (3550352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550352)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550352)Termination reason: Instruction limit
% 9.40/2.20 % (3550352)Termination phase: Saturation
% 9.40/2.20 % (3550352)Time elapsed: 0.054 s
% 9.40/2.20 % (3550352)Peak memory usage: 89 MB
% 9.40/2.20 % (3550352)Instructions burned: 107 (million)
% 9.40/2.20 % (3550357)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=820718990:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2991 on theBenchmark for (2991ds/242Mi)
% 9.40/2.20 % (3550359)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3795882731:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 9.40/2.20 % (3550353)------------------------------
% 9.40/2.20 % (3550353)------------------------------
% 9.40/2.20 % (3550326)First to succeed.
% 9.40/2.20 % (3550326)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3550321"
% 9.40/2.20 % (3550357)Instruction limit reached!
% 9.40/2.20 % (3550357)------------------------------
% 9.40/2.20 % (3550357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550357)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550357)Termination reason: Instruction limit
% 9.40/2.20 % (3550357)Termination phase: Saturation
% 9.40/2.20 % (3550357)Time elapsed: 0.162 s
% 9.40/2.20 % (3550357)Peak memory usage: 90 MB
% 9.40/2.20 % (3550357)Instructions burned: 242 (million)
% 9.40/2.20 % (3550362)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=2097347416:i=134:sd=2:doe=on:ss=axioms:sgt=14_2989 on theBenchmark for (2989ds/134Mi)
% 9.40/2.20 % (3550351)Also succeeded, but the first one will report.
% 9.40/2.20 % (3550363)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=2086271667:i=499:bd=all_2988 on theBenchmark for (2988ds/499Mi)
% 9.40/2.20 % (3550362)Instruction limit reached!
% 9.40/2.20 % (3550362)------------------------------
% 9.40/2.20 % (3550362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.40/2.20 % (3550362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.40/2.20 % (3550362)CaDiCaL version: 2.1.3
% 9.40/2.20 % (3550362)Termination reason: Instruction limit
% 9.40/2.20 % (3550362)Termination phase: Saturation
% 9.40/2.20 % (3550362)Time elapsed: 0.086 s
% 9.40/2.20 % (3550362)Peak memory usage: 90 MB
% 9.40/2.20 % (3550362)Instructions burned: 135 (million)
% 9.40/2.20 % (3550326)Refutation found. Thanks to Tanya!
% 9.40/2.20 % SZS status Unsatisfiable for theBenchmark
% 9.40/2.20 % SZS output start Proof for theBenchmark
% See solution above
% 10.00/2.39 % (3550326)------------------------------
% 10.00/2.39 % (3550326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.00/2.39 % (3550326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.00/2.39 % (3550326)CaDiCaL version: 2.1.3
% 10.00/2.39 % (3550326)Termination reason: Refutation
% 10.00/2.39 % (3550326)Time elapsed: 0.906 s
% 10.00/2.39 % (3550326)Peak memory usage: 131 MB
% 10.00/2.39 % (3550326)Instructions burned: 1362 (million)
% 10.00/2.39 % (3550326)------------------------------
% 10.00/2.39 % (3550326)------------------------------
% 10.00/2.39 % (3550321)Success in time 1.341 s
% 10.00/2.39 % Vampire exiting
%------------------------------------------------------------------------------