%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:33:39 PM UTC 2026
% Result : Unsatisfiable 5.16s 1.70s
% Output : Refutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 27
% Syntax : Number of formulae : 149 ( 136 unt; 15 def)
% Number of atoms : 162 ( 144 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 30 ( 17 ~; 11 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-2 aty)
% Number of variables : 129 ( 0 sgn 129 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f23,negated_conjecture,
( join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2))) != meet(converse(sk1),converse(sk2))
| join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) != converse(meet(sk1,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
( meet(converse(sk1),converse(sk2)) != join(converse(meet(sk1,sk2)),meet(converse(sk1),converse(sk2)))
| converse(meet(sk1,sk2)) != join(meet(converse(sk1),converse(sk2)),converse(meet(sk1,sk2))) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f29,plain,
( complement(join(complement(converse(sk1)),complement(converse(sk2)))) != join(converse(complement(join(complement(sk1),complement(sk2)))),complement(join(complement(converse(sk1)),complement(converse(sk2)))))
| converse(complement(join(complement(sk1),complement(sk2)))) != join(complement(join(complement(converse(sk1)),complement(converse(sk2)))),converse(complement(join(complement(sk1),complement(sk2))))) ),
inference(definition_unfolding,[],[f24,f6,f6,f6,f6,f6,f6]) ).
fof(f30,definition,
sF0 = converse(sk1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f31,plain,
converse(sk1) = sF0,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF1 = complement(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f33,plain,
complement(sF0) = sF1,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF2 = converse(sk2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f35,plain,
converse(sk2) = sF2,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF3 = complement(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f37,plain,
complement(sF2) = sF3,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF4 = join(sF1,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f39,plain,
join(sF1,sF3) = sF4,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF5 = complement(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f41,plain,
complement(sF4) = sF5,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF6 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f43,plain,
complement(sk1) = sF6,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF7 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f45,plain,
complement(sk2) = sF7,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF8 = join(sF6,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f47,plain,
join(sF6,sF7) = sF8,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f49,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF10 = converse(sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f51,plain,
converse(sF9) = sF10,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF11 = join(sF10,sF5),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f53,plain,
join(sF10,sF5) = sF11,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF12 = join(sF5,sF10),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f55,plain,
join(sF5,sF10) = sF12,
inference(reorient_equations,[],[f54]) ).
fof(f56,plain,
( sF5 != sF11
| sF10 != sF12 ),
inference(definition_folding,[],[f29,f55,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31,f51,f49,f47,f45,f43,f53,f41,f39,f37,f35,f33,f31,f51,f49,f47,f45,f43,f41,f39,f37,f35,f33,f31]) ).
fof(f58,definition,
( spl13_1
<=> sF10 = sF12 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f60,plain,
( sF10 != sF12
| spl13_1 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl13_2
<=> sF5 = sF11 ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f65,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f56,f62,f58]) ).
fof(f66,plain,
zero = complement(top),
inference(backward_demodulation,[],[f25,f15]) ).
fof(f67,plain,
complement(converse(sk2)) = sF3,
inference(forward_demodulation,[],[f37,f35]) ).
fof(f68,plain,
sF8 = join(sF6,complement(sk2)),
inference(forward_demodulation,[],[f47,f45]) ).
fof(f69,plain,
sF11 = join(sF5,sF10),
inference(forward_demodulation,[],[f53,f1]) ).
fof(f70,plain,
sF8 = join(complement(sk2),sF6),
inference(forward_demodulation,[],[f68,f1]) ).
fof(f71,plain,
sF11 = sF12,
inference(backward_demodulation,[],[f55,f69]) ).
fof(f72,plain,
sF8 = join(complement(sk2),complement(sk1)),
inference(forward_demodulation,[],[f70,f43]) ).
fof(f73,plain,
join(complement(sk1),complement(sk2)) = sF8,
inference(forward_demodulation,[],[f72,f1]) ).
fof(f74,plain,
( sF10 != sF11
| spl13_1 ),
inference(forward_demodulation,[],[f60,f71]) ).
fof(f75,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(join(complement(X0),complement(X1))),join(complement(X0),X1)))),
inference(superposition,[],[f4,f4]) ).
fof(f78,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(join(complement(X0),X1),complement(join(complement(X0),complement(X1)))))),
inference(forward_demodulation,[],[f75,f1]) ).
fof(f79,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(X0),join(X1,complement(join(complement(X0),complement(X1))))))),
inference(forward_demodulation,[],[f78,f2]) ).
fof(f81,plain,
! [X0] : join(complement(join(complement(X0),zero)),complement(join(complement(X0),top))) = X0,
inference(superposition,[],[f4,f66]) ).
fof(f82,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(forward_demodulation,[],[f81,f1]) ).
fof(f84,plain,
! [X0] : join(complement(join(complement(X0),top)),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f82,f1]) ).
fof(f85,plain,
! [X0] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f84,f1]) ).
fof(f93,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(superposition,[],[f4,f1]) ).
fof(f125,plain,
! [X0,X1] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[],[f11,f10]) ).
fof(f149,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),complement(X1))),join(complement(join(complement(X0),X1)),X2)),
inference(superposition,[],[f2,f4]) ).
fof(f157,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f159,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))),
inference(forward_demodulation,[],[f149,f157]) ).
fof(f173,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f185,plain,
! [X0,X1] : composition(converse(X1),X0) = converse(composition(converse(X0),X1)),
inference(superposition,[],[f12,f10]) ).
fof(f263,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f185,f8]) ).
fof(f273,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f263,f10]) ).
fof(f282,plain,
! [X0] : complement(X0) = join(complement(composition(one,X0)),complement(X0)),
inference(superposition,[],[f14,f273]) ).
fof(f289,plain,
one = converse(one),
inference(superposition,[],[f8,f273]) ).
fof(f290,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f273,f289]) ).
fof(f295,plain,
! [X0] : complement(X0) = join(complement(X0),complement(composition(one,X0))),
inference(forward_demodulation,[],[f282,f1]) ).
fof(f298,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(forward_demodulation,[],[f295,f290]) ).
fof(f384,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(complement(join(complement(X0),X1)),X0),
inference(superposition,[],[f159,f4]) ).
fof(f386,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(X0,complement(join(complement(X0),complement(X1)))),
inference(superposition,[],[f159,f298]) ).
fof(f394,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(X1)))) = X0,
inference(forward_demodulation,[],[f386,f93]) ).
fof(f395,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),complement(complement(X1))))) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f384,f1]) ).
fof(f410,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f395,f394]) ).
fof(f438,plain,
! [X2,X0,X1] : join(complement(X0),X2) = join(join(complement(X0),X2),complement(join(X0,X1))),
inference(superposition,[],[f410,f159]) ).
fof(f440,plain,
! [X0,X1] : join(X1,complement(join(X0,complement(X1)))) = X1,
inference(superposition,[],[f410,f1]) ).
fof(f441,plain,
! [X0] : join(X0,complement(top)) = X0,
inference(superposition,[],[f410,f15]) ).
fof(f444,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),X0) = join(X0,X0),
inference(superposition,[],[f159,f410]) ).
fof(f450,plain,
! [X2,X0,X1] : join(X0,X1) = join(complement(complement(X0)),join(X1,complement(join(complement(X0),complement(complement(join(complement(complement(X0)),X2))))))),
inference(superposition,[],[f159,f410]) ).
fof(f457,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = join(X0,X0),
inference(forward_demodulation,[],[f444,f1]) ).
fof(f460,plain,
! [X0] : join(X0,zero) = X0,
inference(forward_demodulation,[],[f441,f66]) ).
fof(f462,plain,
! [X0,X1] : join(complement(X0),complement(X1)) = join(complement(X0),complement(join(complement(X0),X1))),
inference(backward_demodulation,[],[f79,f440]) ).
fof(f463,plain,
! [X2,X0,X1] : join(complement(X0),X2) = join(complement(X0),join(X2,complement(join(X0,X1)))),
inference(forward_demodulation,[],[f438,f2]) ).
fof(f469,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f457,f410]) ).
fof(f472,plain,
! [X0,X1] : join(X0,X1) = join(complement(complement(X0)),X1),
inference(backward_demodulation,[],[f450,f463]) ).
fof(f519,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,complement(join(complement(complement(complement(X0))),X1))),
inference(superposition,[],[f410,f472]) ).
fof(f520,plain,
! [X0,X1] : complement(complement(X0)) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f519,f472]) ).
fof(f532,plain,
! [X0] : complement(complement(X0)) = X0,
inference(forward_demodulation,[],[f520,f410]) ).
fof(f560,plain,
! [X0] : join(zero,complement(X0)) = join(zero,complement(join(zero,X0))),
inference(superposition,[],[f462,f66]) ).
fof(f570,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(complement(X0),complement(complement(join(complement(complement(X0)),X1)))),
inference(superposition,[],[f462,f410]) ).
fof(f578,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(complement(X0),join(complement(complement(X0)),X1)),
inference(forward_demodulation,[],[f570,f532]) ).
fof(f584,plain,
! [X0,X1] : join(complement(X0),complement(complement(X0))) = join(top,X1),
inference(forward_demodulation,[],[f578,f173]) ).
fof(f590,plain,
! [X1] : top = join(top,X1),
inference(forward_demodulation,[],[f584,f15]) ).
fof(f597,plain,
! [X0] : join(complement(top),complement(join(zero,complement(X0)))) = X0,
inference(backward_demodulation,[],[f85,f590]) ).
fof(f604,plain,
! [X0] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(forward_demodulation,[],[f597,f66]) ).
fof(f607,plain,
! [X0] : join(zero,complement(complement(X0))) = X0,
inference(forward_demodulation,[],[f604,f560]) ).
fof(f610,plain,
! [X0] : join(zero,X0) = X0,
inference(forward_demodulation,[],[f607,f532]) ).
fof(f814,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f462,f532]) ).
fof(f822,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f814,f1]) ).
fof(f1245,plain,
! [X0] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[],[f125,f15]) ).
fof(f1289,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = join(X0,complement(converse(top))),
inference(superposition,[],[f814,f1245]) ).
fof(f1290,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(converse(complement(converse(X0))),complement(converse(top))),
inference(superposition,[],[f822,f1245]) ).
fof(f1296,plain,
top = converse(top),
inference(superposition,[],[f590,f1245]) ).
fof(f1305,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(complement(converse(top)),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1290,f1]) ).
fof(f1306,plain,
! [X0] : join(X0,complement(top)) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f1289,f1296]) ).
fof(f1325,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(complement(top),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1305,f1296]) ).
fof(f1326,plain,
! [X0] : join(X0,zero) = join(X0,complement(converse(complement(converse(X0))))),
inference(forward_demodulation,[],[f1306,f66]) ).
fof(f1336,plain,
! [X0] : join(converse(complement(converse(X0))),complement(X0)) = join(zero,converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1325,f66]) ).
fof(f1337,plain,
! [X0] : join(X0,complement(converse(complement(converse(X0))))) = X0,
inference(forward_demodulation,[],[f1326,f460]) ).
fof(f1342,plain,
! [X0] : converse(complement(converse(X0))) = join(converse(complement(converse(X0))),complement(X0)),
inference(forward_demodulation,[],[f1336,f610]) ).
fof(f1345,plain,
! [X0] : converse(complement(converse(X0))) = join(complement(X0),converse(complement(converse(X0)))),
inference(forward_demodulation,[],[f1342,f1]) ).
fof(f1425,plain,
! [X0] : converse(converse(X0)) = join(X0,converse(complement(converse(complement(converse(converse(X0))))))),
inference(superposition,[],[f125,f1337]) ).
fof(f1428,plain,
! [X0] : join(X0,converse(complement(converse(complement(X0))))) = X0,
inference(forward_demodulation,[],[f1425,f10]) ).
fof(f1441,plain,
! [X0] : complement(X0) = join(complement(X0),converse(complement(converse(X0)))),
inference(superposition,[],[f1428,f532]) ).
fof(f1481,plain,
! [X0] : complement(X0) = converse(complement(converse(X0))),
inference(backward_demodulation,[],[f1345,f1441]) ).
fof(f1531,plain,
complement(sk1) = converse(complement(sF0)),
inference(superposition,[],[f1481,f31]) ).
fof(f1533,plain,
complement(sk2) = converse(sF3),
inference(superposition,[],[f1481,f67]) ).
fof(f1534,plain,
! [X0] : complement(converse(X0)) = converse(complement(X0)),
inference(superposition,[],[f10,f1481]) ).
fof(f1572,plain,
complement(sk1) = converse(sF1),
inference(forward_demodulation,[],[f1531,f33]) ).
fof(f1652,plain,
! [X0] : converse(join(sF1,X0)) = join(complement(sk1),converse(X0)),
inference(superposition,[],[f11,f1572]) ).
fof(f2798,plain,
join(complement(sk1),complement(sk2)) = converse(join(sF1,sF3)),
inference(superposition,[],[f1652,f1533]) ).
fof(f2800,plain,
join(complement(sk1),complement(sk2)) = converse(sF4),
inference(forward_demodulation,[],[f2798,f39]) ).
fof(f2805,plain,
sF8 = converse(sF4),
inference(forward_demodulation,[],[f2800,f73]) ).
fof(f2821,plain,
complement(sF8) = converse(complement(sF4)),
inference(superposition,[],[f1534,f2805]) ).
fof(f2825,plain,
complement(sF8) = converse(sF5),
inference(forward_demodulation,[],[f2821,f41]) ).
fof(f2848,plain,
sF9 = converse(sF5),
inference(forward_demodulation,[],[f2825,f49]) ).
fof(f2870,plain,
sF5 = converse(sF9),
inference(superposition,[],[f10,f2848]) ).
fof(f2894,plain,
sF5 = sF10,
inference(backward_demodulation,[],[f51,f2870]) ).
fof(f2900,plain,
sF11 = join(sF5,sF5),
inference(backward_demodulation,[],[f69,f2894]) ).
fof(f2901,plain,
( sF5 != sF11
| spl13_1 ),
inference(backward_demodulation,[],[f74,f2894]) ).
fof(f2932,plain,
( ~ spl13_2
| spl13_1 ),
inference(avatar_split_clause,[],[f2901,f58,f62]) ).
fof(f2933,plain,
sF5 = sF11,
inference(forward_demodulation,[],[f2900,f469]) ).
fof(f2949,plain,
spl13_2,
inference(avatar_split_clause,[],[f2933,f62]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f65]) ).
cnf(s2,plain,
( spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f2932]) ).
cnf(s3,plain,
spl13_2,
inference(sat_conversion,[],[f2949]) ).
cnf(s4,plain,
spl13_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
fof(f2950,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL005-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n010.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:50:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.16/1.70 % (1384488)Input is clausal, will run a generic CNF schedule.
% 5.16/1.70 % (1384495)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1401783532:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.16/1.70 % (1384498)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4036935802:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.16/1.70 % (1384496)lrs+10_1_sil=8000:sp=occurrence:random_seed=2915954492:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.16/1.70 % (1384494)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2540572123:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.16/1.70 % (1384493)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=3938077311:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.16/1.70 % (1384497)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2645413945:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.16/1.70 % (1384499)dis-21_1_sil=8000:lcm=predicate:random_seed=2127776189: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)
% 5.16/1.70 % (1384499)Refutation not found, incomplete strategy
% 5.16/1.70 % (1384499)------------------------------
% 5.16/1.70 % (1384499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384499)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384499)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.70 % (1384499)Time elapsed: 0.002 s
% 5.16/1.70 % (1384499)Peak memory usage: 88 MB
% 5.16/1.70 % (1384499)Instructions burned: 1 (million)
% 5.16/1.70 % (1384496)Instruction limit reached!
% 5.16/1.70 % (1384496)------------------------------
% 5.16/1.70 % (1384496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384496)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384496)Termination reason: Instruction limit
% 5.16/1.70 % (1384496)Termination phase: Saturation
% 5.16/1.70 % (1384496)Time elapsed: 0.065 s
% 5.16/1.70 % (1384496)Peak memory usage: 89 MB
% 5.16/1.70 % (1384496)Instructions burned: 108 (million)
% 5.16/1.70 % (1384497)Instruction limit reached!
% 5.16/1.70 % (1384497)------------------------------
% 5.16/1.70 % (1384497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384497)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384497)Termination reason: Instruction limit
% 5.16/1.70 % (1384497)Termination phase: Saturation
% 5.16/1.70 % (1384497)Time elapsed: 0.070 s
% 5.16/1.70 % (1384497)Peak memory usage: 89 MB
% 5.16/1.70 % (1384497)Instructions burned: 116 (million)
% 5.16/1.70 % (1384498)Instruction limit reached!
% 5.16/1.70 % (1384498)------------------------------
% 5.16/1.70 % (1384498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384498)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384498)Termination reason: Instruction limit
% 5.16/1.70 % (1384498)Termination phase: Saturation
% 5.16/1.70 % (1384498)Time elapsed: 0.109 s
% 5.16/1.70 % (1384498)Peak memory usage: 90 MB
% 5.16/1.70 % (1384498)Instructions burned: 181 (million)
% 5.16/1.70 % (1384507)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=2752632608:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.16/1.70 % (1384507)Refutation not found, incomplete strategy
% 5.16/1.70 % (1384507)------------------------------
% 5.16/1.70 % (1384507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384507)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384507)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.70 % (1384507)Time elapsed: 0.002 s
% 5.16/1.70 % (1384507)Peak memory usage: 88 MB
% 5.16/1.70 % (1384507)Instructions burned: 1 (million)
% 5.16/1.70 % (1384508)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3587588509: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)
% 5.16/1.70 % (1384508)Refutation not found, incomplete strategy
% 5.16/1.70 % (1384508)------------------------------
% 5.16/1.70 % (1384508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384508)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384508)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.70 % (1384508)Time elapsed: 0.003 s
% 5.16/1.70 % (1384508)Peak memory usage: 88 MB
% 5.16/1.70 % (1384508)Instructions burned: 2 (million)
% 5.16/1.70 % (1384509)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3392997217:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.16/1.70 % (1384509)Refutation not found, incomplete strategy
% 5.16/1.70 % (1384509)------------------------------
% 5.16/1.70 % (1384509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384509)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384509)Termination reason: Refutation not found, incomplete strategy
% 5.16/1.70 % (1384509)Time elapsed: 0.002 s
% 5.16/1.70 % (1384509)Peak memory usage: 88 MB
% 5.16/1.70 % (1384509)Instructions burned: 1 (million)
% 5.16/1.70 % (1384499)------------------------------
% 5.16/1.70 % (1384499)------------------------------
% 5.16/1.70 % (1384513)lrs+10_64_to=lpo:sil=8000:random_seed=2045778340:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.16/1.70 % (1384507)------------------------------
% 5.16/1.70 % (1384507)------------------------------
% 5.16/1.70 % (1384508)------------------------------
% 5.16/1.70 % (1384508)------------------------------
% 5.16/1.70 % (1384509)------------------------------
% 5.16/1.70 % (1384509)------------------------------
% 5.16/1.70 % (1384513)Instruction limit reached!
% 5.16/1.70 % (1384513)------------------------------
% 5.16/1.70 % (1384513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384513)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384513)Termination reason: Instruction limit
% 5.16/1.70 % (1384513)Termination phase: Saturation
% 5.16/1.70 % (1384513)Time elapsed: 0.077 s
% 5.16/1.70 % (1384513)Peak memory usage: 89 MB
% 5.16/1.70 % (1384513)Instructions burned: 126 (million)
% 5.16/1.70 % (1384495)First to succeed.
% 5.16/1.70 % (1384495)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1384488"
% 5.16/1.70 % (1384515)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=954733057:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.16/1.70 % (1384516)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4170040920:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.16/1.70 % (1384517)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3991932265:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 5.16/1.70 % (1384518)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=2834264518:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 5.16/1.70 % (1384518)Instruction limit reached!
% 5.16/1.70 % (1384518)------------------------------
% 5.16/1.70 % (1384518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384518)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384518)Termination reason: Instruction limit
% 5.16/1.70 % (1384518)Termination phase: Saturation
% 5.16/1.70 % (1384518)Time elapsed: 0.063 s
% 5.16/1.70 % (1384518)Peak memory usage: 89 MB
% 5.16/1.70 % (1384518)Instructions burned: 106 (million)
% 5.16/1.70 % (1384516)Instruction limit reached!
% 5.16/1.70 % (1384516)------------------------------
% 5.16/1.70 % (1384516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384516)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384516)Termination reason: Instruction limit
% 5.16/1.70 % (1384516)Termination phase: Saturation
% 5.16/1.70 % (1384516)Time elapsed: 0.093 s
% 5.16/1.70 % (1384516)Peak memory usage: 91 MB
% 5.16/1.70 % (1384516)Instructions burned: 157 (million)
% 5.16/1.70 % (1384515)Instruction limit reached!
% 5.16/1.70 % (1384515)------------------------------
% 5.16/1.70 % (1384515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.16/1.70 % (1384515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.16/1.70 % (1384515)CaDiCaL version: 2.1.3
% 5.16/1.70 % (1384515)Termination reason: Instruction limit
% 5.16/1.70 % (1384515)Termination phase: Saturation
% 5.16/1.70 % (1384515)Time elapsed: 0.124 s
% 5.16/1.70 % (1384515)Peak memory usage: 90 MB
% 5.16/1.70 % (1384515)Instructions burned: 195 (million)
% 5.16/1.70 % (1384495)Refutation found. Thanks to Tanya!
% 5.16/1.70 % SZS status Unsatisfiable for theBenchmark
% 5.16/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 6.43/1.79 % (1384495)------------------------------
% 6.43/1.79 % (1384495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.43/1.79 % (1384495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.43/1.79 % (1384495)CaDiCaL version: 2.1.3
% 6.43/1.79 % (1384495)Termination reason: Refutation
% 6.43/1.79 % (1384495)Time elapsed: 0.584 s
% 6.43/1.79 % (1384495)Peak memory usage: 134 MB
% 6.43/1.79 % (1384495)Instructions burned: 1418 (million)
% 6.43/1.79 % (1384495)------------------------------
% 6.43/1.79 % (1384495)------------------------------
% 6.43/1.79 % (1384488)Success in time 0.847 s
% 6.43/1.79 % Vampire exiting
%------------------------------------------------------------------------------