%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL016-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:33:44 PM UTC 2026
% Result : Unsatisfiable 5.37s 2.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 33
% Syntax : Number of formulae : 171 ( 171 unt; 20 def)
% Number of atoms : 171 ( 170 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 26 con; 0-2 aty)
% Number of variables : 132 ( 132 !; 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,negated_conjecture,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,negated_conjecture,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,negated_conjecture,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,negated_conjecture,
! [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,negated_conjecture,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_top_12) ).
fof(f16,negated_conjecture,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',def_zero_13) ).
fof(f17,negated_conjecture,
tuple(join(meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))),meet(composition(sk1,sk2),complement(composition(sk1,sk3)))),join(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3))))) != tuple(meet(composition(sk1,sk2),complement(composition(sk1,sk3))),meet(composition(sk1,meet(sk2,complement(sk3))),complement(composition(sk1,sk3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f19,plain,
tuple(join(complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3)))))),join(complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3))))))) != tuple(complement(join(complement(composition(sk1,sk2)),complement(complement(composition(sk1,sk3))))),complement(join(complement(composition(sk1,complement(join(complement(sk2),complement(complement(sk3)))))),complement(complement(composition(sk1,sk3)))))),
inference(definition_unfolding,[],[f17,f6,f6,f6,f6,f6,f6,f6,f6,f6]) ).
fof(f20,definition,
sF0 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f21,plain,
complement(sk2) = sF0,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF1 = complement(sk3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f23,plain,
complement(sk3) = sF1,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF2 = complement(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f25,plain,
complement(sF1) = sF2,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF3 = join(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f27,plain,
join(sF0,sF2) = sF3,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f29,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF5 = composition(sk1,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f31,plain,
composition(sk1,sF4) = sF5,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF6 = complement(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f33,plain,
complement(sF5) = sF6,
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF7 = composition(sk1,sk3),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f35,plain,
composition(sk1,sk3) = sF7,
inference(reorient_equations,[],[f34]) ).
fof(f36,definition,
sF8 = complement(sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f37,plain,
complement(sF7) = sF8,
inference(reorient_equations,[],[f36]) ).
fof(f38,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f39,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF10 = join(sF6,sF9),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f41,plain,
join(sF6,sF9) = sF10,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF11 = complement(sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f43,plain,
complement(sF10) = sF11,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF12 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f45,plain,
composition(sk1,sk2) = sF12,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF13 = complement(sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f47,plain,
complement(sF12) = sF13,
inference(reorient_equations,[],[f46]) ).
fof(f48,definition,
sF14 = join(sF13,sF9),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f49,plain,
join(sF13,sF9) = sF14,
inference(reorient_equations,[],[f48]) ).
fof(f50,definition,
sF15 = complement(sF14),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f51,plain,
complement(sF14) = sF15,
inference(reorient_equations,[],[f50]) ).
fof(f52,definition,
sF16 = join(sF11,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f53,plain,
join(sF11,sF15) = sF16,
inference(reorient_equations,[],[f52]) ).
fof(f54,definition,
sF17 = join(sF15,sF11),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f55,plain,
join(sF15,sF11) = sF17,
inference(reorient_equations,[],[f54]) ).
fof(f56,definition,
sF18 = tuple(sF16,sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f57,plain,
tuple(sF16,sF17) = sF18,
inference(reorient_equations,[],[f56]) ).
fof(f58,definition,
sF19 = tuple(sF15,sF11),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f59,plain,
tuple(sF15,sF11) = sF19,
inference(reorient_equations,[],[f58]) ).
fof(f60,plain,
sF18 != sF19,
inference(definition_folding,[],[f19,f59,f43,f41,f39,f37,f35,f33,f31,f29,f27,f25,f23,f21,f51,f49,f39,f37,f35,f47,f45,f57,f55,f43,f41,f39,f37,f35,f33,f31,f29,f27,f25,f23,f21,f51,f49,f39,f37,f35,f47,f45,f53,f51,f49,f39,f37,f35,f47,f45,f43,f41,f39,f37,f35,f33,f31,f29,f27,f25,f23,f21]) ).
fof(f61,plain,
zero = complement(top),
inference(backward_demodulation,[],[f18,f15]) ).
fof(f62,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f63,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f64,plain,
sF10 = join(sF9,sF6),
inference(forward_demodulation,[],[f41,f1]) ).
fof(f65,plain,
sF14 = join(sF9,sF13),
inference(forward_demodulation,[],[f49,f1]) ).
fof(f66,plain,
join(sF11,sF15) = sF17,
inference(forward_demodulation,[],[f55,f1]) ).
fof(f67,plain,
sF16 = sF17,
inference(forward_demodulation,[],[f66,f53]) ).
fof(f68,plain,
sF18 = tuple(sF16,sF16),
inference(backward_demodulation,[],[f57,f67]) ).
fof(f159,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f63,f15]) ).
fof(f160,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f159,f61]) ).
fof(f194,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f63,f1]) ).
fof(f198,plain,
! [X2,X0,X1] : composition(join(converse(X1),X2),converse(X0)) = join(converse(composition(X0,X1)),composition(X2,converse(X0))),
inference(superposition,[],[f9,f12]) ).
fof(f218,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f351,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f194,f15]) ).
fof(f361,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f351,f1]) ).
fof(f391,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f361,f1]) ).
fof(f407,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f391,f61]) ).
fof(f416,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f160,f407]) ).
fof(f427,plain,
sk2 = complement(sF0),
inference(superposition,[],[f416,f21]) ).
fof(f428,plain,
sk3 = complement(sF1),
inference(superposition,[],[f416,f23]) ).
fof(f431,plain,
sF5 = complement(sF6),
inference(superposition,[],[f416,f33]) ).
fof(f432,plain,
sF7 = complement(sF8),
inference(superposition,[],[f416,f37]) ).
fof(f434,plain,
sF10 = complement(sF11),
inference(superposition,[],[f416,f43]) ).
fof(f435,plain,
sF12 = complement(sF13),
inference(superposition,[],[f416,f47]) ).
fof(f436,plain,
sF14 = complement(sF15),
inference(superposition,[],[f416,f51]) ).
fof(f442,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f194,f416]) ).
fof(f459,plain,
sF7 = sF9,
inference(forward_demodulation,[],[f432,f39]) ).
fof(f461,plain,
sk3 = sF2,
inference(forward_demodulation,[],[f428,f25]) ).
fof(f465,plain,
composition(sk1,sk3) = sF9,
inference(backward_demodulation,[],[f35,f459]) ).
fof(f480,plain,
sF9 = composition(sk1,sF2),
inference(forward_demodulation,[],[f465,f461]) ).
fof(f498,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(complement(join(complement(X1),X0))),complement(join(X0,X1))))),
inference(superposition,[],[f442,f442]) ).
fof(f507,plain,
! [X0,X1] : complement(X1) = join(complement(join(X1,complement(X0))),complement(join(X0,X1))),
inference(superposition,[],[f442,f416]) ).
fof(f535,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(forward_demodulation,[],[f507,f1]) ).
fof(f542,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),complement(complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f498,f1]) ).
fof(f559,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(complement(X1),X0)))),
inference(forward_demodulation,[],[f542,f416]) ).
fof(f570,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(join(X0,X1)),complement(X1))))),
inference(forward_demodulation,[],[f559,f218]) ).
fof(f578,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f570,f1]) ).
fof(f580,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f578,f416]) ).
fof(f581,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f580,f416]) ).
fof(f706,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f710,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f62,f10]) ).
fof(f810,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f706,f8]) ).
fof(f821,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f810,f10]) ).
fof(f908,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(join(complement(join(X0,complement(X1))),join(X1,X0))),complement(complement(X0))),
inference(superposition,[],[f442,f535]) ).
fof(f921,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(complement(join(X0,complement(X1))),join(X1,X0)))),
inference(forward_demodulation,[],[f908,f1]) ).
fof(f945,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(X0,complement(X1)))))),
inference(forward_demodulation,[],[f921,f1]) ).
fof(f965,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f945,f2]) ).
fof(f980,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f965,f416]) ).
fof(f993,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f980,f416]) ).
fof(f1306,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f710,f821]) ).
fof(f1312,plain,
one = converse(one),
inference(superposition,[],[f8,f821]) ).
fof(f1315,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f821,f1312]) ).
fof(f1321,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f1306,f1315]) ).
fof(f1334,plain,
! [X0] : join(X0,X0) = X0,
inference(superposition,[],[f1321,f416]) ).
fof(f1464,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X0,X1)),
inference(superposition,[],[f218,f1334]) ).
fof(f1465,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(superposition,[],[f218,f1334]) ).
fof(f1682,plain,
! [X0,X1] : join(complement(join(X0,complement(X1))),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f1464,f535]) ).
fof(f1693,plain,
join(sF13,sF9) = join(sF9,sF14),
inference(superposition,[],[f1464,f65]) ).
fof(f1694,plain,
join(sF6,sF9) = join(sF9,sF10),
inference(superposition,[],[f1464,f64]) ).
fof(f1753,plain,
join(sF9,sF6) = join(sF9,sF10),
inference(forward_demodulation,[],[f1694,f1]) ).
fof(f1754,plain,
join(sF9,sF13) = join(sF9,sF14),
inference(forward_demodulation,[],[f1693,f1]) ).
fof(f1764,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X0,complement(X1))),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1682,f1]) ).
fof(f1798,plain,
sF10 = join(sF9,sF10),
inference(forward_demodulation,[],[f1753,f64]) ).
fof(f1799,plain,
sF14 = join(sF9,sF14),
inference(forward_demodulation,[],[f1754,f65]) ).
fof(f1809,plain,
! [X0,X1] : join(complement(X0),complement(join(X1,X0))) = join(complement(join(X1,X0)),complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f1764,f1]) ).
fof(f1827,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f1809,f535]) ).
fof(f1842,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f581,f1827]) ).
fof(f1847,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f993,f1842]) ).
fof(f1852,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(forward_demodulation,[],[f1847,f1465]) ).
fof(f1873,plain,
! [X0,X1] : join(X1,complement(join(X0,X1))) = join(X1,complement(X0)),
inference(superposition,[],[f1852,f1]) ).
fof(f1897,plain,
join(sF9,complement(sF13)) = join(sF9,complement(sF14)),
inference(superposition,[],[f1852,f65]) ).
fof(f1898,plain,
join(sF9,complement(sF6)) = join(sF9,complement(sF10)),
inference(superposition,[],[f1852,f64]) ).
fof(f1954,plain,
join(sF9,complement(sF6)) = join(sF9,sF11),
inference(forward_demodulation,[],[f1898,f43]) ).
fof(f1955,plain,
join(sF9,complement(sF13)) = join(sF9,sF15),
inference(forward_demodulation,[],[f1897,f51]) ).
fof(f1986,plain,
join(sF9,complement(sF6)) = join(sF11,sF9),
inference(forward_demodulation,[],[f1954,f1]) ).
fof(f1987,plain,
join(sF9,complement(sF13)) = join(sF15,sF9),
inference(forward_demodulation,[],[f1955,f1]) ).
fof(f2014,plain,
join(sF9,sF5) = join(sF11,sF9),
inference(forward_demodulation,[],[f1986,f431]) ).
fof(f2015,plain,
join(sF9,sF12) = join(sF15,sF9),
inference(forward_demodulation,[],[f1987,f435]) ).
fof(f2535,plain,
join(sF2,complement(sF0)) = join(sF2,complement(sF3)),
inference(superposition,[],[f1873,f27]) ).
fof(f2616,plain,
join(sF2,complement(sF0)) = join(sF2,sF4),
inference(forward_demodulation,[],[f2535,f29]) ).
fof(f2651,plain,
join(sF2,sk2) = join(sF2,sF4),
inference(forward_demodulation,[],[f2616,f427]) ).
fof(f5660,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f198,f12]) ).
fof(f5695,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f5660,f11]) ).
fof(f5712,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f5695,f11]) ).
fof(f5719,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = converse(composition(X0,join(X2,X1))),
inference(forward_demodulation,[],[f5712,f12]) ).
fof(f8525,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f5719]) ).
fof(f8552,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f8525,f10]) ).
fof(f8652,plain,
! [X0] : composition(sk1,join(X0,sk2)) = join(composition(sk1,X0),sF12),
inference(superposition,[],[f8552,f45]) ).
fof(f8654,plain,
! [X0] : composition(sk1,join(X0,sF4)) = join(composition(sk1,X0),sF5),
inference(superposition,[],[f8552,f31]) ).
fof(f8711,plain,
! [X0] : join(sF5,composition(sk1,X0)) = composition(sk1,join(X0,sF4)),
inference(forward_demodulation,[],[f8654,f1]) ).
fof(f8713,plain,
! [X0] : join(sF12,composition(sk1,X0)) = composition(sk1,join(X0,sk2)),
inference(forward_demodulation,[],[f8652,f1]) ).
fof(f8805,plain,
join(sF12,composition(sk1,sF2)) = composition(sk1,join(sF2,sF4)),
inference(superposition,[],[f8713,f2651]) ).
fof(f8828,plain,
join(sF12,composition(sk1,sF2)) = join(sF5,composition(sk1,sF2)),
inference(forward_demodulation,[],[f8805,f8711]) ).
fof(f8838,plain,
join(sF5,sF9) = join(sF12,sF9),
inference(forward_demodulation,[],[f8828,f480]) ).
fof(f8844,plain,
join(sF9,sF12) = join(sF5,sF9),
inference(forward_demodulation,[],[f8838,f1]) ).
fof(f8846,plain,
join(sF9,sF5) = join(sF9,sF12),
inference(forward_demodulation,[],[f8844,f1]) ).
fof(f8847,plain,
join(sF9,sF5) = join(sF15,sF9),
inference(forward_demodulation,[],[f8846,f2015]) ).
fof(f8848,plain,
join(sF11,sF9) = join(sF15,sF9),
inference(forward_demodulation,[],[f8847,f2014]) ).
fof(f8959,plain,
join(sF9,complement(join(sF11,sF9))) = join(sF9,complement(sF15)),
inference(superposition,[],[f1873,f8848]) ).
fof(f8966,plain,
join(sF9,sF14) = join(sF9,complement(join(sF11,sF9))),
inference(forward_demodulation,[],[f8959,f436]) ).
fof(f8983,plain,
join(sF9,sF14) = join(sF9,complement(sF11)),
inference(forward_demodulation,[],[f8966,f1873]) ).
fof(f8998,plain,
join(sF9,sF14) = join(sF9,sF10),
inference(forward_demodulation,[],[f8983,f434]) ).
fof(f9007,plain,
sF10 = join(sF9,sF14),
inference(forward_demodulation,[],[f8998,f1798]) ).
fof(f9015,plain,
sF10 = sF14,
inference(backward_demodulation,[],[f1799,f9007]) ).
fof(f9021,plain,
complement(sF10) = sF15,
inference(backward_demodulation,[],[f51,f9015]) ).
fof(f9096,plain,
sF11 = sF15,
inference(forward_demodulation,[],[f9021,f43]) ).
fof(f9105,plain,
sF16 = join(sF11,sF11),
inference(backward_demodulation,[],[f53,f9096]) ).
fof(f9106,plain,
sF19 = tuple(sF11,sF11),
inference(backward_demodulation,[],[f59,f9096]) ).
fof(f9194,plain,
sF11 = sF16,
inference(forward_demodulation,[],[f9105,f1334]) ).
fof(f9215,plain,
sF18 = tuple(sF11,sF11),
inference(backward_demodulation,[],[f68,f9194]) ).
fof(f9265,plain,
sF18 = sF19,
inference(backward_demodulation,[],[f9106,f9215]) ).
fof(f9271,plain,
$false,
inference(forward_subsumption_resolution,[],[f9265,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL016-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n020.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 22:51:36 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 5.37/2.51 % (3854688)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.37/2.51 % (3854851)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2936349221:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.37/2.51 % (3854843)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=679074701:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.37/2.51 % (3854848)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1912673803:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.37/2.51 % (3854844)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1065422607:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.37/2.51 % (3854846)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2420823480:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.37/2.51 % (3854841)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2350399782:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.37/2.51 % (3854849)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3121338620:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.37/2.51 % (3854846)Instruction limit reached!
% 5.37/2.51 % (3854846)------------------------------
% 5.37/2.51 % (3854846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854846)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854846)Termination reason: Instruction limit
% 5.37/2.51 % (3854846)Termination phase: Saturation
% 5.37/2.51 % (3854846)Time elapsed: 0.080 s
% 5.37/2.51 % (3854846)Peak memory usage: 88 MB
% 5.37/2.51 % (3854846)Instructions burned: 136 (million)
% 5.37/2.51 % (3854848)Instruction limit reached!
% 5.37/2.51 % (3854848)------------------------------
% 5.37/2.51 % (3854848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854848)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854848)Termination reason: Instruction limit
% 5.37/2.51 % (3854848)Termination phase: Saturation
% 5.37/2.51 % (3854848)Time elapsed: 0.103 s
% 5.37/2.51 % (3854848)Peak memory usage: 90 MB
% 5.37/2.51 % (3854848)Instructions burned: 181 (million)
% 5.37/2.51 % (3854849)Instruction limit reached!
% 5.37/2.51 % (3854849)------------------------------
% 5.37/2.51 % (3854849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854849)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854849)Termination reason: Instruction limit
% 5.37/2.51 % (3854849)Termination phase: Saturation
% 5.37/2.51 % (3854849)Time elapsed: 0.169 s
% 5.37/2.51 % (3854849)Peak memory usage: 90 MB
% 5.37/2.51 % (3854849)Instructions burned: 258 (million)
% 5.37/2.51 % (3854859)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=826827389:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.37/2.51 % (3854860)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1345950804:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.37/2.51 % (3854851)Instruction limit reached!
% 5.37/2.51 % (3854851)------------------------------
% 5.37/2.51 % (3854851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854851)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854851)Termination reason: Instruction limit
% 5.37/2.51 % (3854851)Termination phase: Saturation
% 5.37/2.51 % (3854851)Time elapsed: 0.353 s
% 5.37/2.51 % (3854851)Peak memory usage: 99 MB
% 5.37/2.51 % (3854851)Instructions burned: 1189 (million)
% 5.37/2.51 % (3854861)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1592385151:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.37/2.51 % (3854861)Instruction limit reached!
% 5.37/2.51 % (3854861)------------------------------
% 5.37/2.51 % (3854861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854861)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854861)Termination reason: Instruction limit
% 5.37/2.51 % (3854861)Termination phase: Saturation
% 5.37/2.51 % (3854861)Time elapsed: 0.099 s
% 5.37/2.51 % (3854861)Peak memory usage: 90 MB
% 5.37/2.51 % (3854861)Instructions burned: 217 (million)
% 5.37/2.51 % (3854864)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=3217555906:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2995 on theBenchmark for (2995ds/317Mi)
% 5.37/2.51 % (3854864)Instruction limit reached!
% 5.37/2.51 % (3854864)------------------------------
% 5.37/2.51 % (3854864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/2.51 % (3854864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/2.51 % (3854864)CaDiCaL version: 2.1.3
% 5.37/2.51 % (3854864)Termination reason: Instruction limit
% 5.37/2.51 % (3854864)Termination phase: Saturation
% 5.37/2.51 % (3854864)Time elapsed: 0.108 s
% 5.37/2.51 % (3854864)Peak memory usage: 94 MB
% 5.37/2.51 % (3854864)Instructions burned: 318 (million)
% 5.37/2.51 % (3854867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=114559624:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2994 on theBenchmark for (2994ds/12125Mi)
% 5.37/2.51 % (3854868)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2711666327:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2992 on theBenchmark for (2992ds/2836Mi)
% 5.37/2.51 % (3854844)First to succeed.
% 5.37/2.51 % (3854844)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3854688"
% 5.37/2.51 % (3854841)Also succeeded, but the first one will report.
% 5.37/2.51 % (3854844)Refutation found. Thanks to Tanya!
% 5.37/2.51 % SZS status Unsatisfiable for theBenchmark
% 5.37/2.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/2.71 % (3854844)------------------------------
% 0.21/2.71 % (3854844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/2.71 % (3854844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/2.71 % (3854844)CaDiCaL version: 2.1.3
% 0.21/2.71 % (3854844)Termination reason: Refutation
% 0.21/2.71 % (3854844)Time elapsed: 1.194 s
% 0.21/2.71 % (3854844)Peak memory usage: 136 MB
% 0.21/2.71 % (3854844)Instructions burned: 1848 (million)
% 0.21/2.71 % (3854844)------------------------------
% 0.21/2.71 % (3854844)------------------------------
% 0.21/2.71 % (3854688)Success in time 1.62 s
% 0.21/2.71 % Vampire exiting
%------------------------------------------------------------------------------