%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL033-1 : 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 : n012.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 12:33:59 PM UTC 2026
% Result : Unsatisfiable 32.62s 5.38s
% Output : Refutation 33.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 25
% Syntax : Number of formulae : 326 ( 326 unt; 10 def)
% Number of atoms : 326 ( 325 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-2 aty)
% Number of variables : 307 ( 307 !; 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(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_associativity_5) ).
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,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
composition(meet(sk1,sk2),sk3) != meet(sk1,composition(sk2,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f21,plain,
composition(complement(join(complement(sk1),complement(sk2))),sk3) != complement(join(complement(sk1),complement(composition(sk2,sk3)))),
inference(definition_unfolding,[],[f19,f6,f6]) ).
fof(f22,definition,
sF0 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
composition(sk1,top) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
sk1 = sF0,
inference(definition_folding,[],[f18,f23]) ).
fof(f25,definition,
sF1 = complement(sk1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
complement(sk1) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = complement(sk2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
complement(sk2) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF3 = join(sF1,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f30,plain,
join(sF1,sF2) = sF3,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF4 = complement(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f32,plain,
complement(sF3) = sF4,
inference(reorient_equations,[],[f31]) ).
fof(f33,definition,
sF5 = composition(sF4,sk3),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f34,plain,
composition(sF4,sk3) = sF5,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF6 = composition(sk2,sk3),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f36,plain,
composition(sk2,sk3) = sF6,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF7 = complement(sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f38,plain,
complement(sF6) = sF7,
inference(reorient_equations,[],[f37]) ).
fof(f39,definition,
sF8 = join(sF1,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f40,plain,
join(sF1,sF7) = sF8,
inference(reorient_equations,[],[f39]) ).
fof(f41,definition,
sF9 = complement(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f42,plain,
complement(sF8) = sF9,
inference(reorient_equations,[],[f41]) ).
fof(f43,plain,
sF5 != sF9,
inference(definition_folding,[],[f21,f42,f40,f38,f36,f26,f34,f32,f30,f28,f26]) ).
fof(f44,plain,
zero = complement(top),
inference(backward_demodulation,[],[f20,f15]) ).
fof(f45,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(backward_demodulation,[],[f14,f1]) ).
fof(f46,plain,
! [X0,X1] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(backward_demodulation,[],[f4,f1]) ).
fof(f47,plain,
sk1 = composition(sk1,top),
inference(forward_demodulation,[],[f23,f24]) ).
fof(f57,plain,
! [X0] : join(complement(join(complement(X0),sk2)),complement(join(complement(X0),sF2))) = X0,
inference(superposition,[],[f46,f28]) ).
fof(f62,plain,
! [X0] : join(complement(join(complement(X0),sF2)),complement(join(complement(X0),sk2))) = X0,
inference(forward_demodulation,[],[f57,f1]) ).
fof(f66,plain,
! [X0] : join(complement(join(complement(X0),sF2)),complement(join(sk2,complement(X0)))) = X0,
inference(forward_demodulation,[],[f62,f1]) ).
fof(f70,plain,
! [X0] : join(complement(join(sk2,complement(X0))),complement(join(complement(X0),sF2))) = X0,
inference(forward_demodulation,[],[f66,f1]) ).
fof(f73,plain,
! [X0] : join(complement(join(sk2,complement(X0))),complement(join(sF2,complement(X0)))) = X0,
inference(forward_demodulation,[],[f70,f1]) ).
fof(f75,plain,
! [X0] : join(complement(join(sF2,complement(X0))),complement(join(sk2,complement(X0)))) = X0,
inference(forward_demodulation,[],[f73,f1]) ).
fof(f98,plain,
! [X0] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[],[f46,f15]) ).
fof(f99,plain,
! [X0] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(forward_demodulation,[],[f98,f44]) ).
fof(f104,plain,
complement(top) = join(complement(top),composition(converse(sk1),complement(sk1))),
inference(superposition,[],[f45,f47]) ).
fof(f105,plain,
complement(top) = join(complement(top),composition(converse(sk1),sF1)),
inference(forward_demodulation,[],[f104,f26]) ).
fof(f106,plain,
zero = join(zero,composition(converse(sk1),sF1)),
inference(forward_demodulation,[],[f105,f44]) ).
fof(f112,plain,
! [X0,X1] : join(complement(join(complement(X1),X0)),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[],[f46,f1]) ).
fof(f113,plain,
! [X0] : composition(join(sF4,X0),sk3) = join(sF5,composition(X0,sk3)),
inference(superposition,[],[f9,f34]) ).
fof(f116,plain,
! [X0] : composition(join(X0,sF4),sk3) = join(composition(X0,sk3),sF5),
inference(superposition,[],[f9,f34]) ).
fof(f118,plain,
! [X0] : composition(join(X0,sk2),sk3) = join(composition(X0,sk3),sF6),
inference(superposition,[],[f9,f36]) ).
fof(f123,plain,
! [X0] : join(sF6,composition(X0,sk3)) = composition(join(X0,sk2),sk3),
inference(forward_demodulation,[],[f118,f1]) ).
fof(f125,plain,
! [X0] : join(sF5,composition(X0,sk3)) = composition(join(X0,sF4),sk3),
inference(forward_demodulation,[],[f116,f1]) ).
fof(f129,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X1),converse(X0)),
inference(superposition,[],[f1,f11]) ).
fof(f131,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(f134,plain,
top = join(top,zero),
inference(superposition,[],[f15,f44]) ).
fof(f137,plain,
! [X0] : zero = join(zero,composition(converse(X0),complement(composition(X0,top)))),
inference(superposition,[],[f45,f44]) ).
fof(f142,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[],[f2,f15]) ).
fof(f144,plain,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f146,plain,
! [X2,X0,X1] : join(complement(X0),join(composition(converse(X1),complement(composition(X1,X0))),X2)) = join(complement(X0),X2),
inference(superposition,[],[f2,f45]) ).
fof(f150,plain,
! [X0] : join(sF1,join(sF7,X0)) = join(sF8,X0),
inference(superposition,[],[f2,f40]) ).
fof(f151,plain,
! [X0] : join(sF1,join(sF2,X0)) = join(sF3,X0),
inference(superposition,[],[f2,f30]) ).
fof(f157,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(X2,join(X0,X1)),
inference(superposition,[],[f1,f2]) ).
fof(f198,plain,
! [X0] : complement(X0) = join(complement(join(complement(complement(X0)),X0)),complement(top)),
inference(superposition,[],[f112,f15]) ).
fof(f205,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(complement(complement(X0)),X0))),
inference(forward_demodulation,[],[f198,f1]) ).
fof(f225,plain,
! [X0] : complement(X0) = join(complement(top),complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f205,f1]) ).
fof(f236,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,complement(complement(X0))))),
inference(forward_demodulation,[],[f225,f44]) ).
fof(f243,plain,
! [X0] : complement(complement(X0)) = X0,
inference(backward_demodulation,[],[f99,f236]) ).
fof(f246,plain,
! [X0] : complement(X0) = join(zero,complement(join(X0,X0))),
inference(backward_demodulation,[],[f236,f243]) ).
fof(f257,plain,
top = complement(zero),
inference(superposition,[],[f243,f44]) ).
fof(f258,plain,
sk1 = complement(sF1),
inference(superposition,[],[f243,f26]) ).
fof(f259,plain,
sk2 = complement(sF2),
inference(superposition,[],[f243,f28]) ).
fof(f261,plain,
sF6 = complement(sF7),
inference(superposition,[],[f243,f38]) ).
fof(f262,plain,
sF8 = complement(sF9),
inference(superposition,[],[f243,f42]) ).
fof(f265,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(X0,complement(X1)))),
inference(superposition,[],[f46,f243]) ).
fof(f268,plain,
! [X0,X1] : complement(X0) = join(complement(join(X0,X1)),complement(join(complement(X1),X0))),
inference(superposition,[],[f112,f243]) ).
fof(f283,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(X1,complement(X0)))),
inference(superposition,[],[f265,f1]) ).
fof(f303,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(join(complement(join(X0,X1)),join(X0,complement(X1)))),complement(complement(X0))),
inference(superposition,[],[f265,f265]) ).
fof(f308,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(complement(join(X0,X1)),join(X0,complement(X1))))),
inference(forward_demodulation,[],[f303,f1]) ).
fof(f323,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(complement(complement(X0)),complement(join(join(X0,complement(X1)),complement(join(X0,X1))))),
inference(forward_demodulation,[],[f308,f1]) ).
fof(f331,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,[],[f323,f2]) ).
fof(f336,plain,
! [X0,X1] : complement(complement(join(X0,X1))) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f331,f243]) ).
fof(f338,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,join(complement(X1),complement(join(X0,X1)))))),
inference(forward_demodulation,[],[f336,f243]) ).
fof(f342,plain,
! [X0,X1] : complement(X1) = join(complement(join(X0,X1)),complement(join(complement(X0),X1))),
inference(superposition,[],[f268,f1]) ).
fof(f509,plain,
! [X0,X1] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[],[f12,f10]) ).
fof(f512,plain,
! [X0,X1] : join(X0,converse(X1)) = converse(join(converse(X0),X1)),
inference(superposition,[],[f11,f10]) ).
fof(f513,plain,
! [X0,X1] : complement(X1) = join(complement(X1),composition(X0,complement(composition(converse(X0),X1)))),
inference(superposition,[],[f45,f10]) ).
fof(f540,plain,
! [X0] : converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[],[f509,f8]) ).
fof(f551,plain,
! [X0] : composition(converse(one),X0) = X0,
inference(forward_demodulation,[],[f540,f10]) ).
fof(f557,plain,
! [X0,X1] : join(top,X1) = join(complement(X0),join(X0,X1)),
inference(superposition,[],[f144,f15]) ).
fof(f607,plain,
! [X0,X1] : join(top,X1) = join(X0,join(X1,complement(X0))),
inference(forward_demodulation,[],[f557,f157]) ).
fof(f655,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(join(X0,X0)),complement(zero)))),
inference(superposition,[],[f283,f246]) ).
fof(f657,plain,
complement(sF2) = join(complement(sF3),complement(join(sF2,complement(sF1)))),
inference(superposition,[],[f283,f30]) ).
fof(f677,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,[],[f268,f283]) ).
fof(f690,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,[],[f677,f1]) ).
fof(f697,plain,
complement(sF2) = join(complement(sF3),complement(join(sF2,sk1))),
inference(forward_demodulation,[],[f657,f258]) ).
fof(f699,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(complement(zero),complement(join(X0,X0))))),
inference(forward_demodulation,[],[f655,f1]) ).
fof(f710,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,[],[f690,f1]) ).
fof(f716,plain,
complement(sF2) = join(sF4,complement(join(sF2,sk1))),
inference(forward_demodulation,[],[f697,f32]) ).
fof(f718,plain,
! [X0] : complement(complement(join(X0,X0))) = join(complement(complement(X0)),complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f699,f257]) ).
fof(f726,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,[],[f710,f2]) ).
fof(f731,plain,
sk2 = join(sF4,complement(join(sF2,sk1))),
inference(forward_demodulation,[],[f716,f259]) ).
fof(f733,plain,
! [X0] : complement(complement(join(X0,X0))) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f718,f243]) ).
fof(f740,plain,
! [X0,X1] : complement(complement(join(X0,complement(X1)))) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f726,f243]) ).
fof(f745,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(top,complement(join(X0,X0))))),
inference(forward_demodulation,[],[f733,f243]) ).
fof(f752,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,complement(join(X0,complement(X1))))))),
inference(forward_demodulation,[],[f740,f243]) ).
fof(f770,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(join(X1,X0),complement(X0)),
inference(superposition,[],[f142,f283]) ).
fof(f805,plain,
! [X0,X1] : join(top,complement(join(X0,complement(X1)))) = join(complement(X0),join(X1,X0)),
inference(forward_demodulation,[],[f770,f1]) ).
fof(f818,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(top,complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f805,f157]) ).
fof(f823,plain,
! [X0,X1] : join(top,X1) = join(top,complement(join(X0,complement(X1)))),
inference(forward_demodulation,[],[f818,f142]) ).
fof(f1006,plain,
! [X0] : join(top,complement(join(sk2,complement(X0)))) = join(join(sF2,complement(X0)),X0),
inference(superposition,[],[f142,f75]) ).
fof(f1025,plain,
! [X0] : join(top,complement(join(sk2,complement(X0)))) = join(X0,join(sF2,complement(X0))),
inference(forward_demodulation,[],[f1006,f1]) ).
fof(f1044,plain,
! [X0] : join(top,complement(join(sk2,complement(X0)))) = join(top,sF2),
inference(forward_demodulation,[],[f1025,f607]) ).
fof(f1058,plain,
! [X0] : join(sF2,top) = join(top,complement(join(sk2,complement(X0)))),
inference(forward_demodulation,[],[f1044,f1]) ).
fof(f1067,plain,
! [X0] : join(top,X0) = join(sF2,top),
inference(forward_demodulation,[],[f1058,f823]) ).
fof(f1070,plain,
! [X0,X1] : join(X0,join(complement(X0),X1)) = join(sF2,top),
inference(backward_demodulation,[],[f142,f1067]) ).
fof(f1097,plain,
! [X0] : join(X0,X0) = join(X0,complement(join(sF2,top))),
inference(backward_demodulation,[],[f745,f1067]) ).
fof(f1100,plain,
top = join(sF2,top),
inference(backward_demodulation,[],[f134,f1067]) ).
fof(f1101,plain,
! [X0] : top = join(top,X0),
inference(backward_demodulation,[],[f1067,f1100]) ).
fof(f1102,plain,
! [X0] : join(X0,X0) = join(X0,complement(top)),
inference(forward_demodulation,[],[f1097,f1100]) ).
fof(f1129,plain,
! [X0,X1] : top = join(X0,join(complement(X0),X1)),
inference(forward_demodulation,[],[f1070,f1100]) ).
fof(f1130,plain,
! [X0] : join(X0,X0) = join(X0,zero),
inference(forward_demodulation,[],[f1102,f44]) ).
fof(f1161,plain,
! [X0,X1] : join(X0,join(X0,X1)) = join(X1,join(X0,zero)),
inference(superposition,[],[f157,f1130]) ).
fof(f1162,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,join(X0,zero)),
inference(superposition,[],[f157,f1130]) ).
fof(f1172,plain,
! [X0,X1] : join(X0,join(X1,join(X0,X1))) = join(join(X0,X1),zero),
inference(superposition,[],[f2,f1130]) ).
fof(f1174,plain,
! [X0,X1] : composition(join(X0,X0),X1) = join(composition(X0,X1),zero),
inference(superposition,[],[f9,f1130]) ).
fof(f1176,plain,
! [X0] : converse(join(converse(X0),zero)) = join(X0,converse(converse(X0))),
inference(superposition,[],[f512,f1130]) ).
fof(f1178,plain,
! [X0] : join(zero,X0) = join(X0,X0),
inference(superposition,[],[f1,f1130]) ).
fof(f1199,plain,
! [X0] : join(X0,X0) = converse(join(converse(X0),zero)),
inference(forward_demodulation,[],[f1176,f10]) ).
fof(f1201,plain,
! [X0,X1] : composition(join(X0,X0),X1) = join(zero,composition(X0,X1)),
inference(forward_demodulation,[],[f1174,f1]) ).
fof(f1203,plain,
! [X0,X1] : join(X0,join(X1,join(X0,X1))) = join(zero,join(X0,X1)),
inference(forward_demodulation,[],[f1172,f1]) ).
fof(f1227,plain,
! [X0] : join(X0,X0) = join(X0,converse(zero)),
inference(forward_demodulation,[],[f1199,f512]) ).
fof(f1274,plain,
! [X0,X1] : join(X1,join(X0,X0)) = join(zero,join(X0,X1)),
inference(superposition,[],[f157,f1178]) ).
fof(f1275,plain,
! [X0,X1] : join(X0,join(X1,zero)) = join(X1,join(X0,X0)),
inference(superposition,[],[f157,f1178]) ).
fof(f2293,plain,
! [X0] : complement(X0) = join(complement(X0),composition(one,complement(X0))),
inference(superposition,[],[f513,f551]) ).
fof(f2296,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(composition(X1,X0),X0),
inference(superposition,[],[f9,f551]) ).
fof(f2297,plain,
! [X0,X1] : composition(join(converse(one),X1),X0) = join(X0,composition(X1,X0)),
inference(superposition,[],[f9,f551]) ).
fof(f2299,plain,
one = converse(one),
inference(superposition,[],[f8,f551]) ).
fof(f2302,plain,
! [X0] : composition(one,X0) = X0,
inference(backward_demodulation,[],[f551,f2299]) ).
fof(f2304,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(forward_demodulation,[],[f2297,f2299]) ).
fof(f2305,plain,
! [X0,X1] : composition(join(X1,converse(one)),X0) = join(X0,composition(X1,X0)),
inference(forward_demodulation,[],[f2296,f1]) ).
fof(f2308,plain,
! [X0] : complement(X0) = join(complement(X0),complement(X0)),
inference(backward_demodulation,[],[f2293,f2302]) ).
fof(f2310,plain,
! [X0,X1] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(forward_demodulation,[],[f2305,f2299]) ).
fof(f2311,plain,
! [X0] : complement(X0) = join(complement(X0),zero),
inference(forward_demodulation,[],[f2308,f1130]) ).
fof(f2314,plain,
! [X0] : complement(X0) = join(zero,complement(X0)),
inference(forward_demodulation,[],[f2311,f1]) ).
fof(f2319,plain,
! [X0] : complement(X0) = complement(join(X0,X0)),
inference(backward_demodulation,[],[f246,f2314]) ).
fof(f2380,plain,
! [X0] : complement(complement(X0)) = join(X0,X0),
inference(superposition,[],[f243,f2319]) ).
fof(f2390,plain,
! [X0] : join(X0,X0) = X0,
inference(forward_demodulation,[],[f2380,f243]) ).
fof(f2411,plain,
! [X0] : join(X0,zero) = X0,
inference(backward_demodulation,[],[f1130,f2390]) ).
fof(f2412,plain,
! [X0] : join(zero,X0) = X0,
inference(backward_demodulation,[],[f1178,f2390]) ).
fof(f2416,plain,
! [X0,X1] : composition(X0,X1) = join(zero,composition(X0,X1)),
inference(backward_demodulation,[],[f1201,f2390]) ).
fof(f2417,plain,
! [X0] : join(X0,converse(zero)) = X0,
inference(backward_demodulation,[],[f1227,f2390]) ).
fof(f2418,plain,
! [X0,X1] : join(X1,X0) = join(zero,join(X0,X1)),
inference(backward_demodulation,[],[f1274,f2390]) ).
fof(f2419,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,zero)),
inference(backward_demodulation,[],[f1275,f2390]) ).
fof(f2462,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(backward_demodulation,[],[f1161,f2419]) ).
fof(f2463,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X1,X0)),
inference(backward_demodulation,[],[f1162,f2419]) ).
fof(f2465,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,join(X0,X1))),
inference(backward_demodulation,[],[f1203,f2418]) ).
fof(f2474,plain,
zero = composition(converse(sk1),sF1),
inference(backward_demodulation,[],[f106,f2416]) ).
fof(f2475,plain,
! [X0] : zero = composition(converse(X0),complement(composition(X0,top))),
inference(backward_demodulation,[],[f137,f2416]) ).
fof(f2499,plain,
! [X0,X1] : join(X1,X0) = join(X0,join(X1,X0)),
inference(forward_demodulation,[],[f2465,f2463]) ).
fof(f2676,plain,
join(sF2,sF1) = join(sF3,sF1),
inference(superposition,[],[f151,f2499]) ).
fof(f2677,plain,
join(sF7,sF1) = join(sF8,sF1),
inference(superposition,[],[f150,f2499]) ).
fof(f2684,plain,
join(sF7,sF1) = join(sF1,sF8),
inference(forward_demodulation,[],[f2677,f1]) ).
fof(f2685,plain,
join(sF2,sF1) = join(sF1,sF3),
inference(forward_demodulation,[],[f2676,f1]) ).
fof(f2714,plain,
join(sF1,sF7) = join(sF1,sF8),
inference(forward_demodulation,[],[f2684,f1]) ).
fof(f2715,plain,
join(sF1,sF2) = join(sF1,sF3),
inference(forward_demodulation,[],[f2685,f1]) ).
fof(f2729,plain,
sF8 = join(sF1,sF8),
inference(forward_demodulation,[],[f2714,f40]) ).
fof(f2730,plain,
sF3 = join(sF1,sF3),
inference(forward_demodulation,[],[f2715,f30]) ).
fof(f2864,plain,
complement(sF1) = join(complement(sF3),complement(join(sF1,complement(sF3)))),
inference(superposition,[],[f265,f2730]) ).
fof(f2869,plain,
complement(sF1) = join(sF4,complement(join(sF1,sF4))),
inference(forward_demodulation,[],[f2864,f32]) ).
fof(f2873,plain,
sk1 = join(sF4,complement(join(sF1,sF4))),
inference(forward_demodulation,[],[f2869,f258]) ).
fof(f2879,plain,
complement(sF1) = join(complement(sF8),complement(join(sF1,complement(sF8)))),
inference(superposition,[],[f265,f2729]) ).
fof(f2884,plain,
complement(sF1) = join(sF9,complement(join(sF1,sF9))),
inference(forward_demodulation,[],[f2879,f42]) ).
fof(f2888,plain,
sk1 = join(sF9,complement(join(sF1,sF9))),
inference(forward_demodulation,[],[f2884,f258]) ).
fof(f2916,plain,
zero = converse(zero),
inference(superposition,[],[f2412,f2417]) ).
fof(f2975,plain,
! [X0,X1] : complement(X0) = join(complement(join(X1,X0)),complement(X0)),
inference(superposition,[],[f2462,f283]) ).
fof(f3035,plain,
! [X0,X1] : complement(X0) = join(complement(X0),complement(join(X1,X0))),
inference(forward_demodulation,[],[f2975,f1]) ).
fof(f3051,plain,
! [X0,X1] : join(X0,X1) = join(X0,complement(join(X0,complement(X1)))),
inference(backward_demodulation,[],[f338,f3035]) ).
fof(f3058,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,join(X0,X1)))),
inference(backward_demodulation,[],[f752,f3051]) ).
fof(f3061,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f3058,f2463]) ).
fof(f3071,plain,
sk1 = join(sF4,complement(sF1)),
inference(backward_demodulation,[],[f2873,f3061]) ).
fof(f3072,plain,
sk1 = join(sF9,complement(sF1)),
inference(backward_demodulation,[],[f2888,f3061]) ).
fof(f3073,plain,
sk1 = join(sF9,sk1),
inference(forward_demodulation,[],[f3072,f258]) ).
fof(f3074,plain,
sk1 = join(sF4,sk1),
inference(forward_demodulation,[],[f3071,f258]) ).
fof(f3080,plain,
sk1 = join(sk1,sF9),
inference(forward_demodulation,[],[f3073,f1]) ).
fof(f3098,plain,
! [X0,X1] : join(X0,complement(X1)) = join(X0,complement(join(X0,X1))),
inference(superposition,[],[f3061,f1]) ).
fof(f3119,plain,
join(sF2,complement(sF1)) = join(sF2,complement(sF3)),
inference(superposition,[],[f3061,f30]) ).
fof(f3177,plain,
join(sF2,complement(sF1)) = join(sF2,sF4),
inference(forward_demodulation,[],[f3119,f32]) ).
fof(f3215,plain,
join(sF2,sk1) = join(sF2,sF4),
inference(forward_demodulation,[],[f3177,f258]) ).
fof(f3241,plain,
sk2 = join(sF4,complement(join(sF2,sF4))),
inference(backward_demodulation,[],[f731,f3215]) ).
fof(f3257,plain,
sk2 = join(sF4,complement(sF2)),
inference(forward_demodulation,[],[f3241,f3061]) ).
fof(f3265,plain,
sk2 = join(sF4,sk2),
inference(forward_demodulation,[],[f3257,f259]) ).
fof(f3286,plain,
composition(sk2,sk3) = join(sF5,composition(sk2,sk3)),
inference(superposition,[],[f113,f3265]) ).
fof(f3302,plain,
sF6 = join(sF5,sF6),
inference(forward_demodulation,[],[f3286,f36]) ).
fof(f3306,plain,
sF6 = join(sF6,sF5),
inference(forward_demodulation,[],[f3302,f1]) ).
fof(f3320,plain,
complement(sF5) = join(complement(sF6),complement(join(sF5,complement(sF6)))),
inference(superposition,[],[f283,f3306]) ).
fof(f3324,plain,
complement(sF5) = join(complement(sF6),complement(sF5)),
inference(forward_demodulation,[],[f3320,f3061]) ).
fof(f3327,plain,
complement(sF5) = join(sF7,complement(sF5)),
inference(forward_demodulation,[],[f3324,f38]) ).
fof(f3328,plain,
! [X0] : join(sk1,X0) = join(sk1,join(sF9,X0)),
inference(superposition,[],[f2,f3080]) ).
fof(f3555,plain,
! [X0] : join(one,converse(X0)) = converse(join(X0,one)),
inference(superposition,[],[f129,f2299]) ).
fof(f3572,plain,
composition(sk1,sk3) = join(sF5,composition(sk1,sk3)),
inference(superposition,[],[f113,f3074]) ).
fof(f3602,plain,
converse(zero) = composition(converse(sF1),sk1),
inference(superposition,[],[f509,f2474]) ).
fof(f3603,plain,
! [X0] : composition(zero,X0) = composition(converse(sk1),composition(sF1,X0)),
inference(superposition,[],[f7,f2474]) ).
fof(f3610,plain,
zero = composition(converse(sF1),sk1),
inference(forward_demodulation,[],[f3602,f2916]) ).
fof(f4017,plain,
! [X0,X1] : join(X0,complement(top)) = join(X0,complement(join(complement(X0),X1))),
inference(superposition,[],[f3098,f1129]) ).
fof(f4040,plain,
join(sF1,complement(sF2)) = join(sF1,complement(sF3)),
inference(superposition,[],[f3098,f30]) ).
fof(f4106,plain,
join(sF1,complement(sF2)) = join(sF1,sF4),
inference(forward_demodulation,[],[f4040,f32]) ).
fof(f4123,plain,
! [X0,X1] : join(X0,zero) = join(X0,complement(join(complement(X0),X1))),
inference(forward_demodulation,[],[f4017,f44]) ).
fof(f4145,plain,
join(sF1,sk2) = join(sF1,sF4),
inference(forward_demodulation,[],[f4106,f259]) ).
fof(f4159,plain,
! [X0,X1] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(forward_demodulation,[],[f4123,f2411]) ).
fof(f4258,plain,
! [X2,X0,X1] : join(X0,X2) = join(complement(join(complement(X0),X1)),join(X0,X2)),
inference(superposition,[],[f144,f4159]) ).
fof(f4292,plain,
! [X2,X0,X1] : join(X0,X2) = join(X0,join(X2,complement(join(complement(X0),X1)))),
inference(forward_demodulation,[],[f4258,f157]) ).
fof(f4545,plain,
join(sF8,complement(sF5)) = join(sF1,complement(sF5)),
inference(superposition,[],[f150,f3327]) ).
fof(f5660,plain,
complement(sk1) = join(complement(sk1),composition(sF1,complement(zero))),
inference(superposition,[],[f513,f3610]) ).
fof(f5670,plain,
complement(sk1) = join(complement(sk1),composition(sF1,top)),
inference(forward_demodulation,[],[f5660,f257]) ).
fof(f5673,plain,
sF1 = join(sF1,composition(sF1,top)),
inference(forward_demodulation,[],[f5670,f26]) ).
fof(f7204,plain,
! [X0,X1] : complement(complement(join(complement(X1),X0))) = join(complement(join(join(X1,X0),complement(join(complement(X1),X0)))),complement(complement(X0))),
inference(superposition,[],[f342,f342]) ).
fof(f7289,plain,
! [X0,X1] : complement(complement(join(complement(X1),X0))) = join(complement(complement(X0)),complement(join(join(X1,X0),complement(join(complement(X1),X0))))),
inference(forward_demodulation,[],[f7204,f1]) ).
fof(f7378,plain,
! [X0,X1] : complement(complement(join(complement(X1),X0))) = join(complement(complement(X0)),complement(join(X1,join(X0,complement(join(complement(X1),X0)))))),
inference(forward_demodulation,[],[f7289,f2]) ).
fof(f7449,plain,
! [X0,X1] : complement(complement(join(complement(X1),X0))) = join(complement(complement(X0)),complement(join(X1,X0))),
inference(forward_demodulation,[],[f7378,f4292]) ).
fof(f7503,plain,
! [X0,X1] : join(X0,complement(join(X1,X0))) = complement(complement(join(complement(X1),X0))),
inference(forward_demodulation,[],[f7449,f243]) ).
fof(f7544,plain,
! [X0,X1] : join(complement(X1),X0) = join(X0,complement(join(X1,X0))),
inference(forward_demodulation,[],[f7503,f243]) ).
fof(f8657,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(join(top,composition(X0,top)))),
inference(superposition,[],[f2475,f2310]) ).
fof(f8679,plain,
! [X0] : zero = composition(converse(join(X0,one)),complement(top)),
inference(forward_demodulation,[],[f8657,f1101]) ).
fof(f8690,plain,
! [X0] : zero = composition(converse(join(X0,one)),zero),
inference(forward_demodulation,[],[f8679,f44]) ).
fof(f8699,plain,
! [X0] : zero = composition(join(one,converse(X0)),zero),
inference(forward_demodulation,[],[f8690,f3555]) ).
fof(f8703,plain,
! [X0] : zero = join(zero,composition(converse(X0),zero)),
inference(forward_demodulation,[],[f8699,f2304]) ).
fof(f8705,plain,
! [X0] : zero = composition(converse(X0),zero),
inference(forward_demodulation,[],[f8703,f2412]) ).
fof(f9118,plain,
! [X0] : converse(zero) = composition(converse(zero),X0),
inference(superposition,[],[f509,f8705]) ).
fof(f9126,plain,
! [X0] : zero = composition(zero,X0),
inference(forward_demodulation,[],[f9118,f2916]) ).
fof(f9133,plain,
! [X0] : zero = composition(converse(sk1),composition(sF1,X0)),
inference(backward_demodulation,[],[f3603,f9126]) ).
fof(f10875,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = join(converse(composition(X0,X2)),converse(composition(X0,X1))),
inference(superposition,[],[f131,f12]) ).
fof(f10922,plain,
! [X2,X0,X1] : composition(join(converse(X2),converse(X1)),converse(X0)) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f10875,f11]) ).
fof(f10964,plain,
! [X2,X0,X1] : converse(join(composition(X0,X2),composition(X0,X1))) = composition(converse(join(X2,X1)),converse(X0)),
inference(forward_demodulation,[],[f10922,f11]) ).
fof(f10989,plain,
! [X2,X0,X1] : converse(composition(X0,join(X2,X1))) = converse(join(composition(X0,X2),composition(X0,X1))),
inference(forward_demodulation,[],[f10964,f12]) ).
fof(f11071,plain,
! [X2,X0,X1] : join(composition(X0,X1),composition(X0,X2)) = converse(converse(composition(X0,join(X1,X2)))),
inference(superposition,[],[f10,f10989]) ).
fof(f11099,plain,
! [X2,X0,X1] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(forward_demodulation,[],[f11071,f10]) ).
fof(f11228,plain,
! [X0] : composition(sk1,join(top,X0)) = join(sk1,composition(sk1,X0)),
inference(superposition,[],[f11099,f47]) ).
fof(f11234,plain,
! [X0,X1] : composition(X0,join(X1,one)) = join(composition(X0,X1),X0),
inference(superposition,[],[f11099,f8]) ).
fof(f11329,plain,
! [X0,X1] : join(X0,composition(X0,X1)) = composition(X0,join(X1,one)),
inference(forward_demodulation,[],[f11234,f1]) ).
fof(f11331,plain,
! [X0] : composition(sk1,top) = join(sk1,composition(sk1,X0)),
inference(forward_demodulation,[],[f11228,f1101]) ).
fof(f11367,plain,
! [X0] : sk1 = join(sk1,composition(sk1,X0)),
inference(forward_demodulation,[],[f11331,f47]) ).
fof(f11558,plain,
! [X0,X1] : join(sk1,X1) = join(composition(sk1,X0),join(sk1,X1)),
inference(superposition,[],[f144,f11367]) ).
fof(f11581,plain,
! [X0,X1] : join(sk1,X1) = join(sk1,join(X1,composition(sk1,X0))),
inference(forward_demodulation,[],[f11558,f157]) ).
fof(f11625,plain,
! [X0] : composition(X0,top) = join(X0,composition(X0,top)),
inference(superposition,[],[f11329,f1101]) ).
fof(f11712,plain,
sF1 = composition(sF1,top),
inference(backward_demodulation,[],[f5673,f11625]) ).
fof(f11819,plain,
! [X0] : join(sF1,composition(sF1,X0)) = composition(sF1,join(top,X0)),
inference(superposition,[],[f11099,f11712]) ).
fof(f11822,plain,
! [X0] : composition(sF1,top) = join(sF1,composition(sF1,X0)),
inference(forward_demodulation,[],[f11819,f1101]) ).
fof(f11829,plain,
! [X0] : sF1 = join(sF1,composition(sF1,X0)),
inference(forward_demodulation,[],[f11822,f11712]) ).
fof(f13151,plain,
join(sF6,composition(sF1,sk3)) = composition(join(sF1,sF4),sk3),
inference(superposition,[],[f123,f4145]) ).
fof(f13182,plain,
join(sF6,composition(sF1,sk3)) = join(sF5,composition(sF1,sk3)),
inference(forward_demodulation,[],[f13151,f125]) ).
fof(f13218,plain,
join(complement(sF5),composition(sF1,sk3)) = join(composition(sF1,sk3),complement(join(sF6,composition(sF1,sk3)))),
inference(superposition,[],[f7544,f13182]) ).
fof(f13221,plain,
join(complement(sF5),composition(sF1,sk3)) = join(composition(sF1,sk3),complement(sF6)),
inference(forward_demodulation,[],[f13218,f3061]) ).
fof(f13231,plain,
join(complement(sF5),composition(sF1,sk3)) = join(complement(sF6),composition(sF1,sk3)),
inference(forward_demodulation,[],[f13221,f1]) ).
fof(f13236,plain,
join(complement(sF5),composition(sF1,sk3)) = join(sF7,composition(sF1,sk3)),
inference(forward_demodulation,[],[f13231,f38]) ).
fof(f14872,plain,
! [X0] : join(sF8,join(complement(sF5),X0)) = join(join(sF1,complement(sF5)),X0),
inference(superposition,[],[f2,f4545]) ).
fof(f14874,plain,
! [X0] : join(sF8,join(complement(sF5),X0)) = join(X0,join(sF1,complement(sF5))),
inference(superposition,[],[f157,f4545]) ).
fof(f14888,plain,
join(complement(sF8),complement(sF5)) = join(complement(sF5),complement(join(sF1,complement(sF5)))),
inference(superposition,[],[f7544,f4545]) ).
fof(f14891,plain,
join(complement(sF8),complement(sF5)) = join(complement(sF5),complement(sF1)),
inference(forward_demodulation,[],[f14888,f3061]) ).
fof(f14904,plain,
! [X0] : join(sF8,join(complement(sF5),X0)) = join(sF1,join(complement(sF5),X0)),
inference(forward_demodulation,[],[f14872,f2]) ).
fof(f14909,plain,
join(complement(sF8),complement(sF5)) = join(complement(sF1),complement(sF5)),
inference(forward_demodulation,[],[f14891,f1]) ).
fof(f14920,plain,
join(complement(sF8),complement(sF5)) = join(sk1,complement(sF5)),
inference(forward_demodulation,[],[f14909,f258]) ).
fof(f14926,plain,
join(sF9,complement(sF5)) = join(sk1,complement(sF5)),
inference(forward_demodulation,[],[f14920,f42]) ).
fof(f14952,plain,
join(sF9,complement(complement(sF5))) = join(sF9,complement(join(sk1,complement(sF5)))),
inference(superposition,[],[f3098,f14926]) ).
fof(f14957,plain,
join(sF9,sF5) = join(sF9,complement(join(sk1,complement(sF5)))),
inference(forward_demodulation,[],[f14952,f243]) ).
fof(f14975,plain,
join(sF5,sF9) = join(sF9,complement(join(sk1,complement(sF5)))),
inference(forward_demodulation,[],[f14957,f1]) ).
fof(f15584,plain,
! [X0] : complement(composition(sF1,X0)) = join(complement(composition(sF1,X0)),complement(sF1)),
inference(superposition,[],[f3035,f11829]) ).
fof(f15591,plain,
! [X0] : complement(composition(sF1,X0)) = join(complement(sF1),complement(composition(sF1,X0))),
inference(forward_demodulation,[],[f15584,f1]) ).
fof(f15601,plain,
! [X0] : complement(composition(sF1,X0)) = join(sk1,complement(composition(sF1,X0))),
inference(forward_demodulation,[],[f15591,f258]) ).
fof(f18073,plain,
complement(complement(sF5)) = join(complement(join(sF7,composition(sF1,sk3))),complement(join(complement(sF5),complement(composition(sF1,sk3))))),
inference(superposition,[],[f265,f13236]) ).
fof(f18099,plain,
sF5 = join(complement(join(sF7,composition(sF1,sk3))),complement(join(complement(sF5),complement(composition(sF1,sk3))))),
inference(forward_demodulation,[],[f18073,f243]) ).
fof(f54206,plain,
join(sk1,sF5) = join(sk1,composition(sk1,sk3)),
inference(superposition,[],[f11581,f3572]) ).
fof(f54291,plain,
sk1 = join(sk1,sF5),
inference(forward_demodulation,[],[f54206,f11367]) ).
fof(f54367,plain,
complement(sF5) = join(complement(sF5),complement(sk1)),
inference(superposition,[],[f3035,f54291]) ).
fof(f54369,plain,
join(sk1,complement(sk1)) = join(sk1,complement(sF5)),
inference(superposition,[],[f3098,f54291]) ).
fof(f54388,plain,
top = join(sk1,complement(sF5)),
inference(forward_demodulation,[],[f54369,f15]) ).
fof(f54389,plain,
complement(sF5) = join(complement(sk1),complement(sF5)),
inference(forward_demodulation,[],[f54367,f1]) ).
fof(f54408,plain,
join(sF9,complement(top)) = join(sF5,sF9),
inference(backward_demodulation,[],[f14975,f54388]) ).
fof(f54412,plain,
complement(sF5) = join(sF1,complement(sF5)),
inference(forward_demodulation,[],[f54389,f26]) ).
fof(f54420,plain,
join(sF9,zero) = join(sF5,sF9),
inference(forward_demodulation,[],[f54408,f44]) ).
fof(f54426,plain,
! [X0] : join(X0,complement(sF5)) = join(sF8,join(complement(sF5),X0)),
inference(backward_demodulation,[],[f14874,f54412]) ).
fof(f54432,plain,
sF9 = join(sF5,sF9),
inference(forward_demodulation,[],[f54420,f2411]) ).
fof(f54434,plain,
! [X0] : join(X0,complement(sF5)) = join(sF1,join(complement(sF5),X0)),
inference(backward_demodulation,[],[f14904,f54426]) ).
fof(f54446,plain,
! [X0] : join(sF9,X0) = join(sF5,join(sF9,X0)),
inference(superposition,[],[f2,f54432]) ).
fof(f54738,plain,
! [X0] : join(sF5,sF9) = join(sF9,complement(join(complement(sF5),X0))),
inference(superposition,[],[f4292,f54446]) ).
fof(f54783,plain,
! [X0] : sF9 = join(sF9,complement(join(complement(sF5),X0))),
inference(forward_demodulation,[],[f54738,f54432]) ).
fof(f58467,plain,
join(composition(sF1,sk3),complement(sF5)) = join(sF1,join(sF7,composition(sF1,sk3))),
inference(superposition,[],[f54434,f13236]) ).
fof(f58655,plain,
join(composition(sF1,sk3),complement(sF5)) = join(sF8,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58467,f150]) ).
fof(f58717,plain,
join(complement(sF5),composition(sF1,sk3)) = join(sF8,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58655,f1]) ).
fof(f58734,plain,
join(sF7,composition(sF1,sk3)) = join(sF8,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58717,f13236]) ).
fof(f58770,plain,
join(composition(sF1,sk3),complement(join(sF7,composition(sF1,sk3)))) = join(complement(sF8),composition(sF1,sk3)),
inference(superposition,[],[f7544,f58734]) ).
fof(f58786,plain,
join(composition(sF1,sk3),complement(join(sF7,composition(sF1,sk3)))) = join(sF9,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58770,f42]) ).
fof(f58810,plain,
join(composition(sF1,sk3),complement(sF7)) = join(sF9,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58786,f3061]) ).
fof(f58822,plain,
join(complement(sF7),composition(sF1,sk3)) = join(sF9,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58810,f1]) ).
fof(f58826,plain,
join(sF6,composition(sF1,sk3)) = join(sF9,composition(sF1,sk3)),
inference(forward_demodulation,[],[f58822,f261]) ).
fof(f58843,plain,
complement(sF9) = join(complement(join(sF6,composition(sF1,sk3))),complement(join(sF9,complement(composition(sF1,sk3))))),
inference(superposition,[],[f265,f58826]) ).
fof(f58885,plain,
sF8 = join(complement(join(sF6,composition(sF1,sk3))),complement(join(sF9,complement(composition(sF1,sk3))))),
inference(forward_demodulation,[],[f58843,f262]) ).
fof(f61808,plain,
! [X0,X1] : join(complement(composition(sF1,X0)),X1) = join(complement(composition(sF1,X0)),join(composition(converse(converse(sk1)),complement(zero)),X1)),
inference(superposition,[],[f146,f9133]) ).
fof(f61859,plain,
! [X0,X1] : join(complement(composition(sF1,X0)),X1) = join(complement(composition(sF1,X0)),join(composition(converse(converse(sk1)),top),X1)),
inference(forward_demodulation,[],[f61808,f257]) ).
fof(f61901,plain,
! [X0,X1] : join(complement(composition(sF1,X0)),X1) = join(complement(composition(sF1,X0)),join(composition(sk1,top),X1)),
inference(forward_demodulation,[],[f61859,f10]) ).
fof(f61927,plain,
! [X0,X1] : join(complement(composition(sF1,X0)),X1) = join(composition(sk1,top),join(X1,complement(composition(sF1,X0)))),
inference(forward_demodulation,[],[f61901,f157]) ).
fof(f61943,plain,
! [X0,X1] : join(complement(composition(sF1,X0)),X1) = join(sk1,join(X1,complement(composition(sF1,X0)))),
inference(forward_demodulation,[],[f61927,f47]) ).
fof(f63903,plain,
! [X0] : join(sk1,complement(composition(sF1,X0))) = join(complement(composition(sF1,X0)),sF9),
inference(superposition,[],[f61943,f3328]) ).
fof(f63986,plain,
! [X0] : join(sk1,complement(composition(sF1,X0))) = join(sF9,complement(composition(sF1,X0))),
inference(forward_demodulation,[],[f63903,f1]) ).
fof(f64049,plain,
! [X0] : complement(composition(sF1,X0)) = join(sF9,complement(composition(sF1,X0))),
inference(forward_demodulation,[],[f63986,f15601]) ).
fof(f64079,plain,
sF8 = join(complement(join(sF6,composition(sF1,sk3))),complement(complement(composition(sF1,sk3)))),
inference(backward_demodulation,[],[f58885,f64049]) ).
fof(f64094,plain,
sF8 = join(complement(complement(composition(sF1,sk3))),complement(join(sF6,composition(sF1,sk3)))),
inference(forward_demodulation,[],[f64079,f1]) ).
fof(f64098,plain,
sF8 = join(composition(sF1,sk3),complement(join(sF6,composition(sF1,sk3)))),
inference(forward_demodulation,[],[f64094,f243]) ).
fof(f64101,plain,
sF8 = join(composition(sF1,sk3),complement(sF6)),
inference(forward_demodulation,[],[f64098,f3061]) ).
fof(f64102,plain,
sF8 = join(complement(sF6),composition(sF1,sk3)),
inference(forward_demodulation,[],[f64101,f1]) ).
fof(f64103,plain,
sF8 = join(sF7,composition(sF1,sk3)),
inference(forward_demodulation,[],[f64102,f38]) ).
fof(f64108,plain,
sF5 = join(complement(sF8),complement(join(complement(sF5),complement(composition(sF1,sk3))))),
inference(backward_demodulation,[],[f18099,f64103]) ).
fof(f64130,plain,
sF5 = join(sF9,complement(join(complement(sF5),complement(composition(sF1,sk3))))),
inference(forward_demodulation,[],[f64108,f42]) ).
fof(f64138,plain,
sF5 = sF9,
inference(forward_demodulation,[],[f64130,f54783]) ).
fof(f64385,plain,
$false,
inference(forward_subsumption_resolution,[],[f64138,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL033-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 22:54:34 UTC 2026
% 0.11/0.34 % CPUTime :
% 0.11/0.34 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 Running first-order theorem proving
% 0.11/0.37 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
% 32.62/5.38 % (2847120)Detected a unit-equality problem, will run specialized UEQ schedule.
% 32.62/5.38 % (2847127)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2498523148:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 32.62/5.38 % (2847131)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1169675052:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 32.62/5.38 % (2847129)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=372108837:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 32.62/5.38 % (2847126)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=1833828425:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 32.62/5.38 % (2847128)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2848197330:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 32.62/5.38 % (2847130)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2485072294:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 32.62/5.38 % (2847125)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=2491037856:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 32.62/5.38 % (2847128)Instruction limit reached!
% 32.62/5.38 % (2847128)------------------------------
% 32.62/5.38 % (2847128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847128)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847128)Termination reason: Instruction limit
% 32.62/5.38 % (2847128)Termination phase: Saturation
% 32.62/5.38 % (2847128)Time elapsed: 0.075 s
% 32.62/5.38 % (2847128)Peak memory usage: 89 MB
% 32.62/5.38 % (2847128)Instructions burned: 137 (million)
% 32.62/5.38 % (2847129)Instruction limit reached!
% 32.62/5.38 % (2847129)------------------------------
% 32.62/5.38 % (2847129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847129)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847129)Termination reason: Instruction limit
% 32.62/5.38 % (2847129)Termination phase: Saturation
% 32.62/5.38 % (2847129)Time elapsed: 0.084 s
% 32.62/5.38 % (2847129)Peak memory usage: 89 MB
% 32.62/5.38 % (2847129)Instructions burned: 182 (million)
% 32.62/5.38 % (2847130)Instruction limit reached!
% 32.62/5.38 % (2847130)------------------------------
% 32.62/5.38 % (2847130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847130)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847130)Termination reason: Instruction limit
% 32.62/5.38 % (2847130)Termination phase: Saturation
% 32.62/5.38 % (2847130)Time elapsed: 0.155 s
% 32.62/5.38 % (2847130)Peak memory usage: 90 MB
% 32.62/5.38 % (2847130)Instructions burned: 258 (million)
% 32.62/5.38 % (2847141)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3256834751:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 32.62/5.38 % (2847140)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3845400759:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 32.62/5.38 % (2847139)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2762756949:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 32.62/5.38 % (2847141)Instruction limit reached!
% 32.62/5.38 % (2847141)------------------------------
% 32.62/5.38 % (2847141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847141)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847141)Termination reason: Instruction limit
% 32.62/5.38 % (2847141)Termination phase: Saturation
% 32.62/5.38 % (2847141)Time elapsed: 0.074 s
% 32.62/5.38 % (2847141)Peak memory usage: 92 MB
% 32.62/5.38 % (2847141)Instructions burned: 217 (million)
% 32.62/5.38 % (2847131)Instruction limit reached!
% 32.62/5.38 % (2847131)------------------------------
% 32.62/5.38 % (2847131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847131)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847131)Termination reason: Instruction limit
% 32.62/5.38 % (2847131)Termination phase: Saturation
% 32.62/5.38 % (2847131)Time elapsed: 0.578 s
% 32.62/5.38 % (2847131)Peak memory usage: 99 MB
% 32.62/5.38 % (2847131)Instructions burned: 1189 (million)
% 32.62/5.38 % (2847145)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=1678839482:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 32.62/5.38 % (2847145)Instruction limit reached!
% 32.62/5.38 % (2847145)------------------------------
% 32.62/5.38 % (2847145)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847145)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847145)Termination reason: Instruction limit
% 32.62/5.38 % (2847145)Termination phase: Saturation
% 32.62/5.38 % (2847145)Time elapsed: 0.179 s
% 32.62/5.38 % (2847145)Peak memory usage: 92 MB
% 32.62/5.38 % (2847145)Instructions burned: 318 (million)
% 32.62/5.38 % (2847146)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=2534442887:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 32.62/5.38 % (2847148)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=137131754:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 32.62/5.38 % (2847139)Instruction limit reached!
% 32.62/5.38 % (2847139)------------------------------
% 32.62/5.38 % (2847139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847139)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847139)Termination reason: Instruction limit
% 32.62/5.38 % (2847139)Termination phase: Saturation
% 32.62/5.38 % (2847139)Time elapsed: 1.131 s
% 32.62/5.38 % (2847139)Peak memory usage: 141 MB
% 32.62/5.38 % (2847139)Instructions burned: 2052 (million)
% 32.62/5.38 % (2847151)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2039421534:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2984 on theBenchmark for (2984ds/14534Mi)
% 32.62/5.38 % (2847148)Instruction limit reached!
% 32.62/5.38 % (2847148)------------------------------
% 32.62/5.38 % (2847148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847148)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847148)Termination reason: Instruction limit
% 32.62/5.38 % (2847148)Termination phase: Saturation
% 32.62/5.38 % (2847148)Time elapsed: 1.733 s
% 32.62/5.38 % (2847148)Peak memory usage: 118 MB
% 32.62/5.38 % (2847148)Instructions burned: 2837 (million)
% 32.62/5.38 % (2847153)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=2327858694:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2970 on theBenchmark for (2970ds/11832Mi)
% 32.62/5.38 % (2847140)Instruction limit reached!
% 32.62/5.38 % (2847140)------------------------------
% 32.62/5.38 % (2847140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 32.62/5.38 % (2847140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 32.62/5.38 % (2847140)CaDiCaL version: 2.1.3
% 32.62/5.38 % (2847140)Termination reason: Instruction limit
% 32.62/5.38 % (2847140)Termination phase: Saturation
% 32.62/5.38 % (2847140)Time elapsed: 2.738 s
% 32.62/5.38 % (2847140)Peak memory usage: 163 MB
% 32.62/5.38 % (2847140)Instructions burned: 4950 (million)
% 32.62/5.38 % (2847155)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=673877085:i=2279:fgj=on:bd=all_2967 on theBenchmark for (2967ds/2279Mi)
% 32.62/5.38 % (2847127)First to succeed.
% 32.62/5.38 % (2847127)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2847120"
% 32.62/5.38 % (2847125)Also succeeded, but the first one will report.
% 32.62/5.38 % (2847127)Refutation found. Thanks to Tanya!
% 32.62/5.38 % SZS status Unsatisfiable for theBenchmark
% 32.62/5.38 % SZS output start Proof for theBenchmark
% See solution above
% 33.28/5.58 % (2847127)------------------------------
% 33.28/5.58 % (2847127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 33.28/5.58 % (2847127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.28/5.58 % (2847127)CaDiCaL version: 2.1.3
% 33.28/5.58 % (2847127)Termination reason: Refutation
% 33.28/5.58 % (2847127)Time elapsed: 4.220 s
% 33.28/5.58 % (2847127)Peak memory usage: 187 MB
% 33.28/5.58 % (2847127)Instructions burned: 7103 (million)
% 33.28/5.58 % (2847127)------------------------------
% 33.28/5.58 % (2847127)------------------------------
% 33.28/5.58 % (2847120)Success in time 4.665 s
% 33.28/5.58 % Vampire exiting
%------------------------------------------------------------------------------