%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 : Fri Sep 25 02:36:35 PM UTC 2026
% Result : Theorem 28.22s 4.83s
% Output : CNFRefutation 28.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 26
% Syntax : Number of formulae : 304 ( 300 unt; 11 def)
% Number of atoms : 966 ( 307 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 226 ( 0 sgn 223 !; 3 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f15,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
=> meet(composition(X1,X0),X2) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
=> meet(composition(X1,X0),X2) = zero ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( meet(X0,composition(converse(X1),X2)) = zero
& zero != meet(composition(X1,X0),X2) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( zero = meet(sK0,composition(converse(sK1),sK2))
& zero != meet(composition(sK1,sK0),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f35,plain,
! [X2,X0,X1] : meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
zero = meet(sK0,composition(converse(sK1),sK2)),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
zero != meet(composition(sK1,sK0),sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f41,plain,
! [X2,X0,X1] : complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))),
inference(definition_unfolding,[],[f35,f24,f24,f24,f24,f24]) ).
fof(f43,plain,
zero != complement(join(complement(composition(sK1,sK0)),complement(sK2))),
inference(definition_unfolding,[],[f38,f24]) ).
fof(f44,plain,
zero = complement(join(complement(sK0),complement(composition(converse(sK1),sK2)))),
inference(definition_unfolding,[],[f37,f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))) = complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
complement(join(complement(composition(sK1,sK0)),complement(sK2))) != zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,negated_conjecture,
complement(join(complement(sK0),complement(composition(converse(sK1),sK2)))) = zero,
inference(cnf_transformation,[],[f44]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_51,c_50,c_49]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_58,c_50,c_49]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))) = complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))),
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_85,negated_conjecture,
complement(join(complement(sK2),complement(composition(sK1,sK0)))) != zero,
inference(theory_normalisation,[status(thm)],[c_64,c_50,c_49]) ).
tcf(c_124,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_131,definition,
iPr_def_10 = complement(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = composition(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,definition,
iPr_def_13 = join(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_135,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_136,definition,
iPr_def_15 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_137,definition,
iPr_def_16 = converse(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_138,definition,
iPr_def_17 = composition(iPr_def_16,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_139,definition,
iPr_def_18 = complement(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_140,definition,
iPr_def_19 = join(iPr_def_15,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_141,definition,
iPr_def_20 = complement(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_142,negated_conjecture,
iPr_def_14 != zero,
inference(demodulation,[status(thm)],[c_85,c_132,c_133,c_131,c_134,c_135]) ).
tcf(c_143,negated_conjecture,
iPr_def_20 = zero,
inference(demodulation,[status(thm)],[c_65,c_137,c_138,c_139,c_136,c_140,c_141]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_239,plain,
iPr_def_14 != iPr_def_20,
inference(light_normalisation,[status(thm)],[c_142,c_143]) ).
tcf(c_240,plain,
complement(top) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_124,c_143]) ).
tcf(c_248,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = sK2,
inference(superposition,[status(thm)],[c_131,c_81]) ).
tcf(c_249,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_136,c_81]) ).
tcf(c_250,plain,
! [X0: $i] : join(complement(join(iPr_def_20,X0)),complement(join(iPr_def_20,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_240,c_81]) ).
tcf(c_251,plain,
! [X0: $i] : join(complement(join(iPr_def_12,X0)),complement(join(iPr_def_12,complement(X0)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_133,c_81]) ).
tcf(c_252,plain,
! [X0: $i] : join(complement(join(iPr_def_14,X0)),complement(join(iPr_def_14,complement(X0)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_135,c_81]) ).
tcf(c_254,plain,
! [X0: $i] : join(complement(join(complement(X0),sK0)),complement(join(complement(X0),iPr_def_15))) = X0,
inference(superposition,[status(thm)],[c_136,c_81]) ).
tcf(c_256,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_11)),complement(join(complement(X0),iPr_def_12))) = X0,
inference(superposition,[status(thm)],[c_133,c_81]) ).
tcf(c_257,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_13)),complement(join(complement(X0),iPr_def_14))) = X0,
inference(superposition,[status(thm)],[c_135,c_81]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_81,c_81]) ).
tcf(c_260,plain,
! [X0: $i] : join(complement(join(iPr_def_13,complement(X0))),complement(join(iPr_def_14,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_257,c_50,c_49]) ).
tcf(c_261,plain,
! [X0: $i] : join(complement(join(iPr_def_11,complement(X0))),complement(join(iPr_def_12,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_256,c_50,c_49]) ).
tcf(c_263,plain,
! [X0: $i] : join(complement(join(iPr_def_15,complement(X0))),complement(join(sK0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_254,c_50,c_49]) ).
tcf(c_267,plain,
! [X0: $i] : join(complement(join(iPr_def_18,X0)),complement(join(iPr_def_18,complement(X0)))) = iPr_def_17,
inference(superposition,[status(thm)],[c_139,c_81]) ).
tcf(c_268,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_17)),complement(join(complement(X0),iPr_def_18))) = X0,
inference(superposition,[status(thm)],[c_139,c_81]) ).
tcf(c_269,plain,
! [X0: $i] : join(complement(join(iPr_def_17,complement(X0))),complement(join(iPr_def_18,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_268,c_50,c_49]) ).
tcf(c_270,plain,
! [X0: $i] : join(complement(join(iPr_def_20,X0)),complement(join(iPr_def_20,complement(X0)))) = iPr_def_19,
inference(superposition,[status(thm)],[c_141,c_81]) ).
tcf(c_273,plain,
converse(iPr_def_16) = sK1,
inference(superposition,[status(thm)],[c_137,c_55]) ).
tcf(c_274,plain,
converse(sK1) = iPr_def_16,
inference(superposition,[status(thm)],[c_273,c_55]) ).
tcf(c_277,plain,
top = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_250,c_270]) ).
tcf(c_278,plain,
complement(iPr_def_19) = iPr_def_20,
inference(demodulation,[status(thm)],[c_240,c_277]) ).
tcf(c_284,plain,
! [X0: $i] : join(X0,complement(X0)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_59,c_277]) ).
tcf(c_285,plain,
join(sK2,iPr_def_10) = iPr_def_19,
inference(superposition,[status(thm)],[c_131,c_284]) ).
tcf(c_286,plain,
join(sK0,iPr_def_15) = iPr_def_19,
inference(superposition,[status(thm)],[c_136,c_284]) ).
tcf(c_287,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_19,
inference(superposition,[status(thm)],[c_133,c_284]) ).
tcf(c_288,plain,
join(iPr_def_13,iPr_def_14) = iPr_def_19,
inference(superposition,[status(thm)],[c_135,c_284]) ).
tcf(c_292,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(iPr_def_19)) = X0,
inference(superposition,[status(thm)],[c_284,c_81]) ).
tcf(c_293,plain,
! [X0: $i] : join(complement(iPr_def_19),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_284,c_81]) ).
tcf(c_294,plain,
join(iPr_def_15,sK0) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_286,c_50,c_49]) ).
tcf(c_295,plain,
join(iPr_def_10,sK2) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_285,c_50,c_49]) ).
tcf(c_296,plain,
! [X0: $i] : join(complement(iPr_def_19),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_292,c_50,c_49]) ).
tcf(c_297,plain,
! [X0: $i] : join(iPr_def_20,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_296,c_278]) ).
tcf(c_298,plain,
! [X0: $i] : join(iPr_def_20,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_293,c_278]) ).
tcf(c_307,plain,
join(iPr_def_20,complement(join(iPr_def_10,iPr_def_10))) = sK2,
inference(superposition,[status(thm)],[c_131,c_297]) ).
tcf(c_308,plain,
join(iPr_def_20,complement(join(iPr_def_15,iPr_def_15))) = sK0,
inference(superposition,[status(thm)],[c_136,c_297]) ).
tcf(c_310,plain,
join(iPr_def_20,complement(join(iPr_def_14,iPr_def_14))) = iPr_def_13,
inference(superposition,[status(thm)],[c_135,c_297]) ).
tcf(c_319,plain,
! [X0: $i] : join(iPr_def_20,composition(converse(X0),complement(composition(X0,iPr_def_19)))) = iPr_def_20,
inference(superposition,[status(thm)],[c_278,c_82]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(iPr_def_19,X1),
inference(superposition,[status(thm)],[c_284,c_50]) ).
tcf(c_364,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_18,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_140,c_50]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = iPr_def_19,
inference(superposition,[status(thm)],[c_50,c_284]) ).
tcf(c_371,plain,
! [X0: $i] : join(iPr_def_15,join(sK0,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_294,c_50]) ).
tcf(c_374,plain,
! [X0: $i] : join(iPr_def_20,composition(X0,complement(composition(converse(X0),iPr_def_19)))) = iPr_def_20,
inference(superposition,[status(thm)],[c_55,c_319]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,X1)),iPr_def_10)),complement(join(iPr_def_10,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK2))))))))) = complement(join(iPr_def_10,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK2)))))))),
inference(superposition,[status(thm)],[c_131,c_83]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,X1)),iPr_def_20)),complement(join(iPr_def_20,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19))))))))) = complement(join(iPr_def_20,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19)))))))),
inference(superposition,[status(thm)],[c_278,c_83]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,iPr_def_19)),complement(X1))),complement(join(complement(X1),complement(composition(X0,complement(join(iPr_def_20,complement(composition(converse(X0),X1))))))))) = complement(join(complement(X1),complement(composition(X0,complement(join(iPr_def_20,complement(composition(converse(X0),X1)))))))),
inference(superposition,[status(thm)],[c_278,c_83]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_20,complement(composition(X0,X1)))),complement(join(iPr_def_20,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19))))))))) = complement(join(iPr_def_20,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19)))))))),
inference(theory_normalisation,[status(thm)],[c_419,c_50,c_49]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_10,complement(composition(X0,X1)))),complement(join(iPr_def_10,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK2))))))))) = complement(join(iPr_def_10,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK2)))))))),
inference(theory_normalisation,[status(thm)],[c_414,c_50,c_49]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(X0),composition(converse(composition(X1,X2)),complement(composition(X1,composition(X2,X0))))) = complement(X0),
inference(superposition,[status(thm)],[c_52,c_82]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : join(composition(X0,X1),composition(X2,composition(X3,X1))) = composition(join(X0,composition(X2,X3)),X1),
inference(superposition,[status(thm)],[c_52,c_54]) ).
tcf(c_601,plain,
! [X0: $i] : join(iPr_def_10,join(sK2,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_295,c_50]) ).
tcf(c_823,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_12)) = join(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_134,c_238]) ).
tcf(c_824,plain,
! [X0: $i] : join(iPr_def_15,join(X0,iPr_def_18)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_140,c_238]) ).
tcf(c_826,plain,
! [X0: $i] : join(iPr_def_13,join(X0,iPr_def_14)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_288,c_238]) ).
tcf(c_829,plain,
! [X0: $i] : join(iPr_def_15,join(X0,sK0)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_294,c_238]) ).
tcf(c_830,plain,
! [X0: $i] : join(iPr_def_10,join(X0,sK2)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_295,c_238]) ).
tcf(c_1716,plain,
join(complement(join(iPr_def_15,iPr_def_13)),complement(join(iPr_def_15,iPr_def_14))) = sK0,
inference(superposition,[status(thm)],[c_135,c_249]) ).
tcf(c_1731,plain,
join(complement(join(iPr_def_13,iPr_def_15)),complement(join(iPr_def_14,iPr_def_15))) = sK0,
inference(theory_normalisation,[status(thm)],[c_1716,c_50,c_49]) ).
tcf(c_2208,plain,
join(iPr_def_10,iPr_def_19) = join(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_287,c_823]) ).
tcf(c_2216,plain,
join(sK2,iPr_def_13) = join(iPr_def_19,iPr_def_12),
inference(superposition,[status(thm)],[c_823,c_601]) ).
tcf(c_2217,plain,
join(iPr_def_12,iPr_def_19) = join(iPr_def_13,sK2),
inference(theory_normalisation,[status(thm)],[c_2216,c_50,c_49]) ).
tcf(c_2345,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(iPr_def_19),complement(complement(join(complement(X0),complement(complement(complement(X0))))))))) = iPr_def_19,
inference(superposition,[status(thm)],[c_284,c_259]) ).
tcf(c_2426,plain,
! [X0: $i] : join(complement(X0),complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0))))))))) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_2345,c_278]) ).
tcf(c_2491,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_18,X0)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_49,c_824]) ).
tcf(c_2502,plain,
join(sK0,iPr_def_19) = join(iPr_def_19,iPr_def_18),
inference(superposition,[status(thm)],[c_824,c_371]) ).
tcf(c_2503,plain,
join(iPr_def_18,iPr_def_19) = join(iPr_def_19,sK0),
inference(theory_normalisation,[status(thm)],[c_2502,c_50,c_49]) ).
tcf(c_2538,plain,
! [X0: $i] : join(iPr_def_13,join(iPr_def_14,X0)) = join(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_49,c_826]) ).
tcf(c_2593,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(iPr_def_19),complement(complement(join(complement(X0),complement(complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0))))))))))))))) = iPr_def_19,
inference(superposition,[status(thm)],[c_2426,c_259]) ).
tcf(c_2610,plain,
! [X0: $i] : join(complement(X0),complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0))))))))))))))) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_2593,c_278]) ).
tcf(c_2881,plain,
join(complement(join(iPr_def_13,iPr_def_18)),complement(join(iPr_def_14,iPr_def_18))) = iPr_def_17,
inference(superposition,[status(thm)],[c_139,c_260]) ).
tcf(c_3555,plain,
join(complement(join(iPr_def_15,iPr_def_18)),complement(join(sK0,iPr_def_18))) = iPr_def_17,
inference(superposition,[status(thm)],[c_139,c_263]) ).
tcf(c_3569,plain,
join(complement(join(iPr_def_15,iPr_def_18)),complement(join(iPr_def_18,sK0))) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_3555,c_50,c_49]) ).
tcf(c_3570,plain,
join(iPr_def_20,complement(join(iPr_def_18,sK0))) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_3569,c_140,c_278]) ).
tcf(c_3876,plain,
! [X0: $i] : join(complement(join(complement(X0),join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0))))))))))))))),complement(iPr_def_19)) = X0,
inference(superposition,[status(thm)],[c_2610,c_81]) ).
tcf(c_3889,plain,
! [X0: $i] : join(complement(iPr_def_19),complement(join(iPr_def_20,join(complement(X0),complement(complement(join(complement(X0),complement(complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0)))))))))))))))) = X0,
inference(theory_normalisation,[status(thm)],[c_3876,c_50,c_49]) ).
tcf(c_3890,plain,
! [X0: $i] : join(iPr_def_20,complement(join(iPr_def_20,join(complement(X0),complement(complement(join(complement(X0),complement(complement(join(iPr_def_20,complement(complement(join(complement(X0),complement(complement(complement(X0)))))))))))))))) = X0,
inference(light_normalisation,[status(thm)],[c_3889,c_278]) ).
tcf(c_4116,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(iPr_def_19),
inference(superposition,[status(thm)],[c_284,c_337]) ).
tcf(c_4818,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(X0),composition(X1,converse(X2))) = converse(join(X0,composition(X2,converse(X1)))),
inference(superposition,[status(thm)],[c_349,c_56]) ).
tcf(c_4836,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_353]) ).
tcf(c_4897,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_4836,c_55]) ).
tcf(c_4924,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_4897,c_53]) ).
tcf(c_4955,plain,
join(iPr_def_20,composition(one,complement(iPr_def_19))) = iPr_def_20,
inference(superposition,[status(thm)],[c_4897,c_374]) ).
tcf(c_4960,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_4897,c_457]) ).
tcf(c_4967,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_4960,c_4897]) ).
tcf(c_4968,plain,
join(iPr_def_20,composition(one,iPr_def_20)) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_4955,c_278]) ).
tcf(c_5081,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_4967,c_54]) ).
tcf(c_5093,plain,
! [X0: $i] : join(complement(join(complement(iPr_def_19),complement(X0))),complement(join(complement(X0),complement(composition(one,complement(join(iPr_def_20,complement(composition(converse(one),X0))))))))) = complement(join(complement(X0),complement(composition(one,complement(join(iPr_def_20,complement(composition(converse(one),X0)))))))),
inference(superposition,[status(thm)],[c_4967,c_428]) ).
tcf(c_5119,plain,
! [X0: $i] : join(complement(join(iPr_def_20,complement(X0))),complement(join(complement(X0),complement(composition(one,complement(join(iPr_def_20,complement(X0)))))))) = complement(join(complement(X0),complement(composition(one,complement(join(iPr_def_20,complement(X0))))))),
inference(light_normalisation,[status(thm)],[c_5093,c_278,c_4924,c_4967]) ).
tcf(c_5134,plain,
join(iPr_def_20,iPr_def_20) = iPr_def_20,
inference(demodulation,[status(thm)],[c_4968,c_4967]) ).
tcf(c_5148,plain,
! [X0: $i] : join(iPr_def_20,join(iPr_def_20,X0)) = join(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_5134,c_50]) ).
tcf(c_5576,plain,
! [X0: $i] : join(iPr_def_20,X0) = X0,
inference(superposition,[status(thm)],[c_3890,c_5148]) ).
tcf(c_5593,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(complement(X0))))) = X0,
inference(demodulation,[status(thm)],[c_298,c_5576]) ).
tcf(c_5594,plain,
complement(join(iPr_def_10,iPr_def_10)) = sK2,
inference(demodulation,[status(thm)],[c_307,c_5576]) ).
tcf(c_5595,plain,
complement(join(iPr_def_15,iPr_def_15)) = sK0,
inference(demodulation,[status(thm)],[c_308,c_5576]) ).
tcf(c_5597,plain,
complement(join(iPr_def_14,iPr_def_14)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_310,c_5576]) ).
tcf(c_5599,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,iPr_def_19))) = iPr_def_20,
inference(demodulation,[status(thm)],[c_319,c_5576]) ).
tcf(c_5641,plain,
complement(join(iPr_def_18,sK0)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_3570,c_5576]) ).
tcf(c_5658,plain,
! [X0: $i] : join(X0,iPr_def_20) = X0,
inference(superposition,[status(thm)],[c_5576,c_49]) ).
tcf(c_5663,plain,
complement(iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_5576,c_284]) ).
tcf(c_5999,plain,
join(complement(join(iPr_def_17,complement(iPr_def_18))),complement(iPr_def_19)) = iPr_def_18,
inference(superposition,[status(thm)],[c_284,c_269]) ).
tcf(c_6017,plain,
join(complement(iPr_def_19),complement(join(iPr_def_17,complement(iPr_def_18)))) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_5999,c_50,c_49]) ).
tcf(c_6018,plain,
join(iPr_def_20,complement(join(iPr_def_17,complement(iPr_def_18)))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_6017,c_278]) ).
tcf(c_6056,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(iPr_def_19,X1),
inference(superposition,[status(thm)],[c_49,c_360]) ).
tcf(c_6345,plain,
! [X0: $i] : join(complement(iPr_def_19),complement(join(iPr_def_10,complement(join(X0,complement(join(iPr_def_10,X0))))))) = sK2,
inference(superposition,[status(thm)],[c_367,c_248]) ).
tcf(c_6505,plain,
! [X0: $i] : join(iPr_def_20,complement(join(iPr_def_10,complement(join(X0,complement(join(iPr_def_10,X0))))))) = sK2,
inference(light_normalisation,[status(thm)],[c_6345,c_278]) ).
tcf(c_6566,plain,
join(complement(join(iPr_def_13,sK2)),complement(join(iPr_def_14,sK2))) = join(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_5594,c_260]) ).
tcf(c_6586,plain,
join(iPr_def_10,join(iPr_def_10,sK2)) = iPr_def_19,
inference(superposition,[status(thm)],[c_5594,c_367]) ).
tcf(c_6587,plain,
join(iPr_def_10,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_6586,c_295]) ).
tcf(c_6599,plain,
join(complement(join(iPr_def_12,iPr_def_19)),complement(join(iPr_def_14,sK2))) = join(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_6566,c_2217]) ).
tcf(c_6608,plain,
join(iPr_def_11,iPr_def_13) = iPr_def_19,
inference(demodulation,[status(thm)],[c_2208,c_6587]) ).
tcf(c_6618,plain,
join(complement(iPr_def_19),complement(join(iPr_def_10,complement(iPr_def_19)))) = sK2,
inference(superposition,[status(thm)],[c_6587,c_248]) ).
tcf(c_6620,plain,
join(iPr_def_20,complement(join(iPr_def_10,iPr_def_20))) = sK2,
inference(light_normalisation,[status(thm)],[c_6618,c_278]) ).
tcf(c_6622,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_13,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_6608,c_50]) ).
tcf(c_6631,plain,
join(complement(join(iPr_def_15,sK0)),complement(join(sK0,sK0))) = join(iPr_def_15,iPr_def_15),
inference(superposition,[status(thm)],[c_5595,c_263]) ).
tcf(c_6653,plain,
join(iPr_def_15,join(iPr_def_15,sK0)) = iPr_def_19,
inference(superposition,[status(thm)],[c_5595,c_367]) ).
tcf(c_6654,plain,
join(iPr_def_15,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_6653,c_294]) ).
tcf(c_6664,plain,
join(iPr_def_20,complement(join(sK0,sK0))) = join(iPr_def_15,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_6631,c_278,c_294]) ).
tcf(c_6686,plain,
complement(iPr_def_10) = sK2,
inference(demodulation,[status(thm)],[c_6620,c_5576,c_5658]) ).
tcf(c_6693,plain,
join(complement(join(iPr_def_11,sK2)),complement(join(iPr_def_12,sK2))) = iPr_def_10,
inference(superposition,[status(thm)],[c_6686,c_261]) ).
tcf(c_6694,plain,
join(complement(join(iPr_def_13,sK2)),complement(join(iPr_def_14,sK2))) = iPr_def_10,
inference(superposition,[status(thm)],[c_6686,c_260]) ).
tcf(c_6717,plain,
join(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_6694,c_2217,c_6599]) ).
tcf(c_6753,plain,
complement(join(iPr_def_17,complement(iPr_def_18))) = iPr_def_18,
inference(demodulation,[status(thm)],[c_6018,c_5576]) ).
tcf(c_6761,plain,
join(complement(join(iPr_def_13,iPr_def_18)),complement(join(iPr_def_14,iPr_def_18))) = join(iPr_def_17,complement(iPr_def_18)),
inference(superposition,[status(thm)],[c_6753,c_260]) ).
tcf(c_6790,plain,
join(iPr_def_17,complement(iPr_def_18)) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_6761,c_2881]) ).
tcf(c_6808,plain,
complement(iPr_def_17) = iPr_def_18,
inference(demodulation,[status(thm)],[c_6753,c_6790]) ).
tcf(c_6856,plain,
join(iPr_def_11,iPr_def_19) = join(iPr_def_19,iPr_def_14),
inference(superposition,[status(thm)],[c_288,c_6622]) ).
tcf(c_6876,plain,
join(iPr_def_11,iPr_def_19) = join(iPr_def_14,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_6856,c_50,c_49]) ).
tcf(c_6963,plain,
join(complement(iPr_def_19),complement(join(iPr_def_15,complement(iPr_def_19)))) = sK0,
inference(superposition,[status(thm)],[c_6654,c_249]) ).
tcf(c_6965,plain,
join(iPr_def_20,complement(join(iPr_def_15,iPr_def_20))) = sK0,
inference(light_normalisation,[status(thm)],[c_6963,c_278]) ).
tcf(c_6972,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_10,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_6717,c_50]) ).
tcf(c_6978,plain,
complement(iPr_def_15) = sK0,
inference(demodulation,[status(thm)],[c_6965,c_5576,c_5658]) ).
tcf(c_6984,plain,
join(complement(join(iPr_def_15,sK0)),complement(join(sK0,sK0))) = iPr_def_15,
inference(superposition,[status(thm)],[c_6978,c_263]) ).
tcf(c_7005,plain,
join(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_6984,c_278,c_294,c_6664]) ).
tcf(c_7113,plain,
join(iPr_def_20,complement(join(sK0,sK0))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_6664,c_7005]) ).
tcf(c_7114,plain,
complement(join(sK0,sK0)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_7113,c_5576]) ).
tcf(c_7122,plain,
join(complement(join(iPr_def_13,iPr_def_15)),complement(join(iPr_def_14,iPr_def_15))) = join(sK0,sK0),
inference(superposition,[status(thm)],[c_7114,c_260]) ).
tcf(c_7150,plain,
join(sK0,sK0) = sK0,
inference(light_normalisation,[status(thm)],[c_7122,c_1731]) ).
tcf(c_7169,plain,
complement(sK0) = iPr_def_15,
inference(demodulation,[status(thm)],[c_7114,c_7150]) ).
tcf(c_7245,plain,
join(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_134,c_6972]) ).
tcf(c_7288,plain,
join(complement(iPr_def_13),complement(join(iPr_def_10,complement(iPr_def_13)))) = sK2,
inference(superposition,[status(thm)],[c_7245,c_248]) ).
tcf(c_7293,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_14))) = sK2,
inference(light_normalisation,[status(thm)],[c_7288,c_135]) ).
tcf(c_7412,plain,
join(sK0,iPr_def_19) = join(iPr_def_15,sK0),
inference(superposition,[status(thm)],[c_7150,c_829]) ).
tcf(c_7413,plain,
join(iPr_def_15,sK0) = join(iPr_def_19,sK0),
inference(theory_normalisation,[status(thm)],[c_7412,c_50,c_49]) ).
tcf(c_7414,plain,
join(iPr_def_19,sK0) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_7413,c_294,c_2503]) ).
tcf(c_7420,plain,
join(iPr_def_18,iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_2503,c_7414]) ).
tcf(c_8019,plain,
join(complement(iPr_def_19),complement(join(iPr_def_18,complement(iPr_def_19)))) = iPr_def_17,
inference(superposition,[status(thm)],[c_7420,c_267]) ).
tcf(c_8026,plain,
join(iPr_def_20,complement(join(iPr_def_18,iPr_def_20))) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_8019,c_278]) ).
tcf(c_8035,plain,
complement(iPr_def_18) = iPr_def_17,
inference(demodulation,[status(thm)],[c_8026,c_5576,c_5658]) ).
tcf(c_8043,plain,
join(complement(join(iPr_def_13,iPr_def_17)),complement(join(iPr_def_14,iPr_def_17))) = iPr_def_18,
inference(superposition,[status(thm)],[c_8035,c_260]) ).
tcf(c_8110,plain,
! [X0: $i] : complement(join(iPr_def_10,complement(join(X0,complement(join(iPr_def_10,X0)))))) = sK2,
inference(demodulation,[status(thm)],[c_6505,c_5576]) ).
tcf(c_8118,plain,
complement(join(iPr_def_10,complement(join(iPr_def_12,complement(iPr_def_13))))) = sK2,
inference(superposition,[status(thm)],[c_134,c_8110]) ).
tcf(c_8177,plain,
complement(join(iPr_def_10,complement(join(iPr_def_12,iPr_def_14)))) = sK2,
inference(light_normalisation,[status(thm)],[c_8118,c_135]) ).
tcf(c_8487,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_12,iPr_def_13))) = join(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_5597,c_261]) ).
tcf(c_8508,plain,
join(iPr_def_14,join(iPr_def_14,iPr_def_13)) = iPr_def_19,
inference(superposition,[status(thm)],[c_5597,c_367]) ).
tcf(c_8509,plain,
join(iPr_def_13,join(iPr_def_14,iPr_def_14)) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_8508,c_50,c_49]) ).
tcf(c_8521,plain,
join(iPr_def_20,complement(join(iPr_def_12,iPr_def_13))) = join(iPr_def_14,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_8487,c_278,c_6608]) ).
tcf(c_8849,plain,
complement(join(iPr_def_12,iPr_def_13)) = join(iPr_def_14,iPr_def_14),
inference(demodulation,[status(thm)],[c_8521,c_5576]) ).
tcf(c_8877,plain,
join(iPr_def_12,join(iPr_def_13,join(iPr_def_14,iPr_def_14))) = iPr_def_19,
inference(superposition,[status(thm)],[c_8849,c_367]) ).
tcf(c_8878,plain,
join(iPr_def_12,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_8877,c_8509]) ).
tcf(c_8909,plain,
join(iPr_def_13,sK2) = iPr_def_19,
inference(demodulation,[status(thm)],[c_2217,c_8878]) ).
tcf(c_9011,plain,
join(complement(join(iPr_def_11,sK2)),complement(join(iPr_def_12,sK2))) = join(iPr_def_10,complement(join(iPr_def_12,iPr_def_14))),
inference(superposition,[status(thm)],[c_8177,c_261]) ).
tcf(c_9012,plain,
join(complement(join(iPr_def_13,sK2)),complement(join(iPr_def_14,sK2))) = join(iPr_def_10,complement(join(iPr_def_12,iPr_def_14))),
inference(superposition,[status(thm)],[c_8177,c_260]) ).
tcf(c_9044,plain,
join(iPr_def_10,complement(join(iPr_def_12,iPr_def_14))) = join(iPr_def_20,complement(join(iPr_def_14,sK2))),
inference(light_normalisation,[status(thm)],[c_9012,c_278,c_8909]) ).
tcf(c_9045,plain,
join(iPr_def_10,complement(join(iPr_def_12,iPr_def_14))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_9011,c_6693]) ).
tcf(c_9102,plain,
join(complement(iPr_def_19),complement(join(iPr_def_12,complement(iPr_def_19)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_8878,c_251]) ).
tcf(c_9109,plain,
join(iPr_def_20,complement(join(iPr_def_12,iPr_def_20))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_9102,c_278]) ).
tcf(c_9134,plain,
complement(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_9109,c_5576,c_5658]) ).
tcf(c_9189,plain,
join(iPr_def_20,complement(join(iPr_def_14,sK2))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_9044,c_9045]) ).
tcf(c_9190,plain,
complement(join(iPr_def_14,sK2)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_9189,c_5576]) ).
tcf(c_9198,plain,
join(complement(join(iPr_def_13,iPr_def_10)),complement(join(iPr_def_14,iPr_def_10))) = join(iPr_def_14,sK2),
inference(superposition,[status(thm)],[c_9190,c_260]) ).
tcf(c_9230,plain,
join(complement(join(iPr_def_10,iPr_def_13)),complement(join(iPr_def_10,iPr_def_14))) = join(iPr_def_14,sK2),
inference(theory_normalisation,[status(thm)],[c_9198,c_50,c_49]) ).
tcf(c_9231,plain,
join(iPr_def_14,sK2) = sK2,
inference(light_normalisation,[status(thm)],[c_9230,c_135,c_7245,c_7293]) ).
tcf(c_9449,plain,
join(iPr_def_10,sK2) = join(iPr_def_14,iPr_def_19),
inference(superposition,[status(thm)],[c_9231,c_830]) ).
tcf(c_9450,plain,
join(iPr_def_14,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_9449,c_295,c_6876]) ).
tcf(c_9465,plain,
join(complement(iPr_def_19),complement(join(iPr_def_14,complement(iPr_def_19)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_9450,c_252]) ).
tcf(c_9468,plain,
join(iPr_def_20,complement(join(iPr_def_14,iPr_def_20))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_9465,c_278]) ).
tcf(c_9537,plain,
complement(iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_9468,c_5576,c_5658]) ).
tcf(c_9808,plain,
join(complement(join(iPr_def_13,iPr_def_17)),complement(join(iPr_def_14,iPr_def_17))) = join(iPr_def_18,sK0),
inference(superposition,[status(thm)],[c_5641,c_260]) ).
tcf(c_9840,plain,
join(iPr_def_18,sK0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_9808,c_8043]) ).
tcf(c_9867,plain,
! [X0: $i] : join(iPr_def_18,join(sK0,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_9840,c_50]) ).
tcf(c_10254,plain,
join(iPr_def_18,complement(sK0)) = join(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_284,c_9867]) ).
tcf(c_10274,plain,
join(iPr_def_18,iPr_def_15) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_10254,c_7169,c_7420]) ).
tcf(c_10275,plain,
join(iPr_def_15,iPr_def_18) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_10274,c_50,c_49]) ).
tcf(c_11160,plain,
! [X0: $i] : join(X0,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_5119,c_49,c_4967,c_5576,c_5593]) ).
tcf(c_11523,plain,
! [X0: $i] : join(complement(X0),X0) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_11160,c_6056]) ).
tcf(c_11718,plain,
! [X0: $i] : join(X0,complement(X0)) = join(iPr_def_19,X0),
inference(theory_normalisation,[status(thm)],[c_11523,c_50,c_49]) ).
tcf(c_11719,plain,
! [X0: $i] : join(iPr_def_19,X0) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_11718,c_284]) ).
tcf(c_11882,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_18,X0)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_364,c_11719]) ).
tcf(c_11885,plain,
! [X0: $i] : join(X0,iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_2491,c_11882]) ).
tcf(c_11889,plain,
! [X0: $i] : join(iPr_def_13,join(iPr_def_14,X0)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_2538,c_11885]) ).
tcf(c_11929,plain,
converse(iPr_def_19) = iPr_def_19,
inference(superposition,[status(thm)],[c_11719,c_4116]) ).
tcf(c_11978,plain,
! [X0: $i] : join(complement(iPr_def_19),complement(join(complement(X0),complement(iPr_def_19)))) = X0,
inference(superposition,[status(thm)],[c_11885,c_81]) ).
tcf(c_12000,plain,
! [X0: $i] : join(iPr_def_20,complement(join(complement(X0),iPr_def_20))) = X0,
inference(light_normalisation,[status(thm)],[c_11978,c_278]) ).
tcf(c_12001,plain,
! [X0: $i] : join(iPr_def_20,complement(join(iPr_def_20,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_12000,c_50,c_49]) ).
tcf(c_12458,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_12001,c_5576]) ).
tcf(c_12475,plain,
complement(iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_9134,c_12458]) ).
tcf(c_12476,plain,
complement(iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_9537,c_12458]) ).
tcf(c_14467,plain,
composition(iPr_def_19,complement(composition(iPr_def_19,iPr_def_19))) = iPr_def_20,
inference(superposition,[status(thm)],[c_11929,c_5599]) ).
tcf(c_24725,plain,
! [X0: $i,X1: $i] : join(composition(X0,X1),composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19)))))) = composition(X0,complement(join(complement(X1),complement(composition(converse(X0),iPr_def_19))))),
inference(demodulation,[status(thm)],[c_440,c_5576,c_12458]) ).
tcf(c_24767,plain,
! [X0: $i] : join(composition(X0,iPr_def_19),composition(X0,complement(join(iPr_def_20,complement(composition(converse(X0),iPr_def_19)))))) = composition(X0,complement(join(iPr_def_20,complement(composition(converse(X0),iPr_def_19))))),
inference(superposition,[status(thm)],[c_278,c_24725]) ).
tcf(c_24997,plain,
! [X0: $i] : composition(join(X0,composition(X0,converse(X0))),iPr_def_19) = composition(X0,composition(converse(X0),iPr_def_19)),
inference(demodulation,[status(thm)],[c_24767,c_473,c_5576,c_12458]) ).
tcf(c_25001,plain,
composition(iPr_def_19,composition(converse(iPr_def_19),iPr_def_19)) = composition(iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_11719,c_24997]) ).
tcf(c_25033,plain,
! [X0: $i] : join(composition(X0,composition(converse(X0),iPr_def_19)),composition(join(X0,composition(X0,converse(X0))),complement(join(complement(iPr_def_19),complement(composition(converse(join(X0,composition(X0,converse(X0)))),iPr_def_19)))))) = composition(join(X0,composition(X0,converse(X0))),complement(join(complement(iPr_def_19),complement(composition(converse(join(X0,composition(X0,converse(X0)))),iPr_def_19))))),
inference(superposition,[status(thm)],[c_24997,c_24725]) ).
tcf(c_25054,plain,
composition(iPr_def_19,composition(iPr_def_19,iPr_def_19)) = composition(iPr_def_19,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_25001,c_11929]) ).
tcf(c_25074,plain,
! [X0: $i] : join(composition(X0,composition(converse(X0),iPr_def_19)),composition(join(X0,composition(X0,converse(X0))),complement(join(iPr_def_20,complement(composition(converse(join(X0,composition(X0,converse(X0)))),iPr_def_19)))))) = composition(join(X0,composition(X0,converse(X0))),complement(join(iPr_def_20,complement(composition(converse(join(X0,composition(X0,converse(X0)))),iPr_def_19))))),
inference(light_normalisation,[status(thm)],[c_25033,c_278]) ).
tcf(c_25094,plain,
! [X0: $i] : composition(join(X0,composition(join(X0,composition(X0,converse(X0))),join(one,X0))),composition(converse(X0),iPr_def_19)) = composition(join(X0,composition(X0,converse(X0))),composition(join(one,X0),composition(converse(X0),iPr_def_19))),
inference(demodulation,[status(thm)],[c_25074,c_52,c_473,c_4818,c_5081,c_5576,c_12458]) ).
tcf(c_25097,plain,
composition(join(iPr_def_19,composition(iPr_def_19,converse(iPr_def_19))),composition(join(one,iPr_def_19),composition(converse(iPr_def_19),iPr_def_19))) = composition(iPr_def_19,composition(converse(iPr_def_19),iPr_def_19)),
inference(superposition,[status(thm)],[c_11719,c_25094]) ).
tcf(c_25191,plain,
composition(join(iPr_def_19,composition(iPr_def_19,converse(iPr_def_19))),composition(join(iPr_def_19,one),composition(converse(iPr_def_19),iPr_def_19))) = composition(iPr_def_19,composition(converse(iPr_def_19),iPr_def_19)),
inference(theory_normalisation,[status(thm)],[c_25097,c_50,c_49]) ).
tcf(c_25192,plain,
composition(join(iPr_def_19,composition(iPr_def_19,iPr_def_19)),composition(join(iPr_def_19,one),composition(iPr_def_19,iPr_def_19))) = composition(iPr_def_19,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_25191,c_11929,c_25054]) ).
tcf(c_30464,plain,
join(complement(join(iPr_def_10,complement(iPr_def_11))),complement(join(iPr_def_10,complement(composition(sK1,complement(join(complement(sK0),complement(composition(converse(sK1),sK2))))))))) = complement(join(iPr_def_10,complement(composition(sK1,complement(join(complement(sK0),complement(composition(converse(sK1),sK2)))))))),
inference(superposition,[status(thm)],[c_132,c_445]) ).
tcf(c_30553,plain,
join(iPr_def_14,complement(join(iPr_def_10,complement(composition(sK1,iPr_def_20))))) = complement(join(iPr_def_10,complement(composition(sK1,iPr_def_20)))),
inference(light_normalisation,[status(thm)],[c_30464,c_134,c_138,c_274,c_278,c_6808,c_7169,c_10275,c_12475,c_12476]) ).
tcf(c_30713,plain,
join(iPr_def_13,complement(join(iPr_def_10,complement(composition(sK1,iPr_def_20))))) = iPr_def_19,
inference(superposition,[status(thm)],[c_30553,c_11889]) ).
tcf(c_33751,plain,
! [X0: $i] : join(complement(iPr_def_19),composition(converse(composition(join(X0,composition(join(X0,composition(X0,converse(X0))),join(one,X0))),converse(X0))),complement(composition(join(X0,composition(X0,converse(X0))),composition(join(one,X0),composition(converse(X0),iPr_def_19)))))) = complement(iPr_def_19),
inference(superposition,[status(thm)],[c_25094,c_463]) ).
tcf(c_33831,plain,
! [X0: $i] : join(iPr_def_20,composition(converse(composition(join(X0,composition(join(X0,composition(X0,converse(X0))),join(one,X0))),converse(X0))),complement(composition(join(X0,composition(X0,converse(X0))),composition(join(one,X0),composition(converse(X0),iPr_def_19)))))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_33751,c_278]) ).
tcf(c_34527,plain,
! [X0: $i] : composition(X0,composition(converse(join(X0,composition(join(X0,composition(X0,converse(X0))),join(one,X0)))),complement(composition(join(X0,composition(X0,converse(X0))),composition(join(one,X0),composition(converse(X0),iPr_def_19)))))) = iPr_def_20,
inference(demodulation,[status(thm)],[c_33831,c_52,c_349,c_5576]) ).
tcf(c_34538,plain,
composition(iPr_def_19,composition(converse(iPr_def_19),complement(composition(join(iPr_def_19,composition(iPr_def_19,converse(iPr_def_19))),composition(join(one,iPr_def_19),composition(converse(iPr_def_19),iPr_def_19)))))) = iPr_def_20,
inference(superposition,[status(thm)],[c_11719,c_34527]) ).
tcf(c_34761,plain,
composition(iPr_def_19,composition(converse(iPr_def_19),complement(composition(join(iPr_def_19,composition(iPr_def_19,converse(iPr_def_19))),composition(join(iPr_def_19,one),composition(converse(iPr_def_19),iPr_def_19)))))) = iPr_def_20,
inference(theory_normalisation,[status(thm)],[c_34538,c_50,c_49]) ).
tcf(c_34762,plain,
composition(iPr_def_19,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_34761,c_11929,c_14467,c_25192]) ).
tcf(c_35499,plain,
! [X0: $i] : join(composition(X0,iPr_def_20),iPr_def_20) = composition(join(X0,iPr_def_19),iPr_def_20),
inference(superposition,[status(thm)],[c_34762,c_54]) ).
tcf(c_35517,plain,
! [X0: $i] : join(iPr_def_20,composition(X0,iPr_def_20)) = composition(join(X0,iPr_def_19),iPr_def_20),
inference(theory_normalisation,[status(thm)],[c_35499,c_50,c_49]) ).
tcf(c_35518,plain,
! [X0: $i] : join(iPr_def_20,composition(X0,iPr_def_20)) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_35517,c_11885,c_34762]) ).
tcf(c_35676,plain,
! [X0: $i] : composition(X0,iPr_def_20) = iPr_def_20,
inference(demodulation,[status(thm)],[c_35518,c_5576]) ).
tcf(c_35687,plain,
join(iPr_def_13,complement(join(iPr_def_10,complement(iPr_def_20)))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_30713,c_35676]) ).
tcf(c_35696,plain,
join(iPr_def_13,complement(join(iPr_def_10,iPr_def_19))) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_35687,c_5663]) ).
tcf(c_40961,plain,
iPr_def_13 = iPr_def_19,
inference(demodulation,[status(thm)],[c_35696,c_278,c_5658,c_11885]) ).
tcf(c_41062,plain,
complement(iPr_def_13) = iPr_def_20,
inference(demodulation,[status(thm)],[c_141,c_40961]) ).
tcf(c_41063,plain,
iPr_def_14 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_41062,c_12476]) ).
tcf(c_41064,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_41063,c_239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Thu Sep 24 07:11:40 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.42
% 0.03/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.42
% 0.03/0.42 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 28.22/4.83 % SZS status Started for theBenchmark.p
% 28.22/4.83 % SZS status Theorem for theBenchmark.p
% 28.22/4.83
% 28.22/4.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.22/4.83
% 28.22/4.83 % ------ iProver source info
% 28.22/4.83
% 28.22/4.83 % git: date: 2026-07-19 20:42:38 +0200
% 28.22/4.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.22/4.83 % git: non_committed_changes: false
% 28.22/4.83
% 28.22/4.83 % ------ Parsing...
% 28.22/4.83 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 28.22/4.83 %
% 28.22/4.83
% 28.22/4.83 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 28.22/4.83
% 28.22/4.83 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 28.22/4.83 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 28.22/4.83
% 28.22/4.83 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 28.22/4.83 % ------ Proving...
% 28.22/4.83 % ------ Problem Properties
% 28.22/4.83
% 28.22/4.83 %
% 28.22/4.83 % clauses 28
% 28.22/4.83 % conjectures 2
% 28.22/4.83 % EPR 2
% 28.22/4.83 % Horn 28
% 28.22/4.83 % unary 28
% 28.22/4.83 % binary 0
% 28.22/4.83 % lits 28
% 28.22/4.83 % lits eq 28
% 28.22/4.83 % fd_pure 0
% 28.22/4.83 % fd_pseudo 0
% 28.22/4.83 % fd_cond 0
% 28.22/4.83 % fd_pseudo_cond 0
% 28.22/4.83 % AC symbols 1
% 28.22/4.83
% 28.22/4.83 % ------ Schedule UEQ
% 28.22/4.83
% 28.22/4.83 % ------ Option_UEQ Time Limit: 10.
% 28.22/4.83
% 28.22/4.83
% 28.22/4.83 % ------
% 28.22/4.83 % Current options:
% 28.22/4.83 % ------
% 28.22/4.83
% 28.22/4.83
% 28.22/4.83 %
% 28.22/4.83
% 28.22/4.83 % ------ Proving...
% 28.22/4.83 %
% 28.22/4.83
% 28.22/4.83 % SZS status Theorem for theBenchmark.p
% 28.22/4.83
% 28.22/4.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.22/4.84
% 28.22/4.84
%------------------------------------------------------------------------------