%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 23.14s 10.36s
% Output : CNFRefutation 23.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 27
% Syntax : Number of formulae : 331 ( 327 unt; 11 def)
% Number of atoms : 1192 ( 334 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 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 : 240 ( 0 sgn 237 !; 3 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f14,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
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/sandbox/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
=> meet(X1,composition(converse(X0),X2)) = zero ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( meet(composition(X0,X1),X2) = zero
& zero != meet(X1,composition(converse(X0),X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( zero = meet(composition(sK0,sK1),sK2)
& zero != meet(sK1,composition(converse(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(f34,plain,
! [X2,X0,X1] : composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))),
inference(cnf_transformation,[],[f14]) ).
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(composition(sK0,sK1),sK2),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
zero != meet(sK1,composition(converse(sK0),sK2)),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f40,plain,
! [X2,X0,X1] : composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))),
inference(definition_unfolding,[],[f34,f24,f24,f24,f24,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(sK1),complement(composition(converse(sK0),sK2)))),
inference(definition_unfolding,[],[f38,f24]) ).
fof(f44,plain,
zero = complement(join(complement(composition(sK0,sK1)),complement(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_61,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))) = composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))),
inference(cnf_transformation,[],[f40]) ).
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(sK1),complement(composition(converse(sK0),sK2)))) != zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(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(sK0,sK1)))) = zero,
inference(theory_normalisation,[status(thm)],[c_65,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(sK0,sK1),
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(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_137,definition,
iPr_def_16 = converse(sK0),
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_64,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_143,c_142]) ).
tcf(c_240,plain,
complement(top) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_124,c_142]) ).
tcf(c_249,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_250,plain,
! [X0: $i] : join(complement(join(iPr_def_14,X0)),complement(join(iPr_def_14,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_253,plain,
! [X0: $i] : join(complement(join(complement(X0),sK1)),complement(join(complement(X0),iPr_def_15))) = X0,
inference(superposition,[status(thm)],[c_136,c_81]) ).
tcf(c_254,plain,
! [X0: $i] : join(complement(join(complement(X0),sK2)),complement(join(complement(X0),iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_131,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_10,complement(X0))),complement(join(sK2,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_254,c_50,c_49]) ).
tcf(c_264,plain,
! [X0: $i] : join(complement(join(iPr_def_15,complement(X0))),complement(join(sK1,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_253,c_50,c_49]) ).
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_271,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_19)),complement(join(complement(X0),iPr_def_20))) = X0,
inference(superposition,[status(thm)],[c_141,c_81]) ).
tcf(c_272,plain,
! [X0: $i] : join(complement(join(iPr_def_19,complement(X0))),complement(join(iPr_def_20,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_271,c_50,c_49]) ).
tcf(c_273,plain,
converse(iPr_def_16) = sK0,
inference(superposition,[status(thm)],[c_137,c_55]) ).
tcf(c_277,plain,
top = iPr_def_13,
inference(demodulation,[status(thm)],[c_250,c_252]) ).
tcf(c_278,plain,
complement(iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_240,c_277]) ).
tcf(c_284,plain,
! [X0: $i] : join(X0,complement(X0)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_59,c_277]) ).
tcf(c_285,plain,
join(sK1,iPr_def_15) = iPr_def_13,
inference(superposition,[status(thm)],[c_136,c_284]) ).
tcf(c_286,plain,
join(sK2,iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_131,c_284]) ).
tcf(c_287,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_133,c_284]) ).
tcf(c_288,plain,
join(iPr_def_13,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_278,c_284]) ).
tcf(c_290,plain,
join(iPr_def_17,iPr_def_18) = iPr_def_13,
inference(superposition,[status(thm)],[c_139,c_284]) ).
tcf(c_291,plain,
join(iPr_def_19,iPr_def_20) = iPr_def_13,
inference(superposition,[status(thm)],[c_141,c_284]) ).
tcf(c_292,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(iPr_def_13)) = X0,
inference(superposition,[status(thm)],[c_284,c_81]) ).
tcf(c_293,plain,
! [X0: $i] : join(complement(iPr_def_13),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_284,c_81]) ).
tcf(c_294,plain,
join(iPr_def_10,sK2) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_286,c_50,c_49]) ).
tcf(c_295,plain,
join(iPr_def_15,sK1) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_285,c_50,c_49]) ).
tcf(c_296,plain,
! [X0: $i] : join(complement(iPr_def_13),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_14,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_14,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_14,complement(join(iPr_def_15,iPr_def_15))) = sK1,
inference(superposition,[status(thm)],[c_136,c_297]) ).
tcf(c_308,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_10))) = sK2,
inference(superposition,[status(thm)],[c_131,c_297]) ).
tcf(c_310,plain,
join(iPr_def_14,complement(join(iPr_def_14,iPr_def_14))) = iPr_def_13,
inference(superposition,[status(thm)],[c_278,c_297]) ).
tcf(c_313,plain,
join(iPr_def_14,complement(join(iPr_def_20,iPr_def_20))) = iPr_def_19,
inference(superposition,[status(thm)],[c_141,c_297]) ).
tcf(c_317,plain,
! [X0: $i] : join(iPr_def_14,composition(converse(X0),complement(composition(X0,iPr_def_13)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_278,c_82]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_55,c_82]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_49,c_81]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),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_363,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_12,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_134,c_50]) ).
tcf(c_365,plain,
! [X0: $i] : join(iPr_def_13,join(iPr_def_14,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_288,c_50]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_50,c_284]) ).
tcf(c_370,plain,
! [X0: $i] : join(iPr_def_19,join(iPr_def_20,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_291,c_50]) ).
tcf(c_371,plain,
! [X0: $i] : join(iPr_def_10,join(sK2,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_294,c_50]) ).
tcf(c_390,plain,
join(iPr_def_14,complement(join(iPr_def_14,complement(complement(iPr_def_14))))) = iPr_def_13,
inference(superposition,[status(thm)],[c_278,c_298]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,X1)),iPr_def_15)),complement(join(iPr_def_15,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK1))))))))) = complement(join(iPr_def_15,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK1)))))))),
inference(superposition,[status(thm)],[c_136,c_83]) ).
tcf(c_431,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(converse(X2)))),complement(join(complement(converse(X2)),complement(composition(X0,complement(join(complement(X1),complement(converse(composition(X2,X0)))))))))) = complement(join(complement(converse(X2)),complement(composition(X0,complement(join(complement(X1),complement(converse(composition(X2,X0))))))))),
inference(superposition,[status(thm)],[c_57,c_83]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_15,complement(composition(X0,X1)))),complement(join(iPr_def_15,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK1))))))))) = complement(join(iPr_def_15,complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),sK1)))))))),
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_817,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_818,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_823,plain,
! [X0: $i] : join(iPr_def_10,join(X0,sK2)) = join(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_294,c_238]) ).
tcf(c_1701,plain,
join(complement(join(iPr_def_10,sK1)),complement(join(iPr_def_10,iPr_def_15))) = sK2,
inference(superposition,[status(thm)],[c_136,c_249]) ).
tcf(c_1722,plain,
join(complement(join(iPr_def_10,iPr_def_15)),complement(join(iPr_def_10,sK1))) = sK2,
inference(theory_normalisation,[status(thm)],[c_1701,c_50,c_49]) ).
tcf(c_1735,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_12)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_49,c_363]) ).
tcf(c_1761,plain,
join(iPr_def_13,complement(iPr_def_14)) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_284,c_365]) ).
tcf(c_1764,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(X0),complement(complement(complement(X0)))))) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_298,c_365]) ).
tcf(c_1772,plain,
join(iPr_def_13,complement(join(iPr_def_14,complement(complement(iPr_def_14))))) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_390,c_365]) ).
tcf(c_1874,plain,
join(complement(join(iPr_def_12,sK1)),complement(join(iPr_def_12,iPr_def_15))) = iPr_def_11,
inference(superposition,[status(thm)],[c_136,c_251]) ).
tcf(c_1875,plain,
join(complement(join(iPr_def_12,sK2)),complement(join(iPr_def_12,iPr_def_10))) = iPr_def_11,
inference(superposition,[status(thm)],[c_131,c_251]) ).
tcf(c_1890,plain,
join(complement(join(iPr_def_10,iPr_def_12)),complement(join(iPr_def_12,sK2))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1875,c_50,c_49]) ).
tcf(c_1891,plain,
join(iPr_def_14,complement(join(iPr_def_12,sK2))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1890,c_134,c_278]) ).
tcf(c_1892,plain,
join(complement(join(iPr_def_12,iPr_def_15)),complement(join(iPr_def_12,sK1))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1874,c_50,c_49]) ).
tcf(c_2093,plain,
join(complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14))),complement(iPr_def_13)) = iPr_def_13,
inference(superposition,[status(thm)],[c_310,c_252]) ).
tcf(c_2139,plain,
join(complement(iPr_def_13),complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14)))) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_2093,c_50,c_49]) ).
tcf(c_2140,plain,
join(iPr_def_14,complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14)))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2139,c_278]) ).
tcf(c_2328,plain,
join(sK2,iPr_def_13) = join(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_817,c_371]) ).
tcf(c_2329,plain,
join(iPr_def_12,iPr_def_13) = join(iPr_def_13,sK2),
inference(theory_normalisation,[status(thm)],[c_2328,c_50,c_49]) ).
tcf(c_2346,plain,
join(iPr_def_15,iPr_def_13) = join(iPr_def_17,iPr_def_19),
inference(superposition,[status(thm)],[c_290,c_818]) ).
tcf(c_2356,plain,
join(iPr_def_13,iPr_def_15) = join(iPr_def_17,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_2346,c_50,c_49]) ).
tcf(c_2365,plain,
join(iPr_def_13,complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14)))) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_2140,c_365]) ).
tcf(c_2524,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(join(complement(X0),complement(X0))),complement(complement(iPr_def_13))))) = join(complement(X0),complement(X0)),
inference(superposition,[status(thm)],[c_284,c_259]) ).
tcf(c_2570,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(complement(iPr_def_13)),complement(join(complement(X0),complement(X0)))))) = join(complement(X0),complement(X0)),
inference(theory_normalisation,[status(thm)],[c_2524,c_50,c_49]) ).
tcf(c_2571,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(iPr_def_14),complement(join(complement(X0),complement(X0)))))) = join(complement(X0),complement(X0)),
inference(light_normalisation,[status(thm)],[c_2570,c_278]) ).
tcf(c_2967,plain,
join(complement(join(iPr_def_13,complement(iPr_def_14))),complement(iPr_def_13)) = iPr_def_14,
inference(superposition,[status(thm)],[c_284,c_260]) ).
tcf(c_2969,plain,
! [X0: $i] : join(complement(join(iPr_def_13,complement(join(complement(X0),complement(complement(complement(X0))))))),complement(X0)) = join(complement(X0),complement(complement(complement(X0)))),
inference(superposition,[status(thm)],[c_298,c_260]) ).
tcf(c_2979,plain,
join(complement(join(iPr_def_13,complement(join(iPr_def_14,complement(complement(iPr_def_14)))))),complement(iPr_def_13)) = join(iPr_def_14,complement(complement(iPr_def_14))),
inference(superposition,[status(thm)],[c_390,c_260]) ).
tcf(c_2992,plain,
join(complement(join(iPr_def_13,complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14))))),complement(iPr_def_13)) = join(iPr_def_14,join(iPr_def_14,iPr_def_14)),
inference(superposition,[status(thm)],[c_2140,c_260]) ).
tcf(c_3022,plain,
join(complement(iPr_def_13),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_2967,c_50,c_49]) ).
tcf(c_3023,plain,
join(iPr_def_14,complement(join(iPr_def_13,iPr_def_13))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_3022,c_278,c_1761]) ).
tcf(c_3049,plain,
join(complement(iPr_def_13),complement(join(iPr_def_13,complement(join(iPr_def_14,join(iPr_def_14,iPr_def_14)))))) = join(iPr_def_14,join(iPr_def_14,iPr_def_14)),
inference(theory_normalisation,[status(thm)],[c_2992,c_50,c_49]) ).
tcf(c_3050,plain,
join(iPr_def_14,complement(join(iPr_def_13,iPr_def_13))) = join(iPr_def_14,join(iPr_def_14,iPr_def_14)),
inference(light_normalisation,[status(thm)],[c_3049,c_278,c_2365]) ).
tcf(c_3055,plain,
join(complement(iPr_def_13),complement(join(iPr_def_13,complement(join(iPr_def_14,complement(complement(iPr_def_14))))))) = join(iPr_def_14,complement(complement(iPr_def_14))),
inference(theory_normalisation,[status(thm)],[c_2979,c_50,c_49]) ).
tcf(c_3056,plain,
join(iPr_def_14,complement(join(iPr_def_13,iPr_def_13))) = join(iPr_def_14,complement(complement(iPr_def_14))),
inference(light_normalisation,[status(thm)],[c_3055,c_278,c_1772]) ).
tcf(c_3072,plain,
! [X0: $i] : join(complement(X0),complement(join(iPr_def_13,complement(join(complement(X0),complement(complement(complement(X0)))))))) = join(complement(X0),complement(complement(complement(X0)))),
inference(theory_normalisation,[status(thm)],[c_2969,c_50,c_49]) ).
tcf(c_3073,plain,
! [X0: $i] : join(complement(X0),complement(join(iPr_def_13,X0))) = join(complement(X0),complement(complement(complement(X0)))),
inference(light_normalisation,[status(thm)],[c_3072,c_1764]) ).
tcf(c_3133,plain,
join(iPr_def_13,complement(join(iPr_def_13,iPr_def_13))) = join(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_3023,c_365]) ).
tcf(c_3138,plain,
join(iPr_def_13,complement(join(iPr_def_13,iPr_def_13))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_3133,c_288]) ).
tcf(c_3146,plain,
join(complement(iPr_def_13),complement(join(iPr_def_14,complement(join(iPr_def_13,iPr_def_13))))) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_3138,c_260]) ).
tcf(c_3147,plain,
join(iPr_def_13,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_3146,c_278,c_2140,c_3050]) ).
tcf(c_3149,plain,
join(iPr_def_14,complement(iPr_def_13)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3023,c_3147]) ).
tcf(c_3152,plain,
join(iPr_def_14,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_3149,c_278]) ).
tcf(c_3163,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_14,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_3152,c_50]) ).
tcf(c_3194,plain,
join(iPr_def_14,complement(complement(iPr_def_14))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_3056,c_278,c_3147,c_3152]) ).
tcf(c_3203,plain,
join(iPr_def_13,complement(complement(iPr_def_14))) = join(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_3194,c_365]) ).
tcf(c_3208,plain,
join(iPr_def_13,complement(complement(iPr_def_14))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_3203,c_288]) ).
tcf(c_3226,plain,
join(complement(join(iPr_def_11,complement(iPr_def_12))),complement(iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_284,c_261]) ).
tcf(c_3232,plain,
join(complement(join(iPr_def_11,iPr_def_18)),complement(join(iPr_def_12,iPr_def_18))) = iPr_def_17,
inference(superposition,[status(thm)],[c_139,c_261]) ).
tcf(c_3233,plain,
join(complement(join(iPr_def_11,iPr_def_20)),complement(join(iPr_def_12,iPr_def_20))) = iPr_def_19,
inference(superposition,[status(thm)],[c_141,c_261]) ).
tcf(c_3241,plain,
join(complement(iPr_def_13),complement(join(iPr_def_11,complement(iPr_def_12)))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_3226,c_50,c_49]) ).
tcf(c_3242,plain,
join(iPr_def_14,complement(join(iPr_def_11,complement(iPr_def_12)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3241,c_278]) ).
tcf(c_3320,plain,
join(complement(iPr_def_13),complement(join(iPr_def_14,complement(complement(iPr_def_14))))) = complement(iPr_def_14),
inference(superposition,[status(thm)],[c_3208,c_260]) ).
tcf(c_3321,plain,
join(iPr_def_14,complement(iPr_def_14)) = complement(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_3320,c_278,c_3194]) ).
tcf(c_3322,plain,
complement(iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3321,c_284]) ).
tcf(c_4285,plain,
! [X0: $i] : join(iPr_def_14,X0) = X0,
inference(superposition,[status(thm)],[c_297,c_3163]) ).
tcf(c_4330,plain,
! [X0: $i] : complement(join(complement(X0),complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_297,c_4285]) ).
tcf(c_4332,plain,
complement(join(iPr_def_15,iPr_def_15)) = sK1,
inference(demodulation,[status(thm)],[c_307,c_4285]) ).
tcf(c_4333,plain,
complement(join(iPr_def_10,iPr_def_10)) = sK2,
inference(demodulation,[status(thm)],[c_308,c_4285]) ).
tcf(c_4336,plain,
complement(join(iPr_def_20,iPr_def_20)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_313,c_4285]) ).
tcf(c_4337,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,iPr_def_13))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_317,c_4285]) ).
tcf(c_4353,plain,
complement(join(iPr_def_12,sK2)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1891,c_4285]) ).
tcf(c_4354,plain,
complement(join(iPr_def_11,complement(iPr_def_12))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3242,c_4285]) ).
tcf(c_4394,plain,
! [X0: $i] : join(X0,iPr_def_14) = X0,
inference(superposition,[status(thm)],[c_4285,c_49]) ).
tcf(c_4504,plain,
join(join(iPr_def_15,iPr_def_15),sK1) = iPr_def_13,
inference(superposition,[status(thm)],[c_4332,c_284]) ).
tcf(c_4515,plain,
join(iPr_def_15,join(iPr_def_15,sK1)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_4504,c_50,c_49]) ).
tcf(c_4516,plain,
join(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4515,c_295]) ).
tcf(c_4517,plain,
join(iPr_def_13,iPr_def_15) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_4516,c_50,c_49]) ).
tcf(c_4530,plain,
join(iPr_def_17,iPr_def_19) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2356,c_4517]) ).
tcf(c_4692,plain,
! [X0: $i] : join(complement(X0),complement(complement(complement(X0)))) = join(complement(X0),complement(X0)),
inference(light_normalisation,[status(thm)],[c_2571,c_3073,c_3322,c_4330]) ).
tcf(c_4903,plain,
join(complement(join(iPr_def_10,sK2)),complement(join(sK2,sK2))) = join(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_4333,c_263]) ).
tcf(c_4912,plain,
join(join(iPr_def_10,iPr_def_10),sK2) = iPr_def_13,
inference(superposition,[status(thm)],[c_4333,c_284]) ).
tcf(c_4923,plain,
join(iPr_def_10,join(iPr_def_10,sK2)) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_4912,c_50,c_49]) ).
tcf(c_4924,plain,
join(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4923,c_294]) ).
tcf(c_4933,plain,
join(iPr_def_14,complement(join(sK2,sK2))) = join(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_4903,c_278,c_294]) ).
tcf(c_4962,plain,
join(complement(iPr_def_13),complement(join(iPr_def_10,complement(iPr_def_13)))) = sK2,
inference(superposition,[status(thm)],[c_4924,c_249]) ).
tcf(c_4963,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_14))) = sK2,
inference(light_normalisation,[status(thm)],[c_4962,c_278]) ).
tcf(c_4964,plain,
complement(iPr_def_10) = sK2,
inference(demodulation,[status(thm)],[c_4963,c_4285,c_4394]) ).
tcf(c_4969,plain,
join(complement(join(iPr_def_10,sK2)),complement(join(sK2,sK2))) = iPr_def_10,
inference(superposition,[status(thm)],[c_4964,c_263]) ).
tcf(c_4993,plain,
join(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4969,c_278,c_294,c_4933]) ).
tcf(c_5024,plain,
join(iPr_def_14,complement(join(sK2,sK2))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4933,c_4993]) ).
tcf(c_5025,plain,
complement(join(sK2,sK2)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5024,c_4285]) ).
tcf(c_5029,plain,
join(complement(join(iPr_def_15,iPr_def_10)),complement(join(sK1,iPr_def_10))) = join(sK2,sK2),
inference(superposition,[status(thm)],[c_5025,c_264]) ).
tcf(c_5061,plain,
join(complement(join(iPr_def_10,iPr_def_15)),complement(join(iPr_def_10,sK1))) = join(sK2,sK2),
inference(theory_normalisation,[status(thm)],[c_5029,c_50,c_49]) ).
tcf(c_5062,plain,
join(sK2,sK2) = sK2,
inference(light_normalisation,[status(thm)],[c_5061,c_1722]) ).
tcf(c_5108,plain,
join(complement(join(iPr_def_17,complement(iPr_def_18))),complement(iPr_def_13)) = iPr_def_18,
inference(superposition,[status(thm)],[c_284,c_269]) ).
tcf(c_5127,plain,
join(complement(iPr_def_13),complement(join(iPr_def_17,complement(iPr_def_18)))) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_5108,c_50,c_49]) ).
tcf(c_5128,plain,
join(iPr_def_14,complement(join(iPr_def_17,complement(iPr_def_18)))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_5127,c_278]) ).
tcf(c_5202,plain,
join(sK2,iPr_def_13) = join(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_5062,c_823]) ).
tcf(c_5203,plain,
join(iPr_def_10,sK2) = join(iPr_def_13,sK2),
inference(theory_normalisation,[status(thm)],[c_5202,c_50,c_49]) ).
tcf(c_5204,plain,
join(iPr_def_13,sK2) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_5203,c_294,c_2329]) ).
tcf(c_5207,plain,
join(iPr_def_12,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2329,c_5204]) ).
tcf(c_5221,plain,
join(complement(iPr_def_13),complement(join(iPr_def_12,complement(iPr_def_13)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_5207,c_251]) ).
tcf(c_5224,plain,
join(iPr_def_14,complement(join(iPr_def_12,iPr_def_14))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_5221,c_278]) ).
tcf(c_5225,plain,
complement(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_5224,c_4285,c_4394]) ).
tcf(c_5234,plain,
join(complement(join(iPr_def_11,iPr_def_11)),complement(join(iPr_def_12,iPr_def_11))) = iPr_def_12,
inference(superposition,[status(thm)],[c_5225,c_261]) ).
tcf(c_5259,plain,
join(complement(join(iPr_def_11,iPr_def_11)),complement(join(iPr_def_11,iPr_def_12))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_5234,c_50,c_49]) ).
tcf(c_5260,plain,
join(complement(join(iPr_def_11,iPr_def_11)),iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_5259,c_278,c_287]) ).
tcf(c_5261,plain,
join(iPr_def_14,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_5260,c_50,c_49]) ).
tcf(c_5273,plain,
complement(join(iPr_def_17,complement(iPr_def_18))) = iPr_def_18,
inference(demodulation,[status(thm)],[c_5128,c_4285]) ).
tcf(c_5280,plain,
join(complement(join(iPr_def_11,iPr_def_18)),complement(join(iPr_def_12,iPr_def_18))) = join(iPr_def_17,complement(iPr_def_18)),
inference(superposition,[status(thm)],[c_5273,c_261]) ).
tcf(c_5304,plain,
join(iPr_def_17,complement(iPr_def_18)) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_5280,c_3232]) ).
tcf(c_5319,plain,
complement(iPr_def_17) = iPr_def_18,
inference(demodulation,[status(thm)],[c_5273,c_5304]) ).
tcf(c_5732,plain,
join(complement(join(iPr_def_19,complement(iPr_def_20))),complement(iPr_def_13)) = iPr_def_20,
inference(superposition,[status(thm)],[c_284,c_272]) ).
tcf(c_5758,plain,
join(complement(iPr_def_13),complement(join(iPr_def_19,complement(iPr_def_20)))) = iPr_def_20,
inference(theory_normalisation,[status(thm)],[c_5732,c_50,c_49]) ).
tcf(c_5759,plain,
join(iPr_def_14,complement(join(iPr_def_19,complement(iPr_def_20)))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_5758,c_278]) ).
tcf(c_5929,plain,
join(complement(join(iPr_def_19,iPr_def_19)),complement(join(iPr_def_20,iPr_def_19))) = join(iPr_def_20,iPr_def_20),
inference(superposition,[status(thm)],[c_4336,c_272]) ).
tcf(c_5931,plain,
join(complement(join(iPr_def_17,iPr_def_19)),complement(join(iPr_def_18,iPr_def_19))) = join(iPr_def_20,iPr_def_20),
inference(superposition,[status(thm)],[c_4336,c_269]) ).
tcf(c_5933,plain,
join(iPr_def_19,complement(complement(iPr_def_19))) = join(iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_4336,c_4692]) ).
tcf(c_5957,plain,
join(iPr_def_19,complement(iPr_def_20)) = join(iPr_def_19,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_5933,c_141]) ).
tcf(c_5966,plain,
join(iPr_def_14,complement(join(iPr_def_18,iPr_def_19))) = join(iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_5931,c_278,c_4530]) ).
tcf(c_5969,plain,
join(complement(join(iPr_def_19,iPr_def_19)),complement(join(iPr_def_19,iPr_def_20))) = join(iPr_def_20,iPr_def_20),
inference(theory_normalisation,[status(thm)],[c_5929,c_50,c_49]) ).
tcf(c_5970,plain,
join(complement(join(iPr_def_19,iPr_def_19)),iPr_def_14) = join(iPr_def_20,iPr_def_20),
inference(light_normalisation,[status(thm)],[c_5969,c_278,c_291]) ).
tcf(c_5971,plain,
join(iPr_def_14,complement(join(iPr_def_19,iPr_def_19))) = join(iPr_def_20,iPr_def_20),
inference(theory_normalisation,[status(thm)],[c_5970,c_50,c_49]) ).
tcf(c_6058,plain,
join(complement(join(iPr_def_11,iPr_def_11)),complement(join(iPr_def_12,iPr_def_11))) = join(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_4353,c_261]) ).
tcf(c_6086,plain,
join(complement(join(iPr_def_11,iPr_def_11)),complement(join(iPr_def_11,iPr_def_12))) = join(iPr_def_12,sK2),
inference(theory_normalisation,[status(thm)],[c_6058,c_50,c_49]) ).
tcf(c_6087,plain,
join(complement(join(iPr_def_11,iPr_def_11)),iPr_def_14) = join(iPr_def_12,sK2),
inference(light_normalisation,[status(thm)],[c_6086,c_278,c_287]) ).
tcf(c_6088,plain,
join(iPr_def_14,complement(join(iPr_def_11,iPr_def_11))) = join(iPr_def_12,sK2),
inference(theory_normalisation,[status(thm)],[c_6087,c_50,c_49]) ).
tcf(c_6089,plain,
join(iPr_def_12,sK2) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_6088,c_5261]) ).
tcf(c_6108,plain,
join(iPr_def_20,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_5759,c_5957,c_5971]) ).
tcf(c_6193,plain,
join(iPr_def_14,complement(join(iPr_def_18,iPr_def_19))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_5966,c_6108]) ).
tcf(c_6194,plain,
complement(join(iPr_def_18,iPr_def_19)) = iPr_def_20,
inference(demodulation,[status(thm)],[c_6193,c_4285]) ).
tcf(c_6203,plain,
join(complement(join(iPr_def_11,iPr_def_20)),complement(join(iPr_def_12,iPr_def_20))) = join(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_6194,c_261]) ).
tcf(c_6229,plain,
join(iPr_def_18,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_6203,c_3233]) ).
tcf(c_6249,plain,
complement(iPr_def_19) = iPr_def_20,
inference(demodulation,[status(thm)],[c_6194,c_6229]) ).
tcf(c_6468,plain,
! [X0: $i] : join(iPr_def_12,join(sK2,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_6089,c_50]) ).
tcf(c_6744,plain,
join(iPr_def_12,complement(sK2)) = join(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_284,c_6468]) ).
tcf(c_6757,plain,
join(iPr_def_12,iPr_def_10) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_6744,c_131,c_5207]) ).
tcf(c_6758,plain,
join(iPr_def_10,iPr_def_12) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_6757,c_50,c_49]) ).
tcf(c_7344,plain,
complement(join(iPr_def_11,iPr_def_11)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_4354,c_5225]) ).
tcf(c_7351,plain,
join(complement(join(iPr_def_15,iPr_def_12)),complement(join(sK1,iPr_def_12))) = join(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_7344,c_264]) ).
tcf(c_7383,plain,
join(complement(join(iPr_def_12,iPr_def_15)),complement(join(iPr_def_12,sK1))) = join(iPr_def_11,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_7351,c_50,c_49]) ).
tcf(c_7384,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_7383,c_1892]) ).
tcf(c_7398,plain,
complement(iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_7344,c_7384]) ).
tcf(c_7842,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(join(X0,X0)),
inference(superposition,[status(thm)],[c_4330,c_4330]) ).
tcf(c_7904,plain,
! [X0: $i] : join(complement(X0),complement(complement(complement(X0)))) = complement(join(X0,X0)),
inference(demodulation,[status(thm)],[c_4692,c_7842]) ).
tcf(c_8679,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(converse(X1),X0),
inference(superposition,[status(thm)],[c_49,c_341]) ).
tcf(c_8842,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_353]) ).
tcf(c_8902,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_8842,c_55]) ).
tcf(c_8920,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_8902,c_53]) ).
tcf(c_8951,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_8902,c_457]) ).
tcf(c_8954,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_8951,c_8902]) ).
tcf(c_9025,plain,
! [X0: $i] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(superposition,[status(thm)],[c_8954,c_321]) ).
tcf(c_9040,plain,
! [X0: $i] : complement(join(X0,X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_9025,c_7842,c_8920,c_8954]) ).
tcf(c_9160,plain,
! [X0: $i] : join(complement(iPr_def_13),complement(join(complement(complement(complement(X0))),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_284,c_333]) ).
tcf(c_9278,plain,
! [X0: $i] : join(complement(iPr_def_13),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(theory_normalisation,[status(thm)],[c_9160,c_50,c_49]) ).
tcf(c_9279,plain,
! [X0: $i] : join(iPr_def_14,complement(complement(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_9278,c_278,c_7904,c_9040]) ).
tcf(c_9420,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_9279,c_4285]) ).
tcf(c_9434,plain,
complement(sK2) = iPr_def_10,
inference(superposition,[status(thm)],[c_4964,c_9420]) ).
tcf(c_11808,plain,
! [X0: $i] : join(X0,join(X0,complement(X0))) = iPr_def_13,
inference(superposition,[status(thm)],[c_9040,c_367]) ).
tcf(c_11812,plain,
! [X0: $i] : join(X0,iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_11808,c_284]) ).
tcf(c_11837,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_817,c_11812]) ).
tcf(c_11838,plain,
! [X0: $i] : join(iPr_def_13,X0) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1735,c_11837]) ).
tcf(c_11865,plain,
! [X0: $i] : join(iPr_def_19,join(iPr_def_20,X0)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_370,c_11838]) ).
tcf(c_11945,plain,
! [X0: $i] : join(converse(iPr_def_13),X0) = converse(iPr_def_13),
inference(superposition,[status(thm)],[c_11812,c_8679]) ).
tcf(c_13607,plain,
converse(iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_11945,c_11812]) ).
tcf(c_14013,plain,
composition(iPr_def_13,complement(composition(iPr_def_13,iPr_def_13))) = iPr_def_14,
inference(superposition,[status(thm)],[c_13607,c_4337]) ).
tcf(c_14028,plain,
! [X0: $i] : composition(iPr_def_13,converse(X0)) = converse(composition(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_13607,c_349]) ).
tcf(c_14031,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,iPr_def_13)),complement(X1))),composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),complement(join(complement(iPr_def_13),complement(composition(converse(X0),X1)))))) = composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),complement(join(complement(iPr_def_13),complement(composition(converse(X0),X1))))),
inference(superposition,[status(thm)],[c_13607,c_61]) ).
tcf(c_14033,plain,
! [X0: $i] : composition(converse(X0),iPr_def_13) = converse(composition(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_13607,c_57]) ).
tcf(c_14048,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,iPr_def_13)),complement(X1))),composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),complement(join(iPr_def_14,complement(composition(converse(X0),X1)))))) = composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),complement(join(iPr_def_14,complement(composition(converse(X0),X1))))),
inference(light_normalisation,[status(thm)],[c_14031,c_278]) ).
tcf(c_14057,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,iPr_def_13)),complement(X1))),composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),composition(converse(X0),X1))) = composition(complement(join(complement(X0),complement(composition(X1,iPr_def_13)))),composition(converse(X0),X1)),
inference(demodulation,[status(thm)],[c_14048,c_4285,c_9420]) ).
tcf(c_14071,plain,
! [X0: $i] : join(complement(join(complement(composition(X0,iPr_def_13)),iPr_def_14)),composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X0),iPr_def_13))) = composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X0),iPr_def_13)),
inference(superposition,[status(thm)],[c_278,c_14057]) ).
tcf(c_14163,plain,
! [X0: $i] : join(complement(join(iPr_def_14,complement(composition(X0,iPr_def_13)))),composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X0),iPr_def_13))) = composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X0),iPr_def_13)),
inference(theory_normalisation,[status(thm)],[c_14071,c_50,c_49]) ).
tcf(c_16782,plain,
! [X0: $i] : composition(join(X0,composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),converse(X0))),iPr_def_13) = composition(complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X0),iPr_def_13)),
inference(demodulation,[status(thm)],[c_14163,c_473,c_4285,c_9420]) ).
tcf(c_16785,plain,
composition(complement(join(complement(iPr_def_13),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(iPr_def_13),iPr_def_13)) = composition(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_11838,c_16782]) ).
tcf(c_16852,plain,
composition(complement(join(iPr_def_14,complement(composition(iPr_def_13,iPr_def_13)))),composition(iPr_def_13,iPr_def_13)) = composition(iPr_def_13,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_16785,c_278,c_13607]) ).
tcf(c_16905,plain,
composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,iPr_def_13))) = composition(iPr_def_13,iPr_def_13),
inference(demodulation,[status(thm)],[c_16852,c_52,c_4285,c_9420]) ).
tcf(c_16919,plain,
! [X0: $i] : join(complement(join(complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),X0)),complement(converse(iPr_def_13)))),complement(join(complement(converse(iPr_def_13)),complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13)))))))))) = complement(join(complement(converse(iPr_def_13)),complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13))))))))),
inference(superposition,[status(thm)],[c_16905,c_431]) ).
tcf(c_16943,plain,
! [X0: $i] : join(complement(join(complement(converse(iPr_def_13)),complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),X0)))),complement(join(complement(converse(iPr_def_13)),complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13)))))))))) = complement(join(complement(converse(iPr_def_13)),complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13))))))))),
inference(theory_normalisation,[status(thm)],[c_16919,c_50,c_49]) ).
tcf(c_16944,plain,
! [X0: $i] : join(complement(join(iPr_def_14,complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),X0)))),complement(join(iPr_def_14,complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13)))))))))) = complement(join(iPr_def_14,complement(composition(composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)),complement(join(complement(X0),complement(converse(composition(iPr_def_13,iPr_def_13))))))))),
inference(light_normalisation,[status(thm)],[c_16943,c_278,c_13607]) ).
tcf(c_17392,plain,
! [X0: $i] : join(composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,X0))),composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13)))))))) = composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(complement(X0),complement(composition(iPr_def_13,iPr_def_13))))))),
inference(demodulation,[status(thm)],[c_16944,c_52,c_4285,c_9420,c_13607,c_14033]) ).
tcf(c_17393,plain,
join(composition(iPr_def_13,iPr_def_13),composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(complement(iPr_def_13),complement(composition(iPr_def_13,iPr_def_13)))))))) = composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(complement(iPr_def_13),complement(composition(iPr_def_13,iPr_def_13))))))),
inference(superposition,[status(thm)],[c_16905,c_17392]) ).
tcf(c_17424,plain,
join(composition(iPr_def_13,iPr_def_13),composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(iPr_def_14,complement(composition(iPr_def_13,iPr_def_13)))))))) = composition(iPr_def_13,composition(iPr_def_13,composition(iPr_def_13,complement(join(iPr_def_14,complement(composition(iPr_def_13,iPr_def_13))))))),
inference(light_normalisation,[status(thm)],[c_17393,c_278]) ).
tcf(c_17432,plain,
composition(iPr_def_13,composition(iPr_def_13,iPr_def_13)) = composition(iPr_def_13,iPr_def_13),
inference(demodulation,[status(thm)],[c_17424,c_473,c_4285,c_9420,c_11838,c_16905]) ).
tcf(c_28490,plain,
join(complement(join(iPr_def_15,complement(iPr_def_17))),complement(join(iPr_def_15,complement(composition(iPr_def_16,complement(join(complement(sK2),complement(composition(converse(iPr_def_16),sK1))))))))) = complement(join(iPr_def_15,complement(composition(iPr_def_16,complement(join(complement(sK2),complement(composition(converse(iPr_def_16),sK1)))))))),
inference(superposition,[status(thm)],[c_138,c_445]) ).
tcf(c_28579,plain,
join(iPr_def_20,complement(join(iPr_def_15,complement(composition(iPr_def_16,iPr_def_14))))) = complement(join(iPr_def_15,complement(composition(iPr_def_16,iPr_def_14)))),
inference(light_normalisation,[status(thm)],[c_28490,c_132,c_140,c_273,c_278,c_5319,c_6249,c_6758,c_7398,c_9434]) ).
tcf(c_29009,plain,
join(iPr_def_19,complement(join(iPr_def_15,complement(composition(iPr_def_16,iPr_def_14))))) = iPr_def_13,
inference(superposition,[status(thm)],[c_28579,c_11865]) ).
tcf(c_36680,plain,
! [X0: $i,X1: $i] : join(complement(iPr_def_13),composition(converse(composition(X0,join(X1,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),converse(X1))))),complement(composition(X0,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X1),iPr_def_13)))))) = complement(iPr_def_13),
inference(superposition,[status(thm)],[c_16782,c_463]) ).
tcf(c_36735,plain,
! [X0: $i,X1: $i] : join(iPr_def_14,composition(converse(composition(X0,join(X1,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),converse(X1))))),complement(composition(X0,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X1),iPr_def_13)))))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_36680,c_278]) ).
tcf(c_37964,plain,
! [X0: $i,X1: $i] : composition(converse(composition(X0,join(X1,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),converse(X1))))),complement(composition(X0,composition(complement(join(complement(X1),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(X1),iPr_def_13))))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_36735,c_4285]) ).
tcf(c_37974,plain,
! [X0: $i] : composition(converse(composition(X0,iPr_def_13)),complement(composition(X0,composition(complement(join(complement(iPr_def_13),complement(composition(iPr_def_13,iPr_def_13)))),composition(converse(iPr_def_13),iPr_def_13))))) = iPr_def_14,
inference(superposition,[status(thm)],[c_11838,c_37964]) ).
tcf(c_38129,plain,
! [X0: $i] : composition(composition(iPr_def_13,converse(X0)),complement(composition(X0,composition(complement(join(iPr_def_14,complement(composition(iPr_def_13,iPr_def_13)))),composition(iPr_def_13,iPr_def_13))))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_37974,c_278,c_13607,c_14028]) ).
tcf(c_38445,plain,
! [X0: $i] : composition(iPr_def_13,composition(converse(X0),complement(composition(X0,composition(iPr_def_13,iPr_def_13))))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_38129,c_52,c_4285,c_9420,c_17432]) ).
tcf(c_38474,plain,
composition(iPr_def_13,composition(converse(iPr_def_13),complement(composition(iPr_def_13,iPr_def_13)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_17432,c_38445]) ).
tcf(c_38534,plain,
composition(iPr_def_13,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_38474,c_13607,c_14013]) ).
tcf(c_39436,plain,
! [X0: $i] : join(composition(X0,iPr_def_14),iPr_def_14) = composition(join(X0,iPr_def_13),iPr_def_14),
inference(superposition,[status(thm)],[c_38534,c_54]) ).
tcf(c_39468,plain,
! [X0: $i] : join(iPr_def_14,composition(X0,iPr_def_14)) = composition(join(X0,iPr_def_13),iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_39436,c_50,c_49]) ).
tcf(c_39469,plain,
! [X0: $i] : join(iPr_def_14,composition(X0,iPr_def_14)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_39468,c_11812,c_38534]) ).
tcf(c_39656,plain,
! [X0: $i] : composition(X0,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_39469,c_4285]) ).
tcf(c_39673,plain,
join(iPr_def_19,complement(join(iPr_def_15,complement(iPr_def_14)))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_29009,c_39656]) ).
tcf(c_39676,plain,
join(iPr_def_19,complement(join(iPr_def_15,iPr_def_13))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_39673,c_3322]) ).
tcf(c_39677,plain,
join(iPr_def_19,complement(join(iPr_def_13,iPr_def_15))) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_39676,c_50,c_49]) ).
tcf(c_41851,plain,
iPr_def_13 = iPr_def_19,
inference(demodulation,[status(thm)],[c_39677,c_278,c_4394,c_11838]) ).
tcf(c_41901,plain,
complement(iPr_def_13) = iPr_def_20,
inference(demodulation,[status(thm)],[c_141,c_41851]) ).
tcf(c_41902,plain,
iPr_def_14 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_41901,c_278]) ).
tcf(c_41903,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_41902,c_239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.59 % Computer : n004.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.59 % WCLimit : 300
% 0.09/5.59 % DateTime : Thu Sep 24 07:07:15 UTC 2026
% 0.09/5.59 % CPUTime :
% 0.09/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.63 Running first-order theorem proving
% 0.15/5.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.64
% 0.15/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.64
% 0.15/5.64 % Detected problem language: tptp
% 0.15/5.65 % Proving...
% 23.14/10.36 % SZS status Started for theBenchmark.p
% 23.14/10.36 % SZS status Theorem for theBenchmark.p
% 23.14/10.36
% 23.14/10.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 23.14/10.36
% 23.14/10.36 % ------ iProver source info
% 23.14/10.36
% 23.14/10.36 % git: date: 2026-07-19 20:42:38 +0200
% 23.14/10.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 23.14/10.36 % git: non_committed_changes: false
% 23.14/10.36
% 23.14/10.36 % ------ Parsing...
% 23.14/10.36 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 23.14/10.36 %
% 23.14/10.36
% 23.14/10.36 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 23.14/10.36
% 23.14/10.36 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 23.14/10.36 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 23.14/10.36
% 23.14/10.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 23.14/10.36 % ------ Proving...
% 23.14/10.36 % ------ Problem Properties
% 23.14/10.36
% 23.14/10.36 %
% 23.14/10.36 % clauses 28
% 23.14/10.36 % conjectures 2
% 23.14/10.36 % EPR 2
% 23.14/10.36 % Horn 28
% 23.14/10.36 % unary 28
% 23.14/10.36 % binary 0
% 23.14/10.36 % lits 28
% 23.14/10.36 % lits eq 28
% 23.14/10.36 % fd_pure 0
% 23.14/10.36 % fd_pseudo 0
% 23.14/10.36 % fd_cond 0
% 23.14/10.36 % fd_pseudo_cond 0
% 23.14/10.36 % AC symbols 1
% 23.14/10.36
% 23.14/10.36 % ------ Schedule UEQ
% 23.14/10.36
% 23.14/10.36 % ------ Option_UEQ Time Limit: 10.
% 23.14/10.36
% 23.14/10.36
% 23.14/10.36 % ------
% 23.14/10.36 % Current options:
% 23.14/10.36 % ------
% 23.14/10.36
% 23.14/10.36
% 23.14/10.36 %
% 23.14/10.36
% 23.14/10.36 % ------ Proving...
% 23.14/10.36 %
% 23.14/10.36
% 23.14/10.36 % SZS status Theorem for theBenchmark.p
% 23.14/10.36
% 23.14/10.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.14/10.37
% 23.14/10.37
%------------------------------------------------------------------------------