%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL005+3 : 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 : 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 02:36:31 PM UTC 2026
% Result : Theorem 38.19s 7.37s
% Output : CNFRefutation 38.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 25
% Syntax : Number of formulae : 345 ( 345 unt; 11 def)
% Number of atoms : 921 ( 344 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 183 ( 0 sgn 181 !; 2 ?; 126 :)
% 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(f17,conjecture,
! [X0,X1] : converse(meet(X0,X1)) = meet(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] : converse(meet(X0,X1)) = meet(converse(X0),converse(X1)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1] : converse(meet(X0,X1)) != meet(converse(X0),converse(X1)),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
converse(meet(sK0,sK1)) != meet(converse(sK0),converse(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[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(f37,plain,
converse(meet(sK0,sK1)) != meet(converse(sK0),converse(sK1)),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f42,plain,
converse(complement(join(complement(sK0),complement(sK1)))) != complement(join(complement(converse(sK0)),complement(converse(sK1)))),
inference(definition_unfolding,[],[f37,f24,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,[],[f38]) ).
tcf(c_64,negated_conjecture,
complement(join(complement(converse(sK0)),complement(converse(sK1)))) != converse(complement(join(complement(sK0),complement(sK1)))),
inference(cnf_transformation,[],[f42]) ).
tcf(c_80,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_81,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_120,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_127,definition,
iPr_def_10 = converse(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_128,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_129,definition,
iPr_def_12 = converse(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_130,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_131,definition,
iPr_def_14 = join(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_132,definition,
iPr_def_15 = complement(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_133,definition,
iPr_def_16 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_134,definition,
iPr_def_17 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_135,definition,
iPr_def_18 = join(iPr_def_16,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_136,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_137,definition,
iPr_def_20 = converse(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_138,negated_conjecture,
iPr_def_15 != iPr_def_20,
inference(demodulation,[status(thm)],[c_64,c_134,c_133,c_135,c_136,c_137,c_129,c_130,c_127,c_128,c_131,c_132]) ).
tcf(c_231,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,
! [X0: $i] : join(complement(join(iPr_def_16,X0)),complement(join(iPr_def_16,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_133,c_80]) ).
tcf(c_241,plain,
! [X0: $i] : join(complement(join(iPr_def_11,X0)),complement(join(iPr_def_11,complement(X0)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_80]) ).
tcf(c_242,plain,
! [X0: $i] : join(complement(join(iPr_def_13,X0)),complement(join(iPr_def_13,complement(X0)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_130,c_80]) ).
tcf(c_243,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_132,c_80]) ).
tcf(c_244,plain,
! [X0: $i] : join(complement(join(complement(X0),sK0)),complement(join(complement(X0),iPr_def_16))) = X0,
inference(superposition,[status(thm)],[c_133,c_80]) ).
tcf(c_245,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_120,c_80]) ).
tcf(c_246,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_10)),complement(join(complement(X0),iPr_def_11))) = X0,
inference(superposition,[status(thm)],[c_128,c_80]) ).
tcf(c_247,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_12)),complement(join(complement(X0),iPr_def_13))) = X0,
inference(superposition,[status(thm)],[c_130,c_80]) ).
tcf(c_252,plain,
! [X0: $i] : join(complement(join(iPr_def_12,complement(X0))),complement(join(iPr_def_13,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_247,c_50,c_49]) ).
tcf(c_253,plain,
! [X0: $i] : join(complement(join(iPr_def_10,complement(X0))),complement(join(iPr_def_11,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_246,c_50,c_49]) ).
tcf(c_254,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_245,c_50,c_49]) ).
tcf(c_255,plain,
! [X0: $i] : join(complement(join(iPr_def_16,complement(X0))),complement(join(sK0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_244,c_50,c_49]) ).
tcf(c_258,plain,
! [X0: $i] : join(complement(join(iPr_def_17,X0)),complement(join(iPr_def_17,complement(X0)))) = sK1,
inference(superposition,[status(thm)],[c_134,c_80]) ).
tcf(c_264,plain,
converse(iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_127,c_55]) ).
tcf(c_265,plain,
converse(iPr_def_12) = sK1,
inference(superposition,[status(thm)],[c_129,c_55]) ).
tcf(c_266,plain,
converse(iPr_def_20) = iPr_def_19,
inference(superposition,[status(thm)],[c_137,c_55]) ).
tcf(c_267,plain,
converse(sK0) = iPr_def_10,
inference(superposition,[status(thm)],[c_264,c_55]) ).
tcf(c_268,plain,
converse(sK1) = iPr_def_12,
inference(superposition,[status(thm)],[c_265,c_55]) ).
tcf(c_269,plain,
converse(iPr_def_19) = iPr_def_20,
inference(superposition,[status(thm)],[c_266,c_55]) ).
tcf(c_273,plain,
join(sK0,iPr_def_16) = top,
inference(superposition,[status(thm)],[c_133,c_59]) ).
tcf(c_274,plain,
join(sK1,iPr_def_17) = top,
inference(superposition,[status(thm)],[c_134,c_59]) ).
tcf(c_275,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_120,c_59]) ).
tcf(c_276,plain,
join(iPr_def_10,iPr_def_11) = top,
inference(superposition,[status(thm)],[c_128,c_59]) ).
tcf(c_277,plain,
join(iPr_def_12,iPr_def_13) = top,
inference(superposition,[status(thm)],[c_130,c_59]) ).
tcf(c_278,plain,
join(iPr_def_14,iPr_def_15) = top,
inference(superposition,[status(thm)],[c_132,c_59]) ).
tcf(c_280,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_282,plain,
join(iPr_def_17,sK1) = top,
inference(theory_normalisation,[status(thm)],[c_274,c_50,c_49]) ).
tcf(c_283,plain,
join(iPr_def_16,sK0) = top,
inference(theory_normalisation,[status(thm)],[c_273,c_50,c_49]) ).
tcf(c_284,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_280,c_50,c_49]) ).
tcf(c_285,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_284,c_120]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_55,c_81]) ).
tcf(c_308,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_80]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_317,plain,
! [X0: $i] : join(iPr_def_20,converse(X0)) = converse(join(iPr_def_19,X0)),
inference(superposition,[status(thm)],[c_269,c_56]) ).
tcf(c_319,plain,
! [X0: $i] : join(sK0,converse(X0)) = converse(join(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_264,c_56]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_325,plain,
! [X0: $i] : join(converse(X0),iPr_def_12) = converse(join(X0,sK1)),
inference(superposition,[status(thm)],[c_268,c_56]) ).
tcf(c_327,plain,
! [X0: $i] : join(converse(X0),iPr_def_20) = converse(join(X0,iPr_def_19)),
inference(superposition,[status(thm)],[c_269,c_56]) ).
tcf(c_331,plain,
! [X0: $i] : join(converse(X0),iPr_def_19) = converse(join(X0,iPr_def_20)),
inference(superposition,[status(thm)],[c_266,c_56]) ).
tcf(c_334,plain,
! [X0: $i] : join(iPr_def_19,converse(X0)) = converse(join(X0,iPr_def_20)),
inference(theory_normalisation,[status(thm)],[c_331,c_50,c_49]) ).
tcf(c_337,plain,
! [X0: $i] : join(iPr_def_20,converse(X0)) = converse(join(X0,iPr_def_19)),
inference(theory_normalisation,[status(thm)],[c_327,c_50,c_49]) ).
tcf(c_338,plain,
! [X0: $i] : join(iPr_def_12,converse(X0)) = converse(join(X0,sK1)),
inference(theory_normalisation,[status(thm)],[c_325,c_50,c_49]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_351,plain,
! [X0: $i] : composition(converse(X0),iPr_def_10) = converse(composition(sK0,X0)),
inference(superposition,[status(thm)],[c_267,c_57]) ).
tcf(c_353,plain,
! [X0: $i] : composition(converse(X0),iPr_def_12) = converse(composition(sK1,X0)),
inference(superposition,[status(thm)],[c_268,c_57]) ).
tcf(c_357,plain,
! [X0: $i] : composition(converse(X0),sK0) = converse(composition(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_264,c_57]) ).
tcf(c_358,plain,
! [X0: $i] : composition(converse(X0),sK1) = converse(composition(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_265,c_57]) ).
tcf(c_366,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_13,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_131,c_50]) ).
tcf(c_367,plain,
! [X0: $i] : join(iPr_def_16,join(iPr_def_17,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_135,c_50]) ).
tcf(c_368,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_275,c_50]) ).
tcf(c_369,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_276,c_50]) ).
tcf(c_371,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_13,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_277,c_50]) ).
tcf(c_372,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_15,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_278,c_50]) ).
tcf(c_375,plain,
! [X0: $i] : join(iPr_def_16,join(sK0,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_283,c_50]) ).
tcf(c_427,plain,
join(sK0,converse(iPr_def_11)) = converse(top),
inference(superposition,[status(thm)],[c_276,c_319]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_978,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_13)) = join(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_131,c_231]) ).
tcf(c_979,plain,
! [X0: $i] : join(iPr_def_16,join(X0,iPr_def_17)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_135,c_231]) ).
tcf(c_983,plain,
! [X0: $i] : join(iPr_def_14,join(X0,iPr_def_15)) = join(X0,top),
inference(superposition,[status(thm)],[c_278,c_231]) ).
tcf(c_1103,plain,
composition(converse(one),iPr_def_10) = converse(sK0),
inference(superposition,[status(thm)],[c_53,c_351]) ).
tcf(c_1120,plain,
composition(converse(one),iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1103,c_267]) ).
tcf(c_1135,plain,
join(complement(iPr_def_10),composition(converse(converse(one)),complement(iPr_def_10))) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_1120,c_81]) ).
tcf(c_1140,plain,
join(iPr_def_11,composition(converse(converse(one)),iPr_def_11)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1135,c_128]) ).
tcf(c_1164,plain,
composition(converse(one),iPr_def_12) = converse(sK1),
inference(superposition,[status(thm)],[c_53,c_353]) ).
tcf(c_1181,plain,
composition(converse(one),iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1164,c_268]) ).
tcf(c_1194,plain,
join(complement(iPr_def_12),composition(converse(converse(one)),complement(iPr_def_12))) = complement(iPr_def_12),
inference(superposition,[status(thm)],[c_1181,c_81]) ).
tcf(c_1199,plain,
join(iPr_def_13,composition(converse(converse(one)),iPr_def_13)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_1194,c_130]) ).
tcf(c_1272,plain,
composition(converse(one),sK0) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_53,c_357]) ).
tcf(c_1289,plain,
composition(converse(one),sK0) = sK0,
inference(light_normalisation,[status(thm)],[c_1272,c_264]) ).
tcf(c_1308,plain,
join(complement(join(iPr_def_16,iPr_def_16)),complement(top)) = sK0,
inference(superposition,[status(thm)],[c_59,c_239]) ).
tcf(c_1310,plain,
join(complement(join(iPr_def_16,sK1)),complement(join(iPr_def_16,iPr_def_17))) = sK0,
inference(superposition,[status(thm)],[c_134,c_239]) ).
tcf(c_1321,plain,
join(complement(top),complement(join(iPr_def_16,iPr_def_16))) = sK0,
inference(theory_normalisation,[status(thm)],[c_1308,c_50,c_49]) ).
tcf(c_1322,plain,
join(zero,complement(join(iPr_def_16,iPr_def_16))) = sK0,
inference(light_normalisation,[status(thm)],[c_1321,c_120]) ).
tcf(c_1328,plain,
join(complement(join(iPr_def_16,iPr_def_17)),complement(join(iPr_def_16,sK1))) = sK0,
inference(theory_normalisation,[status(thm)],[c_1310,c_50,c_49]) ).
tcf(c_1329,plain,
join(iPr_def_19,complement(join(iPr_def_16,sK1))) = sK0,
inference(light_normalisation,[status(thm)],[c_1328,c_135,c_136]) ).
tcf(c_1356,plain,
join(complement(sK0),composition(converse(converse(one)),complement(sK0))) = complement(sK0),
inference(superposition,[status(thm)],[c_1289,c_81]) ).
tcf(c_1361,plain,
join(iPr_def_16,composition(converse(converse(one)),iPr_def_16)) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_1356,c_133]) ).
tcf(c_1378,plain,
join(iPr_def_20,converse(complement(join(iPr_def_16,sK1)))) = converse(sK0),
inference(superposition,[status(thm)],[c_1329,c_317]) ).
tcf(c_1379,plain,
join(iPr_def_20,converse(complement(join(iPr_def_16,sK1)))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1378,c_267]) ).
tcf(c_1387,plain,
composition(converse(one),sK1) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_53,c_358]) ).
tcf(c_1404,plain,
composition(converse(one),sK1) = sK1,
inference(light_normalisation,[status(thm)],[c_1387,c_265]) ).
tcf(c_1417,plain,
join(complement(sK1),composition(converse(converse(one)),complement(sK1))) = complement(sK1),
inference(superposition,[status(thm)],[c_1404,c_81]) ).
tcf(c_1422,plain,
join(iPr_def_17,composition(converse(converse(one)),iPr_def_17)) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_1417,c_134]) ).
tcf(c_1536,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_368]) ).
tcf(c_1615,plain,
join(top,iPr_def_13) = join(iPr_def_10,iPr_def_14),
inference(superposition,[status(thm)],[c_131,c_369]) ).
tcf(c_1622,plain,
join(iPr_def_10,iPr_def_14) = join(iPr_def_13,top),
inference(theory_normalisation,[status(thm)],[c_1615,c_50,c_49]) ).
tcf(c_1707,plain,
join(top,converse(iPr_def_11)) = join(iPr_def_16,converse(top)),
inference(superposition,[status(thm)],[c_427,c_375]) ).
tcf(c_1893,plain,
join(iPr_def_11,top) = join(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_277,c_978]) ).
tcf(c_1926,plain,
join(top,iPr_def_17) = join(sK0,iPr_def_18),
inference(superposition,[status(thm)],[c_979,c_375]) ).
tcf(c_1927,plain,
join(iPr_def_17,top) = join(iPr_def_18,sK0),
inference(theory_normalisation,[status(thm)],[c_1926,c_50,c_49]) ).
tcf(c_1992,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_15,X0)) = join(X0,top),
inference(superposition,[status(thm)],[c_49,c_983]) ).
tcf(c_2068,plain,
join(complement(join(iPr_def_15,iPr_def_15)),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_59,c_243]) ).
tcf(c_2083,plain,
join(complement(top),complement(join(iPr_def_15,iPr_def_15))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_2068,c_50,c_49]) ).
tcf(c_2084,plain,
join(zero,complement(join(iPr_def_15,iPr_def_15))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_2083,c_120]) ).
tcf(c_2105,plain,
join(top,complement(join(iPr_def_15,iPr_def_15))) = join(top,iPr_def_14),
inference(superposition,[status(thm)],[c_2084,c_368]) ).
tcf(c_2107,plain,
join(top,complement(join(iPr_def_15,iPr_def_15))) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_2105,c_50,c_49]) ).
tcf(c_2117,plain,
join(iPr_def_11,composition(one,iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1140,c_55]) ).
tcf(c_2122,plain,
join(top,composition(one,iPr_def_11)) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2117,c_369]) ).
tcf(c_2123,plain,
join(top,composition(one,iPr_def_11)) = top,
inference(light_normalisation,[status(thm)],[c_2122,c_276]) ).
tcf(c_2128,plain,
join(iPr_def_13,composition(one,iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1199,c_55]) ).
tcf(c_2133,plain,
join(top,composition(one,iPr_def_13)) = join(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_2128,c_371]) ).
tcf(c_2134,plain,
join(iPr_def_14,composition(one,iPr_def_13)) = join(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_2128,c_366]) ).
tcf(c_2135,plain,
join(iPr_def_14,composition(one,iPr_def_13)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_2134,c_131]) ).
tcf(c_2136,plain,
join(top,composition(one,iPr_def_13)) = top,
inference(light_normalisation,[status(thm)],[c_2133,c_277]) ).
tcf(c_2267,plain,
join(iPr_def_16,composition(one,iPr_def_16)) = iPr_def_16,
inference(demodulation,[status(thm)],[c_1361,c_55]) ).
tcf(c_2273,plain,
join(iPr_def_17,composition(one,iPr_def_17)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_1422,c_55]) ).
tcf(c_2277,plain,
join(iPr_def_18,composition(one,iPr_def_17)) = join(iPr_def_16,iPr_def_17),
inference(superposition,[status(thm)],[c_2273,c_367]) ).
tcf(c_2278,plain,
join(iPr_def_18,composition(one,iPr_def_17)) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_2277,c_135]) ).
tcf(c_2895,plain,
join(zero,complement(join(iPr_def_17,iPr_def_17))) = sK1,
inference(superposition,[status(thm)],[c_134,c_285]) ).
tcf(c_2900,plain,
join(zero,complement(join(iPr_def_19,iPr_def_19))) = iPr_def_18,
inference(superposition,[status(thm)],[c_136,c_285]) ).
tcf(c_2945,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_312]) ).
tcf(c_3457,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_350]) ).
tcf(c_3535,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_3457,c_55]) ).
tcf(c_3553,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_3535,c_53]) ).
tcf(c_3571,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_3535,c_505]) ).
tcf(c_3573,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_3571,c_3535]) ).
tcf(c_3581,plain,
join(top,iPr_def_11) = top,
inference(demodulation,[status(thm)],[c_2123,c_3573]) ).
tcf(c_3582,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2117,c_3573]) ).
tcf(c_3583,plain,
join(top,iPr_def_13) = top,
inference(demodulation,[status(thm)],[c_2136,c_3573]) ).
tcf(c_3584,plain,
join(iPr_def_14,iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2135,c_3573]) ).
tcf(c_3586,plain,
join(iPr_def_16,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_2267,c_3573]) ).
tcf(c_3587,plain,
join(iPr_def_18,iPr_def_17) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2278,c_3573]) ).
tcf(c_3588,plain,
join(iPr_def_17,iPr_def_17) = iPr_def_17,
inference(demodulation,[status(thm)],[c_2273,c_3573]) ).
tcf(c_3589,plain,
join(zero,complement(iPr_def_17)) = sK1,
inference(demodulation,[status(thm)],[c_2895,c_3588]) ).
tcf(c_3590,plain,
join(iPr_def_17,iPr_def_18) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_3587,c_50,c_49]) ).
tcf(c_3591,plain,
join(zero,complement(iPr_def_16)) = sK0,
inference(demodulation,[status(thm)],[c_1322,c_3586]) ).
tcf(c_3593,plain,
join(iPr_def_13,iPr_def_14) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_3584,c_50,c_49]) ).
tcf(c_3594,plain,
join(iPr_def_13,top) = top,
inference(theory_normalisation,[status(thm)],[c_3583,c_50,c_49]) ).
tcf(c_3595,plain,
join(iPr_def_10,iPr_def_14) = top,
inference(demodulation,[status(thm)],[c_1622,c_3594]) ).
tcf(c_3597,plain,
join(iPr_def_11,top) = top,
inference(theory_normalisation,[status(thm)],[c_3581,c_50,c_49]) ).
tcf(c_3599,plain,
join(iPr_def_12,iPr_def_14) = top,
inference(demodulation,[status(thm)],[c_1893,c_3597]) ).
tcf(c_3638,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_3573,c_54]) ).
tcf(c_3667,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_3582,c_50]) ).
tcf(c_3706,plain,
! [X0: $i] : join(iPr_def_16,join(iPr_def_16,X0)) = join(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_3586,c_50]) ).
tcf(c_3710,plain,
! [X0: $i] : join(iPr_def_17,join(iPr_def_17,X0)) = join(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_3588,c_50]) ).
tcf(c_3730,plain,
join(complement(iPr_def_14),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_3593,c_242]) ).
tcf(c_3731,plain,
join(top,iPr_def_14) = join(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_3593,c_371]) ).
tcf(c_3733,plain,
join(iPr_def_12,iPr_def_14) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_3731,c_50,c_49]) ).
tcf(c_3734,plain,
join(iPr_def_14,top) = top,
inference(light_normalisation,[status(thm)],[c_3733,c_3599]) ).
tcf(c_3735,plain,
join(iPr_def_15,complement(join(iPr_def_13,iPr_def_15))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3730,c_132]) ).
tcf(c_3743,plain,
join(top,top) = join(iPr_def_12,top),
inference(superposition,[status(thm)],[c_3594,c_371]) ).
tcf(c_3749,plain,
join(top,complement(zero)) = join(iPr_def_12,top),
inference(demodulation,[status(thm)],[c_1536,c_3743]) ).
tcf(c_3750,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_14,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_3595,c_50]) ).
tcf(c_3764,plain,
join(top,top) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_3597,c_369]) ).
tcf(c_3782,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_254]) ).
tcf(c_3785,plain,
join(complement(join(top,complement(join(iPr_def_15,iPr_def_15)))),complement(iPr_def_14)) = join(iPr_def_15,iPr_def_15),
inference(superposition,[status(thm)],[c_2084,c_254]) ).
tcf(c_3804,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_3782,c_50,c_49]) ).
tcf(c_3805,plain,
join(zero,complement(join(iPr_def_12,top))) = zero,
inference(light_normalisation,[status(thm)],[c_3804,c_120,c_3749]) ).
tcf(c_3829,plain,
join(complement(iPr_def_14),complement(join(top,complement(join(iPr_def_15,iPr_def_15))))) = join(iPr_def_15,iPr_def_15),
inference(theory_normalisation,[status(thm)],[c_3785,c_50,c_49]) ).
tcf(c_3830,plain,
join(iPr_def_15,zero) = join(iPr_def_15,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_3829,c_120,c_132,c_2107,c_3734]) ).
tcf(c_3974,plain,
join(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_131,c_3667]) ).
tcf(c_3980,plain,
join(iPr_def_11,converse(top)) = converse(top),
inference(superposition,[status(thm)],[c_2945,c_3667]) ).
tcf(c_4003,plain,
join(complement(iPr_def_14),complement(join(iPr_def_11,complement(iPr_def_14)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_3974,c_241]) ).
tcf(c_4007,plain,
join(iPr_def_15,complement(join(iPr_def_11,iPr_def_15))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_4003,c_132]) ).
tcf(c_4136,plain,
join(complement(join(iPr_def_16,iPr_def_17)),complement(join(sK0,iPr_def_17))) = sK1,
inference(superposition,[status(thm)],[c_134,c_255]) ).
tcf(c_4156,plain,
join(complement(join(iPr_def_16,iPr_def_17)),complement(join(iPr_def_17,sK0))) = sK1,
inference(theory_normalisation,[status(thm)],[c_4136,c_50,c_49]) ).
tcf(c_4157,plain,
join(iPr_def_19,complement(join(iPr_def_17,sK0))) = sK1,
inference(light_normalisation,[status(thm)],[c_4156,c_135,c_136]) ).
tcf(c_4189,plain,
join(iPr_def_20,converse(complement(join(iPr_def_17,sK0)))) = converse(sK1),
inference(superposition,[status(thm)],[c_4157,c_317]) ).
tcf(c_4190,plain,
join(iPr_def_20,converse(complement(join(iPr_def_17,sK0)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_4189,c_268]) ).
tcf(c_4228,plain,
join(iPr_def_16,iPr_def_18) = iPr_def_18,
inference(superposition,[status(thm)],[c_135,c_3706]) ).
tcf(c_4239,plain,
join(iPr_def_16,converse(top)) = converse(top),
inference(superposition,[status(thm)],[c_2945,c_3706]) ).
tcf(c_4262,plain,
join(top,converse(iPr_def_11)) = converse(top),
inference(demodulation,[status(thm)],[c_1707,c_4239]) ).
tcf(c_4306,plain,
join(iPr_def_10,top) = join(iPr_def_12,top),
inference(light_normalisation,[status(thm)],[c_3743,c_3764]) ).
tcf(c_4336,plain,
join(iPr_def_14,join(iPr_def_15,iPr_def_15)) = join(top,zero),
inference(superposition,[status(thm)],[c_3830,c_372]) ).
tcf(c_4341,plain,
join(iPr_def_14,join(iPr_def_15,iPr_def_15)) = top,
inference(light_normalisation,[status(thm)],[c_4336,c_275]) ).
tcf(c_4470,plain,
join(iPr_def_17,top) = top,
inference(superposition,[status(thm)],[c_282,c_3710]) ).
tcf(c_4494,plain,
join(iPr_def_18,sK0) = top,
inference(demodulation,[status(thm)],[c_1927,c_4470]) ).
tcf(c_4620,plain,
join(converse(iPr_def_11),top) = converse(converse(top)),
inference(superposition,[status(thm)],[c_3980,c_322]) ).
tcf(c_4621,plain,
join(top,converse(iPr_def_11)) = converse(converse(top)),
inference(theory_normalisation,[status(thm)],[c_4620,c_50,c_49]) ).
tcf(c_4622,plain,
converse(converse(top)) = converse(top),
inference(light_normalisation,[status(thm)],[c_4621,c_4262]) ).
tcf(c_4624,plain,
converse(top) = top,
inference(demodulation,[status(thm)],[c_4622,c_55]) ).
tcf(c_4628,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = top,
inference(demodulation,[status(thm)],[c_2945,c_4624]) ).
tcf(c_4792,plain,
join(complement(iPr_def_18),complement(join(iPr_def_17,complement(iPr_def_18)))) = sK1,
inference(superposition,[status(thm)],[c_3590,c_258]) ).
tcf(c_4813,plain,
join(iPr_def_19,complement(join(iPr_def_17,iPr_def_19))) = sK1,
inference(light_normalisation,[status(thm)],[c_4792,c_136]) ).
tcf(c_4847,plain,
join(top,iPr_def_15) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_278,c_3750]) ).
tcf(c_4869,plain,
join(iPr_def_10,top) = join(iPr_def_15,top),
inference(theory_normalisation,[status(thm)],[c_4847,c_50,c_49]) ).
tcf(c_5065,plain,
join(iPr_def_10,top) = top,
inference(demodulation,[status(thm)],[c_4341,c_1992,c_4869]) ).
tcf(c_5067,plain,
join(iPr_def_12,top) = top,
inference(demodulation,[status(thm)],[c_4306,c_5065]) ).
tcf(c_6530,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_3805,c_120,c_5067]) ).
tcf(c_6532,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_6530,c_50]) ).
tcf(c_7863,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_285,c_6532]) ).
tcf(c_7897,plain,
! [X0: $i] : complement(join(complement(X0),complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_285,c_7863]) ).
tcf(c_7900,plain,
complement(iPr_def_16) = sK0,
inference(demodulation,[status(thm)],[c_3591,c_7863]) ).
tcf(c_7901,plain,
complement(iPr_def_17) = sK1,
inference(demodulation,[status(thm)],[c_3589,c_7863]) ).
tcf(c_7904,plain,
complement(join(iPr_def_15,iPr_def_15)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2084,c_7863]) ).
tcf(c_7906,plain,
complement(join(iPr_def_19,iPr_def_19)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_2900,c_7863]) ).
tcf(c_8162,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_7863,c_49]) ).
tcf(c_8167,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_7863,c_59]) ).
tcf(c_8183,plain,
join(iPr_def_19,converse(zero)) = converse(iPr_def_20),
inference(superposition,[status(thm)],[c_7863,c_334]) ).
tcf(c_8198,plain,
converse(complement(converse(zero))) = top,
inference(superposition,[status(thm)],[c_7863,c_4628]) ).
tcf(c_8211,plain,
join(iPr_def_19,converse(zero)) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_8183,c_266]) ).
tcf(c_8231,plain,
join(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3830,c_8162]) ).
tcf(c_8256,plain,
! [X0: $i] : join(complement(join(top,X0)),complement(join(top,complement(X0)))) = zero,
inference(superposition,[status(thm)],[c_8167,c_80]) ).
tcf(c_8529,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_15,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_8231,c_50]) ).
tcf(c_8540,plain,
complement(iPr_def_15) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7904,c_8231]) ).
tcf(c_8605,plain,
join(complement(join(iPr_def_16,iPr_def_18)),complement(join(sK0,iPr_def_18))) = join(iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_7906,c_255]) ).
tcf(c_8634,plain,
join(complement(join(iPr_def_16,iPr_def_18)),complement(join(iPr_def_18,sK0))) = join(iPr_def_19,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_8605,c_50,c_49]) ).
tcf(c_8635,plain,
join(iPr_def_19,zero) = join(iPr_def_19,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_8634,c_120,c_136,c_4228,c_4494]) ).
tcf(c_8668,plain,
complement(converse(zero)) = converse(top),
inference(superposition,[status(thm)],[c_8198,c_55]) ).
tcf(c_8677,plain,
complement(converse(zero)) = top,
inference(light_normalisation,[status(thm)],[c_8668,c_4624]) ).
tcf(c_8710,plain,
! [X0: $i] : join(complement(join(top,X0)),complement(join(top,complement(X0)))) = converse(zero),
inference(superposition,[status(thm)],[c_8677,c_80]) ).
tcf(c_8740,plain,
converse(zero) = zero,
inference(light_normalisation,[status(thm)],[c_8710,c_8256]) ).
tcf(c_8793,plain,
join(iPr_def_19,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_8211,c_8635,c_8740]) ).
tcf(c_8794,plain,
complement(iPr_def_19) = iPr_def_18,
inference(demodulation,[status(thm)],[c_7906,c_8793]) ).
tcf(c_8799,plain,
! [X0: $i] : join(iPr_def_19,join(iPr_def_19,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_8793,c_50]) ).
tcf(c_8808,plain,
join(iPr_def_20,converse(iPr_def_19)) = converse(iPr_def_19),
inference(superposition,[status(thm)],[c_8793,c_337]) ).
tcf(c_8809,plain,
join(iPr_def_20,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_8808,c_269]) ).
tcf(c_8869,plain,
! [X0: $i] : join(iPr_def_20,join(iPr_def_20,X0)) = join(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_8809,c_50]) ).
tcf(c_9113,plain,
! [X0: $i] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(superposition,[status(thm)],[c_3573,c_294]) ).
tcf(c_9168,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_9113,c_3553,c_3573]) ).
tcf(c_9207,plain,
join(iPr_def_15,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_3735,c_8529]) ).
tcf(c_9208,plain,
join(iPr_def_15,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_4007,c_8529]) ).
tcf(c_9215,plain,
join(iPr_def_10,iPr_def_15) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_9208,c_50,c_49]) ).
tcf(c_9216,plain,
join(iPr_def_12,iPr_def_15) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_9207,c_50,c_49]) ).
tcf(c_9367,plain,
join(iPr_def_19,sK1) = sK1,
inference(superposition,[status(thm)],[c_4813,c_8799]) ).
tcf(c_9389,plain,
join(iPr_def_20,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_1379,c_8869]) ).
tcf(c_9395,plain,
join(iPr_def_10,iPr_def_20) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_9389,c_50,c_49]) ).
tcf(c_9473,plain,
join(iPr_def_12,converse(iPr_def_19)) = converse(sK1),
inference(superposition,[status(thm)],[c_9367,c_338]) ).
tcf(c_9474,plain,
join(iPr_def_12,iPr_def_20) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_9473,c_268,c_269]) ).
tcf(c_9486,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_20,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_9395,c_50]) ).
tcf(c_9495,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_20,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_9474,c_50]) ).
tcf(c_9906,plain,
join(iPr_def_10,complement(iPr_def_20)) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_59,c_9486]) ).
tcf(c_9933,plain,
join(iPr_def_10,complement(iPr_def_20)) = top,
inference(light_normalisation,[status(thm)],[c_9906,c_5065]) ).
tcf(c_9946,plain,
join(iPr_def_12,complement(iPr_def_20)) = join(iPr_def_12,top),
inference(superposition,[status(thm)],[c_59,c_9495]) ).
tcf(c_9971,plain,
join(iPr_def_12,complement(iPr_def_20)) = top,
inference(light_normalisation,[status(thm)],[c_9946,c_5067]) ).
tcf(c_9990,plain,
join(complement(top),complement(join(iPr_def_11,complement(iPr_def_20)))) = iPr_def_20,
inference(superposition,[status(thm)],[c_9933,c_253]) ).
tcf(c_9994,plain,
join(zero,complement(join(iPr_def_11,complement(iPr_def_20)))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_9990,c_120]) ).
tcf(c_9998,plain,
join(complement(top),complement(join(iPr_def_13,complement(iPr_def_20)))) = iPr_def_20,
inference(superposition,[status(thm)],[c_9971,c_252]) ).
tcf(c_10002,plain,
join(zero,complement(join(iPr_def_13,complement(iPr_def_20)))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_9998,c_120]) ).
tcf(c_10271,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_7897,c_9168]) ).
tcf(c_10281,plain,
complement(iPr_def_18) = iPr_def_19,
inference(superposition,[status(thm)],[c_8794,c_10271]) ).
tcf(c_10282,plain,
complement(sK0) = iPr_def_16,
inference(superposition,[status(thm)],[c_7900,c_10271]) ).
tcf(c_10283,plain,
complement(sK1) = iPr_def_17,
inference(superposition,[status(thm)],[c_7901,c_10271]) ).
tcf(c_12360,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_10271,c_9168]) ).
tcf(c_12400,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_12360,c_50]) ).
tcf(c_13386,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_308,c_12400]) ).
tcf(c_13393,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_13386,c_50,c_49]) ).
tcf(c_21080,plain,
complement(join(iPr_def_11,complement(iPr_def_20))) = iPr_def_20,
inference(demodulation,[status(thm)],[c_9994,c_7863]) ).
tcf(c_21089,plain,
join(iPr_def_11,complement(iPr_def_20)) = complement(iPr_def_20),
inference(superposition,[status(thm)],[c_21080,c_10271]) ).
tcf(c_21237,plain,
complement(join(iPr_def_13,complement(iPr_def_20))) = iPr_def_20,
inference(demodulation,[status(thm)],[c_10002,c_7863]) ).
tcf(c_21246,plain,
join(iPr_def_13,complement(iPr_def_20)) = complement(iPr_def_20),
inference(superposition,[status(thm)],[c_21237,c_10271]) ).
tcf(c_21278,plain,
join(iPr_def_11,complement(iPr_def_20)) = join(iPr_def_14,complement(iPr_def_20)),
inference(superposition,[status(thm)],[c_21246,c_366]) ).
tcf(c_21280,plain,
join(iPr_def_14,complement(iPr_def_20)) = complement(iPr_def_20),
inference(light_normalisation,[status(thm)],[c_21278,c_21089]) ).
tcf(c_24318,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X0,X1))) = complement(X0),
inference(superposition,[status(thm)],[c_10271,c_13393]) ).
tcf(c_24330,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_19,X0))) = iPr_def_18,
inference(superposition,[status(thm)],[c_10281,c_13393]) ).
tcf(c_24338,plain,
! [X0: $i] : join(iPr_def_15,complement(join(iPr_def_14,X0))) = iPr_def_15,
inference(superposition,[status(thm)],[c_8540,c_13393]) ).
tcf(c_24368,plain,
! [X0: $i] : join(iPr_def_20,converse(complement(join(complement(iPr_def_19),X0)))) = converse(iPr_def_19),
inference(superposition,[status(thm)],[c_13393,c_317]) ).
tcf(c_24442,plain,
! [X0: $i] : join(iPr_def_20,converse(complement(join(iPr_def_18,X0)))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_24368,c_269,c_8794]) ).
tcf(c_25408,plain,
join(iPr_def_15,complement(complement(iPr_def_20))) = iPr_def_15,
inference(superposition,[status(thm)],[c_21280,c_24338]) ).
tcf(c_25544,plain,
join(iPr_def_15,iPr_def_20) = iPr_def_15,
inference(demodulation,[status(thm)],[c_25408,c_10271]) ).
tcf(c_25547,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_20,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_25544,c_50]) ).
tcf(c_25558,plain,
join(iPr_def_19,converse(iPr_def_15)) = converse(iPr_def_15),
inference(superposition,[status(thm)],[c_25544,c_334]) ).
tcf(c_25570,plain,
join(iPr_def_18,complement(converse(iPr_def_15))) = iPr_def_18,
inference(superposition,[status(thm)],[c_25558,c_24330]) ).
tcf(c_27430,plain,
join(iPr_def_15,converse(complement(join(iPr_def_16,sK1)))) = join(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_1379,c_25547]) ).
tcf(c_27432,plain,
join(iPr_def_15,converse(complement(join(iPr_def_17,sK0)))) = join(iPr_def_15,iPr_def_12),
inference(superposition,[status(thm)],[c_4190,c_25547]) ).
tcf(c_27529,plain,
join(iPr_def_15,converse(complement(join(iPr_def_17,sK0)))) = join(iPr_def_12,iPr_def_15),
inference(theory_normalisation,[status(thm)],[c_27432,c_50,c_49]) ).
tcf(c_27530,plain,
join(iPr_def_15,converse(complement(join(iPr_def_17,sK0)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_27529,c_9216]) ).
tcf(c_27531,plain,
join(iPr_def_15,converse(complement(join(iPr_def_16,sK1)))) = join(iPr_def_10,iPr_def_15),
inference(theory_normalisation,[status(thm)],[c_27430,c_50,c_49]) ).
tcf(c_27532,plain,
join(iPr_def_15,converse(complement(join(iPr_def_16,sK1)))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_27531,c_9215]) ).
tcf(c_35203,plain,
! [X0: $i] : join(iPr_def_15,converse(complement(join(iPr_def_18,X0)))) = join(iPr_def_15,iPr_def_20),
inference(superposition,[status(thm)],[c_24442,c_25547]) ).
tcf(c_35223,plain,
! [X0: $i] : join(iPr_def_15,converse(complement(join(iPr_def_18,X0)))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_35203,c_25544]) ).
tcf(c_36637,plain,
join(converse(iPr_def_15),complement(join(iPr_def_17,sK0))) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_27530,c_322]) ).
tcf(c_36639,plain,
join(converse(iPr_def_15),complement(join(iPr_def_17,sK0))) = sK1,
inference(light_normalisation,[status(thm)],[c_36637,c_265]) ).
tcf(c_36662,plain,
join(converse(iPr_def_15),complement(join(iPr_def_16,sK1))) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_27532,c_322]) ).
tcf(c_36664,plain,
join(converse(iPr_def_15),complement(join(iPr_def_16,sK1))) = sK0,
inference(light_normalisation,[status(thm)],[c_36662,c_264]) ).
tcf(c_41379,plain,
! [X0: $i] : join(X0,composition(complement(one),X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_59,c_3638]) ).
tcf(c_41635,plain,
join(iPr_def_15,converse(complement(composition(top,iPr_def_18)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_41379,c_35223]) ).
tcf(c_41638,plain,
join(iPr_def_20,converse(complement(composition(top,iPr_def_18)))) = iPr_def_20,
inference(superposition,[status(thm)],[c_41379,c_24442]) ).
tcf(c_116171,plain,
join(complement(converse(iPr_def_15)),complement(sK1)) = complement(converse(iPr_def_15)),
inference(superposition,[status(thm)],[c_36639,c_24318]) ).
tcf(c_116172,plain,
join(complement(converse(iPr_def_15)),complement(sK0)) = complement(converse(iPr_def_15)),
inference(superposition,[status(thm)],[c_36664,c_24318]) ).
tcf(c_116664,plain,
join(complement(sK0),complement(converse(iPr_def_15))) = complement(converse(iPr_def_15)),
inference(theory_normalisation,[status(thm)],[c_116172,c_50,c_49]) ).
tcf(c_116665,plain,
join(iPr_def_16,complement(converse(iPr_def_15))) = complement(converse(iPr_def_15)),
inference(light_normalisation,[status(thm)],[c_116664,c_10282]) ).
tcf(c_116666,plain,
join(complement(sK1),complement(converse(iPr_def_15))) = complement(converse(iPr_def_15)),
inference(theory_normalisation,[status(thm)],[c_116171,c_50,c_49]) ).
tcf(c_116667,plain,
join(iPr_def_17,complement(converse(iPr_def_15))) = complement(converse(iPr_def_15)),
inference(light_normalisation,[status(thm)],[c_116666,c_10283]) ).
tcf(c_116836,plain,
join(iPr_def_16,complement(converse(iPr_def_15))) = join(iPr_def_18,complement(converse(iPr_def_15))),
inference(superposition,[status(thm)],[c_116667,c_367]) ).
tcf(c_116850,plain,
complement(converse(iPr_def_15)) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_116836,c_25570,c_116665]) ).
tcf(c_116929,plain,
complement(iPr_def_18) = converse(iPr_def_15),
inference(superposition,[status(thm)],[c_116850,c_10271]) ).
tcf(c_117016,plain,
converse(iPr_def_15) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_116929,c_10281]) ).
tcf(c_117193,plain,
! [X0: $i] : join(iPr_def_15,converse(X0)) = converse(join(iPr_def_19,X0)),
inference(superposition,[status(thm)],[c_117016,c_312]) ).
tcf(c_117292,plain,
! [X0: $i] : join(iPr_def_15,converse(X0)) = join(iPr_def_20,converse(X0)),
inference(demodulation,[status(thm)],[c_317,c_117193]) ).
tcf(c_117310,plain,
join(iPr_def_15,converse(complement(composition(top,iPr_def_18)))) = iPr_def_20,
inference(demodulation,[status(thm)],[c_41638,c_117292]) ).
tcf(c_117311,plain,
iPr_def_15 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_117310,c_41635]) ).
tcf(c_117312,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_117311,c_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL005+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 07:06:38 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.37 Running first-order theorem proving
% 0.13/0.37 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
% 0.13/0.38
% 0.13/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.38
% 0.13/0.38 % Detected problem language: tptp
% 0.13/0.39 % Proving...
% 38.19/7.37 % SZS status Started for theBenchmark.p
% 38.19/7.37 % SZS status Theorem for theBenchmark.p
% 38.19/7.37
% 38.19/7.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 38.19/7.37
% 38.19/7.37 % ------ iProver source info
% 38.19/7.37
% 38.19/7.37 % git: date: 2026-07-19 20:42:38 +0200
% 38.19/7.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 38.19/7.37 % git: non_committed_changes: false
% 38.19/7.37
% 38.19/7.37 % ------ Parsing...
% 38.19/7.37 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 38.19/7.37 %
% 38.19/7.37
% 38.19/7.37 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 38.19/7.37
% 38.19/7.37 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 38.19/7.37 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 38.19/7.37
% 38.19/7.37 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 38.19/7.37 % ------ Proving...
% 38.19/7.37 % ------ Problem Properties
% 38.19/7.37
% 38.19/7.37 %
% 38.19/7.37 % clauses 27
% 38.19/7.37 % conjectures 1
% 38.19/7.37 % EPR 1
% 38.19/7.37 % Horn 27
% 38.19/7.37 % unary 27
% 38.19/7.37 % binary 0
% 38.19/7.37 % lits 27
% 38.19/7.37 % lits eq 27
% 38.19/7.37 % fd_pure 0
% 38.19/7.37 % fd_pseudo 0
% 38.19/7.37 % fd_cond 0
% 38.19/7.37 % fd_pseudo_cond 0
% 38.19/7.37 % AC symbols 1
% 38.19/7.37
% 38.19/7.37 % ------ Schedule UEQ
% 38.19/7.37
% 38.19/7.37 % ------ Option_UEQ Time Limit: 10.
% 38.19/7.37
% 38.19/7.37
% 38.19/7.37 % ------
% 38.19/7.37 % Current options:
% 38.19/7.37 % ------
% 38.19/7.37
% 38.19/7.37
% 38.19/7.37 %
% 38.19/7.37
% 38.19/7.37 % ------ Proving...
% 38.19/7.37 %
% 38.19/7.37
% 38.19/7.37 % SZS status Theorem for theBenchmark.p
% 38.19/7.37
% 38.19/7.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 38.19/7.38
% 38.19/7.38
%------------------------------------------------------------------------------