%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL007+1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:36:32 PM UTC 2026
% Result : Theorem 10.81s 2.74s
% Output : CNFRefutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 23
% Syntax : Number of formulae : 287 ( 283 unt; 10 def)
% Number of atoms : 925 ( 290 equ)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 13 ( 9 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 0 sgn 179 !; 2 ?; 130 :)
% 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(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(f14,conjecture,
! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( meet(X0,converse(X1)) = zero
=> meet(converse(X0),X1) = zero ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( meet(X0,converse(X1)) = zero
& zero != meet(converse(X0),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( zero = meet(sK0,converse(sK1))
& zero != meet(converse(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
zero = meet(sK0,converse(sK1)),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
zero != meet(converse(sK0),sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
fof(f34,plain,
zero != complement(join(complement(converse(sK0)),complement(sK1))),
inference(definition_unfolding,[],[f32,f21]) ).
fof(f35,plain,
zero = complement(join(complement(sK0),complement(converse(sK1)))),
inference(definition_unfolding,[],[f31,f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f33]) ).
tcf(c_61,negated_conjecture,
complement(join(complement(converse(sK0)),complement(sK1))) != zero,
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,negated_conjecture,
complement(join(complement(sK0),complement(converse(sK1)))) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_75,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_76,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_77,negated_conjecture,
complement(join(complement(sK1),complement(converse(sK0)))) != zero,
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
tcf(c_108,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_115,definition,
iPr_def_10 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_116,definition,
iPr_def_11 = converse(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_117,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_118,definition,
iPr_def_13 = join(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_119,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_120,definition,
iPr_def_15 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_121,definition,
iPr_def_16 = converse(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_122,definition,
iPr_def_17 = complement(iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_123,definition,
iPr_def_18 = join(iPr_def_15,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_124,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_125,negated_conjecture,
iPr_def_14 != zero,
inference(demodulation,[status(thm)],[c_77,c_116,c_117,c_115,c_118,c_119]) ).
tcf(c_126,negated_conjecture,
iPr_def_19 = zero,
inference(demodulation,[status(thm)],[c_62,c_121,c_122,c_120,c_123,c_124]) ).
tcf(c_213,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_214,plain,
iPr_def_14 != iPr_def_19,
inference(light_normalisation,[status(thm)],[c_125,c_126]) ).
tcf(c_215,plain,
complement(top) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_108,c_126]) ).
tcf(c_223,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = sK1,
inference(superposition,[status(thm)],[c_115,c_75]) ).
tcf(c_224,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_120,c_75]) ).
tcf(c_225,plain,
! [X0: $i] : join(complement(join(iPr_def_19,X0)),complement(join(iPr_def_19,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_215,c_75]) ).
tcf(c_226,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_117,c_75]) ).
tcf(c_228,plain,
! [X0: $i] : join(complement(join(complement(X0),sK1)),complement(join(complement(X0),iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_115,c_75]) ).
tcf(c_231,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_11)),complement(join(complement(X0),iPr_def_12))) = X0,
inference(superposition,[status(thm)],[c_117,c_75]) ).
tcf(c_232,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_13)),complement(join(complement(X0),iPr_def_14))) = X0,
inference(superposition,[status(thm)],[c_119,c_75]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1)))),complement(X0)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_75,c_75]) ).
tcf(c_235,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_232,c_50,c_49]) ).
tcf(c_236,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_231,c_50,c_49]) ).
tcf(c_239,plain,
! [X0: $i] : join(complement(join(iPr_def_10,complement(X0))),complement(join(sK1,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_228,c_50,c_49]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))) = join(complement(X0),X1),
inference(theory_normalisation,[status(thm)],[c_233,c_50,c_49]) ).
tcf(c_245,plain,
! [X0: $i] : join(complement(join(iPr_def_19,X0)),complement(join(iPr_def_19,complement(X0)))) = iPr_def_18,
inference(superposition,[status(thm)],[c_124,c_75]) ).
tcf(c_246,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_18)),complement(join(complement(X0),iPr_def_19))) = X0,
inference(superposition,[status(thm)],[c_124,c_75]) ).
tcf(c_247,plain,
! [X0: $i] : join(complement(join(iPr_def_18,complement(X0))),complement(join(iPr_def_19,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_246,c_50,c_49]) ).
tcf(c_248,plain,
converse(iPr_def_11) = sK0,
inference(superposition,[status(thm)],[c_116,c_55]) ).
tcf(c_249,plain,
converse(iPr_def_16) = sK1,
inference(superposition,[status(thm)],[c_121,c_55]) ).
tcf(c_250,plain,
converse(sK0) = iPr_def_11,
inference(superposition,[status(thm)],[c_248,c_55]) ).
tcf(c_251,plain,
converse(sK1) = iPr_def_16,
inference(superposition,[status(thm)],[c_249,c_55]) ).
tcf(c_254,plain,
top = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_225,c_245]) ).
tcf(c_255,plain,
complement(iPr_def_18) = iPr_def_19,
inference(demodulation,[status(thm)],[c_215,c_254]) ).
tcf(c_262,plain,
! [X0: $i] : join(X0,complement(X0)) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_59,c_254]) ).
tcf(c_263,plain,
join(sK1,iPr_def_10) = iPr_def_18,
inference(superposition,[status(thm)],[c_115,c_262]) ).
tcf(c_264,plain,
join(sK0,iPr_def_15) = iPr_def_18,
inference(superposition,[status(thm)],[c_120,c_262]) ).
tcf(c_265,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_18,
inference(superposition,[status(thm)],[c_117,c_262]) ).
tcf(c_267,plain,
join(iPr_def_16,iPr_def_17) = iPr_def_18,
inference(superposition,[status(thm)],[c_122,c_262]) ).
tcf(c_268,plain,
join(iPr_def_18,iPr_def_19) = iPr_def_18,
inference(superposition,[status(thm)],[c_255,c_262]) ).
tcf(c_270,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(iPr_def_18)) = X0,
inference(superposition,[status(thm)],[c_262,c_75]) ).
tcf(c_272,plain,
join(iPr_def_15,sK0) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_264,c_50,c_49]) ).
tcf(c_273,plain,
join(iPr_def_10,sK1) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_263,c_50,c_49]) ).
tcf(c_274,plain,
! [X0: $i] : join(complement(iPr_def_18),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_270,c_50,c_49]) ).
tcf(c_275,plain,
! [X0: $i] : join(iPr_def_19,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_274,c_255]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_304,plain,
! [X0: $i] : join(sK0,converse(X0)) = converse(join(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_248,c_56]) ).
tcf(c_309,plain,
! [X0: $i] : join(converse(X0),iPr_def_16) = converse(join(X0,sK1)),
inference(superposition,[status(thm)],[c_251,c_56]) ).
tcf(c_317,plain,
! [X0: $i] : join(iPr_def_16,converse(X0)) = converse(join(X0,sK1)),
inference(theory_normalisation,[status(thm)],[c_309,c_50,c_49]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_327,plain,
! [X0: $i] : composition(converse(X0),iPr_def_11) = converse(composition(sK0,X0)),
inference(superposition,[status(thm)],[c_250,c_57]) ).
tcf(c_331,plain,
! [X0: $i] : composition(converse(X0),sK0) = converse(composition(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_248,c_57]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(iPr_def_18,X1),
inference(superposition,[status(thm)],[c_262,c_50]) ).
tcf(c_339,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_12,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_118,c_50]) ).
tcf(c_340,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_17,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_123,c_50]) ).
tcf(c_341,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_19,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_268,c_50]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = iPr_def_18,
inference(superposition,[status(thm)],[c_50,c_262]) ).
tcf(c_345,plain,
! [X0: $i] : join(iPr_def_16,join(iPr_def_17,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_267,c_50]) ).
tcf(c_346,plain,
! [X0: $i] : join(iPr_def_15,join(sK0,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_272,c_50]) ).
tcf(c_355,plain,
join(iPr_def_19,complement(join(iPr_def_10,iPr_def_10))) = sK1,
inference(superposition,[status(thm)],[c_115,c_275]) ).
tcf(c_356,plain,
join(iPr_def_19,complement(join(iPr_def_15,iPr_def_15))) = sK0,
inference(superposition,[status(thm)],[c_120,c_275]) ).
tcf(c_357,plain,
join(iPr_def_19,complement(join(iPr_def_12,iPr_def_12))) = iPr_def_11,
inference(superposition,[status(thm)],[c_117,c_275]) ).
tcf(c_358,plain,
join(iPr_def_19,complement(join(iPr_def_14,iPr_def_14))) = iPr_def_13,
inference(superposition,[status(thm)],[c_119,c_275]) ).
tcf(c_359,plain,
join(iPr_def_19,complement(join(iPr_def_17,iPr_def_17))) = iPr_def_16,
inference(superposition,[status(thm)],[c_122,c_275]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(X0),X1)),join(X2,complement(join(complement(X0),complement(X1))))) = join(X2,X0),
inference(superposition,[status(thm)],[c_75,c_213]) ).
tcf(c_417,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_12)) = join(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_118,c_213]) ).
tcf(c_418,plain,
! [X0: $i] : join(iPr_def_15,join(X0,iPr_def_17)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_123,c_213]) ).
tcf(c_422,plain,
! [X0: $i] : join(iPr_def_18,join(X0,iPr_def_19)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_268,c_213]) ).
tcf(c_423,plain,
! [X0: $i] : join(iPr_def_15,join(X0,sK0)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_272,c_213]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(X0,join(complement(X1),X2))),complement(join(complement(X1),complement(join(X0,X2))))) = X1,
inference(superposition,[status(thm)],[c_213,c_75]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_454,plain,
! [X0: $i] : join(iPr_def_10,join(sK1,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_273,c_50]) ).
tcf(c_506,plain,
join(iPr_def_18,complement(iPr_def_19)) = join(iPr_def_18,iPr_def_18),
inference(superposition,[status(thm)],[c_262,c_341]) ).
tcf(c_530,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_19,X0)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_49,c_422]) ).
tcf(c_581,plain,
join(complement(join(iPr_def_10,iPr_def_11)),complement(join(iPr_def_10,iPr_def_12))) = sK1,
inference(superposition,[status(thm)],[c_117,c_223]) ).
tcf(c_595,plain,
join(complement(join(iPr_def_10,iPr_def_11)),iPr_def_14) = sK1,
inference(light_normalisation,[status(thm)],[c_581,c_118,c_119]) ).
tcf(c_596,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_11))) = sK1,
inference(theory_normalisation,[status(thm)],[c_595,c_50,c_49]) ).
tcf(c_737,plain,
join(complement(iPr_def_18),complement(join(iPr_def_15,complement(iPr_def_17)))) = sK0,
inference(superposition,[status(thm)],[c_123,c_224]) ).
tcf(c_745,plain,
join(complement(join(iPr_def_15,iPr_def_16)),complement(join(iPr_def_15,iPr_def_17))) = sK0,
inference(superposition,[status(thm)],[c_122,c_224]) ).
tcf(c_746,plain,
join(complement(join(iPr_def_15,iPr_def_18)),complement(join(iPr_def_15,iPr_def_19))) = sK0,
inference(superposition,[status(thm)],[c_255,c_224]) ).
tcf(c_756,plain,
join(iPr_def_19,complement(join(iPr_def_15,complement(iPr_def_17)))) = sK0,
inference(light_normalisation,[status(thm)],[c_737,c_255]) ).
tcf(c_757,plain,
join(complement(join(iPr_def_15,iPr_def_16)),iPr_def_19) = sK0,
inference(light_normalisation,[status(thm)],[c_745,c_123,c_255]) ).
tcf(c_758,plain,
join(iPr_def_19,complement(join(iPr_def_15,iPr_def_16))) = sK0,
inference(theory_normalisation,[status(thm)],[c_757,c_50,c_49]) ).
tcf(c_912,plain,
! [X0: $i] : join(iPr_def_19,join(X0,complement(join(iPr_def_15,complement(iPr_def_17))))) = join(X0,sK0),
inference(superposition,[status(thm)],[c_756,c_213]) ).
tcf(c_1068,plain,
composition(converse(one),iPr_def_11) = converse(sK0),
inference(superposition,[status(thm)],[c_53,c_327]) ).
tcf(c_1083,plain,
composition(converse(one),iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1068,c_250]) ).
tcf(c_1091,plain,
join(complement(iPr_def_11),composition(converse(converse(one)),complement(iPr_def_11))) = complement(iPr_def_11),
inference(superposition,[status(thm)],[c_1083,c_76]) ).
tcf(c_1094,plain,
join(iPr_def_12,composition(converse(converse(one)),iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_1091,c_117]) ).
tcf(c_1134,plain,
composition(converse(one),sK0) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_53,c_331]) ).
tcf(c_1149,plain,
composition(converse(one),sK0) = sK0,
inference(light_normalisation,[status(thm)],[c_1134,c_248]) ).
tcf(c_1294,plain,
join(complement(sK0),composition(converse(converse(one)),complement(sK0))) = complement(sK0),
inference(superposition,[status(thm)],[c_1149,c_76]) ).
tcf(c_1297,plain,
join(iPr_def_15,composition(converse(converse(one)),iPr_def_15)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_1294,c_120]) ).
tcf(c_1355,plain,
join(iPr_def_18,complement(iPr_def_17)) = join(iPr_def_15,iPr_def_18),
inference(superposition,[status(thm)],[c_262,c_340]) ).
tcf(c_1378,plain,
join(join(iPr_def_15,complement(iPr_def_17)),sK0) = join(iPr_def_19,iPr_def_18),
inference(superposition,[status(thm)],[c_262,c_912]) ).
tcf(c_1392,plain,
join(iPr_def_15,join(sK0,complement(iPr_def_17))) = join(iPr_def_18,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_1378,c_50,c_49]) ).
tcf(c_1393,plain,
join(iPr_def_15,join(sK0,complement(iPr_def_17))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_1392,c_268]) ).
tcf(c_1401,plain,
join(iPr_def_15,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_1393,c_346,c_1355]) ).
tcf(c_1402,plain,
join(complement(iPr_def_18),complement(join(iPr_def_15,iPr_def_19))) = sK0,
inference(demodulation,[status(thm)],[c_746,c_1401]) ).
tcf(c_1403,plain,
join(iPr_def_19,complement(join(iPr_def_15,iPr_def_19))) = sK0,
inference(light_normalisation,[status(thm)],[c_1402,c_255]) ).
tcf(c_1404,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_18,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_1401,c_50]) ).
tcf(c_1622,plain,
join(iPr_def_18,complement(iPr_def_17)) = join(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_262,c_345]) ).
tcf(c_1628,plain,
join(iPr_def_16,iPr_def_18) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_1622,c_1355,c_1401]) ).
tcf(c_1969,plain,
join(iPr_def_10,iPr_def_18) = join(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_265,c_417]) ).
tcf(c_1985,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_17,X0)) = join(X0,iPr_def_18),
inference(superposition,[status(thm)],[c_49,c_418]) ).
tcf(c_1996,plain,
join(sK0,iPr_def_18) = join(iPr_def_18,iPr_def_17),
inference(superposition,[status(thm)],[c_418,c_346]) ).
tcf(c_1997,plain,
join(iPr_def_17,iPr_def_18) = join(iPr_def_18,sK0),
inference(theory_normalisation,[status(thm)],[c_1996,c_50,c_49]) ).
tcf(c_2257,plain,
! [X0: $i] : join(iPr_def_10,join(X0,sK1)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_49,c_454]) ).
tcf(c_2536,plain,
join(complement(join(iPr_def_17,iPr_def_17)),iPr_def_18) = join(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_359,c_530]) ).
tcf(c_2590,plain,
join(iPr_def_18,complement(join(iPr_def_17,iPr_def_17))) = join(iPr_def_16,iPr_def_18),
inference(theory_normalisation,[status(thm)],[c_2536,c_50,c_49]) ).
tcf(c_2591,plain,
join(iPr_def_18,complement(join(iPr_def_17,iPr_def_17))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_2590,c_1628]) ).
tcf(c_3129,plain,
! [X0: $i] : join(iPr_def_19,complement(join(iPr_def_19,join(complement(X0),complement(join(iPr_def_19,X0)))))) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_255,c_240]) ).
tcf(c_3204,plain,
join(iPr_def_12,composition(one,iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1094,c_55]) ).
tcf(c_3209,plain,
join(iPr_def_13,composition(one,iPr_def_12)) = join(iPr_def_10,iPr_def_12),
inference(superposition,[status(thm)],[c_3204,c_339]) ).
tcf(c_3211,plain,
join(iPr_def_13,composition(one,iPr_def_12)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_3209,c_118]) ).
tcf(c_3226,plain,
join(iPr_def_19,complement(join(iPr_def_19,join(iPr_def_19,complement(join(iPr_def_19,iPr_def_18)))))) = join(iPr_def_19,iPr_def_18),
inference(superposition,[status(thm)],[c_255,c_3129]) ).
tcf(c_3333,plain,
join(iPr_def_19,complement(join(iPr_def_19,join(iPr_def_19,complement(join(iPr_def_18,iPr_def_19)))))) = join(iPr_def_18,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_3226,c_50,c_49]) ).
tcf(c_3334,plain,
join(iPr_def_19,complement(join(iPr_def_19,join(iPr_def_19,iPr_def_19)))) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_3333,c_255,c_268]) ).
tcf(c_3446,plain,
join(iPr_def_18,complement(join(iPr_def_19,join(iPr_def_19,iPr_def_19)))) = join(iPr_def_18,iPr_def_18),
inference(superposition,[status(thm)],[c_3334,c_341]) ).
tcf(c_3612,plain,
join(iPr_def_15,composition(one,iPr_def_15)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1297,c_55]) ).
tcf(c_3899,plain,
join(iPr_def_18,sK0) = join(iPr_def_18,iPr_def_18),
inference(superposition,[status(thm)],[c_1404,c_423]) ).
tcf(c_3900,plain,
join(iPr_def_17,iPr_def_18) = join(iPr_def_18,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_3899,c_1997]) ).
tcf(c_3910,plain,
join(iPr_def_18,complement(iPr_def_19)) = join(iPr_def_17,iPr_def_18),
inference(demodulation,[status(thm)],[c_506,c_3900]) ).
tcf(c_4858,plain,
join(complement(join(iPr_def_18,complement(iPr_def_19))),complement(iPr_def_18)) = iPr_def_19,
inference(superposition,[status(thm)],[c_262,c_247]) ).
tcf(c_4865,plain,
join(complement(join(iPr_def_18,complement(join(iPr_def_17,iPr_def_17)))),complement(iPr_def_16)) = join(iPr_def_17,iPr_def_17),
inference(superposition,[status(thm)],[c_359,c_247]) ).
tcf(c_4912,plain,
join(complement(join(iPr_def_18,complement(join(iPr_def_19,join(iPr_def_19,iPr_def_19))))),complement(iPr_def_18)) = join(iPr_def_19,join(iPr_def_19,iPr_def_19)),
inference(superposition,[status(thm)],[c_3334,c_247]) ).
tcf(c_4949,plain,
join(complement(iPr_def_18),complement(join(iPr_def_18,complement(iPr_def_19)))) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_4858,c_50,c_49]) ).
tcf(c_4950,plain,
join(iPr_def_19,complement(join(iPr_def_17,iPr_def_18))) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_4949,c_255,c_3910]) ).
tcf(c_4973,plain,
join(complement(iPr_def_16),complement(join(iPr_def_18,complement(join(iPr_def_17,iPr_def_17))))) = join(iPr_def_17,iPr_def_17),
inference(theory_normalisation,[status(thm)],[c_4865,c_50,c_49]) ).
tcf(c_4974,plain,
join(iPr_def_17,iPr_def_17) = join(iPr_def_17,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_4973,c_122,c_255,c_2591]) ).
tcf(c_5002,plain,
join(complement(iPr_def_18),complement(join(iPr_def_18,complement(join(iPr_def_19,join(iPr_def_19,iPr_def_19)))))) = join(iPr_def_19,join(iPr_def_19,iPr_def_19)),
inference(theory_normalisation,[status(thm)],[c_4912,c_50,c_49]) ).
tcf(c_5003,plain,
join(iPr_def_19,complement(join(iPr_def_17,iPr_def_18))) = join(iPr_def_19,join(iPr_def_19,iPr_def_19)),
inference(light_normalisation,[status(thm)],[c_5002,c_255,c_3446,c_3900]) ).
tcf(c_5465,plain,
join(iPr_def_15,join(iPr_def_17,iPr_def_17)) = join(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_4974,c_340]) ).
tcf(c_5470,plain,
join(iPr_def_15,join(iPr_def_17,iPr_def_17)) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_5465,c_268]) ).
tcf(c_5475,plain,
join(iPr_def_17,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_5470,c_1985]) ).
tcf(c_5477,plain,
join(iPr_def_18,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_3900,c_5475]) ).
tcf(c_5491,plain,
join(iPr_def_19,iPr_def_19) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_4950,c_255,c_5003,c_5475]) ).
tcf(c_5497,plain,
! [X0: $i] : join(iPr_def_19,join(iPr_def_19,X0)) = join(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_5491,c_50]) ).
tcf(c_5911,plain,
! [X0: $i] : join(iPr_def_19,X0) = X0,
inference(superposition,[status(thm)],[c_275,c_5497]) ).
tcf(c_5971,plain,
complement(join(iPr_def_10,iPr_def_10)) = sK1,
inference(demodulation,[status(thm)],[c_355,c_5911]) ).
tcf(c_5972,plain,
complement(join(iPr_def_15,iPr_def_15)) = sK0,
inference(demodulation,[status(thm)],[c_356,c_5911]) ).
tcf(c_5973,plain,
complement(join(iPr_def_12,iPr_def_12)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_357,c_5911]) ).
tcf(c_5974,plain,
complement(join(iPr_def_14,iPr_def_14)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_358,c_5911]) ).
tcf(c_5987,plain,
complement(join(iPr_def_15,iPr_def_16)) = sK0,
inference(demodulation,[status(thm)],[c_758,c_5911]) ).
tcf(c_5988,plain,
complement(join(iPr_def_15,iPr_def_19)) = sK0,
inference(demodulation,[status(thm)],[c_1403,c_5911]) ).
tcf(c_6167,plain,
! [X0: $i] : join(X0,iPr_def_19) = X0,
inference(superposition,[status(thm)],[c_5911,c_49]) ).
tcf(c_6257,plain,
! [X0: $i] : join(X0,converse(iPr_def_19)) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_6167,c_299]) ).
tcf(c_6284,plain,
! [X0: $i] : join(X0,converse(iPr_def_19)) = X0,
inference(light_normalisation,[status(thm)],[c_6257,c_55]) ).
tcf(c_6539,plain,
join(join(iPr_def_10,iPr_def_10),sK1) = iPr_def_18,
inference(superposition,[status(thm)],[c_5971,c_262]) ).
tcf(c_6545,plain,
join(iPr_def_10,join(iPr_def_10,sK1)) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_6539,c_50,c_49]) ).
tcf(c_6546,plain,
join(iPr_def_10,iPr_def_18) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_6545,c_273]) ).
tcf(c_6560,plain,
join(iPr_def_11,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_1969,c_6546]) ).
tcf(c_6572,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_18,X0)) = join(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_6546,c_50]) ).
tcf(c_6761,plain,
join(iPr_def_18,sK1) = join(iPr_def_18,iPr_def_18),
inference(superposition,[status(thm)],[c_6572,c_2257]) ).
tcf(c_6763,plain,
join(iPr_def_18,sK1) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_6761,c_5477]) ).
tcf(c_7100,plain,
join(complement(join(iPr_def_13,sK0)),complement(join(iPr_def_14,sK0))) = join(iPr_def_15,iPr_def_15),
inference(superposition,[status(thm)],[c_5972,c_235]) ).
tcf(c_7136,plain,
join(complement(join(iPr_def_13,iPr_def_11)),complement(join(iPr_def_14,iPr_def_11))) = join(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_5973,c_235]) ).
tcf(c_7139,plain,
join(complement(join(iPr_def_12,join(iPr_def_12,iPr_def_12))),complement(join(iPr_def_12,iPr_def_11))) = iPr_def_11,
inference(superposition,[status(thm)],[c_5973,c_226]) ).
tcf(c_7143,plain,
join(join(iPr_def_12,iPr_def_12),iPr_def_11) = iPr_def_18,
inference(superposition,[status(thm)],[c_5973,c_262]) ).
tcf(c_7149,plain,
join(iPr_def_11,join(iPr_def_12,iPr_def_12)) = iPr_def_18,
inference(theory_normalisation,[status(thm)],[c_7143,c_50,c_49]) ).
tcf(c_7152,plain,
join(complement(join(iPr_def_11,iPr_def_12)),complement(join(iPr_def_12,join(iPr_def_12,iPr_def_12)))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_7139,c_50,c_49]) ).
tcf(c_7153,plain,
join(iPr_def_19,complement(join(iPr_def_12,join(iPr_def_12,iPr_def_12)))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_7152,c_255,c_265]) ).
tcf(c_7155,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_11,iPr_def_14))) = join(iPr_def_12,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_7136,c_50,c_49]) ).
tcf(c_7156,plain,
join(iPr_def_19,complement(join(iPr_def_11,iPr_def_14))) = join(iPr_def_12,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_7155,c_255,c_6560]) ).
tcf(c_7267,plain,
complement(join(iPr_def_12,join(iPr_def_12,iPr_def_12))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_7153,c_5911]) ).
tcf(c_7274,plain,
join(complement(join(iPr_def_13,iPr_def_11)),complement(join(iPr_def_14,iPr_def_11))) = join(iPr_def_12,join(iPr_def_12,iPr_def_12)),
inference(superposition,[status(thm)],[c_7267,c_235]) ).
tcf(c_7296,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_11,iPr_def_14))) = join(iPr_def_12,join(iPr_def_12,iPr_def_12)),
inference(theory_normalisation,[status(thm)],[c_7274,c_50,c_49]) ).
tcf(c_7297,plain,
join(iPr_def_12,join(iPr_def_12,iPr_def_12)) = join(iPr_def_12,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_7296,c_255,c_6560,c_7156]) ).
tcf(c_7332,plain,
complement(join(iPr_def_11,iPr_def_14)) = join(iPr_def_12,iPr_def_12),
inference(demodulation,[status(thm)],[c_7156,c_5911]) ).
tcf(c_7338,plain,
join(complement(join(iPr_def_11,join(iPr_def_12,iPr_def_12))),complement(join(iPr_def_12,join(iPr_def_12,iPr_def_12)))) = join(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_7332,c_236]) ).
tcf(c_7362,plain,
join(iPr_def_11,iPr_def_14) = join(iPr_def_19,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_7338,c_255,c_5973,c_7149,c_7297]) ).
tcf(c_7363,plain,
join(iPr_def_11,iPr_def_14) = join(iPr_def_11,iPr_def_19),
inference(theory_normalisation,[status(thm)],[c_7362,c_50,c_49]) ).
tcf(c_7623,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_12,iPr_def_13))) = join(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_5974,c_236]) ).
tcf(c_7647,plain,
join(iPr_def_19,complement(join(iPr_def_12,iPr_def_13))) = join(iPr_def_14,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_7623,c_255,c_6560]) ).
tcf(c_7668,plain,
join(complement(join(iPr_def_13,sK0)),complement(join(iPr_def_14,sK0))) = join(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_5987,c_235]) ).
tcf(c_7688,plain,
join(iPr_def_15,iPr_def_15) = join(iPr_def_15,iPr_def_16),
inference(light_normalisation,[status(thm)],[c_7668,c_7100]) ).
tcf(c_7703,plain,
complement(iPr_def_15) = sK0,
inference(demodulation,[status(thm)],[c_5988,c_6167]) ).
tcf(c_7787,plain,
complement(join(iPr_def_12,iPr_def_13)) = join(iPr_def_14,iPr_def_14),
inference(demodulation,[status(thm)],[c_7647,c_5911]) ).
tcf(c_7884,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_326]) ).
tcf(c_7943,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_7884,c_55]) ).
tcf(c_7980,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_7943,c_435]) ).
tcf(c_7982,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_7980,c_7943]) ).
tcf(c_7990,plain,
join(iPr_def_13,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3211,c_7982]) ).
tcf(c_7991,plain,
join(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3204,c_7982]) ).
tcf(c_7992,plain,
join(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3612,c_7982]) ).
tcf(c_7999,plain,
complement(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_5973,c_7991]) ).
tcf(c_8002,plain,
join(iPr_def_12,iPr_def_13) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_7990,c_50,c_49]) ).
tcf(c_8003,plain,
join(iPr_def_14,iPr_def_14) = complement(iPr_def_13),
inference(demodulation,[status(thm)],[c_7787,c_8002]) ).
tcf(c_8004,plain,
join(iPr_def_14,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_8003,c_119]) ).
tcf(c_8361,plain,
join(complement(iPr_def_12),complement(join(iPr_def_12,complement(iPr_def_12)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_7991,c_226]) ).
tcf(c_8376,plain,
join(iPr_def_11,complement(join(iPr_def_12,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8361,c_7999]) ).
tcf(c_8377,plain,
join(iPr_def_11,complement(join(iPr_def_11,iPr_def_12))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_8376,c_50,c_49]) ).
tcf(c_8378,plain,
join(iPr_def_11,iPr_def_14) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8377,c_255,c_265,c_7363]) ).
tcf(c_8402,plain,
join(sK0,converse(iPr_def_14)) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_8378,c_304]) ).
tcf(c_8409,plain,
join(sK0,converse(iPr_def_14)) = sK0,
inference(light_normalisation,[status(thm)],[c_8402,c_248]) ).
tcf(c_8500,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_14,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_8004,c_50]) ).
tcf(c_8783,plain,
join(iPr_def_14,sK1) = sK1,
inference(superposition,[status(thm)],[c_596,c_8500]) ).
tcf(c_8883,plain,
join(iPr_def_16,converse(iPr_def_14)) = converse(sK1),
inference(superposition,[status(thm)],[c_8783,c_317]) ).
tcf(c_8884,plain,
join(iPr_def_16,converse(iPr_def_14)) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_8883,c_251]) ).
tcf(c_8916,plain,
converse(iPr_def_19) = iPr_def_19,
inference(superposition,[status(thm)],[c_6284,c_5911]) ).
tcf(c_9562,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(iPr_def_18,X1),
inference(superposition,[status(thm)],[c_49,c_336]) ).
tcf(c_9570,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_10,complement(X0)))) = join(join(iPr_def_10,X0),sK1),
inference(superposition,[status(thm)],[c_223,c_336]) ).
tcf(c_9837,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_10,complement(X0)))) = join(iPr_def_10,join(X0,sK1)),
inference(theory_normalisation,[status(thm)],[c_9570,c_50,c_49]) ).
tcf(c_9838,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_10,complement(X0)))) = join(iPr_def_18,X0),
inference(light_normalisation,[status(thm)],[c_9837,c_2257]) ).
tcf(c_10080,plain,
! [X0: $i,X1: $i] : join(complement(iPr_def_18),complement(join(complement(X0),complement(join(X1,complement(join(complement(X0),X1))))))) = X0,
inference(superposition,[status(thm)],[c_342,c_75]) ).
tcf(c_10453,plain,
! [X0: $i,X1: $i] : join(iPr_def_19,complement(join(complement(X0),complement(join(X1,complement(join(complement(X0),X1))))))) = X0,
inference(light_normalisation,[status(thm)],[c_10080,c_255]) ).
tcf(c_10523,plain,
! [X0: $i] : join(sK0,join(converse(iPr_def_14),X0)) = join(sK0,X0),
inference(superposition,[status(thm)],[c_8409,c_50]) ).
tcf(c_11776,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_10,complement(X0)))) = join(join(sK1,complement(X0)),X0),
inference(superposition,[status(thm)],[c_239,c_9562]) ).
tcf(c_12084,plain,
! [X0: $i] : join(iPr_def_18,complement(join(iPr_def_10,complement(X0)))) = join(sK1,join(X0,complement(X0))),
inference(theory_normalisation,[status(thm)],[c_11776,c_50,c_49]) ).
tcf(c_12085,plain,
! [X0: $i] : join(iPr_def_18,X0) = join(sK1,iPr_def_18),
inference(light_normalisation,[status(thm)],[c_12084,c_262,c_9838]) ).
tcf(c_12086,plain,
! [X0: $i] : join(iPr_def_18,X0) = join(iPr_def_18,sK1),
inference(theory_normalisation,[status(thm)],[c_12085,c_50,c_49]) ).
tcf(c_12087,plain,
! [X0: $i] : join(iPr_def_18,X0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_12086,c_6763]) ).
tcf(c_12136,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_17,X0)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_340,c_12087]) ).
tcf(c_12139,plain,
! [X0: $i] : join(X0,iPr_def_18) = iPr_def_18,
inference(demodulation,[status(thm)],[c_1985,c_12136]) ).
tcf(c_12159,plain,
join(sK0,complement(converse(iPr_def_14))) = join(sK0,iPr_def_18),
inference(superposition,[status(thm)],[c_262,c_10523]) ).
tcf(c_12175,plain,
join(sK0,complement(converse(iPr_def_14))) = join(iPr_def_18,sK0),
inference(theory_normalisation,[status(thm)],[c_12159,c_50,c_49]) ).
tcf(c_13270,plain,
! [X0: $i,X1: $i] : complement(join(complement(X0),complement(join(X1,complement(join(complement(X0),X1)))))) = X0,
inference(demodulation,[status(thm)],[c_10453,c_5911]) ).
tcf(c_13321,plain,
! [X0: $i] : complement(join(complement(X0),complement(join(iPr_def_18,complement(iPr_def_18))))) = X0,
inference(superposition,[status(thm)],[c_12139,c_13270]) ).
tcf(c_13391,plain,
! [X0: $i] : complement(join(complement(X0),complement(join(iPr_def_18,iPr_def_19)))) = X0,
inference(light_normalisation,[status(thm)],[c_13321,c_255]) ).
tcf(c_13479,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_13391,c_255,c_6167,c_12087]) ).
tcf(c_14271,plain,
join(iPr_def_15,iPr_def_16) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_7688,c_7992]) ).
tcf(c_14273,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_16,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_14271,c_50]) ).
tcf(c_14301,plain,
join(iPr_def_15,converse(iPr_def_14)) = join(iPr_def_15,iPr_def_16),
inference(superposition,[status(thm)],[c_8884,c_14273]) ).
tcf(c_14315,plain,
join(iPr_def_15,converse(iPr_def_14)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_14301,c_14271]) ).
tcf(c_14688,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(X0,X1)),join(X2,complement(join(X0,complement(X1))))) = join(X2,complement(X0)),
inference(superposition,[status(thm)],[c_13479,c_415]) ).
tcf(c_14797,plain,
! [X0: $i,X1: $i] : join(X0,complement(complement(X1))) = join(X0,X1),
inference(demodulation,[status(thm)],[c_415,c_14688]) ).
tcf(c_17329,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,iPr_def_18)),complement(join(complement(X1),complement(join(X0,complement(complement(X1))))))) = X1,
inference(superposition,[status(thm)],[c_262,c_432]) ).
tcf(c_17723,plain,
! [X0: $i,X1: $i] : join(iPr_def_19,complement(join(complement(X0),complement(join(X1,X0))))) = X0,
inference(light_normalisation,[status(thm)],[c_17329,c_255,c_12139,c_14797]) ).
tcf(c_18346,plain,
! [X0: $i,X1: $i] : complement(join(complement(X0),complement(join(X1,X0)))) = X0,
inference(demodulation,[status(thm)],[c_17723,c_5911]) ).
tcf(c_18492,plain,
complement(join(complement(converse(iPr_def_14)),complement(iPr_def_15))) = converse(iPr_def_14),
inference(superposition,[status(thm)],[c_14315,c_18346]) ).
tcf(c_18568,plain,
complement(join(complement(iPr_def_15),complement(converse(iPr_def_14)))) = converse(iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_18492,c_50,c_49]) ).
tcf(c_18569,plain,
complement(join(iPr_def_18,sK0)) = converse(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_18568,c_7703,c_12175]) ).
tcf(c_20228,plain,
converse(iPr_def_14) = iPr_def_19,
inference(demodulation,[status(thm)],[c_18569,c_255,c_12087]) ).
tcf(c_20272,plain,
converse(iPr_def_19) = iPr_def_14,
inference(superposition,[status(thm)],[c_20228,c_55]) ).
tcf(c_20300,plain,
iPr_def_14 = iPr_def_19,
inference(demodulation,[status(thm)],[c_8916,c_20272]) ).
tcf(c_20301,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20300,c_214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL007+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:11:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 10.81/2.74 % SZS status Started for theBenchmark.p
% 10.81/2.74 % SZS status Theorem for theBenchmark.p
% 10.81/2.74
% 10.81/2.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.81/2.74
% 10.81/2.74 % ------ iProver source info
% 10.81/2.74
% 10.81/2.74 % git: date: 2026-07-19 20:42:38 +0200
% 10.81/2.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.81/2.74 % git: non_committed_changes: false
% 10.81/2.74
% 10.81/2.74 % ------ Parsing...
% 10.81/2.74 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 10.81/2.74 %
% 10.81/2.74
% 10.81/2.74 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.81/2.74
% 10.81/2.74 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 10.81/2.74 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.81/2.74
% 10.81/2.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.81/2.74 % ------ Proving...
% 10.81/2.74 % ------ Problem Properties
% 10.81/2.74
% 10.81/2.74 %
% 10.81/2.74 % clauses 24
% 10.81/2.74 % conjectures 2
% 10.81/2.74 % EPR 2
% 10.81/2.74 % Horn 24
% 10.81/2.74 % unary 24
% 10.81/2.74 % binary 0
% 10.81/2.74 % lits 24
% 10.81/2.74 % lits eq 24
% 10.81/2.74 % fd_pure 0
% 10.81/2.74 % fd_pseudo 0
% 10.81/2.74 % fd_cond 0
% 10.81/2.74 % fd_pseudo_cond 0
% 10.81/2.74 % AC symbols 1
% 10.81/2.74
% 10.81/2.74 % ------ Schedule UEQ
% 10.81/2.74
% 10.81/2.74 % ------ Option_UEQ Time Limit: 10.
% 10.81/2.74
% 10.81/2.74
% 10.81/2.74 % ------
% 10.81/2.74 % Current options:
% 10.81/2.74 % ------
% 10.81/2.74
% 10.81/2.74
% 10.81/2.74 %
% 10.81/2.74
% 10.81/2.74 % ------ Proving...
% 10.81/2.74 %
% 10.81/2.74
% 10.81/2.74 % SZS status Theorem for theBenchmark.p
% 10.81/2.74
% 10.81/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.81/2.75
% 10.81/2.75
%------------------------------------------------------------------------------