%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL027+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 : n013.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 02:36:54 PM UTC 2026
% Result : Theorem 115.32s 26.01s
% Output : CNFRefutation 115.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 25
% Syntax : Number of formulae : 309 ( 305 unt; 11 def)
% Number of atoms : 874 ( 312 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 12 ( 8 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 11 ( 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn 210 !; 1 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f14,conjecture,
! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] :
( join(X0,one) = one
=> meet(complement(composition(X0,top)),one) = meet(complement(X0),one) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] :
( join(X0,one) = one
& meet(complement(composition(X0,top)),one) != meet(complement(X0),one) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( one = join(sK0,one)
& meet(complement(composition(sK0,top)),one) != meet(complement(sK0),one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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(f24,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
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,
one = join(sK0,one),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
meet(complement(composition(sK0,top)),one) != meet(complement(sK0),one),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
fof(f34,plain,
complement(join(complement(complement(composition(sK0,top))),complement(one))) != complement(join(complement(complement(sK0)),complement(one))),
inference(definition_unfolding,[],[f32,f21,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_54,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f24]) ).
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(complement(composition(sK0,top))),complement(one))) != complement(join(complement(complement(sK0)),complement(one))),
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,negated_conjecture,
join(sK0,one) = one,
inference(cnf_transformation,[],[f31]) ).
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(one),complement(complement(composition(sK0,top))))) != complement(join(complement(one),complement(complement(sK0)))),
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
tcf(c_78,negated_conjecture,
join(one,sK0) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_109,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_116,definition,
iPr_def_10 = join(one,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_117,definition,
iPr_def_11 = complement(one),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_118,definition,
iPr_def_12 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_119,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_120,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_121,definition,
iPr_def_15 = join(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_122,definition,
iPr_def_16 = complement(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_123,definition,
iPr_def_17 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_124,definition,
iPr_def_18 = complement(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_125,definition,
iPr_def_19 = join(iPr_def_11,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_126,definition,
iPr_def_20 = complement(iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_127,negated_conjecture,
iPr_def_10 = one,
inference(demodulation,[status(thm)],[c_78,c_116]) ).
tcf(c_128,negated_conjecture,
iPr_def_16 != iPr_def_20,
inference(demodulation,[status(thm)],[c_77,c_123,c_124,c_125,c_126,c_118,c_119,c_120,c_117,c_121,c_122]) ).
tcf(c_217,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_218,plain,
complement(iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_117,c_127]) ).
tcf(c_232,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_218,c_75]) ).
tcf(c_234,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_109,c_75]) ).
tcf(c_245,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_234,c_50,c_49]) ).
tcf(c_255,plain,
! [X0: $i] : composition(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_53,c_127]) ).
tcf(c_256,plain,
join(iPr_def_10,sK0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_116,c_127]) ).
tcf(c_268,plain,
! [X0: $i] : join(complement(join(complement(join(iPr_def_11,X0)),join(iPr_def_11,complement(X0)))),complement(iPr_def_10)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_232,c_75]) ).
tcf(c_269,plain,
! [X0: $i] : join(complement(iPr_def_10),complement(join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0))))))) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_232,c_75]) ).
tcf(c_278,plain,
! [X0: $i] : join(complement(iPr_def_10),complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0)))))) = join(iPr_def_11,X0),
inference(theory_normalisation,[status(thm)],[c_268,c_50,c_49]) ).
tcf(c_279,plain,
! [X0: $i] : join(iPr_def_11,complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0)))))) = join(iPr_def_11,X0),
inference(light_normalisation,[status(thm)],[c_278,c_218]) ).
tcf(c_280,plain,
! [X0: $i] : join(iPr_def_11,complement(join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0))))))) = join(iPr_def_11,X0),
inference(light_normalisation,[status(thm)],[c_269,c_218]) ).
tcf(c_321,plain,
! [X0: $i] : join(iPr_def_11,complement(join(complement(join(iPr_def_11,join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0))))))),complement(complement(join(iPr_def_11,X0)))))) = join(iPr_def_11,join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0)))))),
inference(superposition,[status(thm)],[c_280,c_280]) ).
tcf(c_333,plain,
! [X0: $i] : join(iPr_def_11,complement(join(complement(complement(join(iPr_def_11,X0))),complement(join(iPr_def_11,join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0)))))))))) = join(iPr_def_11,join(complement(join(iPr_def_11,X0)),complement(complement(join(iPr_def_11,complement(X0)))))),
inference(theory_normalisation,[status(thm)],[c_321,c_50,c_49]) ).
tcf(c_370,plain,
! [X0: $i] : join(complement(iPr_def_10),composition(converse(X0),complement(X0))) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_255,c_76]) ).
tcf(c_372,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(X0))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_370,c_218]) ).
tcf(c_375,plain,
join(sK0,iPr_def_17) = top,
inference(superposition,[status(thm)],[c_123,c_59]) ).
tcf(c_376,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_109,c_59]) ).
tcf(c_382,plain,
join(iPr_def_10,iPr_def_11) = top,
inference(superposition,[status(thm)],[c_218,c_59]) ).
tcf(c_383,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_75]) ).
tcf(c_389,plain,
join(complement(join(iPr_def_11,iPr_def_11)),complement(top)) = iPr_def_10,
inference(superposition,[status(thm)],[c_59,c_232]) ).
tcf(c_390,plain,
join(iPr_def_17,sK0) = top,
inference(theory_normalisation,[status(thm)],[c_375,c_50,c_49]) ).
tcf(c_391,plain,
join(complement(top),complement(join(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_389,c_50,c_49]) ).
tcf(c_392,plain,
join(zero,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_391,c_109]) ).
tcf(c_394,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_383,c_50,c_49]) ).
tcf(c_395,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_394,c_109]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_431,plain,
join(iPr_def_11,composition(converse(iPr_def_10),iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_218,c_372]) ).
tcf(c_438,plain,
join(complement(iPr_def_11),complement(join(iPr_def_11,complement(composition(converse(iPr_def_10),iPr_def_11))))) = iPr_def_10,
inference(superposition,[status(thm)],[c_431,c_232]) ).
tcf(c_494,plain,
! [X0: $i] : join(iPr_def_10,join(X0,sK0)) = join(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_256,c_217]) ).
tcf(c_499,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_11)) = join(X0,top),
inference(superposition,[status(thm)],[c_382,c_217]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] : join(iPr_def_11,join(X0,complement(join(iPr_def_11,join(complement(X1),complement(join(iPr_def_11,X1))))))) = join(X0,join(iPr_def_11,X1)),
inference(superposition,[status(thm)],[c_279,c_217]) ).
tcf(c_529,plain,
! [X0: $i] : join(iPr_def_10,join(sK0,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_256,c_50]) ).
tcf(c_534,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_382,c_50]) ).
tcf(c_538,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_376,c_50]) ).
tcf(c_547,plain,
! [X0: $i] : join(iPr_def_11,join(composition(converse(iPr_def_10),iPr_def_11),X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_431,c_50]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] : composition(X0,composition(iPr_def_10,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_255,c_52]) ).
tcf(c_580,plain,
! [X0: $i] : join(iPr_def_17,join(sK0,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_390,c_50]) ).
tcf(c_595,plain,
join(iPr_def_10,top) = join(iPr_def_17,iPr_def_10),
inference(superposition,[status(thm)],[c_390,c_494]) ).
tcf(c_601,plain,
join(iPr_def_10,top) = join(iPr_def_10,iPr_def_17),
inference(theory_normalisation,[status(thm)],[c_595,c_50,c_49]) ).
tcf(c_749,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(X0,top),
inference(superposition,[status(thm)],[c_49,c_499]) ).
tcf(c_757,plain,
join(sK0,top) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_499,c_529]) ).
tcf(c_758,plain,
join(sK0,top) = top,
inference(light_normalisation,[status(thm)],[c_757,c_382]) ).
tcf(c_771,plain,
join(top,complement(iPr_def_11)) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_59,c_534]) ).
tcf(c_799,plain,
join(top,complement(iPr_def_11)) = join(iPr_def_10,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_771,c_601]) ).
tcf(c_1313,plain,
join(iPr_def_11,complement(composition(converse(iPr_def_10),iPr_def_11))) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_59,c_547]) ).
tcf(c_1383,plain,
join(complement(iPr_def_11),complement(join(iPr_def_11,top))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_438,c_1313]) ).
tcf(c_1386,plain,
join(complement(join(complement(iPr_def_11),join(iPr_def_11,top))),complement(iPr_def_10)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1383,c_75]) ).
tcf(c_1387,plain,
join(complement(iPr_def_10),complement(join(complement(iPr_def_11),complement(complement(join(iPr_def_11,top)))))) = iPr_def_11,
inference(superposition,[status(thm)],[c_1383,c_75]) ).
tcf(c_1389,plain,
join(complement(iPr_def_10),complement(join(iPr_def_11,join(top,complement(iPr_def_11))))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1386,c_50,c_49]) ).
tcf(c_1390,plain,
join(iPr_def_11,complement(join(iPr_def_11,join(iPr_def_10,iPr_def_17)))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1389,c_218,c_799]) ).
tcf(c_1391,plain,
join(iPr_def_11,complement(join(iPr_def_10,join(iPr_def_11,iPr_def_17)))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1390,c_50,c_49]) ).
tcf(c_1392,plain,
join(iPr_def_11,complement(join(complement(iPr_def_11),complement(complement(join(iPr_def_11,top)))))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1387,c_218]) ).
tcf(c_1519,plain,
join(iPr_def_11,complement(join(iPr_def_17,top))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1391,c_749]) ).
tcf(c_1523,plain,
join(top,complement(join(iPr_def_17,top))) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1519,c_534]) ).
tcf(c_1531,plain,
join(top,complement(join(iPr_def_17,top))) = top,
inference(light_normalisation,[status(thm)],[c_1523,c_382]) ).
tcf(c_1709,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_538]) ).
tcf(c_1712,plain,
join(top,complement(join(iPr_def_11,iPr_def_11))) = join(top,iPr_def_10),
inference(superposition,[status(thm)],[c_392,c_538]) ).
tcf(c_1729,plain,
join(top,complement(join(iPr_def_11,iPr_def_11))) = join(iPr_def_10,top),
inference(theory_normalisation,[status(thm)],[c_1712,c_50,c_49]) ).
tcf(c_1730,plain,
join(top,complement(join(iPr_def_11,iPr_def_11))) = join(iPr_def_10,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_1729,c_601]) ).
tcf(c_2516,plain,
join(top,top) = join(iPr_def_17,top),
inference(superposition,[status(thm)],[c_758,c_580]) ).
tcf(c_2532,plain,
join(top,complement(zero)) = join(iPr_def_17,top),
inference(demodulation,[status(thm)],[c_1709,c_2516]) ).
tcf(c_3820,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_245]) ).
tcf(c_3821,plain,
join(complement(join(top,complement(join(iPr_def_11,iPr_def_11)))),complement(iPr_def_10)) = join(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_392,c_245]) ).
tcf(c_3843,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_3820,c_50,c_49]) ).
tcf(c_3844,plain,
join(zero,complement(join(iPr_def_17,top))) = zero,
inference(light_normalisation,[status(thm)],[c_3843,c_109,c_2532]) ).
tcf(c_3874,plain,
join(complement(iPr_def_10),complement(join(top,complement(join(iPr_def_11,iPr_def_11))))) = join(iPr_def_11,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_3821,c_50,c_49]) ).
tcf(c_3875,plain,
join(iPr_def_11,complement(join(iPr_def_10,iPr_def_17))) = join(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_3874,c_218,c_1730]) ).
tcf(c_4283,plain,
join(complement(join(top,complement(join(iPr_def_17,top)))),complement(zero)) = join(iPr_def_17,top),
inference(superposition,[status(thm)],[c_3844,c_245]) ).
tcf(c_4290,plain,
join(complement(zero),complement(join(top,complement(join(iPr_def_17,top))))) = join(iPr_def_17,top),
inference(theory_normalisation,[status(thm)],[c_4283,c_50,c_49]) ).
tcf(c_4291,plain,
join(complement(zero),zero) = join(iPr_def_17,top),
inference(light_normalisation,[status(thm)],[c_4290,c_109,c_1531]) ).
tcf(c_4292,plain,
join(zero,complement(zero)) = join(iPr_def_17,top),
inference(theory_normalisation,[status(thm)],[c_4291,c_50,c_49]) ).
tcf(c_5082,plain,
join(iPr_def_17,top) = top,
inference(demodulation,[status(thm)],[c_4292,c_59]) ).
tcf(c_5083,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_3844,c_5082]) ).
tcf(c_5091,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_5083,c_109]) ).
tcf(c_5102,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_5091,c_50]) ).
tcf(c_11107,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_395,c_5102]) ).
tcf(c_11131,plain,
complement(join(iPr_def_11,iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_392,c_11107]) ).
tcf(c_11248,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_11107,c_59]) ).
tcf(c_11481,plain,
join(join(iPr_def_11,iPr_def_11),iPr_def_10) = top,
inference(superposition,[status(thm)],[c_11131,c_59]) ).
tcf(c_11505,plain,
join(iPr_def_10,join(iPr_def_11,iPr_def_11)) = top,
inference(theory_normalisation,[status(thm)],[c_11481,c_50,c_49]) ).
tcf(c_12073,plain,
join(iPr_def_11,top) = top,
inference(demodulation,[status(thm)],[c_11505,c_749]) ).
tcf(c_12080,plain,
join(iPr_def_11,complement(join(complement(iPr_def_11),complement(complement(top))))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1392,c_12073]) ).
tcf(c_12087,plain,
join(iPr_def_11,complement(join(complement(iPr_def_11),top))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_12080,c_109,c_11248]) ).
tcf(c_12088,plain,
join(iPr_def_11,complement(join(top,complement(iPr_def_11)))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_12087,c_50,c_49]) ).
tcf(c_12089,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_12088,c_799,c_3875]) ).
tcf(c_13928,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_12089,c_50]) ).
tcf(c_14573,plain,
! [X0: $i] : join(complement(join(iPr_def_11,X0)),complement(join(iPr_def_11,complement(join(iPr_def_11,X0))))) = iPr_def_10,
inference(superposition,[status(thm)],[c_13928,c_232]) ).
tcf(c_23988,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_255,c_420]) ).
tcf(c_24021,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = X0,
inference(light_normalisation,[status(thm)],[c_23988,c_55]) ).
tcf(c_24044,plain,
! [X0: $i] : join(complement(X0),complement(composition(iPr_def_10,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_24021,c_76]) ).
tcf(c_24054,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = composition(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_24021,c_554]) ).
tcf(c_24060,plain,
! [X0: $i] : composition(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_24054,c_24021]) ).
tcf(c_59900,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_24044,c_24060]) ).
tcf(c_59937,plain,
! [X0: $i] : join(complement(join(complement(X0),X0)),complement(complement(X0))) = X0,
inference(superposition,[status(thm)],[c_59900,c_75]) ).
tcf(c_59942,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(X1,complement(X0))) = join(X1,complement(X0)),
inference(superposition,[status(thm)],[c_59900,c_217]) ).
tcf(c_59946,plain,
! [X0: $i] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_59937,c_50,c_49]) ).
tcf(c_59947,plain,
! [X0: $i] : join(complement(complement(X0)),zero) = X0,
inference(light_normalisation,[status(thm)],[c_59946,c_59,c_109]) ).
tcf(c_59948,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(theory_normalisation,[status(thm)],[c_59947,c_50,c_49]) ).
tcf(c_60009,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_59948,c_11107]) ).
tcf(c_60193,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_60009,c_59900]) ).
tcf(c_60314,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_60193,c_50]) ).
tcf(c_60319,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,X0)) = join(X1,X0),
inference(superposition,[status(thm)],[c_60193,c_217]) ).
tcf(c_60364,plain,
! [X0: $i] : join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0)))) = join(iPr_def_11,complement(join(iPr_def_11,X0))),
inference(demodulation,[status(thm)],[c_333,c_49,c_50,c_217,c_500,c_60009,c_60314,c_60319]) ).
tcf(c_60418,plain,
! [X0: $i] : join(iPr_def_11,join(join(complement(X0),complement(join(iPr_def_11,X0))),complement(join(iPr_def_11,complement(join(iPr_def_11,X0)))))) = top,
inference(superposition,[status(thm)],[c_60364,c_548]) ).
tcf(c_60488,plain,
! [X0: $i] : join(iPr_def_11,join(complement(X0),join(complement(join(iPr_def_11,X0)),complement(join(iPr_def_11,complement(join(iPr_def_11,X0))))))) = top,
inference(theory_normalisation,[status(thm)],[c_60418,c_50,c_49]) ).
tcf(c_60489,plain,
! [X0: $i] : join(iPr_def_11,join(complement(X0),iPr_def_10)) = top,
inference(light_normalisation,[status(thm)],[c_60488,c_14573]) ).
tcf(c_60490,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,complement(X0))) = top,
inference(theory_normalisation,[status(thm)],[c_60489,c_50,c_49]) ).
tcf(c_118023,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_118024,plain,
! [X0: $i] : join(zero,join(X0,zero)) = join(X0,zero),
inference(superposition,[status(thm)],[c_109,c_59942]) ).
tcf(c_118027,plain,
complement(iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_117,c_127]) ).
tcf(c_118028,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_11)) = join(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_118027,c_59942]) ).
tcf(c_118036,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_118027,c_75]) ).
tcf(c_118038,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_10)),complement(join(complement(X0),iPr_def_11))) = X0,
inference(superposition,[status(thm)],[c_118027,c_75]) ).
tcf(c_118043,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_118038,c_50,c_49]) ).
tcf(c_118047,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_119,c_75]) ).
tcf(c_118055,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_13)),complement(join(complement(X0),iPr_def_14))) = X0,
inference(superposition,[status(thm)],[c_120,c_75]) ).
tcf(c_118057,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_118055,c_50,c_49]) ).
tcf(c_118058,plain,
! [X0: $i] : join(complement(join(iPr_def_16,X0)),complement(join(iPr_def_16,complement(X0)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_122,c_75]) ).
tcf(c_118059,plain,
! [X0: $i] : join(iPr_def_16,join(X0,iPr_def_16)) = join(X0,iPr_def_16),
inference(superposition,[status(thm)],[c_122,c_59942]) ).
tcf(c_118074,plain,
! [X0: $i] : join(complement(join(iPr_def_20,X0)),complement(join(iPr_def_20,complement(X0)))) = iPr_def_19,
inference(superposition,[status(thm)],[c_126,c_75]) ).
tcf(c_118075,plain,
! [X0: $i] : join(iPr_def_20,join(X0,iPr_def_20)) = join(X0,iPr_def_20),
inference(superposition,[status(thm)],[c_126,c_59942]) ).
tcf(c_118079,plain,
! [X0: $i] : composition(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_53,c_127]) ).
tcf(c_118090,plain,
! [X0: $i] : join(complement(join(complement(join(iPr_def_11,X0)),join(iPr_def_11,complement(X0)))),complement(iPr_def_10)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_118036,c_75]) ).
tcf(c_118100,plain,
! [X0: $i] : join(complement(iPr_def_10),complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0)))))) = join(iPr_def_11,X0),
inference(theory_normalisation,[status(thm)],[c_118090,c_50,c_49]) ).
tcf(c_118101,plain,
! [X0: $i] : join(iPr_def_11,complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0)))))) = join(iPr_def_11,X0),
inference(light_normalisation,[status(thm)],[c_118100,c_118027]) ).
tcf(c_118113,plain,
! [X0: $i] : join(complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0))))),join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_118101,c_59942]) ).
tcf(c_118117,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = top,
inference(superposition,[status(thm)],[c_118101,c_60490]) ).
tcf(c_118119,plain,
! [X0: $i] : join(X0,join(iPr_def_11,complement(join(iPr_def_11,join(complement(X0),complement(join(iPr_def_11,X0))))))) = join(iPr_def_11,X0),
inference(theory_normalisation,[status(thm)],[c_118113,c_50,c_49]) ).
tcf(c_118120,plain,
! [X0: $i] : join(X0,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(light_normalisation,[status(thm)],[c_118119,c_118101]) ).
tcf(c_118157,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_11)) = top,
inference(superposition,[status(thm)],[c_118028,c_118117]) ).
tcf(c_118170,plain,
join(iPr_def_11,iPr_def_10) = top,
inference(superposition,[status(thm)],[c_118120,c_118117]) ).
tcf(c_118171,plain,
join(iPr_def_10,iPr_def_11) = top,
inference(theory_normalisation,[status(thm)],[c_118170,c_50,c_49]) ).
tcf(c_118190,plain,
! [X0: $i] : join(complement(iPr_def_10),composition(converse(X0),complement(X0))) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_118079,c_76]) ).
tcf(c_118192,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(X0))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_118190,c_118027]) ).
tcf(c_118194,plain,
join(iPr_def_10,sK0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_116,c_127]) ).
tcf(c_118362,plain,
! [X0: $i] : join(X0,join(iPr_def_10,iPr_def_11)) = top,
inference(superposition,[status(thm)],[c_118023,c_118157]) ).
tcf(c_118367,plain,
! [X0: $i] : join(X0,top) = top,
inference(light_normalisation,[status(thm)],[c_118362,c_118171]) ).
tcf(c_118374,plain,
join(iPr_def_13,iPr_def_14) = top,
inference(superposition,[status(thm)],[c_120,c_59]) ).
tcf(c_118425,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_49,c_118028]) ).
tcf(c_118426,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_49,c_118024]) ).
tcf(c_118429,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_118430,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_118436,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_118440,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_49,c_118367]) ).
tcf(c_118445,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(top)))) = X0,
inference(superposition,[status(thm)],[c_118367,c_75]) ).
tcf(c_118452,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),zero))) = X0,
inference(light_normalisation,[status(thm)],[c_118445,c_109]) ).
tcf(c_118453,plain,
! [X0: $i] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_118452,c_50,c_49]) ).
tcf(c_118541,plain,
join(iPr_def_11,iPr_def_19) = iPr_def_19,
inference(superposition,[status(thm)],[c_125,c_118425]) ).
tcf(c_118545,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_118192,c_118425]) ).
tcf(c_118570,plain,
join(complement(iPr_def_11),complement(join(iPr_def_11,complement(iPr_def_11)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_118545,c_118036]) ).
tcf(c_118720,plain,
! [X0: $i,X1: $i] : composition(X0,composition(iPr_def_10,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_118079,c_52]) ).
tcf(c_118857,plain,
join(zero,complement(iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_118570,c_49,c_59,c_109]) ).
tcf(c_118984,plain,
join(complement(iPr_def_19),complement(join(iPr_def_11,complement(iPr_def_19)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_118541,c_118036]) ).
tcf(c_118985,plain,
join(iPr_def_20,complement(join(iPr_def_11,iPr_def_20))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_118984,c_126]) ).
tcf(c_119767,plain,
join(complement(join(iPr_def_10,iPr_def_18)),complement(join(iPr_def_11,iPr_def_18))) = iPr_def_17,
inference(superposition,[status(thm)],[c_124,c_118043]) ).
tcf(c_119785,plain,
join(complement(join(iPr_def_10,iPr_def_18)),iPr_def_20) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_119767,c_125,c_126]) ).
tcf(c_119786,plain,
join(iPr_def_20,complement(join(iPr_def_10,iPr_def_18))) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_119785,c_50,c_49]) ).
tcf(c_120512,plain,
join(complement(top),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_118374,c_118047]) ).
tcf(c_120545,plain,
join(zero,complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_120512,c_109]) ).
tcf(c_121362,plain,
join(complement(join(iPr_def_13,complement(iPr_def_14))),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_59,c_118057]) ).
tcf(c_121382,plain,
join(complement(top),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_121362,c_50,c_49]) ).
tcf(c_121383,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_121382,c_109,c_120545]) ).
tcf(c_121417,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_121,c_121383]) ).
tcf(c_121690,plain,
join(complement(join(iPr_def_16,iPr_def_16)),complement(top)) = iPr_def_15,
inference(superposition,[status(thm)],[c_59,c_118058]) ).
tcf(c_121714,plain,
join(complement(top),complement(join(iPr_def_16,iPr_def_16))) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_121690,c_50,c_49]) ).
tcf(c_121715,plain,
join(zero,complement(join(iPr_def_16,iPr_def_16))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_121714,c_109]) ).
tcf(c_121771,plain,
join(zero,complement(join(zero,iPr_def_17))) = sK0,
inference(superposition,[status(thm)],[c_123,c_118453]) ).
tcf(c_121783,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_118453,c_118426]) ).
tcf(c_121799,plain,
join(zero,complement(join(iPr_def_17,zero))) = sK0,
inference(theory_normalisation,[status(thm)],[c_121771,c_50,c_49]) ).
tcf(c_121816,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_118453,c_121783]) ).
tcf(c_121818,plain,
complement(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_118857,c_121783]) ).
tcf(c_121822,plain,
complement(join(iPr_def_16,iPr_def_16)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_121715,c_121783]) ).
tcf(c_121902,plain,
join(iPr_def_11,composition(converse(iPr_def_11),iPr_def_10)) = iPr_def_11,
inference(superposition,[status(thm)],[c_121818,c_118192]) ).
tcf(c_122185,plain,
complement(join(iPr_def_17,zero)) = sK0,
inference(demodulation,[status(thm)],[c_121799,c_121783]) ).
tcf(c_122396,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_121783,c_49]) ).
tcf(c_122402,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_121783,c_59942]) ).
tcf(c_122419,plain,
join(iPr_def_16,iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_121783,c_118059]) ).
tcf(c_122432,plain,
complement(iPr_def_17) = sK0,
inference(demodulation,[status(thm)],[c_122185,c_122396]) ).
tcf(c_122434,plain,
sK0 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_122432,c_124]) ).
tcf(c_122444,plain,
composition(iPr_def_18,top) = iPr_def_12,
inference(demodulation,[status(thm)],[c_118,c_122434]) ).
tcf(c_122445,plain,
join(iPr_def_10,iPr_def_18) = iPr_def_10,
inference(demodulation,[status(thm)],[c_118194,c_122434]) ).
tcf(c_122446,plain,
complement(iPr_def_18) = iPr_def_17,
inference(demodulation,[status(thm)],[c_123,c_122434]) ).
tcf(c_122449,plain,
join(iPr_def_20,complement(iPr_def_10)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_119786,c_122445]) ).
tcf(c_122450,plain,
join(iPr_def_20,iPr_def_11) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_122449,c_118027]) ).
tcf(c_122451,plain,
join(iPr_def_11,iPr_def_20) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_122450,c_50,c_49]) ).
tcf(c_122453,plain,
join(iPr_def_20,complement(iPr_def_17)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_118985,c_122451]) ).
tcf(c_122454,plain,
join(iPr_def_20,iPr_def_18) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_122453,c_124]) ).
tcf(c_122455,plain,
join(iPr_def_18,iPr_def_20) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_122454,c_50,c_49]) ).
tcf(c_123568,plain,
join(iPr_def_20,iPr_def_17) = iPr_def_17,
inference(superposition,[status(thm)],[c_122451,c_118075]) ).
tcf(c_123571,plain,
join(iPr_def_17,iPr_def_20) = iPr_def_17,
inference(theory_normalisation,[status(thm)],[c_123568,c_50,c_49]) ).
tcf(c_123661,plain,
join(complement(join(iPr_def_20,iPr_def_18)),complement(join(iPr_def_20,iPr_def_17))) = iPr_def_19,
inference(superposition,[status(thm)],[c_122446,c_118074]) ).
tcf(c_123688,plain,
join(complement(join(iPr_def_17,iPr_def_20)),complement(join(iPr_def_18,iPr_def_20))) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_123661,c_50,c_49]) ).
tcf(c_123689,plain,
join(iPr_def_18,iPr_def_11) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_123688,c_124,c_118027,c_122455,c_123571]) ).
tcf(c_123690,plain,
join(iPr_def_11,iPr_def_18) = iPr_def_19,
inference(theory_normalisation,[status(thm)],[c_123689,c_50,c_49]) ).
tcf(c_124340,plain,
complement(iPr_def_16) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_121822,c_122419]) ).
tcf(c_124391,plain,
join(iPr_def_11,converse(iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_121902,c_118079]) ).
tcf(c_125211,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_121816,c_121783]) ).
tcf(c_125268,plain,
complement(iPr_def_15) = iPr_def_16,
inference(superposition,[status(thm)],[c_124340,c_125211]) ).
tcf(c_130079,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_118429]) ).
tcf(c_130093,plain,
! [X0: $i,X1: $i] : join(iPr_def_11,composition(join(X0,converse(X1)),complement(join(converse(X0),X1)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_118429,c_118192]) ).
tcf(c_130163,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_130079,c_118440]) ).
tcf(c_130198,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_130163,c_57]) ).
tcf(c_130419,plain,
composition(top,converse(iPr_def_18)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_122444,c_130198]) ).
tcf(c_130771,plain,
join(converse(iPr_def_11),iPr_def_11) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_124391,c_118430]) ).
tcf(c_130804,plain,
join(iPr_def_11,converse(iPr_def_11)) = converse(iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_130771,c_50,c_49]) ).
tcf(c_130805,plain,
converse(iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_130804,c_124391]) ).
tcf(c_130854,plain,
! [X0: $i] : composition(iPr_def_11,converse(X0)) = converse(composition(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_130805,c_57]) ).
tcf(c_130855,plain,
! [X0: $i] : join(iPr_def_11,converse(X0)) = converse(join(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_130805,c_56]) ).
tcf(c_131074,plain,
join(iPr_def_11,converse(iPr_def_18)) = converse(iPr_def_19),
inference(superposition,[status(thm)],[c_123690,c_130855]) ).
tcf(c_131078,plain,
join(iPr_def_11,converse(iPr_def_12)) = converse(iPr_def_15),
inference(superposition,[status(thm)],[c_121417,c_130855]) ).
tcf(c_133549,plain,
! [X0: $i] : join(iPr_def_11,join(converse(iPr_def_18),X0)) = join(converse(iPr_def_19),X0),
inference(superposition,[status(thm)],[c_131074,c_50]) ).
tcf(c_134059,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_118079,c_118436]) ).
tcf(c_134114,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = X0,
inference(light_normalisation,[status(thm)],[c_134059,c_55]) ).
tcf(c_134139,plain,
converse(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_134114,c_118079]) ).
tcf(c_134150,plain,
! [X0: $i] : composition(converse(iPr_def_10),X0) = composition(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_134114,c_118720]) ).
tcf(c_134161,plain,
! [X0: $i] : composition(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_134150,c_134114]) ).
tcf(c_134189,plain,
! [X0: $i] : join(iPr_def_11,composition(join(iPr_def_10,converse(X0)),complement(join(iPr_def_10,X0)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_134139,c_130093]) ).
tcf(c_134194,plain,
! [X0: $i] : join(iPr_def_10,converse(X0)) = converse(join(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_134139,c_56]) ).
tcf(c_134225,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(iPr_def_10,X1),X0),
inference(superposition,[status(thm)],[c_134161,c_54]) ).
tcf(c_134315,plain,
join(iPr_def_10,converse(iPr_def_18)) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_122445,c_134194]) ).
tcf(c_134371,plain,
join(iPr_def_10,converse(iPr_def_18)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_134315,c_134139]) ).
tcf(c_135644,plain,
join(iPr_def_11,composition(join(iPr_def_10,converse(converse(iPr_def_18))),complement(iPr_def_10))) = iPr_def_11,
inference(superposition,[status(thm)],[c_134371,c_134189]) ).
tcf(c_135687,plain,
join(iPr_def_11,composition(join(iPr_def_10,converse(converse(iPr_def_18))),iPr_def_11)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_135644,c_118027]) ).
tcf(c_135840,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_125211,c_122402]) ).
tcf(c_135875,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_135840,c_50]) ).
tcf(c_136067,plain,
join(iPr_def_11,composition(iPr_def_18,iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_135687,c_55,c_134225,c_135875]) ).
tcf(c_136075,plain,
join(iPr_def_11,converse(composition(iPr_def_18,iPr_def_11))) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_136067,c_130855]) ).
tcf(c_136080,plain,
join(iPr_def_11,converse(composition(iPr_def_18,iPr_def_11))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_136075,c_130805]) ).
tcf(c_140663,plain,
join(iPr_def_11,composition(iPr_def_11,converse(iPr_def_18))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_136080,c_130854]) ).
tcf(c_140667,plain,
! [X0: $i] : join(iPr_def_11,join(composition(iPr_def_11,converse(iPr_def_18)),X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_140663,c_50]) ).
tcf(c_153064,plain,
! [X0: $i] : join(iPr_def_11,join(X0,converse(iPr_def_18))) = join(converse(iPr_def_19),X0),
inference(superposition,[status(thm)],[c_49,c_133549]) ).
tcf(c_153887,plain,
! [X0: $i] : join(X0,composition(iPr_def_11,X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_118171,c_134225]) ).
tcf(c_342753,plain,
join(converse(iPr_def_19),composition(iPr_def_11,converse(iPr_def_18))) = join(iPr_def_11,converse(iPr_def_18)),
inference(superposition,[status(thm)],[c_140667,c_153064]) ).
tcf(c_342904,plain,
join(converse(iPr_def_19),composition(iPr_def_11,converse(iPr_def_18))) = converse(iPr_def_19),
inference(light_normalisation,[status(thm)],[c_342753,c_131074]) ).
tcf(c_390812,plain,
join(converse(iPr_def_19),composition(iPr_def_11,converse(iPr_def_18))) = join(iPr_def_11,composition(top,converse(iPr_def_18))),
inference(superposition,[status(thm)],[c_153887,c_133549]) ).
tcf(c_391066,plain,
converse(iPr_def_15) = converse(iPr_def_19),
inference(light_normalisation,[status(thm)],[c_390812,c_131078,c_130419,c_342904]) ).
tcf(c_391260,plain,
converse(converse(iPr_def_15)) = iPr_def_19,
inference(superposition,[status(thm)],[c_391066,c_55]) ).
tcf(c_391421,plain,
iPr_def_15 = iPr_def_19,
inference(demodulation,[status(thm)],[c_391260,c_55]) ).
tcf(c_391632,plain,
complement(iPr_def_15) = iPr_def_20,
inference(demodulation,[status(thm)],[c_126,c_391421]) ).
tcf(c_391633,plain,
iPr_def_16 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_391632,c_125268]) ).
tcf(c_391634,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_391633,c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL027+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 07:21:23 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 115.32/26.01 % SZS status Started for theBenchmark.p
% 115.32/26.01 % SZS status Theorem for theBenchmark.p
% 115.32/26.01
% 115.32/26.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 115.32/26.01
% 115.32/26.01 % ------ iProver source info
% 115.32/26.01
% 115.32/26.01 % git: date: 2026-07-19 20:42:38 +0200
% 115.32/26.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 115.32/26.01 % git: non_committed_changes: false
% 115.32/26.01
% 115.32/26.01 % ------ Parsing...
% 115.32/26.01 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 115.32/26.01 %
% 115.32/26.01
% 115.32/26.01 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 115.32/26.01
% 115.32/26.01 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 115.32/26.01 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 115.32/26.01
% 115.32/26.01 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 115.32/26.01 % ------ Proving...
% 115.32/26.01 % ------ Problem Properties
% 115.32/26.01
% 115.32/26.01 %
% 115.32/26.01 % clauses 25
% 115.32/26.01 % conjectures 2
% 115.32/26.01 % EPR 2
% 115.32/26.01 % Horn 25
% 115.32/26.01 % unary 25
% 115.32/26.01 % binary 0
% 115.32/26.01 % lits 25
% 115.32/26.01 % lits eq 25
% 115.32/26.01 % fd_pure 0
% 115.32/26.01 % fd_pseudo 0
% 115.32/26.01 % fd_cond 0
% 115.32/26.01 % fd_pseudo_cond 0
% 115.32/26.01 % AC symbols 1
% 115.32/26.01
% 115.32/26.01 % ------ Schedule UEQ
% 115.32/26.01
% 115.32/26.01 % ------ Option_UEQ Time Limit: 10.
% 115.32/26.01
% 115.32/26.01
% 115.32/26.01 % ------
% 115.32/26.01 % Current options:
% 115.32/26.01 % ------
% 115.32/26.01
% 115.32/26.01
% 115.32/26.01 %
% 115.32/26.01
% 115.32/26.01 % ------ Proving...
% 115.32/26.01 % Proof_search_loop: time out after: 1982 full_loop iterations
% 115.32/26.01
% 115.32/26.01 % ------ Option_UEQ Time Limit: 15.
% 115.32/26.01
% 115.32/26.01
% 115.32/26.01 %
% 115.32/26.01
% 115.32/26.01 % ------ Proving...
% 115.32/26.01 %
% 115.32/26.01
% 115.32/26.01 % SZS status Theorem for theBenchmark.p
% 115.32/26.01
% 115.32/26.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 115.32/26.02
% 115.32/26.02
%------------------------------------------------------------------------------