%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL042-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:37:00 PM UTC 2026
% Result : Unsatisfiable 65.37s 9.32s
% Output : CNFRefutation 65.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 19
% Syntax : Number of formulae : 231 ( 231 unt; 4 def)
% Number of atoms : 408 ( 230 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 320 ( 0 sgn 320 !; 0 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
fof(f17,negated_conjecture,
! [X0] : meet(composition(sk1,X0),composition(sk1,complement(X0))) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
! [X0] : zero = meet(composition(sk1,X0),composition(sk1,complement(X0))),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
join(composition(converse(sk1),sk1),one) != one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
one != join(composition(converse(sk1),sk1),one),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f22,plain,
! [X0] : zero = complement(join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0))))),
inference(definition_unfolding,[],[f18,f6]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_75,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f21]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] : complement(join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0))))) = zero,
inference(cnf_transformation,[],[f22]) ).
tcf(c_77,negated_conjecture,
join(composition(converse(sk1),sk1),one) != one,
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,negated_conjecture,
join(one,composition(converse(sk1),sk1)) != one,
inference(theory_normalisation,[status(thm)],[c_77,c_65,c_64]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_66,c_65,c_64]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_73,c_65,c_64]) ).
tcf(c_124,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[c_75,c_74]) ).
tcf(c_131,definition,
iPr_def_10 = converse(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = composition(iPr_def_10,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = join(one,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,definition,
iPr_def_13 = complement(top),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_135,negated_conjecture,
iPr_def_12 != one,
inference(demodulation,[status(thm)],[c_91,c_131,c_132,c_133]) ).
tcf(c_136,negated_conjecture,
! [X0: $i] : complement(join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0))))) = zero,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_137,plain,
iPr_def_13 = zero,
inference(demodulation,[status(thm)],[c_124,c_134]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_140,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_143,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_145,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_147,c_148]) ).
tcf(c_226,plain,
! [X0: $i] : complement(join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0))))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_136,c_137]) ).
tcf(c_253,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0))))))) = composition(sk1,X0),
inference(superposition,[status(thm)],[c_226,c_139]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0)))) = join(complement(join(iPr_def_13,X1)),complement(join(iPr_def_13,complement(X1)))),
inference(superposition,[status(thm)],[c_226,c_139]) ).
tcf(c_264,plain,
! [X0: $i] : join(complement(join(iPr_def_13,X0)),complement(join(iPr_def_13,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_134,c_139]) ).
tcf(c_267,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),iPr_def_13))) = X0,
inference(superposition,[status(thm)],[c_134,c_139]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_139,c_139]) ).
tcf(c_271,plain,
! [X0: $i] : join(complement(join(iPr_def_13,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_267,c_148]) ).
tcf(c_274,plain,
! [X0: $i] : join(complement(composition(sk1,X0)),complement(composition(sk1,complement(X0)))) = top,
inference(demodulation,[status(thm)],[c_263,c_264]) ).
tcf(c_284,plain,
complement(top) = iPr_def_13,
inference(demodulation,[status(thm)],[c_226,c_274]) ).
tcf(c_293,plain,
join(top,iPr_def_13) = top,
inference(superposition,[status(thm)],[c_134,c_140]) ).
tcf(c_294,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_140,c_139]) ).
tcf(c_295,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_140,c_139]) ).
tcf(c_296,plain,
join(iPr_def_13,top) = top,
inference(demodulation,[status(thm)],[c_293,c_148]) ).
tcf(c_297,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_294,c_148,c_284]) ).
tcf(c_298,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(demodulation,[status(thm)],[c_295,c_284]) ).
tcf(c_311,plain,
converse(iPr_def_10) = sk1,
inference(superposition,[status(thm)],[c_131,c_143]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_143,c_138]) ).
tcf(c_318,plain,
! [X0: $i] : join(complement(one),composition(converse(X0),complement(X0))) = complement(one),
inference(superposition,[status(thm)],[c_145,c_138]) ).
tcf(c_322,plain,
join(iPr_def_11,one) = iPr_def_12,
inference(demodulation,[status(thm)],[c_133,c_148]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_148,c_139]) ).
tcf(c_328,plain,
! [X0: $i] : composition(iPr_def_10,converse(X0)) = converse(composition(X0,sk1)),
inference(superposition,[status(thm)],[c_131,c_141]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_143,c_141]) ).
tcf(c_341,plain,
! [X0: $i] : converse(join(sk1,X0)) = join(iPr_def_10,converse(X0)),
inference(superposition,[status(thm)],[c_131,c_142]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_145,c_146]) ).
tcf(c_384,plain,
! [X0: $i] : composition(iPr_def_10,composition(sk1,X0)) = composition(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_132,c_146]) ).
tcf(c_403,plain,
join(iPr_def_13,complement(join(iPr_def_13,iPr_def_13))) = top,
inference(superposition,[status(thm)],[c_284,c_297]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_140,c_147]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(X0),X1)),join(complement(join(complement(X0),complement(X1))),X2)) = join(X0,X2),
inference(superposition,[status(thm)],[c_139,c_147]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(X0),join(composition(converse(X1),complement(composition(X1,X0))),X2)) = join(complement(X0),X2),
inference(superposition,[status(thm)],[c_138,c_147]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] : join(iPr_def_13,join(complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0)))))),X1)) = join(composition(sk1,X0),X1),
inference(superposition,[status(thm)],[c_253,c_147]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c_147,c_140]) ).
tcf(c_498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : join(composition(X0,X1),join(X2,composition(X3,X1))) = join(X2,composition(join(X0,X3),X1)),
inference(superposition,[status(thm)],[c_144,c_223]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_140,c_223]) ).
tcf(c_501,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_139,c_223]) ).
tcf(c_509,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_223,c_139]) ).
tcf(c_528,plain,
join(complement(sk1),complement(composition(sk1,complement(one)))) = top,
inference(superposition,[status(thm)],[c_145,c_274]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] : join(complement(composition(sk1,X0)),join(complement(composition(sk1,complement(X0))),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_274,c_147]) ).
tcf(c_538,plain,
join(iPr_def_13,complement(join(iPr_def_13,complement(complement(iPr_def_13))))) = top,
inference(superposition,[status(thm)],[c_284,c_298]) ).
tcf(c_553,plain,
composition(iPr_def_10,converse(iPr_def_10)) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_132,c_328]) ).
tcf(c_560,plain,
converse(iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_553,c_132,c_311]) ).
tcf(c_575,plain,
! [X0: $i] : converse(join(iPr_def_11,X0)) = join(iPr_def_11,converse(X0)),
inference(superposition,[status(thm)],[c_560,c_142]) ).
tcf(c_829,plain,
! [X0: $i] : join(complement(composition(sk1,X0)),complement(join(iPr_def_13,complement(complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0)))))))))) = top,
inference(superposition,[status(thm)],[c_253,c_264]) ).
tcf(c_844,plain,
join(complement(join(iPr_def_13,join(iPr_def_13,iPr_def_13))),complement(top)) = top,
inference(superposition,[status(thm)],[c_403,c_264]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_13,X0)),join(complement(join(iPr_def_13,complement(X0))),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_264,c_147]) ).
tcf(c_852,plain,
! [X0: $i] : join(complement(top),complement(join(complement(join(iPr_def_13,X0)),complement(complement(join(iPr_def_13,complement(X0))))))) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_264,c_139]) ).
tcf(c_854,plain,
join(iPr_def_13,complement(join(iPr_def_13,join(iPr_def_13,iPr_def_13)))) = top,
inference(demodulation,[status(thm)],[c_844,c_148,c_284]) ).
tcf(c_863,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(join(iPr_def_13,X0)),complement(complement(join(iPr_def_13,complement(X0))))))) = join(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_852,c_284]) ).
tcf(c_903,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(X1,complement(X0))),complement(complement(join(complement(X0),complement(X1))))))) = join(X1,complement(X0)),
inference(superposition,[status(thm)],[c_148,c_270]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(complement(X0),X1)),complement(complement(join(complement(X1),complement(X0))))))) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_148,c_270]) ).
tcf(c_920,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(join(complement(X0),complement(X0))),complement(complement(top))))) = join(complement(X0),complement(X0)),
inference(superposition,[status(thm)],[c_140,c_270]) ).
tcf(c_932,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))),complement(complement(join(complement(X0),X1)))))) = join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1)))))),
inference(superposition,[status(thm)],[c_270,c_270]) ).
tcf(c_933,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))),complement(join(complement(X0),X1))) = X0,
inference(superposition,[status(thm)],[c_270,c_139]) ).
tcf(c_937,plain,
! [X0: $i] : join(complement(X0),complement(join(complement(iPr_def_13),complement(join(complement(X0),complement(X0)))))) = join(complement(X0),complement(X0)),
inference(demodulation,[status(thm)],[c_920,c_148,c_284]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1)))))))) = X0,
inference(demodulation,[status(thm)],[c_933,c_148]) ).
tcf(c_946,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(complement(join(complement(X0),X1))),complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1)))))))))) = join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1)))))),
inference(demodulation,[status(thm)],[c_932,c_148]) ).
tcf(c_988,plain,
join(complement(top),complement(join(top,complement(join(iPr_def_13,iPr_def_13))))) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_403,c_271]) ).
tcf(c_1002,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_13,complement(X0))),join(X1,complement(join(top,complement(X0))))) = join(X1,X0),
inference(superposition,[status(thm)],[c_271,c_223]) ).
tcf(c_1004,plain,
join(iPr_def_13,complement(join(top,complement(join(iPr_def_13,iPr_def_13))))) = join(iPr_def_13,iPr_def_13),
inference(demodulation,[status(thm)],[c_988,c_284]) ).
tcf(c_1032,plain,
join(complement(join(iPr_def_13,join(iPr_def_13,join(iPr_def_13,iPr_def_13)))),complement(top)) = top,
inference(superposition,[status(thm)],[c_854,c_264]) ).
tcf(c_1033,plain,
join(iPr_def_13,complement(join(iPr_def_13,join(iPr_def_13,join(iPr_def_13,iPr_def_13))))) = top,
inference(demodulation,[status(thm)],[c_1032,c_148,c_284]) ).
tcf(c_1616,plain,
join(iPr_def_11,converse(one)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_322,c_575]) ).
tcf(c_1657,plain,
! [X0: $i] : join(complement(one),composition(join(iPr_def_10,converse(X0)),complement(join(sk1,X0)))) = complement(one),
inference(superposition,[status(thm)],[c_341,c_318]) ).
tcf(c_1717,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),complement(join(complement(X0),complement(X1)))) = X1,
inference(superposition,[status(thm)],[c_148,c_325]) ).
tcf(c_1740,plain,
! [X0: $i] : join(complement(join(complement(complement(X0)),X0)),complement(top)) = complement(X0),
inference(superposition,[status(thm)],[c_140,c_325]) ).
tcf(c_1741,plain,
! [X0: $i] : join(complement(join(complement(composition(sk1,complement(X0))),composition(sk1,X0))),complement(top)) = composition(sk1,complement(X0)),
inference(superposition,[status(thm)],[c_274,c_325]) ).
tcf(c_1746,plain,
! [X0: $i] : join(complement(join(complement(join(iPr_def_13,complement(X0))),join(iPr_def_13,X0))),complement(top)) = join(iPr_def_13,complement(X0)),
inference(superposition,[status(thm)],[c_264,c_325]) ).
tcf(c_1764,plain,
! [X0: $i] : join(iPr_def_13,complement(join(X0,complement(complement(X0))))) = complement(X0),
inference(demodulation,[status(thm)],[c_1740,c_148,c_284]) ).
tcf(c_1765,plain,
! [X0: $i] : join(iPr_def_13,complement(join(iPr_def_13,join(X0,complement(join(iPr_def_13,complement(X0))))))) = join(iPr_def_13,complement(X0)),
inference(demodulation,[status(thm)],[c_1746,c_148,c_223,c_284]) ).
tcf(c_1766,plain,
! [X0: $i] : join(iPr_def_13,complement(join(composition(sk1,X0),complement(composition(sk1,complement(X0)))))) = composition(sk1,complement(X0)),
inference(demodulation,[status(thm)],[c_1741,c_148,c_284]) ).
tcf(c_1774,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_298,c_1764]) ).
tcf(c_1775,plain,
complement(iPr_def_13) = top,
inference(demodulation,[status(thm)],[c_538,c_1764]) ).
tcf(c_1867,plain,
! [X0: $i] : join(iPr_def_13,complement(join(X0,X0))) = complement(X0),
inference(light_normalisation,[status(thm)],[c_1764,c_1774]) ).
tcf(c_1871,plain,
! [X0: $i,X1: $i] : join(iPr_def_13,complement(join(X0,join(X1,join(X0,X1))))) = complement(join(X0,X1)),
inference(superposition,[status(thm)],[c_147,c_1867]) ).
tcf(c_1887,plain,
complement(join(iPr_def_13,iPr_def_13)) = top,
inference(demodulation,[status(thm)],[c_1033,c_1871]) ).
tcf(c_1888,plain,
join(iPr_def_13,complement(join(top,top))) = join(iPr_def_13,iPr_def_13),
inference(demodulation,[status(thm)],[c_1004,c_1887]) ).
tcf(c_1889,plain,
join(iPr_def_13,iPr_def_13) = complement(top),
inference(demodulation,[status(thm)],[c_1888,c_1867]) ).
tcf(c_1890,plain,
join(iPr_def_13,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1889,c_284]) ).
tcf(c_1899,plain,
! [X0: $i] : join(iPr_def_13,join(iPr_def_13,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_1890,c_147]) ).
tcf(c_1919,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X0,complement(X1)))) = complement(X0),
inference(superposition,[status(thm)],[c_1774,c_139]) ).
tcf(c_1920,plain,
! [X0: $i,X1: $i] : join(X0,composition(converse(X1),complement(composition(X1,complement(X0))))) = X0,
inference(superposition,[status(thm)],[c_1774,c_138]) ).
tcf(c_2057,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_145,c_331]) ).
tcf(c_2096,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_2057,c_143]) ).
tcf(c_2326,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_2096,c_145]) ).
tcf(c_2327,plain,
! [X0: $i,X1: $i] : composition(join(X0,converse(one)),X1) = join(composition(X0,X1),X1),
inference(superposition,[status(thm)],[c_2096,c_144]) ).
tcf(c_2338,plain,
! [X0: $i] : join(complement(X0),composition(one,complement(X0))) = complement(X0),
inference(superposition,[status(thm)],[c_2096,c_313]) ).
tcf(c_2346,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2096,c_382]) ).
tcf(c_2350,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_2346,c_2096]) ).
tcf(c_2355,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_2338,c_2350]) ).
tcf(c_2358,plain,
! [X0: $i,X1: $i] : join(composition(X0,X1),X1) = composition(join(X0,one),X1),
inference(demodulation,[status(thm)],[c_2327,c_2326]) ).
tcf(c_2359,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(demodulation,[status(thm)],[c_2358,c_148]) ).
tcf(c_2368,plain,
join(iPr_def_11,one) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_1616,c_2326]) ).
tcf(c_2369,plain,
converse(iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2368,c_322]) ).
tcf(c_2864,plain,
! [X0: $i] : join(iPr_def_13,complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_1867,c_1899]) ).
tcf(c_2873,plain,
! [X0: $i] : complement(join(X0,X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_1867,c_2864]) ).
tcf(c_4941,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(top,X1),
inference(superposition,[status(thm)],[c_148,c_411]) ).
tcf(c_5162,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X0))),join(complement(top),X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_140,c_412]) ).
tcf(c_5177,plain,
! [X0: $i,X1: $i] : join(iPr_def_13,join(X0,X1)) = join(X0,X1),
inference(demodulation,[status(thm)],[c_5162,c_223,c_284,c_1774,c_2873]) ).
tcf(c_5309,plain,
! [X0: $i,X1: $i] : join(X0,join(iPr_def_13,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_5177,c_223]) ).
tcf(c_5319,plain,
! [X0: $i] : join(iPr_def_13,complement(join(iPr_def_13,join(X0,X0)))) = complement(X0),
inference(light_normalisation,[status(thm)],[c_1765,c_1774,c_2864]) ).
tcf(c_5434,plain,
! [X0: $i] : join(X0,complement(join(iPr_def_13,X0))) = top,
inference(superposition,[status(thm)],[c_419,c_5177]) ).
tcf(c_5504,plain,
! [X0: $i] : join(join(iPr_def_13,join(X0,X0)),complement(X0)) = join(iPr_def_13,top),
inference(superposition,[status(thm)],[c_5319,c_500]) ).
tcf(c_5514,plain,
! [X0: $i,X1: $i] : join(top,join(X0,complement(complement(X1)))) = join(X1,join(X0,top)),
inference(superposition,[status(thm)],[c_500,c_411]) ).
tcf(c_5515,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,join(X2,complement(X0)))) = join(X1,join(X2,top)),
inference(superposition,[status(thm)],[c_500,c_223]) ).
tcf(c_5537,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_5504,c_147,c_296,c_4941,c_5177]) ).
tcf(c_5540,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,top)) = top,
inference(demodulation,[status(thm)],[c_5514,c_5537]) ).
tcf(c_5542,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,join(X2,complement(X0)))) = top,
inference(demodulation,[status(thm)],[c_5515,c_5540]) ).
tcf(c_5614,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(composition(one,complement(composition(one,X0))),X1)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_2326,c_413]) ).
tcf(c_5636,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(complement(X0),X1)) = join(complement(X0),X1),
inference(demodulation,[status(thm)],[c_5614,c_2350]) ).
tcf(c_5734,plain,
! [X0: $i,X1: $i] : join(composition(sk1,X0),join(X1,complement(complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0))))))))) = join(iPr_def_13,join(X1,top)),
inference(superposition,[status(thm)],[c_500,c_415]) ).
tcf(c_5752,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_5734,c_148,c_1774,c_5177,c_5542]) ).
tcf(c_5767,plain,
join(iPr_def_13,complement(join(sk1,complement(composition(sk1,complement(one)))))) = composition(sk1,complement(one)),
inference(superposition,[status(thm)],[c_145,c_1766]) ).
tcf(c_5776,plain,
complement(join(sk1,complement(composition(sk1,complement(one))))) = composition(sk1,complement(one)),
inference(demodulation,[status(thm)],[c_5767,c_2864]) ).
tcf(c_5780,plain,
! [X0: $i] : join(iPr_def_13,complement(join(complement(join(iPr_def_13,X0)),complement(X0)))) = join(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_863,c_1774,c_2864]) ).
tcf(c_6108,plain,
! [X0: $i,X1: $i] : join(complement(one),composition(join(X0,converse(X1)),complement(X1))) = join(composition(X0,complement(X1)),complement(one)),
inference(superposition,[status(thm)],[c_318,c_498]) ).
tcf(c_6151,plain,
! [X0: $i,X1: $i] : join(complement(one),composition(join(X0,converse(X1)),complement(X1))) = join(complement(one),composition(X0,complement(X1))),
inference(demodulation,[status(thm)],[c_6108,c_148]) ).
tcf(c_6196,plain,
! [X0: $i] : join(complement(X0),iPr_def_13) = complement(X0),
inference(light_normalisation,[status(thm)],[c_937,c_284,c_1774,c_1775,c_2355,c_5537]) ).
tcf(c_6199,plain,
! [X0: $i] : join(X0,iPr_def_13) = X0,
inference(superposition,[status(thm)],[c_1774,c_6196]) ).
tcf(c_6661,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(top),join(X0,complement(join(complement(X1),complement(join(X2,complement(join(complement(X1),X2)))))))) = join(X0,X1),
inference(superposition,[status(thm)],[c_419,c_501]) ).
tcf(c_6678,plain,
! [X0: $i] : join(complement(join(complement(join(iPr_def_13,X0)),X0)),join(iPr_def_13,X0)) = join(iPr_def_13,join(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_5780,c_501]) ).
tcf(c_6705,plain,
! [X0: $i] : join(iPr_def_13,X0) = X0,
inference(demodulation,[status(thm)],[c_6678,c_148,c_284,c_5177,c_5309,c_5434,c_6199]) ).
tcf(c_6718,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,complement(join(complement(X1),complement(join(X2,complement(join(complement(X1),X2))))))) = join(X0,X1),
inference(demodulation,[status(thm)],[c_6661,c_284,c_5177]) ).
tcf(c_7290,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,top)),complement(join(complement(X1),complement(join(X0,complement(complement(X1))))))) = X1,
inference(superposition,[status(thm)],[c_140,c_509]) ).
tcf(c_7379,plain,
! [X0: $i,X1: $i] : complement(join(complement(X0),complement(join(X1,X0)))) = X0,
inference(demodulation,[status(thm)],[c_7290,c_284,c_1774,c_5752,c_6705]) ).
tcf(c_7454,plain,
! [X0: $i,X1: $i] : complement(join(complement(X0),complement(join(X0,X1)))) = X0,
inference(superposition,[status(thm)],[c_148,c_7379]) ).
tcf(c_7457,plain,
! [X0: $i,X1: $i,X2: $i] : complement(join(complement(X0),complement(join(X1,join(X2,X0))))) = X0,
inference(superposition,[status(thm)],[c_147,c_7379]) ).
tcf(c_7508,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X1,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_7379,c_1774]) ).
tcf(c_7517,plain,
! [X0: $i,X1: $i] : complement(join(complement(complement(join(X0,X1))),X1)) = complement(join(X0,X1)),
inference(superposition,[status(thm)],[c_7379,c_7379]) ).
tcf(c_7520,plain,
! [X0: $i,X1: $i] : complement(join(X0,join(X1,X0))) = complement(join(X1,X0)),
inference(demodulation,[status(thm)],[c_7517,c_148,c_1774]) ).
tcf(c_8397,plain,
! [X0: $i,X1: $i,X2: $i] : complement(join(complement(X0),complement(join(X1,join(X0,X2))))) = X0,
inference(superposition,[status(thm)],[c_223,c_7454]) ).
tcf(c_8442,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X0,X1))) = complement(X0),
inference(superposition,[status(thm)],[c_7454,c_1774]) ).
tcf(c_8645,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,complement(join(complement(composition(sk1,X1)),complement(join(join(complement(composition(sk1,complement(X1))),X2),complement(join(top,X2))))))) = join(X0,composition(sk1,X1)),
inference(superposition,[status(thm)],[c_531,c_6718]) ).
tcf(c_8695,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,complement(join(complement(composition(sk1,X1)),complement(join(complement(composition(sk1,complement(X1))),X2))))) = join(X0,composition(sk1,X1)),
inference(demodulation,[status(thm)],[c_8645,c_147,c_284,c_5537,c_6199]) ).
tcf(c_11267,plain,
! [X0: $i,X1: $i,X2: $i] : complement(join(X0,complement(join(X1,join(X2,complement(X0)))))) = complement(X0),
inference(superposition,[status(thm)],[c_1774,c_7457]) ).
tcf(c_13978,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(join(X0,X1)),join(X0,complement(X1)))),complement(complement(X0))) = complement(complement(join(X0,X1))),
inference(superposition,[status(thm)],[c_1919,c_1919]) ).
tcf(c_13987,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(X0,complement(X1)))) = join(X0,X1),
inference(demodulation,[status(thm)],[c_13978,c_148,c_223,c_1774,c_7508]) ).
tcf(c_23747,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(complement(join(iPr_def_13,complement(X0))),X1)) = join(top,X1),
inference(light_normalisation,[status(thm)],[c_849,c_6705]) ).
tcf(c_25302,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(join(join(complement(join(X1,complement(X0))),complement(complement(join(complement(X0),complement(X1))))),complement(X0))),complement(complement(join(X1,complement(X0))))))) = join(join(complement(join(X1,complement(X0))),complement(complement(join(complement(X0),complement(X1))))),complement(X0)),
inference(superposition,[status(thm)],[c_903,c_903]) ).
tcf(c_25303,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(X0),join(X1,complement(join(complement(join(X2,complement(X0))),complement(complement(join(complement(X0),complement(X2)))))))) = join(X1,join(X2,complement(X0))),
inference(superposition,[status(thm)],[c_903,c_223]) ).
tcf(c_25318,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(X0),join(X1,complement(join(complement(X0),complement(X2))))) = join(X1,join(X2,complement(X0))),
inference(demodulation,[status(thm)],[c_25303,c_148,c_223,c_1774,c_8442]) ).
tcf(c_25327,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),X1))) = join(complement(X0),complement(X1)),
inference(demodulation,[status(thm)],[c_25302,c_148,c_147,c_223,c_1774,c_5636,c_7520,c_8442,c_13987]) ).
tcf(c_27899,plain,
join(complement(composition(sk1,complement(one))),complement(join(complement(join(complement(composition(sk1,complement(one))),sk1)),complement(complement(top))))) = join(complement(composition(sk1,complement(one))),sk1),
inference(superposition,[status(thm)],[c_528,c_918]) ).
tcf(c_27955,plain,
join(sk1,complement(composition(sk1,complement(one)))) = complement(composition(sk1,complement(one))),
inference(demodulation,[status(thm)],[c_27899,c_148,c_284,c_1774,c_5537,c_5776,c_6199]) ).
tcf(c_29405,plain,
! [X0: $i] : join(complement(top),complement(join(complement(complement(composition(sk1,X0))),complement(join(iPr_def_13,complement(complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0)))))))))))) = join(iPr_def_13,complement(complement(join(complement(composition(sk1,X0)),complement(complement(composition(sk1,complement(X0)))))))),
inference(superposition,[status(thm)],[c_829,c_1717]) ).
tcf(c_29450,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(X0,complement(join(complement(composition(sk1,X1)),complement(join(complement(composition(sk1,complement(X1))),X2)))))),complement(join(complement(X0),composition(sk1,X1)))) = join(complement(composition(sk1,X1)),complement(join(complement(composition(sk1,complement(X1))),X2))),
inference(superposition,[status(thm)],[c_8695,c_1717]) ).
tcf(c_29460,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(complement(X0),X1))) = complement(X1),
inference(superposition,[status(thm)],[c_1774,c_1717]) ).
tcf(c_29513,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(X0,composition(sk1,X1))),complement(join(complement(X0),composition(sk1,X1)))) = join(complement(composition(sk1,X1)),complement(join(complement(composition(sk1,complement(X1))),X2))),
inference(demodulation,[status(thm)],[c_29450,c_148,c_8695]) ).
tcf(c_29514,plain,
! [X0: $i,X1: $i] : join(complement(composition(sk1,X0)),complement(join(complement(composition(sk1,complement(X0))),X1))) = iPr_def_15(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_29513]) ).
tcf(c_29515,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,composition(sk1,X1))),complement(join(complement(X0),composition(sk1,X1)))) = iPr_def_15(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_29513]) ).
tcf(c_29516,plain,
! [X0: $i] : complement(composition(sk1,X0)) = iPr_def_15(X0),
inference(demodulation,[status(thm)],[c_29515,c_29460]) ).
tcf(c_29520,plain,
! [X0: $i] : join(complement(top),complement(join(complement(iPr_def_15(X0)),complement(join(iPr_def_13,complement(complement(join(iPr_def_15(X0),complement(iPr_def_15(complement(X0))))))))))) = join(iPr_def_13,complement(complement(join(iPr_def_15(X0),complement(iPr_def_15(complement(X0))))))),
inference(demodulation,[status(thm)],[c_29405,c_29516]) ).
tcf(c_29521,plain,
! [X0: $i] : join(iPr_def_15(X0),complement(iPr_def_15(complement(X0)))) = iPr_def_15(X0),
inference(demodulation,[status(thm)],[c_29520,c_284,c_1774,c_6705,c_8442]) ).
tcf(c_29528,plain,
! [X0: $i,X1: $i] : join(X0,composition(sk1,X1)) = join(X0,complement(iPr_def_15(X1))),
inference(demodulation,[status(thm)],[c_8695,c_29514]) ).
tcf(c_29535,plain,
! [X0: $i] : join(iPr_def_15(X0),complement(composition(sk1,complement(X0)))) = top,
inference(demodulation,[status(thm)],[c_274,c_29516]) ).
tcf(c_29539,plain,
join(sk1,iPr_def_15(complement(one))) = iPr_def_15(complement(one)),
inference(demodulation,[status(thm)],[c_27955,c_29516]) ).
tcf(c_29550,plain,
! [X0: $i] : join(iPr_def_15(X0),iPr_def_15(complement(X0))) = top,
inference(demodulation,[status(thm)],[c_29535,c_29516]) ).
tcf(c_29794,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))),complement(join(complement(join(complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))),join(complement(X0),X1))),complement(complement(X0))))) = join(complement(join(complement(X0),join(complement(join(complement(X0),X1)),complement(complement(join(complement(X0),complement(X1))))))),join(complement(X0),X1)),
inference(superposition,[status(thm)],[c_940,c_918]) ).
tcf(c_29809,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,complement(X1))) = join(complement(X1),X0),
inference(demodulation,[status(thm)],[c_29794,c_148,c_223,c_1774,c_5636,c_7508,c_11267,c_25318,c_25327]) ).
tcf(c_30123,plain,
! [X0: $i] : join(complement(join(iPr_def_15(X0),iPr_def_15(complement(X0)))),complement(iPr_def_15(X0))) = complement(iPr_def_15(X0)),
inference(superposition,[status(thm)],[c_29521,c_1919]) ).
tcf(c_30129,plain,
! [X0: $i] : composition(sk1,X0) = complement(iPr_def_15(X0)),
inference(demodulation,[status(thm)],[c_30123,c_148,c_284,c_6199,c_29528,c_29550]) ).
tcf(c_33718,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_13,complement(X0))),complement(join(complement(complement(join(X1,X0))),complement(join(complement(join(iPr_def_13,complement(X0))),join(complement(join(X1,X0)),complement(complement(join(complement(join(iPr_def_13,complement(X0))),complement(join(X1,complement(join(top,complement(X0)))))))))))))) = join(complement(join(iPr_def_13,complement(X0))),join(complement(join(X1,X0)),complement(complement(join(complement(join(iPr_def_13,complement(X0))),complement(join(X1,complement(join(top,complement(X0)))))))))),
inference(superposition,[status(thm)],[c_1002,c_946]) ).
tcf(c_33758,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(X1,X0))) = join(complement(X1),X0),
inference(demodulation,[status(thm)],[c_33718,c_148,c_223,c_284,c_1774,c_5537,c_6199,c_6705,c_8397,c_8442,c_29809]) ).
tcf(c_33928,plain,
! [X0: $i,X1: $i] : join(join(complement(join(iPr_def_13,complement(X0))),X1),complement(join(top,X1))) = join(complement(complement(X0)),join(complement(join(iPr_def_13,complement(X0))),X1)),
inference(superposition,[status(thm)],[c_23747,c_33758]) ).
tcf(c_34045,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(demodulation,[status(thm)],[c_33928,c_147,c_284,c_1774,c_6705,c_33758]) ).
tcf(c_34327,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,X0)) = join(X1,X0),
inference(superposition,[status(thm)],[c_148,c_34045]) ).
tcf(c_34752,plain,
join(one,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_322,c_34327]) ).
tcf(c_34893,plain,
join(iPr_def_12,one) = iPr_def_12,
inference(demodulation,[status(thm)],[c_34752,c_148]) ).
tcf(c_110838,plain,
join(complement(one),composition(join(iPr_def_10,converse(iPr_def_15(complement(one)))),complement(iPr_def_15(complement(one))))) = complement(one),
inference(superposition,[status(thm)],[c_29539,c_1657]) ).
tcf(c_110920,plain,
composition(iPr_def_12,complement(one)) = complement(one),
inference(demodulation,[status(thm)],[c_110838,c_322,c_384,c_2359,c_6151,c_30129]) ).
tcf(c_112214,plain,
join(one,composition(converse(iPr_def_12),complement(complement(one)))) = one,
inference(superposition,[status(thm)],[c_110920,c_1920]) ).
tcf(c_112221,plain,
one = iPr_def_12,
inference(demodulation,[status(thm)],[c_112214,c_148,c_145,c_1774,c_2369,c_34893]) ).
tcf(c_112373,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_135,c_112221]) ).
tcf(c_112374,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_112373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL042-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 07:34:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running UEQ theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 65.37/9.32 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 65.37/9.32 % SZS status Started for theBenchmark.p
% 65.37/9.32 % SZS status Unsatisfiable for theBenchmark.p
% 65.37/9.32
% 65.37/9.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.37/9.32
% 65.37/9.32 % ------ iProver source info
% 65.37/9.32
% 65.37/9.32 % git: date: 2026-07-19 20:42:38 +0200
% 65.37/9.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.37/9.32 % git: non_committed_changes: false
% 65.37/9.32
% 65.37/9.32 % ------ Parsing...% successful
% 65.37/9.32
% 65.37/9.32
% 65.37/9.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.37/9.32
% 65.37/9.32 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 65.37/9.32
% 65.37/9.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.37/9.32
% 65.37/9.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 65.37/9.32 % ------ Proving...
% 65.37/9.32 % ------ Problem Properties
% 65.37/9.32
% 65.37/9.32 %
% 65.37/9.32 % clauses 18
% 65.37/9.32 % conjectures 2
% 65.37/9.32 % EPR 2
% 65.37/9.32 % Horn 18
% 65.37/9.32 % unary 18
% 65.37/9.32 % binary 0
% 65.37/9.32 % lits 18
% 65.37/9.32 % lits eq 18
% 65.37/9.32 % fd_pure 0
% 65.37/9.32 % fd_pseudo 0
% 65.37/9.32 % fd_cond 0
% 65.37/9.32 % fd_pseudo_cond 0
% 65.37/9.32 % AC symbols 1
% 65.37/9.32
% 65.37/9.32 % ------ Input Options Time Limit: Unbounded
% 65.37/9.32
% 65.37/9.32
% 65.37/9.32 % ------
% 65.37/9.32 % Current options:
% 65.37/9.32 % ------
% 65.37/9.32
% 65.37/9.32
% 65.37/9.32 %
% 65.37/9.32
% 65.37/9.32 % ------ Proving...
% 65.37/9.32 %
% 65.37/9.32
% 65.37/9.32 % SZS status Unsatisfiable for theBenchmark.p
% 65.37/9.32
% 65.37/9.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.37/9.33
% 65.37/9.33
%------------------------------------------------------------------------------