%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL023+2 : 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 : n026.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 02:36:52 PM UTC 2026
% Result : Theorem 2.73s 1.95s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 156 ( 156 unt; 12 def)
% Number of atoms : 330 ( 155 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 107 !; 3 ?; 54 :)
% 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(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f17,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))) = composition(X0,meet(X1,X2)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] : composition(X0,meet(X1,X2)) != join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(X0,meet(X1,X2))),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f42,plain,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(sK0,complement(join(complement(sK1),complement(sK2))))),
inference(definition_unfolding,[],[f37,f24,f24,f24,f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,negated_conjecture,
join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(sK0,complement(join(complement(sK1),complement(sK2))))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(cnf_transformation,[],[f42]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_51,c_50,c_49]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_58,c_50,c_49]) ).
tcf(c_84,negated_conjecture,
join(composition(sK0,complement(join(complement(sK1),complement(sK2)))),composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2))))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(theory_normalisation,[status(thm)],[c_64,c_50,c_49]) ).
tcf(c_121,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_122,plain,
composition(join(complement(join(complement(sK0),complement(converse(sK1)))),sK0),complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(ac_demodulation,[status(thm)],[c_84,c_54,c_50,c_49]) ).
tcf(c_123,plain,
composition(join(sK0,complement(join(complement(sK0),complement(converse(sK1))))),complement(join(complement(sK1),complement(sK2)))) != composition(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(theory_normalisation,[status(thm)],[c_122,c_50,c_49]) ).
tcf(c_130,definition,
iPr_def_10 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_131,definition,
iPr_def_11 = converse(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_132,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_133,definition,
iPr_def_13 = join(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_134,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_135,definition,
iPr_def_15 = join(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_136,definition,
iPr_def_16 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_137,definition,
iPr_def_17 = complement(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_138,definition,
iPr_def_18 = join(iPr_def_16,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_139,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_140,definition,
iPr_def_20 = composition(iPr_def_15,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_141,definition,
iPr_def_21 = composition(sK0,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_142,plain,
iPr_def_20 != iPr_def_21,
inference(demodulation,[status(thm)],[c_123,c_141,c_137,c_136,c_138,c_139,c_131,c_132,c_130,c_133,c_134,c_135,c_140]) ).
tcf(c_248,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_130,c_80]) ).
tcf(c_249,plain,
! [X0: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_121,c_80]) ).
tcf(c_251,plain,
! [X0: $i] : join(complement(join(iPr_def_14,X0)),complement(join(iPr_def_14,complement(X0)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_134,c_80]) ).
tcf(c_255,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_121,c_80]) ).
tcf(c_257,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_13)),complement(join(complement(X0),iPr_def_14))) = X0,
inference(superposition,[status(thm)],[c_134,c_80]) ).
tcf(c_260,plain,
! [X0: $i] : join(complement(join(iPr_def_13,complement(X0))),complement(join(iPr_def_14,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_257,c_50,c_49]) ).
tcf(c_262,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_255,c_50,c_49]) ).
tcf(c_271,plain,
converse(iPr_def_11) = sK1,
inference(superposition,[status(thm)],[c_131,c_55]) ).
tcf(c_272,plain,
converse(sK1) = iPr_def_11,
inference(superposition,[status(thm)],[c_271,c_55]) ).
tcf(c_274,plain,
join(iPr_def_14,sK0) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_135,c_50,c_49]) ).
tcf(c_278,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_121,c_59]) ).
tcf(c_279,plain,
join(iPr_def_11,iPr_def_12) = top,
inference(superposition,[status(thm)],[c_132,c_59]) ).
tcf(c_282,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_283,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_287,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_282,c_50,c_49]) ).
tcf(c_288,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_287,c_121]) ).
tcf(c_289,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_283,c_121]) ).
tcf(c_327,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_328,plain,
! [X0: $i] : composition(converse(X0),iPr_def_11) = converse(composition(sK1,X0)),
inference(superposition,[status(thm)],[c_272,c_57]) ).
tcf(c_339,plain,
! [X0: $i] : join(iPr_def_14,join(sK0,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_274,c_50]) ).
tcf(c_340,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_278,c_50]) ).
tcf(c_341,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_12,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_279,c_50]) ).
tcf(c_433,plain,
composition(converse(one),iPr_def_11) = converse(sK1),
inference(superposition,[status(thm)],[c_53,c_328]) ).
tcf(c_442,plain,
composition(converse(one),iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_433,c_272]) ).
tcf(c_445,plain,
join(complement(iPr_def_11),composition(converse(converse(one)),complement(iPr_def_11))) = complement(iPr_def_11),
inference(superposition,[status(thm)],[c_442,c_81]) ).
tcf(c_448,plain,
join(iPr_def_12,composition(converse(converse(one)),iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_445,c_132]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_788,plain,
join(iPr_def_15,complement(sK0)) = join(iPr_def_14,top),
inference(superposition,[status(thm)],[c_59,c_339]) ).
tcf(c_790,plain,
join(iPr_def_14,top) = join(iPr_def_15,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_788,c_130]) ).
tcf(c_791,plain,
join(iPr_def_10,iPr_def_15) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_790,c_50,c_49]) ).
tcf(c_798,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_340]) ).
tcf(c_892,plain,
join(top,complement(iPr_def_12)) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_59,c_341]) ).
tcf(c_1051,plain,
join(iPr_def_12,composition(one,iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_448,c_55]) ).
tcf(c_1055,plain,
join(top,composition(one,iPr_def_12)) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_1051,c_341]) ).
tcf(c_1058,plain,
join(top,composition(one,iPr_def_12)) = top,
inference(light_normalisation,[status(thm)],[c_1055,c_279]) ).
tcf(c_1438,plain,
join(complement(join(iPr_def_10,iPr_def_11)),complement(join(iPr_def_10,iPr_def_12))) = sK0,
inference(superposition,[status(thm)],[c_132,c_248]) ).
tcf(c_1450,plain,
join(complement(join(iPr_def_10,iPr_def_11)),iPr_def_14) = sK0,
inference(light_normalisation,[status(thm)],[c_1438,c_133,c_134]) ).
tcf(c_1451,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_11))) = sK0,
inference(theory_normalisation,[status(thm)],[c_1450,c_50,c_49]) ).
tcf(c_1710,plain,
join(complement(join(zero,zero)),complement(top)) = top,
inference(superposition,[status(thm)],[c_59,c_249]) ).
tcf(c_1726,plain,
join(complement(top),complement(join(zero,zero))) = top,
inference(theory_normalisation,[status(thm)],[c_1710,c_50,c_49]) ).
tcf(c_1727,plain,
join(zero,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_1726,c_121]) ).
tcf(c_1753,plain,
join(top,complement(join(zero,zero))) = join(top,top),
inference(superposition,[status(thm)],[c_1727,c_340]) ).
tcf(c_2053,plain,
join(zero,complement(join(iPr_def_12,iPr_def_12))) = iPr_def_11,
inference(superposition,[status(thm)],[c_132,c_288]) ).
tcf(c_2054,plain,
join(zero,complement(join(iPr_def_14,iPr_def_14))) = iPr_def_13,
inference(superposition,[status(thm)],[c_134,c_288]) ).
tcf(c_2436,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_327]) ).
tcf(c_2479,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_2436,c_55]) ).
tcf(c_2507,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2479,c_519]) ).
tcf(c_2509,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2507,c_2479]) ).
tcf(c_2517,plain,
join(top,iPr_def_12) = top,
inference(demodulation,[status(thm)],[c_1058,c_2509]) ).
tcf(c_2519,plain,
join(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1051,c_2509]) ).
tcf(c_2522,plain,
join(zero,complement(iPr_def_12)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_2053,c_2519]) ).
tcf(c_2524,plain,
join(iPr_def_12,top) = top,
inference(theory_normalisation,[status(thm)],[c_2517,c_50,c_49]) ).
tcf(c_2826,plain,
join(top,top) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_2524,c_341]) ).
tcf(c_2831,plain,
join(top,complement(zero)) = join(iPr_def_11,top),
inference(demodulation,[status(thm)],[c_798,c_2826]) ).
tcf(c_3188,plain,
join(complement(join(iPr_def_13,complement(iPr_def_14))),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_59,c_260]) ).
tcf(c_3206,plain,
join(complement(top),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_3188,c_50,c_49]) ).
tcf(c_3207,plain,
join(zero,complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_3206,c_121]) ).
tcf(c_3582,plain,
join(top,complement(join(iPr_def_13,complement(iPr_def_14)))) = join(top,iPr_def_14),
inference(superposition,[status(thm)],[c_3207,c_340]) ).
tcf(c_3584,plain,
join(top,complement(join(iPr_def_13,complement(iPr_def_14)))) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_3582,c_50,c_49]) ).
tcf(c_3585,plain,
join(top,complement(join(iPr_def_13,complement(iPr_def_14)))) = join(iPr_def_10,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_3584,c_791]) ).
tcf(c_3863,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_262]) ).
tcf(c_3867,plain,
join(complement(join(top,complement(join(zero,zero)))),complement(top)) = join(zero,zero),
inference(superposition,[status(thm)],[c_1727,c_262]) ).
tcf(c_3871,plain,
join(complement(join(top,complement(iPr_def_12))),complement(iPr_def_11)) = iPr_def_12,
inference(superposition,[status(thm)],[c_2522,c_262]) ).
tcf(c_3874,plain,
join(complement(join(top,complement(join(iPr_def_13,complement(iPr_def_14))))),complement(iPr_def_14)) = join(iPr_def_13,complement(iPr_def_14)),
inference(superposition,[status(thm)],[c_3207,c_262]) ).
tcf(c_3889,plain,
join(complement(iPr_def_11),complement(join(top,complement(iPr_def_12)))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_3871,c_50,c_49]) ).
tcf(c_3890,plain,
join(iPr_def_12,complement(join(iPr_def_11,top))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3889,c_132,c_892]) ).
tcf(c_3893,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_3863,c_50,c_49]) ).
tcf(c_3894,plain,
join(zero,complement(join(iPr_def_11,top))) = zero,
inference(light_normalisation,[status(thm)],[c_3893,c_121,c_2831]) ).
tcf(c_3924,plain,
join(complement(top),complement(join(top,complement(join(zero,zero))))) = join(zero,zero),
inference(theory_normalisation,[status(thm)],[c_3867,c_50,c_49]) ).
tcf(c_3925,plain,
join(zero,complement(join(iPr_def_11,top))) = join(zero,zero),
inference(light_normalisation,[status(thm)],[c_3924,c_121,c_1753,c_2826]) ).
tcf(c_3930,plain,
join(complement(iPr_def_14),complement(join(top,complement(join(iPr_def_13,complement(iPr_def_14)))))) = join(iPr_def_13,complement(iPr_def_14)),
inference(theory_normalisation,[status(thm)],[c_3874,c_50,c_49]) ).
tcf(c_3931,plain,
join(complement(iPr_def_14),complement(join(iPr_def_10,iPr_def_15))) = join(iPr_def_13,complement(iPr_def_14)),
inference(light_normalisation,[status(thm)],[c_3930,c_3585]) ).
tcf(c_4000,plain,
join(top,complement(join(iPr_def_11,top))) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_3890,c_341]) ).
tcf(c_4005,plain,
join(top,complement(join(iPr_def_11,top))) = top,
inference(light_normalisation,[status(thm)],[c_4000,c_279]) ).
tcf(c_4055,plain,
join(complement(top),complement(join(zero,complement(join(iPr_def_11,top))))) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_4005,c_262]) ).
tcf(c_4059,plain,
join(iPr_def_11,top) = top,
inference(light_normalisation,[status(thm)],[c_4055,c_121,c_1727,c_3925]) ).
tcf(c_4062,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_3894,c_4059]) ).
tcf(c_4076,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_4062,c_121]) ).
tcf(c_4289,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_4076,c_50]) ).
tcf(c_4549,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_288,c_4289]) ).
tcf(c_4584,plain,
complement(join(iPr_def_14,iPr_def_14)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2054,c_4549]) ).
tcf(c_4704,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_4549,c_49]) ).
tcf(c_4709,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_4549,c_59]) ).
tcf(c_4833,plain,
join(complement(iPr_def_14),complement(join(iPr_def_14,complement(zero)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_4704,c_251]) ).
tcf(c_4877,plain,
join(iPr_def_13,complement(iPr_def_14)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4833,c_791,c_3931,c_4709]) ).
tcf(c_6744,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(complement(X0))))) = X0,
inference(demodulation,[status(thm)],[c_289,c_4549]) ).
tcf(c_6780,plain,
complement(join(iPr_def_13,complement(complement(iPr_def_13)))) = join(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_4584,c_6744]) ).
tcf(c_6825,plain,
join(iPr_def_14,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6780,c_134,c_4877]) ).
tcf(c_6926,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_14,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_6825,c_50]) ).
tcf(c_8304,plain,
join(iPr_def_14,sK0) = sK0,
inference(superposition,[status(thm)],[c_1451,c_6926]) ).
tcf(c_8318,plain,
sK0 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8304,c_274]) ).
tcf(c_8357,plain,
composition(iPr_def_15,iPr_def_19) = iPr_def_21,
inference(demodulation,[status(thm)],[c_141,c_8318]) ).
tcf(c_8360,plain,
iPr_def_20 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_8357,c_140]) ).
tcf(c_8361,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8360,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL023+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.20/0.46 % Computer : n026.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Thu Sep 24 07:21:25 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.53
% 0.24/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.53
% 0.24/0.54 % Detected problem language: tptp
% 0.24/0.55 % Proving...
% 2.73/1.95 % SZS status Started for theBenchmark.p
% 2.73/1.95 % SZS status Theorem for theBenchmark.p
% 2.73/1.95
% 2.73/1.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.95
% 2.73/1.95 % ------ iProver source info
% 2.73/1.95
% 2.73/1.95 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.95 % git: non_committed_changes: false
% 2.73/1.95
% 2.73/1.95 % ------ Parsing...
% 2.73/1.95 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.73/1.95 %
% 2.73/1.95
% 2.73/1.95 % ------ Preprocessing... sup_sim: 2 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.73/1.95
% 2.73/1.95 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.73/1.95 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.73/1.95
% 2.73/1.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.73/1.95 % ------ Proving...
% 2.73/1.95 % ------ Problem Properties
% 2.73/1.95
% 2.73/1.95 %
% 2.73/1.95 % clauses 28
% 2.73/1.95 % conjectures 0
% 2.73/1.95 % EPR 1
% 2.73/1.95 % Horn 28
% 2.73/1.95 % unary 28
% 2.73/1.95 % binary 0
% 2.73/1.95 % lits 28
% 2.73/1.95 % lits eq 28
% 2.73/1.95 % fd_pure 0
% 2.73/1.95 % fd_pseudo 0
% 2.73/1.95 % fd_cond 0
% 2.73/1.95 % fd_pseudo_cond 0
% 2.73/1.95 % AC symbols 1
% 2.73/1.95
% 2.73/1.95 % ------ Schedule UEQ
% 2.73/1.95
% 2.73/1.95 % ------ Option_UEQ Time Limit: 10.
% 2.73/1.95
% 2.73/1.95
% 2.73/1.95 % ------
% 2.73/1.95 % Current options:
% 2.73/1.95 % ------
% 2.73/1.95
% 2.73/1.95
% 2.73/1.95 %
% 2.73/1.95
% 2.73/1.95 % ------ Proving...
% 2.73/1.95 %
% 2.73/1.95
% 2.73/1.95 % SZS status Theorem for theBenchmark.p
% 2.73/1.95
% 2.73/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.96
% 2.73/1.96
%------------------------------------------------------------------------------