%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL023+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 : 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 0.99s 1.41s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 159 ( 159 unt; 12 def)
% Number of atoms : 342 ( 158 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 : 111 ( 0 sgn 108 !; 3 ?; 55 :)
% 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(f14,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(f15,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)],[f14]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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)],[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(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,
composition(sK0,meet(sK1,sK2)) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(sK0,meet(sK1,sK2))),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
fof(f33,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,[],[f31,f21,f21,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_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,[],[f32]) ).
tcf(c_61,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,[],[f33]) ).
tcf(c_74,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_75,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_76,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_61,c_50,c_49]) ).
tcf(c_105,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_106,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_76,c_54,c_50,c_49]) ).
tcf(c_107,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_106,c_50,c_49]) ).
tcf(c_114,definition,
iPr_def_10 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_115,definition,
iPr_def_11 = converse(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_116,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_117,definition,
iPr_def_13 = join(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_118,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_119,definition,
iPr_def_15 = join(sK0,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_120,definition,
iPr_def_16 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_121,definition,
iPr_def_17 = complement(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_122,definition,
iPr_def_18 = join(iPr_def_16,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_123,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_124,definition,
iPr_def_20 = composition(iPr_def_15,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_125,definition,
iPr_def_21 = composition(sK0,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_126,plain,
iPr_def_20 != iPr_def_21,
inference(demodulation,[status(thm)],[c_107,c_125,c_121,c_120,c_122,c_123,c_115,c_116,c_114,c_117,c_118,c_119,c_124]) ).
tcf(c_226,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_114,c_74]) ).
tcf(c_227,plain,
! [X0: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_105,c_74]) ).
tcf(c_228,plain,
! [X0: $i] : join(complement(join(iPr_def_12,X0)),complement(join(iPr_def_12,complement(X0)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_116,c_74]) ).
tcf(c_229,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_118,c_74]) ).
tcf(c_233,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_105,c_74]) ).
tcf(c_235,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_13)),complement(join(complement(X0),iPr_def_14))) = X0,
inference(superposition,[status(thm)],[c_118,c_74]) ).
tcf(c_238,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_235,c_50,c_49]) ).
tcf(c_240,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_233,c_50,c_49]) ).
tcf(c_249,plain,
converse(iPr_def_11) = sK1,
inference(superposition,[status(thm)],[c_115,c_55]) ).
tcf(c_250,plain,
converse(sK1) = iPr_def_11,
inference(superposition,[status(thm)],[c_249,c_55]) ).
tcf(c_252,plain,
join(iPr_def_14,sK0) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_119,c_50,c_49]) ).
tcf(c_256,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_105,c_59]) ).
tcf(c_257,plain,
join(iPr_def_11,iPr_def_12) = top,
inference(superposition,[status(thm)],[c_116,c_59]) ).
tcf(c_260,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_261,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_265,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_260,c_50,c_49]) ).
tcf(c_266,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_265,c_105]) ).
tcf(c_267,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_261,c_105]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_306,plain,
! [X0: $i] : composition(converse(X0),iPr_def_11) = converse(composition(sK1,X0)),
inference(superposition,[status(thm)],[c_250,c_57]) ).
tcf(c_317,plain,
! [X0: $i] : join(iPr_def_14,join(sK0,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_252,c_50]) ).
tcf(c_318,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_256,c_50]) ).
tcf(c_319,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_12,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_257,c_50]) ).
tcf(c_411,plain,
composition(converse(one),iPr_def_11) = converse(sK1),
inference(superposition,[status(thm)],[c_53,c_306]) ).
tcf(c_420,plain,
composition(converse(one),iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_411,c_250]) ).
tcf(c_423,plain,
join(complement(iPr_def_11),composition(converse(converse(one)),complement(iPr_def_11))) = complement(iPr_def_11),
inference(superposition,[status(thm)],[c_420,c_75]) ).
tcf(c_426,plain,
join(iPr_def_12,composition(converse(converse(one)),iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_423,c_116]) ).
tcf(c_467,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_559,plain,
join(iPr_def_15,complement(sK0)) = join(iPr_def_14,top),
inference(superposition,[status(thm)],[c_59,c_317]) ).
tcf(c_564,plain,
join(iPr_def_14,top) = join(iPr_def_15,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_559,c_114]) ).
tcf(c_565,plain,
join(iPr_def_10,iPr_def_15) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_564,c_50,c_49]) ).
tcf(c_575,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_318]) ).
tcf(c_589,plain,
join(top,complement(iPr_def_12)) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_59,c_319]) ).
tcf(c_791,plain,
join(iPr_def_12,composition(one,iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_426,c_55]) ).
tcf(c_795,plain,
join(top,composition(one,iPr_def_12)) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_791,c_319]) ).
tcf(c_798,plain,
join(top,composition(one,iPr_def_12)) = top,
inference(light_normalisation,[status(thm)],[c_795,c_257]) ).
tcf(c_922,plain,
join(complement(join(iPr_def_10,iPr_def_11)),complement(join(iPr_def_10,iPr_def_12))) = sK0,
inference(superposition,[status(thm)],[c_116,c_226]) ).
tcf(c_934,plain,
join(complement(join(iPr_def_10,iPr_def_11)),iPr_def_14) = sK0,
inference(light_normalisation,[status(thm)],[c_922,c_117,c_118]) ).
tcf(c_935,plain,
join(iPr_def_14,complement(join(iPr_def_10,iPr_def_11))) = sK0,
inference(theory_normalisation,[status(thm)],[c_934,c_50,c_49]) ).
tcf(c_1171,plain,
join(complement(join(zero,zero)),complement(top)) = top,
inference(superposition,[status(thm)],[c_59,c_227]) ).
tcf(c_1187,plain,
join(complement(top),complement(join(zero,zero))) = top,
inference(theory_normalisation,[status(thm)],[c_1171,c_50,c_49]) ).
tcf(c_1188,plain,
join(zero,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_1187,c_105]) ).
tcf(c_1230,plain,
join(top,complement(join(zero,zero))) = join(top,top),
inference(superposition,[status(thm)],[c_1188,c_318]) ).
tcf(c_1485,plain,
join(complement(join(iPr_def_12,iPr_def_12)),complement(top)) = iPr_def_11,
inference(superposition,[status(thm)],[c_59,c_228]) ).
tcf(c_1498,plain,
join(complement(top),complement(join(iPr_def_12,iPr_def_12))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1485,c_50,c_49]) ).
tcf(c_1499,plain,
join(zero,complement(join(iPr_def_12,iPr_def_12))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1498,c_105]) ).
tcf(c_1775,plain,
join(zero,complement(join(iPr_def_14,iPr_def_14))) = iPr_def_13,
inference(superposition,[status(thm)],[c_118,c_266]) ).
tcf(c_2164,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_305]) ).
tcf(c_2203,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_2164,c_55]) ).
tcf(c_2223,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2203,c_467]) ).
tcf(c_2225,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2223,c_2203]) ).
tcf(c_2230,plain,
join(top,iPr_def_12) = top,
inference(demodulation,[status(thm)],[c_798,c_2225]) ).
tcf(c_2232,plain,
join(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_791,c_2225]) ).
tcf(c_2235,plain,
join(zero,complement(iPr_def_12)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1499,c_2232]) ).
tcf(c_2237,plain,
join(iPr_def_12,top) = top,
inference(theory_normalisation,[status(thm)],[c_2230,c_50,c_49]) ).
tcf(c_2566,plain,
join(top,top) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_2237,c_319]) ).
tcf(c_2571,plain,
join(top,complement(zero)) = join(iPr_def_11,top),
inference(demodulation,[status(thm)],[c_575,c_2566]) ).
tcf(c_2675,plain,
join(complement(join(iPr_def_13,complement(iPr_def_14))),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_59,c_238]) ).
tcf(c_2693,plain,
join(complement(top),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_2675,c_50,c_49]) ).
tcf(c_2694,plain,
join(zero,complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_2693,c_105]) ).
tcf(c_2965,plain,
join(top,complement(join(iPr_def_13,complement(iPr_def_14)))) = join(top,iPr_def_14),
inference(superposition,[status(thm)],[c_2694,c_318]) ).
tcf(c_2967,plain,
join(top,complement(join(iPr_def_13,complement(iPr_def_14)))) = join(iPr_def_14,top),
inference(theory_normalisation,[status(thm)],[c_2965,c_50,c_49]) ).
tcf(c_2968,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_2967,c_565]) ).
tcf(c_3127,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_240]) ).
tcf(c_3131,plain,
join(complement(join(top,complement(join(zero,zero)))),complement(top)) = join(zero,zero),
inference(superposition,[status(thm)],[c_1188,c_240]) ).
tcf(c_3135,plain,
join(complement(join(top,complement(iPr_def_12))),complement(iPr_def_11)) = iPr_def_12,
inference(superposition,[status(thm)],[c_2235,c_240]) ).
tcf(c_3138,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_2694,c_240]) ).
tcf(c_3153,plain,
join(complement(iPr_def_11),complement(join(top,complement(iPr_def_12)))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_3135,c_50,c_49]) ).
tcf(c_3154,plain,
join(iPr_def_12,complement(join(iPr_def_11,top))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3153,c_116,c_589]) ).
tcf(c_3157,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_3127,c_50,c_49]) ).
tcf(c_3158,plain,
join(zero,complement(join(iPr_def_11,top))) = zero,
inference(light_normalisation,[status(thm)],[c_3157,c_105,c_2571]) ).
tcf(c_3188,plain,
join(complement(top),complement(join(top,complement(join(zero,zero))))) = join(zero,zero),
inference(theory_normalisation,[status(thm)],[c_3131,c_50,c_49]) ).
tcf(c_3189,plain,
join(zero,complement(join(iPr_def_11,top))) = join(zero,zero),
inference(light_normalisation,[status(thm)],[c_3188,c_105,c_1230,c_2566]) ).
tcf(c_3194,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_3138,c_50,c_49]) ).
tcf(c_3195,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_3194,c_2968]) ).
tcf(c_3536,plain,
join(top,complement(join(iPr_def_11,top))) = join(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_3154,c_319]) ).
tcf(c_3541,plain,
join(top,complement(join(iPr_def_11,top))) = top,
inference(light_normalisation,[status(thm)],[c_3536,c_257]) ).
tcf(c_3677,plain,
join(complement(top),complement(join(zero,complement(join(iPr_def_11,top))))) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_3541,c_240]) ).
tcf(c_3681,plain,
join(iPr_def_11,top) = top,
inference(light_normalisation,[status(thm)],[c_3677,c_105,c_1188,c_3189]) ).
tcf(c_3685,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_3158,c_3681]) ).
tcf(c_3698,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_3685,c_105]) ).
tcf(c_3750,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_3698,c_50]) ).
tcf(c_4207,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_266,c_3750]) ).
tcf(c_4242,plain,
complement(join(iPr_def_14,iPr_def_14)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1775,c_4207]) ).
tcf(c_4330,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_4207,c_49]) ).
tcf(c_4335,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_4207,c_59]) ).
tcf(c_4475,plain,
join(complement(iPr_def_14),complement(join(iPr_def_14,complement(zero)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_4330,c_229]) ).
tcf(c_4519,plain,
join(iPr_def_13,complement(iPr_def_14)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_4475,c_565,c_3195,c_4335]) ).
tcf(c_5536,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(complement(X0))))) = X0,
inference(demodulation,[status(thm)],[c_267,c_4207]) ).
tcf(c_5567,plain,
complement(join(iPr_def_13,complement(complement(iPr_def_13)))) = join(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_4242,c_5536]) ).
tcf(c_5602,plain,
join(iPr_def_14,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_5567,c_118,c_4519]) ).
tcf(c_5649,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_14,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_5602,c_50]) ).
tcf(c_7126,plain,
join(iPr_def_14,sK0) = sK0,
inference(superposition,[status(thm)],[c_935,c_5649]) ).
tcf(c_7140,plain,
sK0 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_7126,c_252]) ).
tcf(c_7180,plain,
composition(iPr_def_15,iPr_def_19) = iPr_def_21,
inference(demodulation,[status(thm)],[c_125,c_7140]) ).
tcf(c_7183,plain,
iPr_def_20 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_7180,c_124]) ).
tcf(c_7184,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7183,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL023+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.58 % Computer : n026.cluster.edu
% 0.11/0.58 % Model : x86_64 x86_64
% 0.11/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.58 % Memory : 8046.5625MB
% 0.11/0.58 % OS : Linux 6.8.0-71-generic
% 0.11/0.58 % CPULimit : 300
% 0.11/0.58 % WCLimit : 300
% 0.11/0.58 % DateTime : Thu Sep 24 07:21:40 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.62 Running first-order theorem proving
% 0.11/0.62 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
% 0.14/0.63
% 0.14/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.63
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 0.99/1.41 % SZS status Started for theBenchmark.p
% 0.99/1.41 % SZS status Theorem for theBenchmark.p
% 0.99/1.41
% 0.99/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.99/1.41
% 0.99/1.41 % ------ iProver source info
% 0.99/1.41
% 0.99/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 0.99/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.99/1.41 % git: non_committed_changes: false
% 0.99/1.41
% 0.99/1.41 % ------ Parsing...
% 0.99/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 0.99/1.41 %
% 0.99/1.41
% 0.99/1.41 % ------ Preprocessing... sup_sim: 2 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.99/1.41
% 0.99/1.41 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 0.99/1.41 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.99/1.41
% 0.99/1.41 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.99/1.41 % ------ Proving...
% 0.99/1.41 % ------ Problem Properties
% 0.99/1.41
% 0.99/1.41 %
% 0.99/1.41 % clauses 25
% 0.99/1.41 % conjectures 0
% 0.99/1.41 % EPR 1
% 0.99/1.41 % Horn 25
% 0.99/1.41 % unary 25
% 0.99/1.41 % binary 0
% 0.99/1.41 % lits 25
% 0.99/1.41 % lits eq 25
% 0.99/1.41 % fd_pure 0
% 0.99/1.41 % fd_pseudo 0
% 0.99/1.41 % fd_cond 0
% 0.99/1.41 % fd_pseudo_cond 0
% 0.99/1.41 % AC symbols 1
% 0.99/1.41
% 0.99/1.41 % ------ Schedule UEQ
% 0.99/1.41
% 0.99/1.41 % ------ Option_UEQ Time Limit: 10.
% 0.99/1.41
% 0.99/1.41
% 0.99/1.41 % ------
% 0.99/1.41 % Current options:
% 0.99/1.41 % ------
% 0.99/1.41
% 0.99/1.41
% 0.99/1.41 %
% 0.99/1.41
% 0.99/1.41 % ------ Proving...
% 0.99/1.41 %
% 0.99/1.41
% 0.99/1.41 % SZS status Theorem for theBenchmark.p
% 0.99/1.41
% 0.99/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.99/1.41
% 0.99/1.41
%------------------------------------------------------------------------------