%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL042+2 : 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 : n018.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 : Theorem 67.30s 14.93s
% Output : CNFRefutation 67.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 18
% Syntax : Number of formulae : 191 ( 187 unt; 3 def)
% Number of atoms : 293 ( 194 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 225 ( 0 sgn 224 !; 1 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f15,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(f17,conjecture,
! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
& one != join(composition(converse(X0),X0),one) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( ! [X1] : zero = meet(composition(sK0,X1),composition(sK0,complement(X1)))
& one != join(composition(converse(sK0),sK0),one) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[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(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
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(f35,plain,
! [X2,X0,X1] : meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X1] : zero = meet(composition(sK0,X1),composition(sK0,complement(X1))),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
one != join(composition(converse(sK0),sK0),one),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
fof(f41,plain,
! [X2,X0,X1] : complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))),
inference(definition_unfolding,[],[f35,f24,f24,f24,f24,f24]) ).
fof(f43,plain,
! [X1] : zero = complement(join(complement(composition(sK0,X1)),complement(composition(sK0,complement(X1))))),
inference(definition_unfolding,[],[f37,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_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
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,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))) = complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
join(composition(converse(sK0),sK0),one) != one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] : complement(join(complement(composition(sK0,X0)),complement(composition(sK0,complement(X0))))) = zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_82,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_83,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,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))) = complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))),
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_86,negated_conjecture,
join(one,composition(converse(sK0),sK0)) != one,
inference(theory_normalisation,[status(thm)],[c_64,c_50,c_49]) ).
tcf(c_125,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_132,definition,
iPr_def_10 = converse(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = composition(iPr_def_10,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = join(one,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,negated_conjecture,
iPr_def_12 != one,
inference(demodulation,[status(thm)],[c_86,c_132,c_133,c_134]) ).
tcf(c_136,negated_conjecture,
! [X0: $i] : complement(join(complement(composition(sK0,X0)),complement(composition(sK0,complement(X0))))) = zero,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = join(complement(composition(sK0,X1)),complement(composition(sK0,complement(X1)))),
inference(superposition,[status(thm)],[c_136,c_82]) ).
tcf(c_382,plain,
! [X0: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_125,c_82]) ).
tcf(c_406,plain,
converse(iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_132,c_55]) ).
tcf(c_407,plain,
converse(sK0) = iPr_def_10,
inference(superposition,[status(thm)],[c_406,c_55]) ).
tcf(c_409,plain,
join(iPr_def_11,one) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_134,c_50,c_49]) ).
tcf(c_450,plain,
! [X0: $i] : join(complement(composition(sK0,X0)),complement(composition(sK0,complement(X0)))) = top,
inference(light_normalisation,[status(thm)],[c_350,c_382]) ).
tcf(c_472,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_125,c_83]) ).
tcf(c_477,plain,
! [X0: $i] : join(complement(one),composition(converse(X0),complement(X0))) = complement(one),
inference(superposition,[status(thm)],[c_53,c_83]) ).
tcf(c_482,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_82]) ).
tcf(c_485,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_482,c_50,c_49]) ).
tcf(c_486,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_485,c_125]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_49,c_82]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),complement(join(complement(X1),complement(X0)))) = X1,
inference(superposition,[status(thm)],[c_49,c_82]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_507,plain,
! [X0: $i] : composition(iPr_def_10,converse(X0)) = converse(composition(X0,sK0)),
inference(superposition,[status(thm)],[c_407,c_57]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(converse(X0),X1)),complement(X2))),complement(join(complement(X2),complement(composition(converse(X0),complement(join(complement(X1),complement(composition(X0,X2))))))))) = complement(join(complement(X2),complement(composition(converse(X0),complement(join(complement(X1),complement(composition(X0,X2)))))))),
inference(superposition,[status(thm)],[c_55,c_84]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_590,plain,
! [X0: $i,X1: $i] : join(complement(composition(sK0,X0)),join(complement(composition(sK0,complement(X0))),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_450,c_50]) ).
tcf(c_597,plain,
! [X0: $i] : join(iPr_def_11,join(one,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_409,c_50]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_608,plain,
! [X0: $i] : composition(iPr_def_10,composition(sK0,X0)) = composition(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_133,c_52]) ).
tcf(c_702,plain,
composition(iPr_def_10,converse(iPr_def_10)) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_133,c_507]) ).
tcf(c_711,plain,
converse(iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_702,c_133,c_406]) ).
tcf(c_764,plain,
! [X0: $i,X1: $i] : join(complement(composition(sK0,X0)),join(X1,complement(composition(sK0,complement(X0))))) = join(top,X1),
inference(superposition,[status(thm)],[c_49,c_590]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_59,c_215]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i] : join(complement(composition(sK0,X0)),join(X1,complement(composition(sK0,complement(X0))))) = join(X1,top),
inference(superposition,[status(thm)],[c_450,c_215]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(X0),join(X1,composition(converse(X2),complement(composition(X2,X0))))) = join(X1,complement(X0)),
inference(superposition,[status(thm)],[c_83,c_215]) ).
tcf(c_893,plain,
! [X0: $i] : join(iPr_def_11,join(X0,one)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_409,c_215]) ).
tcf(c_1004,plain,
! [X0: $i] : join(iPr_def_11,converse(X0)) = converse(join(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_711,c_56]) ).
tcf(c_1338,plain,
join(iPr_def_12,complement(one)) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_59,c_597]) ).
tcf(c_1630,plain,
join(iPr_def_11,converse(one)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_409,c_1004]) ).
tcf(c_2751,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_494]) ).
tcf(c_3471,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_510]) ).
tcf(c_3543,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_3471,c_55]) ).
tcf(c_3603,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_3543,c_53]) ).
tcf(c_3612,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_3543,c_83]) ).
tcf(c_3617,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_3543,c_606]) ).
tcf(c_3650,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_3617,c_3543]) ).
tcf(c_3657,plain,
join(iPr_def_11,one) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_1630,c_3603]) ).
tcf(c_3658,plain,
converse(iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3657,c_409]) ).
tcf(c_3697,plain,
! [X0: $i] : join(converse(X0),one) = converse(join(X0,one)),
inference(superposition,[status(thm)],[c_3603,c_56]) ).
tcf(c_3701,plain,
! [X0: $i] : join(one,converse(X0)) = converse(join(X0,one)),
inference(theory_normalisation,[status(thm)],[c_3697,c_50,c_49]) ).
tcf(c_3748,plain,
! [X0: $i] : join(complement(X0),composition(iPr_def_12,complement(composition(iPr_def_12,X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_3658,c_83]) ).
tcf(c_3762,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_3650,c_54]) ).
tcf(c_3765,plain,
! [X0: $i,X1: $i] : join(composition(X0,X1),X1) = composition(join(X0,one),X1),
inference(superposition,[status(thm)],[c_3650,c_54]) ).
tcf(c_3794,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(theory_normalisation,[status(thm)],[c_3765,c_50,c_49]) ).
tcf(c_4992,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_589]) ).
tcf(c_7065,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_3612,c_3650]) ).
tcf(c_7066,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_486,c_7065]) ).
tcf(c_7067,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_125,c_7065]) ).
tcf(c_7083,plain,
! [X0: $i] : join(X0,complement(X0)) = join(complement(X0),top),
inference(superposition,[status(thm)],[c_7065,c_884]) ).
tcf(c_7108,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(theory_normalisation,[status(thm)],[c_7083,c_50,c_49]) ).
tcf(c_7109,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_7108,c_59]) ).
tcf(c_7145,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_4992,c_7109]) ).
tcf(c_7151,plain,
! [X0: $i,X1: $i] : join(complement(composition(sK0,X0)),join(X1,complement(composition(sK0,complement(X0))))) = top,
inference(demodulation,[status(thm)],[c_885,c_7145]) ).
tcf(c_7153,plain,
join(iPr_def_12,complement(one)) = top,
inference(demodulation,[status(thm)],[c_1338,c_7145]) ).
tcf(c_7154,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_764,c_7151]) ).
tcf(c_7164,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_7067,c_50]) ).
tcf(c_7176,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(top)))) = X0,
inference(superposition,[status(thm)],[c_7145,c_82]) ).
tcf(c_7205,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),zero))) = X0,
inference(light_normalisation,[status(thm)],[c_7176,c_125]) ).
tcf(c_7206,plain,
! [X0: $i] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_7205,c_50,c_49]) ).
tcf(c_7274,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_7154,c_2751]) ).
tcf(c_7467,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_7206,c_7164]) ).
tcf(c_7560,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_7467,c_49]) ).
tcf(c_7565,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_7467,c_59]) ).
tcf(c_8737,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_7066,c_7467]) ).
tcf(c_8747,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_8737,c_7065]) ).
tcf(c_8753,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X0,complement(X1)))) = complement(X0),
inference(superposition,[status(thm)],[c_8737,c_82]) ).
tcf(c_9255,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_8747,c_50]) ).
tcf(c_9285,plain,
join(one,iPr_def_12) = join(iPr_def_11,one),
inference(superposition,[status(thm)],[c_8747,c_893]) ).
tcf(c_9295,plain,
join(iPr_def_11,one) = join(iPr_def_12,one),
inference(theory_normalisation,[status(thm)],[c_9285,c_50,c_49]) ).
tcf(c_9296,plain,
join(iPr_def_12,one) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_9295,c_409]) ).
tcf(c_9324,plain,
join(one,converse(iPr_def_12)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_9296,c_3701]) ).
tcf(c_9328,plain,
join(one,iPr_def_12) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_9324,c_3658]) ).
tcf(c_9855,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_472,c_7467]) ).
tcf(c_10127,plain,
join(complement(one),composition(iPr_def_12,complement(iPr_def_12))) = complement(one),
inference(superposition,[status(thm)],[c_3658,c_477]) ).
tcf(c_10490,plain,
! [X0: $i] : join(X0,composition(complement(one),X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_59,c_3762]) ).
tcf(c_10492,plain,
! [X0: $i] : join(X0,composition(zero,X0)) = composition(one,X0),
inference(superposition,[status(thm)],[c_7560,c_3762]) ).
tcf(c_10527,plain,
! [X0: $i] : join(X0,composition(zero,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_10492,c_3650]) ).
tcf(c_10564,plain,
composition(top,top) = top,
inference(superposition,[status(thm)],[c_10490,c_7154]) ).
tcf(c_10596,plain,
! [X0: $i] : join(X0,composition(iPr_def_11,X0)) = composition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_409,c_3794]) ).
tcf(c_10662,plain,
composition(converse(top),complement(top)) = zero,
inference(superposition,[status(thm)],[c_10564,c_9855]) ).
tcf(c_10665,plain,
composition(top,zero) = zero,
inference(light_normalisation,[status(thm)],[c_10662,c_125,c_7274]) ).
tcf(c_10679,plain,
! [X0: $i] : join(composition(X0,zero),zero) = composition(join(X0,top),zero),
inference(superposition,[status(thm)],[c_10665,c_54]) ).
tcf(c_10684,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = composition(join(X0,top),zero),
inference(theory_normalisation,[status(thm)],[c_10679,c_50,c_49]) ).
tcf(c_10685,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_10684,c_7145,c_10665]) ).
tcf(c_10751,plain,
join(one,iPr_def_11) = composition(iPr_def_12,one),
inference(superposition,[status(thm)],[c_53,c_10596]) ).
tcf(c_10776,plain,
join(iPr_def_11,one) = composition(iPr_def_12,one),
inference(theory_normalisation,[status(thm)],[c_10751,c_50,c_49]) ).
tcf(c_11260,plain,
composition(zero,zero) = zero,
inference(superposition,[status(thm)],[c_10527,c_7467]) ).
tcf(c_11316,plain,
! [X0: $i] : join(composition(X0,zero),zero) = composition(join(X0,zero),zero),
inference(superposition,[status(thm)],[c_11260,c_54]) ).
tcf(c_11324,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = composition(join(X0,zero),zero),
inference(theory_normalisation,[status(thm)],[c_11316,c_50,c_49]) ).
tcf(c_11325,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(light_normalisation,[status(thm)],[c_11324,c_7560,c_10685]) ).
tcf(c_16249,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_490,c_9255]) ).
tcf(c_16261,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_16249,c_50,c_49]) ).
tcf(c_16439,plain,
join(complement(top),complement(join(complement(one),complement(iPr_def_12)))) = one,
inference(superposition,[status(thm)],[c_7153,c_491]) ).
tcf(c_16460,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),X1) = X1,
inference(superposition,[status(thm)],[c_491,c_9255]) ).
tcf(c_16472,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(X1,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_16460,c_50,c_49]) ).
tcf(c_16479,plain,
join(complement(top),complement(join(complement(iPr_def_12),complement(one)))) = one,
inference(theory_normalisation,[status(thm)],[c_16439,c_50,c_49]) ).
tcf(c_16480,plain,
join(zero,complement(join(complement(iPr_def_12),complement(one)))) = one,
inference(light_normalisation,[status(thm)],[c_16479,c_125]) ).
tcf(c_25814,plain,
! [X0: $i] : join(complement(join(complement(composition(converse(sK0),composition(sK0,X0))),complement(complement(X0)))),complement(join(complement(complement(X0)),complement(composition(converse(sK0),complement(top)))))) = complement(join(complement(complement(X0)),complement(composition(converse(sK0),complement(top))))),
inference(superposition,[status(thm)],[c_450,c_573]) ).
tcf(c_25883,plain,
! [X0: $i] : join(complement(join(complement(complement(X0)),complement(composition(converse(sK0),complement(top))))),complement(join(complement(complement(X0)),complement(composition(converse(sK0),composition(sK0,X0)))))) = complement(join(complement(complement(X0)),complement(composition(converse(sK0),complement(top))))),
inference(theory_normalisation,[status(thm)],[c_25814,c_50,c_49]) ).
tcf(c_25884,plain,
! [X0: $i] : join(complement(join(X0,complement(composition(iPr_def_10,zero)))),complement(join(X0,complement(composition(iPr_def_11,X0))))) = complement(join(X0,complement(composition(iPr_def_10,zero)))),
inference(light_normalisation,[status(thm)],[c_25883,c_125,c_407,c_608,c_8737]) ).
tcf(c_38150,plain,
! [X0: $i] : join(X0,complement(composition(iPr_def_12,complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_10596,c_16261]) ).
tcf(c_39970,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,complement(join(X1,join(X2,complement(X0))))) = X0,
inference(superposition,[status(thm)],[c_50,c_16472]) ).
tcf(c_41176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : join(X0,complement(join(X1,join(X2,join(X3,complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_50,c_39970]) ).
tcf(c_69872,plain,
join(iPr_def_12,complement(composition(iPr_def_12,complement(one)))) = join(iPr_def_11,one),
inference(superposition,[status(thm)],[c_38150,c_597]) ).
tcf(c_69970,plain,
join(iPr_def_12,complement(composition(iPr_def_12,complement(one)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_69872,c_409]) ).
tcf(c_77841,plain,
join(composition(iPr_def_12,complement(one)),complement(iPr_def_12)) = composition(iPr_def_12,complement(one)),
inference(superposition,[status(thm)],[c_69970,c_16472]) ).
tcf(c_77869,plain,
join(complement(iPr_def_12),composition(iPr_def_12,complement(one))) = composition(iPr_def_12,complement(one)),
inference(theory_normalisation,[status(thm)],[c_77841,c_50,c_49]) ).
tcf(c_128521,plain,
complement(join(complement(iPr_def_12),complement(one))) = one,
inference(demodulation,[status(thm)],[c_16480,c_7467]) ).
tcf(c_128597,plain,
join(one,composition(iPr_def_12,complement(composition(iPr_def_12,join(complement(iPr_def_12),complement(one)))))) = one,
inference(superposition,[status(thm)],[c_128521,c_3748]) ).
tcf(c_128612,plain,
join(complement(iPr_def_12),complement(one)) = complement(one),
inference(superposition,[status(thm)],[c_128521,c_8737]) ).
tcf(c_128818,plain,
! [X0: $i] : join(complement(iPr_def_12),join(complement(one),X0)) = join(complement(one),X0),
inference(superposition,[status(thm)],[c_128612,c_50]) ).
tcf(c_130720,plain,
! [X0: $i] : join(complement(one),composition(converse(X0),complement(composition(X0,iPr_def_12)))) = join(complement(one),complement(iPr_def_12)),
inference(superposition,[status(thm)],[c_128818,c_887]) ).
tcf(c_130925,plain,
! [X0: $i] : join(complement(one),composition(converse(X0),complement(composition(X0,iPr_def_12)))) = join(complement(iPr_def_12),complement(one)),
inference(theory_normalisation,[status(thm)],[c_130720,c_50,c_49]) ).
tcf(c_130926,plain,
! [X0: $i] : join(complement(one),composition(converse(X0),complement(composition(X0,iPr_def_12)))) = complement(one),
inference(light_normalisation,[status(thm)],[c_130925,c_128612]) ).
tcf(c_131317,plain,
! [X0: $i,X1: $i,X2: $i] : join(iPr_def_12,complement(join(X0,join(X1,join(X2,complement(one)))))) = join(iPr_def_11,one),
inference(superposition,[status(thm)],[c_41176,c_597]) ).
tcf(c_131507,plain,
! [X0: $i,X1: $i,X2: $i] : join(iPr_def_12,complement(join(X0,join(X1,join(X2,complement(one)))))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_131317,c_409]) ).
tcf(c_170576,plain,
! [X0: $i] : complement(join(X0,complement(composition(iPr_def_11,X0)))) = zero,
inference(demodulation,[status(thm)],[c_25884,c_125,c_7145,c_7467,c_7565,c_11325]) ).
tcf(c_170580,plain,
complement(join(one,complement(iPr_def_11))) = zero,
inference(superposition,[status(thm)],[c_53,c_170576]) ).
tcf(c_171675,plain,
join(complement(join(one,iPr_def_11)),zero) = complement(one),
inference(superposition,[status(thm)],[c_170580,c_8753]) ).
tcf(c_171690,plain,
join(zero,complement(join(iPr_def_11,one))) = complement(one),
inference(theory_normalisation,[status(thm)],[c_171675,c_50,c_49]) ).
tcf(c_171691,plain,
join(zero,complement(iPr_def_12)) = complement(one),
inference(light_normalisation,[status(thm)],[c_171690,c_409]) ).
tcf(c_172784,plain,
complement(one) = complement(iPr_def_12),
inference(demodulation,[status(thm)],[c_171691,c_7467]) ).
tcf(c_172806,plain,
join(complement(iPr_def_12),composition(iPr_def_12,complement(iPr_def_12))) = complement(iPr_def_12),
inference(demodulation,[status(thm)],[c_10127,c_172784]) ).
tcf(c_172978,plain,
complement(complement(iPr_def_12)) = one,
inference(superposition,[status(thm)],[c_172784,c_8737]) ).
tcf(c_174158,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_172978,c_172806,c_172784,c_131507,c_131317,c_130926,c_130925,c_128597,c_77869,c_10776,c_9328,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL042+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:37:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 67.30/14.93 % SZS status Started for theBenchmark.p
% 67.30/14.93 % SZS status Theorem for theBenchmark.p
% 67.30/14.93
% 67.30/14.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 67.30/14.93
% 67.30/14.93 % ------ iProver source info
% 67.30/14.93
% 67.30/14.93 % git: date: 2026-07-19 20:42:38 +0200
% 67.30/14.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 67.30/14.93 % git: non_committed_changes: false
% 67.30/14.93
% 67.30/14.93 % ------ Parsing...
% 67.30/14.93 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 67.30/14.93 %
% 67.30/14.93
% 67.30/14.93 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 67.30/14.93
% 67.30/14.93 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 67.30/14.93 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 67.30/14.93
% 67.30/14.93 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 67.30/14.93 % ------ Proving...
% 67.30/14.93 % ------ Problem Properties
% 67.30/14.93
% 67.30/14.93 %
% 67.30/14.93 % clauses 20
% 67.30/14.93 % conjectures 2
% 67.30/14.93 % EPR 1
% 67.30/14.93 % Horn 20
% 67.30/14.93 % unary 20
% 67.30/14.93 % binary 0
% 67.30/14.93 % lits 20
% 67.30/14.93 % lits eq 20
% 67.30/14.93 % fd_pure 0
% 67.30/14.93 % fd_pseudo 0
% 67.30/14.93 % fd_cond 0
% 67.30/14.93 % fd_pseudo_cond 0
% 67.30/14.93 % AC symbols 1
% 67.30/14.93
% 67.30/14.93 % ------ Schedule UEQ
% 67.30/14.93
% 67.30/14.93 % ------ Option_UEQ Time Limit: 10.
% 67.30/14.93
% 67.30/14.93
% 67.30/14.93 % ------
% 67.30/14.93 % Current options:
% 67.30/14.93 % ------
% 67.30/14.93
% 67.30/14.93
% 67.30/14.93 %
% 67.30/14.93
% 67.30/14.93 % ------ Proving...
% 67.30/14.93 %
% 67.30/14.93
% 67.30/14.93 % SZS status Theorem for theBenchmark.p
% 67.30/14.93
% 67.30/14.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 67.30/14.94
% 67.30/14.94
%------------------------------------------------------------------------------