%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL047+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 : n003.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 02:37:01 PM UTC 2026
% Result : Theorem 20.05s 3.71s
% Output : CNFRefutation 20.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 19
% Syntax : Number of formulae : 170 ( 165 unt; 7 def)
% Number of atoms : 380 ( 179 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 19 ( 9 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 116 !; 6 ?; 69 :)
% 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(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(X0,X2) = X2
& join(X0,X1) = X1 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( ( join(X0,X2) = X2
& join(X0,X1) = X1 )
=> join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( join(X0,X2) = X2
& join(X0,X1) = X1
& meet(X1,X2) != join(X0,meet(X1,X2)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
? [X0,X1,X2] :
( join(X0,X2) = X2
& join(X0,X1) = X1
& meet(X1,X2) != join(X0,meet(X1,X2)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( sK2 = join(sK0,sK2)
& sK1 = join(sK0,sK1)
& meet(sK1,sK2) != join(sK0,meet(sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
sK2 = join(sK0,sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
sK1 = join(sK0,sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
meet(sK1,sK2) != join(sK0,meet(sK1,sK2)),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f31,f22]) ).
fof(f36,plain,
complement(join(complement(sK1),complement(sK2))) != join(sK0,complement(join(complement(sK1),complement(sK2)))),
inference(definition_unfolding,[],[f34,f22,f22]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f30]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,negated_conjecture,
join(sK0,complement(join(complement(sK1),complement(sK2)))) != complement(join(complement(sK1),complement(sK2))),
inference(cnf_transformation,[],[f36]) ).
tcf(c_62,negated_conjecture,
join(sK0,sK1) = sK1,
inference(cnf_transformation,[],[f33]) ).
tcf(c_63,negated_conjecture,
join(sK0,sK2) = sK2,
inference(cnf_transformation,[],[f32]) ).
tcf(c_76,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_77,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_78,negated_conjecture,
join(sK1,sK0) = sK1,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_79,negated_conjecture,
join(sK2,sK0) = sK2,
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_112,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_119,definition,
iPr_def_10 = join(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_120,definition,
iPr_def_11 = join(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_121,definition,
iPr_def_12 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_122,definition,
iPr_def_13 = complement(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_123,definition,
iPr_def_14 = join(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_124,definition,
iPr_def_15 = complement(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_125,definition,
iPr_def_16 = join(sK0,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_126,negated_conjecture,
iPr_def_10 = sK2,
inference(demodulation,[status(thm)],[c_79,c_119]) ).
tcf(c_127,negated_conjecture,
iPr_def_11 = sK1,
inference(demodulation,[status(thm)],[c_78,c_120]) ).
tcf(c_128,negated_conjecture,
iPr_def_16 != iPr_def_15,
inference(demodulation,[status(thm)],[c_61,c_122,c_121,c_123,c_124,c_125]) ).
tcf(c_211,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_212,plain,
complement(iPr_def_11) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_121,c_127]) ).
tcf(c_213,plain,
complement(iPr_def_10) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_122,c_126]) ).
tcf(c_220,plain,
! [X0: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_112,c_76]) ).
tcf(c_221,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_124,c_76]) ).
tcf(c_222,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_212,c_76]) ).
tcf(c_223,plain,
! [X0: $i] : join(complement(join(iPr_def_13,X0)),complement(join(iPr_def_13,complement(X0)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_213,c_76]) ).
tcf(c_224,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_112,c_76]) ).
tcf(c_233,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_224,c_50,c_49]) ).
tcf(c_236,plain,
join(iPr_def_10,sK0) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_119,c_126]) ).
tcf(c_237,plain,
join(iPr_def_11,sK0) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_120,c_127]) ).
tcf(c_238,plain,
join(iPr_def_15,sK0) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_125,c_50,c_49]) ).
tcf(c_239,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_112,c_59]) ).
tcf(c_243,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_76]) ).
tcf(c_245,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_243,c_50,c_49]) ).
tcf(c_246,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_245,c_112]) ).
tcf(c_255,plain,
join(complement(join(iPr_def_12,iPr_def_10)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_11,
inference(superposition,[status(thm)],[c_213,c_222]) ).
tcf(c_261,plain,
join(complement(join(iPr_def_10,iPr_def_12)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_255,c_50,c_49]) ).
tcf(c_262,plain,
join(complement(join(iPr_def_10,iPr_def_12)),iPr_def_15) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_261,c_123,c_124]) ).
tcf(c_263,plain,
join(iPr_def_15,complement(join(iPr_def_10,iPr_def_12))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_262,c_50,c_49]) ).
tcf(c_275,plain,
join(complement(join(iPr_def_13,iPr_def_11)),complement(join(iPr_def_13,iPr_def_12))) = iPr_def_10,
inference(superposition,[status(thm)],[c_212,c_223]) ).
tcf(c_283,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_275,c_50,c_49]) ).
tcf(c_284,plain,
join(complement(join(iPr_def_11,iPr_def_13)),iPr_def_15) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_283,c_123,c_124]) ).
tcf(c_285,plain,
join(iPr_def_15,complement(join(iPr_def_11,iPr_def_13))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_284,c_50,c_49]) ).
tcf(c_403,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_76]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_424,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_13,X0)) = join(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_123,c_50]) ).
tcf(c_430,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_239,c_50]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_59,c_211]) ).
tcf(c_541,plain,
! [X0: $i] : join(iPr_def_10,join(X0,sK0)) = join(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_236,c_211]) ).
tcf(c_542,plain,
! [X0: $i] : join(iPr_def_11,join(X0,sK0)) = join(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_237,c_211]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_672,plain,
join(iPr_def_10,iPr_def_16) = join(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_238,c_541]) ).
tcf(c_682,plain,
join(iPr_def_10,iPr_def_15) = join(iPr_def_10,iPr_def_16),
inference(theory_normalisation,[status(thm)],[c_672,c_50,c_49]) ).
tcf(c_697,plain,
join(iPr_def_11,iPr_def_16) = join(iPr_def_15,iPr_def_11),
inference(superposition,[status(thm)],[c_238,c_542]) ).
tcf(c_707,plain,
join(iPr_def_11,iPr_def_15) = join(iPr_def_11,iPr_def_16),
inference(theory_normalisation,[status(thm)],[c_697,c_50,c_49]) ).
tcf(c_836,plain,
join(complement(join(zero,zero)),complement(top)) = top,
inference(superposition,[status(thm)],[c_59,c_220]) ).
tcf(c_848,plain,
join(complement(top),complement(join(zero,zero))) = top,
inference(theory_normalisation,[status(thm)],[c_836,c_50,c_49]) ).
tcf(c_849,plain,
join(zero,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_848,c_112]) ).
tcf(c_1030,plain,
join(complement(iPr_def_16),complement(join(iPr_def_15,complement(sK0)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_238,c_221]) ).
tcf(c_1035,plain,
join(complement(join(iPr_def_15,iPr_def_15)),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_59,c_221]) ).
tcf(c_1048,plain,
join(complement(top),complement(join(iPr_def_15,iPr_def_15))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_1035,c_50,c_49]) ).
tcf(c_1049,plain,
join(zero,complement(join(iPr_def_15,iPr_def_15))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1048,c_112]) ).
tcf(c_1079,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_430]) ).
tcf(c_1083,plain,
join(top,complement(join(zero,zero))) = join(top,top),
inference(superposition,[status(thm)],[c_849,c_430]) ).
tcf(c_2967,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_233]) ).
tcf(c_2973,plain,
join(complement(join(top,complement(join(zero,zero)))),complement(top)) = join(zero,zero),
inference(superposition,[status(thm)],[c_849,c_233]) ).
tcf(c_2989,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_2967,c_50,c_49]) ).
tcf(c_2990,plain,
join(zero,complement(join(top,top))) = zero,
inference(light_normalisation,[status(thm)],[c_2989,c_112,c_1079]) ).
tcf(c_3004,plain,
join(complement(top),complement(join(top,complement(join(zero,zero))))) = join(zero,zero),
inference(theory_normalisation,[status(thm)],[c_2973,c_50,c_49]) ).
tcf(c_3005,plain,
join(zero,complement(join(top,top))) = join(zero,zero),
inference(light_normalisation,[status(thm)],[c_3004,c_112,c_1083]) ).
tcf(c_3028,plain,
join(top,complement(join(top,top))) = join(top,zero),
inference(superposition,[status(thm)],[c_2990,c_430]) ).
tcf(c_3032,plain,
join(top,complement(join(top,top))) = top,
inference(light_normalisation,[status(thm)],[c_3028,c_239]) ).
tcf(c_3159,plain,
join(complement(top),complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(superposition,[status(thm)],[c_3032,c_233]) ).
tcf(c_3161,plain,
join(top,top) = top,
inference(light_normalisation,[status(thm)],[c_3159,c_112,c_849,c_3005]) ).
tcf(c_3163,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_2990,c_3161]) ).
tcf(c_3166,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_3163,c_112]) ).
tcf(c_3174,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_3166,c_50]) ).
tcf(c_3529,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_246,c_3174]) ).
tcf(c_3552,plain,
! [X0: $i] : complement(join(complement(X0),complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_246,c_3529]) ).
tcf(c_3555,plain,
complement(join(iPr_def_15,iPr_def_15)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1049,c_3529]) ).
tcf(c_8710,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_417]) ).
tcf(c_8747,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_8710,c_55]) ).
tcf(c_8763,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_8747,c_77]) ).
tcf(c_8782,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_8747,c_587]) ).
tcf(c_8784,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_8782,c_8747]) ).
tcf(c_9266,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_421]) ).
tcf(c_16395,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_8763,c_8784]) ).
tcf(c_16408,plain,
join(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(superposition,[status(thm)],[c_124,c_16395]) ).
tcf(c_16424,plain,
! [X0: $i] : join(X0,complement(X0)) = join(complement(X0),top),
inference(superposition,[status(thm)],[c_16395,c_535]) ).
tcf(c_16439,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(theory_normalisation,[status(thm)],[c_16424,c_50,c_49]) ).
tcf(c_16440,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_16439,c_59]) ).
tcf(c_16452,plain,
complement(iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3555,c_16408]) ).
tcf(c_16464,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_9266,c_16440]) ).
tcf(c_16515,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_15,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_16408,c_50]) ).
tcf(c_17297,plain,
join(iPr_def_15,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_263,c_16515]) ).
tcf(c_17298,plain,
join(iPr_def_15,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_285,c_16515]) ).
tcf(c_17316,plain,
join(iPr_def_10,iPr_def_15) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_17298,c_50,c_49]) ).
tcf(c_17317,plain,
join(iPr_def_11,iPr_def_15) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_17297,c_50,c_49]) ).
tcf(c_17338,plain,
join(iPr_def_10,iPr_def_16) = iPr_def_10,
inference(demodulation,[status(thm)],[c_682,c_17316]) ).
tcf(c_17341,plain,
join(iPr_def_11,iPr_def_16) = iPr_def_11,
inference(demodulation,[status(thm)],[c_707,c_17317]) ).
tcf(c_17410,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_16,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_17338,c_50]) ).
tcf(c_17423,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_16,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_17341,c_50]) ).
tcf(c_17588,plain,
join(iPr_def_10,complement(iPr_def_16)) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_59,c_17410]) ).
tcf(c_17969,plain,
join(iPr_def_10,complement(iPr_def_16)) = top,
inference(demodulation,[status(thm)],[c_17588,c_16464]) ).
tcf(c_17995,plain,
join(iPr_def_11,complement(iPr_def_16)) = join(iPr_def_11,top),
inference(superposition,[status(thm)],[c_59,c_17423]) ).
tcf(c_18043,plain,
join(iPr_def_11,complement(iPr_def_16)) = top,
inference(demodulation,[status(thm)],[c_17995,c_16464]) ).
tcf(c_24870,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3552,c_16395]) ).
tcf(c_24934,plain,
complement(iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_16452,c_24870]) ).
tcf(c_24937,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_24870,c_16395]) ).
tcf(c_25622,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_24937,c_50]) ).
tcf(c_26202,plain,
join(complement(iPr_def_16),iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_1030,c_25622]) ).
tcf(c_26384,plain,
join(iPr_def_14,complement(iPr_def_16)) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_26202,c_50,c_49]) ).
tcf(c_31286,plain,
join(complement(top),complement(join(complement(iPr_def_16),complement(iPr_def_10)))) = iPr_def_16,
inference(superposition,[status(thm)],[c_17969,c_403]) ).
tcf(c_31287,plain,
join(complement(top),complement(join(complement(iPr_def_16),complement(iPr_def_11)))) = iPr_def_16,
inference(superposition,[status(thm)],[c_18043,c_403]) ).
tcf(c_31372,plain,
join(complement(top),complement(join(complement(iPr_def_11),complement(iPr_def_16)))) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_31287,c_50,c_49]) ).
tcf(c_31373,plain,
join(zero,complement(join(iPr_def_12,complement(iPr_def_16)))) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_31372,c_112,c_212]) ).
tcf(c_31374,plain,
join(complement(top),complement(join(complement(iPr_def_10),complement(iPr_def_16)))) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_31286,c_50,c_49]) ).
tcf(c_31375,plain,
join(zero,complement(join(iPr_def_13,complement(iPr_def_16)))) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_31374,c_112,c_213]) ).
tcf(c_31648,plain,
complement(join(iPr_def_12,complement(iPr_def_16))) = iPr_def_16,
inference(demodulation,[status(thm)],[c_31373,c_3529]) ).
tcf(c_31654,plain,
join(iPr_def_12,complement(iPr_def_16)) = complement(iPr_def_16),
inference(superposition,[status(thm)],[c_31648,c_24870]) ).
tcf(c_31692,plain,
complement(join(iPr_def_13,complement(iPr_def_16))) = iPr_def_16,
inference(demodulation,[status(thm)],[c_31375,c_3529]) ).
tcf(c_31698,plain,
join(iPr_def_13,complement(iPr_def_16)) = complement(iPr_def_16),
inference(superposition,[status(thm)],[c_31692,c_24870]) ).
tcf(c_32106,plain,
join(iPr_def_12,complement(iPr_def_16)) = join(iPr_def_14,complement(iPr_def_16)),
inference(superposition,[status(thm)],[c_31698,c_424]) ).
tcf(c_32115,plain,
complement(iPr_def_16) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_32106,c_26384,c_31654]) ).
tcf(c_32150,plain,
complement(iPr_def_14) = iPr_def_16,
inference(superposition,[status(thm)],[c_32115,c_24870]) ).
tcf(c_32159,plain,
iPr_def_15 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_32150,c_24934]) ).
tcf(c_32204,plain,
iPr_def_15 != iPr_def_15,
inference(demodulation,[status(thm)],[c_128,c_32159]) ).
tcf(c_32205,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_32204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL047+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 07:39:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 20.05/3.71 % SZS status Started for theBenchmark.p
% 20.05/3.71 % SZS status Theorem for theBenchmark.p
% 20.05/3.71
% 20.05/3.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.05/3.71
% 20.05/3.71 % ------ iProver source info
% 20.05/3.71
% 20.05/3.71 % git: date: 2026-07-19 20:42:38 +0200
% 20.05/3.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.05/3.71 % git: non_committed_changes: false
% 20.05/3.71
% 20.05/3.71 % ------ Parsing...
% 20.05/3.71 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 20.05/3.71 %
% 20.05/3.71
% 20.05/3.71 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 20.05/3.71
% 20.05/3.71 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 20.05/3.71 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.05/3.71
% 20.05/3.71 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 20.05/3.71 % ------ Proving...
% 20.05/3.71 % ------ Problem Properties
% 20.05/3.71
% 20.05/3.71 %
% 20.05/3.71 % clauses 22
% 20.05/3.71 % conjectures 3
% 20.05/3.71 % EPR 3
% 20.05/3.71 % Horn 22
% 20.05/3.71 % unary 22
% 20.05/3.71 % binary 0
% 20.05/3.71 % lits 22
% 20.05/3.71 % lits eq 22
% 20.05/3.71 % fd_pure 0
% 20.05/3.71 % fd_pseudo 0
% 20.05/3.71 % fd_cond 0
% 20.05/3.71 % fd_pseudo_cond 0
% 20.05/3.71 % AC symbols 1
% 20.05/3.71
% 20.05/3.71 % ------ Schedule UEQ
% 20.05/3.71
% 20.05/3.71 % ------ Option_UEQ Time Limit: 10.
% 20.05/3.71
% 20.05/3.71
% 20.05/3.71 % ------
% 20.05/3.71 % Current options:
% 20.05/3.71 % ------
% 20.05/3.71
% 20.05/3.71
% 20.05/3.71 %
% 20.05/3.71
% 20.05/3.71 % ------ Proving...
% 20.05/3.71 %
% 20.05/3.71
% 20.05/3.71 % SZS status Theorem for theBenchmark.p
% 20.05/3.71
% 20.05/3.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.05/3.71
%------------------------------------------------------------------------------