%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL019-1 : 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 : n008.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 02:36:51 PM UTC 2026
% Result : Unsatisfiable 43.10s 8.29s
% Output : CNFRefutation 43.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 23
% Syntax : Number of formulae : 213 ( 213 unt; 7 def)
% Number of atoms : 489 ( 212 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 152 ( 0 sgn 152 !; 0 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
fof(f13,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
fof(f17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
composition(sk2,top) = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
sk2 = composition(sk2,top),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
composition(meet(sk1,sk2),top) != meet(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_16) ).
fof(f22,plain,
meet(sk1,sk2) != composition(meet(sk1,sk2),top),
inference(reorient_equations,[],[f21]) ).
fof(f23,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f24,plain,
complement(join(complement(sk1),complement(sk2))) != composition(complement(join(complement(sk1),complement(sk2))),top),
inference(definition_unfolding,[],[f22,f6,f6]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_76,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f23]) ).
tcf(c_77,negated_conjecture,
composition(sk1,top) = sk1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_78,negated_conjecture,
composition(sk2,top) = sk2,
inference(cnf_transformation,[],[f20]) ).
tcf(c_79,negated_conjecture,
composition(complement(join(complement(sk1),complement(sk2))),top) != complement(join(complement(sk1),complement(sk2))),
inference(cnf_transformation,[],[f24]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_67,c_66,c_65]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_74,c_66,c_65]) ).
tcf(c_126,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[c_76,c_75]) ).
tcf(c_133,definition,
iPr_def_10 = complement(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_134,definition,
iPr_def_11 = complement(sk2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_135,definition,
iPr_def_12 = join(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_136,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_137,definition,
iPr_def_14 = composition(iPr_def_13,top),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_138,definition,
iPr_def_15 = composition(sk2,top),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_139,definition,
iPr_def_16 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_140,negated_conjecture,
iPr_def_14 != iPr_def_13,
inference(demodulation,[status(thm)],[c_79,c_134,c_133,c_135,c_136,c_137]) ).
tcf(c_141,negated_conjecture,
iPr_def_15 = sk2,
inference(demodulation,[status(thm)],[c_78,c_138]) ).
tcf(c_142,negated_conjecture,
iPr_def_16 = sk1,
inference(demodulation,[status(thm)],[c_77,c_139]) ).
tcf(c_225,plain,
complement(iPr_def_16) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_133,c_142]) ).
tcf(c_226,plain,
complement(iPr_def_15) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_134,c_141]) ).
tcf(c_227,plain,
composition(iPr_def_15,top) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_138,c_141]) ).
tcf(c_228,plain,
composition(iPr_def_16,top) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_139,c_142]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_66,c_65]) ).
tcf(c_238,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_135,c_66]) ).
tcf(c_251,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_126,c_75]) ).
tcf(c_254,plain,
join(iPr_def_15,iPr_def_11) = top,
inference(superposition,[status(thm)],[c_226,c_75]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_75,c_66]) ).
tcf(c_257,plain,
join(iPr_def_11,iPr_def_15) = top,
inference(demodulation,[status(thm)],[c_254,c_65]) ).
tcf(c_261,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_251,c_66]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_69,c_68]) ).
tcf(c_277,plain,
! [X0: $i] : composition(iPr_def_13,composition(top,X0)) = composition(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_137,c_68]) ).
tcf(c_293,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_11)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_65,c_238]) ).
tcf(c_313,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c_65,c_261]) ).
tcf(c_362,plain,
! [X0: $i] : composition(join(iPr_def_13,X0),top) = join(iPr_def_14,composition(X0,top)),
inference(superposition,[status(thm)],[c_137,c_70]) ).
tcf(c_369,plain,
! [X0: $i] : composition(join(X0,iPr_def_16),top) = join(composition(X0,top),iPr_def_16),
inference(superposition,[status(thm)],[c_228,c_70]) ).
tcf(c_373,plain,
! [X0: $i] : composition(join(X0,iPr_def_16),top) = join(iPr_def_16,composition(X0,top)),
inference(demodulation,[status(thm)],[c_369,c_65]) ).
tcf(c_400,plain,
composition(iPr_def_13,top) = composition(iPr_def_14,one),
inference(superposition,[status(thm)],[c_69,c_277]) ).
tcf(c_405,plain,
composition(iPr_def_13,top) = iPr_def_14,
inference(demodulation,[status(thm)],[c_400,c_69]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_71,c_73]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_71,c_73]) ).
tcf(c_651,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),complement(join(complement(X1),complement(X0)))) = X1,
inference(superposition,[status(thm)],[c_65,c_92]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_65,c_92]) ).
tcf(c_661,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_75,c_92]) ).
tcf(c_666,plain,
! [X0: $i] : join(complement(join(iPr_def_11,X0)),complement(join(iPr_def_11,complement(X0)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_226,c_92]) ).
tcf(c_668,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_12)),complement(join(complement(X0),iPr_def_13))) = X0,
inference(superposition,[status(thm)],[c_136,c_92]) ).
tcf(c_669,plain,
! [X0: $i] : join(complement(join(complement(X0),iPr_def_16)),complement(join(complement(X0),iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_225,c_92]) ).
tcf(c_674,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_661,c_65]) ).
tcf(c_675,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_674,c_126]) ).
tcf(c_677,plain,
! [X0: $i] : join(complement(join(iPr_def_10,complement(X0))),complement(join(iPr_def_16,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_669,c_65]) ).
tcf(c_678,plain,
! [X0: $i] : join(complement(join(iPr_def_12,complement(X0))),complement(join(iPr_def_13,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_668,c_65]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(top,X1),
inference(superposition,[status(thm)],[c_65,c_255]) ).
tcf(c_745,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_75,c_255]) ).
tcf(c_761,plain,
join(iPr_def_12,complement(iPr_def_10)) = join(top,iPr_def_11),
inference(superposition,[status(thm)],[c_255,c_293]) ).
tcf(c_771,plain,
join(iPr_def_12,complement(iPr_def_10)) = join(iPr_def_11,top),
inference(demodulation,[status(thm)],[c_761,c_65]) ).
tcf(c_1049,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_75,c_483]) ).
tcf(c_1523,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_11)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_135,c_229]) ).
tcf(c_1526,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(X0,top),
inference(superposition,[status(thm)],[c_251,c_229]) ).
tcf(c_1529,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_15)) = join(X0,top),
inference(superposition,[status(thm)],[c_257,c_229]) ).
tcf(c_1646,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_65,c_1523]) ).
tcf(c_2468,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_69,c_601]) ).
tcf(c_2488,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_2468,c_71]) ).
tcf(c_2528,plain,
! [X0: $i] : join(complement(X0),composition(converse(converse(one)),complement(X0))) = complement(X0),
inference(superposition,[status(thm)],[c_2488,c_93]) ).
tcf(c_2530,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2488,c_276]) ).
tcf(c_2533,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_2530,c_2488]) ).
tcf(c_2535,plain,
! [X0: $i] : join(complement(X0),composition(one,complement(X0))) = complement(X0),
inference(demodulation,[status(thm)],[c_2528,c_71]) ).
tcf(c_2849,plain,
join(zero,complement(join(iPr_def_13,iPr_def_13))) = iPr_def_12,
inference(superposition,[status(thm)],[c_136,c_675]) ).
tcf(c_2850,plain,
join(zero,complement(join(iPr_def_10,iPr_def_10))) = iPr_def_16,
inference(superposition,[status(thm)],[c_225,c_675]) ).
tcf(c_2851,plain,
join(zero,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_15,
inference(superposition,[status(thm)],[c_226,c_675]) ).
tcf(c_3261,plain,
! [X0: $i] : join(join(complement(X0),complement(X0)),X0) = join(top,zero),
inference(superposition,[status(thm)],[c_675,c_743]) ).
tcf(c_3269,plain,
join(join(iPr_def_11,iPr_def_11),iPr_def_15) = join(top,zero),
inference(superposition,[status(thm)],[c_2851,c_743]) ).
tcf(c_3337,plain,
join(top,zero) = join(iPr_def_11,top),
inference(demodulation,[status(thm)],[c_3269,c_66,c_1529]) ).
tcf(c_3338,plain,
join(iPr_def_11,top) = top,
inference(light_normalisation,[status(thm)],[c_3337,c_251]) ).
tcf(c_3356,plain,
! [X0: $i] : join(top,complement(X0)) = join(top,zero),
inference(demodulation,[status(thm)],[c_3261,c_65,c_66,c_75]) ).
tcf(c_3357,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_3356,c_251]) ).
tcf(c_3386,plain,
join(iPr_def_12,complement(iPr_def_10)) = top,
inference(demodulation,[status(thm)],[c_771,c_3338]) ).
tcf(c_3392,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_745,c_3357]) ).
tcf(c_3403,plain,
! [X0: $i] : join(top,join(X0,zero)) = top,
inference(demodulation,[status(thm)],[c_1526,c_3392]) ).
tcf(c_3404,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_313,c_3403]) ).
tcf(c_3415,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = top,
inference(demodulation,[status(thm)],[c_743,c_3404]) ).
tcf(c_3657,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(top)))) = X0,
inference(superposition,[status(thm)],[c_3392,c_92]) ).
tcf(c_3664,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),zero))) = X0,
inference(light_normalisation,[status(thm)],[c_3657,c_126]) ).
tcf(c_3665,plain,
! [X0: $i] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_3664,c_66,c_65]) ).
tcf(c_3706,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_3404,c_1049]) ).
tcf(c_3709,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = top,
inference(demodulation,[status(thm)],[c_1049,c_3706]) ).
tcf(c_3730,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_3706,c_600]) ).
tcf(c_5938,plain,
join(zero,complement(top)) = zero,
inference(superposition,[status(thm)],[c_75,c_3665]) ).
tcf(c_5941,plain,
join(zero,complement(iPr_def_12)) = join(iPr_def_13,iPr_def_13),
inference(superposition,[status(thm)],[c_2849,c_3665]) ).
tcf(c_5942,plain,
join(zero,complement(iPr_def_16)) = join(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_2850,c_3665]) ).
tcf(c_5943,plain,
join(zero,complement(iPr_def_15)) = join(iPr_def_11,iPr_def_11),
inference(superposition,[status(thm)],[c_2851,c_3665]) ).
tcf(c_5953,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_5938,c_126]) ).
tcf(c_5957,plain,
join(zero,iPr_def_11) = join(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_5943,c_226]) ).
tcf(c_5958,plain,
join(iPr_def_11,zero) = join(iPr_def_11,iPr_def_11),
inference(theory_normalisation,[status(thm)],[c_5957,c_66,c_65]) ).
tcf(c_5959,plain,
join(zero,iPr_def_10) = join(iPr_def_10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_5942,c_225]) ).
tcf(c_5960,plain,
join(iPr_def_10,zero) = join(iPr_def_10,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_5959,c_66,c_65]) ).
tcf(c_5961,plain,
join(zero,iPr_def_13) = join(iPr_def_13,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_5941,c_136]) ).
tcf(c_5962,plain,
join(iPr_def_13,zero) = join(iPr_def_13,iPr_def_13),
inference(theory_normalisation,[status(thm)],[c_5961,c_66,c_65]) ).
tcf(c_6031,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_5953,c_66]) ).
tcf(c_6312,plain,
join(iPr_def_10,join(iPr_def_11,iPr_def_11)) = join(iPr_def_12,zero),
inference(superposition,[status(thm)],[c_5958,c_238]) ).
tcf(c_6313,plain,
join(iPr_def_11,iPr_def_12) = join(iPr_def_12,zero),
inference(demodulation,[status(thm)],[c_6312,c_1646]) ).
tcf(c_6352,plain,
composition(top,converse(iPr_def_13)) = converse(iPr_def_14),
inference(superposition,[status(thm)],[c_405,c_3730]) ).
tcf(c_6441,plain,
! [X0: $i] : join(composition(X0,converse(iPr_def_13)),converse(iPr_def_14)) = composition(join(X0,top),converse(iPr_def_13)),
inference(superposition,[status(thm)],[c_6352,c_70]) ).
tcf(c_6452,plain,
! [X0: $i] : join(converse(iPr_def_14),composition(X0,converse(iPr_def_13))) = composition(top,converse(iPr_def_13)),
inference(demodulation,[status(thm)],[c_6441,c_65,c_3392]) ).
tcf(c_6453,plain,
! [X0: $i] : join(converse(iPr_def_14),composition(X0,converse(iPr_def_13))) = converse(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6452,c_6352]) ).
tcf(c_7946,plain,
join(zero,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_2849,c_6031]) ).
tcf(c_7949,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_3665,c_6031]) ).
tcf(c_7963,plain,
join(iPr_def_12,zero) = iPr_def_12,
inference(demodulation,[status(thm)],[c_7946,c_65]) ).
tcf(c_7965,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_3665,c_7949]) ).
tcf(c_7970,plain,
complement(join(iPr_def_13,iPr_def_13)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2849,c_7949]) ).
tcf(c_7971,plain,
complement(join(iPr_def_10,iPr_def_10)) = iPr_def_16,
inference(demodulation,[status(thm)],[c_2850,c_7949]) ).
tcf(c_7973,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_6313,c_7963]) ).
tcf(c_7988,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_7949,c_65]) ).
tcf(c_8028,plain,
converse(complement(converse(zero))) = top,
inference(superposition,[status(thm)],[c_7949,c_3709]) ).
tcf(c_8040,plain,
join(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5960,c_7988]) ).
tcf(c_8042,plain,
join(iPr_def_13,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5962,c_7988]) ).
tcf(c_8761,plain,
complement(iPr_def_13) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_7970,c_8042]) ).
tcf(c_8771,plain,
complement(iPr_def_10) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_7971,c_8040]) ).
tcf(c_8996,plain,
complement(converse(zero)) = converse(top),
inference(superposition,[status(thm)],[c_8028,c_71]) ).
tcf(c_9003,plain,
complement(converse(zero)) = top,
inference(light_normalisation,[status(thm)],[c_8996,c_3706]) ).
tcf(c_9030,plain,
! [X0: $i] : join(complement(join(top,X0)),complement(join(top,complement(X0)))) = converse(zero),
inference(superposition,[status(thm)],[c_9003,c_92]) ).
tcf(c_9032,plain,
! [X0: $i] : join(complement(join(complement(X0),converse(zero))),complement(join(complement(X0),top))) = X0,
inference(superposition,[status(thm)],[c_9003,c_92]) ).
tcf(c_9035,plain,
join(complement(top),complement(top)) = converse(zero),
inference(demodulation,[status(thm)],[c_9030,c_3404]) ).
tcf(c_9036,plain,
join(zero,zero) = converse(zero),
inference(light_normalisation,[status(thm)],[c_9035,c_126]) ).
tcf(c_9037,plain,
converse(zero) = zero,
inference(ac_demodulation,[status(thm)],[c_9036,c_7949,c_66,c_65]) ).
tcf(c_9038,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),converse(zero)))) = X0,
inference(demodulation,[status(thm)],[c_9032,c_65,c_3392]) ).
tcf(c_9039,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),converse(zero)))) = X0,
inference(light_normalisation,[status(thm)],[c_9038,c_126]) ).
tcf(c_9040,plain,
! [X0: $i] : complement(join(complement(X0),converse(zero))) = X0,
inference(ac_demodulation,[status(thm)],[c_9039,c_7949,c_66,c_65]) ).
tcf(c_9141,plain,
join(zero,complement(iPr_def_12)) = iPr_def_13,
inference(superposition,[status(thm)],[c_8761,c_7965]) ).
tcf(c_9148,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(superposition,[status(thm)],[c_7965,c_7949]) ).
tcf(c_9150,plain,
complement(iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_9141,c_7949]) ).
tcf(c_9989,plain,
! [X0: $i] : complement(join(complement(X0),zero)) = X0,
inference(light_normalisation,[status(thm)],[c_9040,c_9037]) ).
tcf(c_9990,plain,
! [X0: $i] : complement(join(zero,complement(X0))) = X0,
inference(theory_normalisation,[status(thm)],[c_9989,c_66,c_65]) ).
tcf(c_13020,plain,
! [X0: $i] : join(X0,composition(one,X0)) = X0,
inference(superposition,[status(thm)],[c_9990,c_2535]) ).
tcf(c_13032,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_13020,c_2533]) ).
tcf(c_13068,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_13032,c_66]) ).
tcf(c_15525,plain,
join(converse(iPr_def_14),converse(iPr_def_13)) = converse(iPr_def_14),
inference(superposition,[status(thm)],[c_2533,c_6453]) ).
tcf(c_15535,plain,
converse(join(iPr_def_13,iPr_def_14)) = converse(iPr_def_14),
inference(demodulation,[status(thm)],[c_15525,c_65,c_72]) ).
tcf(c_15553,plain,
join(iPr_def_13,iPr_def_14) = converse(converse(iPr_def_14)),
inference(superposition,[status(thm)],[c_15535,c_71]) ).
tcf(c_15561,plain,
join(iPr_def_13,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_15553,c_71]) ).
tcf(c_18488,plain,
join(complement(top),complement(join(complement(iPr_def_10),complement(iPr_def_12)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_3386,c_651]) ).
tcf(c_18538,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),X1) = X1,
inference(superposition,[status(thm)],[c_651,c_13068]) ).
tcf(c_18552,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(X1,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_18538,c_65]) ).
tcf(c_18568,plain,
join(zero,complement(join(iPr_def_16,iPr_def_13))) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_18488,c_126,c_8771,c_9150]) ).
tcf(c_18569,plain,
join(zero,complement(join(iPr_def_13,iPr_def_16))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_18568,c_66,c_65]) ).
tcf(c_18570,plain,
complement(join(iPr_def_13,iPr_def_16)) = iPr_def_10,
inference(ac_demodulation,[status(thm)],[c_18569,c_7949,c_66,c_65]) ).
tcf(c_18913,plain,
join(iPr_def_13,iPr_def_16) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_18570,c_9148]) ).
tcf(c_18920,plain,
join(iPr_def_13,iPr_def_16) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_18913,c_8771]) ).
tcf(c_18948,plain,
join(iPr_def_16,composition(iPr_def_13,top)) = composition(iPr_def_16,top),
inference(superposition,[status(thm)],[c_18920,c_373]) ).
tcf(c_18954,plain,
join(iPr_def_16,iPr_def_14) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_18948,c_228,c_405]) ).
tcf(c_18955,plain,
join(iPr_def_14,iPr_def_16) = iPr_def_16,
inference(theory_normalisation,[status(thm)],[c_18954,c_66,c_65]) ).
tcf(c_18960,plain,
! [X0: $i] : join(iPr_def_14,join(iPr_def_16,X0)) = join(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_18955,c_66]) ).
tcf(c_19155,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_659,c_13068]) ).
tcf(c_19168,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(demodulation,[status(thm)],[c_19155,c_65]) ).
tcf(c_19424,plain,
! [X0: $i] : join(iPr_def_12,complement(join(X0,iPr_def_13))) = iPr_def_12,
inference(superposition,[status(thm)],[c_9150,c_18552]) ).
tcf(c_19430,plain,
! [X0: $i] : join(iPr_def_13,complement(join(X0,iPr_def_12))) = iPr_def_13,
inference(superposition,[status(thm)],[c_8761,c_18552]) ).
tcf(c_19724,plain,
! [X0: $i] : join(iPr_def_12,complement(join(iPr_def_13,X0))) = iPr_def_12,
inference(superposition,[status(thm)],[c_65,c_19424]) ).
tcf(c_20196,plain,
join(iPr_def_12,complement(iPr_def_14)) = iPr_def_12,
inference(superposition,[status(thm)],[c_15561,c_19724]) ).
tcf(c_21988,plain,
join(complement(iPr_def_12),complement(join(iPr_def_11,complement(iPr_def_12)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_7973,c_666]) ).
tcf(c_22033,plain,
join(iPr_def_13,complement(join(iPr_def_11,iPr_def_13))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_21988,c_9150]) ).
tcf(c_22202,plain,
join(iPr_def_14,composition(complement(join(iPr_def_11,iPr_def_13)),top)) = composition(iPr_def_15,top),
inference(superposition,[status(thm)],[c_22033,c_362]) ).
tcf(c_22216,plain,
join(iPr_def_14,composition(complement(join(iPr_def_11,iPr_def_13)),top)) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_22202,c_227]) ).
tcf(c_23274,plain,
join(iPr_def_16,complement(iPr_def_14)) = top,
inference(superposition,[status(thm)],[c_18960,c_3415]) ).
tcf(c_24632,plain,
join(complement(join(iPr_def_10,complement(iPr_def_14))),complement(top)) = iPr_def_14,
inference(superposition,[status(thm)],[c_23274,c_677]) ).
tcf(c_24664,plain,
join(complement(top),complement(join(iPr_def_10,complement(iPr_def_14)))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_24632,c_65]) ).
tcf(c_24665,plain,
join(zero,complement(join(iPr_def_10,complement(iPr_def_14)))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_24664,c_126]) ).
tcf(c_24666,plain,
complement(join(iPr_def_10,complement(iPr_def_14))) = iPr_def_14,
inference(ac_demodulation,[status(thm)],[c_24665,c_7949,c_66,c_65]) ).
tcf(c_24943,plain,
join(iPr_def_10,complement(iPr_def_14)) = complement(iPr_def_14),
inference(superposition,[status(thm)],[c_24666,c_9148]) ).
tcf(c_25183,plain,
join(complement(iPr_def_12),complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_20196,c_678]) ).
tcf(c_25241,plain,
join(iPr_def_13,complement(join(iPr_def_13,complement(iPr_def_14)))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_25183,c_9150]) ).
tcf(c_25897,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X0,X1))) = complement(X0),
inference(superposition,[status(thm)],[c_9148,c_19168]) ).
tcf(c_57510,plain,
join(complement(iPr_def_14),complement(iPr_def_15)) = complement(iPr_def_14),
inference(superposition,[status(thm)],[c_22216,c_25897]) ).
tcf(c_57676,plain,
join(complement(iPr_def_14),iPr_def_11) = complement(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_57510,c_226]) ).
tcf(c_57677,plain,
join(iPr_def_11,complement(iPr_def_14)) = complement(iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_57676,c_66,c_65]) ).
tcf(c_58097,plain,
join(iPr_def_10,complement(iPr_def_14)) = join(iPr_def_12,complement(iPr_def_14)),
inference(superposition,[status(thm)],[c_57677,c_238]) ).
tcf(c_58111,plain,
complement(iPr_def_14) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_58097,c_20196,c_24943]) ).
tcf(c_58144,plain,
join(iPr_def_13,complement(join(iPr_def_13,iPr_def_12))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_25241,c_58111]) ).
tcf(c_58160,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_58144,c_19430]) ).
tcf(c_58243,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_140,c_58160]) ).
tcf(c_58244,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_58243]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 07:16:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running UEQ theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 43.10/8.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 43.10/8.29 % SZS status Started for theBenchmark.p
% 43.10/8.29 % SZS status Unsatisfiable for theBenchmark.p
% 43.10/8.29
% 43.10/8.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 43.10/8.29
% 43.10/8.29 % ------ iProver source info
% 43.10/8.29
% 43.10/8.29 % git: date: 2026-07-19 20:42:38 +0200
% 43.10/8.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 43.10/8.29 % git: non_committed_changes: false
% 43.10/8.29
% 43.10/8.29 % ------ Parsing...% successful
% 43.10/8.29
% 43.10/8.29
% 43.10/8.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 43.10/8.29
% 43.10/8.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 43.10/8.29
% 43.10/8.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 43.10/8.29
% 43.10/8.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 43.10/8.29 % ------ Proving...
% 43.10/8.29 % ------ Problem Properties
% 43.10/8.29
% 43.10/8.29 %
% 43.10/8.29 % clauses 22
% 43.10/8.29 % conjectures 3
% 43.10/8.29 % EPR 3
% 43.10/8.29 % Horn 22
% 43.10/8.29 % unary 22
% 43.10/8.29 % binary 0
% 43.10/8.29 % lits 22
% 43.10/8.29 % lits eq 22
% 43.10/8.29 % fd_pure 0
% 43.10/8.29 % fd_pseudo 0
% 43.10/8.29 % fd_cond 0
% 43.10/8.29 % fd_pseudo_cond 0
% 43.10/8.29 % AC symbols 1
% 43.10/8.29
% 43.10/8.29 % ------ Input Options Time Limit: Unbounded
% 43.10/8.29
% 43.10/8.29
% 43.10/8.29 % ------
% 43.10/8.29 % Current options:
% 43.10/8.29 % ------
% 43.10/8.29
% 43.10/8.29
% 43.10/8.29 %
% 43.10/8.29
% 43.10/8.29 % ------ Proving...
% 43.10/8.29 %
% 43.10/8.29
% 43.10/8.29 % SZS status Unsatisfiable for theBenchmark.p
% 43.10/8.29
% 43.10/8.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 43.10/8.29
% 43.10/8.29
%------------------------------------------------------------------------------