%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : REL050+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:20:32 EDT 2022
% Result : Theorem 0.23s 2.41s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 119 ( 112 unt; 0 def)
% Number of atoms : 126 ( 125 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 5 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 192 ( 18 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modular_law_1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(dedekind_law,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(goals,conjecture,
! [X1] :
( join(complement(composition(X1,top)),composition(complement(composition(X1,top)),top)) = composition(complement(composition(X1,top)),top)
& join(composition(complement(composition(X1,top)),top),complement(composition(X1,top))) = complement(composition(X1,top)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(c_0_16,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6)) = meet(composition(X4,meet(X5,composition(converse(X4),X6))),X6),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
fof(c_0_17,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
fof(c_0_18,plain,
! [X2] : top = join(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_19,plain,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_20,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X3,X4] : join(X3,X4) = join(X4,X3),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_23,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_26,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]) ).
fof(c_0_29,plain,
! [X2] : composition(X2,one) = X2,
inference(variable_rename,[status(thm)],[composition_identity]) ).
fof(c_0_30,plain,
! [X3,X4] : X3 = join(complement(join(complement(X3),complement(X4))),complement(join(complement(X3),X4))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_0_31,plain,
join(top,complement(join(complement(composition(X1,X2)),complement(X3)))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]),c_0_26]) ).
cnf(c_0_32,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_34,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_35,plain,
join(top,complement(join(complement(X1),complement(X2)))) = top,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_37,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
join(top,complement(X1)) = top,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_40,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_27,c_0_38]) ).
cnf(c_0_41,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_42,plain,
join(zero,complement(join(zero,complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_41]),c_0_41]),c_0_26]) ).
fof(c_0_43,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_44,plain,
! [X2] : converse(converse(X2)) = X2,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_45,plain,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
cnf(c_0_46,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_23]),c_0_41]) ).
cnf(c_0_47,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_24,c_0_46]) ).
cnf(c_0_51,plain,
join(zero,complement(join(complement(X1),complement(complement(complement(X1)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_41]) ).
cnf(c_0_52,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_54,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
converse(join(X1,converse(top))) = top,
inference(spm,[status(thm)],[c_0_52,c_0_40]) ).
cnf(c_0_56,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
fof(c_0_57,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
fof(c_0_58,plain,
! [X4,X5,X6] : composition(join(X4,X5),X6) = join(composition(X4,X6),composition(X5,X6)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_59,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_41]),c_0_54]) ).
cnf(c_0_60,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
composition(top,complement(composition(top,top))) = zero,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
fof(c_0_64,plain,
! [X4,X5,X6] : join(meet(composition(X4,X5),X6),composition(meet(X4,composition(X6,converse(X5))),meet(X5,composition(converse(X4),X6)))) = composition(meet(X4,composition(X6,converse(X5))),meet(X5,composition(converse(X4),X6))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
fof(c_0_65,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
cnf(c_0_66,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_54]),c_0_54]) ).
cnf(c_0_67,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_26]),c_0_24]) ).
cnf(c_0_68,plain,
join(complement(join(zero,X1)),complement(join(zero,complement(X1)))) = top,
inference(spm,[status(thm)],[c_0_36,c_0_41]) ).
cnf(c_0_69,plain,
composition(X1,composition(one,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
cnf(c_0_70,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_54]),c_0_56]),c_0_63]) ).
cnf(c_0_71,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_72,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
join(complement(X1),join(complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))),complement(join(complement(X1),join(complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))),complement(join(complement(composition(X2,X3)),complement(X1)))))))) = join(complement(composition(X2,X3)),complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_66]),c_0_66]),c_0_67]),c_0_26]),c_0_24]) ).
cnf(c_0_74,plain,
complement(zero) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_23]),c_0_41]),c_0_42]) ).
cnf(c_0_75,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_70]) ).
cnf(c_0_76,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_77,plain,
converse(composition(converse(X1),converse(X2))) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_48,c_0_72]) ).
cnf(c_0_78,plain,
join(complement(composition(X1,X2)),composition(top,top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_66]),c_0_74]),c_0_40]),c_0_41]),c_0_75]),c_0_74]),c_0_66]),c_0_74]),c_0_40]),c_0_41]),c_0_75]),c_0_74]),c_0_66]),c_0_56]),c_0_40]),c_0_41]),c_0_56]),c_0_40]),c_0_66]) ).
cnf(c_0_79,plain,
join(composition(complement(join(complement(X1),complement(composition(X2,converse(X3))))),complement(join(complement(X3),complement(composition(converse(X1),X2))))),complement(join(complement(composition(X1,X3)),complement(X2)))) = composition(complement(join(complement(X1),complement(composition(X2,converse(X3))))),complement(join(complement(X3),complement(composition(converse(X1),X2))))),
inference(rw,[status(thm)],[c_0_76,c_0_26]) ).
cnf(c_0_80,plain,
converse(composition(top,converse(X1))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_77,c_0_60]) ).
cnf(c_0_81,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_54]) ).
cnf(c_0_82,plain,
join(complement(X1),composition(top,top)) = top,
inference(spm,[status(thm)],[c_0_78,c_0_32]) ).
cnf(c_0_83,plain,
join(composition(X1,X2),composition(complement(join(complement(X1),complement(composition(top,converse(X2))))),complement(join(complement(X2),complement(converse(composition(top,X1))))))) = composition(complement(join(complement(X1),complement(composition(top,converse(X2))))),complement(join(complement(X2),complement(converse(composition(top,X1)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_41]),c_0_80]),c_0_48]),c_0_81]),c_0_66]),c_0_26]),c_0_80]),c_0_48]) ).
cnf(c_0_84,plain,
composition(top,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_41]),c_0_54]) ).
cnf(c_0_85,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_86,plain,
composition(top,composition(converse(X1),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_41]),c_0_54]),c_0_66]),c_0_60]),c_0_41]),c_0_26]),c_0_54]),c_0_66]),c_0_61]),c_0_85]),c_0_56]),c_0_41]),c_0_54]),c_0_66]),c_0_60]),c_0_41]),c_0_26]),c_0_54]),c_0_66]),c_0_61]) ).
cnf(c_0_87,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_72,c_0_60]) ).
cnf(c_0_88,plain,
converse(composition(one,top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_32]),c_0_32]),c_0_87]) ).
cnf(c_0_89,plain,
join(complement(join(complement(converse(composition(X1,X2))),complement(X3))),complement(join(complement(X3),complement(composition(converse(X2),complement(join(complement(converse(X1)),complement(composition(X2,X3))))))))) = complement(join(complement(X3),complement(composition(converse(X2),complement(join(complement(converse(X1)),complement(composition(X2,X3)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_72]),c_0_48]),c_0_48]) ).
cnf(c_0_90,plain,
composition(one,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_88]),c_0_60]) ).
cnf(c_0_91,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_72,c_0_32]) ).
cnf(c_0_92,plain,
converse(join(X1,X1)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_32]),c_0_41]),c_0_81]),c_0_66]),c_0_41]),c_0_41]),c_0_81]),c_0_66]),c_0_91]),c_0_54]),c_0_66]),c_0_52]),c_0_48]),c_0_41]),c_0_41]),c_0_81]),c_0_66]),c_0_91]),c_0_54]),c_0_66]) ).
cnf(c_0_93,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_92]),c_0_48]) ).
cnf(c_0_94,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_93]),c_0_24]),c_0_93]) ).
cnf(c_0_95,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_96,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_97,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_26]) ).
cnf(c_0_98,plain,
join(complement(X1),complement(join(complement(X1),X2))) = join(complement(X1),complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_36]),c_0_67]),c_0_26]),c_0_97]),c_0_26]) ).
cnf(c_0_99,plain,
join(complement(composition(X1,X2)),composition(X1,top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_59]),c_0_66]),c_0_74]),c_0_40]),c_0_41]),c_0_75]),c_0_74]),c_0_66]),c_0_74]),c_0_40]),c_0_41]),c_0_75]),c_0_74]),c_0_66]),c_0_56]),c_0_40]),c_0_41]),c_0_56]),c_0_40]),c_0_66]) ).
fof(c_0_100,negated_conjecture,
~ ! [X1] :
( join(complement(composition(X1,top)),composition(complement(composition(X1,top)),top)) = composition(complement(composition(X1,top)),top)
& join(composition(complement(composition(X1,top)),top),complement(composition(X1,top))) = complement(composition(X1,top)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_101,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_98,c_0_66]) ).
cnf(c_0_102,plain,
join(composition(X1,top),complement(composition(X1,X2))) = top,
inference(spm,[status(thm)],[c_0_26,c_0_99]) ).
fof(c_0_103,negated_conjecture,
( join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top)
| join(composition(complement(composition(esk2_0,top)),top),complement(composition(esk2_0,top))) != complement(composition(esk2_0,top)) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])]) ).
cnf(c_0_104,plain,
join(complement(converse(X1)),composition(X2,complement(converse(composition(X1,X2))))) = complement(converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_72]),c_0_48]) ).
cnf(c_0_105,plain,
converse(join(X1,converse(complement(converse(X1))))) = top,
inference(spm,[status(thm)],[c_0_23,c_0_52]) ).
cnf(c_0_106,plain,
join(composition(X1,top),composition(X1,X2)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_41]),c_0_81]),c_0_66]) ).
cnf(c_0_107,negated_conjecture,
( join(composition(complement(composition(esk2_0,top)),top),complement(composition(esk2_0,top))) != complement(composition(esk2_0,top))
| join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_108,plain,
join(complement(composition(X1,top)),composition(X2,complement(converse(composition(top,composition(converse(X1),X2)))))) = complement(composition(X1,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_80]),c_0_61]) ).
cnf(c_0_109,plain,
complement(converse(zero)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_54]),c_0_48]) ).
cnf(c_0_110,plain,
join(X1,composition(X1,top)) = composition(X1,top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_32]),c_0_26]) ).
cnf(c_0_111,negated_conjecture,
( join(complement(composition(esk1_0,top)),composition(complement(composition(esk1_0,top)),top)) != composition(complement(composition(esk1_0,top)),top)
| join(complement(composition(esk2_0,top)),composition(complement(composition(esk2_0,top)),top)) != complement(composition(esk2_0,top)) ),
inference(rw,[status(thm)],[c_0_107,c_0_26]) ).
cnf(c_0_112,plain,
converse(composition(top,converse(complement(composition(X1,top))))) = complement(composition(X1,top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_59]),c_0_75]),c_0_109]),c_0_110]),c_0_80]) ).
cnf(c_0_113,negated_conjecture,
( join(complement(composition(esk1_0,top)),converse(composition(converse(top),converse(complement(composition(esk1_0,top)))))) != converse(composition(converse(top),converse(complement(composition(esk1_0,top)))))
| join(complement(composition(esk2_0,top)),converse(composition(converse(top),converse(complement(composition(esk2_0,top)))))) != complement(composition(esk2_0,top)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_77]),c_0_77]),c_0_77]) ).
cnf(c_0_114,plain,
composition(top,converse(complement(composition(X1,top)))) = converse(complement(composition(X1,top))),
inference(spm,[status(thm)],[c_0_48,c_0_112]) ).
cnf(c_0_115,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_72,c_0_48]) ).
cnf(c_0_116,negated_conjecture,
( join(complement(converse(composition(top,converse(esk1_0)))),converse(composition(top,converse(complement(converse(composition(top,converse(esk1_0)))))))) != converse(composition(top,converse(complement(converse(composition(top,converse(esk1_0)))))))
| join(complement(converse(composition(top,converse(esk2_0)))),converse(composition(top,converse(complement(converse(composition(top,converse(esk2_0)))))))) != complement(converse(composition(top,converse(esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_60]),c_0_60]),c_0_60]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]),c_0_80]) ).
cnf(c_0_117,plain,
composition(top,converse(complement(converse(composition(top,X1))))) = converse(complement(converse(composition(top,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_60]),c_0_60]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_117]),c_0_48]),c_0_93]),c_0_117]),c_0_48]),c_0_117]),c_0_48]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : REL050+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 8 08:40:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.23/2.41 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.23/2.41 # Preprocessing time : 0.014 s
% 0.23/2.41
% 0.23/2.41 # Proof found!
% 0.23/2.41 # SZS status Theorem
% 0.23/2.41 # SZS output start CNFRefutation
% See solution above
% 0.23/2.41 # Proof object total steps : 119
% 0.23/2.41 # Proof object clause steps : 86
% 0.23/2.41 # Proof object formula steps : 33
% 0.23/2.41 # Proof object conjectures : 8
% 0.23/2.41 # Proof object clause conjectures : 5
% 0.23/2.41 # Proof object formula conjectures : 3
% 0.23/2.41 # Proof object initial clauses used : 16
% 0.23/2.41 # Proof object initial formulas used : 16
% 0.23/2.41 # Proof object generating inferences : 57
% 0.23/2.41 # Proof object simplifying inferences : 173
% 0.23/2.41 # Training examples: 0 positive, 0 negative
% 0.23/2.41 # Parsed axioms : 17
% 0.23/2.41 # Removed by relevancy pruning/SinE : 0
% 0.23/2.41 # Initial clauses : 17
% 0.23/2.41 # Removed in clause preprocessing : 1
% 0.23/2.41 # Initial clauses in saturation : 16
% 0.23/2.41 # Processed clauses : 1654
% 0.23/2.41 # ...of these trivial : 850
% 0.23/2.41 # ...subsumed : 228
% 0.23/2.41 # ...remaining for further processing : 576
% 0.23/2.41 # Other redundant clauses eliminated : 0
% 0.23/2.41 # Clauses deleted for lack of memory : 0
% 0.23/2.41 # Backward-subsumed : 0
% 0.23/2.41 # Backward-rewritten : 166
% 0.23/2.41 # Generated clauses : 103790
% 0.23/2.41 # ...of the previous two non-trivial : 78906
% 0.23/2.41 # Contextual simplify-reflections : 0
% 0.23/2.41 # Paramodulations : 103790
% 0.23/2.41 # Factorizations : 0
% 0.23/2.41 # Equation resolutions : 0
% 0.23/2.41 # Current number of processed clauses : 410
% 0.23/2.41 # Positive orientable unit clauses : 357
% 0.23/2.41 # Positive unorientable unit clauses: 53
% 0.23/2.41 # Negative unit clauses : 0
% 0.23/2.41 # Non-unit-clauses : 0
% 0.23/2.41 # Current number of unprocessed clauses: 67095
% 0.23/2.41 # ...number of literals in the above : 67095
% 0.23/2.41 # Current number of archived formulas : 0
% 0.23/2.41 # Current number of archived clauses : 167
% 0.23/2.41 # Clause-clause subsumption calls (NU) : 0
% 0.23/2.41 # Rec. Clause-clause subsumption calls : 0
% 0.23/2.41 # Non-unit clause-clause subsumptions : 0
% 0.23/2.41 # Unit Clause-clause subsumption calls : 1274
% 0.23/2.41 # Rewrite failures with RHS unbound : 0
% 0.23/2.41 # BW rewrite match attempts : 5496
% 0.23/2.41 # BW rewrite match successes : 834
% 0.23/2.41 # Condensation attempts : 0
% 0.23/2.41 # Condensation successes : 0
% 0.23/2.41 # Termbank termtop insertions : 3313239
% 0.23/2.41
% 0.23/2.41 # -------------------------------------------------
% 0.23/2.41 # User time : 1.477 s
% 0.23/2.41 # System time : 0.058 s
% 0.23/2.41 # Total time : 1.535 s
% 0.23/2.41 # Maximum resident set size: 126364 pages
% 0.23/23.39 eprover: CPU time limit exceeded, terminating
% 0.23/23.40 eprover: CPU time limit exceeded, terminating
% 0.23/23.41 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.41 eprover: No such file or directory
% 0.23/23.41 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.41 eprover: No such file or directory
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.42 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.42 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.43 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.43 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.44 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.44 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.45 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.45 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.23/23.46 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
% 0.23/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.23/23.47 eprover: No such file or directory
%------------------------------------------------------------------------------