TSTP Solution File: REL028+2 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : REL028+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 : 300s
% DateTime : Sat May 4 09:13:04 EDT 2024
% Result : Theorem 3.57s 0.86s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 129 ( 126 unt; 0 def)
% Number of atoms : 135 ( 134 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 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 : 160 ( 6 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux1_join_commutativity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',def_zero) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',def_top) ).
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/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',maddux2_join_associativity) ).
fof(goals,conjecture,
! [X1,X2] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> composition(X1,X2) = meet(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',goals) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',converse_additivity) ).
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/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',dedekind_law) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p',composition_associativity) ).
fof(c_0_15,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_16,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_17,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_20,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X25,X26] : join(composition(converse(X25),complement(composition(X25,X26))),complement(X26)) = complement(X26),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_23,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_24,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]) ).
fof(c_0_25,plain,
! [X28] : zero = meet(X28,complement(X28)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_26,plain,
! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_27,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_30,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_33,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_35,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,plain,
! [X9,X10] : X9 = join(complement(join(complement(X9),complement(X10))),complement(join(complement(X9),X10))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_38,plain,
! [X6,X7,X8] : join(X6,join(X7,X8)) = join(join(X6,X7),X8),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_39,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_34]) ).
cnf(c_0_40,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_45,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_36]),c_0_40]),c_0_28]) ).
cnf(c_0_47,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_48,negated_conjecture,
~ ! [X1,X2] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> composition(X1,X2) = meet(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_49,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_50,negated_conjecture,
( join(esk1_0,one) = one
& join(esk2_0,one) = one
& composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
cnf(c_0_51,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
join(esk2_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_53,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_51]) ).
fof(c_0_54,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_55,negated_conjecture,
join(one,esk2_0) = one,
inference(rw,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_56,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_57,plain,
! [X29,X30,X31] : join(meet(composition(X29,X30),X31),composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31)))) = composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_58,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_44]),c_0_28]) ).
cnf(c_0_59,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_53,c_0_28]) ).
cnf(c_0_60,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
join(one,join(esk2_0,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_63,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_57]) ).
cnf(c_0_64,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_29]) ).
cnf(c_0_66,negated_conjecture,
join(one,complement(join(complement(esk2_0),X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_58]),c_0_55]) ).
cnf(c_0_67,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_42]) ).
fof(c_0_68,plain,
! [X17,X18,X19] : composition(join(X17,X18),X19) = join(composition(X17,X19),composition(X18,X19)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_69,negated_conjecture,
join(one,join(esk1_0,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_62]) ).
cnf(c_0_70,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_63,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_71,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_72,negated_conjecture,
join(one,converse(esk2_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_55]),c_0_29]) ).
cnf(c_0_73,negated_conjecture,
join(complement(one),join(complement(esk2_0),X1)) = join(complement(esk2_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_66]),c_0_42]),c_0_67]) ).
cnf(c_0_74,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_75,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_76,negated_conjecture,
join(one,complement(join(complement(esk1_0),X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_58]),c_0_62]) ).
cnf(c_0_77,plain,
join(complement(join(complement(one),complement(composition(X1,X2)))),composition(complement(join(complement(X1),complement(converse(X2)))),complement(join(complement(X2),complement(converse(X1)))))) = composition(complement(join(complement(X1),complement(converse(X2)))),complement(join(complement(X2),complement(converse(X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_21]),c_0_28]),c_0_34]),c_0_34]) ).
cnf(c_0_78,negated_conjecture,
join(complement(one),complement(converse(esk2_0))) = complement(converse(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_28]) ).
cnf(c_0_79,negated_conjecture,
join(complement(one),complement(esk2_0)) = complement(esk2_0),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_75,c_0_34]) ).
cnf(c_0_81,negated_conjecture,
join(one,converse(esk1_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_62]),c_0_29]) ).
cnf(c_0_82,negated_conjecture,
join(complement(one),join(complement(esk1_0),X1)) = join(complement(esk1_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_76]),c_0_42]),c_0_67]) ).
cnf(c_0_83,negated_conjecture,
join(esk2_0,composition(converse(esk2_0),esk2_0)) = composition(converse(esk2_0),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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_34]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_79]),c_0_49]) ).
cnf(c_0_84,negated_conjecture,
join(X1,composition(converse(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_72]),c_0_34]) ).
cnf(c_0_85,negated_conjecture,
join(complement(one),complement(converse(esk1_0))) = complement(converse(esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_81]),c_0_28]) ).
cnf(c_0_86,negated_conjecture,
join(complement(one),complement(esk1_0)) = complement(esk1_0),
inference(spm,[status(thm)],[c_0_82,c_0_74]) ).
cnf(c_0_87,negated_conjecture,
join(X1,composition(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_55]),c_0_34]) ).
cnf(c_0_88,negated_conjecture,
composition(converse(esk2_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
join(esk1_0,composition(converse(esk1_0),esk1_0)) = composition(converse(esk1_0),esk1_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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_85]),c_0_34]),c_0_86]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_86]),c_0_49]),c_0_49]),c_0_29]),c_0_28]),c_0_86]),c_0_49]) ).
cnf(c_0_90,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_34]) ).
cnf(c_0_91,plain,
join(complement(join(complement(X1),complement(X2))),composition(complement(join(complement(one),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(X2))))) = composition(complement(join(complement(one),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_29]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_92,negated_conjecture,
join(one,composition(esk2_0,esk1_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_87]),c_0_62]) ).
fof(c_0_93,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_94,negated_conjecture,
converse(esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_88]),c_0_88]) ).
cnf(c_0_95,negated_conjecture,
composition(converse(esk1_0),esk1_0) = esk1_0,
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,plain,
composition(complement(join(complement(one),complement(composition(X1,converse(X2))))),complement(join(complement(X2),complement(X1)))) = complement(join(complement(X2),complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_80]),c_0_58]),c_0_34]) ).
cnf(c_0_97,negated_conjecture,
join(complement(one),complement(composition(esk2_0,esk1_0))) = complement(composition(esk2_0,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_92]),c_0_28]) ).
cnf(c_0_98,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_99,negated_conjecture,
converse(join(esk2_0,X1)) = join(esk2_0,converse(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
converse(composition(X1,esk2_0)) = composition(esk2_0,converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_94]) ).
cnf(c_0_101,negated_conjecture,
converse(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_95]),c_0_95]) ).
cnf(c_0_102,negated_conjecture,
composition(esk2_0,composition(esk1_0,composition(esk2_0,esk1_0))) = composition(esk2_0,esk1_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(spm,[status(thm)],[c_0_96,c_0_97]),c_0_29]),c_0_21]),c_0_97]),c_0_49]),c_0_49]),c_0_98]),c_0_49]) ).
cnf(c_0_103,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_75,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_62]),c_0_34]) ).
cnf(c_0_105,negated_conjecture,
join(esk2_0,composition(esk2_0,esk1_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_90]),c_0_94]),c_0_100]),c_0_18]) ).
cnf(c_0_106,negated_conjecture,
converse(composition(esk1_0,X1)) = composition(converse(X1),esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
composition(esk1_0,composition(esk2_0,esk1_0)) = composition(esk2_0,esk1_0),
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_80,c_0_102]),c_0_103]),c_0_55]),c_0_34]),c_0_28]),c_0_104]) ).
cnf(c_0_108,negated_conjecture,
converse(composition(esk2_0,X1)) = composition(converse(X1),esk2_0),
inference(spm,[status(thm)],[c_0_20,c_0_94]) ).
cnf(c_0_109,plain,
join(complement(join(complement(X1),complement(X2))),composition(complement(join(complement(X1),complement(X2))),complement(join(complement(one),complement(composition(converse(X1),X2)))))) = composition(complement(join(complement(X1),complement(X2))),complement(join(complement(one),complement(composition(converse(X1),X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_21]),c_0_29]),c_0_21]),c_0_29]),c_0_21]) ).
cnf(c_0_110,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_111,negated_conjecture,
join(complement(esk2_0),complement(composition(esk2_0,esk1_0))) = complement(composition(esk2_0,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_105]),c_0_28]) ).
cnf(c_0_112,negated_conjecture,
composition(esk2_0,esk1_0) = composition(esk1_0,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(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_101]),c_0_108]),c_0_101]),c_0_98]),c_0_107]) ).
cnf(c_0_113,negated_conjecture,
join(esk2_0,composition(esk2_0,esk2_0)) = composition(esk2_0,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_34]),c_0_79]),c_0_49]),c_0_49]),c_0_29]),c_0_34]),c_0_79]),c_0_49]) ).
cnf(c_0_114,negated_conjecture,
join(X1,join(composition(esk2_0,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_87]) ).
cnf(c_0_115,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_51]),c_0_36]) ).
cnf(c_0_116,plain,
join(complement(join(complement(composition(X1,converse(X2))),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,X2)))),complement(join(complement(converse(X2)),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,X2)))),complement(join(complement(converse(X2)),complement(composition(converse(X1),X3))))),
inference(spm,[status(thm)],[c_0_70,c_0_18]) ).
cnf(c_0_117,negated_conjecture,
join(complement(esk2_0),complement(composition(esk1_0,esk2_0))) = complement(composition(esk1_0,esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_112]) ).
cnf(c_0_118,negated_conjecture,
composition(esk2_0,esk2_0) = esk2_0,
inference(rw,[status(thm)],[c_0_113,c_0_87]) ).
cnf(c_0_119,negated_conjecture,
composition(esk2_0,composition(esk1_0,esk2_0)) = composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_107]),c_0_112]),c_0_112]) ).
cnf(c_0_120,negated_conjecture,
composition(esk1_0,composition(esk1_0,esk2_0)) = composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_112]),c_0_112]) ).
cnf(c_0_121,negated_conjecture,
join(X1,complement(composition(esk2_0,X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_36]),c_0_115]) ).
cnf(c_0_122,negated_conjecture,
join(composition(esk1_0,esk2_0),complement(join(complement(esk1_0),complement(esk2_0)))) = composition(esk1_0,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)],[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_116,c_0_117]),c_0_94]),c_0_118]),c_0_49]),c_0_94]),c_0_94]),c_0_112]),c_0_117]),c_0_49]),c_0_98]),c_0_119]),c_0_120]),c_0_49]),c_0_94]),c_0_94]),c_0_112]),c_0_117]),c_0_49]),c_0_98]),c_0_119]),c_0_120]),c_0_28]),c_0_28]) ).
cnf(c_0_123,negated_conjecture,
composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_124,plain,
join(complement(join(X1,complement(X2))),complement(join(complement(X2),complement(X1)))) = X2,
inference(spm,[status(thm)],[c_0_44,c_0_28]) ).
cnf(c_0_125,negated_conjecture,
join(esk1_0,complement(composition(esk1_0,esk2_0))) = top,
inference(spm,[status(thm)],[c_0_121,c_0_112]) ).
cnf(c_0_126,negated_conjecture,
join(complement(esk1_0),complement(composition(esk1_0,esk2_0))) = join(complement(esk1_0),complement(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_122]),c_0_49]),c_0_42]),c_0_117]),c_0_49]) ).
cnf(c_0_127,negated_conjecture,
composition(esk1_0,esk2_0) != complement(join(complement(esk1_0),complement(esk2_0))),
inference(rw,[status(thm)],[c_0_123,c_0_31]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_40]),c_0_28]),c_0_126]),c_0_47]),c_0_127]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : REL028+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n015.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 10:01:36 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.FMhjWvl1aB/E---3.1_32737.p
% 3.57/0.86 # Version: 3.1.0
% 3.57/0.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86 # Starting new_bool_3 with 300s (1) cores
% 3.57/0.86 # Starting new_bool_1 with 300s (1) cores
% 3.57/0.86 # Starting sh5l with 300s (1) cores
% 3.57/0.86 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 347 completed with status 0
% 3.57/0.86 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.57/0.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86 # No SInE strategy applied
% 3.57/0.86 # Search class: FUUPM-FFMF21-DFFFFFNN
% 3.57/0.86 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.57/0.86 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 3.57/0.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.57/0.86 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 3.57/0.86 # Starting new_bool_3 with 136s (1) cores
% 3.57/0.86 # Starting new_bool_1 with 136s (1) cores
% 3.57/0.86 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 352 completed with status 0
% 3.57/0.86 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.57/0.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.57/0.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.57/0.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.57/0.86 # No SInE strategy applied
% 3.57/0.86 # Search class: FUUPM-FFMF21-DFFFFFNN
% 3.57/0.86 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.57/0.86 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 3.57/0.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.57/0.86 # Preprocessing time : 0.001 s
% 3.57/0.86 # Presaturation interreduction done
% 3.57/0.86
% 3.57/0.86 # Proof found!
% 3.57/0.86 # SZS status Theorem
% 3.57/0.86 # SZS output start CNFRefutation
% See solution above
% 3.57/0.86 # Parsed axioms : 17
% 3.57/0.86 # Removed by relevancy pruning/SinE : 0
% 3.57/0.86 # Initial clauses : 19
% 3.57/0.86 # Removed in clause preprocessing : 1
% 3.57/0.86 # Initial clauses in saturation : 18
% 3.57/0.86 # Processed clauses : 1530
% 3.57/0.86 # ...of these trivial : 899
% 3.57/0.86 # ...subsumed : 90
% 3.57/0.86 # ...remaining for further processing : 541
% 3.57/0.86 # Other redundant clauses eliminated : 0
% 3.57/0.86 # Clauses deleted for lack of memory : 0
% 3.57/0.86 # Backward-subsumed : 0
% 3.57/0.86 # Backward-rewritten : 133
% 3.57/0.86 # Generated clauses : 31238
% 3.57/0.86 # ...of the previous two non-redundant : 17711
% 3.57/0.86 # ...aggressively subsumed : 0
% 3.57/0.86 # Contextual simplify-reflections : 0
% 3.57/0.86 # Paramodulations : 31238
% 3.57/0.86 # Factorizations : 0
% 3.57/0.86 # NegExts : 0
% 3.57/0.86 # Equation resolutions : 0
% 3.57/0.86 # Disequality decompositions : 0
% 3.57/0.86 # Total rewrite steps : 78685
% 3.57/0.86 # ...of those cached : 70111
% 3.57/0.86 # Propositional unsat checks : 0
% 3.57/0.86 # Propositional check models : 0
% 3.57/0.86 # Propositional check unsatisfiable : 0
% 3.57/0.86 # Propositional clauses : 0
% 3.57/0.86 # Propositional clauses after purity: 0
% 3.57/0.86 # Propositional unsat core size : 0
% 3.57/0.86 # Propositional preprocessing time : 0.000
% 3.57/0.86 # Propositional encoding time : 0.000
% 3.57/0.86 # Propositional solver time : 0.000
% 3.57/0.86 # Success case prop preproc time : 0.000
% 3.57/0.86 # Success case prop encoding time : 0.000
% 3.57/0.86 # Success case prop solver time : 0.000
% 3.57/0.86 # Current number of processed clauses : 390
% 3.57/0.86 # Positive orientable unit clauses : 384
% 3.57/0.86 # Positive unorientable unit clauses: 5
% 3.57/0.86 # Negative unit clauses : 1
% 3.57/0.86 # Non-unit-clauses : 0
% 3.57/0.86 # Current number of unprocessed clauses: 16054
% 3.57/0.86 # ...number of literals in the above : 16054
% 3.57/0.86 # Current number of archived formulas : 0
% 3.57/0.86 # Current number of archived clauses : 152
% 3.57/0.86 # Clause-clause subsumption calls (NU) : 0
% 3.57/0.86 # Rec. Clause-clause subsumption calls : 0
% 3.57/0.86 # Non-unit clause-clause subsumptions : 0
% 3.57/0.86 # Unit Clause-clause subsumption calls : 27
% 3.57/0.86 # Rewrite failures with RHS unbound : 0
% 3.57/0.86 # BW rewrite match attempts : 2471
% 3.57/0.86 # BW rewrite match successes : 192
% 3.57/0.86 # Condensation attempts : 0
% 3.57/0.86 # Condensation successes : 0
% 3.57/0.86 # Termbank termtop insertions : 710959
% 3.57/0.86 # Search garbage collected termcells : 38
% 3.57/0.86
% 3.57/0.86 # -------------------------------------------------
% 3.57/0.86 # User time : 0.403 s
% 3.57/0.86 # System time : 0.020 s
% 3.57/0.86 # Total time : 0.423 s
% 3.57/0.86 # Maximum resident set size: 1716 pages
% 3.57/0.86
% 3.57/0.86 # -------------------------------------------------
% 3.57/0.86 # User time : 2.075 s
% 3.57/0.86 # System time : 0.053 s
% 3.57/0.86 # Total time : 2.128 s
% 3.57/0.86 # Maximum resident set size: 1700 pages
% 3.57/0.86 % E---3.1 exiting
% 3.57/0.86 % E exiting
%------------------------------------------------------------------------------