TSTP Solution File: REL026+1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : REL026+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:13:39 EDT 2023
% Result : Theorem 5.66s 1.21s
% Output : CNFRefutation 5.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of formulae : 157 ( 154 unt; 0 def)
% Number of atoms : 160 ( 159 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 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 : 219 ( 10 sgn; 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',maddux1_join_commutativity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',def_zero) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.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/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.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/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',maddux2_join_associativity) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',converse_additivity) ).
fof(goals,conjecture,
! [X1,X2] :
( join(X1,one) = one
=> meet(composition(X1,top),X2) = composition(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',goals) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p',composition_associativity) ).
fof(c_0_14,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_15,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_16,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_19,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,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_22,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_23,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
fof(c_0_24,plain,
! [X28] : zero = meet(X28,complement(X28)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_25,plain,
! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_26,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_29,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_31,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_32,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,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_37,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_38,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_33]) ).
cnf(c_0_39,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_44,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,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_43,c_0_35]),c_0_38]),c_0_39]),c_0_27]) ).
cnf(c_0_46,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_47]) ).
cnf(c_0_49,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_48]) ).
cnf(c_0_50,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_51,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_43]),c_0_27]) ).
cnf(c_0_52,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_27]) ).
fof(c_0_53,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_54,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_50,c_0_27]) ).
fof(c_0_55,negated_conjecture,
~ ! [X1,X2] :
( join(X1,one) = one
=> meet(composition(X1,top),X2) = composition(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_56,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_59,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_38]),c_0_35]) ).
fof(c_0_60,plain,
! [X17,X18,X19] : composition(join(X17,X18),X19) = join(composition(X17,X19),composition(X18,X19)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_61,negated_conjecture,
( join(esk1_0,one) = one
& meet(composition(esk1_0,top),esk2_0) != composition(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])]) ).
cnf(c_0_62,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_56,c_0_47]) ).
cnf(c_0_63,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_17]) ).
cnf(c_0_64,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_43]),c_0_47]),c_0_27]),c_0_41]),c_0_62]) ).
cnf(c_0_68,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_69,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_27,c_0_64]) ).
cnf(c_0_70,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_65,c_0_33]) ).
cnf(c_0_71,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_66,c_0_27]) ).
cnf(c_0_72,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_67,c_0_47]) ).
cnf(c_0_73,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_33]) ).
cnf(c_0_75,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_76,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_72]),c_0_49]) ).
cnf(c_0_77,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_68,c_0_73]) ).
cnf(c_0_78,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_79,negated_conjecture,
join(X1,composition(X1,converse(esk1_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_74]),c_0_17]),c_0_75]) ).
cnf(c_0_80,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_39]),c_0_78]) ).
cnf(c_0_81,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_82,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_79]),c_0_33]),c_0_33]) ).
cnf(c_0_83,plain,
join(composition(X1,converse(X2)),converse(X3)) = converse(join(composition(X2,converse(X1)),X3)),
inference(spm,[status(thm)],[c_0_57,c_0_75]) ).
cnf(c_0_84,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_16,c_0_63]) ).
cnf(c_0_85,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_80]),c_0_17]),c_0_17]) ).
cnf(c_0_86,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_33]),c_0_27]) ).
cnf(c_0_87,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_81,c_0_27]) ).
cnf(c_0_88,negated_conjecture,
join(X1,composition(X1,esk1_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_82]),c_0_17]),c_0_16]),c_0_17]) ).
cnf(c_0_89,plain,
converse(join(composition(X1,converse(X2)),composition(X1,X3))) = converse(composition(X1,join(converse(X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_16]),c_0_83]),c_0_84]) ).
cnf(c_0_90,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_85,c_0_47]) ).
cnf(c_0_91,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_50,c_0_69]) ).
cnf(c_0_92,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_86,c_0_69]) ).
cnf(c_0_93,negated_conjecture,
join(X1,join(X2,composition(X1,esk1_0))) = join(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_81]) ).
cnf(c_0_94,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_89]),c_0_17]) ).
cnf(c_0_95,plain,
complement(converse(complement(converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_90]),c_0_47]),c_0_27]),c_0_80]) ).
cnf(c_0_96,plain,
join(X1,composition(top,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,negated_conjecture,
join(X1,composition(join(X2,X1),esk1_0)) = join(composition(X2,esk1_0),X1),
inference(spm,[status(thm)],[c_0_93,c_0_65]) ).
cnf(c_0_98,negated_conjecture,
join(X1,join(X2,composition(esk1_0,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_74]),c_0_81]) ).
cnf(c_0_99,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_94,c_0_17]) ).
cnf(c_0_100,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_32,c_0_16]),c_0_17]) ).
cnf(c_0_101,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_47,c_0_95]) ).
fof(c_0_102,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_103,plain,
join(complement(X1),composition(top,X1)) = top,
inference(spm,[status(thm)],[c_0_96,c_0_47]) ).
cnf(c_0_104,negated_conjecture,
join(complement(X1),composition(X1,esk1_0)) = join(complement(X1),composition(top,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_35]),c_0_27]) ).
cnf(c_0_105,plain,
join(one,complement(converse(complement(one)))) = one,
inference(spm,[status(thm)],[c_0_80,c_0_28]) ).
cnf(c_0_106,negated_conjecture,
join(X1,composition(esk1_0,join(X2,X1))) = join(composition(esk1_0,X2),X1),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_107,plain,
composition(X1,complement(converse(composition(top,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_73]),c_0_39]),c_0_46]),c_0_39]) ).
cnf(c_0_108,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_101]) ).
cnf(c_0_109,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_73]) ).
cnf(c_0_110,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_111,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_76,c_0_27]) ).
cnf(c_0_112,negated_conjecture,
join(complement(esk1_0),composition(esk1_0,esk1_0)) = top,
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_113,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_57,c_0_17]) ).
cnf(c_0_114,plain,
join(complement(one),converse(complement(one))) = converse(complement(one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_105]),c_0_47]),c_0_47]),c_0_27]) ).
cnf(c_0_115,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_16,c_0_73]) ).
cnf(c_0_116,negated_conjecture,
join(complement(X1),composition(esk1_0,X1)) = join(complement(X1),composition(esk1_0,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_35]),c_0_27]) ).
cnf(c_0_117,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(rw,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_118,plain,
join(converse(composition(top,X1)),composition(X2,top)) = composition(join(converse(X1),X2),top),
inference(spm,[status(thm)],[c_0_65,c_0_109]) ).
cnf(c_0_119,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_65,c_0_110]) ).
cnf(c_0_120,negated_conjecture,
composition(esk1_0,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(spm,[status(thm)],[c_0_111,c_0_112]),c_0_39]),c_0_78]),c_0_47]),c_0_27]),c_0_88]) ).
cnf(c_0_121,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_122,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_17]),c_0_27]),c_0_114]) ).
cnf(c_0_123,plain,
converse(composition(join(X1,converse(X2)),top)) = composition(top,join(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_115,c_0_113]) ).
cnf(c_0_124,negated_conjecture,
composition(join(esk1_0,converse(esk1_0)),top) = converse(composition(top,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_116,c_0_117]),c_0_108]),c_0_47]),c_0_78]),c_0_108]),c_0_47]),c_0_118]),c_0_27]) ).
cnf(c_0_125,negated_conjecture,
composition(join(X1,composition(X2,esk1_0)),esk1_0) = composition(join(X1,X2),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_65]) ).
cnf(c_0_126,plain,
join(complement(one),composition(converse(complement(X1)),X1)) = complement(one),
inference(spm,[status(thm)],[c_0_121,c_0_47]) ).
cnf(c_0_127,plain,
join(complement(one),converse(X1)) = converse(join(complement(one),X1)),
inference(spm,[status(thm)],[c_0_57,c_0_122]) ).
cnf(c_0_128,negated_conjecture,
join(complement(one),complement(esk1_0)) = complement(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_71]),c_0_27]) ).
cnf(c_0_129,negated_conjecture,
composition(top,join(esk1_0,converse(esk1_0))) = composition(top,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_17]),c_0_27]) ).
cnf(c_0_130,plain,
join(X1,join(X2,composition(top,X1))) = join(X2,composition(top,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_92]),c_0_81]) ).
cnf(c_0_131,negated_conjecture,
composition(converse(complement(esk1_0)),esk1_0) = composition(complement(one),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_132,negated_conjecture,
join(composition(top,esk1_0),converse(esk1_0)) = composition(top,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_86,c_0_129]),c_0_41]),c_0_130]),c_0_69]),c_0_129]),c_0_27]) ).
cnf(c_0_133,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_54,c_0_69]) ).
cnf(c_0_134,negated_conjecture,
join(X1,join(composition(X1,esk1_0),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_88]) ).
cnf(c_0_135,negated_conjecture,
join(composition(complement(one),esk1_0),converse(esk1_0)) = composition(top,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_104,c_0_131]),c_0_108]),c_0_47]),c_0_108]),c_0_47]),c_0_27]),c_0_132]),c_0_27]) ).
cnf(c_0_136,plain,
join(X1,converse(join(X2,complement(converse(X1))))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_133]),c_0_73]) ).
cnf(c_0_137,negated_conjecture,
converse(join(esk1_0,complement(one))) = join(esk1_0,complement(one)),
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_134,c_0_135]),c_0_104]),c_0_33]),c_0_27]),c_0_127]),c_0_27]) ).
cnf(c_0_138,plain,
join(X1,join(X2,complement(join(X3,X1)))) = join(X2,join(X1,complement(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_111]),c_0_81]) ).
cnf(c_0_139,negated_conjecture,
join(X1,composition(join(X1,X2),esk1_0)) = join(X1,composition(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_134,c_0_65]) ).
cnf(c_0_140,negated_conjecture,
join(esk1_0,converse(join(X1,complement(esk1_0)))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_41]),c_0_127]),c_0_138]),c_0_128]) ).
cnf(c_0_141,negated_conjecture,
join(X1,composition(complement(X1),esk1_0)) = join(X1,composition(top,esk1_0)),
inference(spm,[status(thm)],[c_0_139,c_0_35]) ).
cnf(c_0_142,negated_conjecture,
join(esk1_0,converse(complement(esk1_0))) = top,
inference(spm,[status(thm)],[c_0_140,c_0_46]) ).
cnf(c_0_143,negated_conjecture,
join(X1,complement(composition(complement(X1),esk1_0))) = join(X1,complement(composition(top,esk1_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_141]),c_0_76]) ).
cnf(c_0_144,negated_conjecture,
join(complement(X1),complement(composition(X1,esk1_0))) = complement(composition(X1,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_88]),c_0_27]) ).
cnf(c_0_145,negated_conjecture,
join(esk1_0,converse(esk1_0)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_142]),c_0_39]),c_0_78]),c_0_108]),c_0_47]) ).
cnf(c_0_146,negated_conjecture,
meet(composition(esk1_0,top),esk2_0) != composition(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_147,negated_conjecture,
join(complement(X1),complement(composition(top,esk1_0))) = complement(composition(X1,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_47]),c_0_144]) ).
cnf(c_0_148,negated_conjecture,
converse(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_145]),c_0_27]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
converse(composition(top,esk1_0)) = composition(esk1_0,top),
inference(rw,[status(thm)],[c_0_124,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
complement(join(complement(composition(esk1_0,top)),complement(esk2_0))) != composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_146,c_0_30]) ).
cnf(c_0_151,negated_conjecture,
join(X1,complement(composition(top,esk1_0))) = complement(composition(complement(X1),esk1_0)),
inference(spm,[status(thm)],[c_0_147,c_0_47]) ).
cnf(c_0_152,negated_conjecture,
composition(converse(X1),esk1_0) = converse(composition(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_148]) ).
cnf(c_0_153,negated_conjecture,
converse(complement(composition(top,esk1_0))) = complement(composition(esk1_0,top)),
inference(spm,[status(thm)],[c_0_108,c_0_149]) ).
cnf(c_0_154,negated_conjecture,
complement(join(complement(esk2_0),complement(composition(esk1_0,top)))) != composition(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_150,c_0_27]) ).
cnf(c_0_155,negated_conjecture,
join(X1,complement(composition(esk1_0,top))) = complement(composition(esk1_0,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_63,c_0_151]),c_0_108]),c_0_152]),c_0_108]),c_0_17]),c_0_153]) ).
cnf(c_0_156,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_155]),c_0_47]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL026+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 2400
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Oct 2 14:40:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.xfuv2Stk8I/E---3.1_14840.p
% 5.66/1.21 # Version: 3.1pre001
% 5.66/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.66/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.66/1.21 # Starting new_bool_3 with 300s (1) cores
% 5.66/1.21 # Starting new_bool_1 with 300s (1) cores
% 5.66/1.21 # Starting sh5l with 300s (1) cores
% 5.66/1.21 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 14945 completed with status 0
% 5.66/1.21 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.66/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.66/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.66/1.21 # No SInE strategy applied
% 5.66/1.21 # Search class: FUUPM-FFSF21-MFFFFFNN
% 5.66/1.21 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.66/1.21 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 675s (1) cores
% 5.66/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.66/1.21 # Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 5.66/1.21 # Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 5.66/1.21 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 5.66/1.21 # H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 14951 completed with status 0
% 5.66/1.21 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 5.66/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.66/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.66/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.66/1.21 # No SInE strategy applied
% 5.66/1.21 # Search class: FUUPM-FFSF21-MFFFFFNN
% 5.66/1.21 # Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.66/1.21 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 675s (1) cores
% 5.66/1.21 # Preprocessing time : 0.001 s
% 5.66/1.21 # Presaturation interreduction done
% 5.66/1.21
% 5.66/1.21 # Proof found!
% 5.66/1.21 # SZS status Theorem
% 5.66/1.21 # SZS output start CNFRefutation
% See solution above
% 5.66/1.21 # Parsed axioms : 14
% 5.66/1.21 # Removed by relevancy pruning/SinE : 0
% 5.66/1.21 # Initial clauses : 15
% 5.66/1.21 # Removed in clause preprocessing : 1
% 5.66/1.21 # Initial clauses in saturation : 14
% 5.66/1.21 # Processed clauses : 3102
% 5.66/1.21 # ...of these trivial : 1865
% 5.66/1.21 # ...subsumed : 565
% 5.66/1.21 # ...remaining for further processing : 672
% 5.66/1.21 # Other redundant clauses eliminated : 0
% 5.66/1.21 # Clauses deleted for lack of memory : 0
% 5.66/1.21 # Backward-subsumed : 1
% 5.66/1.21 # Backward-rewritten : 170
% 5.66/1.21 # Generated clauses : 78917
% 5.66/1.21 # ...of the previous two non-redundant : 40060
% 5.66/1.21 # ...aggressively subsumed : 0
% 5.66/1.21 # Contextual simplify-reflections : 0
% 5.66/1.21 # Paramodulations : 78917
% 5.66/1.21 # Factorizations : 0
% 5.66/1.21 # NegExts : 0
% 5.66/1.21 # Equation resolutions : 0
% 5.66/1.21 # Total rewrite steps : 161215
% 5.66/1.21 # Propositional unsat checks : 0
% 5.66/1.21 # Propositional check models : 0
% 5.66/1.21 # Propositional check unsatisfiable : 0
% 5.66/1.21 # Propositional clauses : 0
% 5.66/1.21 # Propositional clauses after purity: 0
% 5.66/1.21 # Propositional unsat core size : 0
% 5.66/1.21 # Propositional preprocessing time : 0.000
% 5.66/1.21 # Propositional encoding time : 0.000
% 5.66/1.21 # Propositional solver time : 0.000
% 5.66/1.21 # Success case prop preproc time : 0.000
% 5.66/1.21 # Success case prop encoding time : 0.000
% 5.66/1.21 # Success case prop solver time : 0.000
% 5.66/1.21 # Current number of processed clauses : 487
% 5.66/1.21 # Positive orientable unit clauses : 476
% 5.66/1.21 # Positive unorientable unit clauses: 11
% 5.66/1.21 # Negative unit clauses : 0
% 5.66/1.21 # Non-unit-clauses : 0
% 5.66/1.21 # Current number of unprocessed clauses: 36386
% 5.66/1.21 # ...number of literals in the above : 36386
% 5.66/1.21 # Current number of archived formulas : 0
% 5.66/1.21 # Current number of archived clauses : 186
% 5.66/1.21 # Clause-clause subsumption calls (NU) : 0
% 5.66/1.21 # Rec. Clause-clause subsumption calls : 0
% 5.66/1.21 # Non-unit clause-clause subsumptions : 0
% 5.66/1.21 # Unit Clause-clause subsumption calls : 117
% 5.66/1.21 # Rewrite failures with RHS unbound : 0
% 5.66/1.21 # BW rewrite match attempts : 3240
% 5.66/1.21 # BW rewrite match successes : 378
% 5.66/1.21 # Condensation attempts : 0
% 5.66/1.21 # Condensation successes : 0
% 5.66/1.21 # Termbank termtop insertions : 989592
% 5.66/1.21
% 5.66/1.21 # -------------------------------------------------
% 5.66/1.21 # User time : 0.656 s
% 5.66/1.21 # System time : 0.042 s
% 5.66/1.21 # Total time : 0.698 s
% 5.66/1.21 # Maximum resident set size: 1700 pages
% 5.66/1.21
% 5.66/1.21 # -------------------------------------------------
% 5.66/1.21 # User time : 3.325 s
% 5.66/1.21 # System time : 0.158 s
% 5.66/1.21 # Total time : 3.484 s
% 5.66/1.21 # Maximum resident set size: 1676 pages
% 5.66/1.21 % E---3.1 exiting
% 5.66/1.22 % E---3.1 exiting
%------------------------------------------------------------------------------