TSTP Solution File: REL029+2 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : REL029+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.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 19:19:38 EDT 2022
% Result : Theorem 0.33s 27.52s
% Output : CNFRefutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of formulae : 149 ( 142 unt; 0 def)
% Number of atoms : 162 ( 161 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 5 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 206 ( 18 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
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/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> ( join(meet(composition(X1,X3),composition(X2,X3)),composition(meet(X1,X2),X3)) = composition(meet(X1,X2),X3)
& join(composition(meet(X1,X2),X3),meet(composition(X1,X3),composition(X2,X3))) = meet(composition(X1,X3),composition(X2,X3)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',goals) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(c_0_14,plain,
! [X3,X4] : converse(composition(X3,X4)) = composition(converse(X4),converse(X3)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_15,plain,
! [X2] : converse(converse(X2)) = X2,
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,
! [X2] : composition(X2,one) = X2,
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,
! [X3,X4] : join(composition(converse(X3),complement(composition(X3,X4))),complement(X4)) = complement(X4),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
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,
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,
! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_25,plain,
! [X2] : top = join(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_top]) ).
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,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,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_32,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_33,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_28]),c_0_32]) ).
cnf(c_0_35,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_36,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]) ).
fof(c_0_37,plain,
! [X2] : zero = meet(X2,complement(X2)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_38,plain,
! [X3,X4] : meet(X3,X4) = complement(join(complement(X3),complement(X4))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_39,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_40,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_41,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_44,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_47,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_48,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_49,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_29]) ).
cnf(c_0_50,plain,
join(zero,complement(join(complement(X1),complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_30]),c_0_48]),c_0_27]) ).
cnf(c_0_51,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_49,c_0_27]) ).
cnf(c_0_52,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_53,plain,
join(complement(zero),X1) = top,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_55,plain,
join(zero,complement(join(zero,complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_54]),c_0_39]),c_0_48]),c_0_27]),c_0_27]) ).
fof(c_0_56,plain,
! [X3,X4] : converse(join(X3,X4)) = join(converse(X3),converse(X4)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_57,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_58,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_59,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_60,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_57]),c_0_57]) ).
cnf(c_0_61,plain,
join(complement(one),complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_28]),c_0_32]) ).
cnf(c_0_62,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_59,c_0_17]) ).
cnf(c_0_63,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_60]) ).
cnf(c_0_64,plain,
join(complement(one),join(complement(one),X1)) = join(complement(one),X1),
inference(spm,[status(thm)],[c_0_29,c_0_61]) ).
cnf(c_0_65,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_66,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
cnf(c_0_67,plain,
join(complement(one),converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_47]),c_0_27]) ).
cnf(c_0_69,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_27]) ).
cnf(c_0_70,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_59,c_0_17]) ).
cnf(c_0_71,plain,
join(top,converse(top)) = join(one,converse(top)),
inference(spm,[status(thm)],[c_0_33,c_0_67]) ).
cnf(c_0_72,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_73,plain,
join(one,converse(top)) = join(one,top),
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_71]),c_0_70]),c_0_28]),c_0_27]),c_0_71]) ).
cnf(c_0_74,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_29]) ).
cnf(c_0_75,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_72,c_0_60]) ).
cnf(c_0_76,plain,
join(top,converse(top)) = join(one,top),
inference(rw,[status(thm)],[c_0_71,c_0_73]) ).
cnf(c_0_77,plain,
join(complement(one),join(X1,complement(one))) = join(X1,complement(one)),
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
fof(c_0_78,negated_conjecture,
~ ! [X1,X2,X3] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> ( join(meet(composition(X1,X3),composition(X2,X3)),composition(meet(X1,X2),X3)) = composition(meet(X1,X2),X3)
& join(composition(meet(X1,X2),X3),meet(composition(X1,X3),composition(X2,X3))) = meet(composition(X1,X3),composition(X2,X3)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_79,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_47,c_0_47]),c_0_60]),c_0_74]),c_0_27]),c_0_75]) ).
cnf(c_0_80,plain,
join(top,converse(top)) = top,
inference(rw,[status(thm)],[c_0_76,c_0_39]) ).
cnf(c_0_81,plain,
join(complement(one),join(X1,join(complement(one),X2))) = join(X1,join(complement(one),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_77]),c_0_29]),c_0_29]) ).
fof(c_0_82,negated_conjecture,
( join(esk1_0,one) = one
& join(esk2_0,one) = one
& ( join(meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)),composition(meet(esk1_0,esk2_0),esk3_0)) != composition(meet(esk1_0,esk2_0),esk3_0)
| join(composition(meet(esk1_0,esk2_0),esk4_0),meet(composition(esk1_0,esk4_0),composition(esk2_0,esk4_0))) != meet(composition(esk1_0,esk4_0),composition(esk2_0,esk4_0)) ) ),
inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_78])])])]) ).
cnf(c_0_83,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_79,c_0_47]),c_0_74]),c_0_27]),c_0_75]),c_0_27]) ).
cnf(c_0_84,plain,
join(one,converse(complement(one))) = converse(top),
inference(spm,[status(thm)],[c_0_65,c_0_28]) ).
cnf(c_0_85,plain,
converse(top) = top,
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_80]),c_0_27]),c_0_71]),c_0_73]),c_0_39]) ).
fof(c_0_86,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_87,plain,
join(one,complement(join(X1,join(complement(one),X2)))) = one,
inference(spm,[status(thm)],[c_0_68,c_0_81]) ).
cnf(c_0_88,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_68,c_0_60]) ).
cnf(c_0_89,negated_conjecture,
join(esk2_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_90,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_83,c_0_60]) ).
cnf(c_0_91,plain,
join(one,converse(complement(one))) = top,
inference(rw,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_63]),c_0_60]),c_0_30]),c_0_48]) ).
cnf(c_0_93,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_94,plain,
join(one,complement(join(X1,join(X2,complement(one))))) = one,
inference(spm,[status(thm)],[c_0_87,c_0_69]) ).
cnf(c_0_95,negated_conjecture,
join(complement(esk2_0),complement(one)) = complement(esk2_0),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
join(one,complement(converse(complement(one)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_48]),c_0_92]) ).
cnf(c_0_97,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_93,c_0_32]) ).
cnf(c_0_98,negated_conjecture,
join(one,complement(join(X1,complement(esk2_0)))) = one,
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,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_75,c_0_96]),c_0_60]),c_0_60]),c_0_27]) ).
cnf(c_0_100,negated_conjecture,
join(X1,composition(complement(join(X2,complement(esk2_0))),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_32]) ).
cnf(c_0_101,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_102,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_65,c_0_85]) ).
cnf(c_0_103,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_99]),c_0_17]),c_0_27]),c_0_99]) ).
cnf(c_0_104,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_105,plain,
join(X1,complement(join(X2,join(X1,X3)))) = join(X1,complement(join(X2,X3))),
inference(spm,[status(thm)],[c_0_90,c_0_74]) ).
cnf(c_0_106,negated_conjecture,
join(X1,composition(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_60]) ).
cnf(c_0_107,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_90,c_0_27]) ).
cnf(c_0_108,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_102]),c_0_28]),c_0_103]) ).
cnf(c_0_109,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_110,plain,
converse(join(X1,composition(converse(X2),X3))) = join(converse(X1),composition(converse(X3),X2)),
inference(spm,[status(thm)],[c_0_59,c_0_19]) ).
cnf(c_0_111,plain,
join(converse(composition(X1,X2)),composition(X3,converse(X1))) = composition(join(converse(X2),X3),converse(X1)),
inference(spm,[status(thm)],[c_0_93,c_0_16]) ).
cnf(c_0_112,negated_conjecture,
join(complement(esk1_0),complement(one)) = complement(esk1_0),
inference(spm,[status(thm)],[c_0_88,c_0_104]) ).
cnf(c_0_113,negated_conjecture,
join(X1,complement(join(X2,composition(esk2_0,X1)))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]) ).
cnf(c_0_114,plain,
join(X1,composition(X1,complement(one))) = 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_62,c_0_108]),c_0_109]),c_0_85]),c_0_109]),c_0_103]) ).
cnf(c_0_115,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
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_110,c_0_111]),c_0_59]),c_0_16]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_116,negated_conjecture,
join(complement(esk1_0),join(complement(one),X1)) = join(complement(esk1_0),X1),
inference(spm,[status(thm)],[c_0_29,c_0_112]) ).
cnf(c_0_117,negated_conjecture,
join(complement(one),complement(composition(esk2_0,top))) = complement(esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_27]),c_0_95]) ).
cnf(c_0_118,negated_conjecture,
join(X1,complement(composition(esk2_0,join(X2,X1)))) = join(X1,complement(composition(esk2_0,X2))),
inference(spm,[status(thm)],[c_0_113,c_0_115]) ).
cnf(c_0_119,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_28]),c_0_27]) ).
cnf(c_0_120,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_29]) ).
cnf(c_0_121,negated_conjecture,
join(complement(esk1_0),complement(composition(esk2_0,top))) = join(complement(esk1_0),complement(esk2_0)),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
join(complement(X1),complement(composition(esk2_0,top))) = join(complement(X1),complement(composition(esk2_0,X1))),
inference(spm,[status(thm)],[c_0_118,c_0_30]) ).
cnf(c_0_123,negated_conjecture,
join(one,converse(esk1_0)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_104]),c_0_28]) ).
cnf(c_0_124,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_51,c_0_120]) ).
cnf(c_0_125,negated_conjecture,
join(complement(esk1_0),complement(composition(esk2_0,esk1_0))) = join(complement(esk1_0),complement(esk2_0)),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_123]),c_0_32]) ).
cnf(c_0_127,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_32]),c_0_27]) ).
cnf(c_0_128,negated_conjecture,
( join(composition(meet(esk1_0,esk2_0),esk4_0),meet(composition(esk1_0,esk4_0),composition(esk2_0,esk4_0))) != meet(composition(esk1_0,esk4_0),composition(esk2_0,esk4_0))
| join(meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)),composition(meet(esk1_0,esk2_0),esk3_0)) != composition(meet(esk1_0,esk2_0),esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_129,negated_conjecture,
join(complement(esk1_0),join(complement(esk2_0),composition(esk2_0,esk1_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_74]),c_0_27]) ).
cnf(c_0_130,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_62,c_0_126]),c_0_17]),c_0_16]),c_0_17]) ).
cnf(c_0_131,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_104]),c_0_32]) ).
cnf(c_0_132,plain,
join(complement(join(X1,X2)),complement(join(X2,complement(X1)))) = complement(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_107]),c_0_27]),c_0_75]) ).
fof(c_0_133,plain,
! [X4,X5,X6] : composition(X4,composition(X5,X6)) = composition(composition(X4,X5),X6),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_134,negated_conjecture,
( join(complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0)))),composition(complement(join(complement(esk1_0),complement(esk2_0))),esk3_0)) != composition(complement(join(complement(esk1_0),complement(esk2_0))),esk3_0)
| join(composition(complement(join(complement(esk1_0),complement(esk2_0))),esk4_0),complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_0))))) != complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_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)],[c_0_128,c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]) ).
cnf(c_0_135,negated_conjecture,
join(complement(esk2_0),composition(esk2_0,esk1_0)) = join(esk1_0,complement(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(spm,[status(thm)],[c_0_107,c_0_129]),c_0_48]),c_0_29]),c_0_92]),c_0_60]),c_0_29]),c_0_27]),c_0_106]),c_0_27]) ).
cnf(c_0_136,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_75,c_0_130]),c_0_27]) ).
cnf(c_0_137,negated_conjecture,
join(X1,complement(composition(esk1_0,X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_131]),c_0_30]) ).
cnf(c_0_138,negated_conjecture,
join(complement(X1),complement(composition(esk2_0,X1))) = complement(composition(esk2_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_106]),c_0_107]) ).
cnf(c_0_139,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_140,negated_conjecture,
( join(composition(complement(join(complement(esk1_0),complement(esk2_0))),esk4_0),complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_0))))) != complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_0))))
| join(composition(complement(join(complement(esk1_0),complement(esk2_0))),esk3_0),complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0))))) != composition(complement(join(complement(esk1_0),complement(esk2_0))),esk3_0) ),
inference(rw,[status(thm)],[c_0_134,c_0_27]) ).
cnf(c_0_141,negated_conjecture,
join(complement(esk1_0),complement(esk2_0)) = complement(composition(esk2_0,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_135]),c_0_107]),c_0_27]),c_0_136]) ).
cnf(c_0_142,negated_conjecture,
join(complement(composition(esk1_0,X1)),complement(composition(esk2_0,top))) = join(complement(composition(esk1_0,X1)),complement(composition(esk2_0,X1))),
inference(spm,[status(thm)],[c_0_118,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
join(complement(X1),complement(composition(esk2_0,top))) = complement(composition(esk2_0,X1)),
inference(rw,[status(thm)],[c_0_122,c_0_138]) ).
cnf(c_0_144,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_93,c_0_139]) ).
cnf(c_0_145,negated_conjecture,
( join(composition(esk2_0,composition(esk1_0,esk4_0)),complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_0))))) != complement(join(complement(composition(esk1_0,esk4_0)),complement(composition(esk2_0,esk4_0))))
| join(composition(esk2_0,composition(esk1_0,esk3_0)),complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0))))) != composition(esk2_0,composition(esk1_0,esk3_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_140,c_0_141]),c_0_60]),c_0_139]),c_0_141]),c_0_60]),c_0_139]),c_0_141]),c_0_60]),c_0_139]) ).
cnf(c_0_146,negated_conjecture,
join(complement(composition(esk1_0,X1)),complement(composition(esk2_0,X1))) = complement(composition(esk2_0,composition(esk1_0,X1))),
inference(rw,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_147,plain,
join(composition(X1,composition(X2,X3)),composition(X4,composition(X5,X3))) = composition(join(composition(X1,X2),composition(X4,X5)),X3),
inference(spm,[status(thm)],[c_0_144,c_0_139]) ).
cnf(c_0_148,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)],[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_145,c_0_146]),c_0_60]),c_0_147]),c_0_115]),c_0_63]),c_0_139]),c_0_146]),c_0_60]),c_0_146]),c_0_60]),c_0_147]),c_0_115]),c_0_63]),c_0_139])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : REL029+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n020.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 10:04:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.33/23.39 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.40 eprover: CPU time limit exceeded, terminating
% 0.33/23.42 eprover: CPU time limit exceeded, terminating
% 0.33/27.52 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.33/27.52
% 0.33/27.52 # Failure: Resource limit exceeded (time)
% 0.33/27.52 # OLD status Res
% 0.33/27.52 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.33/27.52 # Preprocessing time : 0.014 s
% 0.33/27.52 # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 0.33/27.52 # Preprocessing time : 0.013 s
% 0.33/27.52
% 0.33/27.52 # Proof found!
% 0.33/27.52 # SZS status Theorem
% 0.33/27.52 # SZS output start CNFRefutation
% See solution above
% 0.33/27.52 # Proof object total steps : 149
% 0.33/27.52 # Proof object clause steps : 120
% 0.33/27.52 # Proof object formula steps : 29
% 0.33/27.52 # Proof object conjectures : 35
% 0.33/27.52 # Proof object clause conjectures : 32
% 0.33/27.52 # Proof object formula conjectures : 3
% 0.33/27.52 # Proof object initial clauses used : 16
% 0.33/27.52 # Proof object initial formulas used : 14
% 0.33/27.52 # Proof object generating inferences : 83
% 0.33/27.52 # Proof object simplifying inferences : 134
% 0.33/27.52 # Training examples: 0 positive, 0 negative
% 0.33/27.52 # Parsed axioms : 14
% 0.33/27.52 # Removed by relevancy pruning/SinE : 0
% 0.33/27.52 # Initial clauses : 16
% 0.33/27.52 # Removed in clause preprocessing : 1
% 0.33/27.52 # Initial clauses in saturation : 15
% 0.33/27.52 # Processed clauses : 11244
% 0.33/27.52 # ...of these trivial : 5562
% 0.33/27.52 # ...subsumed : 2436
% 0.33/27.52 # ...remaining for further processing : 3246
% 0.33/27.52 # Other redundant clauses eliminated : 0
% 0.33/27.52 # Clauses deleted for lack of memory : 113655
% 0.33/27.52 # Backward-subsumed : 0
% 0.33/27.52 # Backward-rewritten : 1069
% 0.33/27.52 # Generated clauses : 417617
% 0.33/27.52 # ...of the previous two non-trivial : 225341
% 0.33/27.52 # Contextual simplify-reflections : 0
% 0.33/27.52 # Paramodulations : 417617
% 0.33/27.52 # Factorizations : 0
% 0.33/27.52 # Equation resolutions : 0
% 0.33/27.52 # Current number of processed clauses : 2177
% 0.33/27.52 # Positive orientable unit clauses : 2167
% 0.33/27.52 # Positive unorientable unit clauses: 10
% 0.33/27.52 # Negative unit clauses : 0
% 0.33/27.52 # Non-unit-clauses : 0
% 0.33/27.52 # Current number of unprocessed clauses: 61504
% 0.33/27.52 # ...number of literals in the above : 61504
% 0.33/27.52 # Current number of archived formulas : 0
% 0.33/27.52 # Current number of archived clauses : 1070
% 0.33/27.52 # Clause-clause subsumption calls (NU) : 0
% 0.33/27.52 # Rec. Clause-clause subsumption calls : 0
% 0.33/27.52 # Non-unit clause-clause subsumptions : 0
% 0.33/27.52 # Unit Clause-clause subsumption calls : 71
% 0.33/27.52 # Rewrite failures with RHS unbound : 0
% 0.33/27.52 # BW rewrite match attempts : 73204
% 0.33/27.52 # BW rewrite match successes : 632
% 0.33/27.52 # Condensation attempts : 0
% 0.33/27.52 # Condensation successes : 0
% 0.33/27.52 # Termbank termtop insertions : 6962803
% 0.33/27.52
% 0.33/27.52 # -------------------------------------------------
% 0.33/27.52 # User time : 3.831 s
% 0.33/27.52 # System time : 0.094 s
% 0.33/27.52 # Total time : 3.925 s
% 0.33/27.52 # Maximum resident set size: 151180 pages
% 0.33/46.42 eprover: CPU time limit exceeded, terminating
% 0.33/46.43 eprover: CPU time limit exceeded, terminating
% 0.33/46.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.44 eprover: No such file or directory
% 0.33/46.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.44 eprover: No such file or directory
% 0.33/46.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.45 eprover: No such file or directory
% 0.33/46.45 eprover: CPU time limit exceeded, terminating
% 0.33/46.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.45 eprover: No such file or directory
% 0.33/46.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.45 eprover: No such file or directory
% 0.33/46.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.45 eprover: No such file or directory
% 0.33/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.46 eprover: No such file or directory
% 0.33/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.46 eprover: No such file or directory
% 0.33/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.46 eprover: No such file or directory
% 0.33/46.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.46 eprover: No such file or directory
% 0.33/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.47 eprover: No such file or directory
% 0.33/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.47 eprover: No such file or directory
% 0.33/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.47 eprover: No such file or directory
% 0.33/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.47 eprover: No such file or directory
% 0.33/46.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.47 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.48 eprover: No such file or directory
% 0.33/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.49 eprover: No such file or directory
% 0.33/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.49 eprover: No such file or directory
% 0.33/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.49 eprover: No such file or directory
% 0.33/46.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.49 eprover: No such file or directory
% 0.33/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/46.50 eprover: No such file or directory
% 0.33/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.50 eprover: No such file or directory
% 0.33/46.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.50 eprover: No such file or directory
% 0.33/46.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.51 eprover: No such file or directory
% 0.33/46.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.33/46.52 eprover: No such file or directory
%------------------------------------------------------------------------------