TSTP Solution File: REL029+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : REL029+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 : Thu Aug 31 13:36:13 EDT 2023
% Result : Theorem 9.35s 9.51s
% Output : CNFRefutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of formulae : 167 ( 149 unt; 11 typ; 0 def)
% Number of atoms : 169 ( 168 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 5 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 203 ( 10 sgn; 62 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
join: ( $i * $i ) > $i ).
tff(decl_23,type,
complement: $i > $i ).
tff(decl_24,type,
meet: ( $i * $i ) > $i ).
tff(decl_25,type,
composition: ( $i * $i ) > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
converse: $i > $i ).
tff(decl_28,type,
top: $i ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
esk1_0: $i ).
tff(decl_31,type,
esk2_0: $i ).
tff(decl_32,type,
esk3_0: $i ).
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(modular_law_2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',modular_law_2) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(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,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
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,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_20,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
converse(converse(X1)) = 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(spm,[status(thm)],[c_0_20,c_0_21]) ).
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_18,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]) ).
cnf(c_0_48,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_48]) ).
fof(c_0_50,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_51,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_52,plain,
join(top,zero) = top,
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_53,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
fof(c_0_54,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),esk3_0),meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0))) != meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])]) ).
cnf(c_0_55,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_44]),c_0_28]) ).
cnf(c_0_56,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_28]) ).
fof(c_0_57,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_58,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_59,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_39]),c_0_36]) ).
cnf(c_0_60,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_61,negated_conjecture,
join(esk2_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_62,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_63,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
join(top,X1) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_46]),c_0_59]) ).
fof(c_0_65,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_66,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_60,c_0_28]) ).
cnf(c_0_67,negated_conjecture,
join(one,esk2_0) = one,
inference(rw,[status(thm)],[c_0_61,c_0_28]) ).
cnf(c_0_68,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_28]),c_0_42]) ).
cnf(c_0_69,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_70,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,negated_conjecture,
join(one,converse(esk1_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_66]),c_0_29]),c_0_29]) ).
cnf(c_0_73,negated_conjecture,
join(one,converse(esk2_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_67]),c_0_29]),c_0_29]) ).
cnf(c_0_74,negated_conjecture,
join(one,join(esk2_0,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_67]) ).
cnf(c_0_75,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_44,c_0_44]),c_0_48]),c_0_68]),c_0_28]),c_0_69]) ).
cnf(c_0_76,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_28,c_0_64]) ).
cnf(c_0_77,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_70,c_0_21]) ).
cnf(c_0_78,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]),c_0_34]) ).
cnf(c_0_79,negated_conjecture,
join(X1,composition(converse(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_73]),c_0_34]),c_0_34]) ).
cnf(c_0_80,negated_conjecture,
join(one,complement(esk2_0)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_36]),c_0_28]) ).
cnf(c_0_81,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_75,c_0_48]) ).
cnf(c_0_82,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_63,c_0_36]) ).
cnf(c_0_83,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
join(converse(X1),composition(converse(X1),esk1_0)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_78]),c_0_17]),c_0_21]) ).
cnf(c_0_85,negated_conjecture,
join(converse(X1),composition(converse(X1),esk2_0)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_79]),c_0_17]),c_0_21]) ).
cnf(c_0_86,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_53,c_0_64]) ).
cnf(c_0_87,negated_conjecture,
join(one,complement(esk2_0)) = top,
inference(rw,[status(thm)],[c_0_80,c_0_64]) ).
cnf(c_0_88,negated_conjecture,
join(one,join(esk1_0,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_42,c_0_66]) ).
cnf(c_0_89,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_81]),c_0_51]) ).
cnf(c_0_90,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_91,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
fof(c_0_92,plain,
! [X35,X36,X37] : join(meet(composition(X35,X36),X37),meet(composition(meet(X35,composition(X37,converse(X36))),X36),X37)) = meet(composition(meet(X35,composition(X37,converse(X36))),X36),X37),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_93,negated_conjecture,
join(X1,composition(X1,esk1_0)) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_21]) ).
cnf(c_0_94,negated_conjecture,
join(X1,composition(X1,esk2_0)) = X1,
inference(spm,[status(thm)],[c_0_85,c_0_21]) ).
fof(c_0_95,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_96,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_86,c_0_48]) ).
cnf(c_0_97,negated_conjecture,
join(X1,composition(complement(esk2_0),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_87]),c_0_34]) ).
cnf(c_0_98,negated_conjecture,
join(one,complement(esk1_0)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_36]),c_0_28]) ).
cnf(c_0_99,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_40]),c_0_91]) ).
cnf(c_0_100,plain,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
join(composition(X1,X2),composition(complement(X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_71,c_0_36]) ).
cnf(c_0_102,negated_conjecture,
join(complement(one),complement(esk1_0)) = complement(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_66]),c_0_28]) ).
cnf(c_0_103,negated_conjecture,
join(X1,join(composition(X1,esk1_0),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_93]) ).
cnf(c_0_104,negated_conjecture,
join(X1,join(composition(X1,esk2_0),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_94]) ).
cnf(c_0_105,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_106,negated_conjecture,
join(complement(X1),composition(top,X1)) = top,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_107,negated_conjecture,
join(one,complement(esk1_0)) = top,
inference(rw,[status(thm)],[c_0_98,c_0_64]) ).
cnf(c_0_108,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_99]),c_0_21]),c_0_21]) ).
cnf(c_0_109,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_90,c_0_21]) ).
cnf(c_0_110,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3)))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_111,negated_conjecture,
join(X1,join(X2,composition(X1,esk1_0))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_93]) ).
cnf(c_0_112,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_101,c_0_34]) ).
cnf(c_0_113,negated_conjecture,
join(complement(one),join(X1,complement(esk1_0))) = join(X1,complement(esk1_0)),
inference(spm,[status(thm)],[c_0_68,c_0_102]) ).
cnf(c_0_114,negated_conjecture,
join(X1,join(composition(X1,composition(esk1_0,esk2_0)),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_103]),c_0_105]) ).
cnf(c_0_115,negated_conjecture,
join(X1,join(X2,composition(X1,esk2_0))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_68,c_0_94]) ).
cnf(c_0_116,negated_conjecture,
join(composition(top,composition(X1,X2)),composition(complement(X1),X2)) = composition(top,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_106]),c_0_105]),c_0_28]) ).
cnf(c_0_117,negated_conjecture,
join(X1,composition(complement(esk1_0),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_107]),c_0_34]) ).
cnf(c_0_118,negated_conjecture,
join(X1,composition(complement(X1),esk1_0)) = join(X1,composition(top,esk1_0)),
inference(spm,[status(thm)],[c_0_103,c_0_101]) ).
cnf(c_0_119,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_108,c_0_48]) ).
cnf(c_0_120,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_109]),c_0_40]),c_0_91]) ).
cnf(c_0_121,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_28]),c_0_28]) ).
cnf(c_0_122,negated_conjecture,
join(complement(one),composition(top,esk1_0)) = join(esk1_0,complement(one)),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_123,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_89,c_0_28]) ).
cnf(c_0_124,plain,
join(composition(X1,X2),join(X3,composition(complement(X1),X2))) = join(X3,composition(top,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_101]) ).
cnf(c_0_125,negated_conjecture,
join(complement(esk1_0),composition(complement(one),composition(esk1_0,esk2_0))) = complement(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_102]),c_0_28]) ).
cnf(c_0_126,negated_conjecture,
join(complement(X1),composition(top,composition(X1,esk2_0))) = join(complement(X1),composition(top,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_28]) ).
cnf(c_0_127,negated_conjecture,
join(complement(esk1_0),composition(top,esk2_0)) = join(esk2_0,complement(esk1_0)),
inference(spm,[status(thm)],[c_0_115,c_0_117]) ).
cnf(c_0_128,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_69,c_0_93]),c_0_28]) ).
cnf(c_0_129,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_89,c_0_118]),c_0_89]) ).
cnf(c_0_130,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_69,c_0_119]),c_0_48]),c_0_28]),c_0_120]) ).
cnf(c_0_131,plain,
join(complement(join(complement(composition(X1,converse(X2))),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2)))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2))))),
inference(spm,[status(thm)],[c_0_121,c_0_21]) ).
cnf(c_0_132,negated_conjecture,
join(complement(one),complement(composition(top,esk1_0))) = complement(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_122]),c_0_123]),c_0_102]) ).
cnf(c_0_133,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_66]),c_0_34]),c_0_34]) ).
cnf(c_0_134,negated_conjecture,
join(complement(esk1_0),composition(esk1_0,esk2_0)) = join(esk2_0,complement(esk1_0)),
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_34]),c_0_126]),c_0_127]),c_0_28]) ).
cnf(c_0_135,negated_conjecture,
join(complement(X1),complement(composition(X1,esk2_0))) = complement(composition(X1,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_94]),c_0_28]) ).
cnf(c_0_136,negated_conjecture,
complement(composition(complement(X1),esk1_0)) = join(X1,complement(composition(top,esk1_0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_48]),c_0_129]) ).
cnf(c_0_137,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_48,c_0_130]) ).
cnf(c_0_138,negated_conjecture,
composition(esk1_0,converse(esk1_0)) = converse(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_131,c_0_132]),c_0_34]),c_0_40]),c_0_91]),c_0_48]),c_0_40]),c_0_48]),c_0_47]),c_0_48]),c_0_133]),c_0_40]),c_0_48]),c_0_47]),c_0_48]) ).
cnf(c_0_139,negated_conjecture,
( 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),esk3_0),meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0))) != meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_140,negated_conjecture,
complement(composition(esk1_0,esk2_0)) = join(complement(esk1_0),complement(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_134]),c_0_123]),c_0_135]) ).
cnf(c_0_141,negated_conjecture,
composition(complement(X1),esk1_0) = complement(join(X1,complement(composition(top,esk1_0)))),
inference(spm,[status(thm)],[c_0_48,c_0_136]) ).
cnf(c_0_142,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_21,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
converse(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_138]),c_0_21]),c_0_21]),c_0_138]) ).
cnf(c_0_144,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))),esk3_0),complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0))))) != complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_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)],[c_0_139,c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_145,negated_conjecture,
composition(esk1_0,esk2_0) = complement(join(complement(esk1_0),complement(esk2_0))),
inference(spm,[status(thm)],[c_0_48,c_0_140]) ).
cnf(c_0_146,negated_conjecture,
composition(esk1_0,complement(converse(X1))) = complement(join(complement(composition(esk1_0,top)),converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_141]),c_0_142]),c_0_63]),c_0_142]),c_0_17]),c_0_143]),c_0_83]),c_0_143]),c_0_142]),c_0_28]) ).
cnf(c_0_147,negated_conjecture,
join(X1,composition(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_67]),c_0_34]),c_0_34]) ).
cnf(c_0_148,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)) != complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0))))
| 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) ),
inference(rw,[status(thm)],[c_0_144,c_0_28]) ).
cnf(c_0_149,negated_conjecture,
composition(complement(join(complement(esk1_0),complement(esk2_0))),X1) = composition(esk1_0,composition(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_105,c_0_145]) ).
cnf(c_0_150,negated_conjecture,
composition(esk1_0,complement(X1)) = complement(join(complement(composition(esk1_0,top)),X1)),
inference(spm,[status(thm)],[c_0_146,c_0_21]) ).
cnf(c_0_151,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_69,c_0_147]),c_0_28]) ).
cnf(c_0_152,negated_conjecture,
( join(complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0)))),composition(esk1_0,composition(esk2_0,esk3_0))) != complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0))))
| join(complement(join(complement(composition(esk1_0,esk3_0)),complement(composition(esk2_0,esk3_0)))),composition(esk1_0,composition(esk2_0,esk3_0))) != composition(esk1_0,composition(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149]),c_0_149]),c_0_149]) ).
cnf(c_0_153,negated_conjecture,
composition(esk1_0,X1) = complement(join(complement(composition(esk1_0,top)),complement(X1))),
inference(spm,[status(thm)],[c_0_150,c_0_48]) ).
cnf(c_0_154,negated_conjecture,
join(complement(X1),join(X2,complement(composition(esk2_0,X1)))) = join(X2,complement(composition(esk2_0,X1))),
inference(spm,[status(thm)],[c_0_68,c_0_151]) ).
cnf(c_0_155,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)],[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_152,c_0_153]),c_0_28]),c_0_48]),c_0_42]),c_0_154]),c_0_153]),c_0_49]),c_0_153]),c_0_28]),c_0_48]),c_0_42]),c_0_154]),c_0_153]),c_0_28]),c_0_48]),c_0_42]),c_0_154]),c_0_153]),c_0_49]),c_0_153])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL029+4 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 23:05:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 9.35/9.51 % Version : CSE_E---1.5
% 9.35/9.51 % Problem : theBenchmark.p
% 9.35/9.51 % Proof found
% 9.35/9.51 % SZS status Theorem for theBenchmark.p
% 9.35/9.51 % SZS output start Proof
% See solution above
% 9.35/9.52 % Total time : 8.934000 s
% 9.35/9.52 % SZS output end Proof
% 9.35/9.52 % Total time : 8.938000 s
%------------------------------------------------------------------------------