%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL030+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:04:24 PM UTC 2026
% Result : Theorem 35.26s 21.15s
% Output : CNFRefutation 35.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 14
% Syntax : Number of formulae : 176 ( 169 unt; 0 def)
% Number of atoms : 186 ( 185 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 5 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% 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 : 246 ( 18 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(goals,conjecture,
! [X1,X2,X3] :
( join(X1,one) = one
=> ( join(meet(composition(X1,X2),complement(X3)),meet(composition(X1,X2),complement(composition(X1,X3)))) = meet(composition(X1,X2),complement(composition(X1,X3)))
& join(meet(composition(X1,X2),complement(composition(X1,X3))),meet(composition(X1,X2),complement(X3))) = meet(composition(X1,X2),complement(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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_14,plain,
! [X51,X52] : converse(composition(X51,X52)) = composition(converse(X52),converse(X51)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_15,plain,
! [X44] : composition(X44,one) = X44,
inference(variable_rename,[status(thm)],[composition_identity]) ).
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,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X48] : converse(converse(X48)) = X48,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_19,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X53,X54] : join(composition(converse(X53),complement(composition(X53,X54))),complement(X54)) = complement(X54),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_22,plain,
! [X32,X33] : join(X32,X33) = join(X33,X32),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_23,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,plain,
! [X56] : zero = meet(X56,complement(X56)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_25,plain,
! [X39,X40] : meet(X39,X40) = complement(join(complement(X39),complement(X40))),
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_17,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,
! [X55] : top = join(X55,complement(X55)),
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,
! [X37,X38] : X37 = join(complement(join(complement(X37),complement(X38))),complement(join(complement(X37),X38))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_37,plain,
! [X34,X35,X36] : join(X34,join(X35,X36)) = join(join(X34,X35),X36),
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_38]),c_0_35]),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,
! [X49,X50] : converse(join(X49,X50)) = join(converse(X49),converse(X50)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_54,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_35]) ).
cnf(c_0_55,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_54,c_0_47]) ).
cnf(c_0_58,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_41]) ).
cnf(c_0_59,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_60,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,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_58]),c_0_27]),c_0_59]) ).
cnf(c_0_62,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_27,c_0_57]) ).
cnf(c_0_63,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_64,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_47]) ).
cnf(c_0_65,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_66,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
fof(c_0_67,plain,
! [X45,X46,X47] : composition(join(X45,X46),X47) = join(composition(X45,X47),composition(X46,X47)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_68,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_64]),c_0_49]) ).
cnf(c_0_69,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_71,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
fof(c_0_72,negated_conjecture,
~ ! [X1,X2,X3] :
( join(X1,one) = one
=> ( join(meet(composition(X1,X2),complement(X3)),meet(composition(X1,X2),complement(composition(X1,X3)))) = meet(composition(X1,X2),complement(composition(X1,X3)))
& join(meet(composition(X1,X2),complement(composition(X1,X3))),meet(composition(X1,X2),complement(X3))) = meet(composition(X1,X2),complement(X3)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_73,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_39]),c_0_70]) ).
cnf(c_0_74,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_33]),c_0_27]) ).
fof(c_0_75,negated_conjecture,
( join(esk1_0,one) = one
& ( join(meet(composition(esk1_0,esk2_0),complement(esk3_0)),meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0)))) != meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0)))
| join(meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0))),meet(composition(esk1_0,esk2_0),complement(esk3_0))) != meet(composition(esk1_0,esk2_0),complement(esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])]) ).
cnf(c_0_76,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_73]),c_0_20]),c_0_20]) ).
cnf(c_0_77,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_69,c_0_20]) ).
cnf(c_0_78,plain,
join(composition(join(X1,one),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_41,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_76,c_0_47]) ).
cnf(c_0_81,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_77]),c_0_39]),c_0_70]) ).
cnf(c_0_82,plain,
join(composition(join(one,X1),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_78,c_0_27]) ).
cnf(c_0_83,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_79,c_0_27]) ).
cnf(c_0_84,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_59,c_0_80]),c_0_47]),c_0_27]),c_0_81]) ).
cnf(c_0_85,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_33]) ).
cnf(c_0_86,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_47,c_0_84]) ).
fof(c_0_87,plain,
! [X41,X42,X43] : composition(X41,composition(X42,X43)) = composition(composition(X41,X42),X43),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_88,negated_conjecture,
join(X1,complement(composition(esk1_0,X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_35]),c_0_62]) ).
cnf(c_0_89,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_86]) ).
cnf(c_0_90,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_50,c_0_57]) ).
cnf(c_0_91,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
cnf(c_0_92,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_93,negated_conjecture,
join(converse(X1),complement(composition(converse(X1),converse(esk1_0)))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_88]),c_0_66]),c_0_89]),c_0_16]) ).
cnf(c_0_94,plain,
join(X1,composition(top,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_71,c_0_92]) ).
cnf(c_0_96,negated_conjecture,
join(X1,complement(composition(X1,converse(esk1_0)))) = top,
inference(spm,[status(thm)],[c_0_93,c_0_20]) ).
cnf(c_0_97,plain,
join(converse(X1),composition(converse(complement(X1)),top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_94]),c_0_66]),c_0_16]),c_0_66]) ).
cnf(c_0_98,plain,
join(X1,composition(X2,composition(X3,X1))) = composition(join(one,composition(X2,X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_33]),c_0_27]),c_0_27]) ).
cnf(c_0_99,negated_conjecture,
join(X1,composition(X1,converse(esk1_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_96]),c_0_39]),c_0_70]),c_0_47]) ).
cnf(c_0_100,plain,
join(converse(X1),composition(complement(converse(X1)),top)) = top,
inference(rw,[status(thm)],[c_0_97,c_0_89]) ).
cnf(c_0_101,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_33]),c_0_33]) ).
cnf(c_0_102,plain,
join(X1,composition(complement(X1),top)) = top,
inference(spm,[status(thm)],[c_0_100,c_0_20]) ).
cnf(c_0_103,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_56,c_0_101]),c_0_16]),c_0_20]) ).
cnf(c_0_104,plain,
join(X1,join(X2,composition(complement(X1),top))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_102]),c_0_62]) ).
cnf(c_0_105,plain,
join(converse(X1),composition(converse(X1),converse(X2))) = composition(converse(X1),join(one,converse(X2))),
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_16,c_0_74]),c_0_56]),c_0_16]),c_0_56]),c_0_28]),c_0_27]) ).
cnf(c_0_106,negated_conjecture,
join(X1,composition(X1,esk1_0)) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_20]) ).
cnf(c_0_107,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_85]),c_0_48]),c_0_27]) ).
cnf(c_0_108,plain,
join(X1,composition(join(X2,complement(X1)),top)) = top,
inference(spm,[status(thm)],[c_0_104,c_0_71]) ).
cnf(c_0_109,plain,
join(converse(X1),composition(converse(X1),X2)) = composition(converse(X1),join(one,X2)),
inference(spm,[status(thm)],[c_0_105,c_0_20]) ).
cnf(c_0_110,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
cnf(c_0_111,negated_conjecture,
join(X1,join(composition(X1,esk1_0),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
join(complement(X1),complement(composition(esk1_0,X1))) = complement(composition(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_107]),c_0_27]) ).
cnf(c_0_113,plain,
join(complement(X1),composition(join(X2,X1),top)) = top,
inference(spm,[status(thm)],[c_0_108,c_0_47]) ).
cnf(c_0_114,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[c_0_109,c_0_20]) ).
cnf(c_0_115,plain,
composition(join(one,X1),top) = top,
inference(spm,[status(thm)],[c_0_110,c_0_27]) ).
cnf(c_0_116,negated_conjecture,
join(X1,composition(join(X1,X2),esk1_0)) = join(X1,composition(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_111,c_0_71]) ).
cnf(c_0_117,negated_conjecture,
join(X1,complement(composition(esk1_0,complement(X1)))) = complement(composition(esk1_0,complement(X1))),
inference(spm,[status(thm)],[c_0_112,c_0_47]) ).
cnf(c_0_118,plain,
join(composition(X1,top),complement(composition(X1,X2))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_92]),c_0_115]),c_0_27]) ).
cnf(c_0_119,negated_conjecture,
join(X1,composition(complement(X1),esk1_0)) = join(X1,composition(top,esk1_0)),
inference(spm,[status(thm)],[c_0_116,c_0_35]) ).
cnf(c_0_120,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_27]) ).
cnf(c_0_121,negated_conjecture,
complement(composition(esk1_0,complement(composition(esk1_0,top)))) = top,
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_122,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_90,c_0_47]) ).
cnf(c_0_123,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_59,c_0_106]),c_0_27]) ).
cnf(c_0_124,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_68,c_0_119]),c_0_68]) ).
cnf(c_0_125,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_110,c_0_57]) ).
cnf(c_0_126,negated_conjecture,
composition(esk1_0,complement(composition(esk1_0,top))) = zero,
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_120,c_0_121]),c_0_57]),c_0_39]),c_0_62]),c_0_39]),c_0_46]) ).
cnf(c_0_127,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_128,plain,
join(composition(top,X1),complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_91]),c_0_27]) ).
cnf(c_0_129,negated_conjecture,
join(X1,complement(composition(top,esk1_0))) = complement(composition(complement(X1),esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_47]),c_0_124]) ).
cnf(c_0_130,plain,
composition(top,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_92,c_0_125]) ).
cnf(c_0_131,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_51,c_0_47]) ).
cnf(c_0_132,negated_conjecture,
join(X1,join(X2,composition(esk1_0,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_85,c_0_27]) ).
cnf(c_0_133,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_71,c_0_33]) ).
cnf(c_0_134,negated_conjecture,
composition(join(esk1_0,converse(esk1_0)),top) = composition(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_32,c_0_126]),c_0_47]),c_0_127]),c_0_71]),c_0_47]) ).
cnf(c_0_135,negated_conjecture,
complement(composition(complement(composition(top,esk1_0)),esk1_0)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_136,plain,
join(complement(X1),complement(composition(top,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_131,c_0_91]) ).
cnf(c_0_137,negated_conjecture,
join(X1,composition(esk1_0,join(one,X1))) = join(X1,esk1_0),
inference(spm,[status(thm)],[c_0_132,c_0_114]) ).
cnf(c_0_138,negated_conjecture,
join(X1,composition(complement(converse(esk1_0)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_96]),c_0_33]) ).
cnf(c_0_139,negated_conjecture,
join(composition(esk1_0,top),complement(converse(esk1_0))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_134]),c_0_27]) ).
cnf(c_0_140,plain,
join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))) = composition(converse(X1),join(converse(X2),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_71]),c_0_16]),c_0_56]),c_0_16]),c_0_16]) ).
cnf(c_0_141,negated_conjecture,
composition(complement(composition(top,esk1_0)),esk1_0) = zero,
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_120,c_0_135]),c_0_57]),c_0_39]),c_0_62]),c_0_39]),c_0_46]) ).
cnf(c_0_142,negated_conjecture,
complement(composition(esk1_0,esk1_0)) = complement(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_129]),c_0_47]) ).
cnf(c_0_143,negated_conjecture,
join(esk1_0,complement(converse(esk1_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_17]),c_0_17]),c_0_27]),c_0_139]),c_0_17]),c_0_27]) ).
cnf(c_0_144,plain,
join(composition(X1,converse(X2)),composition(X1,converse(X3))) = composition(X1,join(converse(X2),converse(X3))),
inference(spm,[status(thm)],[c_0_140,c_0_20]) ).
cnf(c_0_145,negated_conjecture,
composition(complement(composition(complement(X1),esk1_0)),esk1_0) = composition(X1,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_141]),c_0_70]),c_0_129]) ).
cnf(c_0_146,negated_conjecture,
composition(esk1_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_142]),c_0_120]) ).
cnf(c_0_147,negated_conjecture,
join(esk1_0,converse(esk1_0)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_143]),c_0_39]),c_0_70]),c_0_47]) ).
cnf(c_0_148,plain,
join(composition(X1,top),complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_47]),c_0_27]) ).
cnf(c_0_149,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_144,c_0_20]) ).
cnf(c_0_150,negated_conjecture,
composition(complement(composition(X1,esk1_0)),esk1_0) = composition(complement(X1),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_145]),c_0_92]),c_0_146]) ).
cnf(c_0_151,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_56,c_0_147]),c_0_20]),c_0_27]),c_0_147]) ).
cnf(c_0_152,plain,
join(X1,composition(X1,top)) = 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_68,c_0_148]),c_0_39]),c_0_70]),c_0_47]),c_0_27]) ).
cnf(c_0_153,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_149,c_0_20]) ).
cnf(c_0_154,negated_conjecture,
composition(esk1_0,complement(composition(esk1_0,converse(X1)))) = composition(esk1_0,complement(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(spm,[status(thm)],[c_0_16,c_0_150]),c_0_16]),c_0_151]),c_0_89]),c_0_151]),c_0_89]),c_0_16]),c_0_151]) ).
cnf(c_0_155,plain,
join(X1,join(X2,composition(X1,top))) = join(X2,composition(X1,top)),
inference(spm,[status(thm)],[c_0_58,c_0_152]) ).
cnf(c_0_156,negated_conjecture,
( join(meet(composition(esk1_0,esk2_0),complement(esk3_0)),meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0)))) != meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0)))
| join(meet(composition(esk1_0,esk2_0),complement(composition(esk1_0,esk3_0))),meet(composition(esk1_0,esk2_0),complement(esk3_0))) != meet(composition(esk1_0,esk2_0),complement(esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_157,negated_conjecture,
join(X1,composition(esk1_0,join(X1,X2))) = join(X1,composition(esk1_0,X2)),
inference(spm,[status(thm)],[c_0_85,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
composition(esk1_0,complement(composition(esk1_0,X1))) = composition(esk1_0,complement(X1)),
inference(spm,[status(thm)],[c_0_154,c_0_20]) ).
cnf(c_0_159,plain,
join(X1,composition(join(X2,X1),top)) = composition(join(X2,X1),top),
inference(spm,[status(thm)],[c_0_155,c_0_71]) ).
cnf(c_0_160,negated_conjecture,
( join(complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(composition(esk1_0,esk3_0))))),complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(esk3_0))))) != complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(esk3_0))))
| join(complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(esk3_0)))),complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(composition(esk1_0,esk3_0)))))) != complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(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)],[c_0_156,c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_161,negated_conjecture,
join(X1,complement(join(composition(esk1_0,X1),X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_68]),c_0_85]) ).
cnf(c_0_162,negated_conjecture,
join(X1,composition(esk1_0,complement(X1))) = join(X1,composition(esk1_0,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_88]),c_0_158]) ).
cnf(c_0_163,plain,
join(composition(X1,X2),composition(X1,top)) = 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_159,c_0_114]),c_0_92]),c_0_115]),c_0_92]),c_0_115]) ).
cnf(c_0_164,negated_conjecture,
( join(complement(join(complement(complement(esk3_0)),complement(composition(esk1_0,esk2_0)))),complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(composition(esk1_0,esk3_0)))))) != complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(composition(esk1_0,esk3_0)))))
| join(complement(join(complement(complement(esk3_0)),complement(composition(esk1_0,esk2_0)))),complement(join(complement(composition(esk1_0,esk2_0)),complement(complement(composition(esk1_0,esk3_0)))))) != complement(join(complement(complement(esk3_0)),complement(composition(esk1_0,esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_165,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(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_158]),c_0_117]) ).
cnf(c_0_166,negated_conjecture,
( join(complement(join(esk3_0,complement(composition(esk1_0,esk2_0)))),complement(join(composition(esk1_0,esk3_0),complement(composition(esk1_0,esk2_0))))) != complement(join(composition(esk1_0,esk3_0),complement(composition(esk1_0,esk2_0))))
| join(complement(join(esk3_0,complement(composition(esk1_0,esk2_0)))),complement(join(composition(esk1_0,esk3_0),complement(composition(esk1_0,esk2_0))))) != complement(join(esk3_0,complement(composition(esk1_0,esk2_0)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_47]),c_0_47]),c_0_27]),c_0_47]),c_0_27]),c_0_47]),c_0_47]),c_0_27]),c_0_47]) ).
cnf(c_0_167,negated_conjecture,
join(complement(join(X1,X2)),complement(join(composition(esk1_0,X1),X2))) = complement(join(composition(esk1_0,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_85]),c_0_27]) ).
cnf(c_0_168,negated_conjecture,
join(X1,complement(composition(esk1_0,complement(X2)))) = complement(composition(esk1_0,complement(join(X1,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_165]),c_0_165]) ).
cnf(c_0_169,negated_conjecture,
composition(esk1_0,composition(esk1_0,X1)) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_92,c_0_146]) ).
cnf(c_0_170,negated_conjecture,
complement(join(composition(esk1_0,esk3_0),complement(composition(esk1_0,esk2_0)))) != complement(join(esk3_0,complement(composition(esk1_0,esk2_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167]),c_0_167])]) ).
cnf(c_0_171,negated_conjecture,
join(X1,complement(composition(esk1_0,X2))) = complement(composition(esk1_0,complement(join(X1,complement(X2))))),
inference(spm,[status(thm)],[c_0_168,c_0_47]) ).
cnf(c_0_172,negated_conjecture,
composition(esk1_0,join(X1,composition(esk1_0,X2))) = composition(esk1_0,join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_169]),c_0_153]) ).
cnf(c_0_173,negated_conjecture,
composition(esk1_0,complement(join(complement(esk2_0),composition(esk1_0,esk3_0)))) != composition(esk1_0,complement(join(complement(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_170,c_0_171]),c_0_27]),c_0_47]),c_0_171]),c_0_27]),c_0_47]) ).
cnf(c_0_174,negated_conjecture,
composition(esk1_0,complement(join(X1,composition(esk1_0,X2)))) = composition(esk1_0,complement(join(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_172]),c_0_158]) ).
cnf(c_0_175,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL030+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:42:53 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 35.26/21.15 % Version : CSE_E---1.7
% 35.26/21.15 % Problem : theBenchmark.p
% 35.26/21.15 % SZS status Theorem for theBenchmark.p
% 35.26/21.15 % SZS output start CNFRefutation
% See solution above
% 35.42/21.31 % Total time : 15.396s
%------------------------------------------------------------------------------