%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL026+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 05:04:21 PM UTC 2026
% Result : Theorem 175.51s 60.98s
% Output : CNFRefutation 175.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 16
% Syntax : Number of formulae : 191 ( 184 unt; 0 def)
% Number of atoms : 201 ( 200 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 5 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 277 ( 17 sgn 66 !; 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(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/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/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(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(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(goals,conjecture,
! [X1,X2] :
( join(X1,one) = one
=> ( join(meet(composition(X1,top),X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X1,X2),meet(composition(X1,top),X2)) = meet(composition(X1,top),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(modular_law_1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(c_0_16,plain,
! [X59,X60] : converse(composition(X59,X60)) = composition(converse(X60),converse(X59)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_17,plain,
! [X52] : composition(X52,one) = X52,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_18,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X56] : converse(converse(X56)) = X56,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_21,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X61,X62] : join(composition(converse(X61),complement(composition(X61,X62))),complement(X62)) = complement(X62),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_24,plain,
! [X40,X41] : join(X40,X41) = join(X41,X40),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_25,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_26,plain,
! [X64] : zero = meet(X64,complement(X64)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_27,plain,
! [X47,X48] : meet(X47,X48) = complement(join(complement(X47),complement(X48))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_28,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_33,plain,
! [X63] : top = join(X63,complement(X63)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_34,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_36,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_38,plain,
! [X45,X46] : X45 = join(complement(join(complement(X45),complement(X46))),complement(join(complement(X45),X46))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_39,plain,
! [X42,X43,X44] : join(X42,join(X43,X44)) = join(join(X42,X43),X44),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_40,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]),c_0_35]) ).
cnf(c_0_41,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_46,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,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_45,c_0_40]),c_0_37]),c_0_41]),c_0_29]) ).
cnf(c_0_48,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_51,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_52,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_43,c_0_37]) ).
cnf(c_0_53,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_45]),c_0_29]) ).
cnf(c_0_54,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
fof(c_0_55,plain,
! [X57,X58] : converse(join(X57,X58)) = join(converse(X57),converse(X58)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_56,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_40]),c_0_37]) ).
cnf(c_0_57,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_60,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_29]),c_0_43]) ).
cnf(c_0_61,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_62,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_63,plain,
! [X53,X54,X55] : composition(join(X53,X54),X55) = join(composition(X53,X55),composition(X54,X55)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_64,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_45,c_0_45]),c_0_49]),c_0_60]),c_0_29]),c_0_61]) ).
cnf(c_0_65,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_29,c_0_59]) ).
cnf(c_0_66,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_62,c_0_22]) ).
cnf(c_0_67,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
fof(c_0_68,negated_conjecture,
~ ! [X1,X2] :
( join(X1,one) = one
=> ( join(meet(composition(X1,top),X2),composition(X1,X2)) = composition(X1,X2)
& join(composition(X1,X2),meet(composition(X1,top),X2)) = meet(composition(X1,top),X2) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_69,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_49]) ).
cnf(c_0_70,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_58,c_0_37]) ).
cnf(c_0_71,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_35]),c_0_29]) ).
fof(c_0_73,negated_conjecture,
( join(esk1_0,one) = one
& ( join(meet(composition(esk1_0,top),esk2_0),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),meet(composition(esk1_0,top),esk2_0)) != meet(composition(esk1_0,top),esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])]) ).
cnf(c_0_74,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_69]),c_0_51]) ).
cnf(c_0_75,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_77,plain,
join(converse(zero),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
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_43,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_80,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_41]),c_0_76]) ).
fof(c_0_81,plain,
! [X68,X69,X70] : join(meet(composition(X68,X69),X70),meet(composition(X68,meet(X69,composition(converse(X68),X70))),X70)) = meet(composition(X68,meet(X69,composition(converse(X68),X70))),X70),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_82,plain,
join(converse(zero),X1) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_22]) ).
cnf(c_0_83,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_72,c_0_59]) ).
cnf(c_0_84,plain,
join(composition(join(one,X1),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_78,c_0_29]) ).
cnf(c_0_85,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_86,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_80]),c_0_22]),c_0_22]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_75,c_0_22]) ).
cnf(c_0_88,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_89,plain,
join(converse(complement(X1)),composition(converse(complement(composition(X2,X1))),X2)) = converse(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_34]),c_0_18]),c_0_22]) ).
cnf(c_0_90,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_76,c_0_82]) ).
cnf(c_0_91,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_83,c_0_59]) ).
cnf(c_0_92,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_35]) ).
cnf(c_0_93,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_86,c_0_49]) ).
cnf(c_0_94,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_87]),c_0_41]),c_0_76]) ).
cnf(c_0_95,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_96,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
cnf(c_0_97,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_98,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_41]),c_0_90]),c_0_48]),c_0_90]) ).
cnf(c_0_99,plain,
composition(converse(top),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_91]),c_0_41]),c_0_41]),c_0_48]),c_0_41]) ).
fof(c_0_100,plain,
! [X71,X72,X73] : join(meet(composition(X71,X72),X73),meet(composition(meet(X71,composition(X73,converse(X72))),X72),X73)) = meet(composition(meet(X71,composition(X73,converse(X72))),X72),X73),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_101,negated_conjecture,
join(X1,complement(composition(esk1_0,X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_37]),c_0_65]) ).
cnf(c_0_102,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_61,c_0_93]),c_0_49]),c_0_29]),c_0_94]) ).
fof(c_0_103,plain,
! [X49,X50,X51] : composition(X49,composition(X50,X51)) = composition(composition(X49,X50),X51),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_104,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_29]),c_0_29]) ).
cnf(c_0_105,plain,
join(X1,join(complement(join(X2,X1)),X3)) = join(X1,join(complement(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_96]),c_0_43]) ).
cnf(c_0_106,plain,
join(X1,complement(join(X2,join(X3,X1)))) = join(X1,complement(join(X2,X3))),
inference(spm,[status(thm)],[c_0_74,c_0_97]) ).
cnf(c_0_107,plain,
join(X1,join(complement(join(X1,X2)),X3)) = join(X1,join(complement(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_74]),c_0_43]) ).
cnf(c_0_108,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_98]),c_0_90]),c_0_22]) ).
cnf(c_0_109,plain,
composition(top,zero) = zero,
inference(rw,[status(thm)],[c_0_99,c_0_71]) ).
cnf(c_0_110,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_92]),c_0_50]),c_0_29]) ).
cnf(c_0_111,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_100]) ).
cnf(c_0_112,negated_conjecture,
join(converse(X1),converse(complement(composition(esk1_0,X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_101]),c_0_71]) ).
cnf(c_0_113,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_49,c_0_102]) ).
cnf(c_0_114,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_115,plain,
join(complement(X1),join(complement(composition(X2,X3)),complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))))) = join(complement(composition(X2,X3)),complement(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_45,c_0_104]),c_0_49]),c_0_49]),c_0_60]),c_0_105]),c_0_49]),c_0_43]),c_0_106]),c_0_29]),c_0_107]) ).
cnf(c_0_116,plain,
composition(X1,complement(composition(converse(X1),top))) = zero,
inference(spm,[status(thm)],[c_0_108,c_0_22]) ).
cnf(c_0_117,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
cnf(c_0_118,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_109]),c_0_48]),c_0_59]),c_0_109]) ).
cnf(c_0_119,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_61,c_0_110]),c_0_29]) ).
cnf(c_0_120,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_111,c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_121,negated_conjecture,
join(X1,converse(complement(composition(esk1_0,converse(X1))))) = top,
inference(spm,[status(thm)],[c_0_112,c_0_22]) ).
cnf(c_0_122,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_113]) ).
cnf(c_0_123,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_67,c_0_114]) ).
cnf(c_0_124,plain,
join(composition(X1,top),complement(composition(X1,X2))) = 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(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_115,c_0_116]),c_0_22]),c_0_49]),c_0_117]),c_0_65]),c_0_41]),c_0_118]),c_0_117]),c_0_65]),c_0_65]),c_0_22]),c_0_49]),c_0_29]) ).
cnf(c_0_125,negated_conjecture,
join(X1,complement(composition(esk1_0,complement(X1)))) = complement(composition(esk1_0,complement(X1))),
inference(spm,[status(thm)],[c_0_119,c_0_49]) ).
cnf(c_0_126,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_120,c_0_29]),c_0_29]) ).
cnf(c_0_127,negated_conjecture,
join(X1,composition(X1,converse(esk1_0))) = 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(spm,[status(thm)],[c_0_74,c_0_121]),c_0_41]),c_0_76]),c_0_122]),c_0_49]),c_0_18]),c_0_22]) ).
cnf(c_0_128,plain,
composition(zero,converse(X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_118]),c_0_90]),c_0_90]) ).
cnf(c_0_129,plain,
composition(join(composition(X1,top),X2),top) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_91]),c_0_67]) ).
cnf(c_0_130,plain,
join(composition(X1,top),composition(X1,X2)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_124]),c_0_41]),c_0_76]),c_0_49]) ).
cnf(c_0_131,negated_conjecture,
complement(composition(esk1_0,complement(composition(esk1_0,top)))) = top,
inference(spm,[status(thm)],[c_0_125,c_0_124]) ).
cnf(c_0_132,plain,
join(complement(X1),join(complement(composition(X2,X3)),complement(composition(complement(join(complement(X2),complement(composition(X1,converse(X3))))),X3)))) = join(complement(composition(X2,X3)),complement(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_45,c_0_126]),c_0_49]),c_0_49]),c_0_60]),c_0_105]),c_0_49]),c_0_43]),c_0_106]),c_0_29]),c_0_107]) ).
cnf(c_0_133,negated_conjecture,
join(X1,complement(composition(X1,converse(esk1_0)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_127]),c_0_37]) ).
cnf(c_0_134,plain,
composition(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_128,c_0_22]) ).
cnf(c_0_135,negated_conjecture,
join(one,join(esk1_0,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_43,c_0_85]) ).
cnf(c_0_136,plain,
join(composition(X1,X2),composition(X1,complement(join(complement(X2),complement(composition(converse(X1),top)))))) = composition(X1,complement(join(complement(X2),complement(composition(converse(X1),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_104,c_0_41]),c_0_76]),c_0_49]),c_0_48]),c_0_49]),c_0_48]),c_0_49]) ).
cnf(c_0_137,plain,
composition(join(X1,composition(X1,X2)),top) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_114]),c_0_91]) ).
cnf(c_0_138,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_45,c_0_131]),c_0_59]),c_0_41]),c_0_59]),c_0_41]),c_0_48]) ).
cnf(c_0_139,negated_conjecture,
join(X1,complement(composition(X1,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_49]),c_0_41]),c_0_134]),c_0_117]),c_0_65]),c_0_65]),c_0_49]),c_0_29]) ).
cnf(c_0_140,negated_conjecture,
join(one,complement(esk1_0)) = join(one,top),
inference(spm,[status(thm)],[c_0_135,c_0_37]) ).
cnf(c_0_141,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_52,c_0_59]) ).
cnf(c_0_142,plain,
composition(X1,composition(converse(X1),top)) = composition(X1,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_136]),c_0_41]),c_0_48]),c_0_49]),c_0_114]),c_0_114]),c_0_91]),c_0_41]),c_0_48]),c_0_49]),c_0_137]) ).
cnf(c_0_143,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_34,c_0_138]),c_0_49]),c_0_117]),c_0_67]),c_0_49]) ).
cnf(c_0_144,negated_conjecture,
join(X1,join(composition(X1,esk1_0),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_139]),c_0_41]),c_0_48]),c_0_49]) ).
cnf(c_0_145,negated_conjecture,
join(one,complement(esk1_0)) = top,
inference(rw,[status(thm)],[c_0_140,c_0_65]) ).
cnf(c_0_146,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_141,c_0_49]) ).
cnf(c_0_147,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_72,c_0_59]) ).
cnf(c_0_148,negated_conjecture,
composition(converse(esk1_0),top) = composition(esk1_0,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_142]),c_0_67]),c_0_29]),c_0_143]) ).
cnf(c_0_149,negated_conjecture,
join(X1,composition(join(X1,X2),esk1_0)) = join(X1,composition(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_144,c_0_67]) ).
cnf(c_0_150,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_74,c_0_139]),c_0_41]),c_0_76]),c_0_49]) ).
cnf(c_0_151,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_67,c_0_35]) ).
cnf(c_0_152,negated_conjecture,
join(one,converse(complement(esk1_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_145]),c_0_30]),c_0_71]) ).
cnf(c_0_153,plain,
join(composition(top,X1),complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_29]) ).
cnf(c_0_154,negated_conjecture,
composition(top,converse(esk1_0)) = composition(top,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_148]),c_0_18]),c_0_71]),c_0_71]),c_0_22]) ).
cnf(c_0_155,plain,
join(X1,composition(top,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_141,c_0_147]) ).
cnf(c_0_156,negated_conjecture,
join(X1,composition(complement(X1),esk1_0)) = join(X1,composition(top,esk1_0)),
inference(spm,[status(thm)],[c_0_149,c_0_37]) ).
cnf(c_0_157,negated_conjecture,
join(X1,join(X2,composition(X1,esk1_0))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_60,c_0_150]) ).
cnf(c_0_158,negated_conjecture,
join(X1,composition(converse(complement(esk1_0)),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_159,negated_conjecture,
join(composition(top,esk1_0),converse(complement(esk1_0))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_122]) ).
cnf(c_0_160,plain,
composition(top,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_114,c_0_91]) ).
cnf(c_0_161,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_58,c_0_155]),c_0_71]),c_0_18]),c_0_71]) ).
cnf(c_0_162,negated_conjecture,
join(complement(X1),complement(composition(X1,esk1_0))) = complement(composition(X1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_139]),c_0_41]),c_0_76]),c_0_29]) ).
cnf(c_0_163,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_74,c_0_156]),c_0_74]) ).
cnf(c_0_164,negated_conjecture,
join(esk1_0,converse(complement(esk1_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_29]),c_0_159]) ).
cnf(c_0_165,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_160]),c_0_71]),c_0_147]) ).
cnf(c_0_166,plain,
join(X1,composition(complement(X1),top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_122]),c_0_22]),c_0_22]) ).
cnf(c_0_167,plain,
join(converse(X1),converse(complement(join(X1,X2)))) = join(converse(X1),converse(complement(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_74]),c_0_58]) ).
cnf(c_0_168,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_162,c_0_49]),c_0_163]) ).
cnf(c_0_169,negated_conjecture,
join(esk1_0,converse(esk1_0)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_164]),c_0_41]),c_0_76]),c_0_122]),c_0_49]) ).
cnf(c_0_170,plain,
complement(join(complement(composition(X1,X2)),complement(composition(complement(join(complement(X1),complement(composition(X1,composition(X2,converse(X2)))))),X2)))) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_50]),c_0_49]),c_0_114]),c_0_114]),c_0_53]) ).
cnf(c_0_171,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_165]),c_0_71]) ).
cnf(c_0_172,plain,
join(X1,complement(composition(complement(X1),top))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_166]),c_0_41]),c_0_76]) ).
cnf(c_0_173,plain,
join(X1,converse(complement(join(converse(X1),X2)))) = join(X1,converse(complement(X2))),
inference(spm,[status(thm)],[c_0_167,c_0_22]) ).
cnf(c_0_174,negated_conjecture,
complement(join(X1,complement(composition(top,esk1_0)))) = composition(complement(X1),esk1_0),
inference(spm,[status(thm)],[c_0_49,c_0_168]) ).
cnf(c_0_175,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_58,c_0_169]),c_0_22]),c_0_29]),c_0_169]) ).
cnf(c_0_176,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,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(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_170,c_0_171]),c_0_122]),c_0_49]),c_0_18]),c_0_71]),c_0_122]),c_0_49]),c_0_18]),c_0_71]),c_0_71]),c_0_91]),c_0_171]),c_0_122]),c_0_49]),c_0_18]),c_0_71]),c_0_67]),c_0_50]),c_0_172]) ).
cnf(c_0_177,negated_conjecture,
( join(meet(composition(esk1_0,top),esk2_0),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),meet(composition(esk1_0,top),esk2_0)) != meet(composition(esk1_0,top),esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_178,negated_conjecture,
join(X1,composition(esk1_0,complement(X1))) = join(X1,composition(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_122]),c_0_18]),c_0_175]),c_0_22]),c_0_49]),c_0_18]),c_0_175]),c_0_71]) ).
cnf(c_0_179,negated_conjecture,
complement(composition(esk1_0,top)) = converse(complement(composition(top,esk1_0))),
inference(spm,[status(thm)],[c_0_176,c_0_175]) ).
cnf(c_0_180,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_58,c_0_67]),c_0_18]),c_0_58]),c_0_18]),c_0_18]) ).
cnf(c_0_181,negated_conjecture,
( join(complement(join(complement(composition(esk1_0,top)),complement(esk2_0))),composition(esk1_0,esk2_0)) != composition(esk1_0,esk2_0)
| join(composition(esk1_0,esk2_0),complement(join(complement(composition(esk1_0,top)),complement(esk2_0)))) != complement(join(complement(composition(esk1_0,top)),complement(esk2_0))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_182,negated_conjecture,
complement(composition(esk1_0,complement(X1))) = join(X1,converse(complement(composition(top,esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_178]),c_0_74]),c_0_179]),c_0_125]) ).
cnf(c_0_183,plain,
join(composition(X1,converse(X2)),composition(X1,converse(X3))) = composition(X1,join(converse(X2),converse(X3))),
inference(spm,[status(thm)],[c_0_180,c_0_22]) ).
cnf(c_0_184,negated_conjecture,
( join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),complement(composition(esk1_0,top))))) != complement(join(complement(esk2_0),complement(composition(esk1_0,top))))
| join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),complement(composition(esk1_0,top))))) != composition(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_181,c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_185,negated_conjecture,
complement(composition(esk1_0,X1)) = join(complement(X1),converse(complement(composition(top,esk1_0)))),
inference(spm,[status(thm)],[c_0_182,c_0_49]) ).
cnf(c_0_186,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_183,c_0_22]) ).
cnf(c_0_187,negated_conjecture,
( join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),converse(complement(composition(top,esk1_0)))))) != complement(join(complement(esk2_0),converse(complement(composition(top,esk1_0)))))
| join(composition(esk1_0,esk2_0),complement(join(complement(esk2_0),converse(complement(composition(top,esk1_0)))))) != composition(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_184,c_0_179]),c_0_179]),c_0_179]) ).
cnf(c_0_188,negated_conjecture,
complement(join(complement(X1),converse(complement(composition(top,esk1_0))))) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_49,c_0_185]) ).
cnf(c_0_189,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_186,c_0_22]) ).
cnf(c_0_190,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)],[c_0_187,c_0_188]),c_0_189]),c_0_50]),c_0_188]),c_0_188]),c_0_189]),c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL026+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n027.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 01:41:19 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 175.51/60.98 % Version : CSE_E---1.7
% 175.51/60.98 % Problem : theBenchmark.p
% 175.51/60.98 % SZS status Theorem for theBenchmark.p
% 175.51/60.98 % SZS output start CNFRefutation
% See solution above
% 175.92/61.34 % Total time : 47.555s
%------------------------------------------------------------------------------