%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL028+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:01 PM UTC 2026
% Result : Theorem 17.32s 3.00s
% Output : CNFRefutation 17.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 151 ( 148 unt; 0 def)
% Number of atoms : 157 ( 156 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 194 ( 11 sgn 54 !; 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(goals,conjecture,
! [X1,X2] :
( ( join(X2,one) = one
& join(X1,one) = one )
=> composition(X1,X2) = meet(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(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,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_15,plain,
! [X16] : composition(X16,one) = X16,
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,
! [X20] : converse(converse(X20)) = X20,
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,
! [X25,X26] : join(composition(converse(X25),complement(composition(X25,X26))),complement(X26)) = complement(X26),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_22,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_23,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_24,plain,
! [X28] : zero = meet(X28,complement(X28)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_25,plain,
! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_26,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_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,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_32,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,plain,
! [X9,X10] : X9 = join(complement(join(complement(X9),complement(X10))),complement(join(complement(X9),X10))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_37,plain,
! [X6,X7,X8] : join(X6,join(X7,X8)) = join(join(X6,X7),X8),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_38,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_28]),c_0_33]) ).
cnf(c_0_39,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_40,c_0_27]) ).
cnf(c_0_44,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_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(top,zero) = top,
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_51,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_41,c_0_35]) ).
cnf(c_0_52,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_53,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_27]) ).
fof(c_0_54,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_55,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_56,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_38]),c_0_35]) ).
cnf(c_0_57,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,plain,
join(top,X1) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_45]),c_0_56]) ).
cnf(c_0_60,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_57,c_0_47]) ).
cnf(c_0_61,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_43]),c_0_47]),c_0_27]),c_0_41]),c_0_60]) ).
cnf(c_0_63,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_64,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_65,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_47]) ).
cnf(c_0_66,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_58,c_0_35]) ).
cnf(c_0_67,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
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_65,c_0_65]),c_0_49]) ).
cnf(c_0_69,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_71,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]) ).
fof(c_0_72,negated_conjecture,
~ ! [X1,X2] :
( ( join(X2,one) = one
& join(X1,one) = one )
=> composition(X1,X2) = meet(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_73,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_74,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_71]),c_0_20]),c_0_20]) ).
cnf(c_0_75,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_69,c_0_20]) ).
fof(c_0_76,negated_conjecture,
( composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0)
& join(esk2_0,one) = one
& join(esk1_0,one) = one ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_72])])])]) ).
cnf(c_0_77,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_78,plain,
join(converse(zero),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_58,c_0_46]) ).
cnf(c_0_79,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_74,c_0_47]) ).
cnf(c_0_80,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_75]),c_0_39]),c_0_70]) ).
cnf(c_0_81,negated_conjecture,
join(esk2_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_82,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_51,c_0_59]) ).
cnf(c_0_83,plain,
composition(converse(X1),join(converse(X2),converse(X3))) = join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))),
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_77]),c_0_58]),c_0_16]),c_0_16]),c_0_58]) ).
cnf(c_0_84,plain,
join(converse(zero),X1) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_20]) ).
cnf(c_0_85,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_60,c_0_79]),c_0_47]),c_0_27]),c_0_80]) ).
cnf(c_0_86,negated_conjecture,
join(one,converse(esk2_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_81]),c_0_28]),c_0_27]),c_0_28]) ).
cnf(c_0_87,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_88,negated_conjecture,
join(esk2_0,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_41,c_0_81]) ).
cnf(c_0_89,plain,
join(X1,join(X2,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_82,c_0_27]) ).
cnf(c_0_90,plain,
composition(converse(X1),join(one,converse(X2))) = join(converse(X1),composition(converse(X1),converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_28]),c_0_17]),c_0_27]),c_0_27]) ).
cnf(c_0_91,negated_conjecture,
join(X1,composition(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_81]),c_0_33]),c_0_27]),c_0_33]) ).
cnf(c_0_92,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_32]),c_0_16]),c_0_20]) ).
cnf(c_0_93,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_70,c_0_84]) ).
cnf(c_0_94,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_47,c_0_85]) ).
cnf(c_0_95,negated_conjecture,
join(X1,composition(converse(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_86]),c_0_33]),c_0_33]) ).
cnf(c_0_96,negated_conjecture,
join(one,converse(esk1_0)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_87]),c_0_28]),c_0_27]),c_0_28]) ).
cnf(c_0_97,negated_conjecture,
join(one,complement(esk2_0)) = top,
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_98,plain,
composition(X1,join(one,converse(X2))) = join(X1,composition(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_90,c_0_20]) ).
cnf(c_0_99,negated_conjecture,
join(X1,join(composition(esk2_0,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_91]) ).
cnf(c_0_100,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_92,c_0_39]),c_0_93]),c_0_46]),c_0_93]) ).
cnf(c_0_101,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_94]) ).
fof(c_0_102,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_103,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_58,c_0_95]),c_0_16]),c_0_20]) ).
cnf(c_0_104,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_96]),c_0_33]),c_0_33]) ).
cnf(c_0_105,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_106,negated_conjecture,
join(X1,composition(complement(esk2_0),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_97]),c_0_33]) ).
cnf(c_0_107,plain,
composition(X1,join(one,X2)) = join(X1,composition(X1,X2)),
inference(spm,[status(thm)],[c_0_98,c_0_20]) ).
cnf(c_0_108,negated_conjecture,
join(X1,composition(converse(esk2_0),composition(esk2_0,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_95]),c_0_91]) ).
cnf(c_0_109,plain,
join(composition(X1,X2),composition(complement(X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_77,c_0_35]) ).
cnf(c_0_110,plain,
composition(complement(composition(top,converse(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101]),c_0_16]),c_0_67]) ).
cnf(c_0_111,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_112,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_82,c_0_47]) ).
cnf(c_0_113,negated_conjecture,
join(X1,composition(X1,esk2_0)) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_20]) ).
cnf(c_0_114,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_58,c_0_104]),c_0_16]),c_0_20]) ).
cnf(c_0_115,negated_conjecture,
join(X1,join(X2,composition(complement(esk2_0),X1))) = join(X2,composition(top,X1)),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,negated_conjecture,
join(X1,composition(X1,composition(converse(esk2_0),esk2_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_17]),c_0_17]) ).
cnf(c_0_117,plain,
composition(top,composition(converse(X1),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_47]),c_0_111]),c_0_46]) ).
cnf(c_0_118,negated_conjecture,
join(complement(X1),composition(top,X1)) = top,
inference(spm,[status(thm)],[c_0_112,c_0_106]) ).
cnf(c_0_119,negated_conjecture,
join(esk1_0,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_41,c_0_87]) ).
cnf(c_0_120,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_87]),c_0_33]),c_0_27]),c_0_33]) ).
cnf(c_0_121,negated_conjecture,
join(X1,join(composition(X1,esk2_0),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_113]) ).
cnf(c_0_122,negated_conjecture,
join(X1,composition(X1,esk1_0)) = X1,
inference(spm,[status(thm)],[c_0_114,c_0_20]) ).
cnf(c_0_123,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_68,c_0_27]) ).
cnf(c_0_124,negated_conjecture,
join(complement(esk2_0),composition(converse(esk2_0),esk2_0)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_117]),c_0_118]),c_0_27]) ).
cnf(c_0_125,negated_conjecture,
join(one,complement(esk1_0)) = top,
inference(spm,[status(thm)],[c_0_119,c_0_89]) ).
cnf(c_0_126,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
join(X1,composition(X1,composition(esk2_0,esk1_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_113]),c_0_111]) ).
cnf(c_0_128,negated_conjecture,
join(one,converse(complement(esk2_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_97]),c_0_28]),c_0_67]) ).
cnf(c_0_129,negated_conjecture,
composition(converse(esk2_0),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_39]),c_0_70]),c_0_47]),c_0_27]),c_0_95]) ).
cnf(c_0_130,negated_conjecture,
join(X1,join(X2,composition(X1,esk1_0))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_105,c_0_122]) ).
cnf(c_0_131,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_77,c_0_118]),c_0_111]),c_0_27]) ).
cnf(c_0_132,negated_conjecture,
join(X1,composition(complement(esk1_0),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_125]),c_0_33]) ).
cnf(c_0_133,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_104]),c_0_120]) ).
cnf(c_0_134,negated_conjecture,
join(X1,join(X2,composition(X1,composition(esk2_0,esk1_0)))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_105,c_0_127]) ).
cnf(c_0_135,negated_conjecture,
join(X1,composition(converse(complement(esk2_0)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_128]),c_0_33]) ).
cnf(c_0_136,negated_conjecture,
converse(esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_129]),c_0_20]),c_0_129]) ).
cnf(c_0_137,negated_conjecture,
join(complement(X1),composition(top,composition(X1,esk1_0))) = join(complement(X1),composition(top,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_27]) ).
cnf(c_0_138,negated_conjecture,
join(complement(esk2_0),composition(top,esk1_0)) = join(esk1_0,complement(esk2_0)),
inference(spm,[status(thm)],[c_0_130,c_0_106]) ).
cnf(c_0_139,negated_conjecture,
join(X1,join(X2,composition(complement(esk1_0),X1))) = join(X2,composition(top,X1)),
inference(spm,[status(thm)],[c_0_105,c_0_132]) ).
cnf(c_0_140,negated_conjecture,
join(X1,composition(X1,composition(converse(esk1_0),esk1_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_133]),c_0_17]),c_0_17]) ).
cnf(c_0_141,negated_conjecture,
join(complement(esk2_0),composition(esk2_0,esk1_0)) = join(esk1_0,complement(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_101]),c_0_136]),c_0_137]),c_0_138]),c_0_101]),c_0_136]),c_0_27]) ).
cnf(c_0_142,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_60,c_0_122]),c_0_27]) ).
cnf(c_0_143,negated_conjecture,
join(complement(esk1_0),composition(converse(esk1_0),esk1_0)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_117]),c_0_118]),c_0_27]) ).
cnf(c_0_144,negated_conjecture,
complement(composition(esk2_0,esk1_0)) = join(complement(esk1_0),complement(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_141]),c_0_123]),c_0_27]),c_0_142]) ).
cnf(c_0_145,negated_conjecture,
composition(converse(esk1_0),esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_143]),c_0_39]),c_0_70]),c_0_47]),c_0_27]),c_0_104]) ).
cnf(c_0_146,negated_conjecture,
composition(esk1_0,esk2_0) != meet(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_147,negated_conjecture,
composition(esk2_0,esk1_0) = complement(join(complement(esk1_0),complement(esk2_0))),
inference(spm,[status(thm)],[c_0_47,c_0_144]) ).
cnf(c_0_148,negated_conjecture,
converse(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_145]),c_0_20]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
composition(esk1_0,esk2_0) != complement(join(complement(esk1_0),complement(esk2_0))),
inference(rw,[status(thm)],[c_0_146,c_0_30]) ).
cnf(c_0_150,negated_conjecture,
$false,
inference(sr,[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_16,c_0_147]),c_0_101]),c_0_58]),c_0_101]),c_0_148]),c_0_101]),c_0_136]),c_0_148]),c_0_136]),c_0_149]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL028+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:02:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.32/3.00 % Version: 3.5.1
% 17.32/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.32/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.32/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.32/3.00 % Starting new_bool_3 with 300s (1) cores
% 17.32/3.00 % Starting new_bool_1 with 300s (1) cores
% 17.32/3.00 % Starting sh5l with 300s (1) cores
% 17.32/3.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4101075 completed with status 0
% 17.32/3.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 17.32/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.32/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.32/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.32/3.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.32/3.00 % No SInE strategy applied
% 17.32/3.00 % Search class: FUUPM-FFSF21-MFFFFFNN
% 17.32/3.00 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 17.32/3.00 % Starting SubtermCWHack with 136s (1) cores
% 17.32/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.32/3.00 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 17.32/3.00 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 17.32/3.00 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 17.32/3.00 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 4101081 completed with status 0
% 17.32/3.00 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 17.32/3.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 17.32/3.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.32/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.32/3.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 17.32/3.00 % No SInE strategy applied
% 17.32/3.00 % Search class: FUUPM-FFSF21-MFFFFFNN
% 17.32/3.00 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 17.32/3.00 % Starting SubtermCWHack with 136s (1) cores
% 17.32/3.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 17.32/3.00 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 17.32/3.00 % Preprocessing time : 0.001 s
% 17.32/3.00
% 17.32/3.00 % Proof found!
% 17.32/3.00 % SZS status Theorem
% 17.32/3.00 % SZS output start CNFRefutation
% See solution above
% 17.32/3.00 % Parsed axioms : 14
% 17.32/3.00 % Removed by relevancy pruning/SinE : 0
% 17.32/3.00 % Initial clauses : 16
% 17.32/3.00 % Removed in clause preprocessing : 1
% 17.32/3.00 % Initial clauses in saturation : 15
% 17.32/3.00 % Processed clauses : 11397
% 17.32/3.00 % ...of these trivial : 7543
% 17.32/3.00 % ...subsumed : 2707
% 17.32/3.00 % ...remaining for further processing : 1147
% 17.32/3.00 % Other redundant clauses eliminated : 0
% 17.32/3.00 % Clauses deleted for lack of memory : 0
% 17.32/3.00 % Backward-subsumed : 0
% 17.32/3.00 % Backward-rewritten : 224
% 17.32/3.00 % Generated clauses : 236168
% 17.32/3.00 % ...of the previous two non-redundant : 110548
% 17.32/3.00 % ...aggressively subsumed : 0
% 17.32/3.00 % Contextual simplify-reflections : 0
% 17.32/3.00 % Paramodulations : 236168
% 17.32/3.00 % Factorizations : 0
% 17.32/3.00 % NegExts : 0
% 17.32/3.00 % Equation resolutions : 0
% 17.32/3.00 % Disequality decompositions : 0
% 17.32/3.00 % Total rewrite steps : 533413
% 17.32/3.00 % ...of those cached : 472051
% 17.32/3.00 % Propositional unsat checks : 0
% 17.32/3.00 % Propositional check models : 0
% 17.32/3.00 % Propositional check unsatisfiable : 0
% 17.32/3.00 % Propositional clauses : 0
% 17.32/3.00 % Propositional clauses after purity: 0
% 17.32/3.00 % Propositional unsat core size : 0
% 17.32/3.00 % Propositional preprocessing time : 0.000
% 17.32/3.00 % Propositional encoding time : 0.000
% 17.32/3.00 % Propositional solver time : 0.000
% 17.32/3.00 % Success case prop preproc time : 0.000
% 17.32/3.00 % Success case prop encoding time : 0.000
% 17.32/3.00 % Success case prop solver time : 0.000
% 17.32/3.00 % Current number of processed clauses : 923
% 17.32/3.00 % Positive orientable unit clauses : 918
% 17.32/3.00 % Positive unorientable unit clauses: 4
% 17.32/3.00 % Negative unit clauses : 1
% 17.32/3.00 % Non-unit-clauses : 0
% 17.32/3.00 % Current number of unprocessed clauses: 97450
% 17.32/3.00 % ...number of literals in the above : 97450
% 17.32/3.00 % Current number of archived formulas : 0
% 17.32/3.00 % Current number of archived clauses : 225
% 17.32/3.00 % Clause-clause subsumption calls (NU) : 0
% 17.32/3.00 % Rec. Clause-clause subsumption calls : 0
% 17.32/3.00 % Non-unit clause-clause subsumptions : 0
% 17.32/3.00 % Unit Clause-clause subsumption calls : 21
% 17.32/3.00 % Rewrite failures with RHS unbound : 197
% 17.32/3.00 % BW rewrite match attempts : 15257
% 17.32/3.00 % BW rewrite match successes : 573
% 17.32/3.00 % Condensation attempts : 0
% 17.32/3.00 % Condensation successes : 0
% 17.32/3.00 % Termbank termtop insertions : 3260429
% 17.32/3.00 % Search garbage collected termcells : 38
% 17.32/3.00
% 17.32/3.00 % -------------------------------------------------
% 17.32/3.00 % User time : 2.369 s
% 17.32/3.00 % System time : 0.114 s
% 17.32/3.00 % Total time : 2.483 s
% 17.32/3.00 % Maximum resident set size: 3648 pages
% 17.32/3.00
% 17.32/3.00 % -------------------------------------------------
% 17.32/3.00 % User time : 11.917 s
% 17.32/3.00 % System time : 0.606 s
% 17.32/3.00 % Total time : 12.524 s
% 17.32/3.00 % Maximum resident set size: 4864 pages
% 17.32/3.00 % E exiting
%------------------------------------------------------------------------------