%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL030+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 02:04:03 PM UTC 2026
% Result : Theorem 140.14s 20.83s
% Output : CNFRefutation 140.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 15
% Syntax : Number of formulae : 125 ( 119 unt; 0 def)
% Number of atoms : 134 ( 133 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 4 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 10 ( 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 : 189 ( 12 sgn 62 !; 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(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(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(goals,conjecture,
! [X1,X2,X3] :
( join(X1,one) = one
=> ( join(meet(composition(X1,X2),complement(composition(X1,X3))),meet(composition(X1,X2),complement(X3))) = meet(composition(X1,X2),complement(X3))
& join(meet(composition(X1,X2),complement(X3)),meet(composition(X1,X2),complement(composition(X1,X3)))) = meet(composition(X1,X2),complement(composition(X1,X3))) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
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(dedekind_law,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
fof(c_0_15,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_16,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
fof(c_0_17,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_18,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
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(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X28] : zero = meet(X28,complement(X28)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_27,plain,
! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
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_21]) ).
cnf(c_0_29,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
composition(X1,composition(one,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_31,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_34,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_35,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_36,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_31]) ).
cnf(c_0_37,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_39,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_40,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_41,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31]) ).
cnf(c_0_42,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_47,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,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_46,c_0_41]),c_0_38]),c_0_42]),c_0_29]) ).
fof(c_0_49,negated_conjecture,
~ ! [X1,X2,X3] :
( join(X1,one) = one
=> ( join(meet(composition(X1,X2),complement(composition(X1,X3))),meet(composition(X1,X2),complement(X3))) = meet(composition(X1,X2),complement(X3))
& join(meet(composition(X1,X2),complement(X3)),meet(composition(X1,X2),complement(composition(X1,X3)))) = meet(composition(X1,X2),complement(composition(X1,X3))) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_50,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_51,plain,
! [X17,X18,X19] : composition(join(X17,X18),X19) = join(composition(X17,X19),composition(X18,X19)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_52,negated_conjecture,
( ( 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))
| 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(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_49])])])]) ).
cnf(c_0_53,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_50]) ).
cnf(c_0_54,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_55,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_56,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_29]),c_0_44]) ).
cnf(c_0_57,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_53]) ).
cnf(c_0_58,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_54,c_0_55]),c_0_36]),c_0_29]),c_0_36]) ).
cnf(c_0_59,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_44]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
join(X1,join(composition(esk1_0,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_44,c_0_58]) ).
cnf(c_0_61,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_46]),c_0_29]) ).
cnf(c_0_62,negated_conjecture,
join(X1,complement(join(complement(composition(esk1_0,X1)),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
join(one,complement(join(complement(esk1_0),X1))) = one,
inference(spm,[status(thm)],[c_0_62,c_0_19]) ).
cnf(c_0_64,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
fof(c_0_65,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_66,negated_conjecture,
join(complement(join(complement(esk1_0),X1)),one) = one,
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
join(X1,join(X2,composition(esk1_0,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_58]) ).
cnf(c_0_68,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_41]),c_0_38]),c_0_29]) ).
cnf(c_0_69,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_70,plain,
join(complement(join(complement(X1),X2)),join(complement(join(complement(X1),complement(X2))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_44,c_0_46]) ).
cnf(c_0_71,negated_conjecture,
join(complement(join(X1,complement(esk1_0))),one) = one,
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_64,c_0_68]) ).
cnf(c_0_73,plain,
join(converse(X1),X2) = converse(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_69,c_0_25]) ).
cnf(c_0_74,negated_conjecture,
join(complement(join(complement(X1),esk1_0)),one) = join(X1,one),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
converse(join(X1,converse(top))) = top,
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_29,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
join(complement(join(X1,esk1_0)),one) = join(complement(X1),one),
inference(spm,[status(thm)],[c_0_74,c_0_53]) ).
cnf(c_0_78,plain,
converse(join(X1,converse(complement(converse(X1))))) = top,
inference(spm,[status(thm)],[c_0_38,c_0_73]) ).
cnf(c_0_79,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
join(complement(join(esk1_0,X1)),one) = join(complement(X1),one),
inference(spm,[status(thm)],[c_0_77,c_0_29]) ).
cnf(c_0_81,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_78]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
join(esk1_0,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_44,c_0_55]) ).
cnf(c_0_83,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_44]) ).
cnf(c_0_84,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_76]) ).
cnf(c_0_85,negated_conjecture,
join(complement(converse(complement(converse(esk1_0)))),one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_42]),c_0_50]) ).
cnf(c_0_86,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_87,negated_conjecture,
join(esk1_0,join(X1,one)) = join(X1,one),
inference(spm,[status(thm)],[c_0_82,c_0_29]) ).
cnf(c_0_88,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_83,c_0_57]) ).
fof(c_0_89,plain,
! [X29,X30,X31] : join(meet(composition(X29,X30),X31),composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31)))) = composition(meet(X29,composition(X31,converse(X30))),meet(X30,composition(converse(X29),X31))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_90,negated_conjecture,
converse(join(complement(converse(esk1_0)),one)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_73]),c_0_86]) ).
cnf(c_0_91,negated_conjecture,
join(complement(esk1_0),one) = top,
inference(spm,[status(thm)],[c_0_87,c_0_84]) ).
cnf(c_0_92,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_88]) ).
cnf(c_0_93,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,negated_conjecture,
join(complement(converse(esk1_0)),one) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_90]),c_0_79]) ).
cnf(c_0_95,negated_conjecture,
join(zero,complement(join(complement(esk1_0),complement(one)))) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_91]),c_0_42]) ).
cnf(c_0_96,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_97,plain,
join(complement(join(complement(X1),X2)),join(X3,complement(join(complement(X1),complement(X2))))) = join(X3,X1),
inference(spm,[status(thm)],[c_0_56,c_0_46]) ).
cnf(c_0_98,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_92,c_0_53]) ).
cnf(c_0_99,plain,
converse(composition(converse(X1),converse(X2))) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_100,plain,
converse(join(composition(X1,X2),composition(X3,X2))) = composition(converse(X2),converse(join(X1,X3))),
inference(spm,[status(thm)],[c_0_18,c_0_54]) ).
cnf(c_0_101,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_102,negated_conjecture,
complement(join(complement(converse(esk1_0)),complement(one))) = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_94]),c_0_42]),c_0_50]) ).
cnf(c_0_103,negated_conjecture,
complement(join(complement(esk1_0),complement(one))) = esk1_0,
inference(rw,[status(thm)],[c_0_95,c_0_50]) ).
cnf(c_0_104,negated_conjecture,
converse(join(X1,composition(X1,converse(esk1_0)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_96]),c_0_73]),c_0_25]) ).
cnf(c_0_105,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_53]),c_0_53]),c_0_29]) ).
cnf(c_0_106,plain,
join(composition(X1,X2),X3) = converse(join(composition(converse(X2),converse(X1)),converse(X3))),
inference(spm,[status(thm)],[c_0_73,c_0_99]) ).
cnf(c_0_107,plain,
converse(join(composition(X1,converse(X2)),converse(composition(X2,X3)))) = composition(X2,converse(join(X1,converse(X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_18]),c_0_25]) ).
cnf(c_0_108,plain,
join(complement(join(complement(X1),complement(X2))),converse(composition(converse(complement(join(complement(X1),complement(X2)))),converse(complement(join(complement(one),complement(composition(X2,converse(X1))))))))) = converse(composition(converse(complement(join(complement(X1),complement(X2)))),converse(complement(join(complement(one),complement(composition(X2,converse(X1)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_36]),c_0_31]),c_0_31]),c_0_99]),c_0_99]) ).
cnf(c_0_109,negated_conjecture,
join(complement(converse(esk1_0)),complement(one)) = complement(converse(esk1_0)),
inference(spm,[status(thm)],[c_0_53,c_0_102]) ).
cnf(c_0_110,negated_conjecture,
join(complement(esk1_0),complement(one)) = complement(esk1_0),
inference(spm,[status(thm)],[c_0_53,c_0_103]) ).
cnf(c_0_111,negated_conjecture,
join(X1,composition(X1,converse(esk1_0))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_104]),c_0_25]) ).
cnf(c_0_112,negated_conjecture,
( 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))
| 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))) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_113,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_105,c_0_53]) ).
cnf(c_0_114,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_69]),c_0_25]) ).
cnf(c_0_115,negated_conjecture,
composition(esk1_0,converse(esk1_0)) = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_108,c_0_109]),c_0_53]),c_0_53]),c_0_25]),c_0_25]),c_0_36]),c_0_29]),c_0_110]),c_0_53]),c_0_73]),c_0_25]),c_0_111]),c_0_53]),c_0_25]),c_0_25]),c_0_36]),c_0_29]),c_0_110]),c_0_53]),c_0_96]) ).
cnf(c_0_116,negated_conjecture,
( 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)))))
| 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)))) ),
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_112,c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_117,negated_conjecture,
join(X1,complement(join(X2,composition(esk1_0,X1)))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_113]),c_0_60]) ).
cnf(c_0_118,plain,
join(composition(X1,X2),composition(X1,complement(X2))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_114,c_0_38]) ).
cnf(c_0_119,plain,
converse(composition(top,converse(X1))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_99,c_0_79]) ).
cnf(c_0_120,negated_conjecture,
converse(esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_115]),c_0_25]),c_0_115]) ).
cnf(c_0_121,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_98,c_0_58]),c_0_29]) ).
cnf(c_0_122,negated_conjecture,
( 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(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)],[c_0_116,c_0_29]) ).
cnf(c_0_123,negated_conjecture,
complement(composition(esk1_0,X1)) = join(complement(X1),complement(converse(composition(top,esk1_0)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_119]),c_0_120]),c_0_121]) ).
cnf(c_0_124,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_123]),c_0_53]),c_0_44]),c_0_123]),c_0_44]),c_0_113]),c_0_53]),c_0_57]),c_0_123]),c_0_44]),c_0_113]),c_0_53]),c_0_123]),c_0_53]),c_0_44]),c_0_123]),c_0_44]),c_0_113]),c_0_53]),c_0_57]),c_0_123]),c_0_53]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL030+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 04:03:51 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 140.14/20.83 % Version: 3.5.1
% 140.14/20.83 % Preprocessing class: FSMSSMSSSSSNFFN.
% 140.14/20.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.14/20.83 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 140.14/20.83 % Starting new_bool_3 with 300s (1) cores
% 140.14/20.83 % Starting new_bool_1 with 300s (1) cores
% 140.14/20.83 % Starting sh5l with 300s (1) cores
% 140.14/20.83 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1525859 completed with status 0
% 140.14/20.83 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 140.14/20.83 % Preprocessing class: FSMSSMSSSSSNFFN.
% 140.14/20.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.14/20.83 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 140.14/20.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 140.14/20.83 % No SInE strategy applied
% 140.14/20.83 % Search class: FUHPM-FFMF21-DFFFFFNN
% 140.14/20.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 140.14/20.83 % Starting SubtermCWHack with 136s (1) cores
% 140.14/20.83 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 140.14/20.83 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 140.14/20.83 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 140.14/20.83 % Starting new_bool_3 with 136s (1) cores
% 140.14/20.83 % G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with pid 1525866 completed with status 0
% 140.14/20.83 % Result found by G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y
% 140.14/20.83 % Preprocessing class: FSMSSMSSSSSNFFN.
% 140.14/20.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 140.14/20.83 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 140.14/20.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 140.14/20.83 % No SInE strategy applied
% 140.14/20.83 % Search class: FUHPM-FFMF21-DFFFFFNN
% 140.14/20.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 140.14/20.83 % Starting SubtermCWHack with 136s (1) cores
% 140.14/20.83 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 140.14/20.83 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S0Y with 136s (1) cores
% 140.14/20.83 % Preprocessing time : 0.001 s
% 140.14/20.83 % Presaturation interreduction done
% 140.14/20.83
% 140.14/20.83 % Proof found!
% 140.14/20.83 % SZS status Theorem
% 140.14/20.83 % SZS output start CNFRefutation
% See solution above
% 140.14/20.83 % Parsed axioms : 17
% 140.14/20.83 % Removed by relevancy pruning/SinE : 0
% 140.14/20.83 % Initial clauses : 18
% 140.14/20.83 % Removed in clause preprocessing : 1
% 140.14/20.83 % Initial clauses in saturation : 17
% 140.14/20.83 % Processed clauses : 9127
% 140.14/20.83 % ...of these trivial : 4995
% 140.14/20.83 % ...subsumed : 2653
% 140.14/20.83 % ...remaining for further processing : 1479
% 140.14/20.83 % Other redundant clauses eliminated : 0
% 140.14/20.83 % Clauses deleted for lack of memory : 0
% 140.14/20.83 % Backward-subsumed : 0
% 140.14/20.83 % Backward-rewritten : 394
% 140.14/20.83 % Generated clauses : 620688
% 140.14/20.83 % ...of the previous two non-redundant : 455375
% 140.14/20.83 % ...aggressively subsumed : 0
% 140.14/20.83 % Contextual simplify-reflections : 0
% 140.14/20.83 % Paramodulations : 620688
% 140.14/20.83 % Factorizations : 0
% 140.14/20.83 % NegExts : 0
% 140.14/20.83 % Equation resolutions : 0
% 140.14/20.83 % Disequality decompositions : 0
% 140.14/20.83 % Total rewrite steps : 2479306
% 140.14/20.83 % ...of those cached : 2206837
% 140.14/20.83 % Propositional unsat checks : 0
% 140.14/20.83 % Propositional check models : 0
% 140.14/20.83 % Propositional check unsatisfiable : 0
% 140.14/20.83 % Propositional clauses : 0
% 140.14/20.83 % Propositional clauses after purity: 0
% 140.14/20.83 % Propositional unsat core size : 0
% 140.14/20.83 % Propositional preprocessing time : 0.000
% 140.14/20.83 % Propositional encoding time : 0.000
% 140.14/20.83 % Propositional solver time : 0.000
% 140.14/20.83 % Success case prop preproc time : 0.000
% 140.14/20.83 % Success case prop encoding time : 0.000
% 140.14/20.83 % Success case prop solver time : 0.000
% 140.14/20.83 % Current number of processed clauses : 1068
% 140.14/20.83 % Positive orientable unit clauses : 932
% 140.14/20.83 % Positive unorientable unit clauses: 134
% 140.14/20.83 % Negative unit clauses : 0
% 140.14/20.83 % Non-unit-clauses : 2
% 140.14/20.83 % Current number of unprocessed clauses: 443948
% 140.14/20.83 % ...number of literals in the above : 443948
% 140.14/20.83 % Current number of archived formulas : 0
% 140.14/20.83 % Current number of archived clauses : 412
% 140.14/20.83 % Clause-clause subsumption calls (NU) : 2
% 140.14/20.83 % Rec. Clause-clause subsumption calls : 2
% 140.14/20.83 % Non-unit clause-clause subsumptions : 1
% 140.14/20.83 % Unit Clause-clause subsumption calls : 8566
% 140.14/20.83 % Rewrite failures with RHS unbound : 310
% 140.14/20.83 % BW rewrite match attempts : 20850
% 140.14/20.83 % BW rewrite match successes : 1844
% 140.14/20.83 % Condensation attempts : 0
% 140.14/20.83 % Condensation successes : 0
% 140.14/20.83 % Termbank termtop insertions : 22886106
% 140.14/20.83 % Search garbage collected termcells : 47
% 140.14/20.83
% 140.14/20.83 % -------------------------------------------------
% 140.14/20.83 % User time : 19.212 s
% 140.14/20.83 % System time : 0.700 s
% 140.14/20.83 % Total time : 19.912 s
% 140.14/20.83 % Maximum resident set size: 3600 pages
% 140.14/20.83
% 140.14/20.83 % -------------------------------------------------
% 140.14/20.83 % User time : 96.890 s
% 140.14/20.83 % System time : 3.468 s
% 140.14/20.83 % Total time : 100.358 s
% 140.14/20.83 % Maximum resident set size: 4608 pages
% 140.14/20.83 % E exiting
%------------------------------------------------------------------------------