%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT065-1 : TPTP v9.3.1. Released v2.5.0.
% 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 01:04:09 PM UTC 2026
% Result : Unsatisfiable 23.05s 14.09s
% Output : CNFRefutation 23.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of clauses : 127 ( 118 unt; 0 nHn; 14 RR)
% Number of literals : 140 ( 139 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 270 ( 30 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(top,axiom,
join(X1,complement(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',top) ).
cnf(c94_37,axiom,
meet(X1,join(meet(X2,join(X3,meet(X1,X2))),meet(X3,join(X1,X2)))) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c94_37) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(bottom,axiom,
meet(X1,complement(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom) ).
cnf(complements_are_unique,axiom,
( meet(X1,X2) != n0
| join(X1,X2) != n1
| complement(X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complements_are_unique) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(prove_distributivity,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(c_0_13,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_14,axiom,
join(X1,complement(X1)) = n1,
top ).
cnf(c_0_15,axiom,
meet(X1,join(meet(X2,join(X3,meet(X1,X2))),meet(X3,join(X1,X2)))) = join(meet(X1,X2),meet(X1,X3)),
c94_37 ).
cnf(c_0_16,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_17,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_18,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_19,plain,
meet(X1,n1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_21,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X3,join(X2,meet(X1,X3))))) = join(meet(X1,X3),meet(X1,X2)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_23,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
meet(X1,complement(X1)) = n0,
bottom ).
cnf(c_0_25,plain,
( meet(X1,X2) != n0
| join(X1,X2) != n1
| complement(X1) = X2 ),
inference(fof_simplification,[status(thm)],[complements_are_unique]) ).
cnf(c_0_26,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
join(meet(X1,X2),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_13]),c_0_13]),c_0_18]) ).
cnf(c_0_28,plain,
meet(X1,n0) = n0,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( meet(X1,X2) != n0
| join(X1,X2) != n1
| complement(X1) = X2 ),
c_0_25 ).
cnf(c_0_30,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_31,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_32,plain,
join(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_33,plain,
meet(X1,join(meet(X2,X1),meet(X1,meet(X3,join(X2,meet(X1,X3)))))) = join(meet(X1,X3),meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_22]),c_0_17]) ).
cnf(c_0_34,plain,
join(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
join(X1,n0) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_36,plain,
( join(X1,X2) != n1
| meet(X2,X1) != n0
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_37,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_13]),c_0_31]) ).
cnf(c_0_38,plain,
join(X1,join(complement(X1),X2)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_32]) ).
cnf(c_0_39,plain,
join(X1,n1) = n1,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_40,plain,
meet(complement(X1),meet(X2,join(X1,meet(complement(X1),X2)))) = meet(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_24]),c_0_34]),c_0_23]),c_0_20]),c_0_24]),c_0_35]) ).
cnf(c_0_41,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_16]),c_0_14])]) ).
cnf(c_0_42,plain,
join(complement(X1),join(X2,X1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_31]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,join(complement(X1),meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_45,plain,
join(X1,complement(meet(X2,X1))) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_16]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,join(complement(X2),meet(X2,X1)))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20]) ).
cnf(c_0_47,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_48,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_49,plain,
meet(X1,join(meet(join(X1,X2),X3),meet(X2,join(X3,meet(X1,X2))))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_50,plain,
join(complement(meet(X1,X2)),meet(X1,join(complement(X1),meet(X1,X2)))) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_16]) ).
cnf(c_0_51,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_47]) ).
cnf(c_0_52,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_37]),c_0_48]) ).
cnf(c_0_53,plain,
join(meet(X1,complement(meet(X1,X2))),meet(X1,join(complement(X1),meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_14]),c_0_26]),c_0_19]),c_0_42]),c_0_19]),c_0_16]) ).
cnf(c_0_54,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_55,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_37]),c_0_31]),c_0_31]) ).
cnf(c_0_56,plain,
join(complement(X1),join(meet(X1,X2),meet(X1,complement(meet(X1,X2))))) = n1,
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_52,c_0_53]),c_0_31]),c_0_16]),c_0_22]),c_0_16]),c_0_14]),c_0_31]) ).
cnf(c_0_57,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_58,plain,
join(X1,join(X2,join(meet(X1,X3),X4))) = join(X1,join(X2,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_55]),c_0_47]) ).
cnf(c_0_59,plain,
join(complement(X1),join(meet(X2,X1),meet(X1,complement(meet(X2,X1))))) = n1,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_61,plain,
join(X1,join(complement(X2),meet(X2,complement(meet(X1,X2))))) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_39]) ).
cnf(c_0_62,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_37]) ).
cnf(c_0_63,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = n0,
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_64,plain,
join(X1,join(X2,meet(complement(X2),complement(meet(X1,complement(X2)))))) = n1,
inference(spm,[status(thm)],[c_0_61,c_0_41]) ).
cnf(c_0_65,plain,
join(complement(X1),join(X2,meet(X1,complement(meet(X2,X1))))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_31]),c_0_26]),c_0_16]) ).
cnf(c_0_66,plain,
( join(X2,meet(X1,complement(meet(X2,X1)))) != n1
| meet(X1,complement(meet(X2,X1))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
cnf(c_0_67,plain,
join(X1,meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2)))))) = n1,
inference(spm,[status(thm)],[c_0_47,c_0_64]) ).
cnf(c_0_68,plain,
meet(X1,join(meet(join(X2,X3),join(X1,X4)),meet(X4,join(X2,join(X3,meet(X1,X4)))))) = join(meet(X1,X4),meet(X1,join(X2,X3))),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_69,plain,
join(complement(X1),join(X2,meet(X1,complement(meet(X1,X2))))) = n1,
inference(spm,[status(thm)],[c_0_65,c_0_20]) ).
cnf(c_0_70,plain,
join(X1,complement(meet(X1,X2))) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_16]) ).
cnf(c_0_71,plain,
meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2))))) = complement(X1),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
join(meet(X1,join(complement(X1),X2)),meet(X1,complement(meet(X1,X2)))) = 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(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_19]),c_0_19]),c_0_31]),c_0_45]),c_0_39]),c_0_19]),c_0_16]) ).
cnf(c_0_73,plain,
meet(X1,complement(meet(X1,complement(meet(X1,X2))))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_71]),c_0_41]),c_0_41]),c_0_20]),c_0_41]) ).
cnf(c_0_74,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_71]),c_0_16]) ).
cnf(c_0_75,plain,
join(meet(X1,X2),meet(X1,complement(meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_73]) ).
cnf(c_0_76,plain,
join(meet(X1,X2),meet(X2,complement(meet(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_77,plain,
complement(meet(X1,complement(meet(X1,X2)))) = join(complement(X1),meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_73]),c_0_20]),c_0_71]),c_0_16]) ).
cnf(c_0_78,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = n0,
inference(spm,[status(thm)],[c_0_63,c_0_20]) ).
cnf(c_0_79,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_73,c_0_77]) ).
cnf(c_0_80,plain,
( join(X2,meet(X1,complement(meet(X1,X2)))) != n1
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_78]) ).
cnf(c_0_81,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_48,c_0_75]) ).
cnf(c_0_82,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_71]),c_0_20]) ).
cnf(c_0_83,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_79,c_0_57]) ).
cnf(c_0_84,plain,
( join(X2,X1) != n1
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_82,c_0_57]) ).
cnf(c_0_86,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
cnf(c_0_87,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_13]),c_0_16]) ).
cnf(c_0_88,plain,
( join(X1,X2) != n1
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_16]) ).
cnf(c_0_89,plain,
join(X1,meet(X2,complement(meet(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_20]) ).
cnf(c_0_90,plain,
complement(n0) = n1,
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_91,plain,
complement(meet(X1,complement(meet(X2,X1)))) = join(complement(X1),meet(X2,X1)),
inference(spm,[status(thm)],[c_0_77,c_0_57]) ).
cnf(c_0_92,plain,
complement(join(complement(X1),meet(X1,X2))) = meet(X1,complement(meet(X1,X2))),
inference(spm,[status(thm)],[c_0_41,c_0_77]) ).
cnf(c_0_93,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_60]),c_0_20]) ).
cnf(c_0_94,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_95,plain,
( join(X2,X1) != n1
| join(complement(X1),meet(X2,X1)) = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_63]),c_0_90]),c_0_19]),c_0_91]) ).
cnf(c_0_96,plain,
join(X1,join(X2,complement(join(X1,X2)))) = n1,
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_97,plain,
complement(join(X1,complement(join(X2,X1)))) = meet(complement(X1),join(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_41]),c_0_41]) ).
cnf(c_0_98,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_94,c_0_16]) ).
cnf(c_0_99,plain,
join(meet(X1,X2),meet(complement(X2),join(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98]),c_0_16]) ).
cnf(c_0_100,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_51,c_0_99]) ).
cnf(c_0_101,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_83,c_0_100]) ).
cnf(c_0_102,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_103,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_104,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_101,c_0_41]) ).
cnf(c_0_105,plain,
join(complement(X1),join(meet(X2,X1),X3)) = join(complement(X1),join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_100]),c_0_31]) ).
cnf(c_0_106,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_107,plain,
meet(X1,join(meet(X2,X1),meet(X1,X3))) = join(meet(X2,X1),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(join(X2,X3),X1),
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_105]),c_0_41]),c_0_101]),c_0_41]),c_0_20]) ).
cnf(c_0_109,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_110,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_111,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_31]) ).
cnf(c_0_112,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_18]),c_0_17]),c_0_103]),c_0_17]),c_0_103]) ).
cnf(c_0_113,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,meet(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_108]),c_0_20]) ).
cnf(c_0_114,plain,
join(meet(X1,X2),join(X3,meet(join(X1,X4),X2))) = join(meet(join(X1,X4),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_109]),c_0_110]) ).
cnf(c_0_115,plain,
meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_17]) ).
cnf(c_0_116,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(X3,meet(X1,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_113]) ).
cnf(c_0_117,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(join(X3,X2),X1),
inference(spm,[status(thm)],[c_0_108,c_0_16]) ).
cnf(c_0_118,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_119,plain,
meet(X1,join(meet(X2,join(X1,meet(join(X1,X3),X4))),meet(join(X1,X3),meet(X4,join(X2,meet(X1,X4)))))) = join(meet(X1,X4),meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_109]),c_0_17]) ).
cnf(c_0_120,plain,
join(X1,meet(join(X2,X1),X3)) = join(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_108]),c_0_31]),c_0_114]),c_0_16]) ).
cnf(c_0_121,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_122,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
cnf(c_0_123,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X3,X2),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(spm,[status(thm)],[c_0_21,c_0_113]),c_0_17]),c_0_13]),c_0_115]),c_0_108]),c_0_103]),c_0_116]),c_0_20]),c_0_117]) ).
cnf(c_0_124,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
c_0_118 ).
cnf(c_0_125,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(join(X2,X3),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_119,c_0_120]),c_0_27]),c_0_121]),c_0_122]),c_0_113]),c_0_23]),c_0_123]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_125]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT065-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/10.58 % Computer : n013.cluster.edu
% 0.08/10.58 % Model : x86_64 x86_64
% 0.08/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.58 % Memory : 8046.5625MB
% 0.08/10.58 % OS : Linux 6.8.0-71-generic
% 0.08/10.58 % CPULimit : 300
% 0.08/10.58 % WCLimit : 300
% 0.08/10.58 % DateTime : Sun Sep 20 23:09:07 UTC 2026
% 0.08/10.58 % CPUTime :
% 0.08/10.58 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/10.62 Running first-order theorem proving
% 0.13/10.62 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
% 23.05/14.09 % Version: 3.5.1
% 23.05/14.09 % Preprocessing class: FSSSSMSSSSSNFFN.
% 23.05/14.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.05/14.09 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 23.05/14.09 % Starting new_bool_3 with 300s (1) cores
% 23.05/14.09 % Starting new_bool_1 with 300s (1) cores
% 23.05/14.09 % Starting sh5l with 300s (1) cores
% 23.05/14.09 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3602245 completed with status 0
% 23.05/14.09 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 23.05/14.09 % Preprocessing class: FSSSSMSSSSSNFFN.
% 23.05/14.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.05/14.09 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 23.05/14.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.05/14.09 % No SInE strategy applied
% 23.05/14.09 % Search class: FHUPM-FFSF21-MFFFFFNN
% 23.05/14.09 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.05/14.09 % Starting SubtermCWHack with 136s (1) cores
% 23.05/14.09 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 23.05/14.09 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 23.05/14.09 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 23.05/14.09 % Starting new_bool_3 with 136s (1) cores
% 23.05/14.09 % G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with pid 3602252 completed with status 0
% 23.05/14.09 % Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S
% 23.05/14.09 % Preprocessing class: FSSSSMSSSSSNFFN.
% 23.05/14.09 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 23.05/14.09 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 23.05/14.09 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 23.05/14.09 % No SInE strategy applied
% 23.05/14.09 % Search class: FHUPM-FFSF21-MFFFFFNN
% 23.05/14.09 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 23.05/14.09 % Starting SubtermCWHack with 136s (1) cores
% 23.05/14.09 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 23.05/14.09 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 23.05/14.09 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 23.05/14.09 % Preprocessing time : 0.001 s
% 23.05/14.09 % Presaturation interreduction done
% 23.05/14.09
% 23.05/14.09 % Proof found!
% 23.05/14.09 % SZS status Unsatisfiable
% 23.05/14.09 % SZS output start CNFRefutation
% See solution above
% 23.05/14.09 % Parsed axioms : 13
% 23.05/14.09 % Removed by relevancy pruning/SinE : 0
% 23.05/14.09 % Initial clauses : 13
% 23.05/14.09 % Removed in clause preprocessing : 0
% 23.05/14.09 % Initial clauses in saturation : 13
% 23.05/14.09 % Processed clauses : 5303
% 23.05/14.09 % ...of these trivial : 1629
% 23.05/14.09 % ...subsumed : 3089
% 23.05/14.09 % ...remaining for further processing : 585
% 23.05/14.09 % Other redundant clauses eliminated : 0
% 23.05/14.09 % Clauses deleted for lack of memory : 0
% 23.05/14.09 % Backward-subsumed : 0
% 23.05/14.09 % Backward-rewritten : 296
% 23.05/14.09 % Generated clauses : 132166
% 23.05/14.09 % ...of the previous two non-redundant : 76691
% 23.05/14.09 % ...aggressively subsumed : 0
% 23.05/14.09 % Contextual simplify-reflections : 0
% 23.05/14.09 % Paramodulations : 132131
% 23.05/14.09 % Factorizations : 0
% 23.05/14.09 % NegExts : 0
% 23.05/14.09 % Equation resolutions : 35
% 23.05/14.09 % Disequality decompositions : 0
% 23.05/14.09 % Total rewrite steps : 344193
% 23.05/14.09 % ...of those cached : 291554
% 23.05/14.09 % Propositional unsat checks : 0
% 23.05/14.09 % Propositional check models : 0
% 23.05/14.09 % Propositional check unsatisfiable : 0
% 23.05/14.09 % Propositional clauses : 0
% 23.05/14.09 % Propositional clauses after purity: 0
% 23.05/14.09 % Propositional unsat core size : 0
% 23.05/14.09 % Propositional preprocessing time : 0.000
% 23.05/14.09 % Propositional encoding time : 0.000
% 23.05/14.09 % Propositional solver time : 0.000
% 23.05/14.09 % Success case prop preproc time : 0.000
% 23.05/14.09 % Success case prop encoding time : 0.000
% 23.05/14.09 % Success case prop solver time : 0.000
% 23.05/14.09 % Current number of processed clauses : 276
% 23.05/14.09 % Positive orientable unit clauses : 174
% 23.05/14.09 % Positive unorientable unit clauses: 6
% 23.05/14.09 % Negative unit clauses : 0
% 23.05/14.09 % Non-unit-clauses : 96
% 23.05/14.09 % Current number of unprocessed clauses: 71032
% 23.05/14.09 % ...number of literals in the above : 79923
% 23.05/14.09 % Current number of archived formulas : 0
% 23.05/14.09 % Current number of archived clauses : 309
% 23.05/14.09 % Clause-clause subsumption calls (NU) : 7819
% 23.05/14.09 % Rec. Clause-clause subsumption calls : 7711
% 23.05/14.09 % Non-unit clause-clause subsumptions : 1803
% 23.05/14.09 % Unit Clause-clause subsumption calls : 194
% 23.05/14.09 % Rewrite failures with RHS unbound : 0
% 23.05/14.09 % BW rewrite match attempts : 3643
% 23.05/14.09 % BW rewrite match successes : 563
% 23.05/14.09 % Condensation attempts : 0
% 23.05/14.09 % Condensation successes : 0
% 23.05/14.09 % Termbank termtop insertions : 2038959
% 23.05/14.09 % Search garbage collected termcells : 8
% 23.05/14.09
% 23.05/14.09 % -------------------------------------------------
% 23.05/14.09 % User time : 3.144 s
% 23.05/14.09 % System time : 0.146 s
% 23.05/14.09 % Total time : 3.291 s
% 23.05/14.09 % Maximum resident set size: 3640 pages
% 23.05/14.09
% 23.05/14.09 % -------------------------------------------------
% 23.05/14.09 % User time : 15.721 s
% 23.05/14.09 % System time : 0.693 s
% 23.05/14.09 % Total time : 16.414 s
% 23.05/14.09 % Maximum resident set size: 4608 pages
% 23.05/14.09 % E exiting
%------------------------------------------------------------------------------