%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT183-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:04:24 PM UTC 2026
% Result : Unsatisfiable 48.62s 11.70s
% Output : CNFRefutation 48.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 12
% Syntax : Number of clauses : 123 ( 111 unt; 0 nHn; 17 RR)
% Number of literals : 139 ( 138 equ; 19 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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 : 253 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
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(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(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(equation_H7,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H7) ).
cnf(meet_join_complement,axiom,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
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(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(c_0_12,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_13,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_14,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_18,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_19,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_20,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_21,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_22,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X1,join(meet(X1,X2),meet(X3,join(X1,X2)))))),
equation_H7 ).
cnf(c_0_23,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_19]) ).
cnf(c_0_24,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_18]) ).
cnf(c_0_25,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_26,plain,
meet(X1,join(complement(X1),join(X2,meet(X1,join(meet(X1,join(complement(X1),X2)),X3))))) = meet(X1,join(complement(X1),join(X2,meet(X1,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14]),c_0_18]),c_0_18]) ).
cnf(c_0_27,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_28,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_25]),c_0_18]) ).
cnf(c_0_29,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
inference(fof_simplification,[status(thm)],[meet_join_complement]) ).
cnf(c_0_30,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_21]) ).
cnf(c_0_31,plain,
meet(X1,join(complement(X1),join(X2,meet(X1,complement(meet(X1,join(complement(X1),X2))))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_14]),c_0_27]),c_0_23]),c_0_14]) ).
cnf(c_0_32,plain,
join(complement(X1),join(X2,join(X3,X1))) = one,
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_33,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
c_0_29 ).
cnf(c_0_34,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_35,plain,
join(complement(X1),join(X2,meet(X1,complement(meet(X1,join(complement(X1),X2)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_18]),c_0_18]),c_0_32]) ).
cnf(c_0_36,plain,
( join(X1,X2) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_33,c_0_15]) ).
cnf(c_0_37,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_38,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_39,plain,
join(X1,join(complement(X2),meet(X2,complement(meet(X2,join(complement(X2),X1)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18]),c_0_16]),c_0_21]) ).
cnf(c_0_40,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_37]),c_0_21]),c_0_13])]) ).
cnf(c_0_41,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_43,plain,
join(X1,join(X2,meet(complement(X2),complement(meet(complement(X2),join(X2,X1)))))) = one,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_45,plain,
( join(X2,meet(X1,complement(meet(X2,X1)))) != one
| meet(X1,complement(meet(X2,X1))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_46,plain,
join(X1,meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21]),c_0_17]),c_0_15]) ).
cnf(c_0_47,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_48,plain,
meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2))))) = complement(X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_50,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_15]) ).
cnf(c_0_51,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_15]) ).
cnf(c_0_52,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_21]) ).
cnf(c_0_53,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(spm,[status(thm)],[c_0_52,c_0_38]) ).
cnf(c_0_55,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
cnf(c_0_56,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_37]) ).
cnf(c_0_57,plain,
meet(complement(X1),complement(join(X1,X2))) = complement(join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_12]),c_0_15]) ).
cnf(c_0_58,plain,
join(X1,join(X2,complement(meet(X3,join(X2,X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_34]),c_0_18]) ).
cnf(c_0_59,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_48]),c_0_21]) ).
cnf(c_0_60,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_55,c_0_15]) ).
cnf(c_0_61,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_21]) ).
cnf(c_0_62,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_63,plain,
meet(join(X1,X2),complement(meet(complement(X1),join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_57]),c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_64,plain,
join(X1,complement(meet(X2,join(complement(X2),X1)))) = one,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_15]) ).
cnf(c_0_66,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_60]) ).
cnf(c_0_67,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_13,c_0_61]) ).
cnf(c_0_68,plain,
meet(X1,complement(meet(complement(X2),join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
join(X1,complement(meet(complement(X2),join(X2,X1)))) = one,
inference(spm,[status(thm)],[c_0_64,c_0_40]) ).
cnf(c_0_70,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_14]),c_0_38]) ).
cnf(c_0_71,plain,
( meet(X2,X1) != zero
| meet(complement(X1),join(X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_68]),c_0_40]),c_0_21]),c_0_69])]) ).
cnf(c_0_72,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_12]),c_0_15]) ).
cnf(c_0_73,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_40]),c_0_21]) ).
cnf(c_0_74,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_73]) ).
cnf(c_0_75,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_21]),c_0_18]) ).
cnf(c_0_76,plain,
( meet(X2,X1) != zero
| join(X1,complement(join(X1,X2))) = complement(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_74]),c_0_75])]) ).
cnf(c_0_77,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_30]),c_0_15]) ).
cnf(c_0_78,plain,
( meet(X1,X2) != zero
| join(X1,complement(join(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_15]) ).
cnf(c_0_79,plain,
meet(join(X1,X2),complement(meet(complement(X2),join(X1,X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_77]),c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_80,plain,
join(X1,complement(join(X1,complement(join(X1,X2))))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_72]),c_0_40]) ).
cnf(c_0_81,plain,
complement(join(X1,complement(join(X1,X2)))) = meet(complement(X1),join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_40]),c_0_15]),c_0_73]),c_0_15]) ).
cnf(c_0_82,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,X2),
inference(rw,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_83,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_82,c_0_21]) ).
cnf(c_0_84,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_85,plain,
join(meet(X1,X2),meet(X1,complement(meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_17]),c_0_15]) ).
cnf(c_0_86,plain,
( join(X2,meet(X1,complement(meet(X1,X2)))) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_65]) ).
cnf(c_0_87,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
( join(X2,X1) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_89,plain,
complement(meet(complement(X1),join(X1,X2))) = join(X1,complement(join(X1,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_81]) ).
cnf(c_0_90,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_53]),c_0_21]) ).
cnf(c_0_91,plain,
( join(X1,X2) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_21]) ).
cnf(c_0_92,plain,
join(X1,meet(X2,complement(meet(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_87,c_0_15]) ).
cnf(c_0_93,plain,
complement(meet(X1,complement(meet(X2,X1)))) = join(complement(X1),meet(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_40]),c_0_40]) ).
cnf(c_0_94,plain,
( join(X2,X1) != one
| 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_91,c_0_92]),c_0_41]),c_0_67]),c_0_14]),c_0_93]) ).
cnf(c_0_95,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_96,plain,
complement(join(X1,complement(join(X2,X1)))) = meet(complement(X1),join(X2,X1)),
inference(spm,[status(thm)],[c_0_81,c_0_21]) ).
cnf(c_0_97,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_21]) ).
cnf(c_0_98,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_94,c_0_95]),c_0_96]),c_0_97]),c_0_21]) ).
cnf(c_0_99,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_98]),c_0_38]),c_0_15]),c_0_12]) ).
cnf(c_0_100,plain,
join(X1,meet(complement(X1),X2)) = join(X2,X1),
inference(rw,[status(thm)],[c_0_83,c_0_99]) ).
cnf(c_0_101,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_102,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_15]) ).
cnf(c_0_103,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_62]),c_0_21]) ).
cnf(c_0_104,plain,
join(complement(X1),meet(X1,X2)) = join(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_100,c_0_40]) ).
cnf(c_0_105,plain,
meet(complement(X1),meet(join(X2,X1),X3)) = meet(complement(X1),meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_99]),c_0_38]) ).
cnf(c_0_106,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_107,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_101,c_0_44]),c_0_38]),c_0_102]),c_0_38]),c_0_102]) ).
cnf(c_0_108,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_38,c_0_12]) ).
cnf(c_0_109,plain,
join(X1,meet(join(X2,X1),join(X3,X1))) = meet(join(X2,X1),join(X3,X1)),
inference(spm,[status(thm)],[c_0_103,c_0_30]) ).
cnf(c_0_110,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_40]),c_0_100]),c_0_40]),c_0_21]) ).
cnf(c_0_111,plain,
meet(X1,meet(X2,join(X3,meet(X2,X1)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_38]) ).
cnf(c_0_112,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_15]) ).
cnf(c_0_113,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_108,c_0_15]) ).
cnf(c_0_114,plain,
join(X1,meet(X2,join(X3,X1))) = meet(join(X2,X1),join(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_21]) ).
cnf(c_0_115,plain,
meet(X1,join(X2,meet(X1,join(meet(X2,X1),meet(X3,join(X1,X2)))))) = meet(X1,join(X2,meet(X1,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_116,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_110]),c_0_112]) ).
cnf(c_0_117,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_118,plain,
meet(join(X1,X2),join(X3,X2)) = join(meet(X3,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_102]),c_0_113]),c_0_114]) ).
cnf(c_0_119,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_114]),c_0_113]),c_0_114]),c_0_108]) ).
cnf(c_0_120,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
c_0_117 ).
cnf(c_0_121,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_17]),c_0_15]),c_0_119]) ).
cnf(c_0_122,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_121]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT183-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.41 % Computer : n015.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.42 % DateTime : Sun Sep 20 23:21:41 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.47 Running first-order theorem proving
% 0.14/5.47 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
% 48.62/11.70 % Version: 3.5.1
% 48.62/11.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 48.62/11.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.62/11.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 48.62/11.70 % Starting new_bool_3 with 300s (1) cores
% 48.62/11.70 % Starting new_bool_1 with 300s (1) cores
% 48.62/11.70 % Starting sh5l with 300s (1) cores
% 48.62/11.70 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 4160644 completed with status 0
% 48.62/11.70 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 48.62/11.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 48.62/11.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.62/11.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 48.62/11.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.62/11.70 % No SInE strategy applied
% 48.62/11.70 % Search class: FHUPM-FFSF21-DFFFFFNN
% 48.62/11.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.62/11.70 % Starting SubtermCWHack with 136s (1) cores
% 48.62/11.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 48.62/11.70 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 48.62/11.70 % Starting new_bool_3 with 136s (1) cores
% 48.62/11.70 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 48.62/11.70 % G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 4160651 completed with status 0
% 48.62/11.70 % Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 48.62/11.70 % Preprocessing class: FSSSSMSSSSSNFFN.
% 48.62/11.70 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 48.62/11.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 48.62/11.70 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 48.62/11.70 % No SInE strategy applied
% 48.62/11.70 % Search class: FHUPM-FFSF21-DFFFFFNN
% 48.62/11.70 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 48.62/11.70 % Starting SubtermCWHack with 136s (1) cores
% 48.62/11.70 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 48.62/11.70 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 48.62/11.70 % Preprocessing time : 0.002 s
% 48.62/11.70 % Presaturation interreduction done
% 48.62/11.70
% 48.62/11.70 % Proof found!
% 48.62/11.70 % SZS status Unsatisfiable
% 48.62/11.70 % SZS output start CNFRefutation
% See solution above
% 48.62/11.71 % Parsed axioms : 13
% 48.62/11.71 % Removed by relevancy pruning/SinE : 0
% 48.62/11.71 % Initial clauses : 13
% 48.62/11.71 % Removed in clause preprocessing : 0
% 48.62/11.71 % Initial clauses in saturation : 13
% 48.62/11.71 % Processed clauses : 8241
% 48.62/11.71 % ...of these trivial : 2676
% 48.62/11.71 % ...subsumed : 4825
% 48.62/11.71 % ...remaining for further processing : 740
% 48.62/11.71 % Other redundant clauses eliminated : 0
% 48.62/11.71 % Clauses deleted for lack of memory : 0
% 48.62/11.71 % Backward-subsumed : 0
% 48.62/11.71 % Backward-rewritten : 362
% 48.62/11.71 % Generated clauses : 235009
% 48.62/11.71 % ...of the previous two non-redundant : 132521
% 48.62/11.71 % ...aggressively subsumed : 0
% 48.62/11.71 % Contextual simplify-reflections : 0
% 48.62/11.71 % Paramodulations : 234953
% 48.62/11.71 % Factorizations : 0
% 48.62/11.71 % NegExts : 0
% 48.62/11.71 % Equation resolutions : 56
% 48.62/11.71 % Disequality decompositions : 0
% 48.62/11.71 % Total rewrite steps : 588669
% 48.62/11.71 % ...of those cached : 493089
% 48.62/11.71 % Propositional unsat checks : 0
% 48.62/11.71 % Propositional check models : 0
% 48.62/11.71 % Propositional check unsatisfiable : 0
% 48.62/11.71 % Propositional clauses : 0
% 48.62/11.71 % Propositional clauses after purity: 0
% 48.62/11.71 % Propositional unsat core size : 0
% 48.62/11.71 % Propositional preprocessing time : 0.000
% 48.62/11.71 % Propositional encoding time : 0.000
% 48.62/11.71 % Propositional solver time : 0.000
% 48.62/11.71 % Success case prop preproc time : 0.000
% 48.62/11.71 % Success case prop encoding time : 0.000
% 48.62/11.71 % Success case prop solver time : 0.000
% 48.62/11.71 % Current number of processed clauses : 365
% 48.62/11.71 % Positive orientable unit clauses : 244
% 48.62/11.71 % Positive unorientable unit clauses: 10
% 48.62/11.71 % Negative unit clauses : 0
% 48.62/11.71 % Non-unit-clauses : 111
% 48.62/11.71 % Current number of unprocessed clauses: 123477
% 48.62/11.71 % ...number of literals in the above : 140886
% 48.62/11.71 % Current number of archived formulas : 0
% 48.62/11.71 % Current number of archived clauses : 375
% 48.62/11.71 % Clause-clause subsumption calls (NU) : 13775
% 48.62/11.71 % Rec. Clause-clause subsumption calls : 13599
% 48.62/11.71 % Non-unit clause-clause subsumptions : 2845
% 48.62/11.71 % Unit Clause-clause subsumption calls : 458
% 48.62/11.71 % Rewrite failures with RHS unbound : 0
% 48.62/11.71 % BW rewrite match attempts : 5190
% 48.62/11.71 % BW rewrite match successes : 1217
% 48.62/11.71 % Condensation attempts : 0
% 48.62/11.71 % Condensation successes : 0
% 48.62/11.71 % Termbank termtop insertions : 3571273
% 48.62/11.71 % Search garbage collected termcells : 8
% 48.62/11.71
% 48.62/11.71 % -------------------------------------------------
% 48.62/11.71 % User time : 5.744 s
% 48.62/11.71 % System time : 0.246 s
% 48.62/11.71 % Total time : 5.991 s
% 48.62/11.71 % Maximum resident set size: 3644 pages
% 48.62/11.71
% 48.62/11.71 % -------------------------------------------------
% 48.62/11.71 % User time : 29.054 s
% 48.62/11.71 % System time : 1.197 s
% 48.62/11.71 % Total time : 30.251 s
% 48.62/11.71 % Maximum resident set size: 4608 pages
% 48.62/11.71 % E exiting
%------------------------------------------------------------------------------