%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LAT182-1 : 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 : n003.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 33.72s 10.52s
% Output : CNFRefutation 33.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of clauses : 134 ( 123 unt; 0 nHn; 16 RR)
% Number of literals : 151 ( 150 equ; 20 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 : 277 ( 32 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(equation_H6,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(meet(X1,join(X2,meet(X1,X3))),meet(X3,join(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H6) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_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(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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
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(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_13,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_14,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_15,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(meet(X1,join(X2,meet(X1,X3))),meet(X3,join(X1,X2)))),
equation_H6 ).
cnf(c_0_16,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_17,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,plain,
meet(X1,join(meet(X2,join(X1,X3)),meet(X1,join(X3,meet(X1,X2))))) = meet(X1,join(X3,meet(X1,X2))),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_21,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_22,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_23,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_13]),c_0_21]),c_0_20]) ).
cnf(c_0_25,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_26,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_27,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_28,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_29,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_25]) ).
cnf(c_0_30,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_31,plain,
meet(X1,join(X2,meet(X1,join(complement(X1),meet(X1,X2))))) = meet(X1,join(complement(X1),meet(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_14]),c_0_17]) ).
cnf(c_0_32,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_33,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_14]),c_0_27]) ).
cnf(c_0_34,plain,
complement(one) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_35,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_36,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_29]),c_0_25]),c_0_25]) ).
cnf(c_0_37,plain,
meet(X1,meet(X2,join(complement(X2),meet(X2,X1)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]) ).
cnf(c_0_38,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_22]) ).
cnf(c_0_39,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_40,plain,
meet(X1,meet(X2,join(complement(X1),meet(X1,X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X1)) = join(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(spm,[status(thm)],[c_0_19,c_0_27]),c_0_17]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_42,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_16]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,join(complement(X1),meet(X2,X1)))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_44,plain,
join(X1,join(X2,complement(X1))) = one,
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_45,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_46,plain,
join(X1,join(X2,join(X1,X3))) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_41]),c_0_22]),c_0_22]) ).
cnf(c_0_47,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_48,plain,
join(complement(meet(X1,X2)),meet(X1,join(complement(X2),meet(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_16]) ).
cnf(c_0_49,plain,
meet(X1,join(X2,meet(X1,join(X3,join(complement(X1),meet(X1,X2)))))) = meet(X1,join(X3,join(complement(X1),meet(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_44]),c_0_17]),c_0_22]),c_0_22]) ).
cnf(c_0_50,plain,
join(complement(meet(X1,X2)),meet(X2,join(meet(X1,X2),X3))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_16]) ).
cnf(c_0_51,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_13]),c_0_22]),c_0_22]),c_0_46]) ).
cnf(c_0_52,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_53,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
inference(fof_simplification,[status(thm)],[meet_join_complement]) ).
cnf(c_0_54,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_55,plain,
join(complement(meet(X1,X2)),meet(X2,join(complement(X1),meet(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_48,c_0_18]) ).
cnf(c_0_56,plain,
meet(X1,join(complement(X1),join(meet(X2,X1),meet(X1,complement(meet(X2,X1)))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_17]),c_0_51]) ).
cnf(c_0_57,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_58,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
c_0_53 ).
cnf(c_0_59,plain,
join(X1,join(X2,join(meet(X1,X3),X4))) = join(X1,join(X2,X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_54]),c_0_22]),c_0_22]) ).
cnf(c_0_60,plain,
join(complement(X1),join(meet(X2,X1),meet(X1,complement(meet(X2,X1))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_16]),c_0_14]),c_0_17]),c_0_57]) ).
cnf(c_0_61,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_62,plain,
( join(X1,X2) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_58,c_0_18]) ).
cnf(c_0_63,plain,
join(X1,join(complement(X2),meet(X2,complement(meet(X1,X2))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_64,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_28]),c_0_16]),c_0_14])]) ).
cnf(c_0_65,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_66,plain,
join(X1,join(X2,meet(complement(X2),complement(meet(X1,complement(X2)))))) = one,
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
( join(X2,meet(X1,complement(meet(X2,X1)))) != one
| meet(X1,complement(meet(X2,X1))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_65]) ).
cnf(c_0_68,plain,
join(X1,meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2)))))) = one,
inference(spm,[status(thm)],[c_0_47,c_0_66]) ).
cnf(c_0_69,plain,
meet(complement(meet(X1,X2)),complement(meet(X1,complement(meet(X1,X2))))) = complement(X1),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,plain,
meet(X1,join(meet(X1,X2),meet(complement(X1),join(X1,X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_28]),c_0_35]),c_0_35]),c_0_16]) ).
cnf(c_0_71,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_69,c_0_69]),c_0_64]),c_0_64]),c_0_18]),c_0_64]) ).
cnf(c_0_72,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_16]) ).
cnf(c_0_73,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_74,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_75,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),c_0_17]),c_0_16]) ).
cnf(c_0_76,plain,
meet(X1,join(meet(X2,X1),meet(complement(X1),join(X1,X2)))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_18]) ).
cnf(c_0_77,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_73]) ).
cnf(c_0_78,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_74,c_0_28]) ).
cnf(c_0_79,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_77]),c_0_78]),c_0_25]) ).
cnf(c_0_81,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_82,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_13]),c_0_16]) ).
cnf(c_0_83,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_29]),c_0_18]),c_0_25]) ).
cnf(c_0_84,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_69]),c_0_18]) ).
cnf(c_0_85,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
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_58,c_0_83]) ).
cnf(c_0_87,plain,
join(complement(X1),join(meet(X1,X2),meet(X1,complement(meet(X1,X2))))) = one,
inference(spm,[status(thm)],[c_0_60,c_0_18]) ).
cnf(c_0_88,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_84,c_0_76]) ).
cnf(c_0_89,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_58,c_0_85]),c_0_32])]) ).
cnf(c_0_90,plain,
complement(join(complement(X1),meet(X1,X2))) = meet(X1,complement(meet(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_75]),c_0_22]),c_0_87])]) ).
cnf(c_0_91,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_24]),c_0_18]) ).
cnf(c_0_92,plain,
( meet(X1,X2) != zero
| join(X1,complement(join(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_18]) ).
cnf(c_0_93,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_24]),c_0_18]) ).
cnf(c_0_94,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_90,c_0_91]),c_0_64]),c_0_64]) ).
cnf(c_0_95,plain,
join(X1,meet(complement(X1),join(X2,X1))) = join(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_64]) ).
cnf(c_0_96,plain,
join(meet(X1,X2),meet(X1,complement(meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_21]),c_0_18]) ).
cnf(c_0_97,plain,
( join(X2,meet(X1,join(X2,X3))) != one
| meet(X2,join(X3,meet(X2,X1))) != zero
| complement(join(meet(X1,join(X2,X3)),meet(X2,join(X3,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_62,c_0_19]),c_0_22]),c_0_16]),c_0_21]),c_0_16]) ).
cnf(c_0_98,plain,
complement(join(complement(X1),meet(X2,X1))) = meet(X1,complement(meet(X2,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_79]),c_0_22]),c_0_60])]) ).
cnf(c_0_99,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_96]) ).
cnf(c_0_100,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_101,plain,
( join(X2,X1) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_39]),c_0_24]),c_0_39]),c_0_24]) ).
cnf(c_0_102,plain,
complement(meet(X1,complement(meet(X2,X1)))) = join(complement(X1),meet(X2,X1)),
inference(spm,[status(thm)],[c_0_64,c_0_98]) ).
cnf(c_0_103,plain,
join(X1,meet(X2,complement(meet(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_99,c_0_18]) ).
cnf(c_0_104,plain,
meet(join(X1,X2),join(X2,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_100,c_0_52]),c_0_22]),c_0_41]),c_0_22]),c_0_41]) ).
cnf(c_0_105,plain,
( join(X2,X1) != one
| join(complement(X1),meet(X2,X1)) = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_65]),c_0_102]),c_0_103]) ).
cnf(c_0_106,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_85,c_0_16]) ).
cnf(c_0_107,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_104]) ).
cnf(c_0_108,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_105,c_0_26]),c_0_94]),c_0_106]),c_0_16]) ).
cnf(c_0_109,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_110,plain,
meet(join(X1,X2),join(X2,complement(join(X2,X1)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_82]),c_0_18]),c_0_24]) ).
cnf(c_0_111,plain,
join(X1,meet(complement(X2),join(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_108]),c_0_16]) ).
cnf(c_0_112,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_29]),c_0_109]) ).
cnf(c_0_113,plain,
join(X1,join(complement(join(X1,X2)),meet(complement(X1),join(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_13]),c_0_18]),c_0_51]) ).
cnf(c_0_114,plain,
meet(complement(X1),join(X2,X1)) = meet(X2,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_85]),c_0_112]) ).
cnf(c_0_115,plain,
complement(join(X1,complement(join(X1,X2)))) = meet(complement(X1),join(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_82]),c_0_18]),c_0_18]),c_0_22]),c_0_113])]) ).
cnf(c_0_116,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_29]),c_0_81]) ).
cnf(c_0_117,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_54,c_0_108]) ).
cnf(c_0_118,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_32]),c_0_17]),c_0_115]),c_0_115]),c_0_116]) ).
cnf(c_0_119,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_22,c_0_117]),c_0_22]) ).
cnf(c_0_120,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_79,c_0_117]) ).
cnf(c_0_121,plain,
join(X1,join(X2,join(X3,X1))) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_122,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_123,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_24,c_0_47]),c_0_18]) ).
cnf(c_0_124,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_118,c_0_119]),c_0_64]),c_0_120]),c_0_64]),c_0_18]) ).
cnf(c_0_125,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_16]) ).
cnf(c_0_127,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_128,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_123,c_0_21]) ).
cnf(c_0_129,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_124,c_0_18]) ).
cnf(c_0_130,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]) ).
cnf(c_0_131,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
c_0_127 ).
cnf(c_0_132,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129]),c_0_18]),c_0_130]) ).
cnf(c_0_133,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_131,c_0_132]),c_0_16]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT182-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/5.46 % Computer : n003.cluster.edu
% 0.19/5.46 % Model : x86_64 x86_64
% 0.19/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.46 % Memory : 8046.5625MB
% 0.19/5.46 % OS : Linux 6.8.0-71-generic
% 0.19/5.46 % CPULimit : 300
% 0.19/5.46 % WCLimit : 300
% 0.19/5.46 % DateTime : Sun Sep 20 23:20:05 UTC 2026
% 0.19/5.46 % CPUTime :
% 0.19/5.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/5.53 Running first-order theorem proving
% 0.24/5.53 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
% 33.72/10.52 % Version: 3.5.1
% 33.72/10.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.72/10.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.72/10.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.72/10.52 % Starting new_bool_3 with 300s (1) cores
% 33.72/10.52 % Starting new_bool_1 with 300s (1) cores
% 33.72/10.52 % Starting sh5l with 300s (1) cores
% 33.72/10.52 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2829914 completed with status 0
% 33.72/10.52 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 33.72/10.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.72/10.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.72/10.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.72/10.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.72/10.52 % No SInE strategy applied
% 33.72/10.52 % Search class: FHUPM-FFSF21-MFFFFFNN
% 33.72/10.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.72/10.52 % Starting SubtermCWHack with 136s (1) cores
% 33.72/10.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 33.72/10.52 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 33.72/10.52 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 33.72/10.52 % Starting new_bool_3 with 136s (1) cores
% 33.72/10.52 % G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with pid 2829923 completed with status 0
% 33.72/10.52 % Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S
% 33.72/10.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 33.72/10.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 33.72/10.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 33.72/10.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 33.72/10.52 % No SInE strategy applied
% 33.72/10.52 % Search class: FHUPM-FFSF21-MFFFFFNN
% 33.72/10.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 33.72/10.52 % Starting SubtermCWHack with 136s (1) cores
% 33.72/10.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 33.72/10.52 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 33.72/10.52 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 33.72/10.52 % Preprocessing time : 0.002 s
% 33.72/10.52 % Presaturation interreduction done
% 33.72/10.52
% 33.72/10.52 % Proof found!
% 33.72/10.52 % SZS status Unsatisfiable
% 33.72/10.52 % SZS output start CNFRefutation
% See solution above
% 33.72/10.52 % Parsed axioms : 13
% 33.72/10.52 % Removed by relevancy pruning/SinE : 0
% 33.72/10.52 % Initial clauses : 13
% 33.72/10.52 % Removed in clause preprocessing : 0
% 33.72/10.52 % Initial clauses in saturation : 13
% 33.72/10.52 % Processed clauses : 8159
% 33.72/10.52 % ...of these trivial : 2737
% 33.72/10.52 % ...subsumed : 4668
% 33.72/10.52 % ...remaining for further processing : 754
% 33.72/10.52 % Other redundant clauses eliminated : 0
% 33.72/10.52 % Clauses deleted for lack of memory : 0
% 33.72/10.52 % Backward-subsumed : 0
% 33.72/10.52 % Backward-rewritten : 402
% 33.72/10.52 % Generated clauses : 235350
% 33.72/10.52 % ...of the previous two non-redundant : 133745
% 33.72/10.52 % ...aggressively subsumed : 0
% 33.72/10.52 % Contextual simplify-reflections : 0
% 33.72/10.52 % Paramodulations : 235307
% 33.72/10.52 % Factorizations : 0
% 33.72/10.52 % NegExts : 0
% 33.72/10.52 % Equation resolutions : 43
% 33.72/10.52 % Disequality decompositions : 0
% 33.72/10.52 % Total rewrite steps : 572515
% 33.72/10.52 % ...of those cached : 484877
% 33.72/10.52 % Propositional unsat checks : 0
% 33.72/10.52 % Propositional check models : 0
% 33.72/10.52 % Propositional check unsatisfiable : 0
% 33.72/10.52 % Propositional clauses : 0
% 33.72/10.52 % Propositional clauses after purity: 0
% 33.72/10.52 % Propositional unsat core size : 0
% 33.72/10.52 % Propositional preprocessing time : 0.000
% 33.72/10.52 % Propositional encoding time : 0.000
% 33.72/10.52 % Propositional solver time : 0.000
% 33.72/10.52 % Success case prop preproc time : 0.000
% 33.72/10.52 % Success case prop encoding time : 0.000
% 33.72/10.52 % Success case prop solver time : 0.000
% 33.72/10.52 % Current number of processed clauses : 339
% 33.72/10.52 % Positive orientable unit clauses : 222
% 33.72/10.52 % Positive unorientable unit clauses: 10
% 33.72/10.52 % Negative unit clauses : 0
% 33.72/10.52 % Non-unit-clauses : 107
% 33.72/10.52 % Current number of unprocessed clauses: 125054
% 33.72/10.52 % ...number of literals in the above : 143442
% 33.72/10.52 % Current number of archived formulas : 0
% 33.72/10.52 % Current number of archived clauses : 415
% 33.72/10.52 % Clause-clause subsumption calls (NU) : 11983
% 33.72/10.52 % Rec. Clause-clause subsumption calls : 11822
% 33.72/10.52 % Non-unit clause-clause subsumptions : 3122
% 33.72/10.52 % Unit Clause-clause subsumption calls : 579
% 33.72/10.52 % Rewrite failures with RHS unbound : 0
% 33.72/10.52 % BW rewrite match attempts : 7043
% 33.72/10.52 % BW rewrite match successes : 1467
% 33.72/10.52 % Condensation attempts : 0
% 33.72/10.52 % Condensation successes : 0
% 33.72/10.52 % Termbank termtop insertions : 3520117
% 33.72/10.52 % Search garbage collected termcells : 8
% 33.72/10.52
% 33.72/10.52 % -------------------------------------------------
% 33.72/10.52 % User time : 4.330 s
% 33.72/10.52 % System time : 0.188 s
% 33.72/10.52 % Total time : 4.518 s
% 33.72/10.52 % Maximum resident set size: 3640 pages
% 33.72/10.52
% 33.72/10.52 % -------------------------------------------------
% 33.72/10.52 % User time : 22.733 s
% 33.72/10.52 % System time : 0.863 s
% 33.72/10.52 % Total time : 23.597 s
% 33.72/10.52 % Maximum resident set size: 4608 pages
% 33.72/10.52 % E exiting
%------------------------------------------------------------------------------