%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LAT204-1 : 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 : n001.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 01:05:44 PM UTC 2026
% Result : Unsatisfiable 13.60s 2.68s
% Output : CNFRefutation 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 13
% Syntax : Number of clauses : 121 ( 110 unt; 0 nHn; 17 RR)
% Number of literals : 136 ( 135 equ; 18 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 : 247 ( 34 sgn)
% Comments :
%------------------------------------------------------------------------------
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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_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(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(equation_H58,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X1,X2))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H58) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
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(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(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_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(c_0_13,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_14,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_15,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_17,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_20,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_22,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_23,axiom,
meet(X1,join(X2,X3)) = meet(X1,join(X2,meet(join(X1,X2),join(X3,meet(X1,X2))))),
equation_H58 ).
cnf(c_0_24,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_20]) ).
cnf(c_0_25,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_26,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_27,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
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(meet(complement(X1),X2),meet(join(X1,meet(complement(X1),X2)),X3))) = meet(X1,join(meet(complement(X1),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_31,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_32,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_33,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_35,plain,
( join(X1,X2) != one
| meet(X1,X2) != zero
| complement(X1) = X2 ),
c_0_29 ).
cnf(c_0_36,plain,
meet(X1,join(meet(complement(X1),X2),complement(join(X1,meet(complement(X1),X2))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_16]),c_0_21]),c_0_24]) ).
cnf(c_0_37,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_38,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_32,c_0_24]),c_0_33]),c_0_34]),c_0_13]) ).
cnf(c_0_39,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_40,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_41,plain,
join(meet(complement(X1),X2),complement(join(X1,meet(complement(X1),X2)))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_42,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_43,plain,
( join(X1,X2) != one
| meet(X2,X1) != zero
| complement(X1) = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_44,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_18]) ).
cnf(c_0_45,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_47,plain,
join(complement(X1),complement(join(X1,meet(complement(X1),X2)))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_16]),c_0_22]),c_0_26])]) ).
cnf(c_0_49,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_50,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_51,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(spm,[status(thm)],[c_0_44,c_0_31]) ).
cnf(c_0_52,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_45,c_0_14]),c_0_13]),c_0_46]),c_0_13]),c_0_46]) ).
cnf(c_0_53,plain,
join(X1,complement(join(complement(X1),meet(X1,X2)))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_55,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_28,c_0_50]) ).
cnf(c_0_56,plain,
meet(X1,meet(X2,complement(join(X3,meet(X2,X1))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_13]) ).
cnf(c_0_57,plain,
meet(X1,complement(join(complement(X1),meet(X1,X2)))) = complement(join(complement(X1),meet(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_53]),c_0_18]) ).
cnf(c_0_58,plain,
join(X1,complement(join(X2,meet(complement(X2),X1)))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_54,c_0_41]) ).
cnf(c_0_59,plain,
join(X1,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_23,c_0_55]),c_0_50]),c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_60,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_26]),c_0_55]) ).
cnf(c_0_61,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_55,c_0_22]) ).
cnf(c_0_62,plain,
meet(X1,complement(join(complement(X2),meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
join(X1,complement(join(complement(X2),meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
cnf(c_0_64,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_31]) ).
cnf(c_0_65,plain,
( join(X2,X1) != one
| join(complement(X1),meet(X1,X2)) = X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_62]),c_0_48]),c_0_22]),c_0_63]) ).
cnf(c_0_66,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_19]),c_0_22]) ).
cnf(c_0_67,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_65,c_0_66]),c_0_48]),c_0_18]) ).
cnf(c_0_68,plain,
( join(X2,meet(X1,complement(meet(X1,X2)))) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_69,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_54,c_0_67]) ).
cnf(c_0_70,plain,
( join(X2,X1) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_71,plain,
( join(X1,X2) != one
| meet(X1,complement(meet(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_72,plain,
join(meet(X1,X2),complement(join(complement(X2),meet(X1,X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_46]),c_0_22]),c_0_49]) ).
cnf(c_0_73,plain,
meet(X1,complement(meet(X1,complement(meet(X1,X2))))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_66]),c_0_48]) ).
cnf(c_0_74,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_13]) ).
cnf(c_0_75,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_13]) ).
cnf(c_0_76,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_13]) ).
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_48]),c_0_22]),c_0_67]),c_0_22]) ).
cnf(c_0_78,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_74,c_0_18]) ).
cnf(c_0_79,plain,
meet(X1,join(meet(X2,meet(X3,X1)),meet(X1,join(X4,meet(X2,meet(X3,X1)))))) = meet(X1,join(meet(X2,meet(X3,X1)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_75]),c_0_76]) ).
cnf(c_0_80,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_81,plain,
join(complement(X1),complement(join(X1,meet(X2,complement(X1))))) = complement(X1),
inference(spm,[status(thm)],[c_0_47,c_0_78]) ).
cnf(c_0_82,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(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_79,c_0_80]),c_0_46]),c_0_46]),c_0_42]),c_0_46]),c_0_46]),c_0_22]) ).
cnf(c_0_83,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_67]),c_0_22]) ).
cnf(c_0_84,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
cnf(c_0_85,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_28]),c_0_22]) ).
cnf(c_0_86,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_28,c_0_83]) ).
cnf(c_0_87,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_22]),c_0_31]) ).
cnf(c_0_89,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_86,c_0_78]) ).
cnf(c_0_90,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_35,c_0_87]),c_0_88])]) ).
cnf(c_0_91,plain,
complement(join(complement(X1),meet(X1,X2))) = meet(X1,complement(meet(X1,X2))),
inference(spm,[status(thm)],[c_0_48,c_0_77]) ).
cnf(c_0_92,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_39]),c_0_18]) ).
cnf(c_0_93,plain,
( meet(X1,X2) != zero
| join(X1,complement(join(X1,X2))) = complement(X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_18]) ).
cnf(c_0_94,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_87,c_0_22]) ).
cnf(c_0_95,plain,
complement(one) = zero,
inference(spm,[status(thm)],[c_0_16,c_0_50]) ).
cnf(c_0_96,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_91,c_0_92]),c_0_48]),c_0_48]) ).
cnf(c_0_97,plain,
( meet(X2,X1) != zero
| meet(complement(X1),join(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_93,c_0_94]),c_0_37]),c_0_95]),c_0_21]),c_0_96]) ).
cnf(c_0_98,plain,
complement(meet(X1,complement(meet(X2,X1)))) = join(complement(X1),meet(X2,X1)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_99,plain,
join(X1,meet(X2,complement(meet(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_69,c_0_18]) ).
cnf(c_0_100,plain,
meet(join(X1,X2),join(complement(X2),meet(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_25]),c_0_98]),c_0_99]),c_0_18]) ).
cnf(c_0_101,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_100]),c_0_31]),c_0_22]),c_0_19]) ).
cnf(c_0_102,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_82,c_0_101]) ).
cnf(c_0_103,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_102,c_0_48]) ).
cnf(c_0_104,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_101]),c_0_31]) ).
cnf(c_0_105,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_106,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_107,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_103,c_0_104]),c_0_48]),c_0_102]),c_0_48]),c_0_18]) ).
cnf(c_0_108,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_54,c_0_105]),c_0_106]) ).
cnf(c_0_109,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_49,c_0_107]),c_0_31]),c_0_108]),c_0_22]) ).
cnf(c_0_110,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_105,c_0_18]) ).
cnf(c_0_111,plain,
meet(X1,join(X2,meet(X3,X1))) = meet(join(X3,X2),X1),
inference(spm,[status(thm)],[c_0_107,c_0_22]) ).
cnf(c_0_112,plain,
join(X1,meet(X2,join(X3,X1))) = join(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_46]),c_0_110]) ).
cnf(c_0_113,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_39,c_0_40]),c_0_18]) ).
cnf(c_0_114,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_107,c_0_18]) ).
cnf(c_0_115,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
inference(fof_simplification,[status(thm)],[prove_distributivity]) ).
cnf(c_0_116,plain,
meet(join(X1,X2),join(X3,X2)) = join(meet(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_117,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X3,X2),X1),
inference(spm,[status(thm)],[c_0_114,c_0_22]) ).
cnf(c_0_118,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
c_0_115 ).
cnf(c_0_119,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_19]),c_0_18]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_22]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT204-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n001.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sun Sep 20 23:25:27 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 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
% 13.60/2.68 % Version: 3.5.1
% 13.60/2.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.60/2.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.60/2.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.60/2.68 % Starting new_bool_3 with 300s (1) cores
% 13.60/2.68 % Starting new_bool_1 with 300s (1) cores
% 13.60/2.68 % Starting sh5l with 300s (1) cores
% 13.60/2.68 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1621924 completed with status 0
% 13.60/2.68 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 13.60/2.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.60/2.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.60/2.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.60/2.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.60/2.68 % No SInE strategy applied
% 13.60/2.68 % Search class: FHUPM-FFSF21-MFFFFFNN
% 13.60/2.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.60/2.68 % Starting SubtermCWHack with 136s (1) cores
% 13.60/2.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 13.60/2.68 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 13.60/2.68 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 13.60/2.68 % Starting new_bool_3 with 136s (1) cores
% 13.60/2.68 % G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with pid 1621933 completed with status 0
% 13.60/2.68 % Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S
% 13.60/2.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 13.60/2.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.60/2.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 13.60/2.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.60/2.68 % No SInE strategy applied
% 13.60/2.68 % Search class: FHUPM-FFSF21-MFFFFFNN
% 13.60/2.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.60/2.68 % Starting SubtermCWHack with 136s (1) cores
% 13.60/2.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 13.60/2.68 % Starting G-E--_303_C18_F1_URBAN_S0Y with 136s (1) cores
% 13.60/2.68 % Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 13.60/2.68 % Preprocessing time : 0.002 s
% 13.60/2.68 % Presaturation interreduction done
% 13.60/2.68
% 13.60/2.68 % Proof found!
% 13.60/2.68 % SZS status Unsatisfiable
% 13.60/2.68 % SZS output start CNFRefutation
% See solution above
% 13.60/2.68 % Parsed axioms : 13
% 13.60/2.68 % Removed by relevancy pruning/SinE : 0
% 13.60/2.68 % Initial clauses : 13
% 13.60/2.68 % Removed in clause preprocessing : 0
% 13.60/2.68 % Initial clauses in saturation : 13
% 13.60/2.68 % Processed clauses : 6105
% 13.60/2.68 % ...of these trivial : 1456
% 13.60/2.68 % ...subsumed : 3977
% 13.60/2.68 % ...remaining for further processing : 672
% 13.60/2.68 % Other redundant clauses eliminated : 0
% 13.60/2.68 % Clauses deleted for lack of memory : 0
% 13.60/2.68 % Backward-subsumed : 0
% 13.60/2.68 % Backward-rewritten : 319
% 13.60/2.68 % Generated clauses : 155136
% 13.60/2.68 % ...of the previous two non-redundant : 89000
% 13.60/2.68 % ...aggressively subsumed : 0
% 13.60/2.68 % Contextual simplify-reflections : 0
% 13.60/2.68 % Paramodulations : 155076
% 13.60/2.68 % Factorizations : 0
% 13.60/2.68 % NegExts : 0
% 13.60/2.68 % Equation resolutions : 60
% 13.60/2.68 % Disequality decompositions : 0
% 13.60/2.68 % Total rewrite steps : 345262
% 13.60/2.68 % ...of those cached : 290716
% 13.60/2.68 % Propositional unsat checks : 0
% 13.60/2.68 % Propositional check models : 0
% 13.60/2.68 % Propositional check unsatisfiable : 0
% 13.60/2.68 % Propositional clauses : 0
% 13.60/2.68 % Propositional clauses after purity: 0
% 13.60/2.68 % Propositional unsat core size : 0
% 13.60/2.68 % Propositional preprocessing time : 0.000
% 13.60/2.68 % Propositional encoding time : 0.000
% 13.60/2.68 % Propositional solver time : 0.000
% 13.60/2.68 % Success case prop preproc time : 0.000
% 13.60/2.68 % Success case prop encoding time : 0.000
% 13.60/2.68 % Success case prop solver time : 0.000
% 13.60/2.68 % Current number of processed clauses : 340
% 13.60/2.68 % Positive orientable unit clauses : 216
% 13.60/2.68 % Positive unorientable unit clauses: 8
% 13.60/2.68 % Negative unit clauses : 0
% 13.60/2.68 % Non-unit-clauses : 116
% 13.60/2.68 % Current number of unprocessed clauses: 81990
% 13.60/2.68 % ...number of literals in the above : 95630
% 13.60/2.68 % Current number of archived formulas : 0
% 13.60/2.68 % Current number of archived clauses : 332
% 13.60/2.68 % Clause-clause subsumption calls (NU) : 14429
% 13.60/2.68 % Rec. Clause-clause subsumption calls : 14256
% 13.60/2.68 % Non-unit clause-clause subsumptions : 2948
% 13.60/2.68 % Unit Clause-clause subsumption calls : 342
% 13.60/2.68 % Rewrite failures with RHS unbound : 0
% 13.60/2.68 % BW rewrite match attempts : 3185
% 13.60/2.68 % BW rewrite match successes : 703
% 13.60/2.68 % Condensation attempts : 0
% 13.60/2.68 % Condensation successes : 0
% 13.60/2.68 % Termbank termtop insertions : 2109481
% 13.60/2.68 % Search garbage collected termcells : 8
% 13.60/2.68
% 13.60/2.68 % -------------------------------------------------
% 13.60/2.68 % User time : 1.911 s
% 13.60/2.68 % System time : 0.087 s
% 13.60/2.68 % Total time : 1.998 s
% 13.60/2.68 % Maximum resident set size: 3384 pages
% 13.60/2.68
% 13.60/2.68 % -------------------------------------------------
% 13.60/2.68 % User time : 9.419 s
% 13.60/2.68 % System time : 0.418 s
% 13.60/2.68 % Total time : 9.837 s
% 13.60/2.68 % Maximum resident set size: 4864 pages
% 13.60/2.68 % E exiting
%------------------------------------------------------------------------------