TSTP Solution File: LAT182-1 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : LAT182-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:10:00 EDT 2023
% Result : Unsatisfiable 24.08s 3.51s
% Output : CNFRefutation 24.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of clauses : 132 ( 122 unt; 0 nHn; 14 RR)
% Number of literals : 147 ( 146 equ; 17 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 : 275 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',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/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',equation_H6) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',commutativity_of_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',commutativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',idempotence_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',absorption2) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',associativity_of_join) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',associativity_of_meet) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',complement_meet) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',idempotence_of_join) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p',meet_join_complement) ).
cnf(prove_distributivity,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.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,join(X2,meet(X1,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_54,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_55,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_56,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_57,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_58,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_53]),c_0_22]),c_0_22]) ).
cnf(c_0_59,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_54,c_0_55]),c_0_16]),c_0_14]),c_0_17]),c_0_56]) ).
cnf(c_0_60,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_61,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_57,c_0_18]) ).
cnf(c_0_62,plain,
join(X1,join(complement(X2),meet(X2,complement(meet(X1,X2))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_63,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_28]),c_0_16]),c_0_14])]) ).
cnf(c_0_64,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_65,plain,
join(X1,join(X2,meet(complement(X2),complement(meet(X1,complement(X2)))))) = one,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
( meet(X1,complement(meet(X2,X1))) = complement(X2)
| join(X2,meet(X1,complement(meet(X2,X1)))) != one ),
inference(spm,[status(thm)],[c_0_57,c_0_64]) ).
cnf(c_0_67,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_65]) ).
cnf(c_0_68,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_69,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_70,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_68,c_0_68]),c_0_63]),c_0_63]),c_0_18]),c_0_63]) ).
cnf(c_0_71,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_72,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_73,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_74,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_69,c_0_70]),c_0_71]),c_0_17]),c_0_16]) ).
cnf(c_0_75,plain,
meet(X1,join(meet(X2,X1),meet(complement(X1),join(X1,X2)))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_69,c_0_18]) ).
cnf(c_0_76,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_72]) ).
cnf(c_0_77,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_73,c_0_28]) ).
cnf(c_0_78,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,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_76]),c_0_77]),c_0_25]) ).
cnf(c_0_80,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_81,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_13]),c_0_16]) ).
cnf(c_0_82,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_29]),c_0_18]),c_0_25]) ).
cnf(c_0_83,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_68]),c_0_18]) ).
cnf(c_0_84,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
( meet(X1,complement(meet(X1,X2))) = complement(X2)
| join(X2,meet(X1,complement(meet(X1,X2)))) != one ),
inference(spm,[status(thm)],[c_0_57,c_0_82]) ).
cnf(c_0_86,plain,
join(complement(X1),join(meet(X1,X2),meet(X1,complement(meet(X1,X2))))) = one,
inference(spm,[status(thm)],[c_0_59,c_0_18]) ).
cnf(c_0_87,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_83,c_0_75]) ).
cnf(c_0_88,plain,
( join(X1,complement(join(X1,X2))) = complement(X2)
| meet(X2,X1) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_84]),c_0_32])]) ).
cnf(c_0_89,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_85,c_0_74]),c_0_22]),c_0_86])]) ).
cnf(c_0_90,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_24]),c_0_18]) ).
cnf(c_0_91,plain,
( join(X1,complement(join(X1,X2))) = complement(X2)
| meet(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_88,c_0_18]) ).
cnf(c_0_92,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_24]),c_0_18]) ).
cnf(c_0_93,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_89,c_0_90]),c_0_63]),c_0_63]) ).
cnf(c_0_94,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_91,c_0_92]),c_0_93]),c_0_63]) ).
cnf(c_0_95,plain,
join(meet(X1,X2),meet(X1,complement(meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_21]),c_0_18]) ).
cnf(c_0_96,plain,
( complement(join(meet(X1,join(X2,X3)),meet(X2,join(X3,meet(X2,X1))))) = X2
| meet(X2,join(X3,meet(X2,X1))) != zero
| join(X2,meet(X1,join(X2,X3))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_19]),c_0_22]),c_0_16]),c_0_21]),c_0_16]) ).
cnf(c_0_97,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_85,c_0_78]),c_0_22]),c_0_59])]) ).
cnf(c_0_98,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_95]) ).
cnf(c_0_99,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_100,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X2,X1) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_39]),c_0_24]),c_0_39]),c_0_24]) ).
cnf(c_0_101,plain,
complement(meet(X1,complement(meet(X2,X1)))) = join(complement(X1),meet(X2,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_97]) ).
cnf(c_0_102,plain,
join(X1,meet(X2,complement(meet(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_98,c_0_18]) ).
cnf(c_0_103,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_99,c_0_52]),c_0_22]),c_0_41]),c_0_22]),c_0_41]) ).
cnf(c_0_104,plain,
( join(complement(X1),meet(X2,X1)) = X2
| join(X2,X1) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_64]),c_0_101]),c_0_102]) ).
cnf(c_0_105,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_16]) ).
cnf(c_0_106,plain,
meet(join(X1,X2),meet(join(X2,X1),X3)) = meet(join(X1,X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_103]) ).
cnf(c_0_107,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_104,c_0_26]),c_0_93]),c_0_105]),c_0_16]) ).
cnf(c_0_108,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_109,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_106,c_0_81]),c_0_18]),c_0_24]) ).
cnf(c_0_110,plain,
join(X1,meet(complement(X2),join(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_107]),c_0_16]) ).
cnf(c_0_111,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_29]),c_0_108]) ).
cnf(c_0_112,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_59,c_0_13]),c_0_18]),c_0_51]) ).
cnf(c_0_113,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_109,c_0_110]),c_0_84]),c_0_111]) ).
cnf(c_0_114,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_85,c_0_81]),c_0_18]),c_0_18]),c_0_22]),c_0_112])]) ).
cnf(c_0_115,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_29]),c_0_80]) ).
cnf(c_0_116,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_53,c_0_107]) ).
cnf(c_0_117,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_113,c_0_32]),c_0_17]),c_0_114]),c_0_114]),c_0_115]) ).
cnf(c_0_118,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_116]),c_0_22]) ).
cnf(c_0_119,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_78,c_0_116]) ).
cnf(c_0_120,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_121,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_122,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_123,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_117,c_0_118]),c_0_63]),c_0_119]),c_0_63]),c_0_18]) ).
cnf(c_0_124,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_16]) ).
cnf(c_0_126,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_122,c_0_21]) ).
cnf(c_0_127,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1),
inference(spm,[status(thm)],[c_0_123,c_0_18]) ).
cnf(c_0_128,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_129,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_130,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_126,c_0_127]),c_0_18]),c_0_128]) ).
cnf(c_0_131,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_16]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT182-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n016.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 2400
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Oct 2 11:28:36 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.MfSuzR0OhV/E---3.1_5789.p
% 24.08/3.51 # Version: 3.1pre001
% 24.08/3.51 # Preprocessing class: FSSSSMSSSSSNFFN.
% 24.08/3.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.08/3.51 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 24.08/3.51 # Starting new_bool_3 with 300s (1) cores
% 24.08/3.51 # Starting new_bool_1 with 300s (1) cores
% 24.08/3.51 # Starting sh5l with 300s (1) cores
% 24.08/3.51 # G-E--_302_C18_F1_URBAN_RG_S04BN with pid 5866 completed with status 0
% 24.08/3.51 # Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 24.08/3.51 # Preprocessing class: FSSSSMSSSSSNFFN.
% 24.08/3.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.08/3.51 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 24.08/3.51 # No SInE strategy applied
% 24.08/3.51 # Search class: FHUPM-FFSF21-MFFFFFNN
% 24.08/3.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 24.08/3.51 # Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 811s (1) cores
% 24.08/3.51 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 24.08/3.51 # Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S2S with 136s (1) cores
% 24.08/3.51 # Starting new_bool_3 with 136s (1) cores
% 24.08/3.51 # Starting new_bool_1 with 136s (1) cores
% 24.08/3.51 # G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 5870 completed with status 0
% 24.08/3.51 # Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 24.08/3.51 # Preprocessing class: FSSSSMSSSSSNFFN.
% 24.08/3.51 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.08/3.51 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 24.08/3.51 # No SInE strategy applied
% 24.08/3.51 # Search class: FHUPM-FFSF21-MFFFFFNN
% 24.08/3.51 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 24.08/3.51 # Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 811s (1) cores
% 24.08/3.51 # Preprocessing time : 0.001 s
% 24.08/3.51 # Presaturation interreduction done
% 24.08/3.51
% 24.08/3.51 # Proof found!
% 24.08/3.51 # SZS status Unsatisfiable
% 24.08/3.51 # SZS output start CNFRefutation
% See solution above
% 24.08/3.51 # Parsed axioms : 13
% 24.08/3.51 # Removed by relevancy pruning/SinE : 0
% 24.08/3.51 # Initial clauses : 13
% 24.08/3.51 # Removed in clause preprocessing : 0
% 24.08/3.51 # Initial clauses in saturation : 13
% 24.08/3.51 # Processed clauses : 8159
% 24.08/3.51 # ...of these trivial : 2737
% 24.08/3.51 # ...subsumed : 4668
% 24.08/3.51 # ...remaining for further processing : 754
% 24.08/3.51 # Other redundant clauses eliminated : 0
% 24.08/3.51 # Clauses deleted for lack of memory : 0
% 24.08/3.51 # Backward-subsumed : 0
% 24.08/3.51 # Backward-rewritten : 402
% 24.08/3.51 # Generated clauses : 235350
% 24.08/3.51 # ...of the previous two non-redundant : 133745
% 24.08/3.51 # ...aggressively subsumed : 0
% 24.08/3.51 # Contextual simplify-reflections : 0
% 24.08/3.51 # Paramodulations : 235307
% 24.08/3.51 # Factorizations : 0
% 24.08/3.51 # NegExts : 0
% 24.08/3.51 # Equation resolutions : 43
% 24.08/3.51 # Total rewrite steps : 572515
% 24.08/3.51 # Propositional unsat checks : 0
% 24.08/3.51 # Propositional check models : 0
% 24.08/3.51 # Propositional check unsatisfiable : 0
% 24.08/3.51 # Propositional clauses : 0
% 24.08/3.51 # Propositional clauses after purity: 0
% 24.08/3.51 # Propositional unsat core size : 0
% 24.08/3.51 # Propositional preprocessing time : 0.000
% 24.08/3.51 # Propositional encoding time : 0.000
% 24.08/3.51 # Propositional solver time : 0.000
% 24.08/3.51 # Success case prop preproc time : 0.000
% 24.08/3.51 # Success case prop encoding time : 0.000
% 24.08/3.51 # Success case prop solver time : 0.000
% 24.08/3.51 # Current number of processed clauses : 339
% 24.08/3.51 # Positive orientable unit clauses : 222
% 24.08/3.51 # Positive unorientable unit clauses: 10
% 24.08/3.51 # Negative unit clauses : 0
% 24.08/3.51 # Non-unit-clauses : 107
% 24.08/3.51 # Current number of unprocessed clauses: 125054
% 24.08/3.51 # ...number of literals in the above : 143442
% 24.08/3.51 # Current number of archived formulas : 0
% 24.08/3.51 # Current number of archived clauses : 415
% 24.08/3.51 # Clause-clause subsumption calls (NU) : 11983
% 24.08/3.51 # Rec. Clause-clause subsumption calls : 11822
% 24.08/3.51 # Non-unit clause-clause subsumptions : 3122
% 24.08/3.51 # Unit Clause-clause subsumption calls : 579
% 24.08/3.51 # Rewrite failures with RHS unbound : 0
% 24.08/3.51 # BW rewrite match attempts : 7043
% 24.08/3.51 # BW rewrite match successes : 1467
% 24.08/3.51 # Condensation attempts : 0
% 24.08/3.51 # Condensation successes : 0
% 24.08/3.51 # Termbank termtop insertions : 3520087
% 24.08/3.51
% 24.08/3.51 # -------------------------------------------------
% 24.08/3.51 # User time : 2.902 s
% 24.08/3.51 # System time : 0.122 s
% 24.08/3.51 # Total time : 3.023 s
% 24.08/3.51 # Maximum resident set size: 1636 pages
% 24.08/3.51
% 24.08/3.51 # -------------------------------------------------
% 24.08/3.51 # User time : 14.743 s
% 24.08/3.51 # System time : 0.337 s
% 24.08/3.51 # Total time : 15.080 s
% 24.08/3.51 # Maximum resident set size: 1676 pages
% 24.08/3.51 % E---3.1 exiting
%------------------------------------------------------------------------------