TSTP Solution File: LAT215-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT215-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:00:03 EDT 2023
% Result : Unsatisfiable 159.85s 159.86s
% Output : CNFRefutation 159.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 21
% Syntax : Number of formulae : 154 ( 135 unt; 8 typ; 0 def)
% Number of atoms : 162 ( 161 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 18 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% 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 : 313 ( 44 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
meet: ( $i * $i ) > $i ).
tff(decl_23,type,
join: ( $i * $i ) > $i ).
tff(decl_24,type,
complement: $i > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
zero: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(equation_H80,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H80) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/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/sandbox/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,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_17,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_18,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_19,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_20,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_21,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_23,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = join(meet(X1,X2),meet(X1,X3)),
equation_H80 ).
cnf(c_0_25,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_27,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_28,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_29,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_30,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_31,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
cnf(c_0_32,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_24,c_0_14]),c_0_15]),c_0_20]),c_0_25]) ).
cnf(c_0_33,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_27]) ).
cnf(c_0_34,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_35,plain,
meet(X1,join(meet(X2,X1),meet(X3,X1))) = join(meet(X2,X1),meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_29]),c_0_17]),c_0_13]),c_0_30]) ).
cnf(c_0_36,plain,
meet(X1,join(meet(join(X1,X2),X3),meet(complement(join(X1,X2)),join(X1,join(X2,X3))))) = meet(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_31]),c_0_26]) ).
cnf(c_0_37,plain,
join(X1,join(X2,complement(X1))) = one,
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_38,plain,
meet(X1,join(meet(X2,X3),meet(X3,X1))) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_13]),c_0_26]) ).
cnf(c_0_40,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_41,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_42,plain,
meet(X1,join(complement(join(X1,X2)),meet(complement(X1),join(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_16]),c_0_15]),c_0_20]),c_0_22]) ).
cnf(c_0_43,plain,
meet(X1,join(X2,meet(join(X2,X3),X1))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_13]) ).
cnf(c_0_44,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_45,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_47,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_39]),c_0_26]),c_0_26]) ).
cnf(c_0_48,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_40,c_0_18]),c_0_17]),c_0_29]),c_0_17]),c_0_29]) ).
cnf(c_0_49,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_50,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_41,c_0_16]) ).
cnf(c_0_51,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_52,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_53,plain,
meet(X1,join(meet(complement(X1),join(X1,X2)),complement(join(X1,meet(complement(X1),join(X1,X2)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_16]),c_0_22]) ).
cnf(c_0_54,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_55,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_26]) ).
cnf(c_0_56,plain,
join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_46]),c_0_22]) ).
cnf(c_0_57,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_58,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(meet(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_39]) ).
cnf(c_0_59,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_49,c_0_16]) ).
cnf(c_0_60,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_50]) ).
cnf(c_0_61,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_14,c_0_51]) ).
cnf(c_0_62,plain,
join(meet(complement(X1),join(X1,X2)),complement(join(X1,meet(complement(X1),join(X1,X2))))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54])]) ).
cnf(c_0_63,plain,
join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_64,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_58]) ).
cnf(c_0_65,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_59,c_0_60]),c_0_61]),c_0_15]),c_0_17]) ).
cnf(c_0_66,plain,
join(complement(X1),complement(join(X1,meet(complement(X1),join(X1,X2))))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_62]),c_0_22]),c_0_62]),c_0_22]) ).
cnf(c_0_67,plain,
join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_68,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_52,c_0_16]) ).
cnf(c_0_69,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_28]),c_0_16]) ).
cnf(c_0_70,plain,
join(complement(X1),complement(join(X1,meet(X2,complement(X1))))) = complement(X1),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_20]),c_0_22]),c_0_14])]) ).
cnf(c_0_72,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(spm,[status(thm)],[c_0_69,c_0_26]) ).
cnf(c_0_73,plain,
join(X1,join(X2,join(X3,X1))) = join(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_74,plain,
join(X1,complement(join(complement(X1),meet(X2,X1)))) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_76,plain,
meet(join(X1,X2),complement(join(X2,join(X3,X1)))) = zero,
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,plain,
join(X1,join(X2,complement(join(X1,complement(join(X1,X2)))))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_13]),c_0_22]),c_0_26]) ).
cnf(c_0_78,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_75]),c_0_26]) ).
cnf(c_0_79,plain,
meet(complement(join(X1,X2)),join(X1,complement(join(X1,complement(join(X1,X2)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_22]),c_0_16]) ).
cnf(c_0_80,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_39]),c_0_22]),c_0_26]) ).
cnf(c_0_81,plain,
join(X1,complement(join(X1,complement(join(X1,X2))))) = join(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_79]),c_0_71]),c_0_80])]) ).
cnf(c_0_82,plain,
join(X1,join(X2,complement(join(X1,complement(join(X2,X1)))))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_77,c_0_22]) ).
cnf(c_0_83,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_84,plain,
join(X1,complement(join(X1,complement(join(X2,X1))))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_85,plain,
meet(X1,meet(X2,complement(join(X3,meet(X1,X2))))) = zero,
inference(spm,[status(thm)],[c_0_17,c_0_69]) ).
cnf(c_0_86,plain,
meet(X1,complement(join(complement(X1),meet(X2,X1)))) = complement(join(complement(X1),meet(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_74]),c_0_16]) ).
cnf(c_0_87,plain,
meet(X1,join(meet(X2,X1),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = join(meet(X2,X1),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_88,plain,
( complement(join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = X1
| join(X1,meet(X3,join(X1,meet(X2,join(X1,X3))))) != one
| join(meet(X1,X2),meet(X1,X3)) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_24]),c_0_26]),c_0_22]),c_0_57]),c_0_22]),c_0_83]) ).
cnf(c_0_89,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_90,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_91,plain,
join(meet(X1,X2),complement(join(complement(X1),meet(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_19]),c_0_22]) ).
cnf(c_0_92,plain,
meet(X1,complement(join(complement(X2),meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_93,plain,
meet(X1,join(meet(X1,X2),meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_87]) ).
cnf(c_0_94,plain,
meet(X1,join(meet(X2,X1),meet(complement(X1),join(X1,X2)))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_95,plain,
( complement(X1) = X2
| join(X2,X1) != one
| meet(X2,X1) != zero ),
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_88,c_0_89]),c_0_28]),c_0_28]),c_0_22]),c_0_30]),c_0_28]),c_0_28]) ).
cnf(c_0_96,plain,
join(X1,complement(join(complement(X2),meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,plain,
meet(X1,complement(join(complement(X2),meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_92,c_0_16]) ).
cnf(c_0_98,plain,
meet(X1,join(meet(X1,X2),meet(X3,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
( join(complement(X1),meet(X1,X2)) = X2
| join(X2,X1) != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_71]),c_0_97])]) ).
cnf(c_0_100,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_19]),c_0_22]) ).
cnf(c_0_101,plain,
meet(X1,join(X2,meet(X1,join(X2,X3)))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_13]),c_0_22]) ).
cnf(c_0_102,plain,
meet(X1,join(complement(join(X1,X2)),meet(complement(X2),join(X1,X2)))) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_14]),c_0_16]),c_0_75]),c_0_15]),c_0_22]) ).
cnf(c_0_103,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_30]),c_0_22]) ).
cnf(c_0_104,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_99,c_0_100]),c_0_71]),c_0_16]) ).
cnf(c_0_105,plain,
meet(X1,join(meet(X1,complement(X2)),complement(join(X1,X2)))) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_22]) ).
cnf(c_0_106,plain,
( meet(X1,X2) = X2
| join(complement(X2),meet(X1,X2)) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_65]),c_0_71]) ).
cnf(c_0_107,plain,
join(X1,join(X2,complement(meet(X3,join(X1,X2))))) = one,
inference(spm,[status(thm)],[c_0_26,c_0_103]) ).
cnf(c_0_108,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_104]),c_0_22]) ).
cnf(c_0_109,plain,
meet(X1,join(meet(X1,X2),complement(join(X1,complement(X2))))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_105,c_0_71]) ).
cnf(c_0_110,plain,
( meet(X1,join(meet(X2,X1),X3)) = meet(X2,X1)
| join(meet(X2,X1),complement(meet(X1,join(meet(X2,X1),X3)))) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_46]),c_0_22]) ).
cnf(c_0_111,plain,
join(X1,complement(meet(X2,join(X1,complement(X2))))) = one,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_13,c_0_108]) ).
cnf(c_0_113,plain,
meet(X1,join(meet(X2,X1),complement(join(X1,complement(X2))))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_109,c_0_16]) ).
cnf(c_0_114,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_22]) ).
cnf(c_0_115,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_117,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_13]),c_0_22]) ).
cnf(c_0_118,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_114,c_0_16]) ).
cnf(c_0_119,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_28]),c_0_16]) ).
cnf(c_0_120,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,plain,
meet(complement(X1),join(X1,complement(join(X2,X1)))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_71]) ).
cnf(c_0_122,plain,
( complement(join(X1,complement(join(X2,X1)))) = X2
| meet(X2,join(X1,complement(join(X2,X1)))) != zero ),
inference(spm,[status(thm)],[c_0_95,c_0_54]) ).
cnf(c_0_123,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_120,c_0_22]) ).
cnf(c_0_124,plain,
complement(join(complement(X1),meet(X1,X2))) = meet(X1,complement(meet(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_91]),c_0_16]) ).
cnf(c_0_125,plain,
( complement(join(X1,complement(join(X2,X1)))) = X2
| meet(X2,X1) != zero ),
inference(rw,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_126,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_124,c_0_119]),c_0_71]),c_0_71]) ).
cnf(c_0_127,plain,
( meet(complement(X1),join(X2,X1)) = X2
| meet(X2,X1) != zero ),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_128,plain,
complement(meet(X1,complement(meet(X1,X2)))) = join(complement(X1),meet(X1,X2)),
inference(spm,[status(thm)],[c_0_71,c_0_124]) ).
cnf(c_0_129,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_90,c_0_104]) ).
cnf(c_0_130,plain,
meet(join(X1,X2),join(complement(X2),meet(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_59]),c_0_128]),c_0_129]),c_0_16]) ).
cnf(c_0_131,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_130]),c_0_26]),c_0_22]),c_0_30]) ).
cnf(c_0_132,plain,
join(X1,join(X2,join(complement(X1),X3))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_27]),c_0_26]) ).
cnf(c_0_133,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_118,c_0_131]) ).
cnf(c_0_134,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(X1,join(X2,X3)),
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_32,c_0_132]),c_0_15]),c_0_22]),c_0_131]),c_0_47]),c_0_133]) ).
cnf(c_0_135,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_131,c_0_71]) ).
cnf(c_0_136,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_39]),c_0_90]) ).
cnf(c_0_137,plain,
meet(X1,join(meet(complement(X1),join(X1,X2)),meet(X1,join(meet(X1,X3),X2)))) = meet(X1,join(meet(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_83]),c_0_22]) ).
cnf(c_0_138,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_134]),c_0_71]) ).
cnf(c_0_139,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_133,c_0_71]) ).
cnf(c_0_140,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_136]),c_0_26]),c_0_57]),c_0_90]) ).
cnf(c_0_141,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_142,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_140]),c_0_136]),c_0_138]) ).
cnf(c_0_143,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_144,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_138]),c_0_142]) ).
cnf(c_0_145,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT215-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.36 % Computer : n002.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 05:52:46 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 159.85/159.86 % Version : CSE_E---1.5
% 159.85/159.86 % Problem : theBenchmark.p
% 159.85/159.86 % Proof found
% 159.85/159.86 % SZS status Theorem for theBenchmark.p
% 159.85/159.86 % SZS output start Proof
% See solution above
% 159.85/159.88 % Total time : 159.272000 s
% 159.85/159.88 % SZS output end Proof
% 159.85/159.88 % Total time : 159.282000 s
%------------------------------------------------------------------------------