TSTP Solution File: LAT066-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT066-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 05:59:23 EDT 2023
% Result : Unsatisfiable 0.51s 0.81s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 21
% Syntax : Number of formulae : 98 ( 87 unt; 8 typ; 0 def)
% Number of atoms : 96 ( 95 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 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 : 178 ( 24 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,
n1: $i ).
tff(decl_26,type,
n0: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
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(bottom,axiom,
meet(X1,complement(X1)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_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(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(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(top,axiom,
join(X1,complement(X1)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',top) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(g61,axiom,
meet(X1,join(X2,join(X3,meet(X4,join(X1,meet(X2,X3)))))) = meet(X1,join(X2,join(X3,meet(X1,X4)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',g61) ).
cnf(complements_are_unique,axiom,
( complement(X1) = X2
| join(X1,X2) != n1
| meet(X1,X2) != n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complements_are_unique) ).
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(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)) = n0,
bottom ).
cnf(c_0_17,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_18,plain,
meet(X1,n0) = n0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_20,plain,
join(X1,n0) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_22,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_23,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_24,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = n0,
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_25,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,axiom,
join(X1,complement(X1)) = n1,
top ).
cnf(c_0_27,plain,
join(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_29,axiom,
meet(X1,join(X2,join(X3,meet(X4,join(X1,meet(X2,X3)))))) = meet(X1,join(X2,join(X3,meet(X1,X4)))),
g61 ).
cnf(c_0_30,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = n0,
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_32,plain,
meet(X1,meet(complement(X1),X2)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_25]) ).
cnf(c_0_33,plain,
complement(n0) = n1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
meet(X1,n1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_35,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_30]),c_0_30]) ).
cnf(c_0_36,plain,
meet(complement(X1),meet(X2,X1)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]),c_0_13]) ).
cnf(c_0_37,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_38,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_39,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_26]),c_0_34]) ).
cnf(c_0_40,plain,
meet(X1,complement(join(X2,X1))) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19]) ).
cnf(c_0_41,plain,
join(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_42,axiom,
( complement(X1) = X2
| join(X1,X2) != n1
| meet(X1,X2) != n0 ),
complements_are_unique ).
cnf(c_0_43,plain,
meet(X1,join(complement(X1),complement(join(X2,X1)))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20]),c_0_16]) ).
cnf(c_0_44,plain,
join(X1,join(complement(X1),X2)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_41]) ).
cnf(c_0_45,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).
cnf(c_0_46,plain,
meet(X1,join(complement(X1),meet(X2,complement(meet(X1,X2))))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_24]),c_0_20]),c_0_16]) ).
cnf(c_0_47,plain,
( complement(X1) = X2
| meet(X2,X1) != n0
| join(X1,X2) != n1 ),
inference(spm,[status(thm)],[c_0_42,c_0_19]) ).
cnf(c_0_48,plain,
meet(complement(X1),complement(join(X2,X1))) = complement(join(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_45]),c_0_19]) ).
cnf(c_0_49,plain,
join(complement(X1),meet(X2,complement(meet(X1,X2)))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_46]),c_0_44])]) ).
cnf(c_0_50,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_16]),c_0_21]),c_0_26])]) ).
cnf(c_0_51,plain,
meet(complement(X1),complement(meet(X1,X2))) = complement(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_17]),c_0_19]) ).
cnf(c_0_52,plain,
meet(X1,complement(join(X1,X2))) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_19]) ).
cnf(c_0_53,plain,
join(X1,meet(X2,complement(meet(complement(X1),X2)))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
meet(X1,complement(meet(complement(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_55,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_56,plain,
meet(X1,join(complement(X1),complement(join(X1,X2)))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_52]),c_0_20]),c_0_16]) ).
cnf(c_0_57,plain,
join(X1,meet(X2,complement(meet(X2,complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_31]),c_0_33]),c_0_34]) ).
cnf(c_0_58,plain,
meet(X1,complement(meet(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_44])]) ).
cnf(c_0_60,plain,
meet(X1,complement(meet(X1,complement(X2)))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_57]),c_0_13]),c_0_19]),c_0_58]) ).
cnf(c_0_61,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_17]),c_0_21]) ).
cnf(c_0_62,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_59,c_0_50]) ).
cnf(c_0_63,plain,
meet(X1,complement(meet(X1,X2))) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_60]),c_0_15]) ).
cnf(c_0_64,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_60]),c_0_39]),c_0_61]),c_0_60]) ).
cnf(c_0_65,plain,
meet(X1,complement(join(complement(X1),X2))) = complement(join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_62]),c_0_19]) ).
cnf(c_0_66,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_63]),c_0_65]) ).
cnf(c_0_67,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(X2)),
inference(spm,[status(thm)],[c_0_66,c_0_50]) ).
cnf(c_0_68,plain,
complement(meet(X1,complement(X2))) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_69,plain,
meet(X1,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_67,c_0_49]),c_0_50]),c_0_50]),c_0_68]) ).
cnf(c_0_70,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_71,plain,
meet(X1,join(complement(X2),meet(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_19]) ).
cnf(c_0_72,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_70,c_0_71]),c_0_22]),c_0_21]),c_0_70]) ).
cnf(c_0_73,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_64,c_0_50]) ).
cnf(c_0_74,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_50]),c_0_50]),c_0_30]) ).
cnf(c_0_75,plain,
meet(X1,meet(join(complement(X1),X2),X3)) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_64]),c_0_13]) ).
cnf(c_0_76,plain,
join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_74]),c_0_50]) ).
cnf(c_0_77,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_28]),c_0_22]) ).
cnf(c_0_78,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_79,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_76]) ).
cnf(c_0_80,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_19]) ).
cnf(c_0_81,plain,
meet(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = meet(X1,join(X2,join(X3,meet(X1,X4)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_22]),c_0_22]),c_0_30]),c_0_30]) ).
cnf(c_0_82,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_78]),c_0_21]) ).
cnf(c_0_83,plain,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_55]),c_0_80]) ).
cnf(c_0_84,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_64]),c_0_26]),c_0_34]),c_0_64]) ).
cnf(c_0_85,plain,
meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_37]),c_0_76]),c_0_83]) ).
cnf(c_0_86,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_84,c_0_21]) ).
cnf(c_0_87,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_88,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_17]),c_0_19]),c_0_86]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT066-1 : TPTP v8.1.2. Released v2.5.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Aug 24 06:37:21 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.51/0.81 % Version : CSE_E---1.5
% 0.51/0.81 % Problem : theBenchmark.p
% 0.51/0.81 % Proof found
% 0.51/0.81 % SZS status Theorem for theBenchmark.p
% 0.51/0.81 % SZS output start Proof
% See solution above
% 0.51/0.81 % Total time : 0.251000 s
% 0.51/0.81 % SZS output end Proof
% 0.51/0.81 % Total time : 0.253000 s
%------------------------------------------------------------------------------