TSTP Solution File: LAT248-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT248-1 : 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 : n010.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 06:00:13 EDT 2023
% Result : Unsatisfiable 14.68s 14.74s
% Output : CNFRefutation 14.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 100 ( 87 unt; 7 typ; 0 def)
% Number of atoms : 105 ( 104 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 136 ( 23 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,
b: $i ).
tff(decl_28,type,
a: $i ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
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(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(equation_H63,axiom,
meet(X1,meet(join(X2,X3),join(X2,X4))) = meet(X1,join(X2,meet(join(X2,X3),join(X4,meet(X2,X3))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H63) ).
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(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_14,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_17,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_19,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_21,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_22,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_24,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_25,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_26,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_27,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_30,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_31,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_32,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_33,hypothesis,
join(a,meet(b,join(X1,a))) = meet(b,join(X1,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_15]),c_0_23]),c_0_15]) ).
cnf(c_0_34,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_35,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_36,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_37,axiom,
meet(X1,meet(join(X2,X3),join(X2,X4))) = meet(X1,join(X2,meet(join(X2,X3),join(X4,meet(X2,X3))))),
equation_H63 ).
cnf(c_0_38,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_39,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_40,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_41,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_42,hypothesis,
join(X1,meet(b,join(X1,a))) = join(X1,a),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_43,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_44,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_45,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_46,plain,
join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_37]),c_0_34]) ).
cnf(c_0_47,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_49,plain,
meet(X1,meet(X2,complement(meet(join(X1,X3),X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_39]) ).
cnf(c_0_50,hypothesis,
join(X1,meet(b,join(a,X1))) = join(a,X1),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_51,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_22]),c_0_26]) ).
cnf(c_0_52,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_43]) ).
cnf(c_0_53,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_54,hypothesis,
meet(join(a,X1),join(b,X1)) = join(a,X1),
inference(spm,[status(thm)],[c_0_28,c_0_45]) ).
cnf(c_0_55,hypothesis,
meet(a,join(b,X1)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_17]) ).
cnf(c_0_56,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_57,hypothesis,
meet(join(a,complement(b)),join(a,X1)) = join(a,meet(join(a,complement(b)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_58,hypothesis,
meet(X1,meet(X2,complement(meet(join(a,X1),X2)))) = zero,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_59,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_60,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_26]) ).
cnf(c_0_61,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_62,hypothesis,
meet(b,join(a,meet(X1,b))) = join(a,meet(X1,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_20]),c_0_15]) ).
cnf(c_0_63,hypothesis,
join(b,join(X1,a)) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_55]),c_0_26]) ).
cnf(c_0_64,hypothesis,
meet(complement(b),join(a,meet(join(a,complement(b)),X1))) = meet(complement(b),join(a,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_65,hypothesis,
meet(X1,complement(meet(join(a,X1),join(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_58]) ).
cnf(c_0_66,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_67,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_59,c_0_15]) ).
cnf(c_0_68,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_20]),c_0_23]) ).
cnf(c_0_69,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_51]) ).
cnf(c_0_70,plain,
( complement(meet(X1,X2)) = X3
| meet(X1,meet(X2,X3)) != zero
| join(meet(X1,X2),X3) != one ),
inference(spm,[status(thm)],[c_0_59,c_0_16]) ).
cnf(c_0_71,hypothesis,
meet(X1,join(a,meet(X1,b))) = meet(X1,b),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_73,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_74,hypothesis,
join(b,join(X1,join(a,X2))) = join(b,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_63]),c_0_26]),c_0_26]) ).
cnf(c_0_75,hypothesis,
join(a,meet(complement(a),join(a,complement(b)))) = join(a,complement(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_24]),c_0_29]),c_0_15]) ).
cnf(c_0_76,plain,
join(X1,join(X2,complement(X1))) = one,
inference(spm,[status(thm)],[c_0_52,c_0_23]) ).
cnf(c_0_77,hypothesis,
meet(complement(b),join(a,complement(join(a,complement(b))))) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_48]),c_0_15]),c_0_38]),c_0_39]),c_0_44]),c_0_26]),c_0_66]) ).
cnf(c_0_78,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_30]),c_0_23]),c_0_24])]) ).
cnf(c_0_79,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_26]) ).
cnf(c_0_80,hypothesis,
( complement(meet(X1,X2)) = join(a,meet(X2,b))
| join(a,join(meet(X2,b),meet(X1,X2))) != one
| meet(X1,meet(X2,b)) != zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_81,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_26,c_0_73]) ).
cnf(c_0_82,hypothesis,
join(b,join(X1,meet(complement(a),join(a,complement(b))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_74]),c_0_76]) ).
cnf(c_0_83,hypothesis,
join(a,complement(join(a,complement(b)))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_77]),c_0_78]),c_0_79])]) ).
cnf(c_0_84,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_39]) ).
cnf(c_0_85,hypothesis,
( complement(X1) = b
| join(b,X1) != one
| meet(X1,b) != zero ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_34]),c_0_29]),c_0_73]),c_0_29]),c_0_81]) ).
cnf(c_0_86,hypothesis,
join(b,meet(complement(a),join(a,complement(b)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_82]),c_0_53]),c_0_44]) ).
cnf(c_0_87,hypothesis,
meet(b,join(a,X1)) = join(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_83]),c_0_84]),c_0_48]) ).
cnf(c_0_88,hypothesis,
complement(meet(complement(a),join(a,complement(b)))) = b,
inference(cn,[status(thm)],[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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_16]),c_0_15]),c_0_87]),c_0_30]),c_0_48]),c_0_15]),c_0_30])]) ).
cnf(c_0_89,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_90,hypothesis,
meet(complement(a),join(a,complement(b))) = complement(b),
inference(spm,[status(thm)],[c_0_78,c_0_88]) ).
cnf(c_0_91,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_89,c_0_23]) ).
cnf(c_0_92,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_90]),c_0_91]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT248-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 07:38:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 14.68/14.74 % Version : CSE_E---1.5
% 14.68/14.74 % Problem : theBenchmark.p
% 14.68/14.74 % Proof found
% 14.68/14.74 % SZS status Theorem for theBenchmark.p
% 14.68/14.74 % SZS output start Proof
% See solution above
% 14.68/14.74 % Total time : 14.167000 s
% 14.68/14.74 % SZS output end Proof
% 14.68/14.74 % Total time : 14.170000 s
%------------------------------------------------------------------------------