TSTP Solution File: LAT225-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 06:00:06 EDT 2023
% Result : Unsatisfiable 166.41s 166.59s
% Output : CNFRefutation 166.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 73 ( 59 unt; 7 typ; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 96 ( 13 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(equation_H10,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H10) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
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(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
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(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_13,axiom,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))),
equation_H10 ).
cnf(c_0_14,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_15,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_16,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_17,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_20,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_21,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_22,plain,
meet(X1,join(X2,meet(X3,join(meet(X2,X3),X1)))) = meet(X1,join(X2,meet(X1,X3))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_23,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_26,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
meet(complement(meet(X1,X2)),join(X1,meet(X2,complement(meet(X1,X2))))) = meet(join(X1,X2),complement(meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]),c_0_18]),c_0_18]) ).
cnf(c_0_28,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_20]) ).
cnf(c_0_30,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_26,c_0_16]) ).
cnf(c_0_31,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_32,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_33,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_34,hypothesis,
meet(complement(a),join(a,meet(b,complement(a)))) = meet(b,complement(a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_28]) ).
cnf(c_0_35,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_36,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_37,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_38,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_39,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_14]) ).
cnf(c_0_40,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_41,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_42,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_43,hypothesis,
meet(complement(meet(b,complement(a))),join(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a)))))) = complement(meet(b,complement(a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_34]),c_0_35]),c_0_16]),c_0_36]) ).
cnf(c_0_44,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
join(X1,join(X2,join(X3,X1))) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_46,plain,
( complement(meet(X1,X2)) = X3
| meet(X2,meet(X3,X1)) != zero
| join(meet(X1,X2),X3) != one ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,hypothesis,
meet(complement(a),meet(join(a,meet(b,complement(a))),complement(meet(b,complement(a))))) = zero,
inference(spm,[status(thm)],[c_0_42,c_0_34]) ).
cnf(c_0_48,hypothesis,
meet(complement(a),join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a))))))) = complement(a),
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_13,c_0_43]),c_0_20]),c_0_16]),c_0_30]),c_0_23]),c_0_20]) ).
cnf(c_0_49,plain,
join(X1,join(X2,join(X3,complement(X1)))) = one,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,hypothesis,
( complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a)))
| join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) != one ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_18]),c_0_18]),c_0_14]),c_0_20]) ).
cnf(c_0_51,hypothesis,
join(a,join(meet(b,complement(a)),meet(complement(a),complement(meet(b,complement(a)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_48]),c_0_20]),c_0_20]),c_0_49]) ).
cnf(c_0_52,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_33]),c_0_14]),c_0_16])]) ).
cnf(c_0_53,hypothesis,
complement(meet(complement(a),complement(meet(b,complement(a))))) = join(a,meet(b,complement(a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51])]) ).
cnf(c_0_54,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_55,plain,
( complement(meet(X1,complement(meet(X2,X1)))) = X2
| join(X2,meet(X1,complement(meet(X2,X1)))) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_42]),c_0_14]) ).
cnf(c_0_56,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(join(a,meet(b,complement(a)))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
join(X1,join(X2,join(meet(X1,X3),X4))) = join(X2,join(X1,X4)),
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_58,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_59,hypothesis,
( join(a,meet(b,complement(a))) = b
| join(b,complement(join(a,meet(b,complement(a))))) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_52]) ).
cnf(c_0_60,hypothesis,
join(b,complement(join(a,meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_51]),c_0_30]),c_0_58]),c_0_56]) ).
cnf(c_0_61,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60])]) ).
cnf(c_0_62,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_63,hypothesis,
meet(complement(a),complement(meet(b,complement(a)))) = complement(b),
inference(rw,[status(thm)],[c_0_56,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_62,c_0_14]) ).
cnf(c_0_65,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_63]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : LAT225-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.16 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Thu Aug 24 06:26:06 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.60 start to proof: theBenchmark
% 166.41/166.59 % Version : CSE_E---1.5
% 166.41/166.59 % Problem : theBenchmark.p
% 166.41/166.59 % Proof found
% 166.41/166.59 % SZS status Theorem for theBenchmark.p
% 166.41/166.59 % SZS output start Proof
% See solution above
% 166.41/166.59 % Total time : 165.786000 s
% 166.41/166.59 % SZS output end Proof
% 166.41/166.59 % Total time : 165.798000 s
%------------------------------------------------------------------------------