TSTP Solution File: LAT222-10 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT222-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 06:00:05 EDT 2023
% Result : Unsatisfiable 31.90s 32.03s
% Output : CNFRefutation 31.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 84 ( 76 unt; 8 typ; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 112 ( 21 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
meet: ( $i * $i ) > $i ).
tff(decl_24,type,
join: ( $i * $i ) > $i ).
tff(decl_25,type,
complement: $i > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
zero: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
a: $i ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
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/sandbox2/benchmark/theBenchmark.p',equation_H6) ).
cnf(meet_join_complement,axiom,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meet_join_complement) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_join) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_14,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_15,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_16,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_17,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_21,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
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_18,c_0_19]) ).
cnf(c_0_24,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_25,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_27,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_28,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_30,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_31,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_32,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_33,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_28]) ).
cnf(c_0_34,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_35,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_36,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20]) ).
cnf(c_0_37,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_38,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_39,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_40,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_17]),c_0_35]) ).
cnf(c_0_41,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_42,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_37,c_0_20]) ).
cnf(c_0_43,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_44,hypothesis,
join(meet(b,X1),complement(meet(a,X1))) = one,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_45,plain,
meet(join(X1,X2),complement(join(X1,join(X2,X3)))) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_46,hypothesis,
meet(a,join(b,X1)) = a,
inference(spm,[status(thm)],[c_0_14,c_0_41]) ).
cnf(c_0_47,plain,
meet(X1,join(X2,meet(X1,join(X3,join(complement(join(X1,X3)),meet(X1,X2)))))) = meet(X1,join(X3,join(complement(join(X1,X3)),meet(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_19]),c_0_22]),c_0_22]) ).
cnf(c_0_48,hypothesis,
join(complement(a),meet(b,join(a,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_14]),c_0_20]) ).
cnf(c_0_49,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_50,hypothesis,
meet(join(X1,a),complement(join(X1,b))) = zero,
inference(spm,[status(thm)],[c_0_45,c_0_36]) ).
cnf(c_0_51,axiom,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
meet_join_complement ).
cnf(c_0_52,hypothesis,
join(b,join(X1,a)) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_46]),c_0_22]) ).
cnf(c_0_53,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_22]) ).
cnf(c_0_54,hypothesis,
meet(b,join(a,join(complement(b),meet(b,complement(a))))) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_19]),c_0_20]),c_0_36]) ).
cnf(c_0_55,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_42,c_0_49]),c_0_19]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_56,hypothesis,
meet(join(X1,a),complement(join(b,X1))) = zero,
inference(spm,[status(thm)],[c_0_50,c_0_20]) ).
cnf(c_0_57,plain,
ifeq(join(X1,X2),one,ifeq(meet(X2,X1),zero,complement(X1),X2),X2) = X2,
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_58,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_59,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_42,c_0_17]),c_0_21]),c_0_21]),c_0_20]) ).
cnf(c_0_60,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_52,c_0_20]) ).
cnf(c_0_61,plain,
ifeq(join(X1,join(X2,X3)),one,ifeq(meet(X2,join(X1,X3)),zero,complement(X2),join(X1,X3)),join(X1,X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_51,c_0_53]) ).
cnf(c_0_62,hypothesis,
join(a,join(complement(b),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_38,c_0_54]),c_0_22]),c_0_22]),c_0_55]),c_0_20]) ).
cnf(c_0_63,hypothesis,
meet(complement(b),join(a,meet(b,X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_16]),c_0_20]),c_0_18]) ).
cnf(c_0_64,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_17]),c_0_20]),c_0_15]),c_0_58]),c_0_58]) ).
cnf(c_0_65,hypothesis,
meet(a,join(meet(b,X1),meet(complement(b),join(b,X1)))) = meet(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_59]),c_0_39]) ).
cnf(c_0_66,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_15]),c_0_28]) ).
cnf(c_0_67,hypothesis,
join(a,meet(b,complement(a))) = b,
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_62]),c_0_63]),c_0_64]),c_0_58]),c_0_58]) ).
cnf(c_0_68,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_69,hypothesis,
meet(a,join(complement(b),meet(b,complement(a)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_19]),c_0_20]),c_0_17]) ).
cnf(c_0_70,hypothesis,
join(a,join(X1,meet(b,complement(a)))) = join(X1,b),
inference(spm,[status(thm)],[c_0_53,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_72,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_68]) ).
cnf(c_0_73,hypothesis,
join(complement(b),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_51,c_0_69]),c_0_70]),c_0_20]),c_0_15]),c_0_58]),c_0_58]) ).
cnf(c_0_74,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_71,c_0_20]) ).
cnf(c_0_75,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_20]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT222-10 : TPTP v8.1.2. Released v7.3.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n024.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 05:18:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 31.90/32.03 % Version : CSE_E---1.5
% 31.90/32.03 % Problem : theBenchmark.p
% 31.90/32.03 % Proof found
% 31.90/32.03 % SZS status Theorem for theBenchmark.p
% 31.90/32.03 % SZS output start Proof
% See solution above
% 31.90/32.03 % Total time : 31.457000 s
% 31.90/32.03 % SZS output end Proof
% 31.90/32.03 % Total time : 31.461000 s
%------------------------------------------------------------------------------