TSTP Solution File: LAT256-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT256-1 : 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 : n011.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 06:00:15 EDT 2023
% Result : Unsatisfiable 174.34s 174.32s
% Output : CNFRefutation 174.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 77 ( 64 unt; 7 typ; 0 def)
% Number of atoms : 81 ( 80 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 : 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 12 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(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(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(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(equation_H81,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = meet(X1,join(meet(X1,X2),meet(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equation_H81) ).
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(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,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_15,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_16,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_19,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_20,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_21,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_22,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_23,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_24,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_25,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_26,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_27,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_28,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_29,axiom,
meet(X1,join(meet(X1,X2),meet(X3,join(X1,meet(X2,join(X1,X3)))))) = meet(X1,join(meet(X1,X2),meet(X1,X3))),
equation_H81 ).
cnf(c_0_30,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_31,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_32,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
join(X1,join(complement(X1),X2)) = join(one,X2),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_34,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_14]) ).
cnf(c_0_36,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_25]) ).
cnf(c_0_37,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_38,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_17]),c_0_22]),c_0_30]),c_0_31]),c_0_32]) ).
cnf(c_0_39,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
join(a,join(X1,b)) = join(X1,b),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_42,plain,
meet(X1,join(meet(X1,X2),meet(complement(X1),join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_25]) ).
cnf(c_0_43,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25]) ).
cnf(c_0_44,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_22]),c_0_25]),c_0_17])]) ).
cnf(c_0_45,plain,
meet(X1,join(meet(X2,X1),meet(complement(X1),join(X1,X2)))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_46,hypothesis,
meet(complement(a),join(a,meet(b,complement(a)))) = meet(b,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_42,c_0_43]),c_0_19]),c_0_44]),c_0_30]),c_0_25]),c_0_19]) ).
cnf(c_0_47,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_48,hypothesis,
meet(join(a,meet(b,complement(a))),join(meet(b,complement(a)),complement(join(a,meet(b,complement(a)))))) = meet(b,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_45,c_0_46]),c_0_14]),c_0_25]),c_0_27]),c_0_17]),c_0_30]) ).
cnf(c_0_49,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_50,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_51,hypothesis,
meet(a,join(meet(b,complement(a)),complement(join(a,meet(b,complement(a)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_22]) ).
cnf(c_0_52,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_53,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_23]) ).
cnf(c_0_54,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_55,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
| meet(X1,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(spm,[status(thm)],[c_0_41,c_0_29]),c_0_14]),c_0_25]),c_0_35]),c_0_50]) ).
cnf(c_0_56,hypothesis,
join(meet(b,complement(a)),complement(join(a,meet(b,complement(a))))) = complement(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_51]),c_0_52])]) ).
cnf(c_0_57,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,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_55,c_0_54]),c_0_54]),c_0_54]),c_0_15]),c_0_32]),c_0_25]),c_0_27]) ).
cnf(c_0_59,hypothesis,
join(b,complement(join(a,meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_56]),c_0_43]) ).
cnf(c_0_60,hypothesis,
meet(b,meet(complement(a),complement(join(a,meet(b,complement(a)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_22]),c_0_19]),c_0_23]) ).
cnf(c_0_61,hypothesis,
meet(complement(a),complement(join(a,meet(b,complement(a))))) = complement(join(a,meet(b,complement(a)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_56]),c_0_19]) ).
cnf(c_0_62,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_63,hypothesis,
( join(a,meet(b,complement(a))) = b
| meet(b,complement(join(a,meet(b,complement(a))))) != zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44]) ).
cnf(c_0_64,hypothesis,
meet(b,complement(join(a,meet(b,complement(a))))) = zero,
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_66,hypothesis,
join(complement(a),complement(join(a,meet(b,complement(a))))) = complement(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_56]),c_0_25]) ).
cnf(c_0_67,hypothesis,
join(a,meet(b,complement(a))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]) ).
cnf(c_0_68,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_65,c_0_25]) ).
cnf(c_0_69,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT256-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:56:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.52 start to proof: theBenchmark
% 174.34/174.32 % Version : CSE_E---1.5
% 174.34/174.32 % Problem : theBenchmark.p
% 174.34/174.32 % Proof found
% 174.34/174.32 % SZS status Theorem for theBenchmark.p
% 174.34/174.32 % SZS output start Proof
% See solution above
% 174.34/174.33 % Total time : 173.788000 s
% 174.34/174.33 % SZS output end Proof
% 174.34/174.33 % Total time : 173.799000 s
%------------------------------------------------------------------------------