TSTP Solution File: LAT005-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 05:59:05 EDT 2023
% Result : Unsatisfiable 0.91s 0.94s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 77 ( 62 unt; 9 typ; 0 def)
% Number of atoms : 74 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 114 ( 14 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,
n0: $i ).
tff(decl_25,type,
n1: $i ).
tff(decl_26,type,
complement: ( $i * $i ) > $o ).
tff(decl_27,type,
r1: $i ).
tff(decl_28,type,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
r2: $i ).
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(modular,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',modular) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
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(complement_join,axiom,
( join(X1,X2) = n1
| ~ complement(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_join) ).
cnf(complement_of_a_meet_b,hypothesis,
complement(r2,meet(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
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(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_meet_1) ).
cnf(complement_meet,axiom,
( meet(X1,X2) = n0
| ~ complement(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-2.ax',complement_meet) ).
cnf(complement_of_a_join_b,hypothesis,
complement(r1,join(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
cnf(x_meet_0,axiom,
meet(X1,n0) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_meet_0) ).
cnf(prove_lemma,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_join_0) ).
cnf(c_0_16,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_17,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_18,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
modular ).
cnf(c_0_19,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_21,plain,
join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_23,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_24,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_25,plain,
meet(join(X1,X2),join(X3,X1)) = join(X1,meet(X2,join(X3,X1))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,join(X1,X3))),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_27,plain,
meet(join(X1,X2),join(X2,X3)) = join(X2,meet(join(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_28,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_29,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_30,plain,
meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_20]) ).
cnf(c_0_31,axiom,
( join(X1,X2) = n1
| ~ complement(X1,X2) ),
complement_join ).
cnf(c_0_32,hypothesis,
complement(r2,meet(a,b)),
complement_of_a_meet_b ).
cnf(c_0_33,plain,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_27]) ).
cnf(c_0_34,plain,
join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_17]) ).
cnf(c_0_35,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_36,plain,
meet(X1,join(meet(X1,X2),X3)) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_37,hypothesis,
join(meet(a,b),r2) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]) ).
cnf(c_0_38,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_39,axiom,
( meet(X1,X2) = n0
| ~ complement(X1,X2) ),
complement_meet ).
cnf(c_0_40,hypothesis,
complement(r1,join(a,b)),
complement_of_a_join_b ).
cnf(c_0_41,axiom,
meet(X1,n0) = n0,
x_meet_0 ).
cnf(c_0_42,plain,
meet(X1,join(meet(X2,X1),X3)) = join(meet(X2,X1),meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_34]) ).
cnf(c_0_43,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_35,c_0_28]) ).
cnf(c_0_44,hypothesis,
join(meet(a,b),meet(a,r2)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
prove_lemma ).
cnf(c_0_46,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_47,hypothesis,
meet(r1,join(a,b)) = n0,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_49,plain,
meet(X1,join(X2,meet(X3,X1))) = join(meet(X3,X1),meet(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_50,hypothesis,
join(b,meet(a,r2)) = join(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_17]) ).
cnf(c_0_51,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_52,negated_conjecture,
meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) != r1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_53,plain,
meet(join(X1,X2),join(X3,X2)) = join(X2,meet(X1,join(X3,X2))),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_54,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_20]) ).
cnf(c_0_55,hypothesis,
meet(r1,meet(join(a,b),X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_47]),c_0_48]) ).
cnf(c_0_56,hypothesis,
meet(join(a,b),r2) = join(meet(a,r2),meet(b,r2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_20]),c_0_20]) ).
cnf(c_0_57,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
join(r1,meet(a,meet(r2,join(r1,meet(b,r2))))) != r1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_26]),c_0_24]) ).
cnf(c_0_59,plain,
meet(X1,join(X2,meet(X3,X1))) = join(meet(X3,X1),meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_28]),c_0_20]) ).
cnf(c_0_60,plain,
meet(X1,join(X2,meet(X3,join(X1,X2)))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_54,c_0_25]) ).
cnf(c_0_61,hypothesis,
meet(r1,join(meet(a,r2),meet(b,r2))) = n0,
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_63,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_64,hypothesis,
meet(a,meet(b,r2)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_20]),c_0_24]) ).
cnf(c_0_65,negated_conjecture,
join(r1,meet(a,join(meet(r1,r2),meet(b,r2)))) != r1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_17]) ).
cnf(c_0_66,hypothesis,
meet(a,join(meet(r1,r2),meet(b,r2))) = n0,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]),c_0_24]),c_0_63]),c_0_64]),c_0_24]),c_0_42]),c_0_20]),c_0_17]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66]),c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT005-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:18:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.91/0.94 % Version : CSE_E---1.5
% 0.91/0.94 % Problem : theBenchmark.p
% 0.91/0.94 % Proof found
% 0.91/0.94 % SZS status Theorem for theBenchmark.p
% 0.91/0.94 % SZS output start Proof
% See solution above
% 0.91/0.95 % Total time : 0.387000 s
% 0.91/0.95 % SZS output end Proof
% 0.91/0.95 % Total time : 0.390000 s
%------------------------------------------------------------------------------