TSTP Solution File: LAT010-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 05:59:07 EDT 2023
% Result : Unsatisfiable 1.94s 2.12s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 50 unt; 6 typ; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 11 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,
a: $i ).
tff(decl_25,type,
b: $i ).
tff(decl_26,type,
c: $i ).
tff(decl_27,type,
d: $i ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
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(nr_3,hypothesis,
meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))) = join(meet(X3,join(X1,meet(X2,X3))),meet(X1,join(X2,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nr_3) ).
cnf(n5_1,hypothesis,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(meet(X1,X2),meet(X3,X4)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n5_1) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
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(prove_this,negated_conjecture,
meet(a,meet(join(b,c),join(b,d))) != meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(c_0_10,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_11,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_12,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_14,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_15,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,hypothesis,
meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))) = join(meet(X3,join(X1,meet(X2,X3))),meet(X1,join(X2,X3))),
nr_3 ).
cnf(c_0_17,hypothesis,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = join(meet(X1,join(X2,meet(X1,X3))),meet(X1,join(meet(X1,X2),meet(X3,X4)))),
n5_1 ).
cnf(c_0_18,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]),c_0_14]) ).
cnf(c_0_19,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_20,hypothesis,
join(meet(X1,join(X2,X3)),meet(X3,join(X1,meet(X2,X3)))) = meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))),
inference(rw,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_21,hypothesis,
meet(X1,meet(join(X2,meet(X3,join(X1,X4))),join(meet(X1,X2),meet(X3,X4)))) = meet(X1,join(meet(X1,X2),meet(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_14]),c_0_18]),c_0_19]) ).
cnf(c_0_22,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_23,hypothesis,
meet(X1,meet(join(X2,X3),meet(join(X1,meet(X2,X3)),join(X3,meet(X1,X2))))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_20]),c_0_14]) ).
cnf(c_0_24,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_25,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_26,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_27,hypothesis,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]),c_0_13]),c_0_23]),c_0_24]) ).
cnf(c_0_28,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_25,c_0_26]),c_0_11]) ).
cnf(c_0_29,hypothesis,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_27]) ).
cnf(c_0_30,hypothesis,
meet(X1,join(X2,meet(X3,X1))) = meet(X1,join(X3,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_31,plain,
join(meet(X1,X2),meet(X2,join(X1,X3))) = meet(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
meet(a,meet(join(b,c),join(b,d))) != meet(meet(a,meet(join(b,c),join(b,d))),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))),
prove_this ).
cnf(c_0_33,hypothesis,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_30]),c_0_22]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,join(b,meet(c,d))),join(meet(a,c),meet(a,d)))))) != meet(a,meet(join(b,c),join(b,d))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_14]),c_0_14]) ).
cnf(c_0_35,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_36,hypothesis,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31]) ).
cnf(c_0_37,hypothesis,
join(X1,meet(X2,join(X1,X3))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_11]) ).
cnf(c_0_38,negated_conjecture,
meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d)))))))) != meet(a,meet(join(b,c),join(b,d))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,hypothesis,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_10]),c_0_37]) ).
cnf(c_0_40,hypothesis,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_19]) ).
cnf(c_0_41,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_42,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_43,negated_conjecture,
meet(a,meet(join(b,c),meet(join(b,d),join(meet(a,c),join(meet(a,d),meet(a,join(b,meet(c,d)))))))) != meet(a,join(b,meet(c,d))),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,hypothesis,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_19]) ).
cnf(c_0_45,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_10]),c_0_22]) ).
cnf(c_0_46,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_11]),c_0_22]) ).
cnf(c_0_47,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_14]) ).
cnf(c_0_48,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_42]) ).
cnf(c_0_49,negated_conjecture,
$false,
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_44]),c_0_11]),c_0_46]),c_0_47]),c_0_39]),c_0_12]),c_0_47]),c_0_39]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n012.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 08:15:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.94/2.12 % Version : CSE_E---1.5
% 1.94/2.12 % Problem : theBenchmark.p
% 1.94/2.12 % Proof found
% 1.94/2.12 % SZS status Theorem for theBenchmark.p
% 1.94/2.12 % SZS output start Proof
% See solution above
% 1.94/2.13 % Total time : 1.531000 s
% 1.94/2.13 % SZS output end Proof
% 1.94/2.13 % Total time : 1.534000 s
%------------------------------------------------------------------------------