TSTP Solution File: LAT023-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT023-1 : 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 : n032.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 05:59:14 EDT 2023
% Result : Unsatisfiable 15.90s 15.99s
% Output : CNFRefutation 15.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 67 unt; 5 typ; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 177 ( 0 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 ).
cnf(modularity_axiom,hypothesis,
join(meet(join(X1,X2),X3),X2) = join(meet(join(X3,X2),X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modularity_axiom) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',commutativity_of_join) ).
cnf(quasi_lattice1,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice1) ).
cnf(quasi_lattice2,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',quasi_lattice2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',commutativity_of_meet) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_join) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',idempotence_of_meet) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',associativity_of_join) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT004-0.ax',associativity_of_meet) ).
cnf(prove_modularity,negated_conjecture,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_modularity) ).
cnf(c_0_10,hypothesis,
join(meet(join(X1,X2),X3),X2) = join(meet(join(X3,X2),X1),X2),
modularity_axiom ).
cnf(c_0_11,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_12,axiom,
join(meet(X1,join(X2,X3)),meet(X1,X2)) = meet(X1,join(X2,X3)),
quasi_lattice1 ).
cnf(c_0_13,axiom,
meet(join(X1,meet(X2,X3)),join(X1,X2)) = join(X1,meet(X2,X3)),
quasi_lattice2 ).
cnf(c_0_14,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_15,hypothesis,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(join(X3,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_16,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_17,plain,
join(meet(X1,X2),meet(X1,join(X2,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_19,plain,
meet(join(X1,X2),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_21,hypothesis,
join(X1,meet(X1,join(X2,X1))) = join(X1,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_22,plain,
join(X1,meet(X1,join(X1,X2))) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_24,hypothesis,
join(X1,meet(join(X2,X1),X3)) = join(X1,meet(X2,join(X3,X1))),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_25,plain,
meet(join(X1,X2),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_26,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_16]) ).
cnf(c_0_27,hypothesis,
join(X1,meet(X1,X2)) = meet(X1,join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_11]),c_0_22]) ).
cnf(c_0_28,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_23]) ).
cnf(c_0_29,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_30,hypothesis,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,join(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_24]),c_0_24]) ).
cnf(c_0_31,plain,
meet(join(X1,X2),join(meet(X3,X2),X1)) = join(meet(X3,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_32,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_11]) ).
cnf(c_0_33,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_34,plain,
meet(X1,meet(join(X1,X2),join(X2,X3))) = meet(X1,join(X2,X3)),
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_19,c_0_17]),c_0_11]),c_0_27]),c_0_23]),c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_20]) ).
cnf(c_0_36,hypothesis,
join(X1,meet(X2,meet(X3,join(X3,X1)))) = join(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_20]),c_0_32]),c_0_23]) ).
cnf(c_0_37,plain,
meet(join(X1,X2),meet(X3,join(X3,X1))) = meet(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,hypothesis,
join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,join(X3,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_39,plain,
join(meet(X1,X2),meet(X1,join(X3,join(X2,X4)))) = meet(X1,join(X3,join(X2,X4))),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_40,hypothesis,
join(X1,meet(X2,join(X3,X1))) = join(X1,meet(X3,join(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_11]),c_0_38]) ).
cnf(c_0_41,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_11]),c_0_20]) ).
cnf(c_0_42,hypothesis,
meet(X1,join(X2,join(meet(X1,X2),X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27]),c_0_37]),c_0_17]),c_0_41]) ).
cnf(c_0_43,plain,
join(X1,join(meet(X2,X3),meet(join(X1,X2),join(X1,join(meet(X2,X3),X4))))) = meet(join(X1,X2),join(X1,join(meet(X2,X3),X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_44,plain,
meet(X1,meet(join(X2,X1),join(X2,X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_11]) ).
cnf(c_0_45,plain,
join(X1,join(meet(X1,join(X1,X2)),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_14]),c_0_41]) ).
cnf(c_0_46,hypothesis,
join(meet(X1,join(X1,X2)),X3) = join(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_47,hypothesis,
meet(X1,join(X2,meet(X1,join(X2,X3)))) = meet(X1,join(X2,X3)),
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_42,c_0_43]),c_0_44]),c_0_42]),c_0_38]),c_0_20]),c_0_20]),c_0_35]),c_0_26]),c_0_42]) ).
cnf(c_0_48,plain,
meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_49,plain,
meet(join(X1,X2),join(meet(X2,X3),X1)) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_50,plain,
join(meet(X1,X2),join(meet(X1,join(X2,X3)),X4)) = join(meet(X1,join(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_51,plain,
join(X1,join(meet(X1,X2),meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_26]) ).
cnf(c_0_52,hypothesis,
join(X1,meet(X2,join(X3,X1))) = meet(join(X2,X1),join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_24]),c_0_20]),c_0_32]),c_0_48]) ).
cnf(c_0_53,hypothesis,
join(X1,meet(X2,X1)) = meet(X1,join(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_54,hypothesis,
join(X1,meet(X2,meet(X3,join(X2,X1)))) = join(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_49]),c_0_20]),c_0_32]),c_0_23]),c_0_32]) ).
cnf(c_0_55,plain,
join(X1,join(meet(X1,X2),join(meet(X3,X2),X4))) = join(X1,join(meet(X3,X2),X4)),
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_50,c_0_25]),c_0_14]),c_0_20]),c_0_20]),c_0_46]),c_0_41]),c_0_26]) ).
cnf(c_0_56,hypothesis,
join(X1,join(meet(X1,X2),meet(join(X1,X2),X3))) = meet(join(X2,X1),join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_46]),c_0_26]),c_0_38]),c_0_52]) ).
cnf(c_0_57,hypothesis,
meet(X1,meet(join(X1,X2),join(meet(X2,X1),X3))) = meet(X1,join(meet(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_23]),c_0_29]) ).
cnf(c_0_58,hypothesis,
join(X1,meet(X2,meet(join(X2,X1),X3))) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_54,c_0_14]) ).
cnf(c_0_59,hypothesis,
join(X1,meet(X2,join(meet(X1,X2),X3))) = join(meet(X2,X3),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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53]),c_0_23]),c_0_57]),c_0_23]),c_0_18]),c_0_11]),c_0_53]),c_0_23]),c_0_51]),c_0_58]) ).
cnf(c_0_60,plain,
join(meet(X1,X2),meet(X1,join(meet(X1,X2),X3))) = meet(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_17,c_0_29]) ).
cnf(c_0_61,hypothesis,
join(X1,meet(X2,join(X1,X3))) = meet(join(X3,X1),join(X1,X2)),
inference(rw,[status(thm)],[c_0_40,c_0_52]) ).
cnf(c_0_62,hypothesis,
join(X1,meet(X2,join(meet(X2,X1),X3))) = join(meet(X2,X3),X1),
inference(spm,[status(thm)],[c_0_59,c_0_14]) ).
cnf(c_0_63,plain,
meet(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))) = meet(X1,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61]),c_0_11]),c_0_27]),c_0_33]),c_0_14]),c_0_28]) ).
cnf(c_0_64,negated_conjecture,
meet(a,join(b,meet(a,c))) != join(meet(a,b),meet(a,c)),
prove_modularity ).
cnf(c_0_65,hypothesis,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X3),X2)),
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_62,c_0_29]),c_0_61]),c_0_11]),c_0_27]),c_0_33]),c_0_14]),c_0_28]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT023-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Thu Aug 24 08:43:26 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.46 start to proof: theBenchmark
% 15.90/15.99 % Version : CSE_E---1.5
% 15.90/15.99 % Problem : theBenchmark.p
% 15.90/15.99 % Proof found
% 15.90/15.99 % SZS status Theorem for theBenchmark.p
% 15.90/15.99 % SZS output start Proof
% See solution above
% 15.90/15.99 % Total time : 15.518000 s
% 15.90/15.99 % SZS output end Proof
% 15.90/15.99 % Total time : 15.522000 s
%------------------------------------------------------------------------------