TSTP Solution File: LAT037-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT037-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n020.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 05:59:18 EDT 2023
% Result : Unsatisfiable 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 22
% Syntax : Number of formulae : 50 ( 39 unt; 7 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 6 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,
xx: $i ).
tff(decl_27,type,
yy: $i ).
tff(decl_28,type,
zz: $i ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',absorption2) ).
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(lhs2,axiom,
join(xx,zz) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs2) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_meet_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(lhs4,axiom,
meet(xx,zz) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs4) ).
cnf(lhs3,axiom,
meet(xx,yy) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs3) ).
cnf(modular,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
cnf(x_join_1,axiom,
join(X1,n1) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_1) ).
cnf(dist_meet,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dist_meet) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_0) ).
cnf(lhs1,axiom,
join(xx,yy) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lhs1) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(rhs,negated_conjecture,
yy != zz,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rhs) ).
cnf(c_0_15,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_16,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_17,axiom,
join(xx,zz) = n1,
lhs2 ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_19,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_20,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_21,axiom,
meet(xx,zz) = n0,
lhs4 ).
cnf(c_0_22,axiom,
meet(xx,yy) = n0,
lhs3 ).
cnf(c_0_23,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
join(zz,xx) = n1,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
modular ).
cnf(c_0_27,axiom,
join(X1,n1) = n1,
x_join_1 ).
cnf(c_0_28,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
dist_meet ).
cnf(c_0_29,plain,
meet(zz,xx) = n0,
inference(rw,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_30,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_31,axiom,
join(xx,yy) = n1,
lhs1 ).
cnf(c_0_32,plain,
meet(yy,xx) = n0,
inference(rw,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_33,plain,
join(zz,join(xx,X1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_34,plain,
( join(X1,X2) = X2
| meet(X1,X2) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_27]),c_0_19]) ).
cnf(c_0_35,hypothesis,
meet(zz,join(X1,xx)) = meet(zz,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_36,plain,
join(yy,xx) = n1,
inference(rw,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_37,hypothesis,
meet(yy,join(X1,xx)) = meet(yy,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_30]) ).
cnf(c_0_38,plain,
( join(zz,X1) = n1
| meet(xx,X1) != xx ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,hypothesis,
meet(yy,zz) = zz,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_20]) ).
cnf(c_0_40,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_41,negated_conjecture,
yy != zz,
rhs ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19]),c_0_39]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT037-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n020.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu Aug 24 09:52:16 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.044000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.047000 s
%------------------------------------------------------------------------------