TSTP Solution File: LAT005-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT005-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 05:59:06 EDT 2023
% Result : Unsatisfiable 0.23s 1.31s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 79 ( 67 unt; 10 typ; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 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,
r2: $i ).
tff(decl_27,type,
a: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
r1: $i ).
tff(decl_30,type,
b2: $i ).
tff(decl_31,type,
a2: $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(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(x_meet_0,axiom,
meet(X1,n0) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_meet_0) ).
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(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(r1_complement_join_a_b_2,negated_conjecture,
meet(r1,join(a,b)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1_complement_join_a_b_2) ).
cnf(define_a2,negated_conjecture,
join(r1,meet(b,r2)) = a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',define_a2) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-1.ax',x_join_0) ).
cnf(define_b2,negated_conjecture,
join(r1,meet(a,r2)) = b2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',define_b2) ).
cnf(r2_complement_meet_a_b_2,negated_conjecture,
meet(r2,meet(a,b)) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_complement_meet_a_b_2) ).
cnf(prove_SAMs_lemma,negated_conjecture,
meet(a2,b2) != r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_SAMs_lemma) ).
cnf(c_0_14,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_15,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_16,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
modular ).
cnf(c_0_17,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
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,plain,
join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
meet(X1,n0) = n0,
x_meet_0 ).
cnf(c_0_22,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_23,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_26,negated_conjecture,
meet(r1,join(a,b)) = n0,
r1_complement_join_a_b_2 ).
cnf(c_0_27,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_28,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_22]) ).
cnf(c_0_30,plain,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_31,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
meet(r1,meet(join(a,b),X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
join(r1,meet(b,r2)) = a2,
define_a2 ).
cnf(c_0_35,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(meet(X3,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31]) ).
cnf(c_0_36,negated_conjecture,
meet(r1,meet(X1,join(a,b))) = n0,
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_37,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_38,negated_conjecture,
join(b,a2) = join(b,r1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,meet(X3,X1))),
inference(spm,[status(thm)],[c_0_35,c_0_15]) ).
cnf(c_0_40,negated_conjecture,
meet(b,r1) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_17]),c_0_19]) ).
cnf(c_0_41,plain,
join(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_42,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_25]) ).
cnf(c_0_43,negated_conjecture,
meet(a2,join(b,r1)) = a2,
inference(spm,[status(thm)],[c_0_17,c_0_38]) ).
cnf(c_0_44,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_45,negated_conjecture,
meet(join(a,b),join(b,r1)) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_37]) ).
cnf(c_0_46,negated_conjecture,
meet(b,join(r1,meet(X1,b))) = meet(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_47,negated_conjecture,
join(r1,meet(a,r2)) = b2,
define_b2 ).
cnf(c_0_48,negated_conjecture,
meet(a2,meet(X1,join(b,r1))) = meet(X1,a2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
meet(a,join(b,r1)) = meet(a,b),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_51,negated_conjecture,
meet(b,join(r1,meet(b,X1))) = meet(b,X1),
inference(spm,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_52,negated_conjecture,
meet(b,meet(r2,a2)) = meet(b,r2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_34]),c_0_25]) ).
cnf(c_0_53,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_25]) ).
cnf(c_0_54,negated_conjecture,
meet(r2,meet(a,b)) = n0,
r2_complement_meet_a_b_2 ).
cnf(c_0_55,negated_conjecture,
join(a,b2) = join(a,r1),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_56,negated_conjecture,
meet(r1,a2) = r1,
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_57,negated_conjecture,
meet(a,meet(b,a2)) = meet(a,a2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_19]),c_0_42]) ).
cnf(c_0_58,negated_conjecture,
meet(b,a2) = meet(b,r2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]) ).
cnf(c_0_59,negated_conjecture,
meet(a,meet(b,r2)) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_21]),c_0_25]) ).
cnf(c_0_60,negated_conjecture,
meet(b2,join(a,r1)) = b2,
inference(spm,[status(thm)],[c_0_17,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
join(r1,meet(X1,a2)) = meet(a2,join(r1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_56]) ).
cnf(c_0_62,negated_conjecture,
meet(a,a2) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
meet(a2,b2) != r1,
prove_SAMs_lemma ).
cnf(c_0_64,negated_conjecture,
meet(b2,meet(X1,join(a,r1))) = meet(X1,b2),
inference(spm,[status(thm)],[c_0_42,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
meet(a2,join(a,r1)) = r1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_37]),c_0_15]) ).
cnf(c_0_66,negated_conjecture,
meet(r1,b2) = r1,
inference(spm,[status(thm)],[c_0_14,c_0_47]) ).
cnf(c_0_67,negated_conjecture,
meet(b2,a2) != r1,
inference(rw,[status(thm)],[c_0_63,c_0_19]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_19]),c_0_66]),c_0_19]),c_0_67]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.35 % Problem : LAT005-4 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.37 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.67 % Computer : n031.cluster.edu
% 0.13/0.67 % Model : x86_64 x86_64
% 0.13/0.67 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.67 % Memory : 8042.1875MB
% 0.13/0.67 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.67 % CPULimit : 300
% 0.13/0.68 % WCLimit : 300
% 0.13/0.68 % DateTime : Thu Aug 24 07:16:51 EDT 2023
% 0.13/0.68 % CPUTime :
% 0.23/1.06 start to proof: theBenchmark
% 0.23/1.31 % Version : CSE_E---1.5
% 0.23/1.31 % Problem : theBenchmark.p
% 0.23/1.31 % Proof found
% 0.23/1.31 % SZS status Theorem for theBenchmark.p
% 0.23/1.31 % SZS output start Proof
% See solution above
% 0.23/1.34 % Total time : 0.247000 s
% 0.23/1.34 % SZS output end Proof
% 0.23/1.34 % Total time : 0.249000 s
%------------------------------------------------------------------------------