TSTP Solution File: LAT251-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT251-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n001.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 06:00:13 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 41 unt; 7 typ; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 7 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,
complement: $i > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
zero: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
a: $i ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(equation_H69,axiom,
meet(X1,join(X2,X3)) = join(meet(X1,join(X3,meet(X1,X2))),meet(X1,join(X2,meet(X1,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H69) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
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(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(c_0_14,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_17,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_19,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_20,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_21,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_22,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_23,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_24,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_25,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,axiom,
meet(X1,join(X2,X3)) = join(meet(X1,join(X3,meet(X1,X2))),meet(X1,join(X2,meet(X1,X3)))),
equation_H69 ).
cnf(c_0_27,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_29,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_30,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_31,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_32,plain,
join(meet(X1,X2),meet(X1,join(complement(X1),meet(X1,X2)))) = meet(X1,join(X2,complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_27]),c_0_28]) ).
cnf(c_0_33,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_35,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_36,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_38,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_39,hypothesis,
meet(a,join(complement(a),complement(b))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27]),c_0_22]),c_0_34]),c_0_28]) ).
cnf(c_0_40,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_42,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT251-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 09:36:41 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.066000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.069000 s
%------------------------------------------------------------------------------