TSTP Solution File: LAT241-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n023.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 06:00:10 EDT 2023
% Result : Unsatisfiable 78.10s 78.09s
% Output : CNFRefutation 78.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 60 ( 52 unt; 8 typ; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 80 ( 15 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
meet: ( $i * $i ) > $i ).
tff(decl_24,type,
join: ( $i * $i ) > $i ).
tff(decl_25,type,
complement: $i > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
zero: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
a: $i ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
cnf(equation_H51,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H51) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
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,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',meet_join_complement) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c_0_13,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_14,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_15,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_16,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_19,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_20,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_22,hypothesis,
join(a,join(b,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_24,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_25,hypothesis,
meet(a,join(b,X1)) = a,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_27,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_24]) ).
cnf(c_0_28,hypothesis,
join(b,join(X1,a)) = join(b,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_25]),c_0_19]) ).
cnf(c_0_29,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_30,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_31,axiom,
meet(X1,join(X2,meet(X3,join(X1,X4)))) = meet(X1,join(X2,join(meet(X1,X3),meet(X3,X4)))),
equation_H51 ).
cnf(c_0_32,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_33,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_34,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_36,plain,
meet(X1,join(X2,meet(complement(X1),join(X1,X3)))) = meet(X1,join(X2,meet(complement(X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_24]),c_0_32]) ).
cnf(c_0_37,hypothesis,
join(b,complement(a)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_23]),c_0_34]) ).
cnf(c_0_38,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_39,hypothesis,
meet(b,join(X1,meet(complement(a),complement(b)))) = meet(b,join(X1,complement(b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26]),c_0_14]) ).
cnf(c_0_40,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_32]) ).
cnf(c_0_41,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_42,hypothesis,
meet(b,join(complement(a),complement(b))) = meet(b,complement(a)),
inference(spm,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_43,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_14]) ).
cnf(c_0_44,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_45,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_46,axiom,
ifeq(join(X1,X2),one,ifeq(meet(X1,X2),zero,complement(X1),X2),X2) = X2,
meet_join_complement ).
cnf(c_0_47,hypothesis,
meet(a,join(complement(a),complement(b))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_48,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_23]),c_0_29]) ).
cnf(c_0_49,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_50,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]),c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT241-10 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n023.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 05:24:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.44/0.61 start to proof: theBenchmark
% 78.10/78.09 % Version : CSE_E---1.5
% 78.10/78.09 % Problem : theBenchmark.p
% 78.10/78.09 % Proof found
% 78.10/78.09 % SZS status Theorem for theBenchmark.p
% 78.10/78.09 % SZS output start Proof
% See solution above
% 78.10/78.10 % Total time : 77.479000 s
% 78.10/78.10 % SZS output end Proof
% 78.10/78.10 % Total time : 77.485000 s
%------------------------------------------------------------------------------