TSTP Solution File: LAT013-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT013-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 05:59:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.72s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 43 unt; 5 typ; 0 def)
% Number of atoms : 43 ( 42 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 : 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 : 106 ( 37 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(mckenzie2,axiom,
meet(X1,join(X2,join(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie2) ).
cnf(mckenzie1,axiom,
join(X1,meet(X2,meet(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie1) ).
cnf(mckenzie4,axiom,
meet(meet(join(X1,X2),join(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie4) ).
cnf(mckenzie3,axiom,
join(join(meet(X1,X2),meet(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie3) ).
cnf(prove_associativity_of_meet,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
cnf(c_0_5,axiom,
meet(X1,join(X2,join(X1,X3))) = X1,
mckenzie2 ).
cnf(c_0_6,axiom,
join(X1,meet(X2,meet(X1,X3))) = X1,
mckenzie1 ).
cnf(c_0_7,axiom,
meet(meet(join(X1,X2),join(X2,X3)),X2) = X2,
mckenzie4 ).
cnf(c_0_8,axiom,
join(join(meet(X1,X2),meet(X2,X3)),X2) = X2,
mckenzie3 ).
cnf(c_0_9,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,plain,
join(X1,meet(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_12,plain,
join(meet(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_13,plain,
meet(meet(X1,X2),X1) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
meet(meet(X1,join(meet(X2,X1),X3)),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,plain,
join(meet(X1,X2),X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
meet(meet(X1,meet(X2,X3)),X2) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_17,plain,
meet(join(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_18,plain,
meet(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
join(meet(X1,meet(X2,X3)),X2) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_20,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
join(meet(X1,meet(X2,X3)),X3) = X3,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
meet(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_24,plain,
join(meet(meet(X1,X2),X3),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_25,plain,
join(meet(meet(X1,X2),X3),X2) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,plain,
meet(meet(X1,X2),meet(meet(X2,X3),X1)) = meet(meet(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).
cnf(c_0_27,plain,
join(meet(X1,X2),join(X3,X1)) = join(X3,X1),
inference(spm,[status(thm)],[c_0_25,c_0_9]) ).
cnf(c_0_28,plain,
join(meet(meet(X1,X2),X3),meet(X3,X1)) = meet(X3,X1),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_29,plain,
meet(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_30,plain,
join(meet(X1,X2),meet(meet(X2,X3),X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_26]) ).
cnf(c_0_31,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_21]) ).
cnf(c_0_32,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_17,c_0_6]) ).
cnf(c_0_33,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_31,c_0_11]) ).
cnf(c_0_34,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_18]) ).
cnf(c_0_35,plain,
meet(meet(X1,X2),meet(X3,meet(X2,X1))) = meet(X3,meet(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_36,plain,
meet(meet(X1,X2),X3) = meet(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_33]),c_0_33]) ).
cnf(c_0_37,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
prove_associativity_of_meet ).
cnf(c_0_38,plain,
meet(X1,meet(X2,X3)) = meet(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(rw,[status(thm)],[c_0_37,c_0_21]) ).
cnf(c_0_41,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT013-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34 % Computer : n021.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu Aug 24 05:12:09 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.72 % Version : CSE_E---1.5
% 0.20/0.72 % Problem : theBenchmark.p
% 0.20/0.72 % Proof found
% 0.20/0.72 % SZS status Theorem for theBenchmark.p
% 0.20/0.72 % SZS output start Proof
% See solution above
% 0.20/0.73 % Total time : 0.149000 s
% 0.20/0.73 % SZS output end Proof
% 0.20/0.73 % Total time : 0.151000 s
%------------------------------------------------------------------------------