TSTP Solution File: LAT169-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT169-1 : 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 : n016.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 05:59:51 EDT 2023
% Result : Unsatisfiable 144.85s 144.89s
% Output : CNFRefutation 144.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 41 unt; 5 typ; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 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 : 98 ( 16 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(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(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(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(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(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(equation_H21_dual,axiom,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X2,meet(X1,join(X2,X3))),join(X3,meet(X1,X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H21_dual) ).
cnf(prove_H58,negated_conjecture,
meet(a,join(b,c)) != meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_H58) ).
cnf(c_0_9,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_10,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_11,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_12,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_13,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_16,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_17,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_19,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_20,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_21,plain,
join(X1,meet(join(X1,X2),join(X3,X1))) = meet(join(X1,X2),join(X3,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_23,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_24,plain,
join(X1,meet(join(X2,X3),join(X1,X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_10]) ).
cnf(c_0_26,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_27,plain,
join(X1,meet(join(X2,X3),join(X1,X3))) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_28,axiom,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X2,meet(X1,join(X2,X3))),join(X3,meet(X1,X2)))),
equation_H21_dual ).
cnf(c_0_29,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_30,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_25]),c_0_11]),c_0_11]) ).
cnf(c_0_31,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_16]) ).
cnf(c_0_32,plain,
join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_9]) ).
cnf(c_0_33,plain,
join(X1,meet(join(X2,meet(X1,X3)),join(X3,meet(X1,join(X3,X2))))) = meet(join(X1,X3),join(X1,X2)),
inference(rw,[status(thm)],[c_0_28,c_0_10]) ).
cnf(c_0_34,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_9]),c_0_11]),c_0_11]),c_0_30]) ).
cnf(c_0_35,plain,
meet(join(X1,X2),join(X2,meet(X1,X3))) = join(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_31]),c_0_10]) ).
cnf(c_0_36,plain,
join(X1,meet(join(X1,X2),join(X3,meet(X1,X2)))) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_10]),c_0_35]) ).
cnf(c_0_37,plain,
join(X1,meet(join(X1,X2),join(X3,meet(X2,X1)))) = meet(join(X1,X2),join(X1,X3)),
inference(spm,[status(thm)],[c_0_36,c_0_10]) ).
cnf(c_0_38,negated_conjecture,
meet(a,join(b,c)) != meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),
prove_H58 ).
cnf(c_0_39,plain,
join(X1,meet(join(X2,X1),join(X3,meet(X2,X1)))) = meet(join(X2,X1),join(X1,X3)),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT169-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 24 08:02:38 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.14/0.54 start to proof: theBenchmark
% 144.85/144.89 % Version : CSE_E---1.5
% 144.85/144.89 % Problem : theBenchmark.p
% 144.85/144.89 % Proof found
% 144.85/144.89 % SZS status Theorem for theBenchmark.p
% 144.85/144.89 % SZS output start Proof
% See solution above
% 144.85/144.90 % Total time : 144.361000 s
% 144.85/144.90 % SZS output end Proof
% 144.85/144.90 % Total time : 144.369000 s
%------------------------------------------------------------------------------