TSTP Solution File: BOO004-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Wed Aug 30 18:05:41 EDT 2023
% Result : Unsatisfiable 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 46 ( 6 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 42 ( 22 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
additive_identity: $i ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
inverse: $i > $i ).
tff(decl_29,type,
x: $i ).
cnf(distributivity8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(prove_both_equalities,negated_conjecture,
~ sum(x,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
cnf(c_0_8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity8 ).
cnf(c_0_9,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_10,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_12,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(X3),X1,multiplicative_identity)
| ~ sum(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_14,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_15,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_16,plain,
( sum(additive_identity,X1,add(X2,X1))
| ~ sum(inverse(X2),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_18,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_20,plain,
sum(additive_identity,X1,add(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_22,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,negated_conjecture,
~ sum(x,x,x),
prove_both_equalities ).
cnf(c_0_24,plain,
sum(X1,X1,X1),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 08:08:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.58 % Total time : 0.011000 s
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 % Total time : 0.014000 s
%------------------------------------------------------------------------------