TSTP Solution File: RNG001-5 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 13:48:20 EDT 2023
% Result : Unsatisfiable 3.43s 3.52s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 64 ( 28 unt; 8 typ; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 104 ( 53 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 6 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 140 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equalish: ( $i * $i ) > $o ).
tff(decl_23,type,
additive_inverse: $i > $i ).
tff(decl_24,type,
add: ( $i * $i ) > $i ).
tff(decl_25,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
multiply: ( $i * $i ) > $i ).
tff(decl_27,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
additive_identity: $i ).
tff(decl_29,type,
a: $i ).
cnf(addition_is_well_defined,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(product_substitution2,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(product_substitution1,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(product_substitution3,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
cnf(prove_multiplicative_identity_axiom,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
cnf(c_0_15,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_16,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_17,plain,
( equalish(X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_19,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_20,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_21,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_22,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_24,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_25,plain,
( product(X1,X2,multiply(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_29,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_30,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_31,plain,
product(X1,add(additive_identity,X2),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_34,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_35,plain,
( sum(X1,multiply(X2,X3),multiply(X2,X4))
| ~ product(X2,X5,X1)
| ~ sum(X5,add(additive_identity,X3),X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
sum(additive_inverse(X1),add(X2,X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_17,c_0_34]) ).
cnf(c_0_38,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X3,additive_inverse(X4),X2)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_39,plain,
( sum(X1,multiply(X2,X3),multiply(X2,additive_identity))
| ~ product(X2,additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
product(X1,additive_inverse(additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_41,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_42,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_43,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_34]) ).
cnf(c_0_44,plain,
sum(multiply(X1,additive_identity),multiply(X1,additive_identity),multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( product(X1,X2,multiply(X3,X2))
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_20]) ).
cnf(c_0_46,plain,
( equalish(X1,X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_42]) ).
cnf(c_0_47,plain,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_49,plain,
product(X1,X2,multiply(add(additive_identity,X1),X2)),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_50,plain,
equalish(additive_identity,multiply(X1,additive_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(add(additive_identity,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
equalish(multiply(X1,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_21,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
~ product(a,additive_identity,additive_identity),
prove_multiplicative_identity_axiom ).
cnf(c_0_54,plain,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG001-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n027.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 : Sun Aug 27 02:54:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 3.43/3.52 % Version : CSE_E---1.5
% 3.43/3.52 % Problem : theBenchmark.p
% 3.43/3.52 % Proof found
% 3.43/3.52 % SZS status Theorem for theBenchmark.p
% 3.43/3.52 % SZS output start Proof
% See solution above
% 3.43/3.53 % Total time : 2.956000 s
% 3.43/3.53 % SZS output end Proof
% 3.43/3.53 % Total time : 2.959000 s
%------------------------------------------------------------------------------