TSTP Solution File: RNG037-2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG037-2 : 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 : n007.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 13:48:39 EDT 2023
% Result : Unsatisfiable 1.98s 2.05s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 55 ( 23 unt; 11 typ; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 78 ( 40 ~; 38 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 2 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 ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
d: $i ).
tff(decl_32,type,
c: $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_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(sum_substitution3,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(sum_substitution2,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).
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(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
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(a_inverse_times_b,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(additive_inverse_substitution,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_substitution) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(c_0_14,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_15,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_16,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_17,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_18,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3 ).
cnf(c_0_19,plain,
( equalish(X1,X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2 ).
cnf(c_0_22,plain,
( sum(X1,additive_identity,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_23,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
sum_substitution2 ).
cnf(c_0_25,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_26,plain,
sum(add(additive_identity,X1),additive_identity,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,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_28,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_29,plain,
( sum(additive_inverse(X1),X2,additive_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_31,hypothesis,
product(a,additive_inverse(b),c),
a_inverse_times_b ).
cnf(c_0_32,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
additive_inverse_substitution ).
cnf(c_0_33,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_34,plain,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_36,hypothesis,
( product(a,X1,c)
| ~ equalish(additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
equalish(additive_inverse(X1),additive_inverse(add(additive_identity,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( sum(X1,X2,additive_identity)
| ~ product(X3,additive_inverse(add(additive_identity,X4)),X1)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,hypothesis,
product(a,additive_inverse(add(additive_identity,b)),c),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,hypothesis,
( sum(c,X1,additive_identity)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_42,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_identity ).
cnf(c_0_43,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG037-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 02:56:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.65 start to proof: theBenchmark
% 1.98/2.05 % Version : CSE_E---1.5
% 1.98/2.05 % Problem : theBenchmark.p
% 1.98/2.05 % Proof found
% 1.98/2.05 % SZS status Theorem for theBenchmark.p
% 1.98/2.05 % SZS output start Proof
% See solution above
% 1.98/2.05 % Total time : 1.390000 s
% 1.98/2.05 % SZS output end Proof
% 1.98/2.05 % Total time : 1.394000 s
%------------------------------------------------------------------------------