TSTP Solution File: RNG005-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG005-2 : 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 : n023.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 13:48:22 EDT 2023
% Result : Unsatisfiable 2.47s 2.55s
% Output : CNFRefutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 24
% Syntax : Number of formulae : 51 ( 21 unt; 11 typ; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 74 ( 38 ~; 36 |; 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 : 82 ( 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_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
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(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
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(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
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(a_inverse_times_b,hypothesis,
product(additive_inverse(a),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_13,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_14,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_15,axiom,
( sum(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ sum(X3,X4,X1) ),
sum_substitution3 ).
cnf(c_0_16,plain,
( equalish(X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_18,plain,
( sum(additive_identity,X1,X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
sum_substitution2 ).
cnf(c_0_21,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_22,plain,
sum(additive_identity,add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_24,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_25,plain,
( sum(additive_inverse(X1),X2,additive_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_27,hypothesis,
product(additive_inverse(a),b,c),
a_inverse_times_b ).
cnf(c_0_28,axiom,
( equalish(additive_inverse(X1),additive_inverse(X2))
| ~ equalish(X1,X2) ),
additive_inverse_substitution ).
cnf(c_0_29,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_30,plain,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X5,X4,X1)
| ~ sum(X5,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_32,hypothesis,
( product(X1,b,c)
| ~ equalish(additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
equalish(additive_inverse(X1),additive_inverse(add(additive_identity,X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( sum(X1,X2,additive_identity)
| ~ product(additive_inverse(add(additive_identity,X3)),X4,X1)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,hypothesis,
product(additive_inverse(add(additive_identity,a)),b,c),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,hypothesis,
( sum(c,X1,additive_identity)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_37,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_38,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_identity ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n023.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 03:00:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 2.47/2.55 % Version : CSE_E---1.5
% 2.47/2.55 % Problem : theBenchmark.p
% 2.47/2.55 % Proof found
% 2.47/2.55 % SZS status Theorem for theBenchmark.p
% 2.47/2.55 % SZS output start Proof
% See solution above
% 2.47/2.56 % Total time : 1.942000 s
% 2.47/2.56 % SZS output end Proof
% 2.47/2.56 % Total time : 1.944000 s
%------------------------------------------------------------------------------