TSTP Solution File: RNG004-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG004-3 : 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 : n008.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 117.55s 117.71s
% Output : CNFRefutation 117.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 33
% Syntax : Number of formulae : 103 ( 47 unt; 11 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 170 ( 86 ~; 84 |; 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 : 215 ( 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 ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
c: $i ).
tff(decl_32,type,
d: $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(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(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
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(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(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
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(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_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_times_b,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
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_c_equals_d,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_22,axiom,
( equalish(X3,X4)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_23,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_24,axiom,
( sum(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ sum(X3,X1,X4) ),
sum_substitution2 ).
cnf(c_0_25,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_26,plain,
( equalish(X1,add(X2,X3))
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_28,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_29,plain,
( sum(X1,X2,X1)
| ~ equalish(additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
equalish(additive_identity,add(additive_inverse(X1),X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_32,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_33,plain,
( sum(X1,X2,X3)
| ~ sum(X4,add(X5,X2),X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_34,plain,
sum(X1,add(additive_inverse(X2),X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( equalish(X1,X2)
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_36,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X4,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_37,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
equalish(additive_identity,additive_inverse(additive_identity)),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_39,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_40,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_41,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_42,axiom,
( product(X3,X2,X4)
| ~ equalish(X1,X2)
| ~ product(X3,X1,X4) ),
product_substitution2 ).
cnf(c_0_43,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_44,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_45,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_46,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_47,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_48,plain,
sum(X1,additive_inverse(additive_identity),X1),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_49,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_39,c_0_40]) ).
cnf(c_0_50,plain,
sum(add(X1,X2),additive_inverse(X2),X1),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_51,plain,
( product(X1,X2,multiply(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_54,plain,
sum(X1,add(X2,additive_inverse(X1)),X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
( sum(X1,X2,add(X1,X3))
| ~ equalish(X3,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_56,plain,
equalish(X1,add(X1,additive_inverse(additive_identity))),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
cnf(c_0_57,plain,
( sum(X1,X2,additive_identity)
| ~ product(X3,add(additive_identity,X4),X1)
| ~ product(X3,additive_inverse(X4),X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_58,plain,
product(X1,add(additive_identity,X2),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
equalish(additive_identity,add(X1,additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
cnf(c_0_60,plain,
( sum(X1,X2,X3)
| ~ sum(X4,add(X3,additive_inverse(X5)),X2)
| ~ sum(X1,X4,X5) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
sum(X1,add(X2,additive_inverse(additive_identity)),add(X1,X2)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
( sum(multiply(X1,X2),X3,additive_identity)
| ~ product(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
a_inverse_times_b_inverse ).
cnf(c_0_64,plain,
sum(X1,add(X2,additive_inverse(X2)),X1),
inference(spm,[status(thm)],[c_0_29,c_0_59]) ).
cnf(c_0_65,plain,
( sum(X1,add(X2,X3),X3)
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,hypothesis,
sum(multiply(additive_inverse(a),b),d,additive_identity),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,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_68,axiom,
product(additive_identity,X1,additive_identity),
multiplicative_identity1 ).
cnf(c_0_69,axiom,
( product(X2,X3,X4)
| ~ equalish(X1,X2)
| ~ product(X1,X3,X4) ),
product_substitution1 ).
cnf(c_0_70,hypothesis,
product(a,b,c),
a_times_b ).
cnf(c_0_71,plain,
( equalish(X1,X2)
| ~ sum(X2,add(X3,additive_inverse(X3)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_64]) ).
cnf(c_0_72,hypothesis,
sum(multiply(additive_inverse(a),b),add(d,X1),X1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,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_67,c_0_68]) ).
cnf(c_0_74,hypothesis,
( product(X1,b,c)
| ~ equalish(a,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,axiom,
( product(X3,X4,X2)
| ~ equalish(X1,X2)
| ~ product(X3,X4,X1) ),
product_substitution3 ).
cnf(c_0_76,hypothesis,
equalish(additive_inverse(d),multiply(additive_inverse(a),b)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,plain,
( sum(additive_inverse(X1),X2,additive_identity)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_78,plain,
( sum(X1,X2,additive_identity)
| ~ product(add(additive_identity,X3),X4,X1)
| ~ product(additive_inverse(X3),X4,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_50]) ).
cnf(c_0_79,hypothesis,
product(add(additive_identity,a),b,c),
inference(spm,[status(thm)],[c_0_74,c_0_52]) ).
cnf(c_0_80,plain,
( product(X1,X2,X3)
| ~ equalish(multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_75,c_0_43]) ).
cnf(c_0_81,hypothesis,
equalish(multiply(additive_inverse(a),b),additive_inverse(d)),
inference(spm,[status(thm)],[c_0_44,c_0_76]) ).
cnf(c_0_82,plain,
sum(additive_inverse(X1),add(X1,additive_inverse(additive_identity)),additive_identity),
inference(spm,[status(thm)],[c_0_77,c_0_56]) ).
cnf(c_0_83,hypothesis,
( sum(c,X1,additive_identity)
| ~ product(additive_inverse(a),b,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,hypothesis,
product(additive_inverse(a),b,additive_inverse(d)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X1,additive_inverse(X2),additive_identity) ),
inference(spm,[status(thm)],[c_0_60,c_0_82]) ).
cnf(c_0_86,hypothesis,
sum(c,additive_inverse(d),additive_identity),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,plain,
( equalish(X1,X2)
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_88,hypothesis,
sum(c,additive_identity,d),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,hypothesis,
equalish(d,c),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_90,negated_conjecture,
~ equalish(c,d),
prove_c_equals_d ).
cnf(c_0_91,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_89]),c_0_90]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG004-3 : 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
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 02:36:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 117.55/117.71 % Version : CSE_E---1.5
% 117.55/117.71 % Problem : theBenchmark.p
% 117.55/117.71 % Proof found
% 117.55/117.71 % SZS status Theorem for theBenchmark.p
% 117.55/117.71 % SZS output start Proof
% See solution above
% 117.59/117.72 % Total time : 116.978000 s
% 117.59/117.72 % SZS output end Proof
% 117.59/117.72 % Total time : 116.985000 s
%------------------------------------------------------------------------------