TSTP Solution File: RNG040-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG040-2 : 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 : n029.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 13:48:40 EDT 2023
% Result : Unsatisfiable 6.28s 6.35s
% Output : CNFRefutation 6.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 36
% Syntax : Number of formulae : 115 ( 43 unt; 14 typ; 0 def)
% Number of atoms : 193 ( 37 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 179 ( 87 ~; 92 |; 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 : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 191 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $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,
add: ( $i * $i ) > $i ).
tff(decl_27,type,
additive_inverse: $i > $i ).
tff(decl_28,type,
multiplicative_identity: $i ).
tff(decl_29,type,
h: $i > $i ).
tff(decl_30,type,
b: $i ).
tff(decl_31,type,
c: $i ).
tff(decl_32,type,
d: $i ).
tff(decl_33,type,
a: $i ).
tff(decl_34,type,
l: $i ).
tff(decl_35,type,
n: $i ).
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(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
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(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
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_inverse1,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
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(right_multiplicative_identity,hypothesis,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_identity) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
cnf(d_plus_a,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
cnf(product_symmetry,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_symmetry) ).
cnf(c_plus_a,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(b_plus_a,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
cnf(left_multiplicative_identity,hypothesis,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_identity) ).
cnf(clause31,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause31) ).
cnf(b_plus_c,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(prove_equation,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(c_0_22,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_23,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_24,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_25,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_26,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_27,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2 ).
cnf(c_0_29,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_30,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,axiom,
sum(additive_inverse(X1),X1,additive_identity),
additive_inverse1 ).
cnf(c_0_34,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X4,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_35,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_37,plain,
sum(X1,additive_identity,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_38,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_39,hypothesis,
product(X1,multiplicative_identity,X1),
right_multiplicative_identity ).
cnf(c_0_40,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_33]) ).
cnf(c_0_41,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X3,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]) ).
cnf(c_0_42,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_35]) ).
cnf(c_0_43,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_45,negated_conjecture,
product(d,a,additive_identity),
d_plus_a ).
cnf(c_0_46,plain,
( X1 = additive_identity
| ~ sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
cnf(c_0_48,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
product_symmetry ).
cnf(c_0_49,negated_conjecture,
product(c,a,n),
c_plus_a ).
cnf(c_0_50,negated_conjecture,
( product(X1,a,X2)
| ~ product(X3,additive_identity,X2)
| ~ product(X3,d,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_52,hypothesis,
( X1 = additive_identity
| ~ product(X2,additive_identity,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_39])]) ).
cnf(c_0_53,negated_conjecture,
product(a,c,n),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( product(X1,a,multiply(X2,additive_identity))
| ~ product(X2,d,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
product(b,a,l),
b_plus_a ).
cnf(c_0_57,negated_conjecture,
( product(X1,c,X2)
| ~ product(X3,n,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
cnf(c_0_58,hypothesis,
product(multiplicative_identity,X1,X1),
left_multiplicative_identity ).
cnf(c_0_59,negated_conjecture,
( product(X1,a,additive_identity)
| ~ product(X2,d,X1) ),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
clause31 ).
cnf(c_0_61,negated_conjecture,
product(a,b,l),
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
cnf(c_0_62,plain,
sum(X1,add(additive_inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_63,negated_conjecture,
sum(b,c,d),
b_plus_c ).
cnf(c_0_64,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_65,hypothesis,
( product(X1,c,n)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,hypothesis,
( d = additive_identity
| product(multiplicative_identity,a,additive_identity) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,hypothesis,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_68,negated_conjecture,
( product(X1,b,X2)
| ~ product(X3,l,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_61]) ).
cnf(c_0_69,plain,
( X1 = X2
| ~ sum(X3,add(additive_inverse(X3),X2),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_62]) ).
cnf(c_0_70,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_71,negated_conjecture,
( X1 = d
| ~ sum(b,c,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_63]) ).
cnf(c_0_72,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_73,hypothesis,
( d = additive_identity
| product(additive_identity,c,n) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_75,hypothesis,
( product(X1,b,l)
| ~ product(multiplicative_identity,a,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_58]) ).
cnf(c_0_76,plain,
( X1 = X2
| ~ sum(X3,X1,add(X3,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_42]) ).
cnf(c_0_77,negated_conjecture,
add(b,c) = d,
inference(spm,[status(thm)],[c_0_71,c_0_26]) ).
cnf(c_0_78,negated_conjecture,
product(a,d,additive_identity),
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_79,negated_conjecture,
~ sum(l,n,additive_identity),
prove_equation ).
cnf(c_0_80,hypothesis,
( d = additive_identity
| n = additive_identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_81,hypothesis,
( d = additive_identity
| product(additive_identity,b,l) ),
inference(spm,[status(thm)],[c_0_75,c_0_66]) ).
cnf(c_0_82,negated_conjecture,
( X1 = c
| ~ sum(b,X1,d) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( sum(X1,X2,additive_identity)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,d) ),
inference(spm,[status(thm)],[c_0_38,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
( d = additive_identity
| ~ sum(l,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,hypothesis,
( d = additive_identity
| l = additive_identity ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_81]),c_0_74]) ).
cnf(c_0_86,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_87,negated_conjecture,
( additive_inverse(X1) = c
| ~ sum(d,X1,b) ),
inference(spm,[status(thm)],[c_0_82,c_0_41]) ).
cnf(c_0_88,negated_conjecture,
( sum(X1,l,additive_identity)
| ~ product(a,X2,X1)
| ~ sum(X2,b,d) ),
inference(spm,[status(thm)],[c_0_83,c_0_61]) ).
cnf(c_0_89,negated_conjecture,
d = additive_identity,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_90,negated_conjecture,
( sum(c,X1,additive_identity)
| ~ sum(d,X1,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( sum(X1,l,additive_identity)
| ~ product(a,X2,X1)
| ~ sum(X2,b,additive_identity) ),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_92,negated_conjecture,
( sum(c,X1,additive_identity)
| ~ sum(additive_identity,X1,b) ),
inference(rw,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_93,plain,
( additive_inverse(X1) = X2
| ~ sum(add(X3,X2),X1,X3) ),
inference(spm,[status(thm)],[c_0_76,c_0_41]) ).
cnf(c_0_94,negated_conjecture,
( sum(X1,l,additive_identity)
| ~ product(a,c,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_23])]) ).
cnf(c_0_95,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_96,negated_conjecture,
( X1 = n
| ~ product(a,c,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_53]) ).
cnf(c_0_97,negated_conjecture,
( additive_inverse(l) = X1
| ~ product(a,c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_98,negated_conjecture,
multiply(a,c) = n,
inference(spm,[status(thm)],[c_0_96,c_0_51]) ).
cnf(c_0_99,negated_conjecture,
additive_inverse(l) = n,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_51]),c_0_98]) ).
cnf(c_0_100,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_99]),c_0_79]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG040-2 : 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
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 01:57:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 6.28/6.35 % Version : CSE_E---1.5
% 6.28/6.35 % Problem : theBenchmark.p
% 6.28/6.35 % Proof found
% 6.28/6.35 % SZS status Theorem for theBenchmark.p
% 6.28/6.35 % SZS output start Proof
% See solution above
% 6.28/6.36 % Total time : 5.799000 s
% 6.28/6.36 % SZS output end Proof
% 6.28/6.36 % Total time : 5.802000 s
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