TSTP Solution File: BOO017-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO017-1 : 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 : n016.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 : Wed Aug 30 18:05:52 EDT 2023
% Result : Unsatisfiable 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 85 ( 40 unt; 10 typ; 0 def)
% Number of atoms : 152 ( 18 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 156 ( 79 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 180 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $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,
additive_identity: $i ).
tff(decl_27,type,
multiplicative_identity: $i ).
tff(decl_28,type,
inverse: $i > $i ).
tff(decl_29,type,
x: $i ).
tff(decl_30,type,
y: $i ).
tff(decl_31,type,
z: $i ).
cnf(distributivity8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
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/Axioms/BOO002-0.ax',distributivity1) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(distributivity7,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity7) ).
cnf(x_plus_y,hypothesis,
sum(x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
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/Axioms/BOO002-0.ax',distributivity3) ).
cnf(prove_product,negated_conjecture,
~ product(x,z,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
cnf(c_0_18,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity8 ).
cnf(c_0_19,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_20,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_22,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(multiplicative_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
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(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_26,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_27,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_30,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,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_32,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_33,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_34,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_25]) ).
cnf(c_0_35,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,plain,
( sum(X1,X2,additive_identity)
| ~ product(inverse(X3),X4,X2)
| ~ product(inverse(X3),X5,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_39,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_40,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_34]),c_0_35]),c_0_36]) ).
cnf(c_0_41,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
distributivity7 ).
cnf(c_0_42,hypothesis,
sum(x,y,z),
x_plus_y ).
cnf(c_0_43,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_44,plain,
( sum(X1,additive_identity,additive_identity)
| ~ product(inverse(X2),X3,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_45,plain,
inverse(multiplicative_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
cnf(c_0_47,plain,
( product(X1,X2,X3)
| ~ sum(inverse(X4),X5,X1)
| ~ sum(additive_identity,X5,X3)
| ~ sum(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_48,hypothesis,
sum(y,x,z),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_49,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_43]) ).
cnf(c_0_50,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_51,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_52,plain,
( sum(X1,additive_identity,additive_identity)
| ~ product(additive_identity,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_53,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_54,hypothesis,
( product(X1,z,X2)
| ~ sum(inverse(y),x,X1)
| ~ sum(additive_identity,x,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_56,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_57,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_58,plain,
sum(multiply(additive_identity,X1),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_52,c_0_50]) ).
cnf(c_0_59,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_60,plain,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_61,hypothesis,
( product(X1,z,x)
| ~ sum(inverse(y),x,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_25]),c_0_55]) ).
cnf(c_0_62,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_58]),c_0_59]) ).
cnf(c_0_64,plain,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_19]),c_0_46])]) ).
cnf(c_0_65,hypothesis,
product(add(x,inverse(y)),z,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_25]),c_0_35]) ).
cnf(c_0_66,plain,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X5),X6,X3)
| ~ sum(X5,X6,X2)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_50]) ).
cnf(c_0_67,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,hypothesis,
sum(x,z,z),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_43]),c_0_67]) ).
cnf(c_0_70,hypothesis,
sum(z,x,z),
inference(spm,[status(thm)],[c_0_26,c_0_68]) ).
cnf(c_0_71,hypothesis,
( product(z,x,X1)
| ~ sum(additive_identity,x,X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,hypothesis,
product(z,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_25]),c_0_55]) ).
cnf(c_0_73,negated_conjecture,
~ product(x,z,x),
prove_product ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_72]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO017-1 : 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 : n016.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 08:38:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.023000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.026000 s
%------------------------------------------------------------------------------