TSTP Solution File: RNG008-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG008-1 : 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 : n015.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 13:48:24 EDT 2023
% Result : Unsatisfiable 0.83s 0.90s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 27
% Syntax : Number of formulae : 153 ( 74 unt; 9 typ; 0 def)
% Number of atoms : 281 ( 40 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 276 ( 139 ~; 137 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 311 ( 7 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,
a: $i ).
tff(decl_29,type,
b: $i ).
tff(decl_30,type,
c: $i ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
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/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_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/Axioms/RNG001-0.ax',distributivity1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
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/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
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/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
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/RNG001-0.ax',distributivity3) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(associativity_of_multiplication1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication1) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_0_18,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_19,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_20,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_21,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_22,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_23,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_24,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,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_29,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_30,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_31,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_32,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_27]) ).
cnf(c_0_33,plain,
( sum(X1,X2,X3)
| ~ product(X4,additive_identity,X1)
| ~ product(X4,X5,X3)
| ~ product(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_34,hypothesis,
( X1 = X2
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_36,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_37,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_38,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(X4))
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_39,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_40,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_41,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_42,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,additive_identity,X1)
| ~ product(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_43,hypothesis,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_45,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_46,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,additive_inverse(X2),additive_inverse(X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_47,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_48,hypothesis,
( sum(X1,X2,X2)
| ~ product(X2,additive_identity,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_35]),c_0_43]) ).
cnf(c_0_49,hypothesis,
( product(X1,b,c)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_37]) ).
cnf(c_0_50,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_51,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,hypothesis,
sum(multiply(X1,additive_identity),X1,X1),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
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,plain,
( sum(X1,X2,X3)
| ~ product(X4,additive_inverse(X5),X1)
| ~ product(X4,additive_identity,X3)
| ~ product(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_55,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_35]),c_0_50]) ).
cnf(c_0_56,hypothesis,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( sum(X1,X2,X3)
| ~ product(additive_identity,X4,X1)
| ~ product(X5,X4,X3)
| ~ product(X5,X4,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_19]) ).
cnf(c_0_58,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_59,hypothesis,
( sum(X1,c,X2)
| ~ product(c,additive_inverse(b),X1)
| ~ product(c,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_56]),c_0_27]) ).
cnf(c_0_61,hypothesis,
( sum(X1,X2,X3)
| ~ product(additive_identity,X3,X1)
| ~ product(X3,X3,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_30]) ).
cnf(c_0_62,plain,
( X1 = X2
| ~ sum(add(additive_inverse(X3),X2),X3,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_58]) ).
cnf(c_0_63,hypothesis,
( sum(X1,c,additive_identity)
| ~ product(c,additive_inverse(b),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_35]),c_0_60]) ).
cnf(c_0_64,hypothesis,
( sum(X1,X2,X2)
| ~ product(additive_identity,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_35]),c_0_43]) ).
cnf(c_0_65,plain,
( X1 = X2
| ~ sum(add(X3,X2),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_47]) ).
cnf(c_0_66,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_25]) ).
cnf(c_0_67,hypothesis,
sum(multiply(c,additive_inverse(b)),c,additive_identity),
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_68,hypothesis,
sum(multiply(additive_identity,X1),X1,X1),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_69,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_21]),c_0_66]) ).
cnf(c_0_70,hypothesis,
add(c,multiply(c,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_67]),c_0_66]) ).
cnf(c_0_71,hypothesis,
sum(multiply(additive_identity,X1),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_51,c_0_68]) ).
cnf(c_0_72,hypothesis,
multiply(c,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_27]) ).
cnf(c_0_73,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_74,plain,
( sum(X1,X2,X3)
| ~ product(additive_inverse(X4),X5,X1)
| ~ product(additive_identity,X5,X3)
| ~ product(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
cnf(c_0_75,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_71]),c_0_27]) ).
cnf(c_0_76,hypothesis,
product(c,additive_inverse(b),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_35,c_0_72]) ).
cnf(c_0_77,hypothesis,
( product(X1,X2,X3)
| ~ product(X1,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_30]) ).
cnf(c_0_78,hypothesis,
( sum(X1,X2,X3)
| ~ product(additive_inverse(X2),X2,X1)
| ~ product(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_30]) ).
cnf(c_0_79,hypothesis,
product(additive_identity,X1,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_75]) ).
cnf(c_0_80,hypothesis,
( X1 = additive_inverse(c)
| ~ product(c,additive_inverse(b),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_76]) ).
cnf(c_0_81,hypothesis,
product(X1,X2,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_77,c_0_35]) ).
cnf(c_0_82,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,hypothesis,
multiply(c,additive_inverse(c)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_72]) ).
cnf(c_0_84,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_85,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_86,hypothesis,
( sum(X1,additive_inverse(X2),additive_identity)
| ~ product(X2,additive_inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_47]) ).
cnf(c_0_87,hypothesis,
product(c,additive_inverse(c),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_35,c_0_83]) ).
cnf(c_0_88,plain,
( sum(X1,X2,X3)
| ~ product(add(X4,X5),X6,X3)
| ~ product(X5,X6,X2)
| ~ product(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_21]) ).
cnf(c_0_89,plain,
( sum(X1,additive_identity,additive_inverse(X2))
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,hypothesis,
sum(additive_inverse(c),additive_inverse(c),additive_identity),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,hypothesis,
( sum(X1,c,X2)
| ~ product(add(X3,c),b,X2)
| ~ product(X3,b,X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_55]) ).
cnf(c_0_92,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_93,hypothesis,
sum(additive_inverse(c),additive_identity,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_47]) ).
cnf(c_0_94,hypothesis,
( sum(c,c,X1)
| ~ product(add(a,c),b,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_37]) ).
cnf(c_0_95,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_92,c_0_25]) ).
cnf(c_0_96,hypothesis,
additive_inverse(c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_93]),c_0_27]) ).
cnf(c_0_97,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1 ).
cnf(c_0_98,hypothesis,
sum(c,c,multiply(add(a,c),b)),
inference(spm,[status(thm)],[c_0_94,c_0_35]) ).
cnf(c_0_99,hypothesis,
add(c,c) = additive_identity,
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_100,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_97,c_0_35]) ).
cnf(c_0_101,hypothesis,
multiply(add(a,c),b) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_98]),c_0_99]) ).
cnf(c_0_102,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_97,c_0_30]) ).
cnf(c_0_103,plain,
( product(X1,multiply(X2,X3),multiply(X4,X3))
| ~ product(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_100,c_0_35]) ).
cnf(c_0_104,hypothesis,
product(add(a,c),b,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_101]) ).
cnf(c_0_105,hypothesis,
( product(X1,multiply(X2,X3),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_102,c_0_35]) ).
cnf(c_0_106,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_107,hypothesis,
product(add(a,c),multiply(b,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_75]) ).
cnf(c_0_108,hypothesis,
( product(c,X1,X2)
| ~ product(a,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_37]) ).
cnf(c_0_109,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_105,c_0_35]) ).
cnf(c_0_110,hypothesis,
multiply(add(a,c),multiply(b,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_108,c_0_35]) ).
cnf(c_0_112,hypothesis,
product(b,additive_identity,multiply(b,add(a,c))),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_113,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_106,c_0_111]) ).
cnf(c_0_114,hypothesis,
multiply(b,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_112]),c_0_60]) ).
cnf(c_0_115,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_116,plain,
( sum(X1,X2,X3)
| ~ product(X4,add(X5,X6),X3)
| ~ product(X4,X6,X2)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_117,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_60]) ).
cnf(c_0_118,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_115]),c_0_66]) ).
cnf(c_0_119,hypothesis,
( sum(X1,c,X2)
| ~ product(c,add(X3,b),X2)
| ~ product(c,X3,X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_55]) ).
cnf(c_0_120,hypothesis,
( sum(X1,X2,X3)
| ~ product(X2,add(X4,X2),X3)
| ~ product(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_116,c_0_30]) ).
cnf(c_0_121,hypothesis,
product(c,add(a,c),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_117]) ).
cnf(c_0_122,hypothesis,
add(c,add(X1,c)) = X1,
inference(spm,[status(thm)],[c_0_118,c_0_96]) ).
cnf(c_0_123,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_124,hypothesis,
( sum(c,c,X1)
| ~ product(c,add(b,c),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_30]),c_0_66]) ).
cnf(c_0_125,hypothesis,
( sum(additive_identity,c,X1)
| ~ product(c,a,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_66]),c_0_122]) ).
cnf(c_0_126,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_19]) ).
cnf(c_0_127,hypothesis,
sum(c,c,multiply(c,add(b,c))),
inference(spm,[status(thm)],[c_0_124,c_0_35]) ).
cnf(c_0_128,hypothesis,
sum(additive_identity,c,multiply(c,a)),
inference(spm,[status(thm)],[c_0_125,c_0_35]) ).
cnf(c_0_129,plain,
( product(add(X1,X2),X3,X4)
| ~ product(X1,X3,additive_identity)
| ~ product(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_126,c_0_21]) ).
cnf(c_0_130,hypothesis,
multiply(c,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_127]),c_0_99]) ).
cnf(c_0_131,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_109,c_0_113]) ).
cnf(c_0_132,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_128]),c_0_41]) ).
cnf(c_0_133,hypothesis,
( product(add(X1,X2),X2,X2)
| ~ product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_129,c_0_30]) ).
cnf(c_0_134,hypothesis,
product(c,add(b,c),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_130]) ).
cnf(c_0_135,hypothesis,
product(b,c,multiply(b,a)),
inference(rw,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_136,hypothesis,
product(b,add(b,c),add(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_122]) ).
cnf(c_0_137,hypothesis,
( sum(multiply(b,a),b,X1)
| ~ product(b,add(b,c),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_135]),c_0_66]) ).
cnf(c_0_138,hypothesis,
multiply(b,add(b,c)) = add(b,c),
inference(spm,[status(thm)],[c_0_106,c_0_136]) ).
cnf(c_0_139,hypothesis,
sum(multiply(b,a),b,add(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_35]),c_0_138]) ).
cnf(c_0_140,hypothesis,
add(b,multiply(b,a)) = add(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_139]),c_0_66]) ).
cnf(c_0_141,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_140]),c_0_69]) ).
cnf(c_0_142,negated_conjecture,
~ product(b,a,c),
prove_b_times_a_is_c ).
cnf(c_0_143,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_141]),c_0_142]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : RNG008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n015.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 01:59:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.83/0.90 % Version : CSE_E---1.5
% 0.83/0.90 % Problem : theBenchmark.p
% 0.83/0.90 % Proof found
% 0.83/0.90 % SZS status Theorem for theBenchmark.p
% 0.83/0.90 % SZS output start Proof
% See solution above
% 0.83/0.91 % Total time : 0.310000 s
% 0.83/0.91 % SZS output end Proof
% 0.83/0.91 % Total time : 0.313000 s
%------------------------------------------------------------------------------