TSTP Solution File: BOO014-3 by E-SAT---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:18:31 EDT 2023
% Result : Unsatisfiable 9.00s 1.55s
% Output : CNFRefutation 9.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 24
% Syntax : Number of clauses : 151 ( 89 unt; 0 nHn; 104 RR)
% Number of literals : 281 ( 46 equ; 134 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 285 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
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/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_identity2) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',addition_is_well_defined) ).
cnf(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',closure_of_addition) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',commutativity_of_addition) ).
cnf(inverse_is_self_cancelling,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',inverse_is_self_cancelling) ).
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/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplication_is_well_defined) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',commutativity_of_multiplication) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_identity2) ).
cnf(x_inverse_times_y_inverse,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',x_inverse_times_y_inverse) ).
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/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity7) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_identity1) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',additive_inverse2) ).
cnf(x_plus_y,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',x_plus_y) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_inverse1) ).
cnf(distributivity6,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity6) ).
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/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',distributivity4) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',multiplicative_inverse2) ).
cnf(inverse_is_unique,axiom,
( X2 = X3
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ product(X1,X2,additive_identity)
| ~ product(X1,X3,additive_identity) ),
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',inverse_is_unique) ).
cnf(prove_equation,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p',prove_equation) ).
cnf(c_0_24,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_25,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_28,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_29,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_30,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(multiplicative_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_32,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_33,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_36,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_37,plain,
add(inverse(X1),X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_38,axiom,
inverse(inverse(X1)) = X1,
inverse_is_self_cancelling ).
cnf(c_0_39,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,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_43,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_40]),c_0_41]) ).
cnf(c_0_44,plain,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
cnf(c_0_45,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_46,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_47,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_48,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_49,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_50,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_45])]) ).
cnf(c_0_51,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_53,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_54,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_50,c_0_47]) ).
cnf(c_0_55,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
x_inverse_times_y_inverse ).
cnf(c_0_56,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_57,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,hypothesis,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_48,c_0_55]) ).
cnf(c_0_60,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_56,c_0_47]) ).
cnf(c_0_61,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_62,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,hypothesis,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_50,c_0_59]) ).
cnf(c_0_64,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_65,hypothesis,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
inference(spm,[status(thm)],[c_0_32,c_0_63]) ).
cnf(c_0_66,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_61]) ).
cnf(c_0_67,hypothesis,
( product(inverse(y),x_inverse_times_y_inverse,X1)
| ~ sum(additive_identity,x_inverse_times_y_inverse,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_69,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X5,X2,multiplicative_identity)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_70,hypothesis,
product(inverse(y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_68]) ).
cnf(c_0_71,hypothesis,
( sum(x_inverse_times_y_inverse,X1,X2)
| ~ sum(inverse(y),X1,X2)
| ~ sum(x_inverse_times_y_inverse,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_73,hypothesis,
( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
| ~ sum(inverse(y),inverse(x_inverse_times_y_inverse),X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_74,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(y),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_73,c_0_31]) ).
cnf(c_0_75,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X5,X6,X1)
| ~ sum(X6,X2,X4)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_76,hypothesis,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_74]),c_0_41]) ).
cnf(c_0_77,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_27]) ).
cnf(c_0_78,hypothesis,
( sum(x_inverse_times_y_inverse,X1,multiply(X2,X3))
| ~ sum(inverse(y),X1,X3)
| ~ sum(inverse(x),X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_55]) ).
cnf(c_0_79,hypothesis,
sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_80,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_47]) ).
cnf(c_0_81,hypothesis,
( sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),X1)
| ~ sum(inverse(x),inverse(x_inverse_times_y_inverse),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_82,hypothesis,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_83,plain,
( product(add(X1,X2),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_31]) ).
cnf(c_0_84,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_85,hypothesis,
sum(x_inverse_times_y_inverse,inverse(x_inverse_times_y_inverse),add(inverse(x),inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_81,c_0_31]) ).
cnf(c_0_86,hypothesis,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_32,c_0_82]) ).
cnf(c_0_87,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_40]) ).
cnf(c_0_88,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_31]),c_0_68]) ).
cnf(c_0_89,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(X3),X1,multiplicative_identity)
| ~ sum(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_84]) ).
cnf(c_0_90,hypothesis,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_85]),c_0_41]) ).
cnf(c_0_91,hypothesis,
( product(x_plus_y,x,X1)
| ~ sum(additive_identity,x,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_86]) ).
cnf(c_0_92,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_87,c_0_57]) ).
cnf(c_0_93,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_88]),c_0_57]) ).
cnf(c_0_94,plain,
( sum(additive_identity,X1,add(X2,X1))
| ~ sum(inverse(X2),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_89,c_0_31]) ).
cnf(c_0_95,hypothesis,
sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_90]) ).
cnf(c_0_96,hypothesis,
product(x_plus_y,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_31]),c_0_68]) ).
cnf(c_0_97,plain,
sum(X1,multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_31,c_0_92]) ).
cnf(c_0_98,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_93,c_0_40]) ).
cnf(c_0_99,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(x,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,hypothesis,
sum(additive_identity,inverse(x_inverse_times_y_inverse),add(y,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_94,c_0_79]) ).
cnf(c_0_101,hypothesis,
( sum(x,X1,multiply(X2,X3))
| ~ sum(x,X1,X3)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_96]) ).
cnf(c_0_102,plain,
sum(add(X1,X2),X1,add(X1,X2)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_103,hypothesis,
add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_99]),c_0_68]) ).
cnf(c_0_104,hypothesis,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_100]),c_0_68]) ).
cnf(c_0_105,hypothesis,
( sum(x,inverse(x),X1)
| ~ sum(x_plus_y,inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_72]),c_0_80]) ).
cnf(c_0_106,hypothesis,
( product(X1,x_plus_y,X2)
| ~ sum(multiply(X3,y),x,X2)
| ~ sum(X3,x,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_86]) ).
cnf(c_0_107,hypothesis,
sum(inverse(x_inverse_times_y_inverse),x,inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,hypothesis,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(spm,[status(thm)],[c_0_98,c_0_104]) ).
cnf(c_0_109,hypothesis,
( X1 = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_82]) ).
cnf(c_0_110,axiom,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity6 ).
cnf(c_0_111,hypothesis,
sum(x,inverse(x),add(x_plus_y,inverse(x))),
inference(spm,[status(thm)],[c_0_105,c_0_31]) ).
cnf(c_0_112,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_113,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_114,hypothesis,
( product(inverse(x_inverse_times_y_inverse),x_plus_y,X1)
| ~ sum(y,x,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_57]),c_0_108]) ).
cnf(c_0_115,hypothesis,
add(x,y) = x_plus_y,
inference(spm,[status(thm)],[c_0_109,c_0_31]) ).
cnf(c_0_116,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X5,X6,X2)
| ~ sum(X1,X6,X4)
| ~ sum(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_47]) ).
cnf(c_0_117,hypothesis,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_111]),c_0_41]) ).
cnf(c_0_118,plain,
( product(X1,inverse(X2),X3)
| ~ product(X4,inverse(X2),X5)
| ~ sum(X5,additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_119,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_31]),c_0_40]),c_0_115]) ).
cnf(c_0_120,hypothesis,
( sum(X1,x_inverse_times_y_inverse,multiply(X2,X3))
| ~ sum(X1,inverse(x),X3)
| ~ sum(X1,inverse(y),X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_59]) ).
cnf(c_0_121,hypothesis,
sum(x_plus_y,inverse(x),multiplicative_identity),
inference(spm,[status(thm)],[c_0_31,c_0_117]) ).
cnf(c_0_122,plain,
( product(X1,inverse(X2),X3)
| ~ sum(multiply(X4,inverse(X2)),additive_identity,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_47]) ).
cnf(c_0_123,hypothesis,
sum(x_plus_y,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_50,c_0_119]) ).
cnf(c_0_124,plain,
( X1 = additive_identity
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_84]) ).
cnf(c_0_125,hypothesis,
( sum(x_plus_y,x_inverse_times_y_inverse,X1)
| ~ sum(x_plus_y,inverse(y),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_80]) ).
cnf(c_0_126,hypothesis,
( product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,X1)
| ~ sum(multiply(x_plus_y,x_inverse_times_y_inverse),additive_identity,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_38]),c_0_38]) ).
cnf(c_0_127,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_31]) ).
cnf(c_0_128,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(spm,[status(thm)],[c_0_124,c_0_47]) ).
cnf(c_0_129,hypothesis,
sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
inference(spm,[status(thm)],[c_0_125,c_0_31]) ).
cnf(c_0_130,hypothesis,
( product(x_plus_y,y,X1)
| ~ sum(additive_identity,y,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_82]) ).
cnf(c_0_131,hypothesis,
product(inverse(x_inverse_times_y_inverse),x_inverse_times_y_inverse,multiply(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_31]),c_0_127]) ).
cnf(c_0_132,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_128,c_0_38]) ).
cnf(c_0_133,plain,
( sum(multiply(X1,X2),X3,multiply(X4,X5))
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_75,c_0_47]) ).
cnf(c_0_134,hypothesis,
add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_35,c_0_129]) ).
cnf(c_0_135,hypothesis,
product(x_plus_y,y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_31]),c_0_68]) ).
cnf(c_0_136,axiom,
( X2 = X3
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(X1,X3,multiplicative_identity)
| ~ product(X1,X2,additive_identity)
| ~ product(X1,X3,additive_identity) ),
inverse_is_unique ).
cnf(c_0_137,hypothesis,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_131]),c_0_57]),c_0_132]) ).
cnf(c_0_138,plain,
( sum(multiply(X1,inverse(X2)),X2,X3)
| ~ sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_29]),c_0_80]) ).
cnf(c_0_139,hypothesis,
sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_31,c_0_134]) ).
cnf(c_0_140,hypothesis,
multiply(y,x_plus_y) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_135]),c_0_57]) ).
cnf(c_0_141,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X2)
| ~ sum(X1,X4,multiplicative_identity)
| ~ sum(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_110,c_0_25]) ).
cnf(c_0_142,plain,
( X1 = inverse(X2)
| ~ product(X2,X1,additive_identity)
| ~ sum(X2,X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_113]),c_0_72])]) ).
cnf(c_0_143,hypothesis,
product(x_plus_y,x_inverse_times_y_inverse,additive_identity),
inference(spm,[status(thm)],[c_0_47,c_0_137]) ).
cnf(c_0_144,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
prove_equation ).
cnf(c_0_145,hypothesis,
sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_38]),c_0_57]),c_0_140]) ).
cnf(c_0_146,hypothesis,
( sum(X1,x_inverse_times_y_inverse,X2)
| ~ sum(X1,inverse(y),multiplicative_identity)
| ~ sum(X1,inverse(x),X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_59]) ).
cnf(c_0_147,hypothesis,
~ sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_144]) ).
cnf(c_0_148,hypothesis,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_145]),c_0_41]) ).
cnf(c_0_149,hypothesis,
~ sum(x_plus_y,inverse(y),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_121]),c_0_147]) ).
cnf(c_0_150,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_148]),c_0_149]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : BOO014-3 : TPTP v8.1.2. Bugfixed v2.2.0.
% 0.00/0.09 % Command : run_E %s %d THM
% 0.09/0.29 % Computer : n023.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 2400
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Oct 2 20:54:07 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.DJF7pHDRCd/E---3.1_22400.p
% 9.00/1.55 # Version: 3.1pre001
% 9.00/1.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55 # Starting new_bool_3 with 300s (1) cores
% 9.00/1.55 # Starting new_bool_1 with 300s (1) cores
% 9.00/1.55 # Starting sh5l with 300s (1) cores
% 9.00/1.55 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 22477 completed with status 0
% 9.00/1.55 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 9.00/1.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55 # No SInE strategy applied
% 9.00/1.55 # Search class: FHUSM-FFMF21-SFFFFFNN
% 9.00/1.55 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 9.00/1.55 # Starting new_bool_3 with 136s (1) cores
% 9.00/1.55 # Starting new_bool_1 with 136s (1) cores
% 9.00/1.55 # Starting sh5l with 136s (1) cores
% 9.00/1.55 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 22481 completed with status 0
% 9.00/1.55 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 9.00/1.55 # Preprocessing class: FSMSSMSSSSSNFFN.
% 9.00/1.55 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 9.00/1.55 # No SInE strategy applied
% 9.00/1.55 # Search class: FHUSM-FFMF21-SFFFFFNN
% 9.00/1.55 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 9.00/1.55 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 9.00/1.55 # Preprocessing time : 0.001 s
% 9.00/1.55 # Presaturation interreduction done
% 9.00/1.55
% 9.00/1.55 # Proof found!
% 9.00/1.55 # SZS status Unsatisfiable
% 9.00/1.55 # SZS output start CNFRefutation
% See solution above
% 9.00/1.55 # Parsed axioms : 27
% 9.00/1.55 # Removed by relevancy pruning/SinE : 0
% 9.00/1.55 # Initial clauses : 27
% 9.00/1.55 # Removed in clause preprocessing : 0
% 9.00/1.55 # Initial clauses in saturation : 27
% 9.00/1.55 # Processed clauses : 14594
% 9.00/1.55 # ...of these trivial : 585
% 9.00/1.55 # ...subsumed : 10203
% 9.00/1.55 # ...remaining for further processing : 3806
% 9.00/1.55 # Other redundant clauses eliminated : 0
% 9.00/1.55 # Clauses deleted for lack of memory : 0
% 9.00/1.55 # Backward-subsumed : 131
% 9.00/1.55 # Backward-rewritten : 282
% 9.00/1.55 # Generated clauses : 60867
% 9.00/1.55 # ...of the previous two non-redundant : 49294
% 9.00/1.55 # ...aggressively subsumed : 0
% 9.00/1.55 # Contextual simplify-reflections : 0
% 9.00/1.55 # Paramodulations : 60867
% 9.00/1.55 # Factorizations : 0
% 9.00/1.55 # NegExts : 0
% 9.00/1.55 # Equation resolutions : 0
% 9.00/1.55 # Total rewrite steps : 32527
% 9.00/1.55 # Propositional unsat checks : 0
% 9.00/1.55 # Propositional check models : 0
% 9.00/1.55 # Propositional check unsatisfiable : 0
% 9.00/1.55 # Propositional clauses : 0
% 9.00/1.55 # Propositional clauses after purity: 0
% 9.00/1.55 # Propositional unsat core size : 0
% 9.00/1.55 # Propositional preprocessing time : 0.000
% 9.00/1.55 # Propositional encoding time : 0.000
% 9.00/1.55 # Propositional solver time : 0.000
% 9.00/1.55 # Success case prop preproc time : 0.000
% 9.00/1.55 # Success case prop encoding time : 0.000
% 9.00/1.55 # Success case prop solver time : 0.000
% 9.00/1.55 # Current number of processed clauses : 3366
% 9.00/1.55 # Positive orientable unit clauses : 278
% 9.00/1.55 # Positive unorientable unit clauses: 2
% 9.00/1.55 # Negative unit clauses : 3
% 9.00/1.55 # Non-unit-clauses : 3083
% 9.00/1.55 # Current number of unprocessed clauses: 34066
% 9.00/1.55 # ...number of literals in the above : 78062
% 9.00/1.55 # Current number of archived formulas : 0
% 9.00/1.55 # Current number of archived clauses : 440
% 9.00/1.55 # Clause-clause subsumption calls (NU) : 1786670
% 9.00/1.55 # Rec. Clause-clause subsumption calls : 1248722
% 9.00/1.55 # Non-unit clause-clause subsumptions : 10326
% 9.00/1.55 # Unit Clause-clause subsumption calls : 4146
% 9.00/1.55 # Rewrite failures with RHS unbound : 0
% 9.00/1.55 # BW rewrite match attempts : 1104
% 9.00/1.55 # BW rewrite match successes : 92
% 9.00/1.55 # Condensation attempts : 0
% 9.00/1.55 # Condensation successes : 0
% 9.00/1.55 # Termbank termtop insertions : 902644
% 9.00/1.55
% 9.00/1.55 # -------------------------------------------------
% 9.00/1.55 # User time : 1.120 s
% 9.00/1.55 # System time : 0.027 s
% 9.00/1.55 # Total time : 1.147 s
% 9.00/1.55 # Maximum resident set size: 1640 pages
% 9.00/1.55
% 9.00/1.55 # -------------------------------------------------
% 9.00/1.55 # User time : 5.685 s
% 9.00/1.55 # System time : 0.065 s
% 9.00/1.55 # Total time : 5.749 s
% 9.00/1.55 # Maximum resident set size: 1692 pages
% 9.00/1.55 % E---3.1 exiting
%------------------------------------------------------------------------------