TSTP Solution File: BOO014-1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : BOO014-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% 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 : Mon May 20 18:56:41 EDT 2024
% Result : Unsatisfiable 7.53s 1.34s
% Output : CNFRefutation 7.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 22
% Syntax : Number of clauses : 157 ( 84 unt; 0 nHn; 118 RR)
% Number of literals : 311 ( 44 equ; 157 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 : 327 ( 13 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/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(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(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(additive_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_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(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(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(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
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(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(x_plus_y,negated_conjecture,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(x_inverse_times_y_inverse,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
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/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(distributivity5,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity5) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(prove_equation,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_22,plain,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity8]) ).
cnf(c_0_23,plain,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
c_0_22 ).
cnf(c_0_24,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_25,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_27,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_28,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_29,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X2,multiplicative_identity)
| ~ sum(multiplicative_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_31,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
c_0_27 ).
cnf(c_0_32,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_33,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
c_0_28 ).
cnf(c_0_34,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_37,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_38,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_39,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
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_36]) ).
cnf(c_0_42,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
c_0_38 ).
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,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_45,plain,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_46,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_26]) ).
cnf(c_0_47,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_48,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_44 ).
cnf(c_0_49,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_50,plain,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
c_0_45 ).
cnf(c_0_51,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_52,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_26]),c_0_47])]) ).
cnf(c_0_53,plain,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity7]) ).
cnf(c_0_54,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_56,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_57,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_52,c_0_49]) ).
cnf(c_0_58,plain,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ sum(X6,X2,X7) ),
c_0_53 ).
cnf(c_0_59,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,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_58,c_0_49]) ).
cnf(c_0_62,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_63,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
sum(x,y,x_plus_y),
x_plus_y ).
cnf(c_0_65,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_66,negated_conjecture,
sum(y,x,x_plus_y),
inference(spm,[status(thm)],[c_0_33,c_0_64]) ).
cnf(c_0_67,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_62]) ).
cnf(c_0_68,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
x_inverse_times_y_inverse ).
cnf(c_0_69,negated_conjecture,
( product(x_plus_y,x,X1)
| ~ sum(additive_identity,x,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_32]) ).
cnf(c_0_71,negated_conjecture,
product(inverse(y),inverse(x),x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_50,c_0_68]) ).
cnf(c_0_72,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_23,c_0_49]) ).
cnf(c_0_73,negated_conjecture,
product(x_plus_y,x,x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_32]),c_0_70]) ).
cnf(c_0_74,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_26]) ).
cnf(c_0_75,negated_conjecture,
sum(x_inverse_times_y_inverse,inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( sum(x,X1,multiply(X2,X3))
| ~ sum(x,X1,X3)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_78,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_49]) ).
cnf(c_0_79,negated_conjecture,
sum(inverse(y),x_inverse_times_y_inverse,inverse(y)),
inference(spm,[status(thm)],[c_0_33,c_0_75]) ).
cnf(c_0_80,plain,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity6]) ).
cnf(c_0_81,negated_conjecture,
( sum(x,inverse(x),X1)
| ~ sum(x_plus_y,inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( product(inverse(y),x_inverse_times_y_inverse,X1)
| ~ sum(additive_identity,x_inverse_times_y_inverse,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_79]) ).
cnf(c_0_83,plain,
( sum(X1,X6,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ product(X3,X5,X7) ),
c_0_80 ).
cnf(c_0_84,negated_conjecture,
sum(x,inverse(x),add(x_plus_y,inverse(x))),
inference(spm,[status(thm)],[c_0_81,c_0_32]) ).
cnf(c_0_85,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X5,X2,multiplicative_identity)
| ~ sum(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_86,negated_conjecture,
product(inverse(y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_32]),c_0_70]) ).
cnf(c_0_87,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_83,c_0_49]) ).
cnf(c_0_88,negated_conjecture,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_84]),c_0_41]) ).
cnf(c_0_89,negated_conjecture,
( 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_85,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
( 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_87,c_0_71]) ).
cnf(c_0_91,negated_conjecture,
sum(x_plus_y,inverse(x),multiplicative_identity),
inference(spm,[status(thm)],[c_0_32,c_0_88]) ).
cnf(c_0_92,negated_conjecture,
( 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_89,c_0_77]) ).
cnf(c_0_93,negated_conjecture,
( 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_90,c_0_91]),c_0_78]) ).
cnf(c_0_94,negated_conjecture,
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_92,c_0_32]) ).
cnf(c_0_95,negated_conjecture,
( product(x_plus_y,y,X1)
| ~ sum(additive_identity,y,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_96,negated_conjecture,
sum(x_plus_y,x_inverse_times_y_inverse,add(x_plus_y,inverse(y))),
inference(spm,[status(thm)],[c_0_93,c_0_32]) ).
cnf(c_0_97,negated_conjecture,
( sum(x_inverse_times_y_inverse,X1,X2)
| ~ sum(inverse(y),X1,multiplicative_identity)
| ~ sum(inverse(x),X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_71]) ).
cnf(c_0_98,negated_conjecture,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_94]),c_0_41]) ).
cnf(c_0_99,negated_conjecture,
product(x_plus_y,y,y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_32]),c_0_70]) ).
cnf(c_0_100,negated_conjecture,
add(x_plus_y,inverse(y)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_35,c_0_96]) ).
cnf(c_0_101,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_102,negated_conjecture,
( sum(x_inverse_times_y_inverse,X1,add(inverse(x),X1))
| ~ sum(inverse(y),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_97,c_0_32]) ).
cnf(c_0_103,negated_conjecture,
sum(inverse(y),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_32,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( sum(y,X1,X2)
| ~ sum(y,X1,multiplicative_identity)
| ~ sum(x_plus_y,X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
sum(x_plus_y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_32,c_0_100]) ).
cnf(c_0_106,plain,
( product(X1,X2,X3)
| ~ sum(inverse(X4),X5,X2)
| ~ sum(additive_identity,X5,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_101]) ).
cnf(c_0_107,negated_conjecture,
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_102,c_0_103]) ).
cnf(c_0_108,plain,
( product(add(X1,X2),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_32]) ).
cnf(c_0_109,negated_conjecture,
sum(y,inverse(y),add(x_plus_y,x_inverse_times_y_inverse)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_77])]) ).
cnf(c_0_110,plain,
( product(add(X1,X2),X3,X4)
| ~ sum(inverse(X2),X1,X3)
| ~ sum(additive_identity,X1,X4) ),
inference(spm,[status(thm)],[c_0_106,c_0_36]) ).
cnf(c_0_111,negated_conjecture,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_107]),c_0_41]) ).
cnf(c_0_112,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_32]),c_0_70]) ).
cnf(c_0_113,negated_conjecture,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_109]),c_0_41]) ).
cnf(c_0_114,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_115,plain,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
inference(fof_simplification,[status(thm)],[distributivity5]) ).
cnf(c_0_116,plain,
( product(add(X1,X2),X3,X1)
| ~ sum(inverse(X2),X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_32]),c_0_70]) ).
cnf(c_0_117,negated_conjecture,
sum(inverse(x),inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(spm,[status(thm)],[c_0_32,c_0_111]) ).
cnf(c_0_118,plain,
( X1 = X2
| ~ product(add(X3,X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_112]) ).
cnf(c_0_119,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_120,plain,
( sum(additive_identity,X1,multiply(X2,X3))
| ~ sum(inverse(X4),X1,X3)
| ~ sum(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_101]) ).
cnf(c_0_121,negated_conjecture,
sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity),
inference(spm,[status(thm)],[c_0_32,c_0_113]) ).
cnf(c_0_122,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_114,c_0_49]) ).
cnf(c_0_123,plain,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
c_0_115 ).
cnf(c_0_124,negated_conjecture,
product(add(x,inverse(x_inverse_times_y_inverse)),multiplicative_identity,inverse(x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_40]) ).
cnf(c_0_125,plain,
( X1 = X2
| ~ product(add(X2,X3),X2,X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_40]) ).
cnf(c_0_126,negated_conjecture,
product(add(y,inverse(x_inverse_times_y_inverse)),multiplicative_identity,inverse(x_inverse_times_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_103]),c_0_40]) ).
cnf(c_0_127,plain,
( sum(X1,additive_identity,multiply(X2,X3))
| ~ sum(X1,inverse(X4),X2)
| ~ sum(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_119]) ).
cnf(c_0_128,negated_conjecture,
( sum(additive_identity,x_inverse_times_y_inverse,X1)
| ~ sum(inverse(x_plus_y),x_inverse_times_y_inverse,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]) ).
cnf(c_0_129,plain,
( product(X1,X2,X3)
| ~ sum(X4,multiply(X5,X6),X3)
| ~ sum(X4,X6,X2)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_49]) ).
cnf(c_0_130,negated_conjecture,
add(x,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_124]),c_0_78]) ).
cnf(c_0_131,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_49]),c_0_59]) ).
cnf(c_0_132,negated_conjecture,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_126]),c_0_78]) ).
cnf(c_0_133,negated_conjecture,
( sum(x_plus_y,additive_identity,X1)
| ~ sum(x_plus_y,inverse(x_inverse_times_y_inverse),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_121]),c_0_78]) ).
cnf(c_0_134,negated_conjecture,
sum(additive_identity,x_inverse_times_y_inverse,add(x_inverse_times_y_inverse,inverse(x_plus_y))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_32]),c_0_40]) ).
cnf(c_0_135,negated_conjecture,
( product(X1,x_plus_y,X2)
| ~ sum(x,multiply(X3,y),X2)
| ~ sum(x,X3,X1) ),
inference(spm,[status(thm)],[c_0_129,c_0_64]) ).
cnf(c_0_136,negated_conjecture,
sum(x,inverse(x_inverse_times_y_inverse),inverse(x_inverse_times_y_inverse)),
inference(spm,[status(thm)],[c_0_32,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,negated_conjecture,
( X1 = x_plus_y
| ~ sum(x,y,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_64]) ).
cnf(c_0_139,negated_conjecture,
sum(x_plus_y,additive_identity,add(x_plus_y,inverse(x_inverse_times_y_inverse))),
inference(spm,[status(thm)],[c_0_133,c_0_32]) ).
cnf(c_0_140,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_36]) ).
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_83,c_0_24]) ).
cnf(c_0_142,negated_conjecture,
add(x_inverse_times_y_inverse,inverse(x_plus_y)) = x_inverse_times_y_inverse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_134]),c_0_70]) ).
cnf(c_0_143,negated_conjecture,
( product(inverse(x_inverse_times_y_inverse),x_plus_y,X1)
| ~ sum(x,y,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_59]),c_0_137]) ).
cnf(c_0_144,negated_conjecture,
add(x,y) = x_plus_y,
inference(spm,[status(thm)],[c_0_138,c_0_32]) ).
cnf(c_0_145,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_112]),c_0_59]) ).
cnf(c_0_146,negated_conjecture,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_139]),c_0_140]) ).
cnf(c_0_147,plain,
( sum(X1,additive_identity,X2)
| ~ sum(X1,inverse(X3),multiplicative_identity)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_141,c_0_119]) ).
cnf(c_0_148,negated_conjecture,
sum(inverse(x_plus_y),x_inverse_times_y_inverse,x_inverse_times_y_inverse),
inference(spm,[status(thm)],[c_0_36,c_0_142]) ).
cnf(c_0_149,negated_conjecture,
product(inverse(x_inverse_times_y_inverse),x_plus_y,x_plus_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_32]),c_0_144]) ).
cnf(c_0_150,negated_conjecture,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_59]) ).
cnf(c_0_151,negated_conjecture,
( sum(inverse(x_plus_y),additive_identity,x_inverse_times_y_inverse)
| ~ sum(inverse(x_plus_y),inverse(x_inverse_times_y_inverse),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_149]),c_0_59]),c_0_150]) ).
cnf(c_0_153,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_154,negated_conjecture,
sum(inverse(x_plus_y),additive_identity,x_inverse_times_y_inverse),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_152]),c_0_30])]) ).
cnf(c_0_155,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
c_0_153 ).
cnf(c_0_156,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_154]),c_0_140]),c_0_155]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : BOO014-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sat May 18 14:36:22 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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/benchmark/theBenchmark.p
% 7.53/1.34 # Version: 3.1.0
% 7.53/1.34 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.53/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.53/1.34 # Starting new_bool_3 with 300s (1) cores
% 7.53/1.34 # Starting new_bool_1 with 300s (1) cores
% 7.53/1.34 # Starting sh5l with 300s (1) cores
% 7.53/1.34 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 31558 completed with status 0
% 7.53/1.34 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.53/1.34 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.53/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.53/1.34 # No SInE strategy applied
% 7.53/1.34 # Search class: FHUSM-FFMF21-SFFFFFNN
% 7.53/1.34 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.53/1.34 # Starting new_bool_3 with 136s (1) cores
% 7.53/1.34 # Starting new_bool_1 with 136s (1) cores
% 7.53/1.34 # Starting sh5l with 136s (1) cores
% 7.53/1.34 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 31562 completed with status 0
% 7.53/1.34 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 7.53/1.34 # Preprocessing class: FSMSSMSSSSSNFFN.
% 7.53/1.34 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.53/1.34 # No SInE strategy applied
% 7.53/1.34 # Search class: FHUSM-FFMF21-SFFFFFNN
% 7.53/1.34 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 7.53/1.34 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 7.53/1.34 # Preprocessing time : 0.001 s
% 7.53/1.34 # Presaturation interreduction done
% 7.53/1.34
% 7.53/1.34 # Proof found!
% 7.53/1.34 # SZS status Unsatisfiable
% 7.53/1.34 # SZS output start CNFRefutation
% See solution above
% 7.53/1.34 # Parsed axioms : 25
% 7.53/1.34 # Removed by relevancy pruning/SinE : 0
% 7.53/1.34 # Initial clauses : 25
% 7.53/1.34 # Removed in clause preprocessing : 0
% 7.53/1.34 # Initial clauses in saturation : 25
% 7.53/1.34 # Processed clauses : 11639
% 7.53/1.34 # ...of these trivial : 575
% 7.53/1.34 # ...subsumed : 7499
% 7.53/1.34 # ...remaining for further processing : 3565
% 7.53/1.34 # Other redundant clauses eliminated : 0
% 7.53/1.34 # Clauses deleted for lack of memory : 0
% 7.53/1.34 # Backward-subsumed : 101
% 7.53/1.34 # Backward-rewritten : 316
% 7.53/1.34 # Generated clauses : 51840
% 7.53/1.34 # ...of the previous two non-redundant : 43553
% 7.53/1.34 # ...aggressively subsumed : 0
% 7.53/1.34 # Contextual simplify-reflections : 0
% 7.53/1.34 # Paramodulations : 51840
% 7.53/1.34 # Factorizations : 0
% 7.53/1.34 # NegExts : 0
% 7.53/1.34 # Equation resolutions : 0
% 7.53/1.34 # Disequality decompositions : 0
% 7.53/1.34 # Total rewrite steps : 20840
% 7.53/1.34 # ...of those cached : 19649
% 7.53/1.34 # Propositional unsat checks : 0
% 7.53/1.34 # Propositional check models : 0
% 7.53/1.34 # Propositional check unsatisfiable : 0
% 7.53/1.34 # Propositional clauses : 0
% 7.53/1.34 # Propositional clauses after purity: 0
% 7.53/1.34 # Propositional unsat core size : 0
% 7.53/1.34 # Propositional preprocessing time : 0.000
% 7.53/1.34 # Propositional encoding time : 0.000
% 7.53/1.34 # Propositional solver time : 0.000
% 7.53/1.34 # Success case prop preproc time : 0.000
% 7.53/1.34 # Success case prop encoding time : 0.000
% 7.53/1.34 # Success case prop solver time : 0.000
% 7.53/1.34 # Current number of processed clauses : 3123
% 7.53/1.34 # Positive orientable unit clauses : 300
% 7.53/1.34 # Positive unorientable unit clauses: 2
% 7.53/1.34 # Negative unit clauses : 1
% 7.53/1.34 # Non-unit-clauses : 2820
% 7.53/1.34 # Current number of unprocessed clauses: 31452
% 7.53/1.34 # ...number of literals in the above : 71598
% 7.53/1.34 # Current number of archived formulas : 0
% 7.53/1.34 # Current number of archived clauses : 442
% 7.53/1.34 # Clause-clause subsumption calls (NU) : 931594
% 7.53/1.34 # Rec. Clause-clause subsumption calls : 813480
% 7.53/1.34 # Non-unit clause-clause subsumptions : 7598
% 7.53/1.34 # Unit Clause-clause subsumption calls : 348
% 7.53/1.34 # Rewrite failures with RHS unbound : 0
% 7.53/1.34 # BW rewrite match attempts : 775
% 7.53/1.34 # BW rewrite match successes : 68
% 7.53/1.34 # Condensation attempts : 0
% 7.53/1.34 # Condensation successes : 0
% 7.53/1.34 # Termbank termtop insertions : 789336
% 7.53/1.34 # Search garbage collected termcells : 68
% 7.53/1.34
% 7.53/1.34 # -------------------------------------------------
% 7.53/1.34 # User time : 0.909 s
% 7.53/1.34 # System time : 0.020 s
% 7.53/1.34 # Total time : 0.929 s
% 7.53/1.34 # Maximum resident set size: 1652 pages
% 7.53/1.34
% 7.53/1.34 # -------------------------------------------------
% 7.53/1.34 # User time : 4.569 s
% 7.53/1.34 # System time : 0.036 s
% 7.53/1.34 # Total time : 4.605 s
% 7.53/1.34 # Maximum resident set size: 1716 pages
% 7.53/1.34 % E---3.1 exiting
%------------------------------------------------------------------------------