%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO015-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 : Tue May 5 04:11:08 PM UTC 2026
% Result : Unsatisfiable 6.66s 4.59s
% Output : CNFRefutation 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 23
% Syntax : Number of clauses : 186 ( 107 unt; 0 nHn; 140 RR)
% Number of literals : 338 ( 51 equ; 154 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 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 : 338 ( 17 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(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(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(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(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(x_times_y,negated_conjecture,
product(x,y,x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
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(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(x_inverse_plus_y_inverse,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_plus_y_inverse) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
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/BOO002-0.ax',distributivity4) ).
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(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(prove_equation,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_23,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_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,
( 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_28,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_29,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_30,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_31,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_32,plain,
( sum(inverse(X1),X1,X2)
| ~ sum(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_35,plain,
( X1 = multiplicative_identity
| ~ sum(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_36,plain,
sum(inverse(X1),X1,add(multiplicative_identity,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_37,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_35,c_0_34]) ).
cnf(c_0_39,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_40,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_41,plain,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_42,plain,
sum(X1,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_43,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_44,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_45,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_46,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_47,plain,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_26]),c_0_42])]) ).
cnf(c_0_48,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_50,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_46]) ).
cnf(c_0_51,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_47,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
product(x,y,x_times_y),
x_times_y ).
cnf(c_0_53,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_54,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
product(y,x,x_times_y),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_57,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_53,c_0_44]) ).
cnf(c_0_58,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_59,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
sum(x_times_y,x,x),
inference(spm,[status(thm)],[c_0_47,c_0_52]) ).
cnf(c_0_61,negated_conjecture,
sum(x_times_y,y,y),
inference(spm,[status(thm)],[c_0_47,c_0_56]) ).
cnf(c_0_62,plain,
( product(X1,X2,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
sum(x,x_times_y,x),
inference(spm,[status(thm)],[c_0_31,c_0_60]) ).
cnf(c_0_64,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
sum(y,x_times_y,y),
inference(spm,[status(thm)],[c_0_31,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( product(x,x_times_y,X1)
| ~ sum(additive_identity,x_times_y,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_30]) ).
cnf(c_0_68,negated_conjecture,
( product(y,x_times_y,X1)
| ~ sum(additive_identity,x_times_y,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_65]) ).
cnf(c_0_69,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_70,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_71,negated_conjecture,
product(x,x_times_y,x_times_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_30]),c_0_67]) ).
cnf(c_0_72,negated_conjecture,
product(y,x_times_y,x_times_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_30]),c_0_67]) ).
cnf(c_0_73,plain,
( sum(X1,additive_identity,multiply(X2,X3))
| ~ product(X2,X4,X1)
| ~ sum(X4,inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
product(x_times_y,x,x_times_y),
inference(spm,[status(thm)],[c_0_45,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
product(x_times_y,y,x_times_y),
inference(spm,[status(thm)],[c_0_45,c_0_72]) ).
cnf(c_0_76,negated_conjecture,
( sum(x_times_y,additive_identity,multiply(x_times_y,X1))
| ~ sum(x,inverse(x_times_y),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
( sum(x_times_y,additive_identity,multiply(x_times_y,X1))
| ~ sum(y,inverse(x_times_y),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_75]) ).
cnf(c_0_78,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_44]) ).
cnf(c_0_79,plain,
( X1 = X2
| ~ product(X2,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_26]) ).
cnf(c_0_80,plain,
sum(multiply(X1,X2),X2,X2),
inference(spm,[status(thm)],[c_0_47,c_0_49]) ).
cnf(c_0_81,negated_conjecture,
sum(x_times_y,additive_identity,multiply(x_times_y,add(x,inverse(x_times_y)))),
inference(spm,[status(thm)],[c_0_76,c_0_30]) ).
cnf(c_0_82,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_34]) ).
cnf(c_0_83,plain,
( product(add(X1,X2),X2,X3)
| ~ sum(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_62,c_0_30]) ).
cnf(c_0_84,negated_conjecture,
sum(x_times_y,additive_identity,multiply(x_times_y,add(y,inverse(x_times_y)))),
inference(spm,[status(thm)],[c_0_77,c_0_30]) ).
cnf(c_0_85,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
x_inverse_plus_y_inverse ).
cnf(c_0_86,negated_conjecture,
( sum(x_times_y,X1,X2)
| ~ sum(x,X1,multiplicative_identity)
| ~ sum(y,X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_87,plain,
( sum(multiply(X1,X2),X3,multiply(X4,X5))
| ~ sum(X1,X3,X5)
| ~ sum(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_78,c_0_49]) ).
cnf(c_0_88,plain,
multiply(X1,multiplicative_identity) = X1,
inference(spm,[status(thm)],[c_0_79,c_0_44]) ).
cnf(c_0_89,plain,
sum(X1,multiply(X2,X1),X1),
inference(spm,[status(thm)],[c_0_31,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
multiply(x_times_y,add(x,inverse(x_times_y))) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_81]),c_0_82]) ).
cnf(c_0_91,plain,
product(add(X1,X2),X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_30]),c_0_67]) ).
cnf(c_0_92,negated_conjecture,
multiply(x_times_y,add(y,inverse(x_times_y))) = x_times_y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_84]),c_0_82]) ).
cnf(c_0_93,negated_conjecture,
sum(inverse(y),inverse(x),x_inverse_plus_y_inverse),
inference(spm,[status(thm)],[c_0_31,c_0_85]) ).
cnf(c_0_94,plain,
( X1 = X2
| ~ sum(multiply(X2,X3),X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_51]) ).
cnf(c_0_95,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(X3),X1,X2)
| ~ sum(X3,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_70]) ).
cnf(c_0_96,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_97,negated_conjecture,
( sum(x_times_y,X1,add(y,X1))
| ~ sum(x,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_86,c_0_30]) ).
cnf(c_0_98,axiom,
sum(X1,inverse(X1),multiplicative_identity),
additive_inverse2 ).
cnf(c_0_99,plain,
( sum(multiply(inverse(X1),X2),X1,X3)
| ~ sum(X2,X1,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_28]),c_0_88]) ).
cnf(c_0_100,negated_conjecture,
sum(add(x,inverse(x_times_y)),x_times_y,add(x,inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_101,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_91]),c_0_54]) ).
cnf(c_0_102,negated_conjecture,
sum(add(y,inverse(x_times_y)),x_times_y,add(y,inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_89,c_0_92]) ).
cnf(c_0_103,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_104,negated_conjecture,
( product(x_inverse_plus_y_inverse,inverse(x),X1)
| ~ sum(additive_identity,inverse(x),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_93]) ).
cnf(c_0_105,plain,
( X1 = X2
| ~ sum(multiply(X3,X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_54]) ).
cnf(c_0_106,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(inverse(X1)),X1,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_28]) ).
cnf(c_0_107,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_53,c_0_96]) ).
cnf(c_0_108,negated_conjecture,
sum(x_times_y,inverse(x),add(y,inverse(x))),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_109,plain,
( X1 = add(X2,X3)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_110,negated_conjecture,
sum(inverse(x_times_y),x_times_y,add(x,inverse(x_times_y))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]) ).
cnf(c_0_111,negated_conjecture,
sum(inverse(x_times_y),x_times_y,add(y,inverse(x_times_y))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_102]),c_0_101]) ).
cnf(c_0_112,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X4,inverse(X2),X1)
| ~ sum(X5,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_103,c_0_96]) ).
cnf(c_0_113,negated_conjecture,
product(x_inverse_plus_y_inverse,inverse(x),inverse(x)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_30]),c_0_67]) ).
cnf(c_0_114,plain,
( X1 = add(X2,X3)
| ~ sum(X3,add(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_101]) ).
cnf(c_0_115,plain,
sum(additive_identity,X1,add(X1,inverse(inverse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_30]),c_0_37]) ).
cnf(c_0_116,negated_conjecture,
( product(X1,add(y,inverse(x)),X2)
| ~ sum(inverse(x_times_y),inverse(x),X1)
| ~ sum(additive_identity,inverse(x),X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_117,negated_conjecture,
add(x,inverse(x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_38]) ).
cnf(c_0_118,plain,
( X1 = X2
| ~ product(multiplicative_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_119,negated_conjecture,
add(y,inverse(x_times_y)) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_111]),c_0_38]) ).
cnf(c_0_120,negated_conjecture,
( product(X1,inverse(x),X2)
| ~ sum(x_inverse_plus_y_inverse,inverse(inverse(x)),X1)
| ~ sum(inverse(x),additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_121,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_82]),c_0_82]),c_0_82]) ).
cnf(c_0_122,negated_conjecture,
( product(X1,add(y,inverse(x)),inverse(x))
| ~ sum(inverse(x_times_y),inverse(x),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_30]),c_0_67]) ).
cnf(c_0_123,plain,
( sum(additive_identity,X1,multiply(X2,X3))
| ~ sum(inverse(X4),X1,X3)
| ~ sum(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_70]) ).
cnf(c_0_124,negated_conjecture,
sum(x,inverse(x_times_y),multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_117]) ).
cnf(c_0_125,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_118,c_0_44]) ).
cnf(c_0_126,negated_conjecture,
sum(y,inverse(x_times_y),multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_119]) ).
cnf(c_0_127,negated_conjecture,
( product(X1,inverse(x),inverse(x))
| ~ sum(x_inverse_plus_y_inverse,inverse(inverse(x)),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_30]),c_0_82]) ).
cnf(c_0_128,plain,
( sum(additive_identity,X1,X2)
| ~ sum(inverse(X3),X1,multiplicative_identity)
| ~ sum(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_96]) ).
cnf(c_0_129,plain,
sum(X1,inverse(inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_30,c_0_121]) ).
cnf(c_0_130,negated_conjecture,
product(add(inverse(x),inverse(x_times_y)),add(y,inverse(x)),inverse(x)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_30]),c_0_37]) ).
cnf(c_0_131,negated_conjecture,
( sum(additive_identity,inverse(x_times_y),X1)
| ~ sum(inverse(x),inverse(x_times_y),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_132,plain,
( X1 = X2
| ~ product(add(X3,X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_91]) ).
cnf(c_0_133,negated_conjecture,
( sum(additive_identity,inverse(x_times_y),X1)
| ~ sum(inverse(y),inverse(x_times_y),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_126]),c_0_125]) ).
cnf(c_0_134,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_135,negated_conjecture,
product(add(x_inverse_plus_y_inverse,inverse(inverse(x))),inverse(x),inverse(x)),
inference(spm,[status(thm)],[c_0_127,c_0_30]) ).
cnf(c_0_136,plain,
sum(additive_identity,inverse(inverse(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_98])]) ).
cnf(c_0_137,negated_conjecture,
( product(x_inverse_plus_y_inverse,inverse(y),X1)
| ~ sum(additive_identity,inverse(y),X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_85]) ).
cnf(c_0_138,negated_conjecture,
sum(inverse(x),add(inverse(x),inverse(x_times_y)),add(inverse(x),inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_47,c_0_130]) ).
cnf(c_0_139,negated_conjecture,
sum(additive_identity,inverse(x_times_y),add(inverse(x),inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_131,c_0_30]) ).
cnf(c_0_140,plain,
( X1 = X2
| ~ product(add(X2,X3),X2,X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_37]) ).
cnf(c_0_141,negated_conjecture,
sum(additive_identity,inverse(x_times_y),add(inverse(y),inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_133,c_0_30]) ).
cnf(c_0_142,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_134,c_0_44]) ).
cnf(c_0_143,negated_conjecture,
multiply(inverse(x),add(x_inverse_plus_y_inverse,inverse(inverse(x)))) = inverse(x),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_135]),c_0_54]) ).
cnf(c_0_144,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_136]),c_0_67]) ).
cnf(c_0_145,negated_conjecture,
product(x_inverse_plus_y_inverse,inverse(y),inverse(y)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_30]),c_0_67]) ).
cnf(c_0_146,negated_conjecture,
sum(add(inverse(x),inverse(x_times_y)),inverse(x),add(inverse(x),inverse(x_times_y))),
inference(spm,[status(thm)],[c_0_31,c_0_138]) ).
cnf(c_0_147,negated_conjecture,
add(inverse(x),inverse(x_times_y)) = inverse(x_times_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_139]),c_0_67]) ).
cnf(c_0_148,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_44]),c_0_54]) ).
cnf(c_0_149,negated_conjecture,
add(inverse(y),inverse(x_times_y)) = inverse(x_times_y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_141]),c_0_67]) ).
cnf(c_0_150,plain,
( sum(X1,multiply(X2,X3),multiply(X4,X5))
| ~ sum(X1,X2,X5)
| ~ sum(X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_142,c_0_49]) ).
cnf(c_0_151,negated_conjecture,
multiply(inverse(x),add(x,x_inverse_plus_y_inverse)) = inverse(x),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_37]) ).
cnf(c_0_152,negated_conjecture,
( product(X1,inverse(y),X2)
| ~ sum(x_inverse_plus_y_inverse,inverse(inverse(y)),X1)
| ~ sum(inverse(y),additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_112,c_0_145]) ).
cnf(c_0_153,axiom,
( product(X3,X5,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X5)
| ~ product(X2,X4,X6)
| ~ sum(X1,X6,X7) ),
distributivity5 ).
cnf(c_0_154,negated_conjecture,
( product(X1,x_inverse_plus_y_inverse,X2)
| ~ sum(multiply(X3,inverse(y)),inverse(x),X2)
| ~ sum(X3,inverse(x),X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_93]) ).
cnf(c_0_155,negated_conjecture,
sum(inverse(x_times_y),inverse(x),inverse(x_times_y)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147]),c_0_147]) ).
cnf(c_0_156,negated_conjecture,
multiply(inverse(y),inverse(x_times_y)) = inverse(y),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_157,negated_conjecture,
( X1 = x_inverse_plus_y_inverse
| ~ sum(inverse(x),inverse(y),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_85]) ).
cnf(c_0_158,plain,
( sum(X1,multiply(inverse(X1),X2),X3)
| ~ sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_98]),c_0_88]) ).
cnf(c_0_159,negated_conjecture,
sum(inverse(x),add(x,x_inverse_plus_y_inverse),add(x,x_inverse_plus_y_inverse)),
inference(spm,[status(thm)],[c_0_80,c_0_151]) ).
cnf(c_0_160,negated_conjecture,
( product(X1,inverse(y),inverse(y))
| ~ sum(x_inverse_plus_y_inverse,inverse(inverse(y)),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_30]),c_0_82]) ).
cnf(c_0_161,plain,
( product(X1,X2,X3)
| ~ sum(X4,inverse(X5),X1)
| ~ sum(X4,additive_identity,X3)
| ~ sum(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_153,c_0_96]) ).
cnf(c_0_162,negated_conjecture,
( product(inverse(x_times_y),x_inverse_plus_y_inverse,X1)
| ~ sum(inverse(y),inverse(x),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_54]),c_0_156]) ).
cnf(c_0_163,negated_conjecture,
add(inverse(x),inverse(y)) = x_inverse_plus_y_inverse,
inference(spm,[status(thm)],[c_0_157,c_0_30]) ).
cnf(c_0_164,negated_conjecture,
sum(inverse(x),x,add(x,x_inverse_plus_y_inverse)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_144]),c_0_148]) ).
cnf(c_0_165,negated_conjecture,
product(add(x_inverse_plus_y_inverse,inverse(inverse(y))),inverse(y),inverse(y)),
inference(spm,[status(thm)],[c_0_160,c_0_30]) ).
cnf(c_0_166,plain,
( product(X1,add(X2,X3),X4)
| ~ sum(X3,inverse(X2),X1)
| ~ sum(X3,additive_identity,X4) ),
inference(spm,[status(thm)],[c_0_161,c_0_34]) ).
cnf(c_0_167,negated_conjecture,
product(inverse(x_times_y),x_inverse_plus_y_inverse,x_inverse_plus_y_inverse),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_30]),c_0_37]),c_0_163]) ).
cnf(c_0_168,negated_conjecture,
( sum(x_times_y,X1,multiply(X2,X3))
| ~ sum(y,X1,X3)
| ~ sum(x,X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_52]) ).
cnf(c_0_169,negated_conjecture,
add(x,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_164]),c_0_38]) ).
cnf(c_0_170,negated_conjecture,
multiply(inverse(y),add(x_inverse_plus_y_inverse,inverse(inverse(y)))) = inverse(y),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_165]),c_0_54]) ).
cnf(c_0_171,plain,
( product(X1,add(X2,X3),X3)
| ~ sum(X3,inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_30]),c_0_82]) ).
cnf(c_0_172,negated_conjecture,
sum(x_inverse_plus_y_inverse,inverse(x_times_y),inverse(x_times_y)),
inference(spm,[status(thm)],[c_0_47,c_0_167]) ).
cnf(c_0_173,negated_conjecture,
( sum(x_times_y,X1,multiply(X2,add(y,X1)))
| ~ sum(x,X1,X2) ),
inference(spm,[status(thm)],[c_0_168,c_0_30]) ).
cnf(c_0_174,negated_conjecture,
sum(x,x_inverse_plus_y_inverse,multiplicative_identity),
inference(spm,[status(thm)],[c_0_30,c_0_169]) ).
cnf(c_0_175,negated_conjecture,
multiply(inverse(y),add(y,x_inverse_plus_y_inverse)) = inverse(y),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_144]),c_0_37]) ).
cnf(c_0_176,negated_conjecture,
product(inverse(x_times_y),add(x_times_y,x_inverse_plus_y_inverse),x_inverse_plus_y_inverse),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_177,negated_conjecture,
sum(x_times_y,x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_125]) ).
cnf(c_0_178,negated_conjecture,
sum(inverse(y),add(y,x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)),
inference(spm,[status(thm)],[c_0_80,c_0_175]) ).
cnf(c_0_179,negated_conjecture,
multiply(inverse(x_times_y),add(x_times_y,x_inverse_plus_y_inverse)) = x_inverse_plus_y_inverse,
inference(spm,[status(thm)],[c_0_48,c_0_176]) ).
cnf(c_0_180,negated_conjecture,
add(x_times_y,x_inverse_plus_y_inverse) = add(y,x_inverse_plus_y_inverse),
inference(spm,[status(thm)],[c_0_33,c_0_177]) ).
cnf(c_0_181,negated_conjecture,
sum(inverse(y),y,add(y,x_inverse_plus_y_inverse)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_178]),c_0_144]),c_0_148]) ).
cnf(c_0_182,negated_conjecture,
multiply(inverse(x_times_y),add(y,x_inverse_plus_y_inverse)) = x_inverse_plus_y_inverse,
inference(rw,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_183,negated_conjecture,
add(y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_181]),c_0_38]) ).
cnf(c_0_184,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
prove_equation ).
cnf(c_0_185,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_183]),c_0_88]),c_0_184]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO015-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n031.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:46:24 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 6.66/4.59 % Version : CSE_E---1.7
% 6.66/4.59 % Problem : theBenchmark.p
% 6.66/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 6.66/4.59 % SZS output start CNFRefutation
% See solution above
% 6.76/4.61 % Total time : 3.371s
%------------------------------------------------------------------------------