%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD027-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:22:44 PM UTC 2026
% Result : Unsatisfiable 98.53s 13.00s
% Output : CNFRefutation 98.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 26
% Syntax : Number of clauses : 214 ( 92 unt; 16 nHn; 214 RR)
% Number of literals : 429 ( 0 equ; 214 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 214 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(transitivity_of_equality,axiom,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(compatibility_of_equality_and_order_relation,axiom,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
cnf(commutativity_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(b_not_equal_to_additive_identity_4,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_4) ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(associativity_multiplication,axiom,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(a_not_equal_to_additive_identity_3,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_3) ).
cnf(well_definedness_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(multiplicative_inverses_equal,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverses_equal) ).
cnf(a_not_equal_to_b_6,negated_conjecture,
~ equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_b_6) ).
cnf(c_0_26,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_27,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_26 ).
cnf(c_0_28,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_29,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_equality]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_31,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_32,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
cnf(c_0_33,hypothesis,
( ~ defined(X1)
| less_or_equal(b,X1)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
c_0_29 ).
cnf(c_0_35,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
c_0_30 ).
cnf(c_0_36,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_37,hypothesis,
( ~ defined(X1)
| less_or_equal(a,X1)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_38,plain,
( ~ equalish(X3,X1)
| ~ less_or_equal(X3,X2)
| less_or_equal(X1,X2) ),
c_0_32 ).
cnf(c_0_39,hypothesis,
less_or_equal(b,b),
inference(spm,[status(thm)],[c_0_33,c_0_28]) ).
cnf(c_0_40,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[symmetry_of_equality]) ).
cnf(c_0_41,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
c_0_36 ).
cnf(c_0_43,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_44,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_45,hypothesis,
( ~ equalish(b,X1)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
c_0_40 ).
cnf(c_0_47,plain,
( ~ defined(X1)
| equalish(add(X1,additive_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_48,hypothesis,
( ~ equalish(a,X1)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_49,hypothesis,
( ~ equalish(X2,X1)
| ~ equalish(b,X2)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_45]) ).
cnf(c_0_50,plain,
( ~ defined(X1)
| equalish(X1,add(X1,additive_identity)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_52,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_53,plain,
( ~ defined(X1)
| less_or_equal(additive_identity,X1)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_54,hypothesis,
( ~ equalish(X2,X1)
| ~ equalish(a,X2)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_48]) ).
cnf(c_0_55,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_56,hypothesis,
( ~ equalish(add(b,additive_identity),X1)
| less_or_equal(X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_28])]) ).
cnf(c_0_57,plain,
( ~ less_or_equal(X1,X3)
| ~ defined(X2)
| less_or_equal(add(X1,X2),add(X3,X2)) ),
c_0_51 ).
cnf(c_0_58,plain,
( ~ defined(X1)
| less_or_equal(multiplicative_identity,X1)
| less_or_equal(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_59,plain,
less_or_equal(additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_53,c_0_43]) ).
cnf(c_0_60,hypothesis,
( ~ equalish(add(a,additive_identity),X1)
| less_or_equal(X1,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_31])]) ).
cnf(c_0_61,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| equalish(X1,X2) ),
c_0_55 ).
cnf(c_0_62,hypothesis,
less_or_equal(add(additive_identity,b),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_42]),c_0_43]),c_0_28])]) ).
cnf(c_0_63,plain,
( ~ equalish(add(X4,X3),X1)
| ~ defined(X3)
| ~ less_or_equal(X4,X2)
| less_or_equal(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_64,plain,
less_or_equal(multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_58,c_0_52]) ).
cnf(c_0_65,plain,
( ~ equalish(additive_identity,X1)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_59]) ).
cnf(c_0_66,hypothesis,
less_or_equal(add(additive_identity,a),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_42]),c_0_43]),c_0_31])]) ).
cnf(c_0_67,hypothesis,
( ~ less_or_equal(b,add(additive_identity,b))
| equalish(b,add(additive_identity,b)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
( ~ defined(X1)
| ~ less_or_equal(additive_identity,X2)
| less_or_equal(X1,add(X2,X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_35]) ).
cnf(c_0_69,plain,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_70,plain,
( ~ equalish(multiplicative_identity,X1)
| less_or_equal(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_64]) ).
cnf(c_0_71,plain,
( ~ equalish(X2,X1)
| ~ equalish(additive_identity,X2)
| less_or_equal(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_65]) ).
cnf(c_0_72,plain,
( ~ defined(X1)
| equalish(X1,add(additive_identity,X1)) ),
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_73,hypothesis,
( ~ less_or_equal(a,add(additive_identity,a))
| equalish(a,add(additive_identity,a)) ),
inference(spm,[status(thm)],[c_0_61,c_0_66]) ).
cnf(c_0_74,plain,
( ~ equalish(X1,add(X3,X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_42]) ).
cnf(c_0_75,hypothesis,
equalish(b,add(additive_identity,b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_59]),c_0_28])]) ).
cnf(c_0_76,plain,
( ~ defined(X1)
| equalish(multiply(multiplicative_identity,X1),X1) ),
c_0_69 ).
cnf(c_0_77,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_78,plain,
( ~ equalish(X2,X1)
| ~ equalish(multiplicative_identity,X2)
| less_or_equal(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_70]) ).
cnf(c_0_79,plain,
( ~ equalish(add(additive_identity,additive_identity),X1)
| less_or_equal(X1,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_43])]) ).
cnf(c_0_80,hypothesis,
equalish(a,add(additive_identity,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_68]),c_0_59]),c_0_31])]) ).
cnf(c_0_81,hypothesis,
equalish(b,add(b,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_28]),c_0_43])]) ).
cnf(c_0_82,plain,
( ~ equalish(X1,multiply(multiplicative_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_76]) ).
cnf(c_0_83,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,X2),multiply(X2,X1)) ),
c_0_77 ).
cnf(c_0_84,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_85,plain,
( ~ equalish(add(multiplicative_identity,additive_identity),X1)
| less_or_equal(X1,multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_50]),c_0_52])]) ).
cnf(c_0_86,plain,
less_or_equal(add(additive_identity,additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_42]),c_0_43])]) ).
cnf(c_0_87,hypothesis,
equalish(a,add(a,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_80]),c_0_31]),c_0_43])]) ).
cnf(c_0_88,hypothesis,
equalish(add(b,additive_identity),b),
inference(spm,[status(thm)],[c_0_46,c_0_81]) ).
cnf(c_0_89,plain,
( ~ defined(X1)
| equalish(multiply(X1,multiplicative_identity),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_52])]) ).
cnf(c_0_90,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_84 ).
cnf(c_0_91,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_addition]) ).
cnf(c_0_92,plain,
less_or_equal(add(additive_identity,multiplicative_identity),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_42]),c_0_43]),c_0_52])]) ).
cnf(c_0_93,plain,
( ~ less_or_equal(additive_identity,add(additive_identity,additive_identity))
| equalish(additive_identity,add(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_61,c_0_86]) ).
cnf(c_0_94,hypothesis,
equalish(add(a,additive_identity),a),
inference(spm,[status(thm)],[c_0_46,c_0_87]) ).
cnf(c_0_95,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_96,negated_conjecture,
~ equalish(b,additive_identity),
inference(fof_simplification,[status(thm)],[b_not_equal_to_additive_identity_4]) ).
cnf(c_0_97,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_multiplication]) ).
cnf(c_0_98,hypothesis,
( ~ equalish(X1,add(b,additive_identity))
| equalish(X1,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_88]) ).
cnf(c_0_99,plain,
( ~ defined(X1)
| ~ defined(X2)
| equalish(multiply(add(X1,X2),multiplicative_identity),add(X2,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_89]),c_0_90]) ).
cnf(c_0_100,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
c_0_91 ).
cnf(c_0_101,plain,
( ~ less_or_equal(multiplicative_identity,add(additive_identity,multiplicative_identity))
| equalish(multiplicative_identity,add(additive_identity,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_61,c_0_92]) ).
cnf(c_0_102,plain,
equalish(additive_identity,add(additive_identity,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_68]),c_0_59]),c_0_43])]) ).
cnf(c_0_103,hypothesis,
( ~ equalish(X1,add(a,additive_identity))
| equalish(X1,a) ),
inference(spm,[status(thm)],[c_0_34,c_0_94]) ).
cnf(c_0_104,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity) ),
c_0_95 ).
cnf(c_0_105,negated_conjecture,
~ equalish(b,additive_identity),
c_0_96 ).
cnf(c_0_106,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_107,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(multiply(X1,X2),multiply(X3,X2)) ),
c_0_97 ).
cnf(c_0_108,hypothesis,
equalish(multiply(add(additive_identity,b),multiplicative_identity),b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_28]),c_0_43])]) ).
cnf(c_0_109,plain,
( ~ equalish(X4,X2)
| ~ equalish(X1,add(X4,X3))
| ~ defined(X3)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_100]) ).
cnf(c_0_110,plain,
equalish(multiplicative_identity,add(additive_identity,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_68]),c_0_59]),c_0_52])]) ).
cnf(c_0_111,plain,
equalish(add(additive_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_46,c_0_102]) ).
cnf(c_0_112,hypothesis,
equalish(multiply(add(additive_identity,a),multiplicative_identity),a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_99]),c_0_31]),c_0_43])]) ).
cnf(c_0_113,hypothesis,
equalish(multiply(b,multiplicative_inverse(b)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_28]),c_0_105]) ).
cnf(c_0_114,plain,
( ~ defined(X1)
| equalish(X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_106 ).
cnf(c_0_115,plain,
( ~ equalish(X4,X2)
| ~ equalish(X1,multiply(X4,X3))
| ~ defined(X3)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_107]) ).
cnf(c_0_116,hypothesis,
equalish(b,multiply(add(additive_identity,b),multiplicative_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_108]) ).
cnf(c_0_117,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(b,add(X1,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_75]),c_0_28])]) ).
cnf(c_0_118,plain,
equalish(multiplicative_identity,add(multiplicative_identity,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_110]),c_0_52]),c_0_43])]) ).
cnf(c_0_119,plain,
( ~ equalish(X1,add(additive_identity,additive_identity))
| equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_111]) ).
cnf(c_0_120,hypothesis,
equalish(a,multiply(add(additive_identity,a),multiplicative_identity)),
inference(spm,[status(thm)],[c_0_46,c_0_112]) ).
cnf(c_0_121,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(a,add(X1,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_80]),c_0_31])]) ).
cnf(c_0_122,hypothesis,
( ~ equalish(X1,multiply(b,multiplicative_inverse(b)))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_113]) ).
cnf(c_0_123,hypothesis,
defined(multiplicative_inverse(b)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_28]),c_0_105]) ).
cnf(c_0_124,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication]) ).
cnf(c_0_125,hypothesis,
( ~ equalish(add(additive_identity,b),X1)
| equalish(b,multiply(X1,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_52])]) ).
cnf(c_0_126,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(add(X1,b),b) ),
inference(spm,[status(thm)],[c_0_46,c_0_117]) ).
cnf(c_0_127,plain,
equalish(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_59]),c_0_59])]) ).
cnf(c_0_128,plain,
equalish(add(multiplicative_identity,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_46,c_0_118]) ).
cnf(c_0_129,plain,
( ~ equalish(X1,additive_identity)
| equalish(add(X1,additive_identity),additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_100]),c_0_43])]) ).
cnf(c_0_130,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(fof_simplification,[status(thm)],[different_identities]) ).
cnf(c_0_131,hypothesis,
( ~ equalish(add(additive_identity,a),X1)
| equalish(a,multiply(X1,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_120]),c_0_52])]) ).
cnf(c_0_132,hypothesis,
( ~ equalish(additive_identity,X1)
| equalish(add(X1,a),a) ),
inference(spm,[status(thm)],[c_0_46,c_0_121]) ).
cnf(c_0_133,hypothesis,
equalish(multiply(multiplicative_inverse(b),b),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_83]),c_0_28]),c_0_123])]) ).
cnf(c_0_134,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3)) ),
c_0_124 ).
cnf(c_0_135,hypothesis,
equalish(b,multiply(b,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127])]) ).
cnf(c_0_136,negated_conjecture,
~ equalish(a,additive_identity),
inference(fof_simplification,[status(thm)],[a_not_equal_to_additive_identity_3]) ).
cnf(c_0_137,plain,
( equalish(multiplicative_identity,additive_identity)
| equalish(multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_104,c_0_52]) ).
cnf(c_0_138,plain,
( ~ equalish(X1,add(multiplicative_identity,additive_identity))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_128]) ).
cnf(c_0_139,plain,
( ~ equalish(X1,additive_identity)
| equalish(additive_identity,add(X1,additive_identity)) ),
inference(spm,[status(thm)],[c_0_46,c_0_129]) ).
cnf(c_0_140,plain,
~ equalish(additive_identity,multiplicative_identity),
c_0_130 ).
cnf(c_0_141,hypothesis,
equalish(a,multiply(a,multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_127])]) ).
cnf(c_0_142,hypothesis,
( ~ equalish(X1,multiply(multiplicative_inverse(b),b))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_133]) ).
cnf(c_0_143,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplication]) ).
cnf(c_0_144,plain,
( ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| equalish(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X3))) ),
inference(spm,[status(thm)],[c_0_46,c_0_134]) ).
cnf(c_0_145,hypothesis,
( ~ equalish(X1,b)
| equalish(X1,multiply(b,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_34,c_0_135]) ).
cnf(c_0_146,hypothesis,
equalish(add(additive_identity,b),b),
inference(spm,[status(thm)],[c_0_46,c_0_75]) ).
cnf(c_0_147,negated_conjecture,
~ equalish(a,additive_identity),
c_0_136 ).
cnf(c_0_148,plain,
( equalish(multiplicative_identity,additive_identity)
| equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))) ),
inference(spm,[status(thm)],[c_0_46,c_0_137]) ).
cnf(c_0_149,plain,
~ equalish(multiplicative_identity,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_140]) ).
cnf(c_0_150,plain,
( equalish(multiplicative_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_114,c_0_52]) ).
cnf(c_0_151,hypothesis,
( ~ equalish(X1,a)
| equalish(X1,multiply(a,multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_34,c_0_141]) ).
cnf(c_0_152,hypothesis,
equalish(add(additive_identity,a),a),
inference(spm,[status(thm)],[c_0_46,c_0_80]) ).
cnf(c_0_153,hypothesis,
( ~ equalish(X1,multiplicative_inverse(b))
| equalish(multiply(X1,b),multiplicative_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_107]),c_0_28])]) ).
cnf(c_0_154,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_inverse(b)),
multiplicative_inverses_equal ).
cnf(c_0_155,plain,
( ~ equalish(X1,multiply(X3,X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_83]) ).
cnf(c_0_156,plain,
( ~ equalish(X1,multiply(X2,multiply(X3,X4)))
| ~ defined(X2)
| ~ defined(X3)
| ~ defined(X4)
| equalish(X1,multiply(multiply(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_34,c_0_134]) ).
cnf(c_0_157,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(multiply(X1,X2)) ),
c_0_143 ).
cnf(c_0_158,plain,
( ~ equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X2)
| ~ defined(X3)
| ~ defined(X4)
| equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_34,c_0_144]) ).
cnf(c_0_159,hypothesis,
equalish(b,multiply(multiply(b,multiplicative_identity),multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_145]),c_0_146])]) ).
cnf(c_0_160,hypothesis,
equalish(multiply(a,multiplicative_inverse(a)),multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_31]),c_0_147]) ).
cnf(c_0_161,plain,
equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_inverse(multiplicative_identity))),
inference(sr,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_162,plain,
defined(multiplicative_inverse(multiplicative_identity)),
inference(sr,[status(thm)],[c_0_150,c_0_149]) ).
cnf(c_0_163,hypothesis,
equalish(a,multiply(multiply(a,multiplicative_identity),multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_151]),c_0_152])]) ).
cnf(c_0_164,negated_conjecture,
equalish(multiply(multiplicative_inverse(a),b),multiplicative_identity),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_165,plain,
( ~ equalish(X1,multiply(X3,multiply(X4,X2)))
| ~ defined(X3)
| ~ defined(X4)
| ~ defined(X2)
| equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_166,hypothesis,
equalish(b,multiply(b,multiply(multiplicative_identity,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_52]),c_0_28])]) ).
cnf(c_0_167,hypothesis,
( ~ equalish(X1,multiply(a,multiplicative_inverse(a)))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_160]) ).
cnf(c_0_168,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_31]),c_0_147]) ).
cnf(c_0_169,plain,
equalish(multiplicative_identity,multiply(multiplicative_inverse(multiplicative_identity),multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_161]),c_0_162]),c_0_52])]) ).
cnf(c_0_170,plain,
equalish(multiplicative_identity,multiplicative_inverse(multiplicative_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_161]),c_0_162])]) ).
cnf(c_0_171,hypothesis,
equalish(a,multiply(a,multiply(multiplicative_identity,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_163]),c_0_52]),c_0_31])]) ).
cnf(c_0_172,negated_conjecture,
( ~ equalish(X1,multiply(multiplicative_inverse(a),b))
| equalish(X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_164]) ).
cnf(c_0_173,hypothesis,
equalish(b,multiply(multiplicative_identity,multiply(b,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_52]),c_0_28])]) ).
cnf(c_0_174,hypothesis,
equalish(multiply(multiplicative_inverse(a),a),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_83]),c_0_31]),c_0_168])]) ).
cnf(c_0_175,plain,
( ~ equalish(multiplicative_inverse(multiplicative_identity),X1)
| equalish(multiplicative_identity,multiply(X1,multiplicative_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_169]),c_0_52])]) ).
cnf(c_0_176,plain,
equalish(multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_46,c_0_170]) ).
cnf(c_0_177,hypothesis,
equalish(a,multiply(multiplicative_identity,multiply(a,multiplicative_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_171]),c_0_52]),c_0_31])]) ).
cnf(c_0_178,negated_conjecture,
equalish(multiply(b,multiplicative_inverse(a)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_83]),c_0_168]),c_0_28])]) ).
cnf(c_0_179,plain,
( ~ equalish(multiply(X5,X4),X2)
| ~ equalish(X1,multiply(X5,multiply(X4,X3)))
| ~ defined(X5)
| ~ defined(X4)
| ~ defined(X3)
| equalish(X1,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_115,c_0_156]) ).
cnf(c_0_180,hypothesis,
equalish(b,multiply(multiplicative_identity,multiply(multiplicative_identity,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_173]),c_0_52]),c_0_28])]) ).
cnf(c_0_181,hypothesis,
equalish(multiplicative_identity,multiply(multiplicative_inverse(a),a)),
inference(spm,[status(thm)],[c_0_46,c_0_174]) ).
cnf(c_0_182,plain,
equalish(multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_183,hypothesis,
equalish(a,multiply(multiplicative_identity,multiply(multiplicative_identity,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_177]),c_0_52]),c_0_31])]) ).
cnf(c_0_184,negated_conjecture,
equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_46,c_0_178]) ).
cnf(c_0_185,hypothesis,
( ~ equalish(multiply(multiplicative_identity,multiplicative_identity),X1)
| equalish(b,multiply(X1,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_28]),c_0_52])]) ).
cnf(c_0_186,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(multiplicative_inverse(a),a)) ),
inference(spm,[status(thm)],[c_0_34,c_0_181]) ).
cnf(c_0_187,plain,
equalish(multiply(multiplicative_identity,multiplicative_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_46,c_0_182]) ).
cnf(c_0_188,negated_conjecture,
equalish(multiplicative_identity,multiply(multiplicative_inverse(a),b)),
inference(spm,[status(thm)],[c_0_46,c_0_164]) ).
cnf(c_0_189,hypothesis,
( ~ equalish(multiply(multiplicative_identity,multiplicative_identity),X1)
| equalish(a,multiply(X1,a)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_183]),c_0_31]),c_0_52])]) ).
cnf(c_0_190,negated_conjecture,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(b,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_34,c_0_184]) ).
cnf(c_0_191,hypothesis,
equalish(b,multiply(multiply(multiplicative_inverse(a),a),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_187])]) ).
cnf(c_0_192,hypothesis,
equalish(multiplicative_identity,multiply(a,multiplicative_inverse(a))),
inference(spm,[status(thm)],[c_0_46,c_0_160]) ).
cnf(c_0_193,negated_conjecture,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(multiplicative_inverse(a),b)) ),
inference(spm,[status(thm)],[c_0_34,c_0_188]) ).
cnf(c_0_194,negated_conjecture,
equalish(a,multiply(multiply(b,multiplicative_inverse(a)),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_187])]) ).
cnf(c_0_195,hypothesis,
equalish(b,multiply(multiplicative_inverse(a),multiply(a,b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_191]),c_0_28]),c_0_31]),c_0_168])]) ).
cnf(c_0_196,hypothesis,
( ~ equalish(X1,a)
| equalish(add(X1,additive_identity),a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_100]),c_0_43])]) ).
cnf(c_0_197,negated_conjecture,
~ equalish(a,b),
inference(fof_simplification,[status(thm)],[a_not_equal_to_b_6]) ).
cnf(c_0_198,hypothesis,
( ~ equalish(X1,multiplicative_identity)
| equalish(X1,multiply(a,multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_34,c_0_192]) ).
cnf(c_0_199,negated_conjecture,
equalish(a,multiply(multiply(multiplicative_inverse(a),b),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_193]),c_0_187])]) ).
cnf(c_0_200,hypothesis,
( ~ equalish(multiply(multiply(X4,X3),X2),X1)
| ~ equalish(b,multiply(X4,multiply(X3,X2)))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_49,c_0_156]) ).
cnf(c_0_201,negated_conjecture,
equalish(multiply(multiply(b,multiplicative_inverse(a)),a),a),
inference(spm,[status(thm)],[c_0_46,c_0_194]) ).
cnf(c_0_202,hypothesis,
equalish(b,multiply(b,multiply(multiplicative_inverse(a),a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_195]),c_0_28]),c_0_31]),c_0_168])]) ).
cnf(c_0_203,hypothesis,
( ~ equalish(X1,a)
| equalish(a,add(X1,additive_identity)) ),
inference(spm,[status(thm)],[c_0_46,c_0_196]) ).
cnf(c_0_204,negated_conjecture,
~ equalish(a,b),
c_0_197 ).
cnf(c_0_205,hypothesis,
equalish(b,multiply(multiply(a,multiplicative_inverse(a)),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_198]),c_0_187])]) ).
cnf(c_0_206,negated_conjecture,
equalish(a,multiply(multiplicative_inverse(a),multiply(b,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_199]),c_0_31]),c_0_28]),c_0_168])]) ).
cnf(c_0_207,hypothesis,
less_or_equal(a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_31]),c_0_168]),c_0_28]),c_0_202])]) ).
cnf(c_0_208,hypothesis,
~ equalish(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_203]),c_0_204]) ).
cnf(c_0_209,hypothesis,
( ~ equalish(multiply(multiply(X4,X3),X2),X1)
| ~ equalish(a,multiply(X4,multiply(X3,X2)))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_54,c_0_156]) ).
cnf(c_0_210,hypothesis,
equalish(multiply(multiply(a,multiplicative_inverse(a)),b),b),
inference(spm,[status(thm)],[c_0_46,c_0_205]) ).
cnf(c_0_211,negated_conjecture,
equalish(a,multiply(a,multiply(multiplicative_inverse(a),b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_206]),c_0_31]),c_0_28]),c_0_168])]) ).
cnf(c_0_212,hypothesis,
~ less_or_equal(b,a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_207]),c_0_208]) ).
cnf(c_0_213,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_28]),c_0_168]),c_0_31]),c_0_211])]),c_0_212]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 15:34:13 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 98.53/13.00 % Version: 3.5.1
% 98.53/13.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 98.53/13.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.53/13.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.53/13.00 % Starting new_bool_3 with 300s (1) cores
% 98.53/13.00 % Starting new_bool_1 with 300s (1) cores
% 98.53/13.00 % Starting sh5l with 300s (1) cores
% 98.53/13.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2663862 completed with status 0
% 98.53/13.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 98.53/13.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 98.53/13.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.53/13.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.53/13.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.53/13.00 % No SInE strategy applied
% 98.53/13.00 % Search class: FGUNF-FFMS21-SFFFFFNN
% 98.53/13.00 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 98.53/13.00 % Starting SubtermCWHack with 136s (1) cores
% 98.53/13.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 98.53/13.00 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 98.53/13.00 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 98.53/13.00 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 98.53/13.00 % U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2663872 completed with status 0
% 98.53/13.00 % Result found by U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 98.53/13.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 98.53/13.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.53/13.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 98.53/13.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.53/13.00 % No SInE strategy applied
% 98.53/13.00 % Search class: FGUNF-FFMS21-SFFFFFNN
% 98.53/13.00 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 98.53/13.00 % Starting SubtermCWHack with 136s (1) cores
% 98.53/13.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 98.53/13.00 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 98.53/13.00 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 98.53/13.00 % Preprocessing time : 0.001 s
% 98.53/13.00 % Presaturation interreduction done
% 98.53/13.00
% 98.53/13.00 % Proof found!
% 98.53/13.00 % SZS status Unsatisfiable
% 98.53/13.00 % SZS output start CNFRefutation
% See solution above
% 98.53/13.00 % Parsed axioms : 33
% 98.53/13.00 % Removed by relevancy pruning/SinE : 0
% 98.53/13.00 % Initial clauses : 33
% 98.53/13.00 % Removed in clause preprocessing : 0
% 98.53/13.00 % Initial clauses in saturation : 33
% 98.53/13.00 % Processed clauses : 34606
% 98.53/13.00 % ...of these trivial : 2160
% 98.53/13.00 % ...subsumed : 22535
% 98.53/13.00 % ...remaining for further processing : 9911
% 98.53/13.00 % Other redundant clauses eliminated : 0
% 98.53/13.00 % Clauses deleted for lack of memory : 0
% 98.53/13.00 % Backward-subsumed : 1674
% 98.53/13.00 % Backward-rewritten : 39
% 98.53/13.00 % Generated clauses : 537875
% 98.53/13.00 % ...of the previous two non-redundant : 507202
% 98.53/13.00 % ...aggressively subsumed : 0
% 98.53/13.00 % Contextual simplify-reflections : 107
% 98.53/13.00 % Paramodulations : 537854
% 98.53/13.00 % Factorizations : 0
% 98.53/13.00 % NegExts : 0
% 98.53/13.00 % Equation resolutions : 0
% 98.53/13.00 % Disequality decompositions : 0
% 98.53/13.00 % Total rewrite steps : 109835
% 98.53/13.00 % ...of those cached : 107766
% 98.53/13.00 % Propositional unsat checks : 0
% 98.53/13.00 % Propositional check models : 0
% 98.53/13.00 % Propositional check unsatisfiable : 0
% 98.53/13.00 % Propositional clauses : 0
% 98.53/13.00 % Propositional clauses after purity: 0
% 98.53/13.00 % Propositional unsat core size : 0
% 98.53/13.00 % Propositional preprocessing time : 0.000
% 98.53/13.00 % Propositional encoding time : 0.000
% 98.53/13.00 % Propositional solver time : 0.000
% 98.53/13.00 % Success case prop preproc time : 0.000
% 98.53/13.00 % Success case prop encoding time : 0.000
% 98.53/13.00 % Success case prop solver time : 0.000
% 98.53/13.00 % Current number of processed clauses : 8144
% 98.53/13.00 % Positive orientable unit clauses : 2379
% 98.53/13.00 % Positive unorientable unit clauses: 0
% 98.53/13.00 % Negative unit clauses : 736
% 98.53/13.00 % Non-unit-clauses : 5029
% 98.53/13.00 % Current number of unprocessed clauses: 471832
% 98.53/13.00 % ...number of literals in the above : 1989032
% 98.53/13.00 % Current number of archived formulas : 0
% 98.53/13.00 % Current number of archived clauses : 1767
% 98.53/13.00 % Clause-clause subsumption calls (NU) : 4015889
% 98.53/13.00 % Rec. Clause-clause subsumption calls : 2693832
% 98.53/13.00 % Non-unit clause-clause subsumptions : 15743
% 98.53/13.00 % Unit Clause-clause subsumption calls : 993032
% 98.53/13.00 % Rewrite failures with RHS unbound : 0
% 98.53/13.00 % BW rewrite match attempts : 26270
% 98.53/13.00 % BW rewrite match successes : 266
% 98.53/13.00 % Condensation attempts : 0
% 98.53/13.00 % Condensation successes : 0
% 98.53/13.00 % Termbank termtop insertions : 14135037
% 98.53/13.00 % Search garbage collected termcells : 75
% 98.53/13.00
% 98.53/13.00 % -------------------------------------------------
% 98.53/13.00 % User time : 11.717 s
% 98.53/13.00 % System time : 0.475 s
% 98.53/13.00 % Total time : 12.191 s
% 98.53/13.00 % Maximum resident set size: 3660 pages
% 98.53/13.00
% 98.53/13.00 % -------------------------------------------------
% 98.53/13.00 % User time : 59.180 s
% 98.53/13.00 % System time : 2.236 s
% 98.53/13.00 % Total time : 61.416 s
% 98.53/13.00 % Maximum resident set size: 4608 pages
% 98.53/13.00 % E exiting
%------------------------------------------------------------------------------