TSTP Solution File: FLD012-2 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : FLD012-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 : Wed Aug 30 22:27:16 EDT 2023
% Result : Unsatisfiable 115.67s 115.62s
% Output : CNFRefutation 115.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 38
% Syntax : Number of formulae : 203 ( 69 unt; 13 typ; 0 def)
% Number of atoms : 383 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 377 ( 184 ~; 193 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
add: ( $i * $i ) > $i ).
tff(decl_23,type,
equalish: ( $i * $i ) > $o ).
tff(decl_24,type,
defined: $i > $o ).
tff(decl_25,type,
additive_identity: $i ).
tff(decl_26,type,
additive_inverse: $i > $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
multiplicative_identity: $i ).
tff(decl_29,type,
multiplicative_inverse: $i > $i ).
tff(decl_30,type,
less_or_equal: ( $i * $i ) > $o ).
tff(decl_31,type,
a: $i ).
tff(decl_32,type,
b: $i ).
tff(decl_33,type,
u: $i ).
tff(decl_34,type,
v: $i ).
cnf(compatibility_of_equality_and_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
cnf(multiply_equals_u_7,negated_conjecture,
equalish(multiply(a,b),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_u_7) ).
cnf(transitivity_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(associativity_multiplication,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_multiplication) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(commutativity_multiplication,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_multiplication) ).
cnf(well_definedness_of_multiplication,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplication) ).
cnf(symmetry_of_equality,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(existence_of_inverse_multiplication,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_multiplication) ).
cnf(b_not_equal_to_additive_identity_6,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_6) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(existence_of_identity_multiplication,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_multiplication) ).
cnf(multiply_equals_v_8,negated_conjecture,
equalish(multiply(multiplicative_inverse(a),multiplicative_inverse(b)),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_equals_v_8) ).
cnf(a_not_equal_to_additive_identity_5,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_5) ).
cnf(existence_of_identity_addition,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(u_is_defined,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
cnf(v_is_defined,hypothesis,
defined(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
cnf(commutativity_addition,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
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(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(compatibility_of_equality_and_addition,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(distributivity,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',distributivity) ).
cnf(multiplicative_inverse_not_equal_to_v_9,negated_conjecture,
~ equalish(multiplicative_inverse(u),v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse_not_equal_to_v_9) ).
cnf(different_identities,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',different_identities) ).
cnf(c_0_25,axiom,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_multiplication ).
cnf(c_0_26,negated_conjecture,
equalish(multiply(a,b),u),
multiply_equals_u_7 ).
cnf(c_0_27,axiom,
( equalish(X1,X2)
| ~ equalish(X1,X3)
| ~ equalish(X3,X2) ),
transitivity_of_equality ).
cnf(c_0_28,negated_conjecture,
( equalish(multiply(multiply(a,b),X1),multiply(u,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( equalish(X1,multiply(u,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(a,b),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,axiom,
( equalish(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),X3))
| ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3) ),
associativity_multiplication ).
cnf(c_0_31,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_32,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_33,axiom,
( equalish(multiply(X1,X2),multiply(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_multiplication ).
cnf(c_0_34,negated_conjecture,
( equalish(multiply(a,multiply(b,X1)),multiply(u,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_35,plain,
( equalish(X1,multiply(X2,X3))
| ~ defined(X2)
| ~ defined(X3)
| ~ equalish(X1,multiply(X3,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_33]) ).
cnf(c_0_36,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_37,axiom,
( defined(multiply(X1,X2))
| ~ defined(X1)
| ~ defined(X2) ),
well_definedness_of_multiplication ).
cnf(c_0_38,negated_conjecture,
( equalish(X1,multiply(u,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(a,multiply(b,X2))) ),
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_39,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(X3,multiply(X2,X1)))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
( equalish(multiply(multiply(X1,b),a),multiply(u,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_31])]) ).
cnf(c_0_41,negated_conjecture,
( equalish(X1,multiply(u,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(X2,b),a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_42,axiom,
( equalish(X1,X2)
| ~ equalish(X2,X1) ),
symmetry_of_equality ).
cnf(c_0_43,axiom,
( equalish(multiply(X1,multiplicative_inverse(X1)),multiplicative_identity)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
existence_of_inverse_multiplication ).
cnf(c_0_44,negated_conjecture,
( equalish(multiply(multiply(b,X1),a),multiply(u,X1))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_32]),c_0_31])]) ).
cnf(c_0_45,plain,
( equalish(multiplicative_identity,multiply(X1,multiplicative_inverse(X1)))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( equalish(X1,multiply(u,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(b,X2),a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_44]) ).
cnf(c_0_47,plain,
( equalish(multiply(multiplicative_identity,X1),multiply(multiply(X2,multiplicative_inverse(X2)),X1))
| equalish(X2,additive_identity)
| ~ defined(X1)
| ~ defined(X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
~ equalish(b,additive_identity),
b_not_equal_to_additive_identity_6 ).
cnf(c_0_49,negated_conjecture,
( equalish(multiply(multiplicative_identity,a),multiply(u,multiplicative_inverse(b)))
| ~ defined(multiplicative_inverse(b)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_32]),c_0_31])]),c_0_48]) ).
cnf(c_0_50,axiom,
( defined(multiplicative_inverse(X1))
| equalish(X1,additive_identity)
| ~ defined(X1) ),
well_definedness_of_multiplicative_inverse ).
cnf(c_0_51,negated_conjecture,
equalish(multiply(multiplicative_identity,a),multiply(u,multiplicative_inverse(b))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_31])]),c_0_48]) ).
cnf(c_0_52,axiom,
( equalish(multiply(multiplicative_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_multiplication ).
cnf(c_0_53,negated_conjecture,
( equalish(X1,multiply(u,multiplicative_inverse(b)))
| ~ equalish(X1,multiply(multiplicative_identity,a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_51]) ).
cnf(c_0_54,plain,
( equalish(X1,multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
equalish(a,multiply(u,multiplicative_inverse(b))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_32])]) ).
cnf(c_0_56,negated_conjecture,
( equalish(multiply(a,X1),multiply(multiply(u,multiplicative_inverse(b)),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( equalish(X1,u)
| ~ equalish(X1,multiply(a,b)) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_58,negated_conjecture,
equalish(u,multiply(a,b)),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_59,negated_conjecture,
equalish(multiply(multiplicative_inverse(a),multiplicative_inverse(b)),v),
multiply_equals_v_8 ).
cnf(c_0_60,negated_conjecture,
( equalish(X1,multiply(multiply(u,multiplicative_inverse(b)),X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(a,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
~ equalish(a,additive_identity),
a_not_equal_to_additive_identity_5 ).
cnf(c_0_62,negated_conjecture,
equalish(u,u),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(multiplicative_inverse(a),multiplicative_inverse(b))) ),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_64,negated_conjecture,
equalish(v,multiply(multiplicative_inverse(a),multiplicative_inverse(b))),
inference(spm,[status(thm)],[c_0_42,c_0_59]) ).
cnf(c_0_65,axiom,
( equalish(add(additive_identity,X1),X1)
| ~ defined(X1) ),
existence_of_identity_addition ).
cnf(c_0_66,negated_conjecture,
( equalish(multiplicative_identity,multiply(multiply(u,multiplicative_inverse(b)),multiplicative_inverse(a)))
| ~ defined(multiplicative_inverse(a)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_45]),c_0_32])]),c_0_61]) ).
cnf(c_0_67,negated_conjecture,
( equalish(multiply(u,X1),multiply(u,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_62]) ).
cnf(c_0_68,hypothesis,
defined(u),
u_is_defined ).
cnf(c_0_69,negated_conjecture,
( equalish(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),v)
| ~ defined(multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_63,c_0_33]) ).
cnf(c_0_70,plain,
( equalish(X1,multiply(multiplicative_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_71,negated_conjecture,
equalish(v,v),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,hypothesis,
defined(v),
v_is_defined ).
cnf(c_0_73,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_65]) ).
cnf(c_0_74,axiom,
( equalish(add(X1,X2),add(X2,X1))
| ~ defined(X1)
| ~ defined(X2) ),
commutativity_addition ).
cnf(c_0_75,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_76,negated_conjecture,
equalish(multiplicative_identity,multiply(multiply(u,multiplicative_inverse(b)),multiplicative_inverse(a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_32])]),c_0_61]) ).
cnf(c_0_77,negated_conjecture,
( equalish(multiply(u,X1),multiply(X1,u))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_67]),c_0_68])]) ).
cnf(c_0_78,negated_conjecture,
( equalish(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),v)
| ~ defined(multiplicative_inverse(b)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_50]),c_0_32])]),c_0_61]) ).
cnf(c_0_79,negated_conjecture,
equalish(v,multiply(multiplicative_identity,v)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_80,plain,
( equalish(add(X1,additive_identity),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75])]) ).
cnf(c_0_81,negated_conjecture,
equalish(multiply(multiply(u,multiplicative_inverse(b)),multiplicative_inverse(a)),multiplicative_identity),
inference(spm,[status(thm)],[c_0_42,c_0_76]) ).
cnf(c_0_82,plain,
( equalish(X1,multiply(multiply(X2,X3),X4))
| ~ defined(X4)
| ~ defined(X3)
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,multiply(X3,X4))) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_83,negated_conjecture,
( equalish(multiply(X1,u),multiply(u,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
equalish(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),v),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_50]),c_0_31])]),c_0_48]) ).
cnf(c_0_85,negated_conjecture,
equalish(multiply(multiplicative_identity,v),v),
inference(spm,[status(thm)],[c_0_42,c_0_79]) ).
cnf(c_0_86,plain,
( equalish(X1,add(X1,additive_identity))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiply(u,multiplicative_inverse(b)),multiplicative_inverse(a))) ),
inference(spm,[status(thm)],[c_0_27,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( equalish(multiply(multiply(X1,X2),u),multiply(multiply(u,X1),X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_68])]),c_0_37]) ).
cnf(c_0_89,negated_conjecture,
( equalish(X1,multiply(u,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,u)) ),
inference(spm,[status(thm)],[c_0_27,c_0_83]) ).
cnf(c_0_90,negated_conjecture,
( equalish(multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),X1),multiply(v,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( equalish(multiply(v,X1),multiply(v,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_71]) ).
cnf(c_0_92,negated_conjecture,
( equalish(X1,v)
| ~ equalish(X1,multiply(multiplicative_identity,v)) ),
inference(spm,[status(thm)],[c_0_27,c_0_85]) ).
cnf(c_0_93,plain,
( equalish(multiply(multiply(X1,multiplicative_inverse(X1)),X2),multiply(multiplicative_identity,X2))
| equalish(X1,additive_identity)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_94,plain,
equalish(additive_identity,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_86]),c_0_75])]) ).
cnf(c_0_95,negated_conjecture,
( equalish(multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u),multiplicative_identity)
| ~ defined(multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(b)) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_96,negated_conjecture,
equalish(multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u),multiply(u,v)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_72]),c_0_68])]) ).
cnf(c_0_97,negated_conjecture,
( equalish(X1,multiply(X2,u))
| ~ defined(X2)
| ~ equalish(X1,multiply(u,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_77]) ).
cnf(c_0_98,negated_conjecture,
( equalish(multiply(v,X1),multiply(X1,v))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_91]),c_0_72])]) ).
cnf(c_0_99,negated_conjecture,
( equalish(multiply(multiply(X1,multiplicative_inverse(X1)),v),v)
| equalish(X1,additive_identity)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_72])]) ).
cnf(c_0_100,plain,
equalish(additive_identity,multiply(multiplicative_identity,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_94]),c_0_75])]) ).
cnf(c_0_101,negated_conjecture,
( equalish(multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u),multiplicative_identity)
| ~ defined(multiplicative_inverse(b)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_50]),c_0_32])]),c_0_61]) ).
cnf(c_0_102,negated_conjecture,
equalish(multiply(u,v),multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u)),
inference(spm,[status(thm)],[c_0_42,c_0_96]) ).
cnf(c_0_103,negated_conjecture,
equalish(multiply(v,u),multiply(v,u)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_72]),c_0_68])]) ).
cnf(c_0_104,negated_conjecture,
( equalish(X1,additive_identity)
| equalish(X2,v)
| ~ defined(X1)
| ~ equalish(X2,multiply(multiply(X1,multiplicative_inverse(X1)),v)) ),
inference(spm,[status(thm)],[c_0_27,c_0_99]) ).
cnf(c_0_105,plain,
equalish(multiply(multiplicative_identity,additive_identity),additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_100]) ).
cnf(c_0_106,negated_conjecture,
equalish(multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u),multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_50]),c_0_31])]),c_0_48]) ).
cnf(c_0_107,negated_conjecture,
( equalish(X1,multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u))
| ~ equalish(X1,multiply(u,v)) ),
inference(spm,[status(thm)],[c_0_27,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
equalish(multiply(v,u),multiply(u,v)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_103]),c_0_68]),c_0_72])]) ).
cnf(c_0_109,negated_conjecture,
( equalish(multiply(multiply(multiplicative_inverse(u),v),u),v)
| equalish(u,additive_identity)
| ~ defined(multiplicative_inverse(u)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_88]),c_0_68]),c_0_72])]) ).
cnf(c_0_110,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(multiplicative_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_105]) ).
cnf(c_0_111,plain,
( equalish(multiply(add(additive_identity,X1),X2),multiply(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_65]) ).
cnf(c_0_112,axiom,
defined(multiplicative_identity),
well_definedness_of_multiplicative_identity ).
cnf(c_0_113,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u)) ),
inference(spm,[status(thm)],[c_0_27,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
equalish(multiply(v,u),multiply(multiply(multiplicative_inverse(b),multiplicative_inverse(a)),u)),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_115,negated_conjecture,
( equalish(multiply(multiply(multiplicative_inverse(u),v),u),v)
| equalish(u,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_50]),c_0_68])]) ).
cnf(c_0_116,plain,
equalish(multiply(add(additive_identity,multiplicative_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_75]),c_0_112])]) ).
cnf(c_0_117,negated_conjecture,
equalish(multiply(v,u),multiplicative_identity),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( equalish(u,additive_identity)
| equalish(X1,v)
| ~ equalish(X1,multiply(multiply(multiplicative_inverse(u),v),u)) ),
inference(spm,[status(thm)],[c_0_27,c_0_115]) ).
cnf(c_0_119,plain,
( equalish(multiply(multiply(X1,X2),X3),multiply(multiply(X3,X1),X2))
| ~ defined(X2)
| ~ defined(X1)
| ~ defined(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_33]),c_0_37]) ).
cnf(c_0_120,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(add(additive_identity,multiplicative_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_116]) ).
cnf(c_0_121,plain,
( equalish(multiply(add(X1,X2),X3),multiply(add(X2,X1),X3))
| ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_74]) ).
cnf(c_0_122,plain,
( equalish(multiply(additive_identity,X1),multiply(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_94]) ).
cnf(c_0_123,plain,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,multiply(multiplicative_identity,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_124,negated_conjecture,
( equalish(multiply(multiply(v,u),X1),multiply(multiplicative_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_117]) ).
cnf(c_0_125,negated_conjecture,
( equalish(multiply(multiply(v,u),multiplicative_inverse(u)),v)
| equalish(u,additive_identity)
| ~ defined(multiplicative_inverse(u)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_68]),c_0_72])]) ).
cnf(c_0_126,plain,
equalish(multiply(add(multiplicative_identity,additive_identity),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_75]),c_0_112])]) ).
cnf(c_0_127,axiom,
( equalish(add(X1,X2),add(X3,X2))
| ~ defined(X2)
| ~ equalish(X1,X3) ),
compatibility_of_equality_and_addition ).
cnf(c_0_128,negated_conjecture,
( equalish(X1,multiply(X2,v))
| ~ defined(X2)
| ~ equalish(X1,multiply(v,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_98]) ).
cnf(c_0_129,plain,
( equalish(multiply(additive_identity,X1),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_122]),c_0_75])]) ).
cnf(c_0_130,negated_conjecture,
( equalish(multiply(multiply(v,u),X1),X1)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,negated_conjecture,
( equalish(multiply(multiply(v,u),multiplicative_inverse(u)),v)
| equalish(u,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_50]),c_0_68])]) ).
cnf(c_0_132,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,multiply(add(multiplicative_identity,additive_identity),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_126]) ).
cnf(c_0_133,axiom,
( equalish(add(multiply(X1,X2),multiply(X3,X2)),multiply(add(X1,X3),X2))
| ~ defined(X1)
| ~ defined(X3)
| ~ defined(X2) ),
distributivity ).
cnf(c_0_134,plain,
( equalish(add(multiply(multiplicative_identity,X1),X2),add(X1,X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_52]) ).
cnf(c_0_135,negated_conjecture,
equalish(multiply(additive_identity,v),multiply(additive_identity,v)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_129]),c_0_75]),c_0_72])]) ).
cnf(c_0_136,negated_conjecture,
( equalish(X1,X2)
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(v,u),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_130]) ).
cnf(c_0_137,negated_conjecture,
( equalish(v,multiply(multiply(v,u),multiplicative_inverse(u)))
| equalish(u,additive_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_131]) ).
cnf(c_0_138,plain,
equalish(add(multiply(multiplicative_identity,additive_identity),multiply(additive_identity,additive_identity)),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_75]),c_0_112])]) ).
cnf(c_0_139,plain,
( equalish(add(multiply(multiplicative_identity,additive_identity),X1),X1)
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_134]),c_0_75])]) ).
cnf(c_0_140,negated_conjecture,
equalish(multiply(additive_identity,v),multiply(v,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_135]),c_0_72]),c_0_75])]) ).
cnf(c_0_141,negated_conjecture,
( equalish(v,multiplicative_inverse(u))
| equalish(u,additive_identity)
| ~ defined(multiplicative_inverse(u)) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_142,plain,
( equalish(X1,additive_identity)
| ~ equalish(X1,add(multiply(multiplicative_identity,additive_identity),multiply(additive_identity,additive_identity))) ),
inference(spm,[status(thm)],[c_0_27,c_0_138]) ).
cnf(c_0_143,plain,
( equalish(X1,add(multiply(multiplicative_identity,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_139]) ).
cnf(c_0_144,negated_conjecture,
( equalish(multiply(multiply(additive_identity,v),X1),multiply(multiply(v,additive_identity),X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
( equalish(v,multiplicative_inverse(u))
| equalish(u,additive_identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_50]),c_0_68])]) ).
cnf(c_0_146,negated_conjecture,
~ equalish(multiplicative_inverse(u),v),
multiplicative_inverse_not_equal_to_v_9 ).
cnf(c_0_147,plain,
( equalish(multiply(additive_identity,additive_identity),additive_identity)
| ~ defined(multiply(additive_identity,additive_identity)) ),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_148,negated_conjecture,
( equalish(multiply(multiply(additive_identity,v),u),multiply(u,multiply(v,additive_identity)))
| ~ defined(multiply(v,additive_identity)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_144]),c_0_68])]) ).
cnf(c_0_149,negated_conjecture,
( equalish(multiply(X1,v),multiply(v,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_98]) ).
cnf(c_0_150,negated_conjecture,
equalish(u,additive_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_145]),c_0_146]) ).
cnf(c_0_151,plain,
equalish(multiply(additive_identity,additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_37]),c_0_75])]) ).
cnf(c_0_152,negated_conjecture,
equalish(multiply(multiply(additive_identity,v),u),multiply(u,multiply(v,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_37]),c_0_75]),c_0_72])]) ).
cnf(c_0_153,plain,
( equalish(multiply(X1,additive_identity),multiply(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_129]) ).
cnf(c_0_154,negated_conjecture,
( equalish(X1,multiply(v,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(X2,v)) ),
inference(spm,[status(thm)],[c_0_27,c_0_149]) ).
cnf(c_0_155,negated_conjecture,
( equalish(multiply(u,X1),multiply(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_150]) ).
cnf(c_0_156,plain,
( equalish(multiply(multiply(additive_identity,additive_identity),X1),multiply(additive_identity,X1))
| ~ defined(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
( equalish(X1,multiply(u,multiply(v,additive_identity)))
| ~ equalish(X1,multiply(multiply(additive_identity,v),u)) ),
inference(spm,[status(thm)],[c_0_27,c_0_152]) ).
cnf(c_0_158,plain,
( equalish(multiply(multiply(X1,X2),additive_identity),multiply(multiply(additive_identity,X1),X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_153]),c_0_75])]),c_0_37]) ).
cnf(c_0_159,negated_conjecture,
equalish(multiply(u,v),multiply(v,additive_identity)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_75]),c_0_72])]) ).
cnf(c_0_160,negated_conjecture,
equalish(multiply(u,v),multiplicative_identity),
inference(spm,[status(thm)],[c_0_113,c_0_102]) ).
cnf(c_0_161,plain,
( equalish(multiply(multiply(additive_identity,additive_identity),X1),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_156]),c_0_75])]) ).
cnf(c_0_162,negated_conjecture,
equalish(multiply(multiply(v,u),additive_identity),multiply(u,multiply(v,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_68]),c_0_72])]) ).
cnf(c_0_163,negated_conjecture,
equalish(multiply(multiply(v,u),additive_identity),additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_124]),c_0_75])]) ).
cnf(c_0_164,negated_conjecture,
( equalish(X1,multiply(v,additive_identity))
| ~ equalish(X1,multiply(u,v)) ),
inference(spm,[status(thm)],[c_0_27,c_0_159]) ).
cnf(c_0_165,negated_conjecture,
equalish(multiplicative_identity,multiply(u,v)),
inference(spm,[status(thm)],[c_0_42,c_0_160]) ).
cnf(c_0_166,plain,
( equalish(X1,multiply(X2,additive_identity))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(additive_identity,additive_identity),X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_161]) ).
cnf(c_0_167,negated_conjecture,
( equalish(X1,multiply(u,multiply(v,additive_identity)))
| ~ equalish(X1,multiply(multiply(v,u),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_162]) ).
cnf(c_0_168,negated_conjecture,
equalish(additive_identity,multiply(multiply(v,u),additive_identity)),
inference(spm,[status(thm)],[c_0_42,c_0_163]) ).
cnf(c_0_169,negated_conjecture,
equalish(multiplicative_identity,multiply(v,additive_identity)),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,plain,
( equalish(multiply(multiply(additive_identity,X1),additive_identity),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_158]),c_0_75])]) ).
cnf(c_0_171,negated_conjecture,
equalish(additive_identity,multiply(u,multiply(v,additive_identity))),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_172,negated_conjecture,
equalish(multiply(v,additive_identity),multiplicative_identity),
inference(spm,[status(thm)],[c_0_42,c_0_169]) ).
cnf(c_0_173,plain,
( equalish(X1,multiply(X2,additive_identity))
| ~ defined(X2)
| ~ equalish(X1,multiply(multiply(additive_identity,X2),additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_170]) ).
cnf(c_0_174,plain,
( equalish(multiply(additive_identity,multiply(X1,X2)),multiply(multiply(additive_identity,X1),X2))
| ~ defined(X2)
| ~ defined(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_122]),c_0_75])]),c_0_37]) ).
cnf(c_0_175,negated_conjecture,
( equalish(X1,multiply(u,multiply(v,additive_identity)))
| ~ equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_27,c_0_171]) ).
cnf(c_0_176,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(v,additive_identity)) ),
inference(spm,[status(thm)],[c_0_27,c_0_172]) ).
cnf(c_0_177,plain,
( equalish(multiply(additive_identity,multiply(X1,additive_identity)),multiply(X1,additive_identity))
| ~ defined(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_75])]) ).
cnf(c_0_178,negated_conjecture,
( equalish(X1,multiply(additive_identity,X2))
| ~ defined(X2)
| ~ equalish(X1,multiply(u,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_155]) ).
cnf(c_0_179,negated_conjecture,
equalish(u,multiply(u,multiply(v,additive_identity))),
inference(spm,[status(thm)],[c_0_175,c_0_150]) ).
cnf(c_0_180,negated_conjecture,
equalish(multiply(additive_identity,multiply(v,additive_identity)),multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_72])]) ).
cnf(c_0_181,negated_conjecture,
( equalish(u,multiply(additive_identity,multiply(v,additive_identity)))
| ~ defined(multiply(v,additive_identity)) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_182,negated_conjecture,
( equalish(X1,multiplicative_identity)
| ~ equalish(X1,multiply(additive_identity,multiply(v,additive_identity))) ),
inference(spm,[status(thm)],[c_0_27,c_0_180]) ).
cnf(c_0_183,negated_conjecture,
equalish(u,multiply(additive_identity,multiply(v,additive_identity))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_37]),c_0_75]),c_0_72])]) ).
cnf(c_0_184,negated_conjecture,
equalish(u,multiplicative_identity),
inference(spm,[status(thm)],[c_0_182,c_0_183]) ).
cnf(c_0_185,negated_conjecture,
( equalish(X1,additive_identity)
| ~ equalish(X1,u) ),
inference(spm,[status(thm)],[c_0_27,c_0_150]) ).
cnf(c_0_186,negated_conjecture,
equalish(multiplicative_identity,u),
inference(spm,[status(thm)],[c_0_42,c_0_184]) ).
cnf(c_0_187,negated_conjecture,
equalish(multiplicative_identity,additive_identity),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_188,axiom,
~ equalish(additive_identity,multiplicative_identity),
different_identities ).
cnf(c_0_189,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_187]),c_0_188]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD012-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 23:45:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 115.67/115.62 % Version : CSE_E---1.5
% 115.67/115.62 % Problem : theBenchmark.p
% 115.67/115.62 % Proof found
% 115.67/115.62 % SZS status Theorem for theBenchmark.p
% 115.67/115.62 % SZS output start Proof
% See solution above
% 115.67/115.64 % Total time : 115.065000 s
% 115.67/115.64 % SZS output end Proof
% 115.67/115.64 % Total time : 115.074000 s
%------------------------------------------------------------------------------