TSTP Solution File: RNG009-5 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Thu Aug 31 13:48:26 EDT 2023
% Result : Unsatisfiable 1.64s 1.76s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 117 ( 111 unt; 6 typ; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 221 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $i ).
tff(decl_23,type,
add: ( $i * $i ) > $i ).
tff(decl_24,type,
additive_inverse: $i > $i ).
tff(decl_25,type,
multiply: ( $i * $i ) > $i ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
b: $i ).
cnf(right_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
cnf(associative_addition,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
cnf(x_cubed_is_x,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_x) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
cnf(prove_commutativity,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_9,axiom,
add(X1,additive_identity) = X1,
right_identity ).
cnf(c_0_10,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_11,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_12,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_13,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_16,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
x_cubed_is_x ).
cnf(c_0_17,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_9]) ).
cnf(c_0_18,hypothesis,
multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10]) ).
cnf(c_0_19,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_16]) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_22,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]),c_0_12]) ).
cnf(c_0_23,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_24,hypothesis,
multiply(X1,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_15]),c_0_24]) ).
cnf(c_0_26,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_27,plain,
add(multiply(X1,X2),add(multiply(X3,X2),X4)) = add(multiply(add(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_28,hypothesis,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_25]),c_0_15]),c_0_11]) ).
cnf(c_0_29,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_30,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_21]) ).
cnf(c_0_31,plain,
add(additive_inverse(multiply(X1,X2)),multiply(add(X1,X3),X2)) = multiply(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_10]) ).
cnf(c_0_32,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_9]),c_0_22]) ).
cnf(c_0_33,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_29]),c_0_10]) ).
cnf(c_0_34,hypothesis,
multiply(X1,add(multiply(X1,X1),X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_35,hypothesis,
multiply(X1,add(multiply(X1,multiply(X1,X2)),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_15]) ).
cnf(c_0_36,plain,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]),c_0_9]) ).
cnf(c_0_37,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_38,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_39,hypothesis,
add(X1,multiply(X1,additive_inverse(multiply(X1,X1)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_12]),c_0_22]) ).
cnf(c_0_40,hypothesis,
multiply(X1,multiply(add(X2,X1),X1)) = add(X1,multiply(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_41,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_12]),c_0_22]) ).
cnf(c_0_42,plain,
additive_inverse(multiply(add(additive_inverse(X1),X2),X3)) = multiply(add(X1,additive_inverse(X2)),X3),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,hypothesis,
multiply(add(X1,multiply(X2,X2)),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_16]),c_0_10]) ).
cnf(c_0_44,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_26]) ).
cnf(c_0_45,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_33,c_0_15]) ).
cnf(c_0_46,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_47,hypothesis,
multiply(X1,additive_inverse(multiply(X1,X1))) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_39]),c_0_9]) ).
cnf(c_0_48,hypothesis,
add(additive_inverse(X1),multiply(additive_inverse(X1),multiply(X1,additive_inverse(X1)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_12]),c_0_32]),c_0_22]) ).
cnf(c_0_49,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_21]) ).
cnf(c_0_50,hypothesis,
multiply(X1,multiply(add(X2,additive_inverse(multiply(X1,multiply(X1,X2)))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_41]),c_0_32]) ).
cnf(c_0_51,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,X2))),X2) = add(multiply(X1,X2),additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_36]),c_0_44]) ).
cnf(c_0_52,plain,
additive_inverse(multiply(X1,additive_inverse(X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_12]),c_0_22]),c_0_46]),c_0_9]) ).
cnf(c_0_53,hypothesis,
multiply(add(X1,X2),multiply(X1,X1)) = add(X1,multiply(X2,multiply(X1,X1))),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_54,hypothesis,
multiply(X1,multiply(X1,additive_inverse(X1))) = additive_inverse(X1),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_55,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_10]) ).
cnf(c_0_56,hypothesis,
add(X1,multiply(X1,multiply(additive_inverse(X1),X1))) = additive_identity,
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_57,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X2,X1)))),X2) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_22]) ).
cnf(c_0_58,hypothesis,
multiply(X1,multiply(add(X2,multiply(X1,X1)),X3)) = multiply(add(X1,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_59,hypothesis,
multiply(add(additive_inverse(multiply(X1,X1)),X2),X1) = add(multiply(X2,X1),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_51,c_0_10]) ).
cnf(c_0_60,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_61,hypothesis,
add(X1,multiply(additive_inverse(X1),multiply(X1,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_12]),c_0_32]) ).
cnf(c_0_62,hypothesis,
multiply(X1,multiply(X1,multiply(additive_inverse(X1),X2))) = multiply(additive_inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_54]),c_0_21]) ).
cnf(c_0_63,hypothesis,
multiply(X1,multiply(additive_inverse(X1),X1)) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_46]),c_0_9]) ).
cnf(c_0_64,hypothesis,
multiply(add(multiply(X1,X1),X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_10]) ).
cnf(c_0_65,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X2,X1)))),multiply(X3,X2)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_50]),c_0_22]),c_0_46]),c_0_9]),c_0_21]) ).
cnf(c_0_66,hypothesis,
multiply(add(X1,additive_inverse(multiply(X1,multiply(X2,X2)))),X2) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_21]),c_0_35]),c_0_12]),c_0_22]),c_0_60]) ).
cnf(c_0_67,hypothesis,
multiply(additive_inverse(X1),multiply(X1,X1)) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_61]),c_0_9]) ).
cnf(c_0_68,hypothesis,
multiply(additive_inverse(X1),X1) = multiply(X1,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,hypothesis,
add(multiply(X1,X2),additive_inverse(multiply(X2,multiply(X2,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_21]),c_0_36]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_49]) ).
cnf(c_0_70,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X2,multiply(X1,X1))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_66]),c_0_22]),c_0_46]),c_0_9]) ).
cnf(c_0_71,hypothesis,
multiply(X1,multiply(additive_inverse(X1),additive_inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_17]) ).
cnf(c_0_72,hypothesis,
multiply(X1,add(multiply(X1,additive_inverse(X1)),X2)) = add(additive_inverse(X1),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_54]) ).
cnf(c_0_73,hypothesis,
add(multiply(X1,additive_inverse(X1)),multiply(X2,X1)) = multiply(add(additive_inverse(X1),X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_68]) ).
cnf(c_0_74,hypothesis,
multiply(X1,multiply(X1,multiply(X2,X1))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_69]),c_0_46]),c_0_9]),c_0_17]) ).
cnf(c_0_75,hypothesis,
multiply(X1,add(X2,add(additive_inverse(multiply(X2,multiply(X1,X1))),X3))) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_70]),c_0_13]),c_0_11]) ).
cnf(c_0_76,hypothesis,
multiply(additive_inverse(X1),additive_inverse(X1)) = multiply(X1,X1),
inference(spm,[status(thm)],[c_0_62,c_0_71]) ).
cnf(c_0_77,hypothesis,
multiply(X1,multiply(add(additive_inverse(X1),X2),X1)) = add(additive_inverse(X1),multiply(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,hypothesis,
multiply(add(X1,X2),multiply(X2,X2)) = add(X2,multiply(X1,multiply(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_10]) ).
cnf(c_0_79,hypothesis,
multiply(X1,add(X2,multiply(X1,additive_inverse(X1)))) = add(multiply(X1,X2),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_54]) ).
cnf(c_0_80,hypothesis,
multiply(X1,multiply(X1,multiply(X2,multiply(X1,X3)))) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_74]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_81,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_12]),c_0_9]),c_0_17]) ).
cnf(c_0_82,hypothesis,
multiply(X1,multiply(X1,add(X1,X2))) = add(X1,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_83,hypothesis,
multiply(additive_inverse(X1),multiply(additive_inverse(X1),X2)) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_76]),c_0_21]) ).
cnf(c_0_84,plain,
add(additive_inverse(multiply(X1,X2)),multiply(X3,X2)) = multiply(add(additive_inverse(X1),X3),X2),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_85,hypothesis,
add(X1,multiply(X1,additive_inverse(X1))) = add(X1,additive_inverse(multiply(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_68]),c_0_21]),c_0_47]),c_0_21]),c_0_79]),c_0_34]),c_0_16]),c_0_21]),c_0_16]),c_0_10]) ).
cnf(c_0_86,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_33]) ).
cnf(c_0_87,hypothesis,
multiply(X1,multiply(add(X2,additive_inverse(multiply(X2,multiply(X1,X1)))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_70]),c_0_32]) ).
cnf(c_0_88,hypothesis,
multiply(add(additive_inverse(X1),X2),multiply(X1,X1)) = add(additive_inverse(X1),multiply(X2,multiply(X1,X1))),
inference(spm,[status(thm)],[c_0_53,c_0_76]) ).
cnf(c_0_89,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X2,multiply(X1,X1)),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,hypothesis,
multiply(X1,add(additive_inverse(multiply(X1,X1)),X2)) = add(additive_inverse(X1),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_47]) ).
cnf(c_0_91,hypothesis,
multiply(X1,multiply(X1,add(additive_inverse(X1),X2))) = add(additive_inverse(X1),multiply(X1,multiply(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_83]) ).
cnf(c_0_92,plain,
add(additive_inverse(multiply(X1,X2)),multiply(X3,multiply(X4,X2))) = multiply(add(additive_inverse(X1),multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_84,c_0_21]) ).
cnf(c_0_93,hypothesis,
multiply(X1,additive_inverse(X1)) = additive_inverse(multiply(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_85]),c_0_76]),c_0_86]),c_0_33]),c_0_17]),c_0_68]) ).
cnf(c_0_94,hypothesis,
multiply(add(X1,multiply(X1,X2)),X1) = multiply(X1,add(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_58,c_0_43]) ).
cnf(c_0_95,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X1,X3)))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_30]),c_0_15]) ).
cnf(c_0_96,hypothesis,
multiply(X1,add(multiply(X1,multiply(X2,X1)),X3)) = add(multiply(X2,X1),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_74]) ).
cnf(c_0_97,hypothesis,
multiply(X1,add(additive_inverse(X2),multiply(X2,multiply(X1,multiply(X1,multiply(X2,X2)))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_36]),c_0_17]),c_0_21]),c_0_21]) ).
cnf(c_0_98,hypothesis,
multiply(add(additive_inverse(X1),multiply(X2,X1)),X1) = multiply(X1,add(additive_inverse(X1),multiply(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_89]),c_0_90]),c_0_21]),c_0_91]),c_0_30]),c_0_21]),c_0_80]),c_0_92]) ).
cnf(c_0_99,hypothesis,
add(additive_inverse(multiply(X1,X1)),multiply(X1,X2)) = multiply(X1,add(additive_inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_93]) ).
cnf(c_0_100,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X3,X1)))) = add(multiply(X1,X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_74]) ).
cnf(c_0_101,hypothesis,
multiply(add(X1,additive_inverse(multiply(X1,X2))),X1) = multiply(X1,add(X1,additive_inverse(multiply(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_60]),c_0_36]) ).
cnf(c_0_102,plain,
add(additive_inverse(X1),add(additive_inverse(X2),X3)) = add(additive_inverse(add(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_11,c_0_86]) ).
cnf(c_0_103,plain,
add(X1,add(additive_inverse(add(X1,X2)),X3)) = add(additive_inverse(X2),X3),
inference(spm,[status(thm)],[c_0_11,c_0_33]) ).
cnf(c_0_104,hypothesis,
multiply(X1,multiply(X1,add(X2,multiply(X1,X3)))) = multiply(X1,add(multiply(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_95,c_0_15]) ).
cnf(c_0_105,hypothesis,
multiply(X1,multiply(X1,add(multiply(X2,X1),X3))) = add(multiply(X2,X1),multiply(X1,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_96,c_0_15]) ).
cnf(c_0_106,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X2,X1))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_92]),c_0_98]),c_0_92]),c_0_98]),c_0_21]),c_0_99]),c_0_21]),c_0_91]),c_0_30]),c_0_21]),c_0_80]),c_0_21]),c_0_100]),c_0_60]),c_0_42]),c_0_101]),c_0_15]),c_0_11]),c_0_102]),c_0_10]),c_0_103]),c_0_104]),c_0_60]),c_0_10]) ).
cnf(c_0_107,hypothesis,
add(multiply(X1,X2),additive_inverse(multiply(X2,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_22]),c_0_21]),c_0_81]),c_0_60]),c_0_60]),c_0_30]) ).
cnf(c_0_108,negated_conjecture,
multiply(a,b) != multiply(b,a),
prove_commutativity ).
cnf(c_0_109,hypothesis,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_107]),c_0_46]),c_0_9]),c_0_17]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG009-5 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 02:52:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 1.64/1.76 % Version : CSE_E---1.5
% 1.64/1.76 % Problem : theBenchmark.p
% 1.64/1.76 % Proof found
% 1.64/1.76 % SZS status Theorem for theBenchmark.p
% 1.64/1.76 % SZS output start Proof
% See solution above
% 1.64/1.77 % Total time : 1.177000 s
% 1.64/1.77 % SZS output end Proof
% 1.64/1.77 % Total time : 1.180000 s
%------------------------------------------------------------------------------