%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 02:05:29 PM UTC 2026
% Result : Unsatisfiable 8.82s 2.27s
% Output : CNFRefutation 8.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 9
% Syntax : Number of clauses : 100 ( 100 unt; 0 nHn; 5 RR)
% Number of literals : 100 ( 99 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% 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 : 197 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutative_addition) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
cnf(x_cubed_is_x,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).
cnf(associative_addition,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_multiplication) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute2) ).
cnf(prove_commutativity,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/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,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_12,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
x_cubed_is_x ).
cnf(c_0_13,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_14,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_15,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,hypothesis,
multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
cnf(c_0_17,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_12]) ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_20,hypothesis,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]) ).
cnf(c_0_21,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_9]) ).
cnf(c_0_22,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_19]) ).
cnf(c_0_23,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,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_11,c_0_22]),c_0_11]) ).
cnf(c_0_25,hypothesis,
multiply(X1,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_26,hypothesis,
multiply(additive_identity,add(X1,multiply(additive_identity,X2))) = multiply(additive_identity,add(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_28,hypothesis,
multiply(additive_identity,add(X1,multiply(X2,X1))) = multiply(additive_identity,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_9]),c_0_10]) ).
cnf(c_0_29,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_30,hypothesis,
multiply(additive_identity,multiply(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_10]),c_0_28]) ).
cnf(c_0_31,hypothesis,
multiply(add(X1,multiply(additive_identity,X2)),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]),c_0_9]) ).
cnf(c_0_32,hypothesis,
multiply(add(multiply(additive_identity,X1),X2),X1) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_31,c_0_10]) ).
cnf(c_0_33,hypothesis,
multiply(add(X1,multiply(X2,X2)),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_10]) ).
cnf(c_0_34,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_35,hypothesis,
add(X1,multiply(additive_identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_19]),c_0_30]),c_0_19]),c_0_12]) ).
cnf(c_0_36,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_37,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_38,hypothesis,
multiply(X1,add(multiply(X1,X1),X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_39,hypothesis,
multiply(additive_identity,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_35]),c_0_14]) ).
cnf(c_0_40,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_10]) ).
cnf(c_0_41,hypothesis,
add(X1,multiply(X1,additive_inverse(multiply(X1,X1)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_14]),c_0_23]) ).
cnf(c_0_42,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_43,hypothesis,
multiply(add(multiply(X1,X1),X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_10]) ).
cnf(c_0_44,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_45,hypothesis,
multiply(X1,additive_inverse(multiply(X1,X1))) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_9]) ).
cnf(c_0_46,hypothesis,
add(X1,multiply(additive_inverse(multiply(X1,X1)),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_14]),c_0_44]) ).
cnf(c_0_47,hypothesis,
multiply(X1,multiply(X1,additive_inverse(X1))) = additive_inverse(X1),
inference(spm,[status(thm)],[c_0_22,c_0_45]) ).
cnf(c_0_48,hypothesis,
multiply(X1,multiply(additive_inverse(multiply(X1,X1)),X2)) = multiply(additive_inverse(X1),X2),
inference(spm,[status(thm)],[c_0_19,c_0_45]) ).
cnf(c_0_49,hypothesis,
multiply(additive_inverse(multiply(X1,X1)),X1) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_42]),c_0_9]) ).
cnf(c_0_50,hypothesis,
multiply(additive_inverse(X1),multiply(additive_inverse(X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_51,hypothesis,
multiply(additive_inverse(X1),X1) = multiply(X1,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_36]),c_0_10]) ).
cnf(c_0_53,hypothesis,
multiply(additive_inverse(X1),multiply(additive_inverse(X1),multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_50]),c_0_19]) ).
cnf(c_0_54,hypothesis,
multiply(additive_inverse(X1),multiply(X1,X1)) = additive_inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_19]),c_0_45]),c_0_47]) ).
cnf(c_0_55,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_11,c_0_22]),c_0_11]) ).
cnf(c_0_56,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_52,c_0_11]) ).
cnf(c_0_57,hypothesis,
multiply(additive_inverse(X1),additive_inverse(X1)) = multiply(X1,X1),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_14]),c_0_23]) ).
cnf(c_0_59,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_56,c_0_14]),c_0_23]),c_0_42]),c_0_9]) ).
cnf(c_0_60,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_19,c_0_57]),c_0_19]) ).
cnf(c_0_61,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_12,c_0_19]),c_0_19]) ).
cnf(c_0_62,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_19,c_0_58]),c_0_44]) ).
cnf(c_0_63,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_21,c_0_59]) ).
cnf(c_0_64,hypothesis,
multiply(additive_inverse(X1),add(X2,additive_inverse(multiply(X1,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(spm,[status(thm)],[c_0_48,c_0_58]),c_0_23]),c_0_60]),c_0_19]),c_0_19]),c_0_22]) ).
cnf(c_0_65,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X2,X1)))),X2) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_23]) ).
cnf(c_0_66,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_34]) ).
cnf(c_0_67,plain,
add(multiply(X1,X2),multiply(add(X1,X3),additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_27]),c_0_63]),c_0_63]) ).
cnf(c_0_68,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(add(multiply(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_69,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,multiply(X2,X3)))))) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_70,hypothesis,
multiply(add(multiply(X1,multiply(X1,X2)),additive_inverse(X2)),X1) = additive_identity,
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_66]),c_0_23]),c_0_42]),c_0_9]) ).
cnf(c_0_71,plain,
multiply(additive_inverse(X1),additive_inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_14]),c_0_44]),c_0_9]) ).
cnf(c_0_72,hypothesis,
multiply(add(multiply(X1,X2),X3),multiply(X2,X2)) = multiply(add(X1,multiply(X3,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_12]),c_0_29]) ).
cnf(c_0_73,hypothesis,
multiply(X1,multiply(X2,multiply(X3,multiply(X1,multiply(X2,multiply(X3,multiply(X1,multiply(X2,multiply(X3,X4))))))))) = multiply(X1,multiply(X2,multiply(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_69]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_74,hypothesis,
multiply(add(additive_inverse(X1),multiply(X2,multiply(X2,X1))),X2) = additive_identity,
inference(spm,[status(thm)],[c_0_70,c_0_10]) ).
cnf(c_0_75,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_71]),c_0_63]),c_0_21]) ).
cnf(c_0_76,hypothesis,
multiply(add(X1,multiply(X2,X3)),multiply(X3,X3)) = multiply(add(X2,multiply(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_72,c_0_10]) ).
cnf(c_0_77,hypothesis,
multiply(add(X1,multiply(X2,multiply(X2,additive_inverse(X1)))),multiply(X3,multiply(X2,X4))) = 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(spm,[status(thm)],[c_0_73,c_0_62]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_63]),c_0_63]) ).
cnf(c_0_78,hypothesis,
multiply(X1,multiply(X1,multiply(X2,additive_inverse(X1)))) = multiply(X2,additive_inverse(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_67,c_0_74]),c_0_9]),c_0_60]),c_0_19]),c_0_19]),c_0_75]) ).
cnf(c_0_79,hypothesis,
multiply(X1,multiply(add(X2,multiply(X1,X1)),X3)) = multiply(add(X1,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_80,hypothesis,
multiply(add(X1,multiply(X2,multiply(X1,additive_inverse(X2)))),multiply(X1,additive_inverse(X2))) = additive_identity,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,hypothesis,
multiply(X1,multiply(X1,multiply(X2,X1))) = multiply(X2,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(spm,[status(thm)],[c_0_75,c_0_78]),c_0_21]),c_0_21]),c_0_75]),c_0_63]),c_0_63]),c_0_59]) ).
cnf(c_0_82,hypothesis,
multiply(add(X1,multiply(X1,X2)),X1) = multiply(X1,add(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_79,c_0_33]) ).
cnf(c_0_83,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_52]) ).
cnf(c_0_84,hypothesis,
multiply(add(additive_inverse(X1),multiply(X2,multiply(X1,X2))),multiply(X1,X2)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_75]),c_0_21]),c_0_21]) ).
cnf(c_0_85,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X3,X1)))) = add(multiply(X1,X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_81]) ).
cnf(c_0_86,hypothesis,
multiply(add(X1,multiply(X1,X2)),additive_inverse(X1)) = multiply(X1,additive_inverse(add(X1,multiply(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_82]),c_0_63]) ).
cnf(c_0_87,plain,
add(additive_inverse(X1),multiply(X2,additive_inverse(X3))) = additive_inverse(add(X1,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_83,c_0_63]) ).
cnf(c_0_88,plain,
additive_inverse(add(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(X2,X3),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_89,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_90,hypothesis,
multiply(X1,add(multiply(X1,X2),multiply(X2,additive_inverse(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_65,c_0_84]),c_0_23]),c_0_42]),c_0_9]),c_0_19]),c_0_85]),c_0_10]) ).
cnf(c_0_91,hypothesis,
multiply(add(multiply(X1,X2),additive_inverse(X1)),X1) = multiply(X1,add(multiply(X2,X1),additive_inverse(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(spm,[status(thm)],[c_0_86,c_0_87]),c_0_75]),c_0_88]),c_0_21]),c_0_71]),c_0_89]),c_0_63]),c_0_75]),c_0_88]) ).
cnf(c_0_92,plain,
additive_inverse(add(multiply(X1,additive_inverse(X2)),X3)) = add(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_89,c_0_63]) ).
cnf(c_0_93,plain,
add(X1,add(X2,add(X3,additive_inverse(X1)))) = add(X2,X3),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_94,hypothesis,
multiply(X1,multiply(X1,add(multiply(X1,X2),X3))) = multiply(X1,add(X2,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_55,c_0_11]) ).
cnf(c_0_95,negated_conjecture,
multiply(a,b) != multiply(b,a),
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_96,hypothesis,
add(multiply(X1,X2),multiply(X2,additive_inverse(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(spm,[status(thm)],[c_0_90,c_0_91]),c_0_75]),c_0_21]),c_0_10]),c_0_21]),c_0_75]),c_0_92]),c_0_11]),c_0_13]),c_0_93]),c_0_94]),c_0_85]),c_0_10]) ).
cnf(c_0_97,negated_conjecture,
multiply(a,b) != multiply(b,a),
c_0_95 ).
cnf(c_0_98,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_52,c_0_96]),c_0_42]),c_0_9]),c_0_59]) ).
cnf(c_0_99,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG009-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:10:21 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 8.82/2.27 % Version: 3.5.1
% 8.82/2.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.82/2.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/2.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.82/2.27 % Starting new_bool_3 with 300s (1) cores
% 8.82/2.27 % Starting new_bool_1 with 300s (1) cores
% 8.82/2.27 % Starting sh5l with 300s (1) cores
% 8.82/2.27 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 4110284 completed with status 0
% 8.82/2.27 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 8.82/2.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.82/2.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/2.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.82/2.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.82/2.27 % No SInE strategy applied
% 8.82/2.27 % Search class: FUUPM-FFSF21-SFFFFFNN
% 8.82/2.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.82/2.27 % Starting SubtermCWHack with 136s (1) cores
% 8.82/2.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.82/2.27 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 8.82/2.27 % Starting new_bool_3 with 136s (1) cores
% 8.82/2.27 % Starting new_bool_1 with 136s (1) cores
% 8.82/2.27 % SAT001_MinMin_p005000_rr_RG with pid 4110291 completed with status 0
% 8.82/2.27 % Result found by SAT001_MinMin_p005000_rr_RG
% 8.82/2.27 % Preprocessing class: FSSSSMSSSSSNFFN.
% 8.82/2.27 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.82/2.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 8.82/2.27 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 8.82/2.27 % No SInE strategy applied
% 8.82/2.27 % Search class: FUUPM-FFSF21-SFFFFFNN
% 8.82/2.27 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 8.82/2.27 % Starting SubtermCWHack with 136s (1) cores
% 8.82/2.27 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 8.82/2.27 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 8.82/2.27 % Preprocessing time : 0.001 s
% 8.82/2.27 % Presaturation interreduction done
% 8.82/2.27
% 8.82/2.27 % Proof found!
% 8.82/2.27 % SZS status Unsatisfiable
% 8.82/2.27 % SZS output start CNFRefutation
% See solution above
% 8.82/2.27 % Parsed axioms : 9
% 8.82/2.27 % Removed by relevancy pruning/SinE : 0
% 8.82/2.27 % Initial clauses : 9
% 8.82/2.27 % Removed in clause preprocessing : 0
% 8.82/2.27 % Initial clauses in saturation : 9
% 8.82/2.27 % Processed clauses : 2963
% 8.82/2.27 % ...of these trivial : 1799
% 8.82/2.27 % ...subsumed : 724
% 8.82/2.27 % ...remaining for further processing : 440
% 8.82/2.27 % Other redundant clauses eliminated : 0
% 8.82/2.27 % Clauses deleted for lack of memory : 0
% 8.82/2.27 % Backward-subsumed : 0
% 8.82/2.27 % Backward-rewritten : 168
% 8.82/2.27 % Generated clauses : 97207
% 8.82/2.27 % ...of the previous two non-redundant : 67125
% 8.82/2.27 % ...aggressively subsumed : 0
% 8.82/2.27 % Contextual simplify-reflections : 0
% 8.82/2.27 % Paramodulations : 97207
% 8.82/2.27 % Factorizations : 0
% 8.82/2.27 % NegExts : 0
% 8.82/2.27 % Equation resolutions : 0
% 8.82/2.27 % Disequality decompositions : 0
% 8.82/2.27 % Total rewrite steps : 302909
% 8.82/2.27 % ...of those cached : 252301
% 8.82/2.27 % Propositional unsat checks : 0
% 8.82/2.27 % Propositional check models : 0
% 8.82/2.27 % Propositional check unsatisfiable : 0
% 8.82/2.27 % Propositional clauses : 0
% 8.82/2.27 % Propositional clauses after purity: 0
% 8.82/2.27 % Propositional unsat core size : 0
% 8.82/2.27 % Propositional preprocessing time : 0.000
% 8.82/2.27 % Propositional encoding time : 0.000
% 8.82/2.27 % Propositional solver time : 0.000
% 8.82/2.27 % Success case prop preproc time : 0.000
% 8.82/2.27 % Success case prop encoding time : 0.000
% 8.82/2.27 % Success case prop solver time : 0.000
% 8.82/2.27 % Current number of processed clauses : 263
% 8.82/2.27 % Positive orientable unit clauses : 247
% 8.82/2.27 % Positive unorientable unit clauses: 16
% 8.82/2.27 % Negative unit clauses : 0
% 8.82/2.27 % Non-unit-clauses : 0
% 8.82/2.27 % Current number of unprocessed clauses: 62940
% 8.82/2.27 % ...number of literals in the above : 62940
% 8.82/2.27 % Current number of archived formulas : 0
% 8.82/2.27 % Current number of archived clauses : 177
% 8.82/2.27 % Clause-clause subsumption calls (NU) : 0
% 8.82/2.27 % Rec. Clause-clause subsumption calls : 0
% 8.82/2.27 % Non-unit clause-clause subsumptions : 0
% 8.82/2.27 % Unit Clause-clause subsumption calls : 338
% 8.82/2.27 % Rewrite failures with RHS unbound : 0
% 8.82/2.27 % BW rewrite match attempts : 3441
% 8.82/2.27 % BW rewrite match successes : 950
% 8.82/2.27 % Condensation attempts : 0
% 8.82/2.27 % Condensation successes : 0
% 8.82/2.27 % Termbank termtop insertions : 1726313
% 8.82/2.27 % Search garbage collected termcells : 2
% 8.82/2.27
% 8.82/2.27 % -------------------------------------------------
% 8.82/2.27 % User time : 1.697 s
% 8.82/2.27 % System time : 0.088 s
% 8.82/2.27 % Total time : 1.785 s
% 8.82/2.27 % Maximum resident set size: 3632 pages
% 8.82/2.27
% 8.82/2.27 % -------------------------------------------------
% 8.82/2.27 % User time : 8.488 s
% 8.82/2.27 % System time : 0.462 s
% 8.82/2.27 % Total time : 8.950 s
% 8.82/2.27 % Maximum resident set size: 4608 pages
% 8.82/2.27 % E exiting
%------------------------------------------------------------------------------