%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG009-7 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 0.16s 10.73s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of clauses : 118 ( 118 unt; 0 nHn; 40 RR)
% Number of literals : 118 ( 117 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 135 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',right_additive_identity) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',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(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',distribute2) ).
cnf(associativity_for_multiplication,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_11,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_12,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_13,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
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,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_17,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_18,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
x_cubed_is_x ).
cnf(c_0_19,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_22,hypothesis,
multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15]) ).
cnf(c_0_23,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
multiply(a,add(X1,b)) = add(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_15]) ).
cnf(c_0_25,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_18]) ).
cnf(c_0_26,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_23]),c_0_15]) ).
cnf(c_0_27,negated_conjecture,
add(c,multiply(a,additive_identity)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_21]) ).
cnf(c_0_28,hypothesis,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_25]),c_0_12]) ).
cnf(c_0_29,negated_conjecture,
additive_inverse(multiply(a,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_12]) ).
cnf(c_0_30,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_31,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_32,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_33,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_34,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_35,negated_conjecture,
multiply(a,add(b,X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_36,negated_conjecture,
multiply(a,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_29]),c_0_16]) ).
cnf(c_0_37,plain,
multiply(add(X1,X1),X2) = multiply(X1,add(X2,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_38,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_31,c_0_12]),c_0_32]),c_0_33]),c_0_16]) ).
cnf(c_0_39,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
associativity_for_multiplication ).
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_23,c_0_34]),c_0_15]) ).
cnf(c_0_41,negated_conjecture,
add(c,multiply(a,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_12]),c_0_36]) ).
cnf(c_0_42,plain,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(spm,[status(thm)],[c_0_37,c_0_13]) ).
cnf(c_0_43,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_44,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_18]),c_0_39]) ).
cnf(c_0_45,negated_conjecture,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33]),c_0_16]) ).
cnf(c_0_46,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_42]),c_0_12]) ).
cnf(c_0_47,negated_conjecture,
additive_inverse(add(c,multiply(a,X1))) = multiply(a,additive_inverse(add(b,X1))),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_48,hypothesis,
multiply(a,multiply(a,additive_inverse(c))) = additive_inverse(c),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
add(multiply(X1,X2),multiply(add(X3,X1),additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_43]),c_0_43]) ).
cnf(c_0_50,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_46]),c_0_16]) ).
cnf(c_0_51,hypothesis,
multiply(a,additive_inverse(add(b,multiply(a,additive_inverse(c))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_12]),c_0_33]) ).
cnf(c_0_52,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_49,c_0_12]),c_0_50]),c_0_16]) ).
cnf(c_0_53,hypothesis,
multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),additive_inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_51]),c_0_50]),c_0_52]) ).
cnf(c_0_54,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_18,c_0_39]),c_0_39]) ).
cnf(c_0_55,hypothesis,
multiply(a,multiply(add(b,multiply(a,additive_inverse(c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_53]),c_0_33]),c_0_43]),c_0_20]) ).
cnf(c_0_56,hypothesis,
multiply(add(b,multiply(a,additive_inverse(c))),a) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_32]) ).
cnf(c_0_57,hypothesis,
multiply(add(b,multiply(a,additive_inverse(c))),multiply(a,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_56]),c_0_50]) ).
cnf(c_0_58,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_26,c_0_30]),c_0_43]),c_0_43]) ).
cnf(c_0_59,hypothesis,
multiply(add(b,multiply(a,additive_inverse(c))),additive_inverse(c)) = additive_identity,
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_60,hypothesis,
multiply(a,multiply(c,c)) = multiply(b,c),
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_16]),c_0_39]),c_0_52]),c_0_20]) ).
cnf(c_0_61,hypothesis,
multiply(a,multiply(c,multiply(c,X1))) = multiply(b,multiply(c,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_60]),c_0_39]),c_0_39]) ).
cnf(c_0_62,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(add(multiply(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_63,hypothesis,
multiply(b,multiply(c,c)) = multiply(a,c),
inference(spm,[status(thm)],[c_0_61,c_0_18]) ).
cnf(c_0_64,hypothesis,
multiply(add(multiply(b,c),X1),c) = multiply(add(a,X1),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_30]) ).
cnf(c_0_65,hypothesis,
multiply(add(a,multiply(b,additive_inverse(c))),c) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_12]),c_0_50]),c_0_43]) ).
cnf(c_0_66,hypothesis,
multiply(X1,multiply(X2,multiply(X3,multiply(X1,multiply(X2,multiply(X3,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_39,c_0_54]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_67,hypothesis,
multiply(add(a,multiply(b,additive_inverse(c))),multiply(c,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_65]),c_0_50]) ).
cnf(c_0_68,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_69,hypothesis,
multiply(c,multiply(X1,add(a,multiply(b,additive_inverse(c))))) = 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_66,c_0_67]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_70,plain,
additive_inverse(add(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(X2,X3),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_43]) ).
cnf(c_0_71,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_72,hypothesis,
multiply(c,multiply(X1,add(multiply(b,c),additive_inverse(a)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_33]),c_0_43]),c_0_70]) ).
cnf(c_0_73,negated_conjecture,
multiply(a,add(multiply(b,X1),X2)) = add(multiply(c,X1),multiply(a,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_71]) ).
cnf(c_0_74,hypothesis,
multiply(X1,add(multiply(X1,X1),X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_75,hypothesis,
multiply(c,add(a,multiply(b,additive_inverse(c)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_67]),c_0_32]) ).
cnf(c_0_76,negated_conjecture,
add(c,multiply(c,multiply(a,additive_inverse(a)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_77,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_30]) ).
cnf(c_0_78,hypothesis,
multiply(c,multiply(add(a,multiply(b,additive_inverse(c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_75]),c_0_50]) ).
cnf(c_0_79,negated_conjecture,
multiply(c,multiply(a,a)) = c,
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_26,c_0_76]),c_0_33]),c_0_16]),c_0_43]),c_0_43]),c_0_20]) ).
cnf(c_0_80,plain,
add(multiply(add(X1,X2),X3),multiply(X2,additive_inverse(X3))) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_12]),c_0_16]),c_0_43]) ).
cnf(c_0_81,hypothesis,
multiply(add(a,multiply(b,additive_inverse(c))),multiply(X1,c)) = 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_66,c_0_78]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_82,negated_conjecture,
multiply(c,multiply(a,multiply(a,X1))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_79]),c_0_39]) ).
cnf(c_0_83,hypothesis,
multiply(b,multiply(c,multiply(X1,c))) = multiply(a,multiply(X1,c)),
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_80,c_0_81]),c_0_43]),c_0_39]),c_0_52]),c_0_43]),c_0_20]),c_0_13]) ).
cnf(c_0_84,negated_conjecture,
multiply(c,multiply(a,c)) = multiply(c,b),
inference(spm,[status(thm)],[c_0_82,c_0_21]) ).
cnf(c_0_85,negated_conjecture,
multiply(a,multiply(a,c)) = c,
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_86,negated_conjecture,
multiply(b,multiply(c,b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_87,hypothesis,
multiply(b,multiply(b,c)) = c,
inference(spm,[status(thm)],[c_0_44,c_0_86]) ).
cnf(c_0_88,hypothesis,
multiply(add(b,multiply(a,additive_inverse(c))),additive_inverse(a)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_56]),c_0_33]) ).
cnf(c_0_89,hypothesis,
multiply(b,add(multiply(b,c),X1)) = add(c,multiply(b,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_87]) ).
cnf(c_0_90,hypothesis,
multiply(a,multiply(c,a)) = multiply(b,a),
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_88]),c_0_16]),c_0_39]),c_0_52]),c_0_20]) ).
cnf(c_0_91,hypothesis,
multiply(c,add(c,multiply(b,additive_inverse(a)))) = additive_identity,
inference(spm,[status(thm)],[c_0_72,c_0_89]) ).
cnf(c_0_92,hypothesis,
multiply(a,multiply(c,multiply(a,X1))) = multiply(b,multiply(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_90]),c_0_39]),c_0_39]) ).
cnf(c_0_93,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_54]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_94,hypothesis,
multiply(c,multiply(add(c,multiply(b,additive_inverse(a))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_91]),c_0_50]) ).
cnf(c_0_95,negated_conjecture,
multiply(c,multiply(b,c)) = multiply(a,c),
inference(spm,[status(thm)],[c_0_71,c_0_87]) ).
cnf(c_0_96,hypothesis,
multiply(b,multiply(a,c)) = multiply(a,multiply(c,b)),
inference(spm,[status(thm)],[c_0_92,c_0_84]) ).
cnf(c_0_97,hypothesis,
multiply(add(c,multiply(b,additive_inverse(a))),multiply(c,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_32]) ).
cnf(c_0_98,negated_conjecture,
multiply(a,multiply(a,multiply(c,X1))) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_44,c_0_71]) ).
cnf(c_0_99,hypothesis,
multiply(a,multiply(c,b)) = multiply(c,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_95]),c_0_96]),c_0_71]) ).
cnf(c_0_100,hypothesis,
multiply(c,multiply(b,b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_18]),c_0_21]) ).
cnf(c_0_101,hypothesis,
multiply(c,multiply(X1,add(c,multiply(b,additive_inverse(a))))) = 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_66,c_0_97]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_102,negated_conjecture,
multiply(a,add(X1,multiply(b,X2))) = add(multiply(a,X1),multiply(c,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_71]) ).
cnf(c_0_103,hypothesis,
multiply(X1,add(multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2)))),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_54]),c_0_17]) ).
cnf(c_0_104,negated_conjecture,
multiply(c,b) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_60]) ).
cnf(c_0_105,hypothesis,
multiply(c,multiply(b,multiply(b,X1))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_100]),c_0_39]) ).
cnf(c_0_106,negated_conjecture,
multiply(c,add(multiply(a,c),multiply(c,additive_inverse(a)))) = additive_identity,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,hypothesis,
multiply(c,add(multiply(a,c),X1)) = multiply(c,add(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_63]) ).
cnf(c_0_108,negated_conjecture,
multiply(c,add(b,multiply(c,additive_inverse(a)))) = additive_identity,
inference(rw,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_109,hypothesis,
multiply(a,multiply(c,multiply(b,a))) = multiply(b,multiply(b,a)),
inference(spm,[status(thm)],[c_0_92,c_0_90]) ).
cnf(c_0_110,negated_conjecture,
multiply(c,multiply(b,X1)) = multiply(b,multiply(c,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_104]),c_0_39]) ).
cnf(c_0_111,negated_conjecture,
add(multiply(b,c),multiply(c,X1)) = multiply(c,add(b,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_104]) ).
cnf(c_0_112,negated_conjecture,
multiply(c,add(multiply(c,a),additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_108]),c_0_33]),c_0_70]) ).
cnf(c_0_113,hypothesis,
multiply(c,multiply(c,a)) = multiply(b,multiply(b,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_71]) ).
cnf(c_0_114,negated_conjecture,
multiply(b,a) != c,
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_115,negated_conjecture,
multiply(b,multiply(b,a)) = multiply(b,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_16]),c_0_19]),c_0_113]) ).
cnf(c_0_116,negated_conjecture,
multiply(b,a) != c,
c_0_114 ).
cnf(c_0_117,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_115]),c_0_87]),c_0_116]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG009-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.40 % Computer : n016.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Mon Sep 21 04:15:48 UTC 2026
% 0.11/10.41 % CPUTime :
% 0.11/10.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.46 Running first-order theorem proving
% 0.11/10.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.16/10.73 % Version: 3.5.1
% 0.16/10.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.73 % Starting new_bool_3 with 300s (1) cores
% 0.16/10.73 % Starting new_bool_1 with 300s (1) cores
% 0.16/10.73 % Starting sh5l with 300s (1) cores
% 0.16/10.73 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1531209 completed with status 0
% 0.16/10.73 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.16/10.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.73 % No SInE strategy applied
% 0.16/10.73 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.16/10.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.73 % Starting SubtermCWHack with 136s (1) cores
% 0.16/10.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.16/10.73 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/10.73 % Starting new_bool_3 with 136s (1) cores
% 0.16/10.73 % Starting new_bool_1 with 136s (1) cores
% 0.16/10.73 % SubtermCWHack with pid 1531213 completed with status 0
% 0.16/10.73 % Result found by SubtermCWHack
% 0.16/10.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.16/10.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/10.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.16/10.73 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/10.73 % No SInE strategy applied
% 0.16/10.73 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.16/10.73 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/10.73 % Starting SubtermCWHack with 136s (1) cores
% 0.16/10.73 % Preprocessing time : 0.001 s
% 0.16/10.73
% 0.16/10.73 % Proof found!
% 0.16/10.73 % SZS status Unsatisfiable
% 0.16/10.73 % SZS output start CNFRefutation
% See solution above
% 0.16/10.74 % Parsed axioms : 12
% 0.16/10.74 % Removed by relevancy pruning/SinE : 0
% 0.16/10.74 % Initial clauses : 12
% 0.16/10.74 % Removed in clause preprocessing : 0
% 0.16/10.74 % Initial clauses in saturation : 12
% 0.16/10.74 % Processed clauses : 1294
% 0.16/10.74 % ...of these trivial : 575
% 0.16/10.74 % ...subsumed : 312
% 0.16/10.74 % ...remaining for further processing : 407
% 0.16/10.74 % Other redundant clauses eliminated : 0
% 0.16/10.74 % Clauses deleted for lack of memory : 0
% 0.16/10.74 % Backward-subsumed : 0
% 0.16/10.74 % Backward-rewritten : 130
% 0.16/10.74 % Generated clauses : 20264
% 0.16/10.74 % ...of the previous two non-redundant : 14248
% 0.16/10.74 % ...aggressively subsumed : 0
% 0.16/10.74 % Contextual simplify-reflections : 0
% 0.16/10.74 % Paramodulations : 20264
% 0.16/10.74 % Factorizations : 0
% 0.16/10.74 % NegExts : 0
% 0.16/10.74 % Equation resolutions : 0
% 0.16/10.74 % Disequality decompositions : 0
% 0.16/10.74 % Total rewrite steps : 42932
% 0.16/10.74 % ...of those cached : 34299
% 0.16/10.74 % Propositional unsat checks : 0
% 0.16/10.74 % Propositional check models : 0
% 0.16/10.74 % Propositional check unsatisfiable : 0
% 0.16/10.74 % Propositional clauses : 0
% 0.16/10.74 % Propositional clauses after purity: 0
% 0.16/10.74 % Propositional unsat core size : 0
% 0.16/10.74 % Propositional preprocessing time : 0.000
% 0.16/10.74 % Propositional encoding time : 0.000
% 0.16/10.74 % Propositional solver time : 0.000
% 0.16/10.74 % Success case prop preproc time : 0.000
% 0.16/10.74 % Success case prop encoding time : 0.000
% 0.16/10.74 % Success case prop solver time : 0.000
% 0.16/10.74 % Current number of processed clauses : 277
% 0.16/10.74 % Positive orientable unit clauses : 270
% 0.16/10.74 % Positive unorientable unit clauses: 6
% 0.16/10.74 % Negative unit clauses : 1
% 0.16/10.74 % Non-unit-clauses : 0
% 0.16/10.74 % Current number of unprocessed clauses: 12509
% 0.16/10.74 % ...number of literals in the above : 12509
% 0.16/10.74 % Current number of archived formulas : 0
% 0.16/10.74 % Current number of archived clauses : 130
% 0.16/10.74 % Clause-clause subsumption calls (NU) : 0
% 0.16/10.74 % Rec. Clause-clause subsumption calls : 0
% 0.16/10.74 % Non-unit clause-clause subsumptions : 0
% 0.16/10.74 % Unit Clause-clause subsumption calls : 24
% 0.16/10.74 % Rewrite failures with RHS unbound : 0
% 0.16/10.74 % BW rewrite match attempts : 671
% 0.16/10.74 % BW rewrite match successes : 172
% 0.16/10.74 % Condensation attempts : 0
% 0.16/10.74 % Condensation successes : 0
% 0.16/10.74 % Termbank termtop insertions : 341916
% 0.16/10.74 % Search garbage collected termcells : 2
% 0.16/10.74
% 0.16/10.74 % -------------------------------------------------
% 0.16/10.74 % User time : 0.211 s
% 0.16/10.74 % System time : 0.017 s
% 0.16/10.74 % Total time : 0.228 s
% 0.16/10.74 % Maximum resident set size: 3640 pages
% 0.16/10.74
% 0.16/10.74 % -------------------------------------------------
% 0.16/10.74 % User time : 0.888 s
% 0.16/10.74 % System time : 0.069 s
% 0.16/10.74 % Total time : 0.957 s
% 0.16/10.74 % Maximum resident set size: 4608 pages
% 0.16/10.74 % E exiting
%------------------------------------------------------------------------------