%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG009-7 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.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 : Tue May 5 05:04:59 PM UTC 2026
% Result : Unsatisfiable 4.24s 3.30s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of clauses : 113 ( 113 unt; 0 nHn; 41 RR)
% Number of literals : 113 ( 112 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 130 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
cnf(associativity_for_multiplication,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).
cnf(x_cubed_is_x,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_x) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/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,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
associativity_for_multiplication ).
cnf(c_0_15,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
x_cubed_is_x ).
cnf(c_0_16,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_17,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_18,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_19,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_20,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_21,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_22,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_17]) ).
cnf(c_0_23,hypothesis,
multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]) ).
cnf(c_0_24,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_25,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
multiply(a,multiply(a,c)) = c,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_28,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_15]) ).
cnf(c_0_29,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_24,c_0_15]),c_0_19]) ).
cnf(c_0_30,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
multiply(a,add(multiply(a,c),X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_32,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]),c_0_12]) ).
cnf(c_0_33,hypothesis,
add(X1,multiply(additive_identity,multiply(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_13]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
multiply(a,add(X1,b)) = add(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_19]) ).
cnf(c_0_35,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_19]) ).
cnf(c_0_36,negated_conjecture,
add(c,multiply(a,additive_inverse(multiply(a,c)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]) ).
cnf(c_0_37,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_38,hypothesis,
multiply(additive_identity,multiply(X1,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_19]),c_0_12]) ).
cnf(c_0_39,hypothesis,
multiply(X1,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
multiply(add(c,multiply(a,X1)),X2) = multiply(a,multiply(add(X1,b),X2)),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
multiply(a,additive_inverse(multiply(a,c))) = additive_inverse(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_17]) ).
cnf(c_0_42,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_43,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_15,c_0_14]),c_0_14]) ).
cnf(c_0_44,negated_conjecture,
multiply(a,multiply(add(b,additive_inverse(multiply(a,c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_12]),c_0_42]),c_0_19]) ).
cnf(c_0_45,negated_conjecture,
multiply(add(b,additive_inverse(multiply(a,c))),a) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_46,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_24]) ).
cnf(c_0_47,negated_conjecture,
multiply(add(b,additive_inverse(multiply(a,c))),multiply(a,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_45]),c_0_42]) ).
cnf(c_0_48,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_25,c_0_46]),c_0_19]) ).
cnf(c_0_49,plain,
add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_50,negated_conjecture,
multiply(add(b,additive_inverse(multiply(a,c))),c) = additive_identity,
inference(spm,[status(thm)],[c_0_47,c_0_21]) ).
cnf(c_0_51,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_48,c_0_12]),c_0_42]),c_0_17]) ).
cnf(c_0_52,plain,
add(additive_inverse(multiply(X1,X2)),multiply(X1,add(X2,X3))) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_49]),c_0_19]) ).
cnf(c_0_53,negated_conjecture,
additive_inverse(multiply(a,multiply(c,c))) = additive_inverse(multiply(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_50]),c_0_17]),c_0_51]),c_0_14]) ).
cnf(c_0_54,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_12]),c_0_32]),c_0_17]) ).
cnf(c_0_55,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
cnf(c_0_56,negated_conjecture,
multiply(a,multiply(c,c)) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_53]),c_0_22]) ).
cnf(c_0_57,plain,
multiply(additive_inverse(multiply(X1,X2)),X3) = multiply(X1,multiply(additive_inverse(X2),X3)),
inference(spm,[status(thm)],[c_0_14,c_0_54]) ).
cnf(c_0_58,hypothesis,
multiply(X1,add(multiply(X1,X1),X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_59,negated_conjecture,
multiply(add(b,additive_inverse(multiply(a,c))),multiply(c,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_47,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
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_14,c_0_56]),c_0_14]),c_0_14]) ).
cnf(c_0_61,negated_conjecture,
additive_inverse(multiply(a,multiply(c,a))) = additive_inverse(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_48,c_0_45]),c_0_17]),c_0_57]),c_0_51]),c_0_54]) ).
cnf(c_0_62,hypothesis,
multiply(X1,multiply(add(X1,X2),X1)) = add(X1,multiply(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_58,c_0_24]) ).
cnf(c_0_63,negated_conjecture,
multiply(a,add(b,X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_64,hypothesis,
multiply(c,add(b,additive_inverse(multiply(a,c)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_59]),c_0_32]) ).
cnf(c_0_65,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_66,hypothesis,
multiply(b,multiply(c,c)) = multiply(a,c),
inference(spm,[status(thm)],[c_0_60,c_0_15]) ).
cnf(c_0_67,negated_conjecture,
multiply(a,multiply(a,multiply(c,X1))) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_20,c_0_55]) ).
cnf(c_0_68,negated_conjecture,
multiply(a,multiply(c,a)) = multiply(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_61]),c_0_22]) ).
cnf(c_0_69,negated_conjecture,
multiply(c,multiply(add(b,X1),b)) = add(c,multiply(c,multiply(X1,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_62]),c_0_63]),c_0_55]) ).
cnf(c_0_70,hypothesis,
multiply(c,multiply(add(b,additive_inverse(multiply(a,c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_64]),c_0_42]) ).
cnf(c_0_71,hypothesis,
multiply(add(X1,multiply(b,c)),c) = multiply(add(X1,a),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_24]) ).
cnf(c_0_72,negated_conjecture,
multiply(c,multiply(a,multiply(c,multiply(a,c)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_43]),c_0_26]) ).
cnf(c_0_73,negated_conjecture,
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_14,c_0_68]),c_0_14]),c_0_14]) ).
cnf(c_0_74,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_30]),c_0_19]) ).
cnf(c_0_75,negated_conjecture,
add(c,additive_inverse(multiply(c,multiply(a,multiply(c,b))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_51]),c_0_14]),c_0_54]) ).
cnf(c_0_76,hypothesis,
multiply(add(multiply(b,c),X1),c) = multiply(add(X1,a),c),
inference(spm,[status(thm)],[c_0_71,c_0_19]) ).
cnf(c_0_77,negated_conjecture,
multiply(c,multiply(b,multiply(a,c))) = c,
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,negated_conjecture,
multiply(c,multiply(a,multiply(c,b))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_37]),c_0_17]),c_0_22]) ).
cnf(c_0_79,hypothesis,
multiply(add(a,additive_inverse(multiply(b,c))),c) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_12]),c_0_42]),c_0_19]) ).
cnf(c_0_80,negated_conjecture,
multiply(c,multiply(b,multiply(a,multiply(c,X1)))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_77]),c_0_14]),c_0_14]) ).
cnf(c_0_81,negated_conjecture,
multiply(b,multiply(a,multiply(c,b))) = multiply(a,c),
inference(spm,[status(thm)],[c_0_73,c_0_78]) ).
cnf(c_0_82,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_83,hypothesis,
multiply(add(a,additive_inverse(multiply(b,c))),multiply(c,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_79]),c_0_42]) ).
cnf(c_0_84,negated_conjecture,
multiply(c,multiply(a,c)) = multiply(c,b),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_85,plain,
additive_inverse(multiply(X1,add(X2,additive_inverse(X3)))) = multiply(X1,add(X3,additive_inverse(X2))),
inference(spm,[status(thm)],[c_0_54,c_0_82]) ).
cnf(c_0_86,hypothesis,
multiply(c,add(a,additive_inverse(multiply(b,c)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_83]),c_0_32]) ).
cnf(c_0_87,negated_conjecture,
multiply(c,multiply(a,multiply(c,X1))) = multiply(c,multiply(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_84]),c_0_14]),c_0_14]) ).
cnf(c_0_88,hypothesis,
multiply(c,add(multiply(b,c),additive_inverse(a))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_37]) ).
cnf(c_0_89,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_18,c_0_20]),c_0_18]) ).
cnf(c_0_90,hypothesis,
multiply(c,multiply(b,add(multiply(b,c),additive_inverse(a)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_32]),c_0_32]) ).
cnf(c_0_91,hypothesis,
multiply(X1,multiply(X1,add(multiply(X1,X2),X3))) = multiply(X1,add(X2,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_89,c_0_18]) ).
cnf(c_0_92,hypothesis,
multiply(c,multiply(b,b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_15]),c_0_21]) ).
cnf(c_0_93,negated_conjecture,
multiply(c,multiply(b,add(c,additive_inverse(multiply(b,a))))) = 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_90]),c_0_32]),c_0_32]),c_0_91]),c_0_54]) ).
cnf(c_0_94,hypothesis,
multiply(c,multiply(b,multiply(b,X1))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_92]),c_0_14]) ).
cnf(c_0_95,hypothesis,
multiply(X1,multiply(X1,add(X1,X2))) = add(X1,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_58,c_0_18]) ).
cnf(c_0_96,negated_conjecture,
multiply(c,add(c,additive_inverse(multiply(b,a)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_93]),c_0_32]),c_0_32]),c_0_94]) ).
cnf(c_0_97,hypothesis,
add(c,additive_inverse(multiply(c,multiply(c,multiply(b,a))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_32]),c_0_54]),c_0_54]) ).
cnf(c_0_98,hypothesis,
multiply(c,multiply(c,multiply(b,a))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_97]),c_0_37]),c_0_17]),c_0_22]) ).
cnf(c_0_99,negated_conjecture,
multiply(a,multiply(c,multiply(b,a))) = multiply(b,multiply(b,a)),
inference(spm,[status(thm)],[c_0_73,c_0_68]) ).
cnf(c_0_100,hypothesis,
multiply(c,multiply(b,a)) = multiply(c,c),
inference(spm,[status(thm)],[c_0_20,c_0_98]) ).
cnf(c_0_101,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_12]),c_0_32]) ).
cnf(c_0_102,negated_conjecture,
multiply(b,multiply(b,a)) = multiply(b,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_56]) ).
cnf(c_0_103,negated_conjecture,
multiply(b,multiply(a,c)) = multiply(a,multiply(c,b)),
inference(spm,[status(thm)],[c_0_73,c_0_84]) ).
cnf(c_0_104,hypothesis,
multiply(b,add(a,additive_inverse(multiply(b,c)))) = additive_identity,
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_105,hypothesis,
multiply(b,multiply(b,multiply(c,b))) = multiply(b,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_43,c_0_102]),c_0_14]),c_0_55]),c_0_66]),c_0_103]),c_0_14]),c_0_67]) ).
cnf(c_0_106,hypothesis,
multiply(b,multiply(b,c)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_20,c_0_102]) ).
cnf(c_0_107,hypothesis,
multiply(b,multiply(add(a,additive_inverse(multiply(b,c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_104]),c_0_42]) ).
cnf(c_0_108,negated_conjecture,
multiply(add(a,X1),b) = add(c,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_109,hypothesis,
multiply(b,multiply(c,b)) = multiply(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_105]),c_0_106]) ).
cnf(c_0_110,hypothesis,
add(c,additive_inverse(multiply(b,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_43,c_0_107]),c_0_32]),c_0_108]),c_0_51]),c_0_14]),c_0_109]) ).
cnf(c_0_111,negated_conjecture,
multiply(b,a) != c,
prove_commutativity ).
cnf(c_0_112,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_110]),c_0_37]),c_0_17]),c_0_22]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG009-7 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:45:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.24/3.30 % Version : CSE_E---1.7
% 4.24/3.30 % Problem : theBenchmark.p
% 4.24/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.24/3.30 % SZS output start CNFRefutation
% See solution above
% 4.24/3.31 % Total time : 2.373s
%------------------------------------------------------------------------------