%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG035-7 : 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 : n026.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 05:05:04 PM UTC 2026
% Result : Unsatisfiable 31.26s 23.14s
% Output : CNFRefutation 31.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 11
% Syntax : Number of clauses : 208 ( 208 unt; 0 nHn; 56 RR)
% Number of literals : 208 ( 207 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 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 : 315 ( 11 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(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
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(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(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_fourthed_is_x,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X1))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_fourthed_is_x) ).
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,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,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,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_19,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_20,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_21,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
multiply(a,add(X1,b)) = add(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_15]) ).
cnf(c_0_23,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_21]),c_0_15]) ).
cnf(c_0_24,negated_conjecture,
add(c,multiply(a,additive_identity)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
additive_inverse(multiply(a,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_12]) ).
cnf(c_0_26,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_27,negated_conjecture,
multiply(a,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_25]),c_0_16]) ).
cnf(c_0_28,negated_conjecture,
multiply(add(X1,a),additive_identity) = multiply(X1,additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16]) ).
cnf(c_0_29,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
associativity_for_multiplication ).
cnf(c_0_30,negated_conjecture,
multiply(additive_identity,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_13]),c_0_27]) ).
cnf(c_0_31,negated_conjecture,
multiply(additive_identity,multiply(additive_identity,X1)) = multiply(additive_identity,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
multiply(additive_identity,add(multiply(additive_identity,X1),X2)) = multiply(additive_identity,add(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_31]),c_0_19]) ).
cnf(c_0_33,plain,
multiply(add(X1,X1),X2) = multiply(X1,add(X2,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_34,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_35,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_36,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_26]) ).
cnf(c_0_37,negated_conjecture,
multiply(additive_identity,add(X1,additive_inverse(multiply(additive_identity,X1)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_12]),c_0_30]) ).
cnf(c_0_38,negated_conjecture,
multiply(additive_identity,add(X1,multiply(additive_identity,X1))) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_32]),c_0_13]),c_0_31]) ).
cnf(c_0_39,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_34]),c_0_15]) ).
cnf(c_0_40,plain,
additive_inverse(multiply(X1,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_16]),c_0_12]) ).
cnf(c_0_41,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_17,c_0_36]),c_0_15]) ).
cnf(c_0_42,negated_conjecture,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_11]),c_0_12]),c_0_16]) ).
cnf(c_0_43,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X3,X2)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_44,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_40]),c_0_16]) ).
cnf(c_0_45,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_46,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X1))) = X1,
x_fourthed_is_x ).
cnf(c_0_47,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_41,c_0_12]),c_0_42]),c_0_16]) ).
cnf(c_0_48,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_12]),c_0_44]),c_0_45]),c_0_16]) ).
cnf(c_0_49,hypothesis,
multiply(X1,multiply(X1,multiply(X1,multiply(X1,X2)))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_46]),c_0_29]),c_0_29]) ).
cnf(c_0_50,hypothesis,
additive_inverse(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(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_47]),c_0_18]),c_0_47]),c_0_48]),c_0_46]),c_0_18]) ).
cnf(c_0_51,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_52,negated_conjecture,
multiply(add(c,multiply(a,X1)),X2) = multiply(a,multiply(add(X1,b),X2)),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_53,negated_conjecture,
multiply(a,multiply(a,multiply(a,c))) = c,
inference(spm,[status(thm)],[c_0_49,c_0_20]) ).
cnf(c_0_54,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[c_0_12,c_0_50]) ).
cnf(c_0_55,hypothesis,
multiply(X1,add(multiply(X1,multiply(X1,X1)),X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_46]) ).
cnf(c_0_56,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,multiply(X5,X2)))) = multiply(add(X1,multiply(X3,multiply(X4,X5))),X2),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_57,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_46]),c_0_29]),c_0_29]) ).
cnf(c_0_58,negated_conjecture,
multiply(a,multiply(add(b,multiply(a,multiply(a,c))),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_15]),c_0_54]),c_0_42]) ).
cnf(c_0_59,hypothesis,
multiply(X1,multiply(add(multiply(X1,multiply(X1,X1)),X2),X3)) = multiply(add(X1,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_55]) ).
cnf(c_0_60,hypothesis,
multiply(add(X1,multiply(X2,multiply(X2,X2))),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_15]) ).
cnf(c_0_61,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X1,multiply(X1,X3))))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_49]),c_0_19]) ).
cnf(c_0_62,hypothesis,
multiply(add(b,multiply(a,multiply(a,c))),a) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_44]) ).
cnf(c_0_63,hypothesis,
multiply(add(X1,multiply(X1,multiply(X2,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_59,c_0_60]),c_0_29]),c_0_29]),c_0_61]),c_0_54]),c_0_44]) ).
cnf(c_0_64,hypothesis,
multiply(add(b,add(multiply(a,multiply(a,c)),X1)),a) = multiply(X1,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_62]),c_0_13]),c_0_11]) ).
cnf(c_0_65,hypothesis,
multiply(X1,multiply(X2,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_57]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_66,hypothesis,
multiply(add(X1,multiply(X1,multiply(X2,multiply(X2,X2)))),multiply(X2,X3)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_63]),c_0_42]) ).
cnf(c_0_67,hypothesis,
multiply(a,multiply(a,multiply(c,a))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_54]),c_0_16]),c_0_29]),c_0_29]) ).
cnf(c_0_68,negated_conjecture,
multiply(a,add(multiply(a,multiply(a,c)),X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_69,hypothesis,
multiply(X1,multiply(X2,multiply(X3,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_57]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_70,hypothesis,
multiply(X1,multiply(add(X2,multiply(X2,multiply(X1,multiply(X1,X1)))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_44]) ).
cnf(c_0_71,hypothesis,
multiply(a,multiply(a,multiply(c,multiply(a,X1)))) = multiply(b,multiply(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_67]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_72,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_73,hypothesis,
multiply(add(b,multiply(a,multiply(a,c))),multiply(a,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_62]),c_0_42]) ).
cnf(c_0_74,negated_conjecture,
multiply(a,multiply(add(a,X1),multiply(a,c))) = add(c,multiply(a,multiply(X1,multiply(a,c)))),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_75,hypothesis,
multiply(add(X1,multiply(X1,multiply(X2,multiply(X2,X2)))),multiply(X3,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_69,c_0_70]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]) ).
cnf(c_0_76,negated_conjecture,
multiply(a,multiply(a,multiply(c,multiply(c,X1)))) = multiply(b,multiply(c,X1)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
multiply(a,add(b,X1)) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_78,negated_conjecture,
multiply(add(b,multiply(a,multiply(a,c))),multiply(c,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_73,c_0_72]) ).
cnf(c_0_79,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_14,c_0_50]) ).
cnf(c_0_80,negated_conjecture,
add(c,multiply(b,multiply(c,multiply(c,multiply(a,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_74,c_0_75]),c_0_44]),c_0_29]),c_0_29]),c_0_29]),c_0_76]) ).
cnf(c_0_81,negated_conjecture,
multiply(add(a,X1),b) = add(c,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_82,negated_conjecture,
add(c,add(multiply(a,X1),multiply(X2,add(b,X1)))) = multiply(add(a,X2),add(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_77]),c_0_11]) ).
cnf(c_0_83,hypothesis,
multiply(c,add(b,multiply(a,multiply(a,c)))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_78]),c_0_44]) ).
cnf(c_0_84,negated_conjecture,
multiply(b,multiply(c,multiply(c,multiply(a,c)))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_16]) ).
cnf(c_0_85,negated_conjecture,
add(c,add(multiply(X1,b),multiply(add(a,X1),X2))) = multiply(add(a,X1),add(b,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_81]),c_0_11]) ).
cnf(c_0_86,negated_conjecture,
multiply(add(a,c),add(b,multiply(a,multiply(a,c)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_53]),c_0_16]),c_0_54]) ).
cnf(c_0_87,negated_conjecture,
multiply(add(a,X1),multiply(a,multiply(a,c))) = add(c,multiply(X1,multiply(a,multiply(a,c)))),
inference(spm,[status(thm)],[c_0_26,c_0_53]) ).
cnf(c_0_88,hypothesis,
multiply(b,multiply(b,multiply(b,c))) = c,
inference(spm,[status(thm)],[c_0_49,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
add(c,multiply(c,multiply(a,multiply(a,c)))) = add(c,multiply(c,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_16]),c_0_79]),c_0_87]) ).
cnf(c_0_90,hypothesis,
multiply(X1,add(multiply(X1,multiply(X1,multiply(X1,X2))),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_49]),c_0_19]) ).
cnf(c_0_91,plain,
add(X1,add(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_17,c_0_50]) ).
cnf(c_0_92,hypothesis,
multiply(X1,add(multiply(X2,multiply(X1,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_19,c_0_57]),c_0_19]) ).
cnf(c_0_93,negated_conjecture,
multiply(c,multiply(b,multiply(b,c))) = multiply(a,c),
inference(spm,[status(thm)],[c_0_72,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
multiply(c,multiply(a,multiply(a,c))) = multiply(c,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_89]),c_0_79]) ).
cnf(c_0_95,hypothesis,
multiply(X1,add(X2,add(X3,multiply(X1,multiply(X1,multiply(X1,X2)))))) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,hypothesis,
multiply(X1,add(X2,add(multiply(X2,multiply(X1,multiply(X1,X1))),X3))) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_66]),c_0_13]),c_0_11]) ).
cnf(c_0_97,negated_conjecture,
multiply(c,multiply(b,multiply(b,multiply(c,X1)))) = multiply(a,multiply(c,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_93]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_98,hypothesis,
multiply(b,multiply(c,multiply(c,c))) = multiply(a,multiply(a,c)),
inference(spm,[status(thm)],[c_0_76,c_0_46]) ).
cnf(c_0_99,negated_conjecture,
multiply(b,multiply(a,multiply(a,c))) = multiply(a,multiply(a,multiply(c,b))),
inference(spm,[status(thm)],[c_0_71,c_0_94]) ).
cnf(c_0_100,negated_conjecture,
multiply(c,multiply(a,multiply(a,multiply(c,X1)))) = multiply(c,multiply(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_94]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_101,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(add(multiply(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_102,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X1,X1)))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_49]) ).
cnf(c_0_103,hypothesis,
multiply(a,multiply(c,multiply(c,c))) = multiply(c,multiply(b,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_100]) ).
cnf(c_0_104,hypothesis,
multiply(add(X1,multiply(X2,multiply(X2,X2))),multiply(X2,X3)) = multiply(add(X2,multiply(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_101]),c_0_15]) ).
cnf(c_0_105,hypothesis,
multiply(b,multiply(c,multiply(c,multiply(c,X1)))) = multiply(a,multiply(a,multiply(c,X1))),
inference(spm,[status(thm)],[c_0_76,c_0_49]) ).
cnf(c_0_106,hypothesis,
multiply(c,multiply(c,multiply(b,b))) = multiply(c,a),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,negated_conjecture,
multiply(a,multiply(c,multiply(b,b))) = multiply(b,multiply(c,c)),
inference(spm,[status(thm)],[c_0_76,c_0_103]) ).
cnf(c_0_108,hypothesis,
multiply(X1,multiply(add(X2,multiply(X1,multiply(X1,multiply(X1,X2)))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_104]),c_0_29]),c_0_29]),c_0_66]) ).
cnf(c_0_109,hypothesis,
multiply(b,multiply(c,multiply(c,a))) = multiply(c,multiply(c,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_72]) ).
cnf(c_0_110,hypothesis,
multiply(add(multiply(X1,multiply(X1,X1)),X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_15]) ).
cnf(c_0_111,hypothesis,
multiply(add(X1,multiply(X2,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_108]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]) ).
cnf(c_0_112,negated_conjecture,
multiply(a,multiply(c,multiply(c,a))) = multiply(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_109]),c_0_98]),c_0_94]) ).
cnf(c_0_113,negated_conjecture,
multiply(a,multiply(add(b,X1),multiply(a,multiply(add(b,X1),multiply(a,multiply(add(b,X1),add(c,multiply(a,X1)))))))) = add(c,multiply(a,X1)),
inference(spm,[status(thm)],[c_0_57,c_0_77]) ).
cnf(c_0_114,hypothesis,
add(multiply(X1,X2),multiply(X2,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_57]) ).
cnf(c_0_115,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(a,multiply(c,b)),
inference(spm,[status(thm)],[c_0_76,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
add(c,multiply(c,multiply(a,multiply(a,a)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_66]),c_0_44]),c_0_72]) ).
cnf(c_0_117,hypothesis,
multiply(X1,multiply(X1,multiply(X1,multiply(X2,X1)))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_114]),c_0_16]) ).
cnf(c_0_118,negated_conjecture,
multiply(b,multiply(c,multiply(a,X1))) = multiply(a,multiply(c,multiply(b,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_115]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_119,negated_conjecture,
multiply(c,multiply(a,multiply(a,a))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_116]),c_0_16]) ).
cnf(c_0_120,hypothesis,
multiply(X1,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_117]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_121,negated_conjecture,
multiply(a,multiply(a,multiply(a,multiply(c,X1)))) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_49,c_0_72]) ).
cnf(c_0_122,negated_conjecture,
multiply(a,multiply(c,multiply(b,multiply(a,a)))) = multiply(b,c),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X1,X1)))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_46]),c_0_15]) ).
cnf(c_0_124,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X2,multiply(X1,multiply(X1,X1))),
inference(spm,[status(thm)],[c_0_120,c_0_102]) ).
cnf(c_0_125,hypothesis,
multiply(c,multiply(c,multiply(c,b))) = multiply(a,multiply(a,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_98]),c_0_29]),c_0_29]),c_0_94]),c_0_29]),c_0_29]),c_0_49]),c_0_29]),c_0_29]),c_0_49]) ).
cnf(c_0_126,negated_conjecture,
multiply(c,multiply(b,multiply(a,a))) = multiply(a,multiply(c,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_72]) ).
cnf(c_0_127,hypothesis,
multiply(b,multiply(c,multiply(b,b))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_102]),c_0_67]),c_0_103]) ).
cnf(c_0_128,hypothesis,
multiply(X1,multiply(X1,add(X2,multiply(X1,X1)))) = add(X1,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_123,c_0_19]) ).
cnf(c_0_129,hypothesis,
multiply(X1,multiply(X1,add(multiply(X1,multiply(X1,X2)),X3))) = multiply(X1,add(X2,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_90,c_0_19]) ).
cnf(c_0_130,hypothesis,
multiply(X1,multiply(add(multiply(X1,X1),X2),X1)) = add(X1,multiply(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_55,c_0_101]) ).
cnf(c_0_131,hypothesis,
add(multiply(X1,multiply(X1,multiply(X1,X2))),multiply(X2,X3)) = multiply(X2,add(multiply(X1,multiply(X1,X1)),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_124]) ).
cnf(c_0_132,hypothesis,
multiply(b,multiply(b,multiply(b,multiply(c,X1)))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_88]),c_0_29]),c_0_29]) ).
cnf(c_0_133,hypothesis,
multiply(b,multiply(c,multiply(c,b))) = multiply(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_125]),c_0_94]),c_0_53]) ).
cnf(c_0_134,hypothesis,
multiply(b,multiply(a,multiply(c,a))) = multiply(a,multiply(c,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(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_117,c_0_126]),c_0_29]),c_0_29]),c_0_121]),c_0_29]),c_0_29]),c_0_72]),c_0_103]),c_0_127]),c_0_29]),c_0_29]),c_0_72]) ).
cnf(c_0_135,negated_conjecture,
multiply(a,multiply(a,multiply(c,c))) = multiply(b,c),
inference(spm,[status(thm)],[c_0_71,c_0_20]) ).
cnf(c_0_136,hypothesis,
multiply(X1,multiply(X1,multiply(add(X2,multiply(X1,X1)),X3))) = multiply(add(X1,multiply(X1,multiply(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_128]),c_0_29]) ).
cnf(c_0_137,plain,
multiply(add(X1,multiply(X1,X2)),X3) = multiply(X1,add(X3,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
cnf(c_0_138,hypothesis,
multiply(X1,multiply(X1,multiply(X1,add(X2,multiply(X1,X3))))) = multiply(X1,add(multiply(X1,multiply(X1,X2)),X3)),
inference(spm,[status(thm)],[c_0_49,c_0_129]) ).
cnf(c_0_139,hypothesis,
multiply(X1,multiply(add(multiply(X1,X1),X2),multiply(X1,X3))) = multiply(add(X1,multiply(X1,multiply(X2,X1))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_130]),c_0_29]) ).
cnf(c_0_140,hypothesis,
multiply(add(multiply(X1,X1),X2),multiply(X1,X2)) = multiply(X2,multiply(X1,add(multiply(X1,X1),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_131]),c_0_19]) ).
cnf(c_0_141,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_142,hypothesis,
multiply(X1,multiply(add(X2,multiply(X1,multiply(X1,X1))),X3)) = multiply(add(X1,multiply(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_29,c_0_123]) ).
cnf(c_0_143,hypothesis,
multiply(X1,multiply(X1,multiply(X1,multiply(X2,multiply(X3,X1))))) = multiply(X2,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_117,c_0_29]) ).
cnf(c_0_144,hypothesis,
multiply(b,multiply(b,multiply(a,c))) = multiply(c,multiply(c,b)),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_145,negated_conjecture,
multiply(c,multiply(a,multiply(c,a))) = multiply(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_134]),c_0_135]) ).
cnf(c_0_146,plain,
add(multiply(X1,multiply(X2,multiply(X3,X4))),multiply(X5,X4)) = multiply(add(multiply(X1,multiply(X2,X3)),X5),X4),
inference(spm,[status(thm)],[c_0_101,c_0_29]) ).
cnf(c_0_147,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X1,X2)))) = multiply(add(X1,multiply(X1,multiply(X1,X1))),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_138]),c_0_15]) ).
cnf(c_0_148,hypothesis,
multiply(X1,multiply(X2,multiply(X1,add(multiply(X1,X1),X2)))) = multiply(add(X1,multiply(X1,multiply(X2,X1))),X2),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_149,plain,
add(multiply(X1,X2),add(X3,multiply(X1,X4))) = add(X3,multiply(X1,add(X4,X2))),
inference(spm,[status(thm)],[c_0_141,c_0_19]) ).
cnf(c_0_150,hypothesis,
multiply(add(X1,multiply(X1,X2)),multiply(X1,X3)) = multiply(X1,multiply(add(X1,multiply(X2,X1)),X3)),
inference(spm,[status(thm)],[c_0_142,c_0_104]) ).
cnf(c_0_151,hypothesis,
multiply(a,multiply(c,multiply(a,multiply(c,c)))) = multiply(c,multiply(c,b)),
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_143,c_0_144]),c_0_29]),c_0_125]),c_0_53]),c_0_29]),c_0_29]) ).
cnf(c_0_152,hypothesis,
multiply(c,multiply(c,multiply(b,c))) = multiply(a,multiply(c,a)),
inference(spm,[status(thm)],[c_0_120,c_0_145]) ).
cnf(c_0_153,hypothesis,
add(multiply(X1,multiply(X2,multiply(X2,X2))),multiply(X3,X1)) = multiply(add(multiply(X2,multiply(X2,X2)),X3),X1),
inference(spm,[status(thm)],[c_0_146,c_0_124]) ).
cnf(c_0_154,hypothesis,
multiply(add(X1,multiply(X1,X1)),add(X1,multiply(X1,X1))) = add(X1,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_15]),c_0_137]),c_0_29]),c_0_123]),c_0_149]),c_0_79]),c_0_123]),c_0_15]),c_0_150]),c_0_29]),c_0_142]) ).
cnf(c_0_155,plain,
add(additive_inverse(X1),add(X2,add(X3,X1))) = add(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_14]),c_0_11]) ).
cnf(c_0_156,hypothesis,
multiply(c,multiply(a,multiply(c,c))) = multiply(b,multiply(c,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_151]),c_0_76]) ).
cnf(c_0_157,negated_conjecture,
multiply(c,multiply(b,multiply(a,multiply(c,c)))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_152]),c_0_134]),c_0_67]) ).
cnf(c_0_158,hypothesis,
add(multiply(X1,add(X2,multiply(X2,X2))),multiply(X3,X1)) = multiply(add(X2,add(multiply(X2,X2),X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_154]),c_0_154]),c_0_11]) ).
cnf(c_0_159,plain,
add(X1,add(X2,add(X3,X1))) = add(X3,X2),
inference(rw,[status(thm)],[c_0_155,c_0_50]) ).
cnf(c_0_160,negated_conjecture,
multiply(add(b,multiply(a,multiply(a,c))),c) = additive_identity,
inference(spm,[status(thm)],[c_0_73,c_0_20]) ).
cnf(c_0_161,negated_conjecture,
multiply(c,multiply(a,multiply(c,multiply(c,b)))) = multiply(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_156]),c_0_72]),c_0_157]) ).
cnf(c_0_162,hypothesis,
multiply(add(multiply(X1,X2),X3),multiply(X2,multiply(X2,X2))) = multiply(add(X1,multiply(X3,multiply(X2,X2))),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_46]),c_0_56]) ).
cnf(c_0_163,hypothesis,
multiply(add(X1,multiply(X1,X1)),X2) = multiply(X2,add(X1,multiply(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_158]),c_0_26]),c_0_159]),c_0_15]) ).
cnf(c_0_164,negated_conjecture,
multiply(add(b,add(multiply(a,multiply(a,c)),X1)),c) = multiply(X1,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_160]),c_0_13]),c_0_11]) ).
cnf(c_0_165,negated_conjecture,
multiply(a,multiply(a,multiply(c,multiply(X1,c)))) = multiply(b,multiply(X1,c)),
inference(spm,[status(thm)],[c_0_76,c_0_117]) ).
cnf(c_0_166,negated_conjecture,
multiply(a,multiply(c,multiply(a,c))) = multiply(b,multiply(b,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_161]),c_0_133]) ).
cnf(c_0_167,hypothesis,
multiply(c,multiply(b,multiply(b,b))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_46]),c_0_20]) ).
cnf(c_0_168,hypothesis,
multiply(add(X1,multiply(X2,multiply(X3,multiply(X3,X3)))),X3) = multiply(add(X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_26]),c_0_29]),c_0_46]),c_0_29]) ).
cnf(c_0_169,hypothesis,
multiply(add(X1,multiply(X1,X2)),X2) = multiply(add(X2,multiply(X2,X2)),X1),
inference(spm,[status(thm)],[c_0_137,c_0_163]) ).
cnf(c_0_170,negated_conjecture,
multiply(add(X1,multiply(a,multiply(a,c))),c) = multiply(add(b,X1),c),
inference(spm,[status(thm)],[c_0_164,c_0_91]) ).
cnf(c_0_171,negated_conjecture,
multiply(c,multiply(b,a)) = multiply(b,multiply(a,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_72]) ).
cnf(c_0_172,hypothesis,
multiply(c,add(multiply(b,multiply(b,b)),X1)) = add(c,multiply(c,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_167]) ).
cnf(c_0_173,hypothesis,
multiply(add(multiply(X1,multiply(X2,multiply(X2,X2))),X3),X2) = multiply(add(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_26]),c_0_29]),c_0_29]),c_0_29]),c_0_46]) ).
cnf(c_0_174,negated_conjecture,
multiply(add(multiply(a,multiply(c,c)),X1),a) = add(multiply(c,b),multiply(X1,a)),
inference(spm,[status(thm)],[c_0_146,c_0_112]) ).
cnf(c_0_175,hypothesis,
multiply(add(X1,multiply(X1,X2)),X2) = multiply(X2,add(X1,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_137,c_0_169]) ).
cnf(c_0_176,negated_conjecture,
multiply(a,multiply(add(X1,multiply(a,c)),c)) = multiply(add(b,multiply(a,X1)),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_19]),c_0_29]) ).
cnf(c_0_177,negated_conjecture,
add(multiply(c,X1),multiply(b,multiply(a,c))) = multiply(c,add(X1,multiply(b,a))),
inference(spm,[status(thm)],[c_0_19,c_0_171]) ).
cnf(c_0_178,hypothesis,
multiply(c,multiply(b,add(multiply(b,b),X1))) = add(c,multiply(c,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_172,c_0_19]) ).
cnf(c_0_179,hypothesis,
multiply(X1,add(X2,multiply(X3,multiply(X1,multiply(X1,X1))))) = multiply(X1,add(X3,X2)),
inference(spm,[status(thm)],[c_0_96,c_0_91]) ).
cnf(c_0_180,hypothesis,
multiply(add(multiply(X1,multiply(X1,multiply(X1,X2))),X3),X1) = multiply(add(X2,X3),X1),
inference(spm,[status(thm)],[c_0_173,c_0_124]) ).
cnf(c_0_181,hypothesis,
multiply(a,multiply(c,multiply(c,multiply(c,X1)))) = multiply(c,multiply(b,multiply(b,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_103]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_182,negated_conjecture,
multiply(c,add(b,multiply(b,a))) = multiply(add(b,c),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(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_174,c_0_175]),c_0_135]),c_0_101]),c_0_15]),c_0_176]),c_0_20]),c_0_29]),c_0_29]),c_0_112]),c_0_29]),c_0_171]),c_0_177]) ).
cnf(c_0_183,hypothesis,
multiply(X1,multiply(X1,multiply(add(X2,X1),X1))) = add(X1,multiply(X1,multiply(X1,multiply(X2,X1)))),
inference(spm,[status(thm)],[c_0_128,c_0_26]) ).
cnf(c_0_184,hypothesis,
multiply(a,add(X1,multiply(a,multiply(c,a)))) = add(multiply(a,X1),multiply(b,a)),
inference(spm,[status(thm)],[c_0_19,c_0_67]) ).
cnf(c_0_185,hypothesis,
multiply(c,multiply(b,multiply(b,add(b,X1)))) = add(c,multiply(c,multiply(b,multiply(b,X1)))),
inference(spm,[status(thm)],[c_0_178,c_0_19]) ).
cnf(c_0_186,hypothesis,
multiply(c,multiply(b,multiply(b,multiply(b,X1)))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_167]),c_0_29]),c_0_29]) ).
cnf(c_0_187,hypothesis,
multiply(add(multiply(X1,multiply(X2,X2)),X3),multiply(X2,X2)) = multiply(add(X1,multiply(X3,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_46]),c_0_51]) ).
cnf(c_0_188,hypothesis,
multiply(X1,multiply(add(X2,multiply(X3,multiply(X1,X1))),X1)) = multiply(X1,add(X3,multiply(X2,X1))),
inference(spm,[status(thm)],[c_0_179,c_0_56]) ).
cnf(c_0_189,hypothesis,
multiply(X1,multiply(add(multiply(X1,multiply(X1,X2)),X3),X1)) = multiply(add(X2,multiply(X1,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_19]),c_0_29]) ).
cnf(c_0_190,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X1,multiply(X3,X1))))) = add(multiply(X1,X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_117]) ).
cnf(c_0_191,hypothesis,
add(multiply(a,c),multiply(b,a)) = add(c,multiply(c,a)),
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_181,c_0_182]),c_0_183]),c_0_152]),c_0_184]),c_0_185]),c_0_186]) ).
cnf(c_0_192,plain,
add(multiply(X1,X2),add(X3,multiply(X4,X2))) = add(X3,multiply(add(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_141,c_0_26]) ).
cnf(c_0_193,negated_conjecture,
multiply(add(X1,multiply(c,multiply(a,a))),a) = add(c,multiply(X1,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_119]),c_0_15]) ).
cnf(c_0_194,hypothesis,
multiply(add(X1,multiply(add(multiply(X1,multiply(X2,X2)),X3),X2)),X2) = multiply(X3,multiply(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_66]),c_0_13]),c_0_11]),c_0_146]) ).
cnf(c_0_195,hypothesis,
multiply(add(X1,multiply(X2,multiply(X3,multiply(X2,X2)))),X2) = add(multiply(X2,X3),multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_29]),c_0_29]),c_0_190]) ).
cnf(c_0_196,hypothesis,
add(c,multiply(add(b,c),a)) = multiply(a,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_191]),c_0_192]),c_0_15]) ).
cnf(c_0_197,negated_conjecture,
multiply(a,add(X1,multiply(a,multiply(a,c)))) = add(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_53]),c_0_15]) ).
cnf(c_0_198,hypothesis,
multiply(b,multiply(c,multiply(b,c))) = multiply(c,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_152]),c_0_145]),c_0_67]),c_0_72]) ).
cnf(c_0_199,negated_conjecture,
multiply(add(multiply(c,multiply(a,a)),X1),a) = add(c,multiply(X1,a)),
inference(spm,[status(thm)],[c_0_193,c_0_15]) ).
cnf(c_0_200,hypothesis,
add(multiply(X1,X2),multiply(X2,add(X1,multiply(X2,X1)))) = multiply(X1,multiply(X2,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_175]),c_0_51]),c_0_195]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_46]),c_0_15]) ).
cnf(c_0_201,hypothesis,
multiply(add(b,c),a) = add(c,multiply(a,c)),
inference(spm,[status(thm)],[c_0_79,c_0_196]) ).
cnf(c_0_202,negated_conjecture,
multiply(a,multiply(a,add(X1,multiply(a,c)))) = add(c,multiply(a,multiply(a,X1))),
inference(spm,[status(thm)],[c_0_197,c_0_19]) ).
cnf(c_0_203,hypothesis,
multiply(b,multiply(c,multiply(b,multiply(c,X1)))) = multiply(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_198]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_204,negated_conjecture,
multiply(c,multiply(a,a)) = multiply(a,multiply(a,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(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_199,c_0_200]),c_0_29]),c_0_46]),c_0_29]),c_0_29]),c_0_29]),c_0_197]),c_0_29]),c_0_52]),c_0_15]),c_0_201]),c_0_202]),c_0_79]) ).
cnf(c_0_205,hypothesis,
multiply(a,multiply(a,multiply(c,b))) = multiply(c,multiply(c,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_109]),c_0_98]),c_0_99]) ).
cnf(c_0_206,negated_conjecture,
multiply(b,a) != c,
prove_commutativity ).
cnf(c_0_207,hypothesis,
$false,
inference(sr,[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_203,c_0_204]),c_0_99]),c_0_205]),c_0_124]),c_0_103]),c_0_127]),c_0_124]),c_0_53]),c_0_206]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.20 % Problem : RNG035-7 : TPTP v9.2.1. Released v1.0.0.
% 0.04/0.20 % 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
% 0.13/0.43 % Computer : n026.cluster.edu
% 0.13/0.43 % Model : x86_64 x86_64
% 0.13/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.43 % Memory : 8042.1875MB
% 0.13/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.43 % CPULimit : 300
% 0.13/0.43 % WCLimit : 300
% 0.13/0.43 % DateTime : Tue May 5 01:47:23 EDT 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 31.26/23.14 % Version : CSE_E---1.7
% 31.26/23.14 % Problem : theBenchmark.p
% 31.26/23.14 % SZS status Unsatisfiable for theBenchmark.p
% 31.26/23.14 % SZS output start CNFRefutation
% See solution above
% 31.33/23.23 % Total time : 19.608s
%------------------------------------------------------------------------------