%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG008-1 : 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 : n008.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 02:05:28 PM UTC 2026
% Result : Unsatisfiable 3.45s 1.01s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 18
% Syntax : Number of clauses : 155 ( 75 unt; 0 nHn; 116 RR)
% Number of literals : 321 ( 42 equ; 169 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 367 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(associativity_of_multiplication2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(distributivity3,axiom,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(associativity_of_multiplication1,axiom,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication1) ).
cnf(distributivity4,axiom,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_0_18,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_19,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_20,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition2]) ).
cnf(c_0_21,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_18 ).
cnf(c_0_22,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_23,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_19 ).
cnf(c_0_24,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_25,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_20 ).
cnf(c_0_26,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_27,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_30,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_31,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
cnf(c_0_32,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_29 ).
cnf(c_0_35,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_30 ).
cnf(c_0_36,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_37,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_multiplication2]) ).
cnf(c_0_38,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_31 ).
cnf(c_0_39,plain,
( ~ sum(X3,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_33]) ).
cnf(c_0_40,plain,
( ~ product(X4,X5,X2)
| ~ product(X4,X5,X3)
| ~ product(X4,additive_identity,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_41,hypothesis,
( ~ product(X2,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_43,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_37 ).
cnf(c_0_44,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_45,plain,
( ~ sum(X3,X4,X2)
| ~ sum(X1,X3,additive_inverse(X4))
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_46,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_47,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_39,c_0_26]) ).
cnf(c_0_48,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_49,hypothesis,
( ~ product(X3,X3,X2)
| ~ product(X3,additive_identity,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_50,hypothesis,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,hypothesis,
( ~ product(X4,X2,X1)
| ~ product(X4,X2,X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_52,hypothesis,
( ~ product(a,b,X1)
| X1 = c ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_53,plain,
( ~ sum(X1,additive_inverse(X2),additive_inverse(X2))
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_54,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_55,hypothesis,
( ~ product(X2,additive_identity,X1)
| sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_42]),c_0_50]) ).
cnf(c_0_56,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity3]) ).
cnf(c_0_57,hypothesis,
( ~ product(a,b,X1)
| product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_51,c_0_44]) ).
cnf(c_0_58,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_52,c_0_42]) ).
cnf(c_0_59,plain,
( ~ sum(X1,X2,X2)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,hypothesis,
sum(multiply(X1,additive_identity),X1,X1),
inference(spm,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_61,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_56 ).
cnf(c_0_62,plain,
( ~ product(X4,X5,X2)
| ~ product(X4,additive_identity,X3)
| ~ product(X4,additive_inverse(X5),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_63,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_42]),c_0_58]) ).
cnf(c_0_64,hypothesis,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( ~ product(X5,X4,X2)
| ~ product(X5,X4,X3)
| ~ product(additive_identity,X4,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_22]) ).
cnf(c_0_66,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_67,hypothesis,
( ~ product(c,additive_identity,X2)
| ~ product(c,additive_inverse(b),X1)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_64]),c_0_33]) ).
cnf(c_0_69,hypothesis,
( ~ product(X3,X3,X2)
| ~ product(additive_identity,X3,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_36]) ).
cnf(c_0_70,plain,
( ~ sum(add(additive_inverse(X3),X2),X3,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_66]) ).
cnf(c_0_71,hypothesis,
( ~ product(c,additive_inverse(b),X1)
| sum(X1,c,additive_identity) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_68]) ).
cnf(c_0_72,hypothesis,
( ~ product(additive_identity,X2,X1)
| sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_42]),c_0_50]) ).
cnf(c_0_73,plain,
( ~ sum(add(X3,X2),additive_inverse(X3),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_70,c_0_54]) ).
cnf(c_0_74,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_28]) ).
cnf(c_0_75,hypothesis,
sum(multiply(c,additive_inverse(b)),c,additive_identity),
inference(spm,[status(thm)],[c_0_71,c_0_42]) ).
cnf(c_0_76,hypothesis,
sum(multiply(additive_identity,X1),X1,X1),
inference(spm,[status(thm)],[c_0_72,c_0_42]) ).
cnf(c_0_77,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_24]),c_0_74]) ).
cnf(c_0_78,hypothesis,
add(c,multiply(c,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_75]),c_0_74]) ).
cnf(c_0_79,hypothesis,
sum(multiply(additive_identity,X1),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_59,c_0_76]) ).
cnf(c_0_80,hypothesis,
multiply(c,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_33]) ).
cnf(c_0_81,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_82,plain,
( ~ product(X4,X5,X2)
| ~ product(additive_identity,X5,X3)
| ~ product(additive_inverse(X4),X5,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_26]) ).
cnf(c_0_83,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_79]),c_0_33]) ).
cnf(c_0_84,hypothesis,
product(c,additive_inverse(b),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_42,c_0_80]) ).
cnf(c_0_85,hypothesis,
( ~ product(X1,multiply(X1,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_81,c_0_36]) ).
cnf(c_0_86,hypothesis,
( ~ product(additive_identity,X2,X3)
| ~ product(additive_inverse(X2),X2,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_36]) ).
cnf(c_0_87,hypothesis,
product(additive_identity,X1,additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_83]) ).
cnf(c_0_88,hypothesis,
( ~ product(c,additive_inverse(b),X1)
| X1 = additive_inverse(c) ),
inference(spm,[status(thm)],[c_0_35,c_0_84]) ).
cnf(c_0_89,hypothesis,
product(X1,X2,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_85,c_0_42]) ).
cnf(c_0_90,hypothesis,
( ~ product(additive_inverse(X2),X2,X1)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,hypothesis,
multiply(c,additive_inverse(c)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_80]) ).
cnf(c_0_92,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_93,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_94,hypothesis,
( ~ product(X2,additive_inverse(X2),X1)
| sum(X1,additive_inverse(X2),additive_identity) ),
inference(spm,[status(thm)],[c_0_90,c_0_54]) ).
cnf(c_0_95,hypothesis,
product(c,additive_inverse(c),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_42,c_0_91]) ).
cnf(c_0_96,plain,
( ~ product(X4,X6,X1)
| ~ product(X5,X6,X2)
| ~ product(add(X4,X5),X6,X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_61,c_0_24]) ).
cnf(c_0_97,plain,
( ~ sum(X1,X2,additive_identity)
| sum(X1,additive_identity,additive_inverse(X2)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_98,hypothesis,
sum(additive_inverse(c),additive_inverse(c),additive_identity),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,hypothesis,
( ~ product(X3,b,X1)
| ~ product(add(X3,c),b,X2)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_63]) ).
cnf(c_0_100,plain,
( ~ sum(additive_inverse(X2),X2,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_101,hypothesis,
sum(additive_inverse(c),additive_identity,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_54]) ).
cnf(c_0_102,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_multiplication1]) ).
cnf(c_0_103,hypothesis,
( ~ product(add(a,c),b,X1)
| sum(c,c,X1) ),
inference(spm,[status(thm)],[c_0_99,c_0_44]) ).
cnf(c_0_104,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_100,c_0_28]) ).
cnf(c_0_105,hypothesis,
additive_inverse(c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_101]),c_0_33]) ).
cnf(c_0_106,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_102 ).
cnf(c_0_107,hypothesis,
sum(c,c,multiply(add(a,c),b)),
inference(spm,[status(thm)],[c_0_103,c_0_42]) ).
cnf(c_0_108,hypothesis,
add(c,c) = additive_identity,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_109,plain,
( ~ product(X1,X5,X3)
| ~ product(X5,X4,X2)
| product(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_106,c_0_42]) ).
cnf(c_0_110,hypothesis,
multiply(add(a,c),b) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_107]),c_0_108]) ).
cnf(c_0_111,hypothesis,
( ~ product(X1,X4,X3)
| ~ product(X4,X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_106,c_0_36]) ).
cnf(c_0_112,plain,
( ~ product(X1,X2,X4)
| product(X1,multiply(X2,X3),multiply(X4,X3)) ),
inference(spm,[status(thm)],[c_0_109,c_0_42]) ).
cnf(c_0_113,hypothesis,
product(add(a,c),b,additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_110]) ).
cnf(c_0_114,hypothesis,
( ~ product(X1,X2,X3)
| product(X1,multiply(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_111,c_0_42]) ).
cnf(c_0_115,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_116,hypothesis,
product(add(a,c),multiply(b,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_83]) ).
cnf(c_0_117,hypothesis,
( ~ product(a,multiply(b,X1),X2)
| product(c,X1,X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_44]) ).
cnf(c_0_118,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_114,c_0_42]) ).
cnf(c_0_119,hypothesis,
multiply(add(a,c),multiply(b,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_117,c_0_42]) ).
cnf(c_0_121,hypothesis,
product(b,additive_identity,multiply(b,add(a,c))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_122,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_115,c_0_120]) ).
cnf(c_0_123,hypothesis,
multiply(b,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_121]),c_0_68]) ).
cnf(c_0_124,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_125,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,X6,X2)
| ~ product(X4,add(X5,X6),X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_126,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_68]) ).
cnf(c_0_127,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_124]),c_0_74]) ).
cnf(c_0_128,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity4]) ).
cnf(c_0_129,hypothesis,
( ~ product(c,X3,X1)
| ~ product(c,add(X3,b),X2)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_63]) ).
cnf(c_0_130,hypothesis,
( ~ product(X2,X4,X1)
| ~ product(X2,add(X4,X2),X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_125,c_0_36]) ).
cnf(c_0_131,hypothesis,
product(c,add(a,c),additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_126]) ).
cnf(c_0_132,hypothesis,
add(c,add(X1,c)) = X1,
inference(spm,[status(thm)],[c_0_127,c_0_105]) ).
cnf(c_0_133,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
c_0_128 ).
cnf(c_0_134,hypothesis,
( ~ product(c,add(b,c),X1)
| sum(c,c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_36]),c_0_74]) ).
cnf(c_0_135,hypothesis,
( ~ product(c,a,X1)
| sum(additive_identity,c,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_74]),c_0_132]) ).
cnf(c_0_136,plain,
( ~ sum(X4,X5,X1)
| ~ product(X5,X2,X3)
| ~ product(X4,X2,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_133,c_0_22]) ).
cnf(c_0_137,hypothesis,
sum(c,c,multiply(c,add(b,c))),
inference(spm,[status(thm)],[c_0_134,c_0_42]) ).
cnf(c_0_138,hypothesis,
sum(additive_identity,c,multiply(c,a)),
inference(spm,[status(thm)],[c_0_135,c_0_42]) ).
cnf(c_0_139,plain,
( ~ product(X2,X3,X4)
| ~ product(X1,X3,additive_identity)
| product(add(X1,X2),X3,X4) ),
inference(spm,[status(thm)],[c_0_136,c_0_24]) ).
cnf(c_0_140,hypothesis,
multiply(c,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_137]),c_0_108]) ).
cnf(c_0_141,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_118,c_0_122]) ).
cnf(c_0_142,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_138]),c_0_48]) ).
cnf(c_0_143,hypothesis,
( ~ product(X1,X2,additive_identity)
| product(add(X1,X2),X2,X2) ),
inference(spm,[status(thm)],[c_0_139,c_0_36]) ).
cnf(c_0_144,hypothesis,
product(c,add(b,c),additive_identity),
inference(spm,[status(thm)],[c_0_42,c_0_140]) ).
cnf(c_0_145,hypothesis,
product(b,c,multiply(b,a)),
inference(rw,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_146,hypothesis,
product(b,add(b,c),add(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_132]) ).
cnf(c_0_147,hypothesis,
( ~ product(b,add(b,c),X1)
| sum(multiply(b,a),b,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_145]),c_0_74]) ).
cnf(c_0_148,hypothesis,
multiply(b,add(b,c)) = add(b,c),
inference(spm,[status(thm)],[c_0_115,c_0_146]) ).
cnf(c_0_149,hypothesis,
sum(multiply(b,a),b,add(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_42]),c_0_148]) ).
cnf(c_0_150,hypothesis,
add(b,multiply(b,a)) = add(b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_149]),c_0_74]) ).
cnf(c_0_151,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_152,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_150]),c_0_77]) ).
cnf(c_0_153,negated_conjecture,
~ product(b,a,c),
c_0_151 ).
cnf(c_0_154,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_152]),c_0_153]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:10:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.44 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
% 3.45/1.01 % Version: 3.5.1
% 3.45/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.45/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.45/1.01 % Starting new_bool_3 with 300s (1) cores
% 3.45/1.01 % Starting new_bool_1 with 300s (1) cores
% 3.45/1.01 % Starting sh5l with 300s (1) cores
% 3.45/1.01 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 112009 completed with status 0
% 3.45/1.01 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.45/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.45/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.45/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.45/1.01 % No SInE strategy applied
% 3.45/1.01 % Search class: FHUSM-FFMF21-SFFFFFNN
% 3.45/1.01 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.45/1.01 % Starting SubtermCWHack with 136s (1) cores
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 3.45/1.01 % Starting new_bool_3 with 136s (1) cores
% 3.45/1.01 % Starting new_bool_1 with 136s (1) cores
% 3.45/1.01 % new_bool_3 with pid 112016 completed with status 0
% 3.45/1.01 % Result found by new_bool_3
% 3.45/1.01 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.45/1.01 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.45/1.01 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 3.45/1.01 % No SInE strategy applied
% 3.45/1.01 % Search class: FHUSM-FFMF21-SFFFFFNN
% 3.45/1.01 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 3.45/1.01 % Starting SubtermCWHack with 136s (1) cores
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.45/1.01 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 3.45/1.01 % Starting new_bool_3 with 136s (1) cores
% 3.45/1.01 % Preprocessing time : 0.002 s
% 3.45/1.01 % Presaturation interreduction done
% 3.45/1.01
% 3.45/1.01 % Proof found!
% 3.45/1.01 % SZS status Unsatisfiable
% 3.45/1.01 % SZS output start CNFRefutation
% See solution above
% 3.45/1.01 % Parsed axioms : 20
% 3.45/1.01 % Removed by relevancy pruning/SinE : 0
% 3.45/1.01 % Initial clauses : 20
% 3.45/1.01 % Removed in clause preprocessing : 0
% 3.45/1.01 % Initial clauses in saturation : 20
% 3.45/1.01 % Processed clauses : 4732
% 3.45/1.01 % ...of these trivial : 424
% 3.45/1.01 % ...subsumed : 2651
% 3.45/1.01 % ...remaining for further processing : 1657
% 3.45/1.01 % Other redundant clauses eliminated : 0
% 3.45/1.01 % Clauses deleted for lack of memory : 0
% 3.45/1.01 % Backward-subsumed : 28
% 3.45/1.01 % Backward-rewritten : 552
% 3.45/1.01 % Generated clauses : 22704
% 3.45/1.01 % ...of the previous two non-redundant : 16011
% 3.45/1.01 % ...aggressively subsumed : 0
% 3.45/1.01 % Contextual simplify-reflections : 0
% 3.45/1.01 % Paramodulations : 22704
% 3.45/1.01 % Factorizations : 0
% 3.45/1.01 % NegExts : 0
% 3.45/1.01 % Equation resolutions : 0
% 3.45/1.01 % Disequality decompositions : 0
% 3.45/1.01 % Total rewrite steps : 21631
% 3.45/1.01 % ...of those cached : 20722
% 3.45/1.01 % Propositional unsat checks : 0
% 3.45/1.01 % Propositional check models : 0
% 3.45/1.01 % Propositional check unsatisfiable : 0
% 3.45/1.01 % Propositional clauses : 0
% 3.45/1.01 % Propositional clauses after purity: 0
% 3.45/1.01 % Propositional unsat core size : 0
% 3.45/1.01 % Propositional preprocessing time : 0.000
% 3.45/1.01 % Propositional encoding time : 0.000
% 3.45/1.01 % Propositional solver time : 0.000
% 3.45/1.01 % Success case prop preproc time : 0.000
% 3.45/1.01 % Success case prop encoding time : 0.000
% 3.45/1.01 % Success case prop solver time : 0.000
% 3.45/1.01 % Current number of processed clauses : 1057
% 3.45/1.01 % Positive orientable unit clauses : 248
% 3.45/1.01 % Positive unorientable unit clauses: 1
% 3.45/1.01 % Negative unit clauses : 1
% 3.45/1.01 % Non-unit-clauses : 807
% 3.45/1.01 % Current number of unprocessed clauses: 10415
% 3.45/1.01 % ...number of literals in the above : 22780
% 3.45/1.01 % Current number of archived formulas : 0
% 3.45/1.01 % Current number of archived clauses : 600
% 3.45/1.01 % Clause-clause subsumption calls (NU) : 137765
% 3.45/1.01 % Rec. Clause-clause subsumption calls : 122985
% 3.45/1.01 % Non-unit clause-clause subsumptions : 2659
% 3.45/1.01 % Unit Clause-clause subsumption calls : 97
% 3.45/1.01 % Rewrite failures with RHS unbound : 0
% 3.45/1.01 % BW rewrite match attempts : 1343
% 3.45/1.01 % BW rewrite match successes : 88
% 3.45/1.01 % Condensation attempts : 0
% 3.45/1.01 % Condensation successes : 0
% 3.45/1.01 % Termbank termtop insertions : 318569
% 3.45/1.01 % Search garbage collected termcells : 61
% 3.45/1.01
% 3.45/1.01 % -------------------------------------------------
% 3.45/1.01 % User time : 0.373 s
% 3.45/1.01 % System time : 0.010 s
% 3.45/1.01 % Total time : 0.383 s
% 3.45/1.01 % Maximum resident set size: 3596 pages
% 3.45/1.01
% 3.45/1.01 % -------------------------------------------------
% 3.45/1.01 % User time : 2.103 s
% 3.45/1.01 % System time : 0.091 s
% 3.45/1.01 % Total time : 2.193 s
% 3.45/1.01 % Maximum resident set size: 4864 pages
% 3.45/1.01 % E exiting
%------------------------------------------------------------------------------