%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:05:29 PM UTC 2026
% Result : Unsatisfiable 7.07s 6.36s
% Output : CNFRefutation 7.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 20
% Syntax : Number of clauses : 158 ( 84 unt; 0 nHn; 112 RR)
% Number of literals : 314 ( 45 equ; 159 neg)
% Maximal clause size : 5 ( 1 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 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_multiplication2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(x_times_identity_x_is_identity,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(identity_times_x_is_identity,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(prove_b_times_a_is_c,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
cnf(c_0_20,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_21,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_22,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_20 ).
cnf(c_0_23,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_24,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_21 ).
cnf(c_0_25,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_26,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_27,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_28,hypothesis,
( ~ product(X4,X2,X1)
| ~ product(X4,X2,X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,hypothesis,
( ~ product(a,b,X1)
| X1 = c ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_31,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_32,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_26 ).
cnf(c_0_33,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_34,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_27 ).
cnf(c_0_35,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_36,hypothesis,
( ~ product(a,b,X1)
| product(X1,b,c) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_37,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_31 ).
cnf(c_0_39,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_40,plain,
( ~ sum(additive_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,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_43,plain,
( ~ product(X4,X5,X1)
| ~ product(X4,multiply(X5,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_44,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_37]) ).
cnf(c_0_45,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_42 ).
cnf(c_0_48,axiom,
product(X1,additive_identity,additive_identity),
x_times_identity_x_is_identity ).
cnf(c_0_49,hypothesis,
( ~ product(c,multiply(b,X1),X2)
| product(c,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,plain,
( ~ sum(X3,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_35]),c_0_46]) ).
cnf(c_0_51,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_52,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_47,c_0_39]) ).
cnf(c_0_53,plain,
( ~ product(X2,additive_identity,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_24,c_0_48]) ).
cnf(c_0_54,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_55,hypothesis,
( ~ product(X1,multiply(X1,X2),X3)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
cnf(c_0_56,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_57,hypothesis,
product(c,X1,multiply(c,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_49,c_0_30]) ).
cnf(c_0_58,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_59,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_41]) ).
cnf(c_0_60,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_61,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_62,hypothesis,
( ~ product(c,additive_identity,X2)
| ~ product(c,additive_inverse(b),X1)
| sum(X1,c,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_44]) ).
cnf(c_0_63,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_53,c_0_30]) ).
cnf(c_0_64,hypothesis,
( ~ product(X3,a,X1)
| ~ product(X3,c,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_65,plain,
( ~ product(X6,X2,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_54 ).
cnf(c_0_66,axiom,
product(additive_identity,X1,additive_identity),
identity_times_x_is_identity ).
cnf(c_0_67,hypothesis,
product(X1,X2,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_55,c_0_30]) ).
cnf(c_0_68,hypothesis,
multiply(c,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_69,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_58]),c_0_59]) ).
cnf(c_0_70,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_60]),c_0_61]) ).
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_62,c_0_30]),c_0_63]) ).
cnf(c_0_72,hypothesis,
( ~ product(X2,a,X1)
| product(X1,b,multiply(X2,c)) ),
inference(spm,[status(thm)],[c_0_64,c_0_30]) ).
cnf(c_0_73,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_65,c_0_39]) ).
cnf(c_0_74,plain,
( ~ product(additive_identity,X2,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_24,c_0_66]) ).
cnf(c_0_75,hypothesis,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,multiply(X2,X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_67]) ).
cnf(c_0_76,hypothesis,
product(c,multiply(b,X1),multiply(c,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_68]) ).
cnf(c_0_77,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,hypothesis,
sum(multiply(c,additive_inverse(b)),c,additive_identity),
inference(spm,[status(thm)],[c_0_71,c_0_30]) ).
cnf(c_0_79,hypothesis,
product(a,b,multiply(a,c)),
inference(spm,[status(thm)],[c_0_72,c_0_23]) ).
cnf(c_0_80,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_81,hypothesis,
( ~ product(additive_identity,X2,X3)
| ~ product(additive_inverse(X2),X2,X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_23]) ).
cnf(c_0_82,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_74,c_0_30]) ).
cnf(c_0_83,hypothesis,
multiply(c,multiply(c,X1)) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_68]) ).
cnf(c_0_84,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_77,c_0_59]) ).
cnf(c_0_85,hypothesis,
add(c,multiply(c,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_78]),c_0_59]) ).
cnf(c_0_86,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_65,c_0_35]) ).
cnf(c_0_87,hypothesis,
multiply(a,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_79]),c_0_37]) ).
cnf(c_0_88,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_80 ).
cnf(c_0_89,hypothesis,
( ~ product(additive_inverse(X2),X2,X1)
| sum(X1,X2,additive_identity) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_30]),c_0_82]) ).
cnf(c_0_90,hypothesis,
product(c,multiply(c,X1),multiply(c,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_83]) ).
cnf(c_0_91,hypothesis,
multiply(c,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_46]) ).
cnf(c_0_92,hypothesis,
( ~ product(X4,X2,X1)
| ~ product(add(X4,X2),X2,X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_86,c_0_23]) ).
cnf(c_0_93,hypothesis,
product(a,c,c),
inference(spm,[status(thm)],[c_0_30,c_0_87]) ).
cnf(c_0_94,plain,
( ~ sum(X1,X5,X4)
| ~ sum(X5,X3,X2)
| sum(X1,X2,add(X3,X4)) ),
inference(spm,[status(thm)],[c_0_88,c_0_41]) ).
cnf(c_0_95,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_96,hypothesis,
( ~ product(X2,additive_inverse(X2),X1)
| sum(X1,additive_inverse(X2),additive_identity) ),
inference(spm,[status(thm)],[c_0_89,c_0_70]) ).
cnf(c_0_97,hypothesis,
product(c,additive_inverse(c),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_98,hypothesis,
( ~ product(add(a,c),c,X1)
| sum(c,c,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
( ~ sum(X1,X2,X3)
| sum(X1,additive_identity,add(additive_inverse(X2),X3)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,hypothesis,
sum(additive_inverse(c),additive_inverse(c),additive_identity),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,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_102,hypothesis,
sum(c,c,multiply(add(a,c),c)),
inference(spm,[status(thm)],[c_0_98,c_0_30]) ).
cnf(c_0_103,plain,
( ~ sum(additive_inverse(X2),X2,X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_104,hypothesis,
sum(additive_inverse(c),additive_identity,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_70]),c_0_46]) ).
cnf(c_0_105,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_47,c_0_35]) ).
cnf(c_0_106,plain,
( ~ product(X3,X4,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X1,X5,X6) ),
c_0_101 ).
cnf(c_0_107,hypothesis,
multiply(add(a,c),c) = add(c,c),
inference(spm,[status(thm)],[c_0_51,c_0_102]) ).
cnf(c_0_108,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_103,c_0_41]) ).
cnf(c_0_109,hypothesis,
additive_inverse(c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_104]),c_0_46]) ).
cnf(c_0_110,hypothesis,
( ~ product(X2,X4,X1)
| ~ product(X2,add(X4,X2),X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_105,c_0_23]) ).
cnf(c_0_111,plain,
( ~ product(X1,X5,X3)
| ~ product(X5,X4,X2)
| product(X1,X2,multiply(X3,X4)) ),
inference(spm,[status(thm)],[c_0_106,c_0_30]) ).
cnf(c_0_112,hypothesis,
product(add(a,c),c,add(c,c)),
inference(spm,[status(thm)],[c_0_30,c_0_107]) ).
cnf(c_0_113,hypothesis,
add(c,c) = additive_identity,
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,hypothesis,
( ~ product(c,add(b,c),X1)
| sum(c,c,X1) ),
inference(spm,[status(thm)],[c_0_110,c_0_44]) ).
cnf(c_0_115,hypothesis,
( ~ product(X1,X4,X3)
| ~ product(X4,X3,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_106,c_0_23]) ).
cnf(c_0_116,plain,
( ~ product(X1,X2,X4)
| product(X1,multiply(X2,X3),multiply(X4,X3)) ),
inference(spm,[status(thm)],[c_0_111,c_0_30]) ).
cnf(c_0_117,hypothesis,
product(add(a,c),c,additive_identity),
inference(rw,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_118,hypothesis,
sum(c,c,multiply(c,add(b,c))),
inference(spm,[status(thm)],[c_0_114,c_0_30]) ).
cnf(c_0_119,hypothesis,
( ~ product(X1,X2,X3)
| product(X1,multiply(X2,X3),X3) ),
inference(spm,[status(thm)],[c_0_115,c_0_30]) ).
cnf(c_0_120,hypothesis,
product(add(a,c),multiply(c,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_82]) ).
cnf(c_0_121,plain,
( ~ product(X1,multiply(X2,X3),X4)
| product(multiply(X1,X2),X3,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_122,hypothesis,
multiply(c,add(b,c)) = add(c,c),
inference(spm,[status(thm)],[c_0_51,c_0_118]) ).
cnf(c_0_123,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_119,c_0_30]) ).
cnf(c_0_124,hypothesis,
multiply(add(a,c),multiply(c,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_56,c_0_120]) ).
cnf(c_0_125,plain,
product(multiply(X1,X2),X3,multiply(X1,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_121,c_0_30]) ).
cnf(c_0_126,hypothesis,
multiply(c,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[c_0_122,c_0_113]) ).
cnf(c_0_127,hypothesis,
product(c,additive_identity,multiply(c,add(a,c))),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
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(multiply(X1,c),add(b,c),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_63]) ).
cnf(c_0_130,hypothesis,
( ~ product(a,multiply(b,X1),X2)
| product(c,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_131,plain,
( ~ product(X4,X6,X1)
| ~ product(X4,X5,X2)
| ~ product(X4,add(X5,X6),X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_132,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_127]),c_0_63]) ).
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(multiply(multiply(X1,X2),X1),X2,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_121,c_0_23]) ).
cnf(c_0_135,hypothesis,
multiply(multiply(X1,c),add(b,c)) = additive_identity,
inference(spm,[status(thm)],[c_0_56,c_0_129]) ).
cnf(c_0_136,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_130,c_0_30]) ).
cnf(c_0_137,hypothesis,
( ~ product(X2,X4,X1)
| ~ product(X2,add(X2,X4),X3)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_131,c_0_23]) ).
cnf(c_0_138,hypothesis,
product(c,add(a,c),additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_132]) ).
cnf(c_0_139,hypothesis,
add(c,add(X1,c)) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_109]) ).
cnf(c_0_140,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_33]) ).
cnf(c_0_141,hypothesis,
product(additive_identity,c,multiply(add(b,c),c)),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_142,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_56,c_0_136]) ).
cnf(c_0_143,hypothesis,
( ~ product(c,a,X1)
| sum(additive_identity,c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]) ).
cnf(c_0_144,plain,
( ~ product(X2,X3,X4)
| ~ product(X1,X3,additive_identity)
| product(add(X1,X2),X3,X4) ),
inference(spm,[status(thm)],[c_0_140,c_0_35]) ).
cnf(c_0_145,hypothesis,
multiply(add(b,c),c) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_141]),c_0_82]) ).
cnf(c_0_146,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_123,c_0_142]) ).
cnf(c_0_147,hypothesis,
sum(additive_identity,c,multiply(c,a)),
inference(spm,[status(thm)],[c_0_143,c_0_30]) ).
cnf(c_0_148,hypothesis,
( ~ product(X1,X2,additive_identity)
| product(add(X1,X2),X2,X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_23]) ).
cnf(c_0_149,hypothesis,
product(add(b,c),c,additive_identity),
inference(spm,[status(thm)],[c_0_30,c_0_145]) ).
cnf(c_0_150,hypothesis,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_56,c_0_146]) ).
cnf(c_0_151,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_147]),c_0_61]) ).
cnf(c_0_152,hypothesis,
product(b,c,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_59]),c_0_139]) ).
cnf(c_0_153,hypothesis,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_154,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_155,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_152]),c_0_153]) ).
cnf(c_0_156,negated_conjecture,
~ product(b,a,c),
c_0_154 ).
cnf(c_0_157,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_155]),c_0_156]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 04:10:53 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.07/6.36 % Version: 3.5.1
% 7.07/6.36 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.07/6.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.07/6.36 % Starting new_bool_3 with 300s (1) cores
% 7.07/6.36 % Starting new_bool_1 with 300s (1) cores
% 7.07/6.36 % Starting sh5l with 300s (1) cores
% 7.07/6.36 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2520670 completed with status 0
% 7.07/6.36 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.07/6.36 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.07/6.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.07/6.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.07/6.36 % No SInE strategy applied
% 7.07/6.36 % Search class: FHUSM-FFMF21-SFFFFFNN
% 7.07/6.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.07/6.36 % Starting SubtermCWHack with 136s (1) cores
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 7.07/6.36 % Starting new_bool_3 with 136s (1) cores
% 7.07/6.36 % Starting new_bool_1 with 136s (1) cores
% 7.07/6.36 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 2520678 completed with status 0
% 7.07/6.36 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 7.07/6.36 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.07/6.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.07/6.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.07/6.36 % No SInE strategy applied
% 7.07/6.36 % Search class: FHUSM-FFMF21-SFFFFFNN
% 7.07/6.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.07/6.36 % Starting SubtermCWHack with 136s (1) cores
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.07/6.36 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 7.07/6.36 % Preprocessing time : 0.001 s
% 7.07/6.36 % Presaturation interreduction done
% 7.07/6.36
% 7.07/6.36 % Proof found!
% 7.07/6.36 % SZS status Unsatisfiable
% 7.07/6.36 % SZS output start CNFRefutation
% See solution above
% 7.07/6.36 % Parsed axioms : 22
% 7.07/6.36 % Removed by relevancy pruning/SinE : 0
% 7.07/6.36 % Initial clauses : 22
% 7.07/6.36 % Removed in clause preprocessing : 0
% 7.07/6.36 % Initial clauses in saturation : 22
% 7.07/6.36 % Processed clauses : 7322
% 7.07/6.36 % ...of these trivial : 486
% 7.07/6.36 % ...subsumed : 4476
% 7.07/6.36 % ...remaining for further processing : 2360
% 7.07/6.36 % Other redundant clauses eliminated : 0
% 7.07/6.36 % Clauses deleted for lack of memory : 0
% 7.07/6.36 % Backward-subsumed : 25
% 7.07/6.36 % Backward-rewritten : 553
% 7.07/6.36 % Generated clauses : 48955
% 7.07/6.36 % ...of the previous two non-redundant : 36795
% 7.07/6.36 % ...aggressively subsumed : 0
% 7.07/6.36 % Contextual simplify-reflections : 0
% 7.07/6.36 % Paramodulations : 48955
% 7.07/6.36 % Factorizations : 0
% 7.07/6.36 % NegExts : 0
% 7.07/6.36 % Equation resolutions : 0
% 7.07/6.36 % Disequality decompositions : 0
% 7.07/6.36 % Total rewrite steps : 39310
% 7.07/6.36 % ...of those cached : 37783
% 7.07/6.36 % Propositional unsat checks : 0
% 7.07/6.36 % Propositional check models : 0
% 7.07/6.36 % Propositional check unsatisfiable : 0
% 7.07/6.36 % Propositional clauses : 0
% 7.07/6.36 % Propositional clauses after purity: 0
% 7.07/6.36 % Propositional unsat core size : 0
% 7.07/6.36 % Propositional preprocessing time : 0.000
% 7.07/6.36 % Propositional encoding time : 0.000
% 7.07/6.36 % Propositional solver time : 0.000
% 7.07/6.36 % Success case prop preproc time : 0.000
% 7.07/6.36 % Success case prop encoding time : 0.000
% 7.07/6.36 % Success case prop solver time : 0.000
% 7.07/6.36 % Current number of processed clauses : 1760
% 7.07/6.36 % Positive orientable unit clauses : 450
% 7.07/6.36 % Positive unorientable unit clauses: 1
% 7.07/6.36 % Negative unit clauses : 1
% 7.07/6.36 % Non-unit-clauses : 1308
% 7.07/6.36 % Current number of unprocessed clauses: 28198
% 7.07/6.36 % ...number of literals in the above : 57929
% 7.07/6.36 % Current number of archived formulas : 0
% 7.07/6.36 % Current number of archived clauses : 600
% 7.07/6.36 % Clause-clause subsumption calls (NU) : 217064
% 7.07/6.36 % Rec. Clause-clause subsumption calls : 195371
% 7.07/6.36 % Non-unit clause-clause subsumptions : 4485
% 7.07/6.36 % Unit Clause-clause subsumption calls : 216
% 7.07/6.36 % Rewrite failures with RHS unbound : 0
% 7.07/6.36 % BW rewrite match attempts : 2799
% 7.07/6.36 % BW rewrite match successes : 108
% 7.07/6.36 % Condensation attempts : 0
% 7.07/6.36 % Condensation successes : 0
% 7.07/6.36 % Termbank termtop insertions : 718972
% 7.07/6.36 % Search garbage collected termcells : 61
% 7.07/6.36
% 7.07/6.36 % -------------------------------------------------
% 7.07/6.36 % User time : 0.882 s
% 7.07/6.36 % System time : 0.032 s
% 7.07/6.36 % Total time : 0.914 s
% 7.07/6.36 % Maximum resident set size: 3392 pages
% 7.07/6.36
% 7.07/6.36 % -------------------------------------------------
% 7.07/6.36 % User time : 4.418 s
% 7.07/6.36 % System time : 0.166 s
% 7.07/6.36 % Total time : 4.584 s
% 7.07/6.36 % Maximum resident set size: 4608 pages
% 7.07/6.36 % E exiting
%------------------------------------------------------------------------------