TSTP Solution File: RNG008-5 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : RNG008-5 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n014.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 21 02:36:36 EDT 2024
% Result : Unsatisfiable 1.36s 0.64s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 23
% Syntax : Number of clauses : 144 ( 73 unt; 0 nHn; 97 RR)
% Number of literals : 296 ( 37 equ; 155 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 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 : 355 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(additive_inverse_additive_inverse,axiom,
sum(additive_inverse(additive_inverse(X1)),additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(multiply_additive_inverse,axiom,
product(X1,additive_inverse(X2),additive_inverse(multiply(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(multiply_additive_id2,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id2) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(distribute_additive_inverse,axiom,
sum(additive_inverse(X1),additive_inverse(X2),additive_inverse(add(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute_additive_inverse) ).
cnf(associativity_of_multiplication1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication1) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(multiply_additive_id1,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_id1) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,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_23,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_24,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_23 ).
cnf(c_0_25,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_26,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_27,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_28,hypothesis,
( X1 = X2
| ~ product(X2,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_30,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
c_0_26 ).
cnf(c_0_31,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_32,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
c_0_27 ).
cnf(c_0_33,axiom,
sum(additive_inverse(additive_inverse(X1)),additive_identity,X1),
additive_inverse_additive_inverse ).
cnf(c_0_34,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity3]) ).
cnf(c_0_35,axiom,
product(X1,additive_inverse(X2),additive_inverse(multiply(X1,X2))),
multiply_additive_inverse ).
cnf(c_0_36,hypothesis,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
sum(additive_identity,additive_inverse(additive_inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
c_0_34 ).
cnf(c_0_40,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_41,hypothesis,
product(X1,additive_inverse(X1),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition2]) ).
cnf(c_0_44,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_45,plain,
( sum(X1,X2,X3)
| ~ product(additive_inverse(X4),X5,X1)
| ~ product(additive_identity,X5,X3)
| ~ product(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_46,hypothesis,
product(additive_inverse(X1),X1,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,axiom,
product(additive_identity,X1,additive_identity),
multiply_additive_id2 ).
cnf(c_0_48,plain,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
c_0_43 ).
cnf(c_0_49,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_50,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_51,hypothesis,
( sum(X1,X2,X3)
| ~ product(additive_identity,X2,X3)
| ~ product(X2,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42]) ).
cnf(c_0_52,plain,
( X1 = additive_identity
| ~ product(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_47]) ).
cnf(c_0_53,plain,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_multiplication2]) ).
cnf(c_0_54,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
cnf(c_0_55,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,hypothesis,
( sum(X1,X1,X2)
| ~ product(additive_identity,X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_29]),c_0_36]) ).
cnf(c_0_57,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_52,c_0_29]) ).
cnf(c_0_58,plain,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
c_0_53 ).
cnf(c_0_59,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_60,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_55]) ).
cnf(c_0_61,hypothesis,
sum(X1,X1,additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_29]),c_0_57]) ).
cnf(c_0_62,hypothesis,
( product(X1,b,X2)
| ~ product(X3,c,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,axiom,
sum(additive_inverse(X1),additive_inverse(X2),additive_inverse(add(X1,X2))),
distribute_additive_inverse ).
cnf(c_0_64,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_65,hypothesis,
sum(additive_identity,X1,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_50]) ).
cnf(c_0_67,hypothesis,
( product(X1,b,multiply(X2,c))
| ~ product(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_29]) ).
cnf(c_0_68,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_69,plain,
( sum(X1,X2,X3)
| ~ product(additive_inverse(add(X4,X5)),X6,X3)
| ~ product(additive_inverse(X5),X6,X2)
| ~ product(additive_inverse(X4),X6,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_63]) ).
cnf(c_0_70,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_71,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_72,hypothesis,
product(a,b,multiply(a,c)),
inference(spm,[status(thm)],[c_0_67,c_0_25]) ).
cnf(c_0_73,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
cnf(c_0_74,plain,
( sum(X1,X2,X3)
| ~ product(add(X4,X5),X6,X3)
| ~ product(X5,X6,X2)
| ~ product(X4,X6,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70]),c_0_70]) ).
cnf(c_0_75,hypothesis,
multiply(a,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).
cnf(c_0_76,hypothesis,
( sum(X1,X2,X3)
| ~ product(add(X4,X2),X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_77,hypothesis,
product(a,c,c),
inference(spm,[status(thm)],[c_0_29,c_0_75]) ).
cnf(c_0_78,plain,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_multiplication1]) ).
cnf(c_0_79,hypothesis,
( sum(c,c,X1)
| ~ product(add(a,c),c,X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
c_0_78 ).
cnf(c_0_81,hypothesis,
sum(c,c,multiply(add(a,c),c)),
inference(spm,[status(thm)],[c_0_79,c_0_29]) ).
cnf(c_0_82,hypothesis,
add(X1,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_64,c_0_61]) ).
cnf(c_0_83,plain,
( product(X1,X2,additive_identity)
| ~ product(X1,X3,additive_identity)
| ~ product(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_84,hypothesis,
multiply(add(a,c),c) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_81]),c_0_82]) ).
cnf(c_0_85,plain,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
cnf(c_0_86,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_87,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_25]) ).
cnf(c_0_88,plain,
( product(X1,multiply(X2,X3),additive_identity)
| ~ product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_83,c_0_29]) ).
cnf(c_0_89,hypothesis,
product(add(a,c),c,additive_identity),
inference(spm,[status(thm)],[c_0_29,c_0_84]) ).
cnf(c_0_90,plain,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
c_0_85 ).
cnf(c_0_91,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
c_0_86 ).
cnf(c_0_92,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_25]) ).
cnf(c_0_93,hypothesis,
( product(X1,multiply(X2,X3),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_87,c_0_29]) ).
cnf(c_0_94,hypothesis,
product(add(a,c),multiply(c,X1),additive_identity),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,axiom,
product(X1,additive_identity,additive_identity),
multiply_additive_id1 ).
cnf(c_0_96,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_90,c_0_31]) ).
cnf(c_0_97,plain,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity4]) ).
cnf(c_0_98,plain,
( sum(X1,X2,X3)
| ~ product(X4,add(X5,X6),X3)
| ~ product(X4,X6,X2)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_50]) ).
cnf(c_0_99,hypothesis,
( product(X1,b,c)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_59]) ).
cnf(c_0_100,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_93,c_0_29]) ).
cnf(c_0_101,hypothesis,
multiply(add(a,c),multiply(c,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_71,c_0_94]) ).
cnf(c_0_102,plain,
( X1 = additive_identity
| ~ product(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_95]) ).
cnf(c_0_103,plain,
( sum(X1,add(X2,X3),X3)
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_96,c_0_50]) ).
cnf(c_0_104,plain,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
c_0_97 ).
cnf(c_0_105,hypothesis,
( sum(X1,X2,X3)
| ~ product(X2,add(X4,X2),X3)
| ~ product(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_25]) ).
cnf(c_0_106,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_29]),c_0_73]) ).
cnf(c_0_107,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_108,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_109,hypothesis,
product(c,additive_identity,multiply(c,add(a,c))),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_110,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_102,c_0_29]) ).
cnf(c_0_111,hypothesis,
sum(X1,add(X1,X2),X2),
inference(spm,[status(thm)],[c_0_103,c_0_61]) ).
cnf(c_0_112,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3)
| ~ sum(X5,X4,X1) ),
inference(spm,[status(thm)],[c_0_104,c_0_44]) ).
cnf(c_0_113,hypothesis,
( sum(c,c,X1)
| ~ product(c,add(b,c),X1) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,hypothesis,
( product(c,X1,X2)
| ~ product(a,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_59]) ).
cnf(c_0_115,plain,
( sum(X1,X2,X3)
| ~ product(X4,add(X5,X6),X3)
| ~ product(X4,X5,X2)
| ~ product(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_108]) ).
cnf(c_0_116,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_109]),c_0_110]) ).
cnf(c_0_117,hypothesis,
add(X1,add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_64,c_0_111]) ).
cnf(c_0_118,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_64,c_0_108]) ).
cnf(c_0_119,hypothesis,
( product(X1,X2,X3)
| ~ product(add(X4,X1),X2,additive_identity)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_112,c_0_111]) ).
cnf(c_0_120,hypothesis,
sum(c,c,multiply(c,add(b,c))),
inference(spm,[status(thm)],[c_0_113,c_0_29]) ).
cnf(c_0_121,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_114,c_0_29]) ).
cnf(c_0_122,hypothesis,
( sum(X1,X2,X3)
| ~ product(X2,add(X2,X4),X3)
| ~ product(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_115,c_0_25]) ).
cnf(c_0_123,hypothesis,
product(c,add(a,c),additive_identity),
inference(spm,[status(thm)],[c_0_29,c_0_116]) ).
cnf(c_0_124,hypothesis,
add(X1,add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_125,hypothesis,
( product(X1,X2,X2)
| ~ product(add(X2,X1),X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_119,c_0_25]) ).
cnf(c_0_126,hypothesis,
multiply(c,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_120]),c_0_82]) ).
cnf(c_0_127,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_71,c_0_121]) ).
cnf(c_0_128,hypothesis,
( sum(additive_identity,c,X1)
| ~ product(c,a,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_129,hypothesis,
( product(add(X1,X2),X2,X2)
| ~ product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_125,c_0_124]) ).
cnf(c_0_130,hypothesis,
product(c,add(b,c),additive_identity),
inference(spm,[status(thm)],[c_0_29,c_0_126]) ).
cnf(c_0_131,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_100,c_0_127]) ).
cnf(c_0_132,hypothesis,
sum(additive_identity,c,multiply(c,a)),
inference(spm,[status(thm)],[c_0_128,c_0_29]) ).
cnf(c_0_133,hypothesis,
product(b,add(b,c),add(b,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_124]) ).
cnf(c_0_134,hypothesis,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_71,c_0_131]) ).
cnf(c_0_135,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_132]),c_0_66]) ).
cnf(c_0_136,hypothesis,
( sum(add(b,c),b,X1)
| ~ product(b,c,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_133]),c_0_117]) ).
cnf(c_0_137,hypothesis,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_138,plain,
( X1 = add(X2,X3)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_108]) ).
cnf(c_0_139,hypothesis,
sum(add(b,c),b,multiply(b,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_29]),c_0_137]) ).
cnf(c_0_140,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_141,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_117]) ).
cnf(c_0_142,negated_conjecture,
~ product(b,a,c),
c_0_140 ).
cnf(c_0_143,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_141]),c_0_142]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG008-5 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 12:21:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order model finding
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.36/0.64 # Version: 3.1.0
% 1.36/0.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.36/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.36/0.64 # Starting sh5l with 300s (1) cores
% 1.36/0.64 # sh5l with pid 27945 completed with status 0
% 1.36/0.64 # Result found by sh5l
% 1.36/0.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.36/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.36/0.64 # Starting sh5l with 300s (1) cores
% 1.36/0.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.36/0.64 # Search class: FHUSM-FFMF21-SFFFFFNN
% 1.36/0.64 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.64 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 181s (1) cores
% 1.36/0.64 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 27952 completed with status 0
% 1.36/0.64 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 1.36/0.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.36/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.36/0.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.36/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.36/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.36/0.64 # Starting sh5l with 300s (1) cores
% 1.36/0.64 # SinE strategy is gf500_gu_R04_F100_L20000
% 1.36/0.64 # Search class: FHUSM-FFMF21-SFFFFFNN
% 1.36/0.64 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.36/0.64 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 181s (1) cores
% 1.36/0.64 # Preprocessing time : 0.001 s
% 1.36/0.64 # Presaturation interreduction done
% 1.36/0.64
% 1.36/0.64 # Proof found!
% 1.36/0.64 # SZS status Unsatisfiable
% 1.36/0.64 # SZS output start CNFRefutation
% See solution above
% 1.36/0.64 # Parsed axioms : 26
% 1.36/0.64 # Removed by relevancy pruning/SinE : 0
% 1.36/0.64 # Initial clauses : 26
% 1.36/0.64 # Removed in clause preprocessing : 0
% 1.36/0.64 # Initial clauses in saturation : 26
% 1.36/0.64 # Processed clauses : 2560
% 1.36/0.64 # ...of these trivial : 154
% 1.36/0.64 # ...subsumed : 1281
% 1.36/0.64 # ...remaining for further processing : 1125
% 1.36/0.64 # Other redundant clauses eliminated : 0
% 1.36/0.64 # Clauses deleted for lack of memory : 0
% 1.36/0.64 # Backward-subsumed : 12
% 1.36/0.64 # Backward-rewritten : 513
% 1.36/0.64 # Generated clauses : 10907
% 1.36/0.64 # ...of the previous two non-redundant : 7431
% 1.36/0.64 # ...aggressively subsumed : 0
% 1.36/0.64 # Contextual simplify-reflections : 0
% 1.36/0.64 # Paramodulations : 10907
% 1.36/0.64 # Factorizations : 0
% 1.36/0.64 # NegExts : 0
% 1.36/0.64 # Equation resolutions : 0
% 1.36/0.64 # Disequality decompositions : 0
% 1.36/0.64 # Total rewrite steps : 8927
% 1.36/0.64 # ...of those cached : 8400
% 1.36/0.64 # Propositional unsat checks : 0
% 1.36/0.64 # Propositional check models : 0
% 1.36/0.64 # Propositional check unsatisfiable : 0
% 1.36/0.64 # Propositional clauses : 0
% 1.36/0.64 # Propositional clauses after purity: 0
% 1.36/0.64 # Propositional unsat core size : 0
% 1.36/0.64 # Propositional preprocessing time : 0.000
% 1.36/0.64 # Propositional encoding time : 0.000
% 1.36/0.64 # Propositional solver time : 0.000
% 1.36/0.64 # Success case prop preproc time : 0.000
% 1.36/0.64 # Success case prop encoding time : 0.000
% 1.36/0.64 # Success case prop solver time : 0.000
% 1.36/0.64 # Current number of processed clauses : 575
% 1.36/0.64 # Positive orientable unit clauses : 112
% 1.36/0.64 # Positive unorientable unit clauses: 1
% 1.36/0.64 # Negative unit clauses : 1
% 1.36/0.64 # Non-unit-clauses : 461
% 1.36/0.64 # Current number of unprocessed clauses: 4199
% 1.36/0.64 # ...number of literals in the above : 9365
% 1.36/0.64 # Current number of archived formulas : 0
% 1.36/0.64 # Current number of archived clauses : 550
% 1.36/0.64 # Clause-clause subsumption calls (NU) : 60234
% 1.36/0.64 # Rec. Clause-clause subsumption calls : 53226
% 1.36/0.64 # Non-unit clause-clause subsumptions : 1291
% 1.36/0.64 # Unit Clause-clause subsumption calls : 128
% 1.36/0.64 # Rewrite failures with RHS unbound : 0
% 1.36/0.64 # BW rewrite match attempts : 929
% 1.36/0.64 # BW rewrite match successes : 87
% 1.36/0.64 # Condensation attempts : 0
% 1.36/0.64 # Condensation successes : 0
% 1.36/0.64 # Termbank termtop insertions : 146265
% 1.36/0.64 # Search garbage collected termcells : 61
% 1.36/0.64
% 1.36/0.64 # -------------------------------------------------
% 1.36/0.64 # User time : 0.143 s
% 1.36/0.64 # System time : 0.005 s
% 1.36/0.64 # Total time : 0.148 s
% 1.36/0.64 # Maximum resident set size: 1596 pages
% 1.36/0.64
% 1.36/0.64 # -------------------------------------------------
% 1.36/0.64 # User time : 0.145 s
% 1.36/0.64 # System time : 0.006 s
% 1.36/0.64 # Total time : 0.151 s
% 1.36/0.64 # Maximum resident set size: 1716 pages
% 1.36/0.64 % E---3.1 exiting
%------------------------------------------------------------------------------