TSTP Solution File: RNG008-2 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : RNG008-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 02:36:35 EDT 2024
% Result : Unsatisfiable 5.68s 1.15s
% Output : CNFRefutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of clauses : 177 ( 80 unt; 0 nHn; 126 RR)
% Number of literals : 377 ( 64 equ; 203 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 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 : 452 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
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(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(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(a_times_b_is_c,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
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(cancellation2,axiom,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
cnf(cancellation1,axiom,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
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(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
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(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(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
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_22,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_23,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_24,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
c_0_22 ).
cnf(c_0_25,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_26,plain,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
c_0_23 ).
cnf(c_0_27,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_28,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_30,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_31,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_32,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_33,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
c_0_30 ).
cnf(c_0_36,plain,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
c_0_31 ).
cnf(c_0_37,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_38,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_32 ).
cnf(c_0_39,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_40,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_41,plain,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
inference(fof_simplification,[status(thm)],[cancellation2]) ).
cnf(c_0_42,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_29]),c_0_34]) ).
cnf(c_0_43,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_44,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_45,plain,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[cancellation1]) ).
cnf(c_0_46,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_47,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_48,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_49,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_50,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
c_0_40 ).
cnf(c_0_51,plain,
( X1 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X3) ),
c_0_41 ).
cnf(c_0_52,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_53,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
( X2 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X4,X3) ),
c_0_45 ).
cnf(c_0_55,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
c_0_46 ).
cnf(c_0_56,hypothesis,
( product(X1,b,c)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_57,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_37]) ).
cnf(c_0_59,plain,
( X1 = X2
| ~ sum(X1,X3,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_60,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_53]) ).
cnf(c_0_61,plain,
( X1 = X2
| ~ sum(additive_inverse(X2),X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_62,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_63,hypothesis,
( sum(X1,X2,c)
| ~ product(X3,b,X2)
| ~ product(X4,b,X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_64,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_57]) ).
cnf(c_0_65,hypothesis,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_37]) ).
cnf(c_0_66,plain,
( X1 = X2
| ~ sum(X1,add(X3,additive_inverse(X2)),X3) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,hypothesis,
( sum(X1,c,c)
| ~ product(X2,b,X1)
| ~ sum(X2,c,a) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_70,hypothesis,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_37]) ).
cnf(c_0_71,hypothesis,
( sum(multiply(X1,X2),X1,X1)
| ~ sum(X2,X1,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_49]) ).
cnf(c_0_72,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_73,plain,
( X1 = additive_inverse(X2)
| ~ sum(X1,add(X3,X2),X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_74,hypothesis,
( sum(multiply(X1,b),c,c)
| ~ sum(X1,c,a) ),
inference(spm,[status(thm)],[c_0_68,c_0_49]) ).
cnf(c_0_75,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_76,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_77,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_69]) ).
cnf(c_0_78,hypothesis,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_37]) ).
cnf(c_0_79,hypothesis,
( product(X1,b,X2)
| ~ product(X3,c,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_39]) ).
cnf(c_0_80,plain,
( X1 = additive_identity
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_69]) ).
cnf(c_0_81,hypothesis,
sum(multiply(X1,additive_identity),X1,X1),
inference(spm,[status(thm)],[c_0_71,c_0_69]) ).
cnf(c_0_82,plain,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
c_0_72 ).
cnf(c_0_83,plain,
( X1 = additive_inverse(add(X2,additive_inverse(X3)))
| ~ sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_73,c_0_60]) ).
cnf(c_0_84,hypothesis,
sum(multiply(add(a,additive_inverse(c)),b),c,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_53]) ).
cnf(c_0_85,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_76,c_0_44]) ).
cnf(c_0_86,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_77,c_0_62]) ).
cnf(c_0_87,hypothesis,
( sum(multiply(X1,X2),X2,X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_49]) ).
cnf(c_0_88,hypothesis,
( product(X1,b,multiply(X2,c))
| ~ product(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_49]) ).
cnf(c_0_89,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_90,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_91,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_49]) ).
cnf(c_0_92,hypothesis,
multiply(add(a,additive_inverse(c)),b) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]),c_0_86]) ).
cnf(c_0_93,hypothesis,
sum(multiply(additive_identity,X1),X1,X1),
inference(spm,[status(thm)],[c_0_87,c_0_69]) ).
cnf(c_0_94,hypothesis,
product(a,b,multiply(a,c)),
inference(spm,[status(thm)],[c_0_88,c_0_37]) ).
cnf(c_0_95,hypothesis,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_89]) ).
cnf(c_0_96,plain,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
c_0_90 ).
cnf(c_0_97,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_82,c_0_37]) ).
cnf(c_0_98,plain,
( product(X1,multiply(X2,X3),multiply(X4,X3))
| ~ product(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_91,c_0_49]) ).
cnf(c_0_99,hypothesis,
product(add(a,additive_inverse(c)),b,additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_92]) ).
cnf(c_0_100,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_80,c_0_93]) ).
cnf(c_0_101,hypothesis,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_48,c_0_94]) ).
cnf(c_0_102,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_103,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_52]),c_0_53]) ).
cnf(c_0_104,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_95]) ).
cnf(c_0_105,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_96,c_0_69]) ).
cnf(c_0_106,plain,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity2]) ).
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_36,c_0_49]) ).
cnf(c_0_108,hypothesis,
( product(X1,multiply(X2,X3),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_97,c_0_49]) ).
cnf(c_0_109,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
cnf(c_0_110,hypothesis,
product(add(a,additive_inverse(c)),multiply(b,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_100]) ).
cnf(c_0_111,hypothesis,
( sum(X1,X2,c)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_112,hypothesis,
product(a,c,c),
inference(spm,[status(thm)],[c_0_49,c_0_101]) ).
cnf(c_0_113,plain,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
c_0_102 ).
cnf(c_0_114,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_103]),c_0_53]) ).
cnf(c_0_115,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_104,c_0_37]) ).
cnf(c_0_116,plain,
( sum(X1,add(X2,X3),X2)
| ~ sum(X1,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_105,c_0_44]) ).
cnf(c_0_117,plain,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
c_0_106 ).
cnf(c_0_118,hypothesis,
( product(c,X1,X2)
| ~ product(a,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_107,c_0_39]) ).
cnf(c_0_119,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_108,c_0_49]) ).
cnf(c_0_120,hypothesis,
multiply(add(a,additive_inverse(c)),multiply(b,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_121,hypothesis,
( sum(X1,c,c)
| ~ product(a,X2,X1)
| ~ sum(X2,c,b) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_122,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,X2,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_37]) ).
cnf(c_0_123,plain,
( X1 = X2
| ~ sum(X1,additive_inverse(add(X2,X3)),additive_inverse(X3)) ),
inference(spm,[status(thm)],[c_0_59,c_0_114]) ).
cnf(c_0_124,hypothesis,
( sum(multiply(X1,X2),X1,additive_identity)
| ~ sum(X2,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_115,c_0_49]) ).
cnf(c_0_125,plain,
sum(additive_inverse(X1),add(X2,X1),X2),
inference(spm,[status(thm)],[c_0_116,c_0_27]) ).
cnf(c_0_126,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_29]) ).
cnf(c_0_127,plain,
( product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X5,multiply(X1,X6),X3)
| ~ sum(X4,X6,X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_49]) ).
cnf(c_0_128,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_118,c_0_49]) ).
cnf(c_0_129,hypothesis,
product(b,additive_identity,multiply(b,add(a,additive_inverse(c)))),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_130,hypothesis,
( sum(multiply(a,X1),c,c)
| ~ sum(X1,c,b) ),
inference(spm,[status(thm)],[c_0_121,c_0_49]) ).
cnf(c_0_131,hypothesis,
( product(X1,X2,X3)
| ~ sum(multiply(X4,X2),X2,X3)
| ~ sum(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_49]) ).
cnf(c_0_132,plain,
( X1 = X2
| ~ sum(X1,additive_inverse(add(X2,additive_inverse(X3))),X3) ),
inference(spm,[status(thm)],[c_0_123,c_0_67]) ).
cnf(c_0_133,hypothesis,
sum(multiply(X1,additive_inverse(X1)),X1,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_126]),c_0_126]) ).
cnf(c_0_134,hypothesis,
( product(X1,X2,X3)
| ~ sum(X1,multiply(X1,X4),X3)
| ~ sum(X1,X4,X2) ),
inference(spm,[status(thm)],[c_0_127,c_0_37]) ).
cnf(c_0_135,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_109,c_0_128]) ).
cnf(c_0_136,hypothesis,
multiply(b,add(a,additive_inverse(c))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_129]),c_0_89]) ).
cnf(c_0_137,hypothesis,
sum(multiply(a,add(b,additive_inverse(c))),c,c),
inference(spm,[status(thm)],[c_0_130,c_0_52]) ).
cnf(c_0_138,hypothesis,
( product(additive_identity,X1,X2)
| ~ sum(multiply(additive_inverse(X1),X1),X1,X2) ),
inference(spm,[status(thm)],[c_0_131,c_0_27]) ).
cnf(c_0_139,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
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_132,c_0_133]),c_0_86]),c_0_34]),c_0_86]),c_0_34]),c_0_67]) ).
cnf(c_0_140,hypothesis,
( product(X1,add(X2,X1),X3)
| ~ sum(X1,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_134,c_0_44]) ).
cnf(c_0_141,hypothesis,
multiply(c,add(a,additive_inverse(c))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_89]) ).
cnf(c_0_142,hypothesis,
multiply(a,add(b,additive_inverse(c))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_137]),c_0_85]),c_0_86]) ).
cnf(c_0_143,hypothesis,
( product(additive_identity,X1,X2)
| ~ sum(X1,X1,X2) ),
inference(rw,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_144,hypothesis,
( product(c,a,X1)
| ~ sum(c,additive_identity,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_53]),c_0_60]) ).
cnf(c_0_145,hypothesis,
product(a,add(b,additive_inverse(c)),additive_identity),
inference(spm,[status(thm)],[c_0_49,c_0_142]) ).
cnf(c_0_146,hypothesis,
product(additive_identity,X1,add(X1,X1)),
inference(spm,[status(thm)],[c_0_143,c_0_29]) ).
cnf(c_0_147,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X5,multiply(X6,X2),X3)
| ~ sum(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_49]) ).
cnf(c_0_148,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_119,c_0_135]) ).
cnf(c_0_149,hypothesis,
product(c,a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_29]),c_0_34]) ).
cnf(c_0_150,hypothesis,
product(a,multiply(add(b,additive_inverse(c)),X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_145]),c_0_100]) ).
cnf(c_0_151,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_75]),c_0_53]) ).
cnf(c_0_152,hypothesis,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_146]),c_0_100]) ).
cnf(c_0_153,hypothesis,
( product(X1,X2,X3)
| ~ sum(X2,multiply(X4,X2),X3)
| ~ sum(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_147,c_0_37]) ).
cnf(c_0_154,hypothesis,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_109,c_0_148]) ).
cnf(c_0_155,hypothesis,
multiply(c,a) = c,
inference(spm,[status(thm)],[c_0_109,c_0_149]) ).
cnf(c_0_156,hypothesis,
multiply(a,multiply(add(b,additive_inverse(c)),X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_109,c_0_150]) ).
cnf(c_0_157,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_34]) ).
cnf(c_0_158,hypothesis,
( product(add(X1,X2),X2,X3)
| ~ sum(X2,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_153,c_0_44]) ).
cnf(c_0_159,hypothesis,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_160,hypothesis,
( X1 = multiply(X2,X3)
| ~ product(X2,multiply(X3,multiply(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_119]) ).
cnf(c_0_161,hypothesis,
multiply(a,multiply(add(b,c),X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_162,hypothesis,
( product(add(b,c),c,X1)
| ~ sum(c,multiply(b,a),X1) ),
inference(spm,[status(thm)],[c_0_158,c_0_159]) ).
cnf(c_0_163,plain,
( X1 = X2
| ~ sum(X1,X3,add(X3,X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_44]) ).
cnf(c_0_164,hypothesis,
product(multiply(X1,a),b,multiply(X1,c)),
inference(spm,[status(thm)],[c_0_88,c_0_49]) ).
cnf(c_0_165,hypothesis,
( X1 = multiply(add(b,c),a)
| ~ product(add(b,c),additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_166,hypothesis,
product(add(b,c),c,add(c,multiply(b,a))),
inference(spm,[status(thm)],[c_0_162,c_0_29]) ).
cnf(c_0_167,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_52]),c_0_53]) ).
cnf(c_0_168,hypothesis,
multiply(multiply(X1,a),b) = multiply(X1,c),
inference(spm,[status(thm)],[c_0_109,c_0_164]) ).
cnf(c_0_169,hypothesis,
multiply(add(b,c),a) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_49]),c_0_89]) ).
cnf(c_0_170,hypothesis,
multiply(add(b,c),c) = add(c,multiply(b,a)),
inference(spm,[status(thm)],[c_0_109,c_0_166]) ).
cnf(c_0_171,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[c_0_167,c_0_157]) ).
cnf(c_0_172,hypothesis,
add(c,multiply(b,a)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_100]),c_0_170]) ).
cnf(c_0_173,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_174,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_34]) ).
cnf(c_0_175,negated_conjecture,
~ product(b,a,c),
c_0_173 ).
cnf(c_0_176,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_174]),c_0_175]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : RNG008-2 : TPTP v8.2.0. Released v1.0.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n023.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Sat May 18 12:07:53 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.15/0.39 Running first-order model finding
% 0.15/0.39 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
% 5.68/1.15 # Version: 3.1.0
% 5.68/1.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.68/1.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.68/1.15 # Starting new_bool_3 with 300s (1) cores
% 5.68/1.15 # Starting new_bool_1 with 300s (1) cores
% 5.68/1.15 # Starting sh5l with 300s (1) cores
% 5.68/1.15 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 23946 completed with status 0
% 5.68/1.15 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.68/1.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.68/1.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.68/1.15 # No SInE strategy applied
% 5.68/1.15 # Search class: FHUSM-FFMF21-SFFFFFNN
% 5.68/1.15 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.68/1.15 # Starting new_bool_3 with 136s (1) cores
% 5.68/1.15 # Starting new_bool_1 with 136s (1) cores
% 5.68/1.15 # Starting sh5l with 136s (1) cores
% 5.68/1.15 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 23950 completed with status 0
% 5.68/1.15 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 5.68/1.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.68/1.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.68/1.15 # No SInE strategy applied
% 5.68/1.15 # Search class: FHUSM-FFMF21-SFFFFFNN
% 5.68/1.15 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.68/1.15 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 5.68/1.15 # Preprocessing time : 0.001 s
% 5.68/1.15 # Presaturation interreduction done
% 5.68/1.15
% 5.68/1.15 # Proof found!
% 5.68/1.15 # SZS status Unsatisfiable
% 5.68/1.15 # SZS output start CNFRefutation
% See solution above
% 5.68/1.15 # Parsed axioms : 22
% 5.68/1.15 # Removed by relevancy pruning/SinE : 0
% 5.68/1.15 # Initial clauses : 22
% 5.68/1.15 # Removed in clause preprocessing : 0
% 5.68/1.15 # Initial clauses in saturation : 22
% 5.68/1.15 # Processed clauses : 9560
% 5.68/1.15 # ...of these trivial : 828
% 5.68/1.15 # ...subsumed : 5648
% 5.68/1.15 # ...remaining for further processing : 3084
% 5.68/1.15 # Other redundant clauses eliminated : 0
% 5.68/1.15 # Clauses deleted for lack of memory : 0
% 5.68/1.15 # Backward-subsumed : 31
% 5.68/1.15 # Backward-rewritten : 1560
% 5.68/1.15 # Generated clauses : 44508
% 5.68/1.15 # ...of the previous two non-redundant : 33902
% 5.68/1.15 # ...aggressively subsumed : 0
% 5.68/1.15 # Contextual simplify-reflections : 0
% 5.68/1.15 # Paramodulations : 44508
% 5.68/1.15 # Factorizations : 0
% 5.68/1.15 # NegExts : 0
% 5.68/1.15 # Equation resolutions : 0
% 5.68/1.15 # Disequality decompositions : 0
% 5.68/1.15 # Total rewrite steps : 32058
% 5.68/1.15 # ...of those cached : 30762
% 5.68/1.15 # Propositional unsat checks : 0
% 5.68/1.15 # Propositional check models : 0
% 5.68/1.15 # Propositional check unsatisfiable : 0
% 5.68/1.15 # Propositional clauses : 0
% 5.68/1.15 # Propositional clauses after purity: 0
% 5.68/1.15 # Propositional unsat core size : 0
% 5.68/1.15 # Propositional preprocessing time : 0.000
% 5.68/1.15 # Propositional encoding time : 0.000
% 5.68/1.15 # Propositional solver time : 0.000
% 5.68/1.15 # Success case prop preproc time : 0.000
% 5.68/1.15 # Success case prop encoding time : 0.000
% 5.68/1.15 # Success case prop solver time : 0.000
% 5.68/1.15 # Current number of processed clauses : 1471
% 5.68/1.15 # Positive orientable unit clauses : 233
% 5.68/1.15 # Positive unorientable unit clauses: 1
% 5.68/1.15 # Negative unit clauses : 1
% 5.68/1.15 # Non-unit-clauses : 1236
% 5.68/1.15 # Current number of unprocessed clauses: 22519
% 5.68/1.15 # ...number of literals in the above : 50589
% 5.68/1.15 # Current number of archived formulas : 0
% 5.68/1.15 # Current number of archived clauses : 1613
% 5.68/1.15 # Clause-clause subsumption calls (NU) : 534965
% 5.68/1.15 # Rec. Clause-clause subsumption calls : 466086
% 5.68/1.15 # Non-unit clause-clause subsumptions : 5634
% 5.68/1.15 # Unit Clause-clause subsumption calls : 904
% 5.68/1.15 # Rewrite failures with RHS unbound : 0
% 5.68/1.15 # BW rewrite match attempts : 2981
% 5.68/1.15 # BW rewrite match successes : 148
% 5.68/1.15 # Condensation attempts : 0
% 5.68/1.15 # Condensation successes : 0
% 5.68/1.15 # Termbank termtop insertions : 641621
% 5.68/1.15 # Search garbage collected termcells : 69
% 5.68/1.15
% 5.68/1.15 # -------------------------------------------------
% 5.68/1.15 # User time : 0.710 s
% 5.68/1.15 # System time : 0.013 s
% 5.68/1.15 # Total time : 0.723 s
% 5.68/1.15 # Maximum resident set size: 1644 pages
% 5.68/1.15
% 5.68/1.15 # -------------------------------------------------
% 5.68/1.15 # User time : 3.656 s
% 5.68/1.15 # System time : 0.031 s
% 5.68/1.15 # Total time : 3.687 s
% 5.68/1.15 # Maximum resident set size: 1716 pages
% 5.68/1.15 % E---3.1 exiting
%------------------------------------------------------------------------------