TSTP Solution File: RNG008-6 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : RNG008-6 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 02:35:48 EDT 2024
% Result : Unsatisfiable 5.94s 1.21s
% Output : CNFRefutation 5.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 20
% Syntax : Number of clauses : 161 ( 84 unt; 0 nHn; 115 RR)
% Number of literals : 320 ( 48 equ; 162 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 : 376 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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_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(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
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,
( 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(x_times_identity_x_is_identity,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
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(identity_times_x_is_identity,axiom,
product(additive_identity,X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
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(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(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(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_20,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_21,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
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(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_24,plain,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
c_0_20 ).
cnf(c_0_25,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_26,plain,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_21 ).
cnf(c_0_27,hypothesis,
product(a,b,c),
a_times_b_is_c ).
cnf(c_0_28,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_29,plain,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
c_0_22 ).
cnf(c_0_30,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_31,plain,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
c_0_23 ).
cnf(c_0_32,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_33,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,hypothesis,
( X1 = c
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_36,plain,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
c_0_28 ).
cnf(c_0_37,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_38,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_39,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,hypothesis,
( product(X1,b,c)
| ~ product(a,b,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_41,hypothesis,
multiply(a,b) = c,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_43,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,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_45,plain,
( product(X1,X2,X3)
| ~ product(X4,multiply(X5,X2),X3)
| ~ product(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_46,hypothesis,
product(c,b,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_35]),c_0_41]) ).
cnf(c_0_47,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_43]) ).
cnf(c_0_48,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
c_0_44 ).
cnf(c_0_49,axiom,
product(X1,additive_identity,additive_identity),
x_times_identity_x_is_identity ).
cnf(c_0_50,hypothesis,
( product(c,X1,X2)
| ~ product(c,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_32]) ).
cnf(c_0_52,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_53,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_47,c_0_37]) ).
cnf(c_0_54,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_55,plain,
( sum(X1,X2,X3)
| ~ product(X4,additive_inverse(X5),X1)
| ~ product(X4,additive_identity,X3)
| ~ product(X4,X5,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_56,plain,
( X1 = additive_identity
| ~ product(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_49]) ).
cnf(c_0_57,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_58,hypothesis,
( product(X1,X2,X3)
| ~ product(X1,multiply(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_25]) ).
cnf(c_0_59,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_60,hypothesis,
product(c,X1,multiply(c,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_61,plain,
( X1 = X2
| ~ sum(add(X2,additive_inverse(X3)),X3,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_51]) ).
cnf(c_0_62,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_63,hypothesis,
( sum(X1,c,X2)
| ~ product(c,additive_inverse(b),X1)
| ~ product(c,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_46]) ).
cnf(c_0_64,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_65,hypothesis,
( product(X1,b,X2)
| ~ product(X3,c,X2)
| ~ product(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_66,plain,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
c_0_57 ).
cnf(c_0_67,axiom,
product(additive_identity,X1,additive_identity),
identity_times_x_is_identity ).
cnf(c_0_68,hypothesis,
product(X1,X2,multiply(X1,multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_58,c_0_35]) ).
cnf(c_0_69,hypothesis,
multiply(c,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_70,plain,
( X1 = X2
| ~ sum(add(X2,X3),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_72,hypothesis,
( sum(X1,c,additive_identity)
| ~ product(c,additive_inverse(b),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_35]),c_0_64]) ).
cnf(c_0_73,hypothesis,
( product(X1,b,multiply(X2,c))
| ~ product(X2,a,X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_35]) ).
cnf(c_0_74,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_66,c_0_37]) ).
cnf(c_0_75,plain,
( X1 = additive_identity
| ~ product(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_67]) ).
cnf(c_0_76,hypothesis,
( X1 = multiply(X2,multiply(X2,X3))
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_68]) ).
cnf(c_0_77,hypothesis,
product(c,multiply(b,X1),multiply(c,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_78,plain,
( X1 = X2
| ~ sum(add(X3,X2),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,hypothesis,
sum(multiply(c,additive_inverse(b)),c,additive_identity),
inference(spm,[status(thm)],[c_0_72,c_0_35]) ).
cnf(c_0_80,hypothesis,
product(a,b,multiply(a,c)),
inference(spm,[status(thm)],[c_0_73,c_0_25]) ).
cnf(c_0_81,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_82,hypothesis,
( sum(X1,X2,X3)
| ~ product(additive_inverse(X2),X2,X1)
| ~ product(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_83,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_75,c_0_35]) ).
cnf(c_0_84,hypothesis,
multiply(c,multiply(c,X1)) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_69]) ).
cnf(c_0_85,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_32]),c_0_71]) ).
cnf(c_0_86,hypothesis,
add(c,multiply(c,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_79]),c_0_71]) ).
cnf(c_0_87,plain,
( sum(X1,X2,X3)
| ~ product(add(X4,X5),X6,X3)
| ~ product(X5,X6,X2)
| ~ product(X4,X6,X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_32]) ).
cnf(c_0_88,hypothesis,
multiply(a,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_80]),c_0_41]) ).
cnf(c_0_89,plain,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
c_0_81 ).
cnf(c_0_90,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(additive_inverse(X2),X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_35]),c_0_83]) ).
cnf(c_0_91,hypothesis,
product(c,multiply(c,X1),multiply(c,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_84]) ).
cnf(c_0_92,hypothesis,
multiply(c,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_43]) ).
cnf(c_0_93,hypothesis,
( sum(X1,X2,X3)
| ~ product(add(X4,X2),X2,X3)
| ~ product(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_87,c_0_25]) ).
cnf(c_0_94,hypothesis,
product(a,c,c),
inference(spm,[status(thm)],[c_0_35,c_0_88]) ).
cnf(c_0_95,plain,
( sum(X1,X2,add(X3,X4))
| ~ sum(X5,X3,X2)
| ~ sum(X1,X5,X4) ),
inference(spm,[status(thm)],[c_0_89,c_0_39]) ).
cnf(c_0_96,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_97,hypothesis,
( sum(X1,additive_inverse(X2),additive_identity)
| ~ product(X2,additive_inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_62]) ).
cnf(c_0_98,hypothesis,
product(c,additive_inverse(c),additive_inverse(c)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,hypothesis,
( sum(c,c,X1)
| ~ product(add(a,c),c,X1) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( sum(X1,additive_identity,add(additive_inverse(X2),X3))
| ~ sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_101,hypothesis,
sum(additive_inverse(c),additive_inverse(c),additive_identity),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_102,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_103,hypothesis,
sum(c,c,multiply(add(a,c),c)),
inference(spm,[status(thm)],[c_0_99,c_0_35]) ).
cnf(c_0_104,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_105,hypothesis,
sum(additive_inverse(c),additive_identity,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_62]),c_0_43]) ).
cnf(c_0_106,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_48,c_0_32]) ).
cnf(c_0_107,plain,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
c_0_102 ).
cnf(c_0_108,hypothesis,
multiply(add(a,c),c) = add(c,c),
inference(spm,[status(thm)],[c_0_52,c_0_103]) ).
cnf(c_0_109,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_104,c_0_39]) ).
cnf(c_0_110,hypothesis,
additive_inverse(c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_105]),c_0_43]) ).
cnf(c_0_111,hypothesis,
( sum(X1,X2,X3)
| ~ product(X2,add(X4,X2),X3)
| ~ product(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_25]) ).
cnf(c_0_112,plain,
( product(X1,X2,multiply(X3,X4))
| ~ product(X5,X4,X2)
| ~ product(X1,X5,X3) ),
inference(spm,[status(thm)],[c_0_107,c_0_35]) ).
cnf(c_0_113,hypothesis,
product(add(a,c),c,add(c,c)),
inference(spm,[status(thm)],[c_0_35,c_0_108]) ).
cnf(c_0_114,hypothesis,
add(c,c) = additive_identity,
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_115,hypothesis,
( sum(c,c,X1)
| ~ product(c,add(b,c),X1) ),
inference(spm,[status(thm)],[c_0_111,c_0_46]) ).
cnf(c_0_116,hypothesis,
( product(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,X3) ),
inference(spm,[status(thm)],[c_0_107,c_0_25]) ).
cnf(c_0_117,plain,
( product(X1,multiply(X2,X3),multiply(X4,X3))
| ~ product(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_112,c_0_35]) ).
cnf(c_0_118,hypothesis,
product(add(a,c),c,additive_identity),
inference(rw,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,hypothesis,
sum(c,c,multiply(c,add(b,c))),
inference(spm,[status(thm)],[c_0_115,c_0_35]) ).
cnf(c_0_120,hypothesis,
( product(X1,multiply(X2,X3),X3)
| ~ product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_116,c_0_35]) ).
cnf(c_0_121,hypothesis,
product(add(a,c),multiply(c,X1),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_83]) ).
cnf(c_0_122,plain,
( product(multiply(X1,X2),X3,X4)
| ~ product(X1,multiply(X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_45,c_0_35]) ).
cnf(c_0_123,hypothesis,
multiply(c,add(b,c)) = add(c,c),
inference(spm,[status(thm)],[c_0_52,c_0_119]) ).
cnf(c_0_124,hypothesis,
product(X1,multiply(X2,multiply(X1,X2)),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_120,c_0_35]) ).
cnf(c_0_125,hypothesis,
multiply(add(a,c),multiply(c,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_59,c_0_121]) ).
cnf(c_0_126,plain,
product(multiply(X1,X2),X3,multiply(X1,multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_122,c_0_35]) ).
cnf(c_0_127,hypothesis,
multiply(c,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[c_0_123,c_0_114]) ).
cnf(c_0_128,hypothesis,
product(c,additive_identity,multiply(c,add(a,c))),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_129,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_51]),c_0_71]) ).
cnf(c_0_130,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_131,hypothesis,
product(multiply(X1,c),add(b,c),additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_64]) ).
cnf(c_0_132,hypothesis,
( product(c,X1,X2)
| ~ product(a,multiply(b,X1),X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_27]) ).
cnf(c_0_133,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_48,c_0_39]) ).
cnf(c_0_134,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_128]),c_0_64]) ).
cnf(c_0_135,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_129,c_0_62]) ).
cnf(c_0_136,plain,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
c_0_130 ).
cnf(c_0_137,hypothesis,
product(multiply(multiply(X1,X2),X1),X2,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_122,c_0_25]) ).
cnf(c_0_138,hypothesis,
multiply(multiply(X1,c),add(b,c)) = additive_identity,
inference(spm,[status(thm)],[c_0_59,c_0_131]) ).
cnf(c_0_139,hypothesis,
product(c,X1,multiply(a,multiply(b,X1))),
inference(spm,[status(thm)],[c_0_132,c_0_35]) ).
cnf(c_0_140,hypothesis,
( sum(X1,X2,X3)
| ~ product(X2,add(X2,X4),X3)
| ~ product(X2,X4,X1) ),
inference(spm,[status(thm)],[c_0_133,c_0_25]) ).
cnf(c_0_141,hypothesis,
product(c,add(a,c),additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_134]) ).
cnf(c_0_142,hypothesis,
add(c,add(X1,c)) = X1,
inference(spm,[status(thm)],[c_0_135,c_0_110]) ).
cnf(c_0_143,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_136,c_0_30]) ).
cnf(c_0_144,hypothesis,
product(additive_identity,c,multiply(add(b,c),c)),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_145,hypothesis,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_59,c_0_139]) ).
cnf(c_0_146,hypothesis,
( sum(additive_identity,c,X1)
| ~ product(c,a,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_147,plain,
( product(add(X1,X2),X3,X4)
| ~ product(X1,X3,additive_identity)
| ~ product(X2,X3,X4) ),
inference(spm,[status(thm)],[c_0_143,c_0_32]) ).
cnf(c_0_148,hypothesis,
multiply(add(b,c),c) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_144]),c_0_83]) ).
cnf(c_0_149,hypothesis,
product(b,multiply(c,a),multiply(b,a)),
inference(spm,[status(thm)],[c_0_124,c_0_145]) ).
cnf(c_0_150,hypothesis,
sum(additive_identity,c,multiply(c,a)),
inference(spm,[status(thm)],[c_0_146,c_0_35]) ).
cnf(c_0_151,hypothesis,
( product(add(X1,X2),X2,X2)
| ~ product(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_147,c_0_25]) ).
cnf(c_0_152,hypothesis,
product(add(b,c),c,additive_identity),
inference(spm,[status(thm)],[c_0_35,c_0_148]) ).
cnf(c_0_153,hypothesis,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_59,c_0_149]) ).
cnf(c_0_154,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_150]),c_0_54]) ).
cnf(c_0_155,hypothesis,
product(b,c,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_71]),c_0_142]) ).
cnf(c_0_156,hypothesis,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_157,negated_conjecture,
~ product(b,a,c),
inference(fof_simplification,[status(thm)],[prove_b_times_a_is_c]) ).
cnf(c_0_158,hypothesis,
multiply(b,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_155]),c_0_156]) ).
cnf(c_0_159,negated_conjecture,
~ product(b,a,c),
c_0_157 ).
cnf(c_0_160,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_158]),c_0_159]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-6 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 12:17:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 5.94/1.21 # Version: 3.1.0
% 5.94/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.94/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.94/1.21 # Starting new_bool_3 with 300s (1) cores
% 5.94/1.21 # Starting new_bool_1 with 300s (1) cores
% 5.94/1.21 # Starting sh5l with 300s (1) cores
% 5.94/1.21 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 909 completed with status 0
% 5.94/1.21 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.94/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.94/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.94/1.21 # No SInE strategy applied
% 5.94/1.21 # Search class: FHUSM-FFMF21-SFFFFFNN
% 5.94/1.21 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.94/1.21 # Starting new_bool_3 with 136s (1) cores
% 5.94/1.21 # Starting new_bool_1 with 136s (1) cores
% 5.94/1.21 # Starting sh5l with 136s (1) cores
% 5.94/1.21 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 913 completed with status 0
% 5.94/1.21 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 5.94/1.21 # Preprocessing class: FSMSSMSSSSSNFFN.
% 5.94/1.21 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.94/1.21 # No SInE strategy applied
% 5.94/1.21 # Search class: FHUSM-FFMF21-SFFFFFNN
% 5.94/1.21 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 5.94/1.21 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 5.94/1.21 # Preprocessing time : 0.001 s
% 5.94/1.21 # Presaturation interreduction done
% 5.94/1.21
% 5.94/1.21 # Proof found!
% 5.94/1.21 # SZS status Unsatisfiable
% 5.94/1.21 # SZS output start CNFRefutation
% See solution above
% 5.94/1.21 # Parsed axioms : 22
% 5.94/1.21 # Removed by relevancy pruning/SinE : 0
% 5.94/1.21 # Initial clauses : 22
% 5.94/1.21 # Removed in clause preprocessing : 0
% 5.94/1.21 # Initial clauses in saturation : 22
% 5.94/1.21 # Processed clauses : 7333
% 5.94/1.21 # ...of these trivial : 524
% 5.94/1.21 # ...subsumed : 4458
% 5.94/1.21 # ...remaining for further processing : 2351
% 5.94/1.21 # Other redundant clauses eliminated : 0
% 5.94/1.21 # Clauses deleted for lack of memory : 0
% 5.94/1.21 # Backward-subsumed : 26
% 5.94/1.21 # Backward-rewritten : 560
% 5.94/1.21 # Generated clauses : 49324
% 5.94/1.21 # ...of the previous two non-redundant : 37048
% 5.94/1.21 # ...aggressively subsumed : 0
% 5.94/1.21 # Contextual simplify-reflections : 0
% 5.94/1.21 # Paramodulations : 49324
% 5.94/1.21 # Factorizations : 0
% 5.94/1.21 # NegExts : 0
% 5.94/1.21 # Equation resolutions : 0
% 5.94/1.21 # Disequality decompositions : 0
% 5.94/1.21 # Total rewrite steps : 38087
% 5.94/1.21 # ...of those cached : 36529
% 5.94/1.21 # Propositional unsat checks : 0
% 5.94/1.21 # Propositional check models : 0
% 5.94/1.21 # Propositional check unsatisfiable : 0
% 5.94/1.21 # Propositional clauses : 0
% 5.94/1.21 # Propositional clauses after purity: 0
% 5.94/1.21 # Propositional unsat core size : 0
% 5.94/1.21 # Propositional preprocessing time : 0.000
% 5.94/1.21 # Propositional encoding time : 0.000
% 5.94/1.21 # Propositional solver time : 0.000
% 5.94/1.21 # Success case prop preproc time : 0.000
% 5.94/1.21 # Success case prop encoding time : 0.000
% 5.94/1.21 # Success case prop solver time : 0.000
% 5.94/1.21 # Current number of processed clauses : 1743
% 5.94/1.21 # Positive orientable unit clauses : 477
% 5.94/1.21 # Positive unorientable unit clauses: 1
% 5.94/1.21 # Negative unit clauses : 1
% 5.94/1.21 # Non-unit-clauses : 1264
% 5.94/1.21 # Current number of unprocessed clauses: 28467
% 5.94/1.21 # ...number of literals in the above : 57964
% 5.94/1.21 # Current number of archived formulas : 0
% 5.94/1.21 # Current number of archived clauses : 608
% 5.94/1.21 # Clause-clause subsumption calls (NU) : 207870
% 5.94/1.21 # Rec. Clause-clause subsumption calls : 187980
% 5.94/1.21 # Non-unit clause-clause subsumptions : 4468
% 5.94/1.21 # Unit Clause-clause subsumption calls : 220
% 5.94/1.21 # Rewrite failures with RHS unbound : 0
% 5.94/1.21 # BW rewrite match attempts : 2792
% 5.94/1.21 # BW rewrite match successes : 105
% 5.94/1.21 # Condensation attempts : 0
% 5.94/1.21 # Condensation successes : 0
% 5.94/1.21 # Termbank termtop insertions : 720276
% 5.94/1.21 # Search garbage collected termcells : 61
% 5.94/1.21
% 5.94/1.21 # -------------------------------------------------
% 5.94/1.21 # User time : 0.707 s
% 5.94/1.21 # System time : 0.026 s
% 5.94/1.21 # Total time : 0.733 s
% 5.94/1.21 # Maximum resident set size: 1644 pages
% 5.94/1.21
% 5.94/1.21 # -------------------------------------------------
% 5.94/1.21 # User time : 3.572 s
% 5.94/1.21 # System time : 0.047 s
% 5.94/1.21 # Total time : 3.619 s
% 5.94/1.21 # Maximum resident set size: 1716 pages
% 5.94/1.21 % E---3.1 exiting
% 5.94/1.21 % E exiting
%------------------------------------------------------------------------------