TSTP Solution File: RNG004-2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : RNG004-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n018.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 02:35:46 EDT 2024

% Result   : Unsatisfiable 2.21s 0.82s
% Output   : CNFRefutation 2.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of clauses     :  105 (  46 unt;   0 nHn;  83 RR)
%            Number of literals    :  237 (  40 equ; 135 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  270 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).

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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).

cnf(associativity_of_addition2,axiom,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).

cnf(additive_identity2,axiom,
    sum(X1,additive_identity,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).

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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).

cnf(a_times_b,hypothesis,
    product(a,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).

cnf(left_inverse,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).

cnf(closure_of_addition,axiom,
    sum(X1,X2,add(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).

cnf(commutativity_of_addition,axiom,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).

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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).

cnf(cancellation2,axiom,
    ( X1 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).

cnf(closure_of_multiplication,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).

cnf(additive_identity1,axiom,
    sum(additive_identity,X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).

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/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).

cnf(multiplication_is_well_defined,axiom,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).

cnf(cancellation1,axiom,
    ( X2 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).

cnf(a_inverse_times_b_inverse,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).

cnf(right_inverse,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).

cnf(prove_c_equals_d,negated_conjecture,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).

cnf(c_0_19,plain,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).

cnf(c_0_20,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_21,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_22,plain,
    ( X3 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X2,X4) ),
    c_0_19 ).

cnf(c_0_23,axiom,
    sum(X1,additive_identity,X1),
    additive_identity2 ).

cnf(c_0_24,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_25,plain,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ product(X1,X6,X7) ),
    c_0_20 ).

cnf(c_0_26,hypothesis,
    product(a,b,c),
    a_times_b ).

cnf(c_0_27,plain,
    ( sum(X3,X4,X6)
    | ~ sum(X1,X2,X3)
    | ~ sum(X2,X4,X5)
    | ~ sum(X1,X5,X6) ),
    c_0_21 ).

cnf(c_0_28,axiom,
    sum(additive_inverse(X1),X1,additive_identity),
    left_inverse ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ sum(X2,additive_identity,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_30,axiom,
    sum(X1,X2,add(X1,X2)),
    closure_of_addition ).

cnf(c_0_31,plain,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).

cnf(c_0_32,plain,
    ( sum(X3,X5,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ product(X6,X2,X7) ),
    c_0_24 ).

cnf(c_0_33,hypothesis,
    ( sum(X1,X2,c)
    | ~ product(a,X3,X2)
    | ~ product(a,X4,X1)
    | ~ sum(X4,X3,b) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_34,plain,
    ( sum(X1,X2,X3)
    | ~ sum(X4,additive_inverse(X2),X1)
    | ~ sum(X4,additive_identity,X3) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,plain,
    add(X1,additive_identity) = X1,
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,plain,
    ( sum(X2,X1,X3)
    | ~ sum(X1,X2,X3) ),
    c_0_31 ).

cnf(c_0_37,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_38,hypothesis,
    ( sum(X1,X2,c)
    | ~ product(X3,b,X2)
    | ~ product(X4,b,X1)
    | ~ sum(X4,X3,a) ),
    inference(spm,[status(thm)],[c_0_32,c_0_26]) ).

cnf(c_0_39,plain,
    ( X1 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X3) ),
    inference(fof_simplification,[status(thm)],[cancellation2]) ).

cnf(c_0_40,hypothesis,
    ( sum(X1,c,c)
    | ~ product(a,X2,X1)
    | ~ sum(X2,b,b) ),
    inference(spm,[status(thm)],[c_0_33,c_0_26]) ).

cnf(c_0_41,axiom,
    product(X1,X2,multiply(X1,X2)),
    closure_of_multiplication ).

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_34,c_0_30]),c_0_35]) ).

cnf(c_0_43,plain,
    ( X1 = additive_identity
    | ~ sum(additive_inverse(X2),X2,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_28]) ).

cnf(c_0_44,plain,
    sum(X1,X2,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_36,c_0_30]) ).

cnf(c_0_45,plain,
    ( product(X1,X6,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X4,X5)
    | ~ sum(X2,X4,X6)
    | ~ sum(X3,X5,X7) ),
    c_0_37 ).

cnf(c_0_46,hypothesis,
    ( sum(X1,c,c)
    | ~ product(X2,b,X1)
    | ~ sum(X2,a,a) ),
    inference(spm,[status(thm)],[c_0_38,c_0_26]) ).

cnf(c_0_47,plain,
    ( X1 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X4,X2,X3) ),
    c_0_39 ).

cnf(c_0_48,axiom,
    sum(additive_identity,X1,X1),
    additive_identity1 ).

cnf(c_0_49,hypothesis,
    ( sum(multiply(a,X1),c,c)
    | ~ sum(X1,b,b) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_50,plain,
    sum(add(X1,additive_inverse(X2)),X2,X1),
    inference(spm,[status(thm)],[c_0_42,c_0_30]) ).

cnf(c_0_51,plain,
    add(X1,additive_inverse(X1)) = additive_identity,
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_52,hypothesis,
    ( product(a,X1,X2)
    | ~ product(a,X3,X4)
    | ~ sum(X4,c,X2)
    | ~ sum(X3,b,X1) ),
    inference(spm,[status(thm)],[c_0_45,c_0_26]) ).

cnf(c_0_53,hypothesis,
    ( sum(multiply(X1,b),c,c)
    | ~ sum(X1,a,a) ),
    inference(spm,[status(thm)],[c_0_46,c_0_41]) ).

cnf(c_0_54,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_55,plain,
    ( X1 = additive_identity
    | ~ sum(X1,X2,X2) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_56,hypothesis,
    sum(multiply(a,additive_identity),c,c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).

cnf(c_0_57,plain,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).

cnf(c_0_58,hypothesis,
    ( product(a,X1,X2)
    | ~ sum(multiply(a,X3),c,X2)
    | ~ sum(X3,b,X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_41]) ).

cnf(c_0_59,plain,
    ( X1 = add(X2,X3)
    | ~ sum(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_30]) ).

cnf(c_0_60,hypothesis,
    sum(multiply(additive_identity,b),c,c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_50]),c_0_51]) ).

cnf(c_0_61,plain,
    ( product(X6,X2,X7)
    | ~ product(X1,X2,X3)
    | ~ product(X4,X2,X5)
    | ~ sum(X1,X4,X6)
    | ~ sum(X3,X5,X7) ),
    c_0_54 ).

cnf(c_0_62,hypothesis,
    multiply(a,additive_identity) = additive_identity,
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_63,plain,
    ( X2 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X4,X3) ),
    inference(fof_simplification,[status(thm)],[cancellation1]) ).

cnf(c_0_64,plain,
    ( X3 = X4
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    c_0_57 ).

cnf(c_0_65,hypothesis,
    ( product(a,additive_identity,X1)
    | ~ sum(multiply(a,additive_inverse(b)),c,X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_28]) ).

cnf(c_0_66,plain,
    add(X1,X2) = add(X2,X1),
    inference(spm,[status(thm)],[c_0_59,c_0_44]) ).

cnf(c_0_67,hypothesis,
    multiply(additive_identity,b) = additive_identity,
    inference(spm,[status(thm)],[c_0_55,c_0_60]) ).

cnf(c_0_68,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_61,c_0_41]) ).

cnf(c_0_69,hypothesis,
    product(a,additive_identity,additive_identity),
    inference(spm,[status(thm)],[c_0_41,c_0_62]) ).

cnf(c_0_70,hypothesis,
    product(additive_inverse(a),additive_inverse(b),d),
    a_inverse_times_b_inverse ).

cnf(c_0_71,plain,
    ( X2 = X4
    | ~ sum(X1,X2,X3)
    | ~ sum(X1,X4,X3) ),
    c_0_63 ).

cnf(c_0_72,plain,
    ( X1 = X2
    | ~ sum(X1,X3,add(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_44]) ).

cnf(c_0_73,plain,
    ( X1 = multiply(X2,X3)
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_64,c_0_41]) ).

cnf(c_0_74,hypothesis,
    product(a,additive_identity,add(c,multiply(a,additive_inverse(b)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_30]),c_0_66]) ).

cnf(c_0_75,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_45,c_0_41]) ).

cnf(c_0_76,hypothesis,
    product(additive_identity,b,additive_identity),
    inference(spm,[status(thm)],[c_0_41,c_0_67]) ).

cnf(c_0_77,hypothesis,
    ( product(X1,additive_identity,X2)
    | ~ sum(additive_identity,multiply(X3,additive_identity),X2)
    | ~ sum(a,X3,X1) ),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_78,plain,
    ( X1 = X2
    | ~ sum(additive_identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_48]) ).

cnf(c_0_79,hypothesis,
    ( product(X1,additive_inverse(b),X2)
    | ~ product(X3,additive_inverse(b),X4)
    | ~ sum(X3,additive_inverse(a),X1)
    | ~ sum(X4,d,X2) ),
    inference(spm,[status(thm)],[c_0_61,c_0_70]) ).

cnf(c_0_80,plain,
    ( X1 = X2
    | ~ sum(additive_inverse(X2),X1,additive_identity) ),
    inference(spm,[status(thm)],[c_0_71,c_0_28]) ).

cnf(c_0_81,axiom,
    sum(X1,additive_inverse(X1),additive_identity),
    right_inverse ).

cnf(c_0_82,plain,
    add(additive_inverse(X1),add(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_50]),c_0_66]) ).

cnf(c_0_83,hypothesis,
    add(c,multiply(a,additive_inverse(b))) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_62]) ).

cnf(c_0_84,hypothesis,
    ( product(additive_identity,X1,X2)
    | ~ sum(additive_identity,multiply(additive_identity,X3),X2)
    | ~ sum(b,X3,X1) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_85,hypothesis,
    ( product(a,additive_identity,X1)
    | ~ sum(additive_identity,multiply(additive_identity,additive_identity),X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_23]) ).

cnf(c_0_86,plain,
    add(additive_identity,X1) = X1,
    inference(spm,[status(thm)],[c_0_78,c_0_30]) ).

cnf(c_0_87,hypothesis,
    ( product(X1,additive_inverse(b),X2)
    | ~ sum(multiply(X3,additive_inverse(b)),d,X2)
    | ~ sum(X3,additive_inverse(a),X1) ),
    inference(spm,[status(thm)],[c_0_79,c_0_41]) ).

cnf(c_0_88,plain,
    additive_inverse(additive_inverse(X1)) = X1,
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_89,hypothesis,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_35]) ).

cnf(c_0_90,hypothesis,
    ( product(additive_identity,additive_identity,X1)
    | ~ sum(additive_identity,multiply(additive_identity,additive_inverse(b)),X1) ),
    inference(spm,[status(thm)],[c_0_84,c_0_81]) ).

cnf(c_0_91,hypothesis,
    product(a,additive_identity,multiply(additive_identity,additive_identity)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_30]),c_0_86]) ).

cnf(c_0_92,plain,
    ( X1 = X2
    | ~ sum(X1,X3,add(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_30]) ).

cnf(c_0_93,hypothesis,
    ( product(additive_identity,additive_inverse(b),X1)
    | ~ sum(additive_inverse(c),d,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_28]),c_0_88]),c_0_89]) ).

cnf(c_0_94,hypothesis,
    product(additive_identity,additive_identity,multiply(additive_identity,additive_inverse(b))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_30]),c_0_86]) ).

cnf(c_0_95,hypothesis,
    multiply(additive_identity,additive_identity) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_91]),c_0_62]) ).

cnf(c_0_96,plain,
    add(additive_inverse(X1),add(X2,X1)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_50]),c_0_66]) ).

cnf(c_0_97,hypothesis,
    product(additive_identity,additive_inverse(b),add(d,additive_inverse(c))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_30]),c_0_66]) ).

cnf(c_0_98,hypothesis,
    multiply(additive_identity,additive_inverse(b)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_94]),c_0_95]) ).

cnf(c_0_99,negated_conjecture,
    c != d,
    inference(fof_simplification,[status(thm)],[prove_c_equals_d]) ).

cnf(c_0_100,plain,
    add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_96]),c_0_66]) ).

cnf(c_0_101,hypothesis,
    add(d,additive_inverse(c)) = additive_identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_97]),c_0_98]) ).

cnf(c_0_102,plain,
    additive_inverse(additive_identity) = additive_identity,
    inference(spm,[status(thm)],[c_0_78,c_0_81]) ).

cnf(c_0_103,negated_conjecture,
    c != d,
    c_0_99 ).

cnf(c_0_104,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_35]),c_0_88]),c_0_103]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : RNG004-2 : TPTP v8.2.0. Released v1.0.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.14/0.35  % Computer : n018.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 12:28:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 2.21/0.82  # Version: 3.1.0
% 2.21/0.82  # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.21/0.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.21/0.82  # Starting new_bool_3 with 300s (1) cores
% 2.21/0.82  # Starting new_bool_1 with 300s (1) cores
% 2.21/0.82  # Starting sh5l with 300s (1) cores
% 2.21/0.82  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 6686 completed with status 0
% 2.21/0.82  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.21/0.82  # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.21/0.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.21/0.82  # No SInE strategy applied
% 2.21/0.82  # Search class: FHUSM-FFMF21-SFFFFFNN
% 2.21/0.82  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.21/0.82  # Starting new_bool_3 with 136s (1) cores
% 2.21/0.82  # Starting new_bool_1 with 136s (1) cores
% 2.21/0.82  # Starting sh5l with 136s (1) cores
% 2.21/0.82  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 6690 completed with status 0
% 2.21/0.82  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 2.21/0.82  # Preprocessing class: FSMSSMSSSSSNFFN.
% 2.21/0.82  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.21/0.82  # No SInE strategy applied
% 2.21/0.82  # Search class: FHUSM-FFMF21-SFFFFFNN
% 2.21/0.82  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 2.21/0.82  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 811s (1) cores
% 2.21/0.82  # Preprocessing time       : 0.001 s
% 2.21/0.82  # Presaturation interreduction done
% 2.21/0.82  
% 2.21/0.82  # Proof found!
% 2.21/0.82  # SZS status Unsatisfiable
% 2.21/0.82  # SZS output start CNFRefutation
% See solution above
% 2.21/0.82  # Parsed axioms                        : 22
% 2.21/0.82  # Removed by relevancy pruning/SinE    : 0
% 2.21/0.82  # Initial clauses                      : 22
% 2.21/0.82  # Removed in clause preprocessing      : 0
% 2.21/0.82  # Initial clauses in saturation        : 22
% 2.21/0.82  # Processed clauses                    : 5529
% 2.21/0.82  # ...of these trivial                  : 259
% 2.21/0.82  # ...subsumed                          : 4025
% 2.21/0.82  # ...remaining for further processing  : 1245
% 2.21/0.82  # Other redundant clauses eliminated   : 0
% 2.21/0.82  # Clauses deleted for lack of memory   : 0
% 2.21/0.82  # Backward-subsumed                    : 11
% 2.21/0.82  # Backward-rewritten                   : 94
% 2.21/0.82  # Generated clauses                    : 32058
% 2.21/0.82  # ...of the previous two non-redundant : 22764
% 2.21/0.82  # ...aggressively subsumed             : 0
% 2.21/0.82  # Contextual simplify-reflections      : 0
% 2.21/0.82  # Paramodulations                      : 32058
% 2.21/0.82  # Factorizations                       : 0
% 2.21/0.82  # NegExts                              : 0
% 2.21/0.82  # Equation resolutions                 : 0
% 2.21/0.82  # Disequality decompositions           : 0
% 2.21/0.82  # Total rewrite steps                  : 33225
% 2.21/0.82  # ...of those cached                   : 30911
% 2.21/0.82  # Propositional unsat checks           : 0
% 2.21/0.82  #    Propositional check models        : 0
% 2.21/0.82  #    Propositional check unsatisfiable : 0
% 2.21/0.82  #    Propositional clauses             : 0
% 2.21/0.82  #    Propositional clauses after purity: 0
% 2.21/0.82  #    Propositional unsat core size     : 0
% 2.21/0.82  #    Propositional preprocessing time  : 0.000
% 2.21/0.82  #    Propositional encoding time       : 0.000
% 2.21/0.82  #    Propositional solver time         : 0.000
% 2.21/0.82  #    Success case prop preproc time    : 0.000
% 2.21/0.82  #    Success case prop encoding time   : 0.000
% 2.21/0.82  #    Success case prop solver time     : 0.000
% 2.21/0.82  # Current number of processed clauses  : 1118
% 2.21/0.82  #    Positive orientable unit clauses  : 160
% 2.21/0.82  #    Positive unorientable unit clauses: 1
% 2.21/0.82  #    Negative unit clauses             : 1
% 2.21/0.82  #    Non-unit-clauses                  : 956
% 2.21/0.82  # Current number of unprocessed clauses: 16810
% 2.21/0.82  # ...number of literals in the above   : 29081
% 2.21/0.82  # Current number of archived formulas  : 0
% 2.21/0.82  # Current number of archived clauses   : 127
% 2.21/0.82  # Clause-clause subsumption calls (NU) : 396933
% 2.21/0.82  # Rec. Clause-clause subsumption calls : 273201
% 2.21/0.82  # Non-unit clause-clause subsumptions  : 3542
% 2.21/0.82  # Unit Clause-clause subsumption calls : 0
% 2.21/0.82  # Rewrite failures with RHS unbound    : 0
% 2.21/0.82  # BW rewrite match attempts            : 3120
% 2.21/0.82  # BW rewrite match successes           : 85
% 2.21/0.82  # Condensation attempts                : 0
% 2.21/0.82  # Condensation successes               : 0
% 2.21/0.82  # Termbank termtop insertions          : 349659
% 2.21/0.82  # Search garbage collected termcells   : 69
% 2.21/0.82  
% 2.21/0.82  # -------------------------------------------------
% 2.21/0.82  # User time                : 0.311 s
% 2.21/0.82  # System time              : 0.013 s
% 2.21/0.82  # Total time               : 0.324 s
% 2.21/0.82  # Maximum resident set size: 1640 pages
% 2.21/0.82  
% 2.21/0.82  # -------------------------------------------------
% 2.21/0.82  # User time                : 1.569 s
% 2.21/0.82  # System time              : 0.028 s
% 2.21/0.82  # Total time               : 1.596 s
% 2.21/0.82  # Maximum resident set size: 1712 pages
% 2.21/0.82  % E---3.1 exiting
% 2.21/0.83  % E exiting
%------------------------------------------------------------------------------