TSTP Solution File: HWV003-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HWV003-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n028.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 : Thu Aug 31 01:59:55 EDT 2023

% Result   : Unsatisfiable 45.27s 45.40s
% Output   : CNFRefutation 45.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  191 ( 170 unt;  21 typ;   0 def)
%            Number of atoms       :  170 ( 161 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   7   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  14 con; 0-3 aty)
%            Number of variables   :  199 (  18 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    n0: $i ).

tff(decl_23,type,
    and: ( $i * $i ) > $i ).

tff(decl_24,type,
    n1: $i ).

tff(decl_25,type,
    or: ( $i * $i ) > $i ).

tff(decl_26,type,
    not: $i > $i ).

tff(decl_27,type,
    xor: ( $i * $i ) > $i ).

tff(decl_28,type,
    carryout: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    sum: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    a11: $i ).

tff(decl_31,type,
    a: $i ).

tff(decl_32,type,
    b: $i ).

tff(decl_33,type,
    a12: $i ).

tff(decl_34,type,
    a13: $i ).

tff(decl_35,type,
    a14: $i ).

tff(decl_36,type,
    a15: $i ).

tff(decl_37,type,
    carryin: $i ).

tff(decl_38,type,
    a16: $i ).

tff(decl_39,type,
    a17: $i ).

tff(decl_40,type,
    s1: $i ).

tff(decl_41,type,
    c1: $i ).

tff(decl_42,type,
    circuit: ( $i * $i ) > $o ).

cnf(karnaugh1,axiom,
    or(and(X1,not(X2)),X2) = or(X1,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',karnaugh1) ).

cnf(or_symmetry,negated_conjecture,
    or(X1,X2) = or(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_symmetry) ).

cnf(circuit3,negated_conjecture,
    a13 = not(and(a11,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit3) ).

cnf(and_symmetry,negated_conjecture,
    and(X1,X2) = and(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_symmetry) ).

cnf(circuit2,negated_conjecture,
    a12 = not(and(a11,a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit2) ).

cnf(and_or_subsumption1,axiom,
    or(and(X1,X2),X2) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_subsumption1) ).

cnf(not_involution,axiom,
    not(not(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_involution) ).

cnf(circuit1,negated_conjecture,
    a11 = not(and(a,b)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit1) ).

cnf(and_or_subsumption2,axiom,
    or(and(X1,X2),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_subsumption2) ).

cnf(and_or_subsumption4,axiom,
    or(or(X1,and(X2,X3)),X3) = or(X1,X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_subsumption4) ).

cnf(circuit4,negated_conjecture,
    a14 = not(and(a12,a13)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit4) ).

cnf(and_or_simplification,negated_conjecture,
    and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_simplification) ).

cnf(and_idempotency,axiom,
    and(X1,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_idempotency) ).

cnf(demorgan1,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).

cnf(or_not_evaluation2,axiom,
    or(or(X1,X2),not(X2)) = n1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_not_evaluation2) ).

cnf(or_commutativity,negated_conjecture,
    or(or(X1,X2),X3) = or(or(X1,X3),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).

cnf(and_commutativity,negated_conjecture,
    and(and(X1,X2),X3) = and(and(X1,X3),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).

cnf(karnaugh3,axiom,
    or(and(and(X1,X2),not(X3)),and(X1,X3)) = or(and(X1,X2),and(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',karnaugh3) ).

cnf(karnaugh2,axiom,
    or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',karnaugh2) ).

cnf(demorgan2,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).

cnf(and_definition2,axiom,
    and(X1,n1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/HWC002-0.ax',and_definition2) ).

cnf(circuit5,negated_conjecture,
    a15 = not(and(a14,carryin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit5) ).

cnf(and_or_subsumption3,axiom,
    or(or(and(X1,X2),X3),X2) = or(X3,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_subsumption3) ).

cnf(circuit7,negated_conjecture,
    a17 = not(and(a15,carryin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit7) ).

cnf(circuit6,negated_conjecture,
    a16 = not(and(a14,a15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit6) ).

cnf(not_definition2,axiom,
    not(n1) = n0,
    file('/export/starexec/sandbox/benchmark/Axioms/HWC002-0.ax',not_definition2) ).

cnf(or_definition1,axiom,
    or(X1,n0) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/HWC002-0.ax',or_definition1) ).

cnf(prove_circuit,negated_conjecture,
    ~ circuit(sum(a,b,carryin),carryout(a,b,carryin)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_circuit) ).

cnf(sum_definition,negated_conjecture,
    sum(X1,X2,X3) = xor(xor(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_definition) ).

cnf(xor_definition,axiom,
    xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).

cnf(carryout_definition,negated_conjecture,
    carryout(X1,X2,X3) = or(and(X1,or(X2,X3)),and(not(X1),and(X2,X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',carryout_definition) ).

cnf(circuit8,negated_conjecture,
    s1 = not(and(a16,a17)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit8) ).

cnf(circuit9,negated_conjecture,
    c1 = not(and(a11,a15)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit9) ).

cnf(the_output_circuit,negated_conjecture,
    circuit(s1,c1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_output_circuit) ).

cnf(c_0_34,axiom,
    or(and(X1,not(X2)),X2) = or(X1,X2),
    karnaugh1 ).

cnf(c_0_35,negated_conjecture,
    or(X1,X2) = or(X2,X1),
    or_symmetry ).

cnf(c_0_36,negated_conjecture,
    a13 = not(and(a11,b)),
    circuit3 ).

cnf(c_0_37,negated_conjecture,
    and(X1,X2) = and(X2,X1),
    and_symmetry ).

cnf(c_0_38,negated_conjecture,
    a12 = not(and(a11,a)),
    circuit2 ).

cnf(c_0_39,axiom,
    or(and(X1,X2),X2) = X2,
    and_or_subsumption1 ).

cnf(c_0_40,plain,
    or(X1,and(X2,not(X1))) = or(X2,X1),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,axiom,
    not(not(X1)) = X1,
    not_involution ).

cnf(c_0_42,negated_conjecture,
    a11 = not(and(a,b)),
    circuit1 ).

cnf(c_0_43,negated_conjecture,
    not(and(b,a11)) = a13,
    inference(rw,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_44,axiom,
    or(and(X1,X2),X1) = X1,
    and_or_subsumption2 ).

cnf(c_0_45,negated_conjecture,
    not(and(a,a11)) = a12,
    inference(rw,[status(thm)],[c_0_38,c_0_37]) ).

cnf(c_0_46,axiom,
    or(or(X1,and(X2,X3)),X3) = or(X1,X3),
    and_or_subsumption4 ).

cnf(c_0_47,negated_conjecture,
    a14 = not(and(a12,a13)),
    circuit4 ).

cnf(c_0_48,negated_conjecture,
    and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
    and_or_simplification ).

cnf(c_0_49,axiom,
    and(X1,X1) = X1,
    and_idempotency ).

cnf(c_0_50,plain,
    or(X1,and(X2,X1)) = X1,
    inference(rw,[status(thm)],[c_0_39,c_0_35]) ).

cnf(c_0_51,plain,
    or(not(X1),and(X2,X1)) = or(X2,not(X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_52,negated_conjecture,
    and(a,b) = not(a11),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_53,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    demorgan1 ).

cnf(c_0_54,negated_conjecture,
    and(b,a11) = not(a13),
    inference(spm,[status(thm)],[c_0_41,c_0_43]) ).

cnf(c_0_55,axiom,
    or(or(X1,X2),not(X2)) = n1,
    or_not_evaluation2 ).

cnf(c_0_56,plain,
    or(X1,and(X1,X2)) = X1,
    inference(rw,[status(thm)],[c_0_44,c_0_35]) ).

cnf(c_0_57,negated_conjecture,
    and(a,a11) = not(a12),
    inference(spm,[status(thm)],[c_0_41,c_0_45]) ).

cnf(c_0_58,negated_conjecture,
    or(or(X1,X2),X3) = or(or(X1,X3),X2),
    or_commutativity ).

cnf(c_0_59,plain,
    or(X1,or(X2,and(X3,X1))) = or(X2,X1),
    inference(rw,[status(thm)],[c_0_46,c_0_35]) ).

cnf(c_0_60,negated_conjecture,
    and(a12,a13) = not(a14),
    inference(spm,[status(thm)],[c_0_41,c_0_47]) ).

cnf(c_0_61,negated_conjecture,
    and(X1,or(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_37]) ).

cnf(c_0_62,negated_conjecture,
    or(a,not(b)) = a13,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),c_0_41]) ).

cnf(c_0_63,plain,
    or(not(X1),or(X2,X1)) = n1,
    inference(rw,[status(thm)],[c_0_55,c_0_35]) ).

cnf(c_0_64,negated_conjecture,
    or(a,not(a12)) = a,
    inference(spm,[status(thm)],[c_0_56,c_0_57]) ).

cnf(c_0_65,negated_conjecture,
    or(or(X1,X2),X3) = or(X2,or(X1,X3)),
    inference(spm,[status(thm)],[c_0_35,c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    and(and(X1,X2),X3) = and(and(X1,X3),X2),
    and_commutativity ).

cnf(c_0_67,axiom,
    or(and(and(X1,X2),not(X3)),and(X1,X3)) = or(and(X1,X2),and(X1,X3)),
    karnaugh3 ).

cnf(c_0_68,axiom,
    or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
    karnaugh2 ).

cnf(c_0_69,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    demorgan2 ).

cnf(c_0_70,negated_conjecture,
    or(X1,or(X2,and(X1,X3))) = or(X2,X1),
    inference(spm,[status(thm)],[c_0_59,c_0_37]) ).

cnf(c_0_71,negated_conjecture,
    or(not(a14),and(X1,a13)) = and(a13,or(X1,a12)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_60]),c_0_35]),c_0_37]) ).

cnf(c_0_72,negated_conjecture,
    and(a,a13) = a,
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_73,negated_conjecture,
    or(a,a12) = n1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_41]),c_0_35]) ).

cnf(c_0_74,axiom,
    and(X1,n1) = X1,
    and_definition2 ).

cnf(c_0_75,negated_conjecture,
    or(b,not(a11)) = b,
    inference(spm,[status(thm)],[c_0_50,c_0_52]) ).

cnf(c_0_76,negated_conjecture,
    a15 = not(and(a14,carryin)),
    circuit5 ).

cnf(c_0_77,axiom,
    or(or(and(X1,X2),X3),X2) = or(X3,X2),
    and_or_subsumption3 ).

cnf(c_0_78,negated_conjecture,
    or(X1,or(X2,X3)) = or(X3,or(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_65]),c_0_65]) ).

cnf(c_0_79,negated_conjecture,
    and(and(X1,X2),X3) = and(X2,and(X1,X3)),
    inference(spm,[status(thm)],[c_0_37,c_0_66]) ).

cnf(c_0_80,plain,
    or(and(X1,X2),and(and(X1,X3),not(X2))) = or(and(X1,X3),and(X1,X2)),
    inference(rw,[status(thm)],[c_0_67,c_0_35]) ).

cnf(c_0_81,plain,
    or(X1,not(or(X2,X1))) = or(X1,not(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_35]) ).

cnf(c_0_82,negated_conjecture,
    or(a12,or(X1,not(a14))) = or(X1,a12),
    inference(spm,[status(thm)],[c_0_70,c_0_60]) ).

cnf(c_0_83,negated_conjecture,
    or(a,not(a14)) = a13,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]),c_0_35]) ).

cnf(c_0_84,negated_conjecture,
    not(and(a11,a13)) = b,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_54]),c_0_53]),c_0_75]) ).

cnf(c_0_85,negated_conjecture,
    or(a11,not(a12)) = a11,
    inference(spm,[status(thm)],[c_0_50,c_0_57]) ).

cnf(c_0_86,negated_conjecture,
    a17 = not(and(a15,carryin)),
    circuit7 ).

cnf(c_0_87,negated_conjecture,
    not(and(carryin,a14)) = a15,
    inference(rw,[status(thm)],[c_0_76,c_0_37]) ).

cnf(c_0_88,negated_conjecture,
    a16 = not(and(a14,a15)),
    circuit6 ).

cnf(c_0_89,plain,
    or(X1,or(and(X2,X1),X3)) = or(X3,X1),
    inference(rw,[status(thm)],[c_0_77,c_0_35]) ).

cnf(c_0_90,negated_conjecture,
    or(X1,or(X2,X3)) = or(X3,or(X1,X2)),
    inference(spm,[status(thm)],[c_0_78,c_0_35]) ).

cnf(c_0_91,negated_conjecture,
    and(X1,and(X2,X3)) = and(X3,and(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_79]),c_0_79]) ).

cnf(c_0_92,plain,
    or(and(X1,X2),and(X1,not(X2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_74]),c_0_56]) ).

cnf(c_0_93,negated_conjecture,
    or(and(X1,X2),and(X2,X3)) = and(or(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_48,c_0_37]) ).

cnf(c_0_94,negated_conjecture,
    and(X1,or(X2,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_35]),c_0_50]),c_0_37]) ).

cnf(c_0_95,negated_conjecture,
    or(X1,not(or(X1,X2))) = or(X1,not(X2)),
    inference(spm,[status(thm)],[c_0_81,c_0_35]) ).

cnf(c_0_96,negated_conjecture,
    or(a12,a13) = n1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_73]) ).

cnf(c_0_97,axiom,
    not(n1) = n0,
    not_definition2 ).

cnf(c_0_98,axiom,
    or(X1,n0) = X1,
    or_definition1 ).

cnf(c_0_99,negated_conjecture,
    and(a11,a13) = not(b),
    inference(spm,[status(thm)],[c_0_41,c_0_84]) ).

cnf(c_0_100,negated_conjecture,
    or(a11,a12) = n1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_85]),c_0_41]),c_0_35]) ).

cnf(c_0_101,negated_conjecture,
    ~ circuit(sum(a,b,carryin),carryout(a,b,carryin)),
    prove_circuit ).

cnf(c_0_102,negated_conjecture,
    sum(X1,X2,X3) = xor(xor(X1,X2),X3),
    sum_definition ).

cnf(c_0_103,axiom,
    xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
    xor_definition ).

cnf(c_0_104,negated_conjecture,
    carryout(X1,X2,X3) = or(and(X1,or(X2,X3)),and(not(X1),and(X2,X3))),
    carryout_definition ).

cnf(c_0_105,negated_conjecture,
    not(and(carryin,a15)) = a17,
    inference(rw,[status(thm)],[c_0_86,c_0_37]) ).

cnf(c_0_106,negated_conjecture,
    and(carryin,a14) = not(a15),
    inference(spm,[status(thm)],[c_0_41,c_0_87]) ).

cnf(c_0_107,negated_conjecture,
    not(and(a15,a14)) = a16,
    inference(rw,[status(thm)],[c_0_88,c_0_37]) ).

cnf(c_0_108,plain,
    or(and(X1,X2),and(X3,and(X1,not(X2)))) = or(and(X1,X3),and(X1,X2)),
    inference(rw,[status(thm)],[c_0_80,c_0_79]) ).

cnf(c_0_109,negated_conjecture,
    or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_89]),c_0_65]),c_0_90]),c_0_59]) ).

cnf(c_0_110,negated_conjecture,
    and(X1,and(X2,X3)) = and(X3,and(X1,X2)),
    inference(spm,[status(thm)],[c_0_91,c_0_37]) ).

cnf(c_0_111,plain,
    not(or(X1,not(X2))) = and(not(X1),X2),
    inference(spm,[status(thm)],[c_0_69,c_0_41]) ).

cnf(c_0_112,negated_conjecture,
    or(not(a11),and(a,not(b))) = a,
    inference(spm,[status(thm)],[c_0_92,c_0_52]) ).

cnf(c_0_113,plain,
    not(and(X1,not(X2))) = or(not(X1),X2),
    inference(spm,[status(thm)],[c_0_53,c_0_41]) ).

cnf(c_0_114,negated_conjecture,
    or(not(X1),or(not(X2),X3)) = or(X3,not(and(X2,X1))),
    inference(spm,[status(thm)],[c_0_78,c_0_53]) ).

cnf(c_0_115,negated_conjecture,
    or(and(X1,X2),and(X1,X3)) = and(or(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_93,c_0_37]) ).

cnf(c_0_116,plain,
    not(and(or(X1,X2),or(X2,not(X1)))) = not(X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_81]),c_0_53]),c_0_53]),c_0_37]),c_0_94]) ).

cnf(c_0_117,negated_conjecture,
    or(a12,not(a13)) = a12,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]),c_0_98]) ).

cnf(c_0_118,negated_conjecture,
    not(and(b,a14)) = a13,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_99]),c_0_53]),c_0_100]),c_0_74]),c_0_37]) ).

cnf(c_0_119,negated_conjecture,
    ~ circuit(or(and(or(and(a,not(b)),and(b,not(a))),not(carryin)),and(carryin,not(or(and(a,not(b)),and(b,not(a)))))),or(and(a,or(b,carryin)),and(not(a),and(b,carryin)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_103]),c_0_104]) ).

cnf(c_0_120,negated_conjecture,
    or(X1,and(not(X1),X2)) = or(X2,X1),
    inference(spm,[status(thm)],[c_0_40,c_0_37]) ).

cnf(c_0_121,negated_conjecture,
    and(carryin,a15) = not(a17),
    inference(spm,[status(thm)],[c_0_41,c_0_105]) ).

cnf(c_0_122,negated_conjecture,
    or(a14,not(a15)) = a14,
    inference(spm,[status(thm)],[c_0_50,c_0_106]) ).

cnf(c_0_123,negated_conjecture,
    or(not(a15),and(carryin,not(a14))) = carryin,
    inference(spm,[status(thm)],[c_0_92,c_0_106]) ).

cnf(c_0_124,negated_conjecture,
    and(a15,a14) = not(a16),
    inference(spm,[status(thm)],[c_0_41,c_0_107]) ).

cnf(c_0_125,negated_conjecture,
    or(and(X1,X2),or(and(X3,and(X1,not(X2))),X4)) = or(X4,or(and(X1,X3),and(X1,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_108]),c_0_109]) ).

cnf(c_0_126,negated_conjecture,
    and(a,and(a11,X1)) = and(X1,not(a12)),
    inference(spm,[status(thm)],[c_0_110,c_0_57]) ).

cnf(c_0_127,negated_conjecture,
    and(a11,not(b)) = not(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_75]),c_0_37]) ).

cnf(c_0_128,negated_conjecture,
    or(b,a12) = a12,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_95,c_0_112]),c_0_53]),c_0_37]),c_0_57]),c_0_41]),c_0_113]),c_0_114]),c_0_57]),c_0_41]) ).

cnf(c_0_129,plain,
    or(and(X1,X2),and(X3,and(X1,not(X2)))) = and(or(X3,X2),X1),
    inference(rw,[status(thm)],[c_0_108,c_0_115]) ).

cnf(c_0_130,negated_conjecture,
    or(not(a11),and(X1,and(a,not(b)))) = or(not(a11),and(a,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_52]),c_0_35]) ).

cnf(c_0_131,negated_conjecture,
    or(and(X1,X2),and(not(X2),and(X1,X3))) = or(and(X1,X3),and(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_37]),c_0_79]) ).

cnf(c_0_132,negated_conjecture,
    or(not(a15),and(X1,and(carryin,not(a14)))) = or(not(a15),and(carryin,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_106]),c_0_35]) ).

cnf(c_0_133,negated_conjecture,
    or(a12,not(a14)) = a12,
    inference(spm,[status(thm)],[c_0_56,c_0_60]) ).

cnf(c_0_134,negated_conjecture,
    not(and(a14,a12)) = a13,
    inference(rw,[status(thm)],[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_116,c_0_117]),c_0_53]),c_0_37]),c_0_60]),c_0_41]),c_0_37]),c_0_41]) ).

cnf(c_0_135,negated_conjecture,
    and(carryin,and(X1,a14)) = and(not(a15),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_106]),c_0_110]) ).

cnf(c_0_136,negated_conjecture,
    and(b,a14) = not(a13),
    inference(spm,[status(thm)],[c_0_41,c_0_118]) ).

cnf(c_0_137,negated_conjecture,
    ~ circuit(or(and(carryin,not(or(and(a,not(b)),and(b,not(a))))),and(not(carryin),or(and(a,not(b)),and(b,not(a))))),or(and(a,or(b,carryin)),and(not(a),and(b,carryin)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_35]),c_0_37]) ).

cnf(c_0_138,negated_conjecture,
    and(b,not(a)) = not(a13),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_62]),c_0_37]) ).

cnf(c_0_139,negated_conjecture,
    or(not(X1),and(X1,X2)) = or(X2,not(X1)),
    inference(spm,[status(thm)],[c_0_120,c_0_41]) ).

cnf(c_0_140,negated_conjecture,
    and(carryin,and(a15,X1)) = and(X1,not(a17)),
    inference(spm,[status(thm)],[c_0_110,c_0_121]) ).

cnf(c_0_141,negated_conjecture,
    and(a15,not(a14)) = not(a14),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_122]),c_0_37]) ).

cnf(c_0_142,negated_conjecture,
    or(a14,a17) = a17,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_95,c_0_123]),c_0_53]),c_0_37]),c_0_121]),c_0_41]),c_0_113]),c_0_114]),c_0_121]),c_0_41]) ).

cnf(c_0_143,negated_conjecture,
    or(carryin,not(a14)) = a16,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_106]),c_0_53]),c_0_37]),c_0_124]),c_0_41]) ).

cnf(c_0_144,negated_conjecture,
    s1 = not(and(a16,a17)),
    circuit8 ).

cnf(c_0_145,negated_conjecture,
    or(not(a11),or(and(X1,and(a,not(b))),X2)) = or(X2,or(not(a11),and(a,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_52]),c_0_35]) ).

cnf(c_0_146,negated_conjecture,
    and(a,not(b)) = not(a12),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_69]),c_0_128]) ).

cnf(c_0_147,negated_conjecture,
    or(not(a11),and(a,X1)) = and(a,or(X1,b)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_52]),c_0_130]),c_0_37]) ).

cnf(c_0_148,negated_conjecture,
    or(and(carryin,X1),not(or(X1,a15))) = or(not(a15),and(carryin,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_106]),c_0_69]) ).

cnf(c_0_149,negated_conjecture,
    or(not(a15),and(carryin,X1)) = and(carryin,or(X1,a14)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_106]),c_0_132]),c_0_37]) ).

cnf(c_0_150,negated_conjecture,
    or(a14,a12) = n1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_133]),c_0_41]) ).

cnf(c_0_151,negated_conjecture,
    c1 = not(and(a11,a15)),
    circuit9 ).

cnf(c_0_152,negated_conjecture,
    and(carryin,and(a14,X1)) = and(X1,not(a15)),
    inference(spm,[status(thm)],[c_0_110,c_0_106]) ).

cnf(c_0_153,negated_conjecture,
    and(a14,a12) = not(a13),
    inference(spm,[status(thm)],[c_0_41,c_0_134]) ).

cnf(c_0_154,negated_conjecture,
    and(carryin,not(a13)) = and(b,not(a15)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_37]) ).

cnf(c_0_155,negated_conjecture,
    ~ circuit(or(and(carryin,and(a13,or(b,not(a)))),and(not(carryin),or(not(a13),and(a,not(b))))),or(and(carryin,not(a13)),and(a,or(b,carryin)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_137,c_0_138]),c_0_111]),c_0_113]),c_0_35]),c_0_37]),c_0_110]),c_0_37]),c_0_138]),c_0_35]),c_0_35]) ).

cnf(c_0_156,negated_conjecture,
    or(b,not(a)) = a12,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_52]),c_0_53]),c_0_57]),c_0_41]) ).

cnf(c_0_157,negated_conjecture,
    and(carryin,not(a14)) = not(a17),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_69]),c_0_142]) ).

cnf(c_0_158,negated_conjecture,
    and(a14,not(carryin)) = not(a16),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_143]),c_0_37]) ).

cnf(c_0_159,negated_conjecture,
    and(a16,a17) = not(s1),
    inference(spm,[status(thm)],[c_0_41,c_0_144]) ).

cnf(c_0_160,negated_conjecture,
    or(not(a11),or(and(X1,not(a12)),X2)) = or(X2,and(a,or(X1,b))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146]),c_0_147]) ).

cnf(c_0_161,negated_conjecture,
    or(and(carryin,X1),not(or(X1,a15))) = and(carryin,or(X1,a14)),
    inference(rw,[status(thm)],[c_0_148,c_0_149]) ).

cnf(c_0_162,negated_conjecture,
    or(a14,not(a12)) = a14,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_150]),c_0_97]),c_0_98]) ).

cnf(c_0_163,negated_conjecture,
    and(a11,a15) = not(c1),
    inference(spm,[status(thm)],[c_0_41,c_0_151]) ).

cnf(c_0_164,plain,
    not(or(not(X1),X2)) = and(X1,not(X2)),
    inference(spm,[status(thm)],[c_0_69,c_0_41]) ).

cnf(c_0_165,negated_conjecture,
    and(a12,not(a15)) = and(b,not(a15)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).

cnf(c_0_166,negated_conjecture,
    ~ circuit(s1,or(and(b,not(a15)),and(a,or(b,carryin)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_155,c_0_154]),c_0_156]),c_0_37]),c_0_60]),c_0_157]),c_0_146]),c_0_53]),c_0_37]),c_0_60]),c_0_41]),c_0_37]),c_0_158]),c_0_53]),c_0_37]),c_0_159]),c_0_41]) ).

cnf(c_0_167,negated_conjecture,
    or(and(b,not(a15)),and(a,or(b,carryin))) = c1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_160,c_0_161]),c_0_35]),c_0_162]),c_0_106]),c_0_53]),c_0_163]),c_0_41]),c_0_164]),c_0_35]),c_0_165]) ).

cnf(c_0_168,negated_conjecture,
    circuit(s1,c1),
    the_output_circuit ).

cnf(c_0_169,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_167]),c_0_168])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : HWV003-1 : TPTP v8.1.2. Released v1.1.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n028.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue Aug 29 14:31:10 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 45.27/45.40  % Version  : CSE_E---1.5
% 45.27/45.40  % Problem  : theBenchmark.p
% 45.27/45.40  % Proof found
% 45.27/45.40  % SZS status Theorem for theBenchmark.p
% 45.27/45.40  % SZS output start Proof
% See solution above
% 45.27/45.42  % Total time : 44.838000 s
% 45.27/45.42  % SZS output end Proof
% 45.27/45.42  % Total time : 44.844000 s
%------------------------------------------------------------------------------