TSTP Solution File: HWV004-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : HWV004-1 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n010.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 01:59:56 EDT 2023

% Result   : Unsatisfiable 85.51s 85.57s
% Output   : CNFRefutation 85.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  139 ( 123 unt;  16 typ;   0 def)
%            Number of atoms       :  123 ( 110 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    :   10 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   7   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   9 con; 0-3 aty)
%            Number of variables   :  206 (  24 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,
    s0: $i ).

tff(decl_31,type,
    a0: $i ).

tff(decl_32,type,
    b0: $i ).

tff(decl_33,type,
    s1: $i ).

tff(decl_34,type,
    a1: $i ).

tff(decl_35,type,
    b1: $i ).

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

tff(decl_37,type,
    circuit: ( $i * $i * $i ) > $o ).

cnf(and_or_subsumption1,axiom,
    or(and(X1,X2),X2) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption1) ).

cnf(or_symmetry,negated_conjecture,
    or(X1,X2) = or(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_symmetry) ).

cnf(and_or_simplification,negated_conjecture,
    and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_simplification) ).

cnf(and_idempotency,axiom,
    and(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_idempotency) ).

cnf(and_symmetry,negated_conjecture,
    and(X1,X2) = and(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_symmetry) ).

cnf(and_or_subsumption3,axiom,
    or(or(and(X1,X2),X3),X2) = or(X3,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption3) ).

cnf(and_or_subsumption4,axiom,
    or(or(X1,and(X2,X3)),X3) = or(X1,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_subsumption4) ).

cnf(karnaugh2,axiom,
    or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',karnaugh2) ).

cnf(or_definition2,axiom,
    or(X1,n1) = n1,
    file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition2) ).

cnf(not_definition1,axiom,
    not(n0) = n1,
    file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition1) ).

cnf(s0_definition,negated_conjecture,
    s0 = sum(a0,b0,n0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s0_definition) ).

cnf(sum_definition,negated_conjecture,
    sum(X1,X2,X3) = xor(xor(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_definition) ).

cnf(xor_definition,axiom,
    xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_definition) ).

cnf(overflow_definition,negated_conjecture,
    overflow = carryout(a1,b1,carryout(a0,b0,n0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',overflow_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/sandbox2/benchmark/theBenchmark.p',carryout_definition) ).

cnf(not_involution,axiom,
    not(not(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_involution) ).

cnf(or_commutativity,negated_conjecture,
    or(or(X1,X2),X3) = or(or(X1,X3),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).

cnf(or_evaluation1,axiom,
    or(or(X1,X2),X2) = or(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_evaluation1) ).

cnf(and_evaluation1,axiom,
    and(and(X1,X2),X2) = and(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_evaluation1) ).

cnf(and_commutativity,negated_conjecture,
    and(and(X1,X2),X3) = and(and(X1,X3),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).

cnf(or_definition1,axiom,
    or(X1,n0) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).

cnf(the_output_circuit,negated_conjecture,
    circuit(s0,s1,overflow),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_output_circuit) ).

cnf(and_definition2,axiom,
    and(X1,n1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition2) ).

cnf(and_definition1,axiom,
    and(X1,n0) = n0,
    file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',and_definition1) ).

cnf(s1_definition,negated_conjecture,
    s1 = sum(a1,b1,carryout(a0,b0,n0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_definition) ).

cnf(prove_circuit,negated_conjecture,
    ~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_circuit) ).

cnf(and_not_evaluation1,axiom,
    and(X1,not(X1)) = n0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_evaluation1) ).

cnf(demorgan1,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1) ).

cnf(demorgan2,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan2) ).

cnf(or_not_evaluation1,axiom,
    or(X1,not(X1)) = n1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_evaluation1) ).

cnf(or_idempotency,axiom,
    or(X1,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_idempotency) ).

cnf(c_0_31,axiom,
    or(and(X1,X2),X2) = X2,
    and_or_subsumption1 ).

cnf(c_0_32,negated_conjecture,
    or(X1,X2) = or(X2,X1),
    or_symmetry ).

cnf(c_0_33,negated_conjecture,
    and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
    and_or_simplification ).

cnf(c_0_34,axiom,
    and(X1,X1) = X1,
    and_idempotency ).

cnf(c_0_35,plain,
    or(X1,and(X2,X1)) = X1,
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_36,negated_conjecture,
    and(X1,X2) = and(X2,X1),
    and_symmetry ).

cnf(c_0_37,axiom,
    or(or(and(X1,X2),X3),X2) = or(X3,X2),
    and_or_subsumption3 ).

cnf(c_0_38,axiom,
    or(or(X1,and(X2,X3)),X3) = or(X1,X3),
    and_or_subsumption4 ).

cnf(c_0_39,negated_conjecture,
    and(X1,or(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]) ).

cnf(c_0_40,plain,
    or(X1,or(and(X2,X1),X3)) = or(X3,X1),
    inference(rw,[status(thm)],[c_0_37,c_0_32]) ).

cnf(c_0_41,axiom,
    or(and(not(X1),not(X2)),X2) = or(X2,not(X1)),
    karnaugh2 ).

cnf(c_0_42,axiom,
    or(X1,n1) = n1,
    or_definition2 ).

cnf(c_0_43,axiom,
    not(n0) = n1,
    not_definition1 ).

cnf(c_0_44,negated_conjecture,
    s0 = sum(a0,b0,n0),
    s0_definition ).

cnf(c_0_45,negated_conjecture,
    sum(X1,X2,X3) = xor(xor(X1,X2),X3),
    sum_definition ).

cnf(c_0_46,axiom,
    xor(X1,X2) = or(and(X1,not(X2)),and(X2,not(X1))),
    xor_definition ).

cnf(c_0_47,negated_conjecture,
    overflow = carryout(a1,b1,carryout(a0,b0,n0)),
    overflow_definition ).

cnf(c_0_48,negated_conjecture,
    carryout(X1,X2,X3) = or(and(X1,or(X2,X3)),and(not(X1),and(X2,X3))),
    carryout_definition ).

cnf(c_0_49,plain,
    or(X1,or(X2,and(X3,X1))) = or(X2,X1),
    inference(rw,[status(thm)],[c_0_38,c_0_32]) ).

cnf(c_0_50,negated_conjecture,
    or(and(X1,X2),and(X2,X3)) = and(or(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_33,c_0_36]) ).

cnf(c_0_51,negated_conjecture,
    and(X1,or(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_52,plain,
    or(X1,and(not(X2),not(X1))) = or(X1,not(X2)),
    inference(rw,[status(thm)],[c_0_41,c_0_32]) ).

cnf(c_0_53,axiom,
    not(not(X1)) = X1,
    not_involution ).

cnf(c_0_54,negated_conjecture,
    or(or(X1,X2),X3) = or(or(X1,X3),X2),
    or_commutativity ).

cnf(c_0_55,axiom,
    or(or(X1,X2),X2) = or(X1,X2),
    or_evaluation1 ).

cnf(c_0_56,axiom,
    and(and(X1,X2),X2) = and(X1,X2),
    and_evaluation1 ).

cnf(c_0_57,negated_conjecture,
    and(and(X1,X2),X3) = and(and(X1,X3),X2),
    and_commutativity ).

cnf(c_0_58,axiom,
    or(X1,n0) = X1,
    or_definition1 ).

cnf(c_0_59,plain,
    or(X1,not(n0)) = not(n0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]) ).

cnf(c_0_60,negated_conjecture,
    circuit(s0,s1,overflow),
    the_output_circuit ).

cnf(c_0_61,negated_conjecture,
    s0 = or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_46]) ).

cnf(c_0_62,axiom,
    and(X1,n1) = X1,
    and_definition2 ).

cnf(c_0_63,negated_conjecture,
    overflow = or(and(a1,or(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))),and(not(a1),and(b1,or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]) ).

cnf(c_0_64,axiom,
    and(X1,n0) = n0,
    and_definition1 ).

cnf(c_0_65,negated_conjecture,
    s1 = sum(a1,b1,carryout(a0,b0,n0)),
    s1_definition ).

cnf(c_0_66,negated_conjecture,
    ~ circuit(xor(a0,b0),xor(xor(a1,b1),carryout(a0,b0,n0)),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
    prove_circuit ).

cnf(c_0_67,negated_conjecture,
    or(X1,and(or(X2,X1),X3)) = or(and(X2,X3),X1),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_68,negated_conjecture,
    or(X1,and(or(X2,X1),X3)) = and(or(X1,X3),or(X2,X1)),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_69,plain,
    or(X1,and(X2,not(X1))) = or(X1,X2),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_70,negated_conjecture,
    or(or(X1,X2),X3) = or(X2,or(X1,X3)),
    inference(spm,[status(thm)],[c_0_32,c_0_54]) ).

cnf(c_0_71,plain,
    or(X1,or(X2,X1)) = or(X2,X1),
    inference(rw,[status(thm)],[c_0_55,c_0_32]) ).

cnf(c_0_72,plain,
    and(X1,and(X2,X1)) = and(X2,X1),
    inference(rw,[status(thm)],[c_0_56,c_0_36]) ).

cnf(c_0_73,negated_conjecture,
    and(and(X1,X2),X3) = and(X2,and(X1,X3)),
    inference(spm,[status(thm)],[c_0_36,c_0_57]) ).

cnf(c_0_74,axiom,
    and(X1,not(X1)) = n0,
    and_not_evaluation1 ).

cnf(c_0_75,negated_conjecture,
    or(n0,X1) = X1,
    inference(spm,[status(thm)],[c_0_58,c_0_32]) ).

cnf(c_0_76,negated_conjecture,
    or(not(n0),X1) = not(n0),
    inference(spm,[status(thm)],[c_0_59,c_0_32]) ).

cnf(c_0_77,axiom,
    not(and(X1,X2)) = or(not(X1),not(X2)),
    demorgan1 ).

cnf(c_0_78,negated_conjecture,
    circuit(or(and(or(and(a0,not(b0)),and(b0,not(a0))),not(n0)),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))),s1,overflow),
    inference(rw,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_79,plain,
    and(X1,not(n0)) = X1,
    inference(rw,[status(thm)],[c_0_62,c_0_43]) ).

cnf(c_0_80,negated_conjecture,
    overflow = or(and(a1,or(b1,and(a0,b0))),and(not(a1),and(b1,and(a0,b0)))),
    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)],[c_0_63,c_0_58]),c_0_64]),c_0_64]),c_0_58]),c_0_58]),c_0_64]),c_0_64]),c_0_58]) ).

cnf(c_0_81,negated_conjecture,
    s1 = or(and(or(and(a1,not(b1)),and(b1,not(a1))),not(or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))),and(or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))),not(or(and(a1,not(b1)),and(b1,not(a1)))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_45]),c_0_46]),c_0_46]),c_0_48]),c_0_48]) ).

cnf(c_0_82,negated_conjecture,
    ~ circuit(or(and(a0,not(b0)),and(b0,not(a0))),or(and(or(and(a1,not(b1)),and(b1,not(a1))),not(or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))))),and(or(and(a0,or(b0,n0)),and(not(a0),and(b0,n0))),not(or(and(a1,not(b1)),and(b1,not(a1)))))),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_46]),c_0_46]),c_0_46]),c_0_48]),c_0_48]) ).

cnf(c_0_83,axiom,
    not(or(X1,X2)) = and(not(X1),not(X2)),
    demorgan2 ).

cnf(c_0_84,negated_conjecture,
    and(or(X1,X2),or(X3,X1)) = or(and(X3,X2),X1),
    inference(rw,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_85,negated_conjecture,
    or(X1,and(not(X1),X2)) = or(X1,X2),
    inference(spm,[status(thm)],[c_0_69,c_0_36]) ).

cnf(c_0_86,negated_conjecture,
    or(X1,or(X2,or(X3,X1))) = or(X3,or(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_51]),c_0_70]) ).

cnf(c_0_87,negated_conjecture,
    or(X1,or(X2,or(X3,X1))) = or(X2,or(X3,X1)),
    inference(spm,[status(thm)],[c_0_71,c_0_70]) ).

cnf(c_0_88,negated_conjecture,
    and(X1,and(X2,and(X3,and(X2,X1)))) = and(X3,and(X2,X1)),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_89,negated_conjecture,
    and(X1,and(X2,and(X1,X3))) = and(X1,and(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_72]),c_0_73]),c_0_73]) ).

cnf(c_0_90,negated_conjecture,
    and(X1,and(X2,and(X3,X1))) = and(X2,and(X3,X1)),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_91,negated_conjecture,
    and(or(X1,X2),not(X1)) = and(X2,not(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_74]),c_0_75]) ).

cnf(c_0_92,negated_conjecture,
    or(or(X1,not(X1)),X2) = or(X1,not(X1)),
    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_76,c_0_74]),c_0_77]),c_0_53]),c_0_77]),c_0_53]),c_0_32]),c_0_32]) ).

cnf(c_0_93,axiom,
    or(X1,not(X1)) = n1,
    or_not_evaluation1 ).

cnf(c_0_94,negated_conjecture,
    circuit(or(or(and(a0,not(b0)),and(b0,not(a0))),and(n0,not(or(and(a0,not(b0)),and(b0,not(a0)))))),s1,or(and(a1,or(b1,and(a0,b0))),and(not(a1),and(b1,and(a0,b0))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).

cnf(c_0_95,negated_conjecture,
    s1 = or(and(not(and(a0,b0)),or(and(not(a1),b1),and(a1,not(b1)))),and(and(a0,b0),not(or(and(not(a1),b1),and(a1,not(b1)))))),
    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)],[c_0_81,c_0_36]),c_0_32]),c_0_58]),c_0_64]),c_0_64]),c_0_58]),c_0_36]),c_0_58]),c_0_64]),c_0_64]),c_0_58]),c_0_36]),c_0_32]) ).

cnf(c_0_96,negated_conjecture,
    ~ circuit(or(and(not(a0),b0),and(a0,not(b0))),or(and(and(a0,b0),and(or(not(a1),b1),or(a1,not(b1)))),and(or(not(a0),not(b0)),or(and(not(a1),b1),and(a1,not(b1))))),or(and(a1,b1),and(and(a0,b0),or(a1,b1)))),
    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(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)],[c_0_82,c_0_32]),c_0_36]),c_0_36]),c_0_32]),c_0_58]),c_0_64]),c_0_64]),c_0_58]),c_0_77]),c_0_36]),c_0_58]),c_0_64]),c_0_64]),c_0_58]),c_0_36]),c_0_32]),c_0_83]),c_0_77]),c_0_53]),c_0_77]),c_0_53]),c_0_36]),c_0_32]) ).

cnf(c_0_97,negated_conjecture,
    or(and(X1,X2),X3) = and(or(X2,X3),or(X1,X3)),
    inference(spm,[status(thm)],[c_0_84,c_0_32]) ).

cnf(c_0_98,negated_conjecture,
    or(not(X1),and(X1,X2)) = or(not(X1),X2),
    inference(spm,[status(thm)],[c_0_85,c_0_53]) ).

cnf(c_0_99,negated_conjecture,
    or(X1,or(X2,X3)) = or(X2,or(X1,X3)),
    inference(rw,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_100,negated_conjecture,
    and(X1,and(X2,X3)) = and(X2,and(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_90]) ).

cnf(c_0_101,negated_conjecture,
    and(not(X1),and(or(X1,X2),X3)) = and(not(X1),and(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_91]),c_0_73]) ).

cnf(c_0_102,negated_conjecture,
    or(X1,and(or(X1,X2),X3)) = and(or(X1,X3),or(X1,X2)),
    inference(spm,[status(thm)],[c_0_50,c_0_39]) ).

cnf(c_0_103,negated_conjecture,
    or(not(X1),or(X1,X2)) = or(X1,not(X1)),
    inference(rw,[status(thm)],[c_0_92,c_0_70]) ).

cnf(c_0_104,negated_conjecture,
    or(X1,or(X2,X3)) = or(X2,or(X3,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_39]),c_0_70]),c_0_71]) ).

cnf(c_0_105,plain,
    or(X1,not(X1)) = not(n0),
    inference(rw,[status(thm)],[c_0_93,c_0_43]) ).

cnf(c_0_106,negated_conjecture,
    and(not(n0),X1) = X1,
    inference(spm,[status(thm)],[c_0_36,c_0_79]) ).

cnf(c_0_107,axiom,
    or(X1,X1) = X1,
    or_idempotency ).

cnf(c_0_108,negated_conjecture,
    circuit(or(and(n0,and(or(not(a0),b0),or(a0,not(b0)))),or(and(not(a0),b0),and(a0,not(b0)))),or(and(and(a0,b0),and(or(not(a1),b1),or(a1,not(b1)))),and(or(not(a0),not(b0)),or(and(not(a1),b1),and(a1,not(b1))))),or(and(not(a1),and(and(a0,b0),b1)),and(a1,or(and(a0,b0),b1)))),
    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(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)],[c_0_94,c_0_32]),c_0_36]),c_0_32]),c_0_36]),c_0_32]),c_0_36]),c_0_32]),c_0_83]),c_0_77]),c_0_53]),c_0_77]),c_0_53]),c_0_36]),c_0_32]),c_0_95]),c_0_77]),c_0_83]),c_0_77]),c_0_53]),c_0_77]),c_0_53]),c_0_36]),c_0_32]) ).

cnf(c_0_109,negated_conjecture,
    and(n0,X1) = n0,
    inference(spm,[status(thm)],[c_0_64,c_0_36]) ).

cnf(c_0_110,negated_conjecture,
    or(X1,or(and(X2,X1),X3)) = or(X1,X3),
    inference(spm,[status(thm)],[c_0_32,c_0_40]) ).

cnf(c_0_111,negated_conjecture,
    ~ circuit(and(or(a0,b0),or(not(a0),not(b0))),and(or(a0,and(or(not(a0),not(b0)),and(or(a1,b1),or(not(a1),not(b1))))),and(or(b0,and(or(not(a0),not(b0)),and(or(a1,b1),or(not(a1),not(b1))))),and(or(not(a1),or(b1,and(or(not(a0),not(b0)),and(or(a1,b1),or(not(a1),not(b1)))))),or(a1,or(not(b1),and(or(not(a0),not(b0)),and(or(a1,b1),or(not(a1),not(b1))))))))),and(or(a1,and(a0,and(b0,or(a1,b1)))),or(b1,and(a0,and(b0,or(a1,b1)))))),
    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(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(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)],[c_0_96,c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_70]),c_0_99]),c_0_70]),c_0_99]),c_0_36]),c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_36]),c_0_73]),c_0_36]),c_0_73]),c_0_100]),c_0_36]),c_0_73]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_97]),c_0_73]),c_0_100]),c_0_73]),c_0_100]),c_0_36]) ).

cnf(c_0_112,negated_conjecture,
    or(X1,and(X2,X3)) = and(or(X1,X3),or(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_101]),c_0_53]),c_0_85]),c_0_53]),c_0_102]) ).

cnf(c_0_113,negated_conjecture,
    or(X1,or(not(X1),X2)) = or(X1,not(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_49]),c_0_104]) ).

cnf(c_0_114,plain,
    and(X1,or(X2,not(X2))) = X1,
    inference(spm,[status(thm)],[c_0_79,c_0_105]) ).

cnf(c_0_115,negated_conjecture,
    or(X1,or(X2,not(X1))) = or(X1,not(X1)),
    inference(spm,[status(thm)],[c_0_85,c_0_51]) ).

cnf(c_0_116,negated_conjecture,
    and(or(X1,not(X1)),X2) = X2,
    inference(spm,[status(thm)],[c_0_106,c_0_105]) ).

cnf(c_0_117,negated_conjecture,
    or(X1,or(X2,or(X1,X3))) = or(X1,or(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_70]),c_0_70]) ).

cnf(c_0_118,negated_conjecture,
    or(X1,or(X1,X2)) = or(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_107]),c_0_32]) ).

cnf(c_0_119,negated_conjecture,
    circuit(or(and(not(a0),b0),and(a0,not(b0))),or(and(and(a0,b0),and(or(not(a1),b1),or(a1,not(b1)))),and(or(not(a0),not(b0)),or(and(not(a1),b1),and(a1,not(b1))))),or(and(not(a1),and(and(a0,b0),b1)),and(a1,or(and(a0,b0),b1)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_75]) ).

cnf(c_0_120,negated_conjecture,
    and(or(X1,X2),or(X1,or(X3,X2))) = or(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_97]),c_0_102]),c_0_36]) ).

cnf(c_0_121,negated_conjecture,
    ~ circuit(and(or(a0,b0),or(not(a0),not(b0))),and(or(a0,or(a1,b1)),and(or(b0,or(a1,b1)),and(or(not(a0),or(not(b0),or(not(a1),b1))),and(or(not(a0),or(not(b0),or(a1,not(b1)))),and(or(a0,or(not(a1),not(b1))),or(b0,or(not(a1),not(b1)))))))),and(or(a0,a1),and(or(b0,a1),and(or(a0,b1),and(or(b0,b1),or(a1,b1)))))),
    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(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(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(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(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_111,c_0_112]),c_0_112]),c_0_112]),c_0_113]),c_0_114]),c_0_112]),c_0_112]),c_0_115]),c_0_114]),c_0_112]),c_0_112]),c_0_115]),c_0_71]),c_0_116]),c_0_112]),c_0_112]),c_0_112]),c_0_71]),c_0_73]),c_0_112]),c_0_112]),c_0_113]),c_0_114]),c_0_117]),c_0_73]),c_0_73]),c_0_73]),c_0_112]),c_0_112]),c_0_118]),c_0_73]),c_0_112]),c_0_71]),c_0_73]),c_0_73]),c_0_73]),c_0_99]),c_0_113]),c_0_105]),c_0_32]),c_0_70]),c_0_99]),c_0_99]),c_0_99]),c_0_32]),c_0_70]),c_0_99]),c_0_99]),c_0_99]),c_0_32]),c_0_105]),c_0_59]),c_0_79]),c_0_106]),c_0_36]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_100]),c_0_32]),c_0_32]),c_0_32]),c_0_32]),c_0_36]),c_0_100]),c_0_100]),c_0_90]) ).

cnf(c_0_122,negated_conjecture,
    $false,
    inference(sr,[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(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(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(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(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(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(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(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(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(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(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)],[c_0_119,c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_70]),c_0_99]),c_0_70]),c_0_99]),c_0_36]),c_0_97]),c_0_69]),c_0_32]),c_0_98]),c_0_97]),c_0_36]),c_0_73]),c_0_36]),c_0_73]),c_0_100]),c_0_36]),c_0_73]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_97]),c_0_73]),c_0_100]),c_0_97]),c_0_36]),c_0_97]),c_0_97]),c_0_36]),c_0_73]),c_0_36]),c_0_36]),c_0_73]),c_0_100]),c_0_97]),c_0_36]),c_0_98]),c_0_73]),c_0_73]),c_0_100]),c_0_36]),c_0_73]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_112]),c_0_112]),c_0_36]),c_0_113]),c_0_105]),c_0_79]),c_0_112]),c_0_112]),c_0_36]),c_0_115]),c_0_105]),c_0_79]),c_0_112]),c_0_112]),c_0_115]),c_0_105]),c_0_71]),c_0_106]),c_0_32]),c_0_70]),c_0_99]),c_0_36]),c_0_112]),c_0_99]),c_0_113]),c_0_105]),c_0_99]),c_0_99]),c_0_106]),c_0_112]),c_0_112]),c_0_71]),c_0_32]),c_0_70]),c_0_115]),c_0_105]),c_0_79]),c_0_32]),c_0_70]),c_0_99]),c_0_36]),c_0_112]),c_0_113]),c_0_105]),c_0_99]),c_0_99]),c_0_106]),c_0_73]),c_0_36]),c_0_73]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_73]),c_0_100]),c_0_100]),c_0_100]),c_0_100]),c_0_112]),c_0_112]),c_0_118]),c_0_36]),c_0_120]),c_0_36]),c_0_112]),c_0_112]),c_0_118]),c_0_99]),c_0_51]),c_0_36]),c_0_112]),c_0_99]),c_0_99]),c_0_36]),c_0_112]),c_0_112]),c_0_71]),c_0_71]),c_0_36]),c_0_32]),c_0_73]),c_0_100]),c_0_73]),c_0_36]),c_0_73]),c_0_120]),c_0_73]),c_0_36]),c_0_36]),c_0_73]),c_0_100]),c_0_36]),c_0_73]),c_0_73]),c_0_100]),c_0_120]),c_0_36]),c_0_73]),c_0_100]),c_0_73]),c_0_100]),c_0_89]),c_0_100]),c_0_73]),c_0_100]),c_0_89]),c_0_100]),c_0_121]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : HWV004-1 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n010.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 13:42:34 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 85.51/85.57  % Version  : CSE_E---1.5
% 85.51/85.57  % Problem  : theBenchmark.p
% 85.51/85.57  % Proof found
% 85.51/85.57  % SZS status Theorem for theBenchmark.p
% 85.51/85.57  % SZS output start Proof
% See solution above
% 85.51/85.59  % Total time : 84.980000 s
% 85.51/85.59  % SZS output end Proof
% 85.51/85.59  % Total time : 84.987000 s
%------------------------------------------------------------------------------