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