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