TSTP Solution File: LCL178-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL178-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 : 600s
% DateTime : Sun Jul 17 12:50:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 12
% Syntax : Number of clauses : 78 ( 45 unt; 0 nHn; 34 RR)
% Number of literals : 120 ( 17 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 150 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(implies(or(A,A),A)) ).
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ theorem(implies(Y,X))
| ~ theorem(Y) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(p,not(not(p)))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(or(A,A),A))
| theorem(implies(or(A,A),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(A,A),A)))]]) ).
cnf(refute_0_1,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[$cnf( axiom(implies(or(A,A),A)) )],[axiom_1_2,refute_0_0]) ).
cnf(refute_0_2,plain,
theorem(implies(or(X_61,X_61),X_61)),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_61))]]) ).
cnf(refute_0_3,plain,
( ~ theorem(implies(or(X_61,X_61),X_61))
| ~ theorem(or(X_61,X_61))
| theorem(X_61) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_61)),bind(Y,$fot(or(X_61,X_61)))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(X_61,X_61))
| theorem(X_61) ),
inference(resolve,[$cnf( theorem(implies(or(X_61,X_61),X_61)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(or(X_662,not(X_662)),or(X_662,not(X_662))))
| theorem(or(X_662,not(X_662))) ),
inference(subst,[],[refute_0_4:[bind(X_61,$fot(or(X_662,not(X_662))))]]) ).
cnf(refute_0_6,plain,
( ~ theorem(implies(or(X_78,or(X_79,X_80)),or(X_79,or(X_78,X_80))))
| ~ theorem(or(X_78,or(X_79,X_80)))
| theorem(or(X_79,or(X_78,X_80))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_79,or(X_78,X_80)))),bind(Y,$fot(or(X_78,or(X_79,X_80))))]]) ).
cnf(refute_0_7,plain,
( ~ axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33))))
| theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))))]]) ).
cnf(refute_0_8,plain,
axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(subst,[],[axiom_1_5:[bind(A,$fot(X_31)),bind(B,$fot(X_32)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_9,plain,
theorem(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))),
inference(resolve,[$cnf( axiom(implies(or(X_31,or(X_32,X_33)),or(X_32,or(X_31,X_33)))) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
theorem(implies(or(X_78,or(X_79,X_80)),or(X_79,or(X_78,X_80)))),
inference(subst,[],[refute_0_9:[bind(X_31,$fot(X_78)),bind(X_32,$fot(X_79)),bind(X_33,$fot(X_80))]]) ).
cnf(refute_0_11,plain,
( ~ theorem(or(X_78,or(X_79,X_80)))
| theorem(or(X_79,or(X_78,X_80))) ),
inference(resolve,[$cnf( theorem(implies(or(X_78,or(X_79,X_80)),or(X_79,or(X_78,X_80)))) )],[refute_0_10,refute_0_6]) ).
cnf(refute_0_12,plain,
( ~ theorem(or(X_660,or(X_661,not(X_660))))
| theorem(or(X_661,or(X_660,not(X_660)))) ),
inference(subst,[],[refute_0_11:[bind(X_78,$fot(X_660)),bind(X_79,$fot(X_661)),bind(X_80,$fot(not(X_660)))]]) ).
cnf(refute_0_13,plain,
( ~ axiom(implies(or(X_5,X_6),or(X_6,X_5)))
| theorem(implies(or(X_5,X_6),or(X_6,X_5))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(or(X_5,X_6),or(X_6,X_5))))]]) ).
cnf(refute_0_14,plain,
axiom(implies(or(X_5,X_6),or(X_6,X_5))),
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_5)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_15,plain,
theorem(implies(or(X_5,X_6),or(X_6,X_5))),
inference(resolve,[$cnf( axiom(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
( ~ theorem(implies(or(X_5,X_6),or(X_6,X_5)))
| ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_6,X_5))),bind(Y,$fot(or(X_5,X_6)))]]) ).
cnf(refute_0_17,plain,
( ~ theorem(or(X_5,X_6))
| theorem(or(X_6,X_5)) ),
inference(resolve,[$cnf( theorem(implies(or(X_5,X_6),or(X_6,X_5))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ theorem(or(or(X_659,not(X_658)),X_658))
| theorem(or(X_658,or(X_659,not(X_658)))) ),
inference(subst,[],[refute_0_17:[bind(X_5,$fot(or(X_659,not(X_658)))),bind(X_6,$fot(X_658))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(or(or(X_657,not(X_655)),X_655),or(or(X_657,not(X_655)),X_655)))
| theorem(or(or(X_657,not(X_655)),X_655)) ),
inference(subst,[],[refute_0_4:[bind(X_61,$fot(or(or(X_657,not(X_655)),X_655)))]]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(or(X_463,not(X_461)),or(X_462,X_461)))
| theorem(or(X_462,or(or(X_463,not(X_461)),X_461))) ),
inference(subst,[],[refute_0_11:[bind(X_78,$fot(or(X_463,not(X_461)))),bind(X_79,$fot(X_462)),bind(X_80,$fot(X_461))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(or(or(X_457,X_456),or(X_458,not(X_456))))
| theorem(or(or(X_458,not(X_456)),or(X_457,X_456))) ),
inference(subst,[],[refute_0_17:[bind(X_5,$fot(or(X_457,X_456))),bind(X_6,$fot(or(X_458,not(X_456))))]]) ).
cnf(refute_0_22,plain,
( ~ axiom(implies(X_3,or(X_4,X_3)))
| theorem(implies(X_3,or(X_4,X_3))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(X_3,or(X_4,X_3))))]]) ).
cnf(refute_0_23,plain,
axiom(implies(X_3,or(X_4,X_3))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_3)),bind(B,$fot(X_4))]]) ).
cnf(refute_0_24,plain,
theorem(implies(X_3,or(X_4,X_3))),
inference(resolve,[$cnf( axiom(implies(X_3,or(X_4,X_3))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
theorem(implies(X_62,or(X_4,X_62))),
inference(subst,[],[refute_0_24:[bind(X_3,$fot(X_62))]]) ).
cnf(refute_0_26,plain,
( ~ theorem(X_62)
| ~ theorem(implies(X_62,or(X_4,X_62)))
| theorem(or(X_4,X_62)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_4,X_62))),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(X_62)
| theorem(or(X_4,X_62)) ),
inference(resolve,[$cnf( theorem(implies(X_62,or(X_4,X_62))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(or(X_130,X_129),not(X_129)))
| theorem(or(X_4,or(or(X_130,X_129),not(X_129)))) ),
inference(subst,[],[refute_0_27:[bind(X_62,$fot(or(or(X_130,X_129),not(X_129))))]]) ).
cnf(refute_0_29,plain,
theorem(implies(X_126,or(X_4,X_126))),
inference(subst,[],[refute_0_24:[bind(X_3,$fot(X_126))]]) ).
cnf(refute_0_30,plain,
theorem(implies(or(not(X),X_14),or(X_14,not(X)))),
inference(subst,[],[refute_0_15:[bind(X_5,$fot(not(X))),bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_31,plain,
implies(X,X_14) = or(not(X),X_14),
inference(subst,[],[implies_definition:[bind(Y,$fot(X_14))]]) ).
cnf(refute_0_32,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_33,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_34,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(X,X_14) != or(not(X),X_14)
| or(not(X),X_14) = implies(X,X_14) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(implies(X,X_14))),bind(Y0,$fot(or(not(X),X_14)))]]) ).
cnf(refute_0_36,plain,
or(not(X),X_14) = implies(X,X_14),
inference(resolve,[$cnf( $equal(implies(X,X_14),or(not(X),X_14)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
( or(not(X),X_14) != implies(X,X_14)
| ~ theorem(implies(or(not(X),X_14),or(X_14,not(X))))
| theorem(implies(implies(X,X_14),or(X_14,not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(or(not(X),X_14),or(X_14,not(X)))) ),[0,0],$fot(implies(X,X_14))]]) ).
cnf(refute_0_38,plain,
( ~ theorem(implies(or(not(X),X_14),or(X_14,not(X))))
| theorem(implies(implies(X,X_14),or(X_14,not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),X_14),implies(X,X_14)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
theorem(implies(implies(X,X_14),or(X_14,not(X)))),
inference(resolve,[$cnf( theorem(implies(or(not(X),X_14),or(X_14,not(X)))) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ theorem(implies(X,X_14))
| ~ theorem(implies(implies(X,X_14),or(X_14,not(X))))
| theorem(or(X_14,not(X))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(X_14,not(X)))),bind(Y,$fot(implies(X,X_14)))]]) ).
cnf(refute_0_41,plain,
( ~ theorem(implies(X,X_14))
| theorem(or(X_14,not(X))) ),
inference(resolve,[$cnf( theorem(implies(implies(X,X_14),or(X_14,not(X)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ theorem(implies(X_126,or(X_4,X_126)))
| theorem(or(or(X_4,X_126),not(X_126))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(X_126)),bind(X_14,$fot(or(X_4,X_126)))]]) ).
cnf(refute_0_43,plain,
theorem(or(or(X_4,X_126),not(X_126))),
inference(resolve,[$cnf( theorem(implies(X_126,or(X_4,X_126))) )],[refute_0_29,refute_0_42]) ).
cnf(refute_0_44,plain,
theorem(or(or(X_130,X_129),not(X_129))),
inference(subst,[],[refute_0_43:[bind(X_126,$fot(X_129)),bind(X_4,$fot(X_130))]]) ).
cnf(refute_0_45,plain,
theorem(or(X_4,or(or(X_130,X_129),not(X_129)))),
inference(resolve,[$cnf( theorem(or(or(X_130,X_129),not(X_129))) )],[refute_0_44,refute_0_28]) ).
cnf(refute_0_46,plain,
theorem(or(X_444,or(or(X_130,X_129),not(X_129)))),
inference(subst,[],[refute_0_45:[bind(X_4,$fot(X_444))]]) ).
cnf(refute_0_47,plain,
( ~ theorem(or(X_444,or(or(X_130,X_129),not(X_129))))
| theorem(or(or(X_130,X_129),or(X_444,not(X_129)))) ),
inference(subst,[],[refute_0_11:[bind(X_78,$fot(X_444)),bind(X_79,$fot(or(X_130,X_129))),bind(X_80,$fot(not(X_129)))]]) ).
cnf(refute_0_48,plain,
theorem(or(or(X_130,X_129),or(X_444,not(X_129)))),
inference(resolve,[$cnf( theorem(or(X_444,or(or(X_130,X_129),not(X_129)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
theorem(or(or(X_457,X_456),or(X_458,not(X_456)))),
inference(subst,[],[refute_0_48:[bind(X_129,$fot(X_456)),bind(X_130,$fot(X_457)),bind(X_444,$fot(X_458))]]) ).
cnf(refute_0_50,plain,
theorem(or(or(X_458,not(X_456)),or(X_457,X_456))),
inference(resolve,[$cnf( theorem(or(or(X_457,X_456),or(X_458,not(X_456)))) )],[refute_0_49,refute_0_21]) ).
cnf(refute_0_51,plain,
theorem(or(or(X_463,not(X_461)),or(X_462,X_461))),
inference(subst,[],[refute_0_50:[bind(X_456,$fot(X_461)),bind(X_457,$fot(X_462)),bind(X_458,$fot(X_463))]]) ).
cnf(refute_0_52,plain,
theorem(or(X_462,or(or(X_463,not(X_461)),X_461))),
inference(resolve,[$cnf( theorem(or(or(X_463,not(X_461)),or(X_462,X_461))) )],[refute_0_51,refute_0_20]) ).
cnf(refute_0_53,plain,
theorem(or(or(or(X_657,not(X_655)),X_655),or(or(X_657,not(X_655)),X_655))),
inference(subst,[],[refute_0_52:[bind(X_461,$fot(X_655)),bind(X_462,$fot(or(or(X_657,not(X_655)),X_655))),bind(X_463,$fot(X_657))]]) ).
cnf(refute_0_54,plain,
theorem(or(or(X_657,not(X_655)),X_655)),
inference(resolve,[$cnf( theorem(or(or(or(X_657,not(X_655)),X_655),or(or(X_657,not(X_655)),X_655))) )],[refute_0_53,refute_0_19]) ).
cnf(refute_0_55,plain,
theorem(or(or(X_659,not(X_658)),X_658)),
inference(subst,[],[refute_0_54:[bind(X_655,$fot(X_658)),bind(X_657,$fot(X_659))]]) ).
cnf(refute_0_56,plain,
theorem(or(X_658,or(X_659,not(X_658)))),
inference(resolve,[$cnf( theorem(or(or(X_659,not(X_658)),X_658)) )],[refute_0_55,refute_0_18]) ).
cnf(refute_0_57,plain,
theorem(or(X_660,or(X_661,not(X_660)))),
inference(subst,[],[refute_0_56:[bind(X_658,$fot(X_660)),bind(X_659,$fot(X_661))]]) ).
cnf(refute_0_58,plain,
theorem(or(X_661,or(X_660,not(X_660)))),
inference(resolve,[$cnf( theorem(or(X_660,or(X_661,not(X_660)))) )],[refute_0_57,refute_0_12]) ).
cnf(refute_0_59,plain,
theorem(or(or(X_662,not(X_662)),or(X_662,not(X_662)))),
inference(subst,[],[refute_0_58:[bind(X_660,$fot(X_662)),bind(X_661,$fot(or(X_662,not(X_662))))]]) ).
cnf(refute_0_60,plain,
theorem(or(X_662,not(X_662))),
inference(resolve,[$cnf( theorem(or(or(X_662,not(X_662)),or(X_662,not(X_662)))) )],[refute_0_59,refute_0_5]) ).
cnf(refute_0_61,plain,
theorem(or(not(X),not(not(X)))),
inference(subst,[],[refute_0_60:[bind(X_662,$fot(not(X)))]]) ).
cnf(refute_0_62,plain,
implies(X,not(not(X))) = or(not(X),not(not(X))),
inference(subst,[],[implies_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_63,plain,
( implies(X,not(not(X))) != or(not(X),not(not(X)))
| or(not(X),not(not(X))) = implies(X,not(not(X))) ),
inference(subst,[],[refute_0_34:[bind(X0,$fot(implies(X,not(not(X))))),bind(Y0,$fot(or(not(X),not(not(X)))))]]) ).
cnf(refute_0_64,plain,
or(not(X),not(not(X))) = implies(X,not(not(X))),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),or(not(X),not(not(X)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( or(not(X),not(not(X))) != implies(X,not(not(X)))
| ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( theorem(or(not(X),not(not(X)))) ),[0],$fot(implies(X,not(not(X))))]]) ).
cnf(refute_0_66,plain,
( ~ theorem(or(not(X),not(not(X))))
| theorem(implies(X,not(not(X)))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(not(X))),implies(X,not(not(X)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(implies(X,not(not(X)))),
inference(resolve,[$cnf( theorem(or(not(X),not(not(X)))) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
theorem(implies(p,not(not(p)))),
inference(subst,[],[refute_0_67:[bind(X,$fot(p))]]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( theorem(implies(p,not(not(p)))) )],[refute_0_68,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL178-3 : TPTP v8.1.0. Released v2.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 12:52:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------