%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL217-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:42:14 PM UTC 2026
% Result : Unsatisfiable 183.32s 183.68s
% Output : CNFRefutation 183.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 9
% Syntax : Number of clauses : 83 ( 46 unt; 0 nHn; 35 RR)
% Number of literals : 130 ( 0 equ; 48 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 186 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_2,axiom,
axiom(or(not(or(A,A)),A)) ).
cnf(axiom_1_3,axiom,
axiom(or(not(A),or(B,A))) ).
cnf(axiom_1_4,axiom,
axiom(or(not(or(A,B)),or(B,A))) ).
cnf(axiom_1_5,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) ).
cnf(axiom_1_6,axiom,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(rule_2,axiom,
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ) ).
cnf(rule_3,axiom,
( theorem(or(not(X),Z))
| ~ axiom(or(not(X),Y))
| ~ theorem(or(not(Y),Z)) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(or(not(or(not(p),q)),or(not(or(not(p),not(q))),not(p)))) ).
cnf(refute_0_0,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(not(or(B,A)),X_609))
| theorem(or(not(or(A,B)),X_609)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_609))]]) ).
cnf(refute_0_1,plain,
( ~ theorem(or(not(or(B,A)),X_609))
| theorem(or(not(or(A,B)),X_609)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ theorem(or(not(or(X_144130,X_144131)),or(not(or(X_144131,not(X_144130))),X_144131)))
| theorem(or(not(or(X_144131,X_144130)),or(not(or(X_144131,not(X_144130))),X_144131))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_144131)),bind(B,$fot(X_144130)),bind(X_609,$fot(or(not(or(X_144131,not(X_144130))),X_144131)))]]) ).
cnf(refute_0_3,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).
cnf(refute_0_4,plain,
( ~ theorem(or(A,or(B,C)))
| theorem(or(B,or(A,C))) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ theorem(or(not(or(X_144127,not(X_144126))),or(not(or(X_144126,X_144127)),X_144127)))
| theorem(or(not(or(X_144126,X_144127)),or(not(or(X_144127,not(X_144126))),X_144127))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(not(or(X_144127,not(X_144126))))),bind(B,$fot(not(or(X_144126,X_144127)))),bind(C,$fot(X_144127))]]) ).
cnf(refute_0_6,plain,
( ~ theorem(or(not(or(not(X_96873),X_96874)),or(not(or(X_96873,X_96874)),X_96874)))
| theorem(or(not(or(X_96874,not(X_96873))),or(not(or(X_96873,X_96874)),X_96874))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_96874)),bind(B,$fot(not(X_96873))),bind(X_609,$fot(or(not(or(X_96873,X_96874)),X_96874)))]]) ).
cnf(refute_0_7,plain,
axiom(or(not(X_607),or(B,X_607))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_607))]]) ).
cnf(refute_0_8,plain,
( ~ axiom(or(not(X_607),or(B,X_607)))
| ~ theorem(or(not(or(B,X_607)),X_609))
| theorem(or(not(X_607),X_609)) ),
inference(subst,[],[rule_3:[bind(X,$fot(X_607)),bind(Y,$fot(or(B,X_607))),bind(Z,$fot(X_609))]]) ).
cnf(refute_0_9,plain,
( ~ theorem(or(not(or(B,X_607)),X_609))
| theorem(or(not(X_607),X_609)) ),
inference(resolve,[$cnf( axiom(or(not(X_607),or(B,X_607))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ theorem(or(not(or(X_96872,or(not(X_96871),X_96872))),or(not(or(X_96871,X_96872)),X_96872)))
| theorem(or(not(or(not(X_96871),X_96872)),or(not(or(X_96871,X_96872)),X_96872))) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_96872)),bind(X_607,$fot(or(not(X_96871),X_96872))),bind(X_609,$fot(or(not(or(X_96871,X_96872)),X_96872)))]]) ).
cnf(refute_0_11,plain,
( ~ axiom(or(not(or(A,or(B,C))),or(B,or(A,C))))
| ~ theorem(or(not(or(B,or(A,C))),X_609))
| theorem(or(not(or(A,or(B,C))),X_609)) ),
inference(subst,[],[rule_3:[bind(X,$fot(or(A,or(B,C)))),bind(Y,$fot(or(B,or(A,C)))),bind(Z,$fot(X_609))]]) ).
cnf(refute_0_12,plain,
( ~ theorem(or(not(or(B,or(A,C))),X_609))
| theorem(or(not(or(A,or(B,C))),X_609)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) )],[axiom_1_5,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ theorem(or(not(or(not(X_92036),or(X_92037,X_92037))),or(not(or(X_92036,X_92037)),X_92037)))
| theorem(or(not(or(X_92037,or(not(X_92036),X_92037))),or(not(or(X_92036,X_92037)),X_92037))) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(X_92037)),bind(B,$fot(not(X_92036))),bind(C,$fot(X_92037)),bind(X_609,$fot(or(not(or(X_92036,X_92037)),X_92037)))]]) ).
cnf(refute_0_14,plain,
( ~ theorem(or(not(or(X_92034,X_92035)),or(not(or(not(X_92034),or(X_92035,X_92035))),X_92035)))
| theorem(or(not(or(not(X_92034),or(X_92035,X_92035))),or(not(or(X_92034,X_92035)),X_92035))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(not(or(X_92034,X_92035)))),bind(B,$fot(not(or(not(X_92034),or(X_92035,X_92035))))),bind(C,$fot(X_92035))]]) ).
cnf(refute_0_15,plain,
( ~ theorem(or(not(or(not(or(not(X_92032),or(X_92033,X_92033))),or(X_92032,X_92033))),or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033)))
| theorem(or(not(or(X_92032,X_92033)),or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033))) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(not(or(not(X_92032),or(X_92033,X_92033))))),bind(X_607,$fot(or(X_92032,X_92033))),bind(X_609,$fot(or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033)))]]) ).
cnf(refute_0_16,plain,
( ~ theorem(or(not(or(or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678),X_28677)),or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678)))
| theorem(or(not(or(X_28677,or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))),or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_28677)),bind(B,$fot(or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))),bind(X_609,$fot(or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678)))]]) ).
cnf(refute_0_17,plain,
axiom(or(not(or(X_23,X_23)),X_23)),
inference(subst,[],[axiom_1_2:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_18,plain,
( ~ axiom(or(not(or(X_23,X_23)),X_23))
| ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(subst,[],[rule_2:[bind(X,$fot(X_23)),bind(Y,$fot(or(X_23,X_23)))]]) ).
cnf(refute_0_19,plain,
( ~ theorem(or(X_23,X_23))
| theorem(X_23) ),
inference(resolve,[$cnf( axiom(or(not(or(X_23,X_23)),X_23)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ theorem(or(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676)),or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676))))
| theorem(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676))) ),
inference(subst,[],[refute_0_19:[bind(X_23,$fot(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676))))]]) ).
cnf(refute_0_21,plain,
( ~ theorem(or(X_21369,or(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)),X_21371)))
| theorem(or(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)),or(X_21369,X_21371))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_21369)),bind(B,$fot(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)))),bind(C,$fot(X_21371))]]) ).
cnf(refute_0_22,plain,
axiom(or(not(X_24),or(B,X_24))),
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_23,plain,
( ~ axiom(or(not(X_24),or(B,X_24)))
| ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,X_24))),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_24,plain,
( ~ theorem(X_24)
| theorem(or(B,X_24)) ),
inference(resolve,[$cnf( axiom(or(not(X_24),or(B,X_24))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ theorem(or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787))
| theorem(or(B,or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787))) ),
inference(subst,[],[refute_0_24:[bind(X_24,$fot(or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787)))]]) ).
cnf(refute_0_26,plain,
( ~ axiom(or(not(or(A,B)),or(B,A)))
| ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(B,A))),bind(Y,$fot(or(A,B)))]]) ).
cnf(refute_0_27,plain,
( ~ theorem(or(A,B))
| theorem(or(B,A)) ),
inference(resolve,[$cnf( axiom(or(not(or(A,B)),or(B,A))) )],[axiom_1_4,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ theorem(or(X_13784,or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785))))
| theorem(or(or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785)),X_13784)) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_13784)),bind(B,$fot(or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785))))]]) ).
cnf(refute_0_29,plain,
( ~ theorem(or(not(or(X_6090,X_6089)),or(X_6090,or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091))))
| theorem(or(X_6090,or(not(or(X_6090,X_6089)),or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091)))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(not(or(X_6090,X_6089)))),bind(B,$fot(X_6090)),bind(C,$fot(or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091)))]]) ).
cnf(refute_0_30,plain,
( ~ axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B))))
| ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(subst,[],[rule_2:[bind(X,$fot(or(not(or(C,A)),or(C,B)))),bind(Y,$fot(or(not(A),B)))]]) ).
cnf(refute_0_31,plain,
( ~ theorem(or(not(A),B))
| theorem(or(not(or(C,A)),or(C,B))) ),
inference(resolve,[$cnf( axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))) )],[axiom_1_6,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ theorem(or(not(A),or(not(or(not(A),or(X_701,X_701))),X_701)))
| theorem(or(not(or(C,A)),or(C,or(not(or(not(A),or(X_701,X_701))),X_701)))) ),
inference(subst,[],[refute_0_31:[bind(B,$fot(or(not(or(not(A),or(X_701,X_701))),X_701)))]]) ).
cnf(refute_0_33,plain,
( ~ theorem(or(not(or(X_692,or(X_691,X_691))),or(X_692,X_691)))
| theorem(or(X_692,or(not(or(X_692,or(X_691,X_691))),X_691))) ),
inference(subst,[],[refute_0_4:[bind(A,$fot(not(or(X_692,or(X_691,X_691))))),bind(B,$fot(X_692)),bind(C,$fot(X_691))]]) ).
cnf(refute_0_34,plain,
( ~ axiom(or(not(or(A,A)),A))
| theorem(or(not(or(A,A)),A)) ),
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_35,plain,
theorem(or(not(or(A,A)),A)),
inference(resolve,[$cnf( axiom(or(not(or(A,A)),A)) )],[axiom_1_2,refute_0_34]) ).
cnf(refute_0_36,plain,
theorem(or(not(or(X_687,X_687)),X_687)),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_687))]]) ).
cnf(refute_0_37,plain,
( ~ theorem(or(not(or(X_687,X_687)),X_687))
| theorem(or(not(or(X_688,or(X_687,X_687))),or(X_688,X_687))) ),
inference(subst,[],[refute_0_31:[bind(A,$fot(or(X_687,X_687))),bind(B,$fot(X_687)),bind(C,$fot(X_688))]]) ).
cnf(refute_0_38,plain,
theorem(or(not(or(X_688,or(X_687,X_687))),or(X_688,X_687))),
inference(resolve,[$cnf( theorem(or(not(or(X_687,X_687)),X_687)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
theorem(or(not(or(X_692,or(X_691,X_691))),or(X_692,X_691))),
inference(subst,[],[refute_0_38:[bind(X_687,$fot(X_691)),bind(X_688,$fot(X_692))]]) ).
cnf(refute_0_40,plain,
theorem(or(X_692,or(not(or(X_692,or(X_691,X_691))),X_691))),
inference(resolve,[$cnf( theorem(or(not(or(X_692,or(X_691,X_691))),or(X_692,X_691))) )],[refute_0_39,refute_0_33]) ).
cnf(refute_0_41,plain,
theorem(or(not(A),or(not(or(not(A),or(X_701,X_701))),X_701))),
inference(subst,[],[refute_0_40:[bind(X_691,$fot(X_701)),bind(X_692,$fot(not(A)))]]) ).
cnf(refute_0_42,plain,
theorem(or(not(or(C,A)),or(C,or(not(or(not(A),or(X_701,X_701))),X_701)))),
inference(resolve,[$cnf( theorem(or(not(A),or(not(or(not(A),or(X_701,X_701))),X_701))) )],[refute_0_41,refute_0_32]) ).
cnf(refute_0_43,plain,
theorem(or(not(or(X_6090,X_6089)),or(X_6090,or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091)))),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_6089)),bind(C,$fot(X_6090)),bind(X_701,$fot(X_6091))]]) ).
cnf(refute_0_44,plain,
theorem(or(X_6090,or(not(or(X_6090,X_6089)),or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091)))),
inference(resolve,[$cnf( theorem(or(not(or(X_6090,X_6089)),or(X_6090,or(not(or(not(X_6089),or(X_6091,X_6091))),X_6091)))) )],[refute_0_43,refute_0_29]) ).
cnf(refute_0_45,plain,
theorem(or(X_13784,or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785)))),
inference(subst,[],[refute_0_44:[bind(X_6089,$fot(X_13783)),bind(X_6090,$fot(X_13784)),bind(X_6091,$fot(X_13785))]]) ).
cnf(refute_0_46,plain,
theorem(or(or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785)),X_13784)),
inference(resolve,[$cnf( theorem(or(X_13784,or(not(or(X_13784,X_13783)),or(not(or(not(X_13783),or(X_13785,X_13785))),X_13785)))) )],[refute_0_45,refute_0_28]) ).
cnf(refute_0_47,plain,
theorem(or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787)),
inference(subst,[],[refute_0_46:[bind(X_13783,$fot(X_13786)),bind(X_13784,$fot(X_13787)),bind(X_13785,$fot(X_13788))]]) ).
cnf(refute_0_48,plain,
theorem(or(B,or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787))),
inference(resolve,[$cnf( theorem(or(or(not(or(X_13787,X_13786)),or(not(or(not(X_13786),or(X_13788,X_13788))),X_13788)),X_13787)) )],[refute_0_47,refute_0_25]) ).
cnf(refute_0_49,plain,
theorem(or(X_21369,or(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)),X_21371))),
inference(subst,[],[refute_0_48:[bind(B,$fot(X_21369)),bind(X_13786,$fot(X_21370)),bind(X_13787,$fot(X_21371)),bind(X_13788,$fot(X_21372))]]) ).
cnf(refute_0_50,plain,
theorem(or(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)),or(X_21369,X_21371))),
inference(resolve,[$cnf( theorem(or(X_21369,or(or(not(or(X_21371,X_21370)),or(not(or(not(X_21370),or(X_21372,X_21372))),X_21372)),X_21371))) )],[refute_0_49,refute_0_21]) ).
cnf(refute_0_51,plain,
theorem(or(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676)),or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676)))),
inference(subst,[],[refute_0_50:[bind(X_21369,$fot(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)))),bind(X_21370,$fot(X_28674)),bind(X_21371,$fot(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676))),bind(X_21372,$fot(X_28676))]]) ).
cnf(refute_0_52,plain,
theorem(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676))),
inference(resolve,[$cnf( theorem(or(or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676)),or(not(or(or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676),X_28674)),or(not(or(not(X_28674),or(X_28676,X_28676))),X_28676)))) )],[refute_0_51,refute_0_20]) ).
cnf(refute_0_53,plain,
theorem(or(not(or(or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678),X_28677)),or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))),
inference(subst,[],[refute_0_52:[bind(X_28674,$fot(X_28677)),bind(X_28676,$fot(X_28678))]]) ).
cnf(refute_0_54,plain,
theorem(or(not(or(X_28677,or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))),or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))),
inference(resolve,[$cnf( theorem(or(not(or(or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678),X_28677)),or(not(or(not(X_28677),or(X_28678,X_28678))),X_28678))) )],[refute_0_53,refute_0_16]) ).
cnf(refute_0_55,plain,
theorem(or(not(or(X_91472,or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))),or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))),
inference(subst,[],[refute_0_54:[bind(X_28677,$fot(X_91472)),bind(X_28678,$fot(X_91473))]]) ).
cnf(refute_0_56,plain,
( ~ theorem(or(not(or(X_91472,or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))),or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473)))
| theorem(or(not(or(not(or(not(X_91472),or(X_91473,X_91473))),or(X_91472,X_91473))),or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(not(or(not(X_91472),or(X_91473,X_91473))))),bind(B,$fot(X_91472)),bind(C,$fot(X_91473)),bind(X_609,$fot(or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473)))]]) ).
cnf(refute_0_57,plain,
theorem(or(not(or(not(or(not(X_91472),or(X_91473,X_91473))),or(X_91472,X_91473))),or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))),
inference(resolve,[$cnf( theorem(or(not(or(X_91472,or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))),or(not(or(not(X_91472),or(X_91473,X_91473))),X_91473))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
theorem(or(not(or(not(or(not(X_92032),or(X_92033,X_92033))),or(X_92032,X_92033))),or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033))),
inference(subst,[],[refute_0_57:[bind(X_91472,$fot(X_92032)),bind(X_91473,$fot(X_92033))]]) ).
cnf(refute_0_59,plain,
theorem(or(not(or(X_92032,X_92033)),or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033))),
inference(resolve,[$cnf( theorem(or(not(or(not(or(not(X_92032),or(X_92033,X_92033))),or(X_92032,X_92033))),or(not(or(not(X_92032),or(X_92033,X_92033))),X_92033))) )],[refute_0_58,refute_0_15]) ).
cnf(refute_0_60,plain,
theorem(or(not(or(X_92034,X_92035)),or(not(or(not(X_92034),or(X_92035,X_92035))),X_92035))),
inference(subst,[],[refute_0_59:[bind(X_92032,$fot(X_92034)),bind(X_92033,$fot(X_92035))]]) ).
cnf(refute_0_61,plain,
theorem(or(not(or(not(X_92034),or(X_92035,X_92035))),or(not(or(X_92034,X_92035)),X_92035))),
inference(resolve,[$cnf( theorem(or(not(or(X_92034,X_92035)),or(not(or(not(X_92034),or(X_92035,X_92035))),X_92035))) )],[refute_0_60,refute_0_14]) ).
cnf(refute_0_62,plain,
theorem(or(not(or(not(X_92036),or(X_92037,X_92037))),or(not(or(X_92036,X_92037)),X_92037))),
inference(subst,[],[refute_0_61:[bind(X_92034,$fot(X_92036)),bind(X_92035,$fot(X_92037))]]) ).
cnf(refute_0_63,plain,
theorem(or(not(or(X_92037,or(not(X_92036),X_92037))),or(not(or(X_92036,X_92037)),X_92037))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_92036),or(X_92037,X_92037))),or(not(or(X_92036,X_92037)),X_92037))) )],[refute_0_62,refute_0_13]) ).
cnf(refute_0_64,plain,
theorem(or(not(or(X_96872,or(not(X_96871),X_96872))),or(not(or(X_96871,X_96872)),X_96872))),
inference(subst,[],[refute_0_63:[bind(X_92036,$fot(X_96871)),bind(X_92037,$fot(X_96872))]]) ).
cnf(refute_0_65,plain,
theorem(or(not(or(not(X_96871),X_96872)),or(not(or(X_96871,X_96872)),X_96872))),
inference(resolve,[$cnf( theorem(or(not(or(X_96872,or(not(X_96871),X_96872))),or(not(or(X_96871,X_96872)),X_96872))) )],[refute_0_64,refute_0_10]) ).
cnf(refute_0_66,plain,
theorem(or(not(or(not(X_96873),X_96874)),or(not(or(X_96873,X_96874)),X_96874))),
inference(subst,[],[refute_0_65:[bind(X_96871,$fot(X_96873)),bind(X_96872,$fot(X_96874))]]) ).
cnf(refute_0_67,plain,
theorem(or(not(or(X_96874,not(X_96873))),or(not(or(X_96873,X_96874)),X_96874))),
inference(resolve,[$cnf( theorem(or(not(or(not(X_96873),X_96874)),or(not(or(X_96873,X_96874)),X_96874))) )],[refute_0_66,refute_0_6]) ).
cnf(refute_0_68,plain,
theorem(or(not(or(X_144127,not(X_144126))),or(not(or(X_144126,X_144127)),X_144127))),
inference(subst,[],[refute_0_67:[bind(X_96873,$fot(X_144126)),bind(X_96874,$fot(X_144127))]]) ).
cnf(refute_0_69,plain,
theorem(or(not(or(X_144126,X_144127)),or(not(or(X_144127,not(X_144126))),X_144127))),
inference(resolve,[$cnf( theorem(or(not(or(X_144127,not(X_144126))),or(not(or(X_144126,X_144127)),X_144127))) )],[refute_0_68,refute_0_5]) ).
cnf(refute_0_70,plain,
theorem(or(not(or(X_144130,X_144131)),or(not(or(X_144131,not(X_144130))),X_144131))),
inference(subst,[],[refute_0_69:[bind(X_144126,$fot(X_144130)),bind(X_144127,$fot(X_144131))]]) ).
cnf(refute_0_71,plain,
theorem(or(not(or(X_144131,X_144130)),or(not(or(X_144131,not(X_144130))),X_144131))),
inference(resolve,[$cnf( theorem(or(not(or(X_144130,X_144131)),or(not(or(X_144131,not(X_144130))),X_144131))) )],[refute_0_70,refute_0_2]) ).
cnf(refute_0_72,plain,
theorem(or(not(or(not(p),q)),or(not(or(not(p),not(q))),not(p)))),
inference(subst,[],[refute_0_71:[bind(X_144130,$fot(q)),bind(X_144131,$fot(not(p)))]]) ).
cnf(refute_0_73,plain,
$false,
inference(resolve,[$cnf( theorem(or(not(or(not(p),q)),or(not(or(not(p),not(q))),not(p)))) )],[refute_0_72,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL217-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 5 03:32:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 183.32/183.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 183.32/183.68
% 183.32/183.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 183.42/183.71
%------------------------------------------------------------------------------