TSTP Solution File: SET853-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET853-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 : Tue Jul 19 03:37:50 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of clauses : 68 ( 13 unt; 46 nHn; 63 RR)
% Number of literals : 207 ( 60 equ; 63 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_x,tc_set(tc_set(t_a)))
| V_U = v_x
| ~ c_lessequals(V_U,v_x,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,tc_set(T_a)) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Osucc__trans_0,axiom,
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ) ).
cnf(refute_0_0,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(V_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_Osucc__trans_0:[bind(T_a,$fot(t_a)),bind(V_x,$fot(c_Zorn_Osucc(v_S,v_xa,t_a))),bind(V_y,$fot(v_x))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_5:[bind(V_U,$fot(v_xa))]]) ).
cnf(refute_0_2,plain,
( ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a)))
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| ~ c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(v_xa)),bind(V_B,$fot(c_Zorn_Osucc(v_S,v_x,t_a)))]]) ).
cnf(refute_0_4,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X_271,t_a) != X_271
| ~ c_in(X_271,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_271,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,X_271,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_2:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(X_271)),bind(V_n,$fot(v_xa))]]) ).
cnf(refute_0_5,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X_271,t_a) != X_271
| ~ c_in(X_271,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_271,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,X_271,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_4]) ).
cnf(refute_0_6,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_5:[bind(X_271,$fot(v_x))]]) ).
cnf(refute_0_7,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ c_in(X_294,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_294,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_294,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_1:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_x)),bind(V_n,$fot(X_294))]]) ).
cnf(refute_0_9,plain,
( ~ c_in(X_294,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(X_294,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_294,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_9:[bind(X_294,$fot(v_xa))]]) ).
cnf(refute_0_11,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) )],[refute_0_11,refute_0_3]) ).
cnf(refute_0_13,plain,
( v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_xa,c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_13,cls_conjecture_3]) ).
cnf(refute_0_15,plain,
( ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_5:[bind(V_U,$fot(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a)))]]) ).
cnf(refute_0_16,plain,
( ~ c_in(X_344,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X_344,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_344,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,X_344,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(X_344)),bind(V_n,$fot(v_xa))]]) ).
cnf(refute_0_17,plain,
( ~ c_in(X_344,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X_344,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X_344,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,X_344,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_17:[bind(X_344,$fot(v_x))]]) ).
cnf(refute_0_19,plain,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[refute_0_19,refute_0_15]) ).
cnf(refute_0_21,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ c_in(X_356,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(X_356,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_356,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_OTFin__linear__lemma1_3:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_m,$fot(v_x)),bind(V_n,$fot(X_356))]]) ).
cnf(refute_0_23,plain,
( ~ c_in(X_356,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(X_356,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_356,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ c_in(X_356,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(X_356,v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X_356,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_0,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_24:[bind(X_356,$fot(v_xa))]]) ).
cnf(refute_0_26,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) )],[refute_0_26,refute_0_3]) ).
cnf(refute_0_28,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_27]) ).
cnf(refute_0_29,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_xa,c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_28,cls_conjecture_3]) ).
cnf(refute_0_30,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) )],[refute_0_29,refute_0_2]) ).
cnf(refute_0_31,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(V_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_30,refute_0_0]) ).
cnf(refute_0_32,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_31:[bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_33,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = v_x ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_32,cls_conjecture_4]) ).
cnf(refute_0_34,plain,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x
| v_x != v_x
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x ),
introduced(tautology,[equality,[$cnf( ~ $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) ),[0],$fot(v_x)]]) ).
cnf(refute_0_35,plain,
( v_x != v_x
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| v_xa = v_x ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( v_x != v_x
| v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x) )],[refute_0_35,refute_0_7]) ).
cnf(refute_0_37,plain,
v_x = v_x,
introduced(tautology,[refl,[$fot(v_x)]]) ).
cnf(refute_0_38,plain,
( v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_x,v_x) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
( ~ c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| v_xa = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))) )],[refute_0_38,refute_0_3]) ).
cnf(refute_0_40,plain,
( v_xa = c_Zorn_Osucc(v_S,v_x,t_a)
| v_xa = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_2,refute_0_39]) ).
cnf(refute_0_41,plain,
( v_xa = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(v_xa,c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_40,cls_conjecture_3]) ).
cnf(refute_0_42,plain,
( v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) )],[refute_0_41,refute_0_2]) ).
cnf(refute_0_43,plain,
( v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(V_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))) )],[refute_0_42,refute_0_0]) ).
cnf(refute_0_44,plain,
( v_xa = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_43:[bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_45,plain,
v_xa = v_x,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_44,cls_conjecture_4]) ).
cnf(refute_0_46,plain,
c_Zorn_Osucc(v_S,v_xa,t_a) = c_Zorn_Osucc(v_S,v_xa,t_a),
introduced(tautology,[refl,[$fot(c_Zorn_Osucc(v_S,v_xa,t_a))]]) ).
cnf(refute_0_47,plain,
( c_Zorn_Osucc(v_S,v_xa,t_a) != c_Zorn_Osucc(v_S,v_xa,t_a)
| v_xa != v_x
| c_Zorn_Osucc(v_S,v_xa,t_a) = c_Zorn_Osucc(v_S,v_x,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_xa,t_a)) ),[1,1],$fot(v_x)]]) ).
cnf(refute_0_48,plain,
( v_xa != v_x
| c_Zorn_Osucc(v_S,v_xa,t_a) = c_Zorn_Osucc(v_S,v_x,t_a) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_xa,t_a)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
c_Zorn_Osucc(v_S,v_xa,t_a) = c_Zorn_Osucc(v_S,v_x,t_a),
inference(resolve,[$cnf( $equal(v_xa,v_x) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( c_Zorn_Osucc(v_S,v_xa,t_a) != c_Zorn_Osucc(v_S,v_x,t_a)
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),[0],$fot(c_Zorn_Osucc(v_S,v_x,t_a))]]) ).
cnf(refute_0_51,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_51,cls_conjecture_4]) ).
cnf(refute_0_53,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(subst,[],[cls_Set_Osubset__refl_0:[bind(T_a,$fot(tc_set(t_a))),bind(V_A,$fot(c_Zorn_Osucc(v_S,v_x,t_a)))]]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_53,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET853-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Sat Jul 9 18:08:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.47
%------------------------------------------------------------------------------