%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 03:37:48 EDT 2022
% Result : Unsatisfiable 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 11 unt; 7 nHn; 20 RR)
% Number of literals : 44 ( 13 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 9 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(V_A,V_A,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(cls_conjecture_1,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| V_U = v_m
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ).
cnf(refute_0_0,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_conjecture_5:[bind(V_U,$fot(v_x))]]) ).
cnf(refute_0_1,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) )],[cls_conjecture_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(X_3,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(subst,[],[cls_Zorn_Osucc__trans_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(X_3)),bind(V_x,$fot(c_Zorn_Osucc(v_S,v_m,t_a))),bind(V_y,$fot(v_x))]]) ).
cnf(refute_0_3,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(X_3,v_x,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) )],[cls_conjecture_4,refute_0_2]) ).
cnf(refute_0_4,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(subst,[],[refute_0_3:[bind(X_3,$fot(v_S))]]) ).
cnf(refute_0_5,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_4,cls_conjecture_3]) ).
cnf(refute_0_6,plain,
( v_x = v_m
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
v_x = v_m,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))) )],[refute_0_6,cls_conjecture_2]) ).
cnf(refute_0_8,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_x,t_a),
introduced(tautology,[refl,[$fot(c_Zorn_Osucc(v_S,v_x,t_a))]]) ).
cnf(refute_0_9,plain,
( c_Zorn_Osucc(v_S,v_x,t_a) != c_Zorn_Osucc(v_S,v_x,t_a)
| v_x != v_m
| c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(tautology,[equality,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a)) ),[1,1],$fot(v_m)]]) ).
cnf(refute_0_10,plain,
( v_x != v_m
| c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_x,t_a)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
c_Zorn_Osucc(v_S,v_x,t_a) = c_Zorn_Osucc(v_S,v_m,t_a),
inference(resolve,[$cnf( $equal(v_x,v_m) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( c_Zorn_Osucc(v_S,v_x,t_a) != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),[1],$fot(c_Zorn_Osucc(v_S,v_m,t_a))]]) ).
cnf(refute_0_13,plain,
( ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) ),
inference(resolve,[$cnf( $equal(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_Osucc(v_S,v_m,t_a)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))) )],[refute_0_13,cls_conjecture_3]) ).
cnf(refute_0_15,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,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_m,t_a)))]]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) )],[refute_0_15,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET851-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 18:17:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------