TSTP Solution File: LAT274-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 06:01:57 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 15
% Syntax : Number of clauses : 114 ( 15 unt; 72 nHn; 78 RR)
% Number of literals : 341 ( 19 equ; 102 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 129 ( 28 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_lessequals(V_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| V_S = c_emptyset ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| V_S = c_emptyset ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2,axiom,
( ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| V_S = c_emptyset ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3,axiom,
( ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| V_S = c_emptyset ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_in(V_x,V_S,T_a)
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ) ).
cnf(cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0,axiom,
( ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a) ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_y,V_S,t_a)
| c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a) ) ).
cnf(cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a)
| ~ c_in(V_z,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_b,v_A,t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) ).
cnf(cls_conjecture_3,negated_conjecture,
v_S != c_emptyset ).
cnf(cls_conjecture_4,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,V_a,v_b,t_a),t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0:[bind(T_a,$fot(t_a)),bind(V_b,$fot(v_b)),bind(V_r,$fot(v_r)),bind(V_x,$fot(v_L))]]) ).
cnf(refute_0_1,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,V_L,t_a)
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| c_in(c_Pair(V_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_1:[bind(V_S,$fot(v_S)),bind(V_z,$fot(v_b))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(X_29,v_S,t_a)
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(X_29,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Ab1_J_A_58_Ar_A_61_61_ATrue_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_a,$fot(v_a)),bind(V_b,$fot(v_b)),bind(V_r,$fot(v_r)),bind(V_x,$fot(X_29))]]) ).
cnf(refute_0_3,plain,
( ~ c_in(X_29,v_S,t_a)
| c_in(c_Pair(X_29,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_3:[bind(X_29,$fot(v_sko__4mi(v_S,v_r,v_b)))]]) ).
cnf(refute_0_5,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(X_14,v_A,t_a)
| c_in(c_Pair(v_L,X_14,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,X_14),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Az1_A_58_AA_59_AALL_Ay_58S1_O_A_Iy_M_Az1_J_A_58_Ar_A_124_93_A_61_61_62_A_IL1_M_Az1_J_A_58_Ar_A_61_61_ATrue_0:[bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S)),bind(V_z,$fot(X_14))]]) ).
cnf(refute_0_6,plain,
( ~ c_in(X_14,v_A,t_a)
| c_in(c_Pair(v_L,X_14,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,X_14),v_S,t_a) ),
inference(resolve,[$cnf( c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )],[cls_conjecture_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ c_in(v_b,v_A,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_6:[bind(X_14,$fot(v_b))]]) ).
cnf(refute_0_8,plain,
( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_b,v_A,t_a) )],[cls_conjecture_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,V_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_9:[bind(V_a,$fot(v_a))]]) ).
cnf(refute_0_11,plain,
( ~ c_in(X_22,v_S,t_a)
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_a,X_22,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_Ainterval_Ar_Aa1_Ab1_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ia1_M_Ax1_J_A_58_Ar_A_61_61_ATrue_0:[bind(T_a,$fot(t_a)),bind(V_S,$fot(v_S)),bind(V_a,$fot(v_a)),bind(V_b,$fot(v_b)),bind(V_r,$fot(v_r)),bind(V_x,$fot(X_22))]]) ).
cnf(refute_0_12,plain,
( ~ c_in(X_22,v_S,t_a)
| c_in(c_Pair(v_a,X_22,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_12:[bind(X_22,$fot(v_sko__4mj(v_S,v_a,v_r)))]]) ).
cnf(refute_0_14,plain,
( ~ c_in(c_Pair(X_70,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,X_70,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_9:[bind(V_a,$fot(X_70))]]) ).
cnf(refute_0_15,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| ~ c_in(X_5,v_S,t_a)
| c_in(c_Pair(X_5,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AisLub_AS1_Acl_AL1_59_Ay1_A_58_AS1_A_124_93_A_61_61_62_A_Iy1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0:[bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S)),bind(V_y,$fot(X_5))]]) ).
cnf(refute_0_16,plain,
( ~ c_in(X_5,v_S,t_a)
| c_in(c_Pair(X_5,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )],[cls_conjecture_4,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_16:[bind(X_5,$fot(v_sko__4mk(v_L,v_S,v_r)))]]) ).
cnf(refute_0_18,plain,
( ~ c_in(c_Pair(X_39,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,X_39,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_9:[bind(V_a,$fot(X_39))]]) ).
cnf(refute_0_19,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(X_37,X_35,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_37,v_r),v_S,t_a)
| c_in(v_sko__4mk(X_35,v_S,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_0:[bind(V_A,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a))),bind(V_L,$fot(X_35)),bind(V_S,$fot(v_S)),bind(V_a,$fot(X_37))]]) ).
cnf(refute_0_20,plain,
( v_S = c_emptyset
| c_in(c_Pair(X_37,X_35,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_37,v_r),v_S,t_a)
| c_in(v_sko__4mk(X_35,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_19]) ).
cnf(refute_0_21,plain,
( c_in(c_Pair(X_37,X_35,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_37,v_r),v_S,t_a)
| c_in(v_sko__4mk(X_35,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_20,cls_conjecture_3]) ).
cnf(refute_0_22,plain,
( c_in(c_Pair(X_39,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_21:[bind(X_35,$fot(v_L)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_23,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X_39,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(X_39,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_23:[bind(X_39,$fot(v_a))]]) ).
cnf(refute_0_25,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_24,cls_conjecture_6]) ).
cnf(refute_0_26,plain,
( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) )],[refute_0_25,refute_0_17]) ).
cnf(refute_0_27,plain,
( ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_64,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(X_67,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_67,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1:[bind(V_A,$fot(X_64)),bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S)),bind(V_a,$fot(X_67))]]) ).
cnf(refute_0_28,plain,
( ~ c_lessequals(v_S,X_64,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(X_67,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_67,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ c_lessequals(v_S,X_64,tc_set(t_a))
| c_in(c_Pair(X_67,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_67,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_28,cls_conjecture_3]) ).
cnf(refute_0_30,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(X_69,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_69,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_29:[bind(X_64,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a))),bind(X_67,$fot(X_69))]]) ).
cnf(refute_0_31,plain,
( c_in(c_Pair(X_69,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_69,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_30]) ).
cnf(refute_0_32,plain,
( c_in(c_Pair(X_70,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_70,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_31:[bind(X_69,$fot(X_70))]]) ).
cnf(refute_0_33,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X_70,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,X_70,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(X_70,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_32,refute_0_14]) ).
cnf(refute_0_34,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_33:[bind(X_70,$fot(v_a))]]) ).
cnf(refute_0_35,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_34,cls_conjecture_6]) ).
cnf(refute_0_36,plain,
( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) )],[refute_0_35,refute_0_13]) ).
cnf(refute_0_37,plain,
( ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_86,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(v_a,X_87,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X_87,v_S,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2:[bind(V_A,$fot(X_86)),bind(V_L,$fot(X_87)),bind(V_S,$fot(v_S)),bind(V_a,$fot(v_a))]]) ).
cnf(refute_0_38,plain,
( ~ c_lessequals(v_S,X_86,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(v_a,X_87,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(X_87,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ c_lessequals(v_S,X_86,tc_set(t_a))
| c_in(c_Pair(v_a,X_87,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(X_87,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_38,cls_conjecture_3]) ).
cnf(refute_0_40,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_a,X_91,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(X_91,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_39:[bind(X_86,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a))),bind(X_87,$fot(X_91))]]) ).
cnf(refute_0_41,plain,
( c_in(c_Pair(v_a,X_91,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(X_91,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_40]) ).
cnf(refute_0_42,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_41:[bind(X_91,$fot(v_L))]]) ).
cnf(refute_0_43,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_42,refute_0_10]) ).
cnf(refute_0_44,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_43,cls_conjecture_6]) ).
cnf(refute_0_45,plain,
( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) )],[refute_0_44,refute_0_17]) ).
cnf(refute_0_46,plain,
( ~ c_in(c_Pair(X_115,v_sko__4mj(v_S,X_115,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_112,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(X_115,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3:[bind(V_A,$fot(X_112)),bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S)),bind(V_a,$fot(X_115))]]) ).
cnf(refute_0_47,plain,
( ~ c_in(c_Pair(X_115,v_sko__4mj(v_S,X_115,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_112,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(X_115,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ c_in(c_Pair(X_115,v_sko__4mj(v_S,X_115,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_112,tc_set(t_a))
| c_in(c_Pair(X_115,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_47,cls_conjecture_3]) ).
cnf(refute_0_49,plain,
( ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_116,tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_48:[bind(X_112,$fot(X_116)),bind(X_115,$fot(v_a))]]) ).
cnf(refute_0_50,plain,
( ~ c_lessequals(v_S,X_116,tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_36,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(subst,[],[refute_0_50:[bind(X_116,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a)))]]) ).
cnf(refute_0_52,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_51]) ).
cnf(refute_0_53,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_52,refute_0_10]) ).
cnf(refute_0_54,plain,
c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_53,cls_conjecture_6]) ).
cnf(refute_0_55,plain,
c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) )],[refute_0_54,refute_0_4]) ).
cnf(refute_0_56,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,V_L,t_a)
| ~ c_in(v_b,v_A,t_a)
| c_in(c_Pair(V_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_55,refute_0_1]) ).
cnf(refute_0_57,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,V_L,t_a)
| c_in(c_Pair(V_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(v_b,v_A,t_a) )],[cls_conjecture_1,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ c_Tarski_OisLub(v_S,v_cl,v_L,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_57:[bind(V_L,$fot(v_L))]]) ).
cnf(refute_0_59,plain,
c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_Tarski_OisLub(v_S,v_cl,v_L,t_a) )],[cls_conjecture_4,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,V_a,v_b,t_a),t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_59,refute_0_0]) ).
cnf(refute_0_61,plain,
( ~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) ),
inference(subst,[],[refute_0_60:[bind(V_a,$fot(v_a))]]) ).
cnf(refute_0_62,plain,
( ~ c_in(c_Pair(X_163,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,X_163,v_b,t_a),t_a) ),
inference(subst,[],[refute_0_60:[bind(V_a,$fot(X_163))]]) ).
cnf(refute_0_63,plain,
( ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,V_a,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_1:[bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_64,plain,
( ~ c_in(c_Pair(X_38,V_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X_39,X_38,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(X_38,c_Tarski_Ointerval(v_r,X_39,V_b,t_a),t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_A_Ia1_M_Ax1_J_A_58_Ar_59_A_Ix1_M_Ab1_J_A_58_Ar_A_124_93_A_61_61_62_Ax1_A_58_Ainterval_Ar_Aa1_Ab1_A_61_61_ATrue_0:[bind(T_a,$fot(t_a)),bind(V_a,$fot(X_39)),bind(V_r,$fot(v_r)),bind(V_x,$fot(X_38))]]) ).
cnf(refute_0_65,plain,
( c_in(c_Pair(X_39,X_38,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(X_38,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_21:[bind(X_35,$fot(X_38)),bind(X_37,$fot(X_39))]]) ).
cnf(refute_0_66,plain,
( ~ c_in(c_Pair(X_38,V_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(X_38,c_Tarski_Ointerval(v_r,X_39,V_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(X_38,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(X_39,X_38,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
( ~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_L,c_Tarski_Ointerval(v_r,X_39,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_66:[bind(V_b,$fot(v_b)),bind(X_38,$fot(v_L))]]) ).
cnf(refute_0_68,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X_39,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,X_39,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_59,refute_0_67]) ).
cnf(refute_0_69,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_68:[bind(X_39,$fot(v_a))]]) ).
cnf(refute_0_70,plain,
( c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_69,cls_conjecture_6]) ).
cnf(refute_0_71,plain,
( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) )],[refute_0_70,refute_0_17]) ).
cnf(refute_0_72,plain,
( ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,V_a,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_71,refute_0_63]) ).
cnf(refute_0_73,plain,
( ~ c_lessequals(v_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,V_a,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_72,cls_conjecture_3]) ).
cnf(refute_0_74,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(X_162,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_162,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_73:[bind(V_A,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a))),bind(V_a,$fot(X_162))]]) ).
cnf(refute_0_75,plain,
( c_in(c_Pair(X_162,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_162,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_74]) ).
cnf(refute_0_76,plain,
( c_in(c_Pair(X_163,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mj(v_S,X_163,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_75:[bind(X_162,$fot(X_163))]]) ).
cnf(refute_0_77,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,X_163,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,X_163,v_r),v_S,t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(X_163,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_76,refute_0_62]) ).
cnf(refute_0_78,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_77:[bind(X_163,$fot(v_a))]]) ).
cnf(refute_0_79,plain,
c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_78,cls_conjecture_6]) ).
cnf(refute_0_80,plain,
c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) )],[refute_0_79,refute_0_13]) ).
cnf(refute_0_81,plain,
( ~ c_in(c_Pair(V_a,v_sko__4mj(v_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_3:[bind(V_L,$fot(v_L)),bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_82,plain,
( ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(v_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(V_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AS1_A_126_61_A_123_125_59_AALL_Ax_58S1_O_A_Ia1_M_Ax_J_A_58_Ar_59_AALL_Ay_58S1_O_A_Iy_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ia1_M_AL1_J_A_58_Ar_A_61_61_ATrue_2:[bind(V_S,$fot(v_S)),bind(V_a,$fot(v_a))]]) ).
cnf(refute_0_83,plain,
( ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(v_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(V_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ c_lessequals(v_S,V_A,tc_set(t_a))
| c_in(c_Pair(v_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(V_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_83,cls_conjecture_3]) ).
cnf(refute_0_85,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_a,X_180,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X_180,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_84:[bind(V_A,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a))),bind(V_L,$fot(X_180))]]) ).
cnf(refute_0_86,plain,
( c_in(c_Pair(v_a,X_180,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(X_180,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_85]) ).
cnf(refute_0_87,plain,
( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_86:[bind(X_180,$fot(v_L))]]) ).
cnf(refute_0_88,plain,
( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a)
| c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_87,refute_0_61]) ).
cnf(refute_0_89,plain,
c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a),
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_88,cls_conjecture_6]) ).
cnf(refute_0_90,plain,
c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) )],[refute_0_89,refute_0_17]) ).
cnf(refute_0_91,plain,
( ~ c_in(c_Pair(V_a,v_sko__4mj(v_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,V_A,tc_set(t_a))
| v_S = c_emptyset
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_90,refute_0_81]) ).
cnf(refute_0_92,plain,
( ~ c_in(c_Pair(V_a,v_sko__4mj(v_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,V_A,tc_set(t_a))
| c_in(c_Pair(V_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(v_S,c_emptyset) )],[refute_0_91,cls_conjecture_3]) ).
cnf(refute_0_93,plain,
( ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X_225,tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_92:[bind(V_A,$fot(X_225)),bind(V_a,$fot(v_a))]]) ).
cnf(refute_0_94,plain,
( ~ c_lessequals(v_S,X_225,tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_80,refute_0_93]) ).
cnf(refute_0_95,plain,
( ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a))
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_94:[bind(X_225,$fot(c_Tarski_Ointerval(v_r,v_a,v_b,t_a)))]]) ).
cnf(refute_0_96,plain,
c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)) )],[cls_conjecture_2,refute_0_95]) ).
cnf(refute_0_97,plain,
c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(resolve,[$cnf( c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_96,refute_0_61]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a) )],[refute_0_97,cls_conjecture_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT274-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 30 05:35:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.50
%------------------------------------------------------------------------------