TSTP Solution File: LAT268-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 06:01:53 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 19
% Syntax : Number of clauses : 49 ( 21 unt; 0 nHn; 40 RR)
% Number of literals : 105 ( 32 equ; 57 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_x,v_S,t_a) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(cls_Tarski_OCL_Olub__upper_0,axiom,
( ~ c_in(V_x,V_S,T_a)
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| c_in(c_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ) ).
cnf(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,axiom,
( ~ c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))
| c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)) ) ).
cnf(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ).
cnf(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ).
cnf(cls_Tarski_Oglb__dual__lub_0,axiom,
c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ).
cnf(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ).
cnf(refute_0_0,plain,
( ~ c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0:[bind(T_a,$fot(t_a)),bind(V_cl,$fot(v_cl)),bind(V_x,$fot(v_x)),bind(V_y,$fot(c_Tarski_Oglb(v_S,v_cl,t_a)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(X_12,X_10,X_9)
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_set(X_9))
| c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),
inference(subst,[],[cls_Tarski_OCL_Olub__upper_0:[bind(T_a,$fot(X_9)),bind(V_S,$fot(X_10)),bind(V_cl,$fot(c_Tarski_Odual(V_cl,X_9))),bind(V_x,$fot(X_12))]]) ).
cnf(refute_0_2,plain,
c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit),
inference(subst,[],[cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0:[bind(T_a,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit) != c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit)
| ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit),tc_set(X_9))
| c_lessequals(X_10,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_set(X_9)) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_set(X_9)) ),[1],$fot(c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit))]]) ).
cnf(refute_0_4,plain,
( ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit),tc_set(X_9))
| c_lessequals(X_10,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_set(X_9)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ c_in(X_12,X_10,X_9)
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit),tc_set(X_9))
| c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),
inference(resolve,[$cnf( c_lessequals(X_10,c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_set(X_9)) )],[refute_0_4,refute_0_1]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( c_Tarski_Oglb(V_S,V_cl,T_a) != c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)
| c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) = c_Tarski_Oglb(V_S,V_cl,T_a) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(c_Tarski_Oglb(V_S,V_cl,T_a))),bind(Y,$fot(c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)))]]) ).
cnf(refute_0_10,plain,
c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) = c_Tarski_Oglb(V_S,V_cl,T_a),
inference(resolve,[$cnf( $equal(c_Tarski_Oglb(V_S,V_cl,T_a),c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a)) )],[cls_Tarski_Oglb__dual__lub_0,refute_0_9]) ).
cnf(refute_0_11,plain,
c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9) = c_Tarski_Oglb(X_10,V_cl,X_9),
inference(subst,[],[refute_0_10:[bind(T_a,$fot(X_9)),bind(V_S,$fot(X_10))]]) ).
cnf(refute_0_12,plain,
c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) = c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),
introduced(tautology,[refl,[$fot(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9))]]) ).
cnf(refute_0_13,plain,
( c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) != c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9)
| c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9) != c_Tarski_Oglb(X_10,V_cl,X_9)
| c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) = c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9)) ),[1,1],$fot(c_Tarski_Oglb(X_10,V_cl,X_9))]]) ).
cnf(refute_0_14,plain,
( c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9) != c_Tarski_Oglb(X_10,V_cl,X_9)
| c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) = c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9) ),
inference(resolve,[$cnf( $equal(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) = c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9),
inference(resolve,[$cnf( $equal(c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),c_Tarski_Oglb(X_10,V_cl,X_9)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9) != c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9)
| ~ c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9))
| c_in(c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),
introduced(tautology,[equality,[$cnf( c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),[0],$fot(c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9))]]) ).
cnf(refute_0_17,plain,
( ~ c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9))
| c_in(c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ c_in(X_12,X_10,X_9)
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(V_cl,X_9),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X_9,tc_Product__Type_Ounit))
| ~ c_lessequals(X_10,c_Tarski_Opotype_Opset(V_cl,X_9,tc_Product__Type_Ounit),tc_set(X_9))
| c_in(c_Pair(X_12,c_Tarski_Oglb(X_10,V_cl,X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) ),
inference(resolve,[$cnf( c_in(c_Pair(X_12,c_Tarski_Olub(X_10,c_Tarski_Odual(V_cl,X_9),X_9),X_9,X_9),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,X_9),X_9,tc_Product__Type_Ounit),tc_prod(X_9,X_9)) )],[refute_0_5,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ c_in(X_17,X_16,t_a)
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(X_16,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| c_in(c_Pair(X_17,c_Tarski_Oglb(X_16,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_18:[bind(V_cl,$fot(v_cl)),bind(X_10,$fot(X_16)),bind(X_12,$fot(X_17)),bind(X_9,$fot(t_a))]]) ).
cnf(refute_0_20,plain,
( v_A != c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A ),
inference(subst,[],[refute_0_8:[bind(X,$fot(v_A)),bind(Y,$fot(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_21,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(resolve,[$cnf( $equal(v_A,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_OA_A_61_61_Apset_Acl_0,refute_0_20]) ).
cnf(refute_0_22,plain,
( c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) != v_A
| ~ c_lessequals(X_16,v_A,tc_set(t_a))
| c_lessequals(X_16,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
introduced(tautology,[equality,[$cnf( ~ c_lessequals(X_16,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),[1],$fot(v_A)]]) ).
cnf(refute_0_23,plain,
( ~ c_lessequals(X_16,v_A,tc_set(t_a))
| c_lessequals(X_16,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ c_in(X_17,X_16,t_a)
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(X_16,v_A,tc_set(t_a))
| c_in(c_Pair(X_17,c_Tarski_Oglb(X_16,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_lessequals(X_16,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)) )],[refute_0_23,refute_0_19]) ).
cnf(refute_0_25,plain,
( ~ c_in(X_17,X_16,t_a)
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lessequals(X_16,v_A,tc_set(t_a))
| c_in(c_Pair(X_17,c_Tarski_Oglb(X_16,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ c_in(X_17,X_16,t_a)
| ~ c_lessequals(X_16,v_A,tc_set(t_a))
| c_in(c_Pair(X_17,c_Tarski_Oglb(X_16,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Odual_Acl_A_58_APartialOrder_0,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ c_in(X_20,v_S,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(X_20,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_26:[bind(X_16,$fot(v_S)),bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_28,plain,
( ~ c_in(X_20,v_S,t_a)
| c_in(c_Pair(X_20,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ c_in(v_x,v_S,t_a)
| c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_28:[bind(X_20,$fot(v_x))]]) ).
cnf(refute_0_30,plain,
c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_x,v_S,t_a) )],[cls_conjecture_1,refute_0_29]) ).
cnf(refute_0_31,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[refute_0_30,refute_0_0]) ).
cnf(refute_0_32,plain,
( v_r != c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r ),
inference(subst,[],[refute_0_8:[bind(X,$fot(v_r)),bind(Y,$fot(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_33,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(resolve,[$cnf( $equal(v_r,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Or_A_61_61_Aorder_Acl_0,refute_0_32]) ).
cnf(refute_0_34,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(tautology,[equality,[$cnf( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),[1],$fot(v_r)]]) ).
cnf(refute_0_35,plain,
( ~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_36,cls_conjecture_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 00:32:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------