TSTP Solution File: LAT276-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT276-2 : 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 06:01:58 EDT 2022
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of clauses : 66 ( 14 unt; 15 nHn; 65 RR)
% Number of literals : 148 ( 19 equ; 71 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) ).
cnf(cls_conjecture_10,negated_conjecture,
( c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_V,v_S,t_a)
| ~ c_in(c_Pair(v_xa,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_conjecture_3,negated_conjecture,
( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(v_xa,v_S,t_a) ) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,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(v_xa,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_conjecture_9,negated_conjecture,
( c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_U,v_S,t_a)
| c_in(v_xa,v_S,t_a) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,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_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_in(V_L,v_A,t_a)
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(V_L,V_S,v_r),V_S,t_a) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1,axiom,
( ~ c_in(V_L,v_A,t_a)
| ~ c_in(c_Pair(v_sko__4mP(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(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
cnf(cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0,axiom,
( ~ c_in(V_x,V_S,t_a)
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| c_in(c_Pair(V_x,c_Tarski_Olub(V_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ).
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,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( v_r != c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)
| c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r ),
inference(subst,[],[refute_0_2:[bind(X,$fot(v_r)),bind(Y,$fot(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_4,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(resolve,[$cnf( $equal(v_r,c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_Or_A_61_61_Aorder_Acl_0,refute_0_3]) ).
cnf(refute_0_5,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),[1],$fot(v_r)]]) ).
cnf(refute_0_6,plain,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[refute_0_6,cls_conjecture_6]) ).
cnf(refute_0_8,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xa,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)) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),[1],$fot(v_r)]]) ).
cnf(refute_0_9,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_xa,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)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_xa,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)) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
( ~ c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_xa,v_A,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,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_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_1:[bind(V_L,$fot(v_xa)),bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_12,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_2:[bind(X,$fot(v_A)),bind(Y,$fot(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)))]]) ).
cnf(refute_0_13,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(resolve,[$cnf( $equal(v_A,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)) )],[cls_Tarski_OA_A_61_61_Apset_Acl_0,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) != v_A
| ~ c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(v_xa,v_A,t_a) ),
introduced(tautology,[equality,[$cnf( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),[1],$fot(v_A)]]) ).
cnf(refute_0_15,plain,
( ~ c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| c_in(v_xa,v_A,t_a) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),v_A) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( c_in(v_xa,v_A,t_a)
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) )],[cls_conjecture_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ c_in(X_5,v_S,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(X_5,v_A,t_a) ),
inference(subst,[],[cls_Set_OsubsetD_0:[bind(T_a,$fot(t_a)),bind(V_A,$fot(v_S)),bind(V_B,$fot(v_A)),bind(V_c,$fot(X_5))]]) ).
cnf(refute_0_18,plain,
( ~ c_in(X_5,v_S,t_a)
| c_in(X_5,v_A,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ c_in(v_xa,v_S,t_a)
| c_in(v_xa,v_A,t_a) ),
inference(subst,[],[refute_0_18:[bind(X_5,$fot(v_xa))]]) ).
cnf(refute_0_20,plain,
c_in(v_xa,v_A,t_a),
inference(resolve,[$cnf( c_in(v_xa,v_S,t_a) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ c_in(X_10,v_A,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),X_10,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(X_10,v_S,v_r),v_S,t_a) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_AL1_A_58_AA_59_AALL_Ax_58S1_O_A_Ix_M_AL1_J_A_58_Ar_A_124_93_A_61_61_62_A_Ilub_AS1_Acl_M_AL1_J_A_58_Ar_A_61_61_ATrue_0:[bind(V_L,$fot(X_10)),bind(V_S,$fot(v_S))]]) ).
cnf(refute_0_22,plain,
( ~ c_in(X_10,v_A,t_a)
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),X_10,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(X_10,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ c_in(v_xa,v_A,t_a)
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(subst,[],[refute_0_22:[bind(X_10,$fot(v_xa))]]) ).
cnf(refute_0_24,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_A,t_a) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_24,refute_0_10]) ).
cnf(refute_0_26,plain,
( ~ c_in(X_8,v_S,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(X_8,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[cls_Tarski_O_91_124_AS1_A_60_61_AA_59_Ax1_A_58_AS1_A_124_93_A_61_61_62_A_Ix1_M_Alub_AS1_Acl_J_A_58_Ar_A_61_61_ATrue_0:[bind(V_S,$fot(v_S)),bind(V_x,$fot(X_8))]]) ).
cnf(refute_0_27,plain,
( ~ c_in(X_8,v_S,t_a)
| c_in(c_Pair(X_8,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ c_in(v_xa,v_S,t_a)
| c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_27:[bind(X_8,$fot(v_xa))]]) ).
cnf(refute_0_29,plain,
( ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[refute_0_6,cls_conjecture_4]) ).
cnf(refute_0_30,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| ~ c_in(c_Pair(V_U,v_xa,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(V_U,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(tautology,[equality,[$cnf( c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),[1],$fot(v_r)]]) ).
cnf(refute_0_31,plain,
( ~ c_in(c_Pair(V_U,v_xa,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(V_U,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[cls_conjecture_9,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(subst,[],[refute_0_32:[bind(V_U,$fot(v_sko__4mP(v_xa,v_S,v_r)))]]) ).
cnf(refute_0_34,plain,
( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_35,plain,
( c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( ~ c_in(v_xa,v_A,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_35,refute_0_11]) ).
cnf(refute_0_37,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_in(v_xa,v_A,t_a) )],[refute_0_20,refute_0_36]) ).
cnf(refute_0_38,plain,
( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_xa,v_S,t_a) ),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_37]) ).
cnf(refute_0_39,plain,
c_in(v_xa,v_S,t_a),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_38,refute_0_29]) ).
cnf(refute_0_40,plain,
c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_xa,v_S,t_a) )],[refute_0_39,refute_0_28]) ).
cnf(refute_0_41,plain,
c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a),
inference(resolve,[$cnf( c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_40,refute_0_25]) ).
cnf(refute_0_42,plain,
( ~ c_in(V_V,v_S,t_a)
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_xa,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)) )],[refute_0_9,cls_conjecture_10]) ).
cnf(refute_0_43,plain,
( c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) != v_r
| ~ c_in(c_Pair(V_V,v_xa,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(V_V,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(tautology,[equality,[$cnf( c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),[1],$fot(v_r)]]) ).
cnf(refute_0_44,plain,
( ~ c_in(c_Pair(V_V,v_xa,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(V_V,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( $equal(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),v_r) )],[refute_0_4,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ c_in(V_V,v_S,t_a)
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(V_V,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(subst,[],[refute_0_46:[bind(V_V,$fot(v_sko__4mP(v_xa,v_S,v_r)))]]) ).
cnf(refute_0_48,plain,
c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ c_in(v_xa,v_A,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_48,refute_0_11]) ).
cnf(refute_0_50,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolve,[$cnf( c_in(v_xa,v_A,t_a) )],[refute_0_20,refute_0_49]) ).
cnf(refute_0_51,plain,
c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_lessequals(v_S,v_A,tc_set(t_a)) )],[cls_conjecture_0,refute_0_50]) ).
cnf(refute_0_52,plain,
~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(resolve,[$cnf( c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_51,refute_0_10]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) )],[refute_0_40,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % 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 : Wed Jun 29 15:14:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------