TSTP Solution File: SET840-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET840-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 03:37:40 EDT 2022
% Result : Unsatisfiable 128.96s 129.12s
% Output : CNFRefutation 128.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of clauses : 81 ( 17 unt; 37 nHn; 39 RR)
% Number of literals : 169 ( 45 equ; 51 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 204 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_lessequals(c_Union(v_S,t_b),V_U,tc_set(t_b))
| ~ c_in(V_U,v_S,tc_set(t_b)) ) ).
cnf(cls_Set_OUnionI_0,axiom,
( ~ c_in(V_A,V_X,T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| c_in(V_A,c_Union(V_C,T_a),T_a) ) ).
cnf(cls_Set_OinsertCI_0,axiom,
( ~ c_in(V_a,V_B,T_a)
| c_in(V_a,c_insert(V_b,V_B,T_a),T_a) ) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a) ).
cnf(cls_Set_OinsertE_0,axiom,
( ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| c_in(V_a,V_A,T_a)
| V_a = V_b ) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,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(refute_0_0,plain,
c_in(c_Union(v_S,t_b),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_set(t_b))),bind(V_B,$fot(c_emptyset)),bind(V_x,$fot(c_Union(v_S,t_b)))]]) ).
cnf(refute_0_1,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(tc_set(t_b))),bind(V_A,$fot(v_S)),bind(V_B,$fot(c_insert(X_18858,c_emptyset,tc_set(t_b))))]]) ).
cnf(refute_0_2,plain,
( ~ c_in(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b)),v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b)),tc_set(t_b)) ),
inference(subst,[],[cls_conjecture_1:[bind(V_U,$fot(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b))))]]) ).
cnf(refute_0_3,plain,
( c_in(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b)),v_S,tc_set(t_b))
| c_lessequals(v_S,X_26,tc_set(tc_set(t_b))) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(tc_set(t_b))),bind(V_A,$fot(v_S)),bind(V_B,$fot(X_26))]]) ).
cnf(refute_0_4,plain,
( c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,X_26,tc_set(tc_set(t_b))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,X_26,tc_set(t_b)),v_S,tc_set(t_b)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,X_18854,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,X_18854,tc_set(tc_set(t_b))) ),
inference(subst,[],[refute_0_4:[bind(X_26,$fot(X_18854))]]) ).
cnf(refute_0_6,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)),c_Union(X_2503,X_2504),tc_set(X_2504))
| ~ c_lessequals(c_Union(X_2503,X_2504),c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)),tc_set(X_2504))
| c_Union(X_2503,X_2504) = c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(X_2504)),bind(V_A,$fot(c_Union(X_2503,X_2504))),bind(V_B,$fot(c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504))))]]) ).
cnf(refute_0_7,plain,
( ~ c_in(c_Main_OsubsetI__1(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551),c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551)
| c_lessequals(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),tc_set(X_551)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_551)),bind(V_A,$fot(X_552)),bind(V_B,$fot(c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551)))]]) ).
cnf(refute_0_8,plain,
( c_in(c_Main_OsubsetI__1(X_124,V_B,X_122),X_124,X_122)
| c_lessequals(X_124,V_B,tc_set(X_122)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_122)),bind(V_A,$fot(X_124))]]) ).
cnf(refute_0_9,plain,
c_in(X_65,c_insert(X_65,V_B,tc_set(X_62)),tc_set(X_62)),
inference(subst,[],[cls_Set_OinsertCI_1:[bind(T_a,$fot(tc_set(X_62))),bind(V_x,$fot(X_65))]]) ).
cnf(refute_0_10,plain,
( ~ c_in(X_63,X_65,X_62)
| ~ c_in(X_65,c_insert(X_65,V_B,tc_set(X_62)),tc_set(X_62))
| c_in(X_63,c_Union(c_insert(X_65,V_B,tc_set(X_62)),X_62),X_62) ),
inference(subst,[],[cls_Set_OUnionI_0:[bind(T_a,$fot(X_62)),bind(V_A,$fot(X_63)),bind(V_C,$fot(c_insert(X_65,V_B,tc_set(X_62)))),bind(V_X,$fot(X_65))]]) ).
cnf(refute_0_11,plain,
( ~ c_in(X_63,X_65,X_62)
| c_in(X_63,c_Union(c_insert(X_65,V_B,tc_set(X_62)),X_62),X_62) ),
inference(resolve,[$cnf( c_in(X_65,c_insert(X_65,V_B,tc_set(X_62)),tc_set(X_62)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ c_in(c_Main_OsubsetI__1(X_124,V_B,X_122),X_124,X_122)
| c_in(c_Main_OsubsetI__1(X_124,V_B,X_122),c_Union(c_insert(X_124,X_121,tc_set(X_122)),X_122),X_122) ),
inference(subst,[],[refute_0_11:[bind(V_B,$fot(X_121)),bind(X_62,$fot(X_122)),bind(X_63,$fot(c_Main_OsubsetI__1(X_124,V_B,X_122))),bind(X_65,$fot(X_124))]]) ).
cnf(refute_0_13,plain,
( c_in(c_Main_OsubsetI__1(X_124,V_B,X_122),c_Union(c_insert(X_124,X_121,tc_set(X_122)),X_122),X_122)
| c_lessequals(X_124,V_B,tc_set(X_122)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_124,V_B,X_122),X_124,X_122) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( c_in(c_Main_OsubsetI__1(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551),c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551)
| c_lessequals(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),tc_set(X_551)) ),
inference(subst,[],[refute_0_13:[bind(V_B,$fot(c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551))),bind(X_121,$fot(X_550)),bind(X_122,$fot(X_551)),bind(X_124,$fot(X_552))]]) ).
cnf(refute_0_15,plain,
c_lessequals(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),tc_set(X_551)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_552,c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551),c_Union(c_insert(X_552,X_550,tc_set(X_551)),X_551),X_551) )],[refute_0_14,refute_0_7]) ).
cnf(refute_0_16,plain,
c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_551),tc_set(X_551)),
inference(subst,[],[refute_0_15:[bind(X_552,$fot(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551))))]]) ).
cnf(refute_0_17,plain,
( ~ c_lessequals(X_2484,c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),tc_set(X_2483))
| ~ c_lessequals(c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),X_2484,tc_set(X_2483))
| X_2484 = c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(X_2483)),bind(V_A,$fot(X_2484)),bind(V_B,$fot(c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483)))]]) ).
cnf(refute_0_18,plain,
( c_in(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186)
| c_lessequals(X_187,V_B,tc_set(X_186)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_186)),bind(V_A,$fot(X_187))]]) ).
cnf(refute_0_19,plain,
( ~ c_in(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),V_B,T_a)
| c_lessequals(c_insert(X_88,V_B,T_a),V_B,tc_set(T_a)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(V_A,$fot(c_insert(X_88,V_B,T_a)))]]) ).
cnf(refute_0_20,plain,
( ~ c_lessequals(X_84,c_insert(X_85,X_84,X_83),tc_set(X_83))
| ~ c_lessequals(c_insert(X_85,X_84,X_83),X_84,tc_set(X_83))
| X_84 = c_insert(X_85,X_84,X_83) ),
inference(subst,[],[cls_Set_Osubset__antisym_0:[bind(T_a,$fot(X_83)),bind(V_A,$fot(X_84)),bind(V_B,$fot(c_insert(X_85,X_84,X_83)))]]) ).
cnf(refute_0_21,plain,
( ~ c_in(c_Main_OsubsetI__1(c_insert(X_82,X_81,X_80),X_81,X_80),X_81,X_80)
| c_lessequals(c_insert(X_82,X_81,X_80),X_81,tc_set(X_80)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_80)),bind(V_A,$fot(c_insert(X_82,X_81,X_80))),bind(V_B,$fot(X_81))]]) ).
cnf(refute_0_22,plain,
( c_in(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58),c_insert(X_61,X_59,X_58),X_58)
| c_lessequals(c_insert(X_61,X_59,X_58),V_B,tc_set(X_58)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_58)),bind(V_A,$fot(c_insert(X_61,X_59,X_58)))]]) ).
cnf(refute_0_23,plain,
( ~ c_in(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58),c_insert(X_61,X_59,X_58),X_58)
| c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58) = X_61
| c_in(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58),X_59,X_58) ),
inference(subst,[],[cls_Set_OinsertE_0:[bind(T_a,$fot(X_58)),bind(V_A,$fot(X_59)),bind(V_a,$fot(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58))),bind(V_b,$fot(X_61))]]) ).
cnf(refute_0_24,plain,
( c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58) = X_61
| c_in(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58),X_59,X_58)
| c_lessequals(c_insert(X_61,X_59,X_58),V_B,tc_set(X_58)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_insert(X_61,X_59,X_58),V_B,X_58),c_insert(X_61,X_59,X_58),X_58) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( c_Main_OsubsetI__1(c_insert(X_82,X_81,X_80),X_81,X_80) = X_82
| c_in(c_Main_OsubsetI__1(c_insert(X_82,X_81,X_80),X_81,X_80),X_81,X_80)
| c_lessequals(c_insert(X_82,X_81,X_80),X_81,tc_set(X_80)) ),
inference(subst,[],[refute_0_24:[bind(V_B,$fot(X_81)),bind(X_58,$fot(X_80)),bind(X_59,$fot(X_81)),bind(X_61,$fot(X_82))]]) ).
cnf(refute_0_26,plain,
( c_Main_OsubsetI__1(c_insert(X_82,X_81,X_80),X_81,X_80) = X_82
| c_lessequals(c_insert(X_82,X_81,X_80),X_81,tc_set(X_80)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_insert(X_82,X_81,X_80),X_81,X_80),X_81,X_80) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
( c_Main_OsubsetI__1(c_insert(X_85,X_84,X_83),X_84,X_83) = X_85
| c_lessequals(c_insert(X_85,X_84,X_83),X_84,tc_set(X_83)) ),
inference(subst,[],[refute_0_26:[bind(X_80,$fot(X_83)),bind(X_81,$fot(X_84)),bind(X_82,$fot(X_85))]]) ).
cnf(refute_0_28,plain,
( ~ c_lessequals(X_84,c_insert(X_85,X_84,X_83),tc_set(X_83))
| X_84 = c_insert(X_85,X_84,X_83)
| c_Main_OsubsetI__1(c_insert(X_85,X_84,X_83),X_84,X_83) = X_85 ),
inference(resolve,[$cnf( c_lessequals(c_insert(X_85,X_84,X_83),X_84,tc_set(X_83)) )],[refute_0_27,refute_0_20]) ).
cnf(refute_0_29,plain,
( ~ c_in(c_Main_OsubsetI__1(X_53,c_insert(X_51,X_53,X_52),X_52),c_insert(X_51,X_53,X_52),X_52)
| c_lessequals(X_53,c_insert(X_51,X_53,X_52),tc_set(X_52)) ),
inference(subst,[],[cls_Set_OsubsetI_1:[bind(T_a,$fot(X_52)),bind(V_A,$fot(X_53)),bind(V_B,$fot(c_insert(X_51,X_53,X_52)))]]) ).
cnf(refute_0_30,plain,
( ~ c_in(c_Main_OsubsetI__1(X_25,X_26,X_24),X_25,X_24)
| c_in(c_Main_OsubsetI__1(X_25,X_26,X_24),c_insert(V_b,X_25,X_24),X_24) ),
inference(subst,[],[cls_Set_OinsertCI_0:[bind(T_a,$fot(X_24)),bind(V_B,$fot(X_25)),bind(V_a,$fot(c_Main_OsubsetI__1(X_25,X_26,X_24)))]]) ).
cnf(refute_0_31,plain,
( c_in(c_Main_OsubsetI__1(X_25,X_26,X_24),X_25,X_24)
| c_lessequals(X_25,X_26,tc_set(X_24)) ),
inference(subst,[],[cls_Set_OsubsetI_0:[bind(T_a,$fot(X_24)),bind(V_A,$fot(X_25)),bind(V_B,$fot(X_26))]]) ).
cnf(refute_0_32,plain,
( c_in(c_Main_OsubsetI__1(X_25,X_26,X_24),c_insert(V_b,X_25,X_24),X_24)
| c_lessequals(X_25,X_26,tc_set(X_24)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_25,X_26,X_24),X_25,X_24) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
( c_in(c_Main_OsubsetI__1(X_53,c_insert(X_51,X_53,X_52),X_52),c_insert(X_51,X_53,X_52),X_52)
| c_lessequals(X_53,c_insert(X_51,X_53,X_52),tc_set(X_52)) ),
inference(subst,[],[refute_0_32:[bind(V_b,$fot(X_51)),bind(X_24,$fot(X_52)),bind(X_25,$fot(X_53)),bind(X_26,$fot(c_insert(X_51,X_53,X_52)))]]) ).
cnf(refute_0_34,plain,
c_lessequals(X_53,c_insert(X_51,X_53,X_52),tc_set(X_52)),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_53,c_insert(X_51,X_53,X_52),X_52),c_insert(X_51,X_53,X_52),X_52) )],[refute_0_33,refute_0_29]) ).
cnf(refute_0_35,plain,
c_lessequals(X_84,c_insert(X_85,X_84,X_83),tc_set(X_83)),
inference(subst,[],[refute_0_34:[bind(X_51,$fot(X_85)),bind(X_52,$fot(X_83)),bind(X_53,$fot(X_84))]]) ).
cnf(refute_0_36,plain,
( X_84 = c_insert(X_85,X_84,X_83)
| c_Main_OsubsetI__1(c_insert(X_85,X_84,X_83),X_84,X_83) = X_85 ),
inference(resolve,[$cnf( c_lessequals(X_84,c_insert(X_85,X_84,X_83),tc_set(X_83)) )],[refute_0_35,refute_0_28]) ).
cnf(refute_0_37,plain,
( V_B = c_insert(X_88,V_B,T_a)
| c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a) = X_88 ),
inference(subst,[],[refute_0_36:[bind(X_83,$fot(T_a)),bind(X_84,$fot(V_B)),bind(X_85,$fot(X_88))]]) ).
cnf(refute_0_38,plain,
( c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a) != X_88
| ~ c_in(X_88,V_B,T_a)
| c_in(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),V_B,T_a) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),V_B,T_a) ),[0],$fot(X_88)]]) ).
cnf(refute_0_39,plain,
( ~ c_in(X_88,V_B,T_a)
| V_B = c_insert(X_88,V_B,T_a)
| c_in(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),V_B,T_a) ),
inference(resolve,[$cnf( $equal(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),X_88) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ c_in(X_88,V_B,T_a)
| V_B = c_insert(X_88,V_B,T_a)
| c_lessequals(c_insert(X_88,V_B,T_a),V_B,tc_set(T_a)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(c_insert(X_88,V_B,T_a),V_B,T_a),V_B,T_a) )],[refute_0_39,refute_0_19]) ).
cnf(refute_0_41,plain,
( ~ c_in(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186)
| X_187 = c_insert(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186)
| c_lessequals(c_insert(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186),X_187,tc_set(X_186)) ),
inference(subst,[],[refute_0_40:[bind(T_a,$fot(X_186)),bind(V_B,$fot(X_187)),bind(X_88,$fot(c_Main_OsubsetI__1(X_187,V_B,X_186)))]]) ).
cnf(refute_0_42,plain,
( X_187 = c_insert(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186)
| c_lessequals(X_187,V_B,tc_set(X_186))
| c_lessequals(c_insert(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186),X_187,tc_set(X_186)) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(X_187,V_B,X_186),X_187,X_186) )],[refute_0_18,refute_0_41]) ).
cnf(refute_0_43,plain,
( X_2484 = c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483)
| c_lessequals(X_2484,X_2482,tc_set(X_2483))
| c_lessequals(c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),X_2484,tc_set(X_2483)) ),
inference(subst,[],[refute_0_42:[bind(V_B,$fot(X_2482)),bind(X_186,$fot(X_2483)),bind(X_187,$fot(X_2484))]]) ).
cnf(refute_0_44,plain,
( ~ c_lessequals(X_2484,c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),tc_set(X_2483))
| X_2484 = c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483)
| c_lessequals(X_2484,X_2482,tc_set(X_2483)) ),
inference(resolve,[$cnf( c_lessequals(c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),X_2484,tc_set(X_2483)) )],[refute_0_43,refute_0_17]) ).
cnf(refute_0_45,plain,
c_lessequals(X_2484,c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),tc_set(X_2483)),
inference(subst,[],[refute_0_34:[bind(X_51,$fot(c_Main_OsubsetI__1(X_2484,X_2482,X_2483))),bind(X_52,$fot(X_2483)),bind(X_53,$fot(X_2484))]]) ).
cnf(refute_0_46,plain,
( X_2484 = c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483)
| c_lessequals(X_2484,X_2482,tc_set(X_2483)) ),
inference(resolve,[$cnf( c_lessequals(X_2484,c_insert(c_Main_OsubsetI__1(X_2484,X_2482,X_2483),X_2484,X_2483),tc_set(X_2483)) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
( X_550 = c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551))
| c_lessequals(X_550,X_2485,tc_set(tc_set(X_551))) ),
inference(subst,[],[refute_0_46:[bind(X_2482,$fot(X_2485)),bind(X_2483,$fot(tc_set(X_551))),bind(X_2484,$fot(X_550))]]) ).
cnf(refute_0_48,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_49,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_50,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( X_550 != c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551))
| c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)) = X_550 ),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_550)),bind(Y,$fot(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551))))]]) ).
cnf(refute_0_52,plain,
( c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)) = X_550
| c_lessequals(X_550,X_2485,tc_set(tc_set(X_551))) ),
inference(resolve,[$cnf( $equal(X_550,c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551))) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)) != X_550
| ~ c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_551),tc_set(X_551))
| c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(X_550,X_551),tc_set(X_551)) ),
introduced(tautology,[equality,[$cnf( c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_551),tc_set(X_551)) ),[1,0],$fot(X_550)]]) ).
cnf(refute_0_54,plain,
( ~ c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_551),tc_set(X_551))
| c_lessequals(X_550,X_2485,tc_set(tc_set(X_551)))
| c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(X_550,X_551),tc_set(X_551)) ),
inference(resolve,[$cnf( $equal(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_550) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( c_lessequals(X_550,X_2485,tc_set(tc_set(X_551)))
| c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(X_550,X_551),tc_set(X_551)) ),
inference(resolve,[$cnf( c_lessequals(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),c_Union(c_insert(c_Main_OsubsetI__1(X_550,X_2485,tc_set(X_551)),X_550,tc_set(X_551)),X_551),tc_set(X_551)) )],[refute_0_16,refute_0_54]) ).
cnf(refute_0_56,plain,
( c_lessequals(X_2503,X_2502,tc_set(tc_set(X_2504)))
| c_lessequals(c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)),c_Union(X_2503,X_2504),tc_set(X_2504)) ),
inference(subst,[],[refute_0_55:[bind(X_2485,$fot(X_2502)),bind(X_550,$fot(X_2503)),bind(X_551,$fot(X_2504))]]) ).
cnf(refute_0_57,plain,
( ~ c_lessequals(c_Union(X_2503,X_2504),c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)),tc_set(X_2504))
| c_Union(X_2503,X_2504) = c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504))
| c_lessequals(X_2503,X_2502,tc_set(tc_set(X_2504))) ),
inference(resolve,[$cnf( c_lessequals(c_Main_OsubsetI__1(X_2503,X_2502,tc_set(X_2504)),c_Union(X_2503,X_2504),tc_set(X_2504)) )],[refute_0_56,refute_0_6]) ).
cnf(refute_0_58,plain,
( ~ c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,X_18854,tc_set(t_b)),tc_set(t_b))
| c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X_18854,tc_set(t_b))
| c_lessequals(v_S,X_18854,tc_set(tc_set(t_b))) ),
inference(subst,[],[refute_0_57:[bind(X_2502,$fot(X_18854)),bind(X_2503,$fot(v_S)),bind(X_2504,$fot(t_b))]]) ).
cnf(refute_0_59,plain,
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,X_18854,tc_set(t_b))
| c_lessequals(v_S,X_18854,tc_set(tc_set(t_b))) ),
inference(resolve,[$cnf( c_lessequals(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,X_18854,tc_set(t_b)),tc_set(t_b)) )],[refute_0_5,refute_0_58]) ).
cnf(refute_0_60,plain,
( c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ),
inference(subst,[],[refute_0_59:[bind(X_18854,$fot(c_insert(V_U,c_emptyset,tc_set(t_b))))]]) ).
cnf(refute_0_61,plain,
c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(resolve,[$cnf( c_lessequals(v_S,c_insert(V_U,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) )],[refute_0_60,cls_conjecture_0]) ).
cnf(refute_0_62,plain,
c_Union(v_S,t_b) = c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(subst,[],[refute_0_61:[bind(V_U,$fot(X_18858))]]) ).
cnf(refute_0_63,plain,
( c_Union(v_S,t_b) != c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(c_Union(v_S,t_b))),bind(Y,$fot(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))))]]) ).
cnf(refute_0_64,plain,
c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) = c_Union(v_S,t_b),
inference(resolve,[$cnf( $equal(c_Union(v_S,t_b),c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) != c_Union(v_S,t_b)
| ~ c_in(c_Union(v_S,t_b),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
introduced(tautology,[equality,[$cnf( ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),[0],$fot(c_Union(v_S,t_b))]]) ).
cnf(refute_0_66,plain,
( ~ c_in(c_Union(v_S,t_b),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_in(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) ),
inference(resolve,[$cnf( $equal(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_Union(v_S,t_b)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ c_in(c_Union(v_S,t_b),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b))
| c_lessequals(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) ),
inference(resolve,[$cnf( c_in(c_Main_OsubsetI__1(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)) )],[refute_0_66,refute_0_1]) ).
cnf(refute_0_68,plain,
~ c_lessequals(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(subst,[],[cls_conjecture_0:[bind(V_U,$fot(X_18858))]]) ).
cnf(refute_0_69,plain,
~ c_in(c_Union(v_S,t_b),c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(resolve,[$cnf( c_lessequals(v_S,c_insert(X_18858,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
~ c_in(c_Union(v_S,t_b),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)),
inference(subst,[],[refute_0_69:[bind(X_18858,$fot(c_Union(v_S,t_b)))]]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( c_in(c_Union(v_S,t_b),c_insert(c_Union(v_S,t_b),c_emptyset,tc_set(t_b)),tc_set(t_b)) )],[refute_0_0,refute_0_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET840-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n029.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 10 04:55:01 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 128.96/129.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 128.96/129.12
% 128.96/129.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 128.96/129.13
%------------------------------------------------------------------------------