TSTP Solution File: SET863-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n021.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 : 300s
% DateTime : Thu Aug 31 14:31:29 EDT 2023
% Result : Unsatisfiable 1.92s 2.04s
% Output : CNFRefutation 1.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 15:57:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 1.92/2.03 %-------------------------------------------
% 1.92/2.03 % File :CSE---1.6
% 1.92/2.03 % Problem :theBenchmark
% 1.92/2.03 % Transform :cnf
% 1.92/2.03 % Format :tptp:raw
% 1.92/2.03 % Command :java -jar mcs_scs.jar %d %s
% 1.92/2.03
% 1.92/2.03 % Result :Theorem 1.370000s
% 1.92/2.03 % Output :CNFRefutation 1.370000s
% 1.92/2.03 %-------------------------------------------
% 1.92/2.03 %------------------------------------------------------------------------------
% 1.92/2.03 % File : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 1.92/2.03 % Domain : Set Theory
% 1.92/2.03 % Problem : Problem about Zorn's lemma
% 1.92/2.03 % Version : [Pau06] axioms : Reduced > Especial.
% 1.92/2.03 % English :
% 1.92/2.03
% 1.92/2.03 % Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% 1.92/2.03 % Source : [Pau06]
% 1.92/2.03 % Names :
% 1.92/2.03
% 1.92/2.03 % Status : Unsatisfiable
% 1.92/2.03 % Rating : 0.14 v8.1.0, 0.00 v7.1.0, 0.17 v7.0.0, 0.25 v6.4.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v5.5.0, 0.12 v5.4.0, 0.10 v5.2.0, 0.00 v5.0.0, 0.14 v4.1.0, 0.00 v4.0.1, 0.20 v4.0.0, 0.29 v3.4.0, 0.25 v3.3.0, 0.33 v3.2.0
% 1.92/2.03 % Syntax : Number of clauses : 14 ( 6 unt; 3 nHn; 12 RR)
% 1.92/2.03 % Number of literals : 33 ( 0 equ; 17 neg)
% 1.92/2.03 % Maximal clause size : 5 ( 2 avg)
% 1.92/2.03 % Maximal term depth : 4 ( 1 avg)
% 1.92/2.03 % Number of predicates : 2 ( 2 usr; 0 prp; 3-3 aty)
% 1.92/2.03 % Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% 1.92/2.03 % Number of variables : 31 ( 0 sgn)
% 1.92/2.03 % SPC : CNF_UNS_RFO_NEQ_NHN
% 1.92/2.03
% 1.92/2.03 % Comments : The problems in the [Pau06] collection each have very many axioms,
% 1.92/2.03 % of which only a small selection are required for the refutation.
% 1.92/2.03 % The mission is to find those few axioms, after which a refutation
% 1.92/2.03 % can be quite easily found. This version has only the necessary
% 1.92/2.03 % axioms.
% 1.92/2.03 %------------------------------------------------------------------------------
% 1.92/2.03 cnf(cls_Set_OsubsetD_0,axiom,
% 1.92/2.03 ( ~ c_in(V_c,V_A,T_a)
% 1.92/2.03 | ~ c_lessequals(V_A,V_B,tc_set(T_a))
% 1.92/2.03 | c_in(V_c,V_B,T_a) ) ).
% 1.92/2.03
% 1.92/2.03 cnf(cls_Set_OsubsetI_0,axiom,
% 1.92/2.03 ( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
% 1.92/2.03 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 1.92/2.03
% 1.92/2.03 cnf(cls_Set_OsubsetI_1,axiom,
% 1.92/2.03 ( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
% 1.92/2.03 | c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
% 1.92/2.03
% 1.92/2.03 cnf(cls_Zorn_Ochain__extend_0,axiom,
% 1.92/2.04 ( ~ c_in(V_z,V_S,tc_set(T_a))
% 1.92/2.04 | ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))
% 1.92/2.04 | c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_Zorn_Ochain__extend_1,axiom,
% 1.92/2.04 ( ~ c_in(V_z,V_S,tc_set(T_a))
% 1.92/2.04 | ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | ~ c_lessequals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))
% 1.92/2.04 | c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
% 1.92/2.04 ( ~ c_in(V_z,V_x,T_a)
% 1.92/2.04 | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | c_in(V_z,V_y,T_a)
% 1.92/2.04 | c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a)) ) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
% 1.92/2.04 ( ~ c_in(V_z,V_x,T_a)
% 1.92/2.04 | ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
% 1.92/2.04 | ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
% 1.92/2.04 | c_in(V_z,V_y,T_a) ) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_0,negated_conjecture,
% 1.92/2.04 c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_1,negated_conjecture,
% 1.92/2.04 c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_3,negated_conjecture,
% 1.92/2.04 c_in(v_x,v_S,tc_set(t_a)) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_4,negated_conjecture,
% 1.92/2.04 c_lessequals(v_y,v_x,tc_set(t_a)) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_5,negated_conjecture,
% 1.92/2.04 c_in(v_xa,v_x,t_a) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_6,negated_conjecture,
% 1.92/2.04 ~ c_in(v_xa,v_y,t_a) ).
% 1.92/2.04
% 1.92/2.04 cnf(cls_conjecture_7,negated_conjecture,
% 1.92/2.04 ( c_lessequals(V_U,v_y,tc_set(t_a))
% 1.92/2.04 | ~ c_in(V_U,v_c,tc_set(t_a)) ) ).
% 1.92/2.04
% 1.92/2.04 %------------------------------------------------------------------------------
% 1.92/2.04 %-------------------------------------------
% 1.92/2.04 % Proof found
% 1.92/2.04 % SZS status Theorem for theBenchmark
% 1.92/2.04 % SZS output start Proof
% 1.92/2.04 %ClaNum:14(EqnAxiom:0)
% 1.92/2.04 %VarNum:109(SingletonVarNum:31)
% 1.92/2.04 %MaxLitNum:5
% 1.92/2.04 %MaxfuncDepth:2
% 1.92/2.04 %SharedTerms:17
% 1.92/2.04 %goalClause: 1 2 3 4 5 6 7
% 1.92/2.04 %singleGoalClaCount:6
% 1.92/2.04 [1]P1(a1,a2,a3)
% 1.92/2.04 [6]~P1(a1,a15,a3)
% 1.92/2.04 [2]P1(a2,a12,f13(a3))
% 1.92/2.04 [3]P2(a15,a2,f13(a3))
% 1.92/2.04 [4]P1(a14,f4(a12,a3),f13(f13(a3)))
% 1.92/2.04 [5]P1(a14,f6(a12,a3),f13(f13(a3)))
% 1.92/2.04 [7]~P1(x71,a14,f13(a3))+P2(x71,a15,f13(a3))
% 1.92/2.04 [8]P1(f5(x81,x82,x83),x81,x83)+P2(x81,x82,f13(x83))
% 1.92/2.04 [10]~P1(f5(x101,x102,x103),x102,x103)+P2(x101,x102,f13(x103))
% 1.92/2.04 [9]P1(x91,x92,x93)+~P1(x91,x94,x93)+~P2(x94,x92,f13(x93))
% 1.92/2.04 [11]~P1(x112,x114,f13(x113))+P1(f7(x111,x112,x113),x111,f13(x113))+~P1(x111,f4(x114,x113),f13(f13(x113)))+P1(f11(f10(x112,a8,f13(x113)),x111,f13(x113)),f4(x114,x113),f13(f13(x113)))
% 1.92/2.04 [12]~P2(f7(x123,x121,x122),x121,f13(x122))+~P1(x121,x124,f13(x122))+~P1(x123,f4(x124,x122),f13(f13(x122)))+P1(f11(f10(x121,a8,f13(x122)),x123,f13(x122)),f4(x124,x122),f13(f13(x122)))
% 1.92/2.04 [13]P1(x131,x132,x133)+~P1(x131,x135,x133)+P1(f9(x134,x132,x133),x134,f13(x133))+~P1(x134,f6(x136,x133),f13(f13(x133)))+~P1(f11(f10(x135,a8,f13(x133)),x134,f13(x133)),f4(x136,x133),f13(f13(x133)))
% 1.92/2.04 [14]P1(x141,x142,x143)+~P1(x141,x144,x143)+~P2(f9(x145,x142,x143),x142,f13(x143))+~P1(x145,f6(x146,x143),f13(f13(x143)))+~P1(f11(f10(x144,a8,f13(x143)),x145,f13(x143)),f4(x146,x143),f13(f13(x143)))
% 1.92/2.04 %EqnAxiom
% 1.92/2.04
% 1.92/2.04 %-------------------------------------------
% 1.92/2.04 cnf(16,plain,
% 1.92/2.04 (~P2(f7(a14,a2,a3),a2,f13(a3))+P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[1,6,2,4,9,12])).
% 1.92/2.04 cnf(17,plain,
% 1.92/2.04 (~P1(a2,a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[1,6,2,4,9,12,7])).
% 1.92/2.04 cnf(19,plain,
% 1.92/2.04 (~P1(f5(a2,a15,a3),a15,a3)),
% 1.92/2.04 inference(scs_inference,[],[1,6,2,4,9,12,7,10])).
% 1.92/2.04 cnf(21,plain,
% 1.92/2.04 (P1(f5(a2,a15,a3),a2,a3)),
% 1.92/2.04 inference(scs_inference,[],[1,6,2,4,9,12,7,10,8])).
% 1.92/2.04 cnf(23,plain,
% 1.92/2.04 (~P2(a12,a14,f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[2,17,9])).
% 1.92/2.04 cnf(25,plain,
% 1.92/2.04 (~P2(f9(a14,a15,a3),a15,f13(a3))+~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[1,5,6,2,17,9,14])).
% 1.92/2.04 cnf(27,plain,
% 1.92/2.04 (~P2(f7(a14,a2,a3),a2,f13(a3))+~P2(f9(a14,a15,a3),a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[1,5,6,2,4,17,9,14,12])).
% 1.92/2.04 cnf(33,plain,
% 1.92/2.04 (P1(f7(a14,a2,a3),a14,f13(a3))+P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[2,4,11])).
% 1.92/2.04 cnf(35,plain,
% 1.92/2.04 (P1(f7(a14,a2,a3),a14,f13(a3))+P1(f9(a14,a15,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[2,5,6,4,1,11,13])).
% 1.92/2.04 cnf(41,plain,
% 1.92/2.04 (P1(f9(a14,a15,a3),a14,f13(a3))+~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[5,21,19,9,13])).
% 1.92/2.04 cnf(50,plain,
% 1.92/2.04 (P1(x501,a2,a3)+~P1(x501,a15,a3)),
% 1.92/2.04 inference(scs_inference,[],[3,23,10,8,9])).
% 1.92/2.04 cnf(128,plain,
% 1.92/2.04 (P2(x1281,a2,f13(a3))+~P1(f5(x1281,a2,a3),a15,a3)),
% 1.92/2.04 inference(scs_inference,[],[50,10])).
% 1.92/2.04 cnf(129,plain,
% 1.92/2.04 (~P2(f9(a14,a15,a3),a15,f13(a3))+~P1(f5(f7(a14,a2,a3),a2,a3),a15,a3)),
% 1.92/2.04 inference(scs_inference,[],[128,27])).
% 1.92/2.04 cnf(130,plain,
% 1.92/2.04 (~P1(f5(f7(a14,a2,a3),a2,a3),a15,a3)+~P1(f9(a14,a15,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[129,7])).
% 1.92/2.04 cnf(131,plain,
% 1.92/2.04 (~P1(f5(f7(a14,a2,a3),a2,a3),x1311,a3)+~P1(f9(a14,a15,a3),a14,f13(a3))+~P2(x1311,a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[130,9])).
% 1.92/2.04 cnf(132,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+~P1(f5(f7(a14,a2,a3),a2,a3),x1321,a3)+~P2(x1321,a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[131,41])).
% 1.92/2.04 cnf(133,plain,
% 1.92/2.04 (~P2(f7(a14,a2,a3),a2,f13(a3))+~P1(f5(f7(a14,a2,a3),a2,a3),x1331,a3)+~P2(x1331,a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[132,16])).
% 1.92/2.04 cnf(143,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+P2(f9(a14,a15,a3),a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[21,5,19,7,13])).
% 1.92/2.04 cnf(156,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+~P1(f9(a14,a15,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[19,21,5,7,14])).
% 1.92/2.04 cnf(157,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+P1(f7(a14,a2,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[156,35])).
% 1.92/2.04 cnf(158,plain,
% 1.92/2.04 (P1(f7(a14,a2,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[157,33])).
% 1.92/2.04 cnf(164,plain,
% 1.92/2.04 (P2(f7(a14,a2,a3),a15,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[158,7])).
% 1.92/2.04 cnf(276,plain,
% 1.92/2.04 (P1(f5(f7(a14,a2,a3),a2,a3),f7(a14,a2,a3),a3)+P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[2,4,8,12])).
% 1.92/2.04 cnf(277,plain,
% 1.92/2.04 (~P2(f9(a14,a15,a3),a15,f13(a3))+P1(f5(f7(a14,a2,a3),a2,a3),f7(a14,a2,a3),a3)),
% 1.92/2.04 inference(scs_inference,[],[276,25])).
% 1.92/2.04 cnf(278,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+P1(f5(f7(a14,a2,a3),a2,a3),f7(a14,a2,a3),a3)),
% 1.92/2.04 inference(scs_inference,[],[277,143])).
% 1.92/2.04 cnf(289,plain,
% 1.92/2.04 (~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)+P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))),
% 1.92/2.04 inference(scs_inference,[],[4,2,10,12])).
% 1.92/2.04 cnf(290,plain,
% 1.92/2.04 (~P2(f9(a14,a15,a3),a15,f13(a3))+~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)),
% 1.92/2.04 inference(scs_inference,[],[289,25])).
% 1.92/2.04 cnf(291,plain,
% 1.92/2.04 (~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)+~P1(f9(a14,a15,a3),a14,f13(a3))),
% 1.92/2.04 inference(scs_inference,[],[290,7])).
% 1.92/2.04 cnf(292,plain,
% 1.92/2.04 (~P1(f11(f10(a2,a8,f13(a3)),a14,f13(a3)),f4(a12,a3),f13(f13(a3)))+~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)),
% 1.92/2.05 inference(scs_inference,[],[291,41])).
% 1.92/2.05 cnf(293,plain,
% 1.92/2.05 (~P2(f7(a14,a2,a3),a2,f13(a3))+~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)),
% 1.92/2.05 inference(scs_inference,[],[292,16])).
% 1.92/2.05 cnf(294,plain,
% 1.92/2.05 (~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)+P1(f5(f7(a14,a2,a3),a2,a3),f7(a14,a2,a3),a3)),
% 1.92/2.05 inference(scs_inference,[],[293,8])).
% 1.92/2.05 cnf(298,plain,
% 1.92/2.05 (~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)+~P1(f5(f7(a14,a2,a3),a2,a3),f7(a14,a2,a3),a3)),
% 1.92/2.05 inference(scs_inference,[],[164,10,133])).
% 1.92/2.05 cnf(299,plain,
% 1.92/2.05 (~P1(f5(f7(a14,a2,a3),a2,a3),a2,a3)),
% 1.92/2.05 inference(scs_inference,[],[298,294])).
% 1.92/2.05 cnf(300,plain,
% 1.92/2.05 (~P1(f5(f7(a14,a2,a3),a2,a3),a15,a3)),
% 1.92/2.05 inference(scs_inference,[],[299,3,9])).
% 1.92/2.05 cnf(308,plain,
% 1.92/2.05 ($false),
% 1.92/2.05 inference(scs_inference,[],[300,164,9,278,276]),
% 1.92/2.05 ['proof']).
% 1.92/2.05 % SZS output end Proof
% 1.92/2.05 % Total time :1.370000s
%------------------------------------------------------------------------------