TSTP Solution File: SET942+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET942+1 : 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 : 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 : 300s
% DateTime : Thu Aug 31 14:31:47 EDT 2023
% Result : Theorem 120.84s 120.88s
% Output : CNFRefutation 120.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET942+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:47:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 120.84/120.88 %-------------------------------------------
% 120.84/120.88 % File :CSE---1.6
% 120.84/120.88 % Problem :theBenchmark
% 120.84/120.88 % Transform :cnf
% 120.84/120.88 % Format :tptp:raw
% 120.84/120.88 % Command :java -jar mcs_scs.jar %d %s
% 120.84/120.88
% 120.84/120.88 % Result :Theorem 120.210000s
% 120.84/120.88 % Output :CNFRefutation 120.210000s
% 120.84/120.88 %-------------------------------------------
% 120.84/120.88 %------------------------------------------------------------------------------
% 120.84/120.88 % File : SET942+1 : TPTP v8.1.2. Released v3.2.0.
% 120.84/120.88 % Domain : Set theory
% 120.84/120.88 % Problem : subset(A,B) => subset(union(A),union(B))
% 120.84/120.88 % Version : [Urb06] axioms : Especial.
% 120.84/120.88 % English :
% 120.84/120.88
% 120.84/120.88 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 120.84/120.88 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 120.84/120.88 % Source : [Urb06]
% 120.84/120.88 % Names : zfmisc_1__t95_zfmisc_1 [Urb06]
% 120.84/120.88
% 120.84/120.88 % Status : Theorem
% 120.84/120.88 % Rating : 0.28 v8.1.0, 0.25 v7.4.0, 0.13 v7.3.0, 0.17 v7.2.0, 0.14 v7.1.0, 0.17 v6.4.0, 0.19 v6.3.0, 0.21 v6.2.0, 0.28 v6.1.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.26 v5.4.0, 0.32 v5.3.0, 0.37 v5.2.0, 0.25 v5.1.0, 0.24 v5.0.0, 0.33 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.32 v3.3.0, 0.36 v3.2.0
% 120.84/120.88 % Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% 120.84/120.88 % Number of atoms : 14 ( 1 equ)
% 120.84/120.88 % Maximal formula atoms : 4 ( 2 avg)
% 120.84/120.88 % Number of connectives : 9 ( 2 ~; 0 |; 1 &)
% 120.84/120.88 % ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% 120.84/120.88 % Maximal formula depth : 8 ( 4 avg)
% 120.84/120.88 % Maximal term depth : 2 ( 1 avg)
% 120.84/120.88 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 120.84/120.88 % Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% 120.84/120.88 % Number of variables : 15 ( 12 !; 3 ?)
% 120.84/120.88 % SPC : FOF_THM_RFO_SEQ
% 120.84/120.88
% 120.84/120.88 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 120.84/120.88 % library, www.mizar.org
% 120.84/120.88 %------------------------------------------------------------------------------
% 120.84/120.88 fof(antisymmetry_r2_hidden,axiom,
% 120.84/120.88 ! [A,B] :
% 120.84/120.88 ( in(A,B)
% 120.84/120.88 => ~ in(B,A) ) ).
% 120.84/120.88
% 120.84/120.88 fof(d3_tarski,axiom,
% 120.84/120.88 ! [A,B] :
% 120.84/120.88 ( subset(A,B)
% 120.84/120.88 <=> ! [C] :
% 120.84/120.88 ( in(C,A)
% 120.84/120.88 => in(C,B) ) ) ).
% 120.84/120.88
% 120.84/120.88 fof(d4_tarski,axiom,
% 120.84/120.88 ! [A,B] :
% 120.84/120.88 ( B = union(A)
% 120.84/120.88 <=> ! [C] :
% 120.84/120.88 ( in(C,B)
% 120.84/120.88 <=> ? [D] :
% 120.84/120.88 ( in(C,D)
% 120.84/120.88 & in(D,A) ) ) ) ).
% 120.84/120.88
% 120.84/120.88 fof(rc1_xboole_0,axiom,
% 120.84/120.88 ? [A] : empty(A) ).
% 120.84/120.88
% 120.84/120.88 fof(rc2_xboole_0,axiom,
% 120.84/120.88 ? [A] : ~ empty(A) ).
% 120.84/120.88
% 120.84/120.88 fof(reflexivity_r1_tarski,axiom,
% 120.84/120.88 ! [A,B] : subset(A,A) ).
% 120.84/120.88
% 120.84/120.88 fof(t95_zfmisc_1,conjecture,
% 120.84/120.88 ! [A,B] :
% 120.84/120.88 ( subset(A,B)
% 120.84/120.88 => subset(union(A),union(B)) ) ).
% 120.84/120.88
% 120.84/120.88 %------------------------------------------------------------------------------
% 120.84/120.88 %-------------------------------------------
% 120.84/120.88 % Proof found
% 120.84/120.88 % SZS status Theorem for theBenchmark
% 120.84/120.88 % SZS output start Proof
% 120.84/120.89 %ClaNum:33(EqnAxiom:18)
% 120.84/120.89 %VarNum:73(SingletonVarNum:27)
% 120.84/120.89 %MaxLitNum:4
% 120.84/120.89 %MaxfuncDepth:1
% 120.84/120.89 %SharedTerms:10
% 120.84/120.89 %goalClause: 20 23
% 120.84/120.89 %singleGoalClaCount:2
% 120.84/120.89 [19]P1(a1)
% 120.84/120.89 [20]P2(a6,a8)
% 120.84/120.89 [22]~P1(a7)
% 120.84/120.89 [23]~P2(f9(a6),f9(a8))
% 120.84/120.89 [21]P2(x211,x211)
% 120.84/120.89 [24]~P3(x242,x241)+~P3(x241,x242)
% 120.84/120.89 [25]P2(x251,x252)+P3(f2(x251,x252),x251)
% 120.84/120.89 [28]P2(x281,x282)+~P3(f2(x281,x282),x282)
% 120.84/120.89 [29]P3(f3(x292,x291),x291)+P3(f5(x292,x291),x292)+E(x291,f9(x292))
% 120.84/120.89 [30]P3(f3(x302,x301),x301)+P3(f3(x302,x301),f5(x302,x301))+E(x301,f9(x302))
% 120.84/120.89 [26]~P2(x263,x262)+P3(x261,x262)+~P3(x261,x263)
% 120.84/120.89 [31]~P3(x311,x313)+~E(x313,f9(x312))+P3(x311,f4(x312,x313,x311))
% 120.84/120.89 [32]~P3(x323,x322)+~E(x322,f9(x321))+P3(f4(x321,x322,x323),x321)
% 120.84/120.89 [33]~P3(x333,x332)+~P3(f3(x332,x331),x333)+~P3(f3(x332,x331),x331)+E(x331,f9(x332))
% 120.84/120.89 [27]~P3(x271,x274)+P3(x271,x272)+~P3(x274,x273)+~E(x272,f9(x273))
% 120.84/120.89 %EqnAxiom
% 120.84/120.89 [1]E(x11,x11)
% 120.84/120.89 [2]E(x22,x21)+~E(x21,x22)
% 120.84/120.89 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 120.84/120.89 [4]~E(x41,x42)+E(f9(x41),f9(x42))
% 120.84/120.89 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 120.84/120.89 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 120.84/120.89 [7]~E(x71,x72)+E(f2(x71,x73),f2(x72,x73))
% 120.84/120.89 [8]~E(x81,x82)+E(f2(x83,x81),f2(x83,x82))
% 120.84/120.89 [9]~E(x91,x92)+E(f5(x91,x93),f5(x92,x93))
% 120.84/120.89 [10]~E(x101,x102)+E(f5(x103,x101),f5(x103,x102))
% 120.84/120.89 [11]~E(x111,x112)+E(f4(x111,x113,x114),f4(x112,x113,x114))
% 120.84/120.89 [12]~E(x121,x122)+E(f4(x123,x121,x124),f4(x123,x122,x124))
% 120.84/120.89 [13]~E(x131,x132)+E(f4(x133,x134,x131),f4(x133,x134,x132))
% 120.84/120.89 [14]~P1(x141)+P1(x142)+~E(x141,x142)
% 120.84/120.89 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 120.84/120.89 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 120.84/120.89 [17]P3(x172,x173)+~E(x171,x172)+~P3(x171,x173)
% 120.84/120.89 [18]P3(x183,x182)+~E(x181,x182)+~P3(x183,x181)
% 120.84/120.89
% 120.84/120.89 %-------------------------------------------
% 120.84/120.89 cnf(35,plain,
% 120.84/120.89 (P2(x351,x351)),
% 120.84/120.89 inference(rename_variables,[],[21])).
% 120.84/120.89 cnf(40,plain,
% 120.84/120.89 (P3(f2(f9(a6),f9(a8)),f9(a6))),
% 120.84/120.89 inference(scs_inference,[],[21,35,23,16,15,28,25])).
% 120.84/120.89 cnf(173,plain,
% 120.84/120.89 (P3(f2(f9(a6),f9(a8)),f4(x1731,f9(a6),f2(f9(a6),f9(a8))))+~E(f9(a6),f9(x1731))),
% 120.84/120.89 inference(scs_inference,[],[23,31,25])).
% 120.84/120.89 cnf(174,plain,
% 120.84/120.89 (P3(f2(f9(a6),f9(a8)),f4(a6,f9(a6),f2(f9(a6),f9(a8))))),
% 120.84/120.89 inference(equality_inference,[],[173])).
% 120.84/120.89 cnf(204,plain,
% 120.84/120.89 (~E(f9(x2041),f9(a6))+P3(f4(x2041,f9(a6),f2(f9(a6),f9(a8))),x2041)),
% 120.84/120.89 inference(scs_inference,[],[40,2,32])).
% 120.84/120.89 cnf(205,plain,
% 120.84/120.89 (P3(f4(a6,f9(a6),f2(f9(a6),f9(a8))),a6)),
% 120.84/120.89 inference(equality_inference,[],[204])).
% 120.84/120.89 cnf(1375,plain,
% 120.84/120.89 (~P3(f2(f9(a6),f9(a8)),x13751)+~P3(x13751,x13752)+~E(f9(a8),f9(x13752))),
% 120.84/120.89 inference(scs_inference,[],[23,28,27])).
% 120.84/120.89 cnf(1376,plain,
% 120.84/120.89 (~P3(f2(f9(a6),f9(a8)),x13761)+~P3(x13761,a8)),
% 120.84/120.89 inference(equality_inference,[],[1375])).
% 120.84/120.89 cnf(2117,plain,
% 120.84/120.89 ($false),
% 120.84/120.89 inference(scs_inference,[],[20,174,205,1376,26]),
% 120.84/120.89 ['proof']).
% 120.84/120.89 % SZS output end Proof
% 120.84/120.89 % Total time :120.210000s
%------------------------------------------------------------------------------