TSTP Solution File: SET920+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET920+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 : 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 14:31:42 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET920+1 : 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
% 0.13/0.34 % Computer : n021.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 : 300
% 0.13/0.34 % DateTime : Sat Aug 26 12:42:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % File :CSE---1.6
% 0.20/0.64 % Problem :theBenchmark
% 0.20/0.64 % Transform :cnf
% 0.20/0.64 % Format :tptp:raw
% 0.20/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.64
% 0.20/0.64 % Result :Theorem 0.010000s
% 0.20/0.64 % Output :CNFRefutation 0.010000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 % File : SET920+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.65 % Domain : Set theory
% 0.20/0.65 % Problem : intersection(uno_pair(A,B),C) = uno_pair(A,B) => in(A,C)
% 0.20/0.65 % Version : [Urb06] axioms : Especial.
% 0.20/0.65 % English :
% 0.20/0.65
% 0.20/0.65 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.65 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.65 % Source : [Urb06]
% 0.20/0.65 % Names : zfmisc_1__t63_zfmisc_1 [Urb06]
% 0.20/0.65
% 0.20/0.65 % Status : Theorem
% 0.20/0.65 % Rating : 0.14 v8.1.0, 0.17 v7.5.0, 0.19 v7.4.0, 0.13 v7.3.0, 0.14 v7.1.0, 0.13 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.24 v6.1.0, 0.27 v6.0.0, 0.26 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.10 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.1, 0.22 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0, 0.14 v3.2.0
% 0.20/0.65 % Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% 0.20/0.65 % Number of atoms : 17 ( 8 equ)
% 0.20/0.65 % Maximal formula atoms : 4 ( 1 avg)
% 0.20/0.65 % Number of connectives : 10 ( 2 ~; 1 |; 1 &)
% 0.20/0.65 % ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% 0.20/0.65 % Maximal formula depth : 8 ( 4 avg)
% 0.20/0.65 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.65 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.65 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.20/0.65 % Number of variables : 21 ( 19 !; 2 ?)
% 0.20/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.65
% 0.20/0.65 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.65 % library, www.mizar.org
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.65 ! [A,B] :
% 0.20/0.65 ( in(A,B)
% 0.20/0.65 => ~ in(B,A) ) ).
% 0.20/0.65
% 0.20/0.65 fof(commutativity_k2_tarski,axiom,
% 0.20/0.65 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.20/0.65
% 0.20/0.65 fof(commutativity_k3_xboole_0,axiom,
% 0.20/0.65 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.20/0.65
% 0.20/0.65 fof(d2_tarski,axiom,
% 0.20/0.65 ! [A,B,C] :
% 0.20/0.65 ( C = unordered_pair(A,B)
% 0.20/0.65 <=> ! [D] :
% 0.20/0.65 ( in(D,C)
% 0.20/0.65 <=> ( D = A
% 0.20/0.65 | D = B ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(d3_xboole_0,axiom,
% 0.20/0.65 ! [A,B,C] :
% 0.20/0.65 ( C = set_intersection2(A,B)
% 0.20/0.65 <=> ! [D] :
% 0.20/0.65 ( in(D,C)
% 0.20/0.65 <=> ( in(D,A)
% 0.20/0.65 & in(D,B) ) ) ) ).
% 0.20/0.65
% 0.20/0.65 fof(idempotence_k3_xboole_0,axiom,
% 0.20/0.65 ! [A,B] : set_intersection2(A,A) = A ).
% 0.20/0.65
% 0.20/0.65 fof(rc1_xboole_0,axiom,
% 0.20/0.65 ? [A] : empty(A) ).
% 0.20/0.65
% 0.20/0.65 fof(rc2_xboole_0,axiom,
% 0.20/0.65 ? [A] : ~ empty(A) ).
% 0.20/0.65
% 0.20/0.65 fof(t63_zfmisc_1,conjecture,
% 0.20/0.65 ! [A,B,C] :
% 0.20/0.65 ( set_intersection2(unordered_pair(A,B),C) = unordered_pair(A,B)
% 0.20/0.65 => in(A,C) ) ).
% 0.20/0.65
% 0.20/0.65 %------------------------------------------------------------------------------
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark
% 0.20/0.65 % SZS output start Proof
% 0.20/0.65 %ClaNum:36(EqnAxiom:16)
% 0.20/0.65 %VarNum:135(SingletonVarNum:49)
% 0.20/0.65 %MaxLitNum:4
% 0.20/0.65 %MaxfuncDepth:2
% 0.20/0.65 %SharedTerms:11
% 0.20/0.65 %goalClause: 21 23
% 0.20/0.65 %singleGoalClaCount:2
% 0.20/0.65 [17]P1(a1)
% 0.20/0.65 [22]~P1(a6)
% 0.20/0.65 [23]~P2(a5,a8)
% 0.20/0.65 [21]E(f4(f9(a5,a7),a8),f9(a5,a7))
% 0.20/0.65 [18]E(f4(x181,x181),x181)
% 0.20/0.65 [19]E(f9(x191,x192),f9(x192,x191))
% 0.20/0.65 [20]E(f4(x201,x202),f4(x202,x201))
% 0.20/0.65 [26]~P2(x262,x261)+~P2(x261,x262)
% 0.20/0.65 [32]P2(f3(x322,x323,x321),x321)+P2(f3(x322,x323,x321),x323)+E(x321,f4(x322,x323))
% 0.20/0.65 [33]P2(f3(x332,x333,x331),x331)+P2(f3(x332,x333,x331),x332)+E(x331,f4(x332,x333))
% 0.20/0.65 [34]~E(f2(x342,x343,x341),x343)+~P2(f2(x342,x343,x341),x341)+E(x341,f9(x342,x343))
% 0.20/0.65 [35]~E(f2(x352,x353,x351),x352)+~P2(f2(x352,x353,x351),x351)+E(x351,f9(x352,x353))
% 0.20/0.65 [24]P2(x241,x242)+~E(x241,x243)+~E(x242,f9(x244,x243))
% 0.20/0.65 [25]P2(x251,x252)+~E(x251,x253)+~E(x252,f9(x253,x254))
% 0.20/0.65 [28]~P2(x281,x283)+P2(x281,x282)+~E(x283,f4(x284,x282))
% 0.20/0.65 [29]~P2(x291,x293)+P2(x291,x292)+~E(x293,f4(x292,x294))
% 0.20/0.65 [31]E(f2(x312,x313,x311),x313)+E(f2(x312,x313,x311),x312)+P2(f2(x312,x313,x311),x311)+E(x311,f9(x312,x313))
% 0.20/0.65 [36]~P2(f3(x362,x363,x361),x361)+~P2(f3(x362,x363,x361),x363)+~P2(f3(x362,x363,x361),x362)+E(x361,f4(x362,x363))
% 0.20/0.65 [27]~P2(x271,x274)+E(x271,x272)+E(x271,x273)+~E(x274,f9(x273,x272))
% 0.20/0.65 [30]~P2(x301,x304)+~P2(x301,x303)+P2(x301,x302)+~E(x302,f4(x303,x304))
% 0.20/0.65 %EqnAxiom
% 0.20/0.65 [1]E(x11,x11)
% 0.20/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.65 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.20/0.65 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.20/0.65 [6]~E(x61,x62)+E(f9(x61,x63),f9(x62,x63))
% 0.20/0.65 [7]~E(x71,x72)+E(f9(x73,x71),f9(x73,x72))
% 0.20/0.65 [8]~E(x81,x82)+E(f3(x81,x83,x84),f3(x82,x83,x84))
% 0.20/0.65 [9]~E(x91,x92)+E(f3(x93,x91,x94),f3(x93,x92,x94))
% 0.20/0.65 [10]~E(x101,x102)+E(f3(x103,x104,x101),f3(x103,x104,x102))
% 0.20/0.65 [11]~E(x111,x112)+E(f2(x111,x113,x114),f2(x112,x113,x114))
% 0.20/0.65 [12]~E(x121,x122)+E(f2(x123,x121,x124),f2(x123,x122,x124))
% 0.20/0.65 [13]~E(x131,x132)+E(f2(x133,x134,x131),f2(x133,x134,x132))
% 0.20/0.65 [14]~P1(x141)+P1(x142)+~E(x141,x142)
% 0.20/0.65 [15]P2(x152,x153)+~E(x151,x152)+~P2(x151,x153)
% 0.20/0.65 [16]P2(x163,x162)+~E(x161,x162)+~P2(x163,x161)
% 0.20/0.65
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 cnf(39,plain,
% 0.20/0.65 (E(f4(x391,x391),x391)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(41,plain,
% 0.20/0.65 (E(f4(x411,x411),x411)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(44,plain,
% 0.20/0.65 (E(f4(x441,x441),x441)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(46,plain,
% 0.20/0.65 (P2(f4(a5,a5),f4(f9(a5,a7),a8))),
% 0.20/0.65 inference(scs_inference,[],[21,23,22,18,39,41,44,2,14,29,28,25])).
% 0.20/0.65 cnf(47,plain,
% 0.20/0.65 (E(f4(x471,x471),x471)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(49,plain,
% 0.20/0.65 (P2(f4(a7,a7),f4(f9(a5,a7),a8))),
% 0.20/0.65 inference(scs_inference,[],[21,23,22,18,39,41,44,47,2,14,29,28,25,24])).
% 0.20/0.65 cnf(50,plain,
% 0.20/0.65 (E(f4(x501,x501),x501)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(52,plain,
% 0.20/0.65 (~P2(f4(f9(a5,a7),a8),f4(a5,a5))),
% 0.20/0.65 inference(scs_inference,[],[21,23,22,18,39,41,44,47,2,14,29,28,25,24,26])).
% 0.20/0.65 cnf(65,plain,
% 0.20/0.65 (E(f4(x651,x651),x651)),
% 0.20/0.65 inference(rename_variables,[],[18])).
% 0.20/0.65 cnf(66,plain,
% 0.20/0.65 (~P2(f4(a5,a5),a8)),
% 0.20/0.65 inference(scs_inference,[],[21,23,22,18,39,41,44,47,50,65,2,14,29,28,25,24,26,13,12,11,10,9,8,7,6,5,4,16,15])).
% 0.20/0.65 cnf(71,plain,
% 0.20/0.65 (E(f4(x711,x712),f4(x712,x711))),
% 0.20/0.65 inference(rename_variables,[],[20])).
% 0.20/0.65 cnf(75,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[20,71,52,46,49,66,30,26,29]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.010000s
%------------------------------------------------------------------------------