TSTP Solution File: SET909+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET909+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 : n008.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 14:31:39 EDT 2023
% Result : Theorem 0.19s 0.71s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 13:07:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof:theBenchmark
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % File :CSE---1.6
% 0.19/0.70 % Problem :theBenchmark
% 0.19/0.70 % Transform :cnf
% 0.19/0.70 % Format :tptp:raw
% 0.19/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.70
% 0.19/0.70 % Result :Theorem 0.080000s
% 0.19/0.70 % Output :CNFRefutation 0.080000s
% 0.19/0.70 %-------------------------------------------
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 % File : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.71 % Domain : Set theory
% 0.19/0.71 % Problem : union(unordered_pair(A,B),C) != empty_set
% 0.19/0.71 % Version : [Urb06] axioms : Especial.
% 0.19/0.71 % English :
% 0.19/0.71
% 0.19/0.71 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.71 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.71 % Source : [Urb06]
% 0.19/0.71 % Names : zfmisc_1__t50_zfmisc_1 [Urb06]
% 0.19/0.71
% 0.19/0.71 % Status : Theorem
% 0.19/0.71 % Rating : 0.19 v7.5.0, 0.22 v7.4.0, 0.10 v7.3.0, 0.14 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.21 v6.2.0, 0.36 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.21 v4.1.0, 0.22 v4.0.1, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.2.0
% 0.19/0.71 % Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% 0.19/0.71 % Number of atoms : 23 ( 9 equ)
% 0.19/0.71 % Maximal formula atoms : 4 ( 1 avg)
% 0.19/0.71 % Number of connectives : 18 ( 8 ~; 2 |; 0 &)
% 0.19/0.71 % ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.71 % Maximal formula depth : 8 ( 4 avg)
% 0.19/0.71 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.71 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.19/0.71 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.71 % Number of variables : 27 ( 25 !; 2 ?)
% 0.19/0.71 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.71
% 0.19/0.71 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.71 % library, www.mizar.org
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.71 ! [A,B] :
% 0.19/0.71 ( in(A,B)
% 0.19/0.71 => ~ in(B,A) ) ).
% 0.19/0.71
% 0.19/0.71 fof(commutativity_k2_tarski,axiom,
% 0.19/0.71 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 0.19/0.71
% 0.19/0.71 fof(commutativity_k2_xboole_0,axiom,
% 0.19/0.71 ! [A,B] : set_union2(A,B) = set_union2(B,A) ).
% 0.19/0.71
% 0.19/0.71 fof(d1_xboole_0,axiom,
% 0.19/0.71 ! [A] :
% 0.19/0.71 ( A = empty_set
% 0.19/0.71 <=> ! [B] : ~ in(B,A) ) ).
% 0.19/0.71
% 0.19/0.71 fof(d2_tarski,axiom,
% 0.19/0.71 ! [A,B,C] :
% 0.19/0.71 ( C = unordered_pair(A,B)
% 0.19/0.71 <=> ! [D] :
% 0.19/0.71 ( in(D,C)
% 0.19/0.71 <=> ( D = A
% 0.19/0.71 | D = B ) ) ) ).
% 0.19/0.71
% 0.19/0.71 fof(d2_xboole_0,axiom,
% 0.19/0.71 ! [A,B,C] :
% 0.19/0.71 ( C = set_union2(A,B)
% 0.19/0.71 <=> ! [D] :
% 0.19/0.71 ( in(D,C)
% 0.19/0.71 <=> ( in(D,A)
% 0.19/0.71 | in(D,B) ) ) ) ).
% 0.19/0.71
% 0.19/0.71 fof(fc1_xboole_0,axiom,
% 0.19/0.71 empty(empty_set) ).
% 0.19/0.71
% 0.19/0.71 fof(fc2_xboole_0,axiom,
% 0.19/0.71 ! [A,B] :
% 0.19/0.71 ( ~ empty(A)
% 0.19/0.71 => ~ empty(set_union2(A,B)) ) ).
% 0.19/0.71
% 0.19/0.71 fof(fc3_xboole_0,axiom,
% 0.19/0.71 ! [A,B] :
% 0.19/0.71 ( ~ empty(A)
% 0.19/0.71 => ~ empty(set_union2(B,A)) ) ).
% 0.19/0.71
% 0.19/0.71 fof(idempotence_k2_xboole_0,axiom,
% 0.19/0.71 ! [A,B] : set_union2(A,A) = A ).
% 0.19/0.71
% 0.19/0.71 fof(rc1_xboole_0,axiom,
% 0.19/0.71 ? [A] : empty(A) ).
% 0.19/0.71
% 0.19/0.71 fof(rc2_xboole_0,axiom,
% 0.19/0.71 ? [A] : ~ empty(A) ).
% 0.19/0.71
% 0.19/0.71 fof(t50_zfmisc_1,conjecture,
% 0.19/0.71 ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set ).
% 0.19/0.71
% 0.19/0.71 %------------------------------------------------------------------------------
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 % Proof found
% 0.19/0.71 % SZS status Theorem for theBenchmark
% 0.19/0.71 % SZS output start Proof
% 0.19/0.71 %ClaNum:41(EqnAxiom:17)
% 0.19/0.71 %VarNum:147(SingletonVarNum:56)
% 0.19/0.71 %MaxLitNum:4
% 0.19/0.71 %MaxfuncDepth:2
% 0.19/0.71 %SharedTerms:12
% 0.19/0.71 %goalClause: 23
% 0.19/0.71 %singleGoalClaCount:1
% 0.19/0.71 [18]P1(a1)
% 0.19/0.71 [19]P1(a2)
% 0.19/0.71 [24]~P1(a8)
% 0.19/0.71 [23]E(f6(f11(a7,a9),a10),a1)
% 0.19/0.71 [20]E(f6(x201,x201),x201)
% 0.19/0.71 [21]E(f11(x211,x212),f11(x212,x211))
% 0.19/0.71 [22]E(f6(x221,x222),f6(x222,x221))
% 0.19/0.71 [25]P2(f3(x251),x251)+E(x251,a1)
% 0.19/0.71 [26]~P2(x262,x261)+~E(x261,a1)
% 0.19/0.71 [29]~P2(x292,x291)+~P2(x291,x292)
% 0.19/0.71 [31]P1(x311)+~P1(f6(x312,x311))
% 0.19/0.71 [32]P1(x321)+~P1(f6(x321,x322))
% 0.19/0.71 [37]~E(f4(x372,x373,x371),x373)+~P2(f4(x372,x373,x371),x371)+E(x371,f11(x372,x373))
% 0.19/0.71 [38]~E(f4(x382,x383,x381),x382)+~P2(f4(x382,x383,x381),x381)+E(x381,f11(x382,x383))
% 0.19/0.71 [40]~P2(f5(x402,x403,x401),x401)+~P2(f5(x402,x403,x401),x403)+E(x401,f6(x402,x403))
% 0.19/0.71 [41]~P2(f5(x412,x413,x411),x411)+~P2(f5(x412,x413,x411),x412)+E(x411,f6(x412,x413))
% 0.19/0.71 [27]P2(x271,x272)+~E(x271,x273)+~E(x272,f11(x274,x273))
% 0.19/0.71 [28]P2(x281,x282)+~E(x281,x283)+~E(x282,f11(x283,x284))
% 0.19/0.71 [33]~P2(x331,x334)+P2(x331,x332)+~E(x332,f6(x333,x334))
% 0.19/0.71 [34]~P2(x341,x343)+P2(x341,x342)+~E(x342,f6(x343,x344))
% 0.19/0.71 [36]E(f4(x362,x363,x361),x363)+E(f4(x362,x363,x361),x362)+P2(f4(x362,x363,x361),x361)+E(x361,f11(x362,x363))
% 0.19/0.71 [39]P2(f5(x392,x393,x391),x391)+P2(f5(x392,x393,x391),x393)+P2(f5(x392,x393,x391),x392)+E(x391,f6(x392,x393))
% 0.19/0.71 [30]~P2(x301,x304)+E(x301,x302)+E(x301,x303)+~E(x304,f11(x303,x302))
% 0.19/0.71 [35]~P2(x351,x354)+P2(x351,x352)+P2(x351,x353)+~E(x354,f6(x353,x352))
% 0.19/0.71 %EqnAxiom
% 0.19/0.71 [1]E(x11,x11)
% 0.19/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.71 [4]~E(x41,x42)+E(f6(x41,x43),f6(x42,x43))
% 0.19/0.71 [5]~E(x51,x52)+E(f6(x53,x51),f6(x53,x52))
% 0.19/0.71 [6]~E(x61,x62)+E(f11(x61,x63),f11(x62,x63))
% 0.19/0.71 [7]~E(x71,x72)+E(f11(x73,x71),f11(x73,x72))
% 0.19/0.71 [8]~E(x81,x82)+E(f4(x81,x83,x84),f4(x82,x83,x84))
% 0.19/0.71 [9]~E(x91,x92)+E(f4(x93,x91,x94),f4(x93,x92,x94))
% 0.19/0.71 [10]~E(x101,x102)+E(f4(x103,x104,x101),f4(x103,x104,x102))
% 0.19/0.71 [11]~E(x111,x112)+E(f5(x111,x113,x114),f5(x112,x113,x114))
% 0.19/0.71 [12]~E(x121,x122)+E(f5(x123,x121,x124),f5(x123,x122,x124))
% 0.19/0.71 [13]~E(x131,x132)+E(f5(x133,x134,x131),f5(x133,x134,x132))
% 0.19/0.71 [14]~E(x141,x142)+E(f3(x141),f3(x142))
% 0.19/0.71 [15]~P1(x151)+P1(x152)+~E(x151,x152)
% 0.19/0.71 [16]P2(x162,x163)+~E(x161,x162)+~P2(x161,x163)
% 0.19/0.71 [17]P2(x173,x172)+~E(x171,x172)+~P2(x173,x171)
% 0.19/0.71
% 0.19/0.71 %-------------------------------------------
% 0.19/0.71 cnf(48,plain,
% 0.19/0.71 (E(f6(x481,x482),f6(x482,x481))),
% 0.19/0.71 inference(rename_variables,[],[22])).
% 0.19/0.71 cnf(50,plain,
% 0.19/0.71 (~P2(x501,f11(a7,a9))),
% 0.19/0.71 inference(scs_inference,[],[23,24,20,22,48,2,26,15,34,33])).
% 0.19/0.71 cnf(208,plain,
% 0.19/0.71 ($false),
% 0.19/0.71 inference(scs_inference,[],[20,21,50,27]),
% 0.19/0.71 ['proof']).
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time :0.080000s
%------------------------------------------------------------------------------