TSTP Solution File: SET867+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET867+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 : n007.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 14:31:31 EDT 2023
% Result : Theorem 0.79s 0.92s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 14:46:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.79/0.92 %-------------------------------------------
% 0.79/0.92 % File :CSE---1.6
% 0.79/0.92 % Problem :theBenchmark
% 0.79/0.92 % Transform :cnf
% 0.79/0.92 % Format :tptp:raw
% 0.79/0.92 % Command :java -jar mcs_scs.jar %d %s
% 0.79/0.92
% 0.79/0.92 % Result :Theorem 0.310000s
% 0.79/0.92 % Output :CNFRefutation 0.310000s
% 0.79/0.92 %-------------------------------------------
% 0.79/0.92 %------------------------------------------------------------------------------
% 0.79/0.92 % File : SET867+1 : TPTP v8.1.2. Released v3.2.0.
% 0.79/0.92 % Domain : Set theory
% 0.79/0.92 % Problem : union(empty_set) = empty_set
% 0.79/0.92 % Version : [Urb06] axioms : Especial.
% 0.79/0.92 % English :
% 0.79/0.92
% 0.79/0.92 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.79/0.92 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.79/0.92 % Source : [Urb06]
% 0.79/0.92 % Names : zfmisc_1__t2_zfmisc_1 [Urb06]
% 0.79/0.92
% 0.79/0.92 % Status : Theorem
% 0.79/0.92 % Rating : 0.14 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.04 v5.3.0, 0.11 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0
% 0.79/0.92 % Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% 0.79/0.92 % Number of atoms : 12 ( 3 equ)
% 0.79/0.92 % Maximal formula atoms : 4 ( 1 avg)
% 0.79/0.92 % Number of connectives : 8 ( 3 ~; 0 |; 1 &)
% 0.79/0.92 % ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% 0.79/0.92 % Maximal formula depth : 8 ( 4 avg)
% 0.79/0.92 % Maximal term depth : 2 ( 1 avg)
% 0.79/0.92 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.79/0.92 % Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% 0.79/0.92 % Number of variables : 10 ( 7 !; 3 ?)
% 0.79/0.92 % SPC : FOF_THM_RFO_SEQ
% 0.79/0.92
% 0.79/0.92 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.79/0.92 % library, www.mizar.org
% 0.79/0.92 %------------------------------------------------------------------------------
% 0.79/0.92 fof(antisymmetry_r2_hidden,axiom,
% 0.79/0.92 ! [A,B] :
% 0.79/0.92 ( in(A,B)
% 0.79/0.92 => ~ in(B,A) ) ).
% 0.79/0.92
% 0.79/0.92 fof(d1_xboole_0,axiom,
% 0.79/0.92 ! [A] :
% 0.79/0.92 ( A = empty_set
% 0.79/0.92 <=> ! [B] : ~ in(B,A) ) ).
% 0.79/0.92
% 0.79/0.92 fof(d4_tarski,axiom,
% 0.79/0.92 ! [A,B] :
% 0.79/0.92 ( B = union(A)
% 0.79/0.92 <=> ! [C] :
% 0.79/0.92 ( in(C,B)
% 0.79/0.92 <=> ? [D] :
% 0.79/0.92 ( in(C,D)
% 0.79/0.92 & in(D,A) ) ) ) ).
% 0.79/0.92
% 0.79/0.92 fof(fc1_xboole_0,axiom,
% 0.79/0.92 empty(empty_set) ).
% 0.79/0.92
% 0.79/0.92 fof(rc1_xboole_0,axiom,
% 0.79/0.92 ? [A] : empty(A) ).
% 0.79/0.92
% 0.79/0.92 fof(rc2_xboole_0,axiom,
% 0.79/0.92 ? [A] : ~ empty(A) ).
% 0.79/0.92
% 0.79/0.92 fof(t2_zfmisc_1,conjecture,
% 0.79/0.92 union(empty_set) = empty_set ).
% 0.79/0.92
% 0.79/0.92 %------------------------------------------------------------------------------
% 0.79/0.92 %-------------------------------------------
% 0.79/0.92 % Proof found
% 0.79/0.92 % SZS status Theorem for theBenchmark
% 0.79/0.92 % SZS output start Proof
% 0.79/0.92 %ClaNum:28(EqnAxiom:15)
% 0.79/0.92 %VarNum:61(SingletonVarNum:22)
% 0.79/0.92 %MaxLitNum:4
% 0.79/0.92 %MaxfuncDepth:1
% 0.79/0.92 %SharedTerms:8
% 0.79/0.92 %goalClause: 18
% 0.79/0.92 %singleGoalClaCount:1
% 0.79/0.92 [16]P1(a1)
% 0.79/0.92 [17]P1(a2)
% 0.79/0.92 [19]~P1(a8)
% 0.79/0.92 [18]~E(f7(a1),a1)
% 0.79/0.92 [20]P2(f3(x201),x201)+E(x201,a1)
% 0.79/0.92 [21]~P2(x212,x211)+~E(x211,a1)
% 0.79/0.92 [22]~P2(x222,x221)+~P2(x221,x222)
% 0.79/0.92 [24]P2(f4(x242,x241),x241)+P2(f6(x242,x241),x242)+E(x241,f7(x242))
% 0.79/0.92 [25]P2(f4(x252,x251),x251)+P2(f4(x252,x251),f6(x252,x251))+E(x251,f7(x252))
% 0.79/0.93 [26]~P2(x261,x263)+~E(x263,f7(x262))+P2(x261,f5(x262,x263,x261))
% 0.79/0.93 [27]~P2(x273,x272)+~E(x272,f7(x271))+P2(f5(x271,x272,x273),x271)
% 0.79/0.93 [28]~P2(x283,x282)+~P2(f4(x282,x281),x283)+~P2(f4(x282,x281),x281)+E(x281,f7(x282))
% 0.79/0.93 [23]~P2(x231,x234)+P2(x231,x232)+~P2(x234,x233)+~E(x232,f7(x233))
% 0.79/0.93 %EqnAxiom
% 0.79/0.93 [1]E(x11,x11)
% 0.79/0.93 [2]E(x22,x21)+~E(x21,x22)
% 0.79/0.93 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.79/0.93 [4]~E(x41,x42)+E(f7(x41),f7(x42))
% 0.79/0.93 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 0.79/0.93 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.79/0.93 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.79/0.93 [8]~E(x81,x82)+E(f5(x81,x83,x84),f5(x82,x83,x84))
% 0.79/0.93 [9]~E(x91,x92)+E(f5(x93,x91,x94),f5(x93,x92,x94))
% 0.79/0.93 [10]~E(x101,x102)+E(f5(x103,x104,x101),f5(x103,x104,x102))
% 0.79/0.93 [11]~E(x111,x112)+E(f6(x111,x113),f6(x112,x113))
% 0.79/0.93 [12]~E(x121,x122)+E(f6(x123,x121),f6(x123,x122))
% 0.79/0.93 [13]~P1(x131)+P1(x132)+~E(x131,x132)
% 0.79/0.93 [14]P2(x142,x143)+~E(x141,x142)+~P2(x141,x143)
% 0.79/0.93 [15]P2(x153,x152)+~E(x151,x152)+~P2(x153,x151)
% 0.79/0.93
% 0.79/0.93 %-------------------------------------------
% 0.79/0.93 cnf(30,plain,
% 0.79/0.93 (~E(a1,f7(a1))),
% 0.79/0.93 inference(scs_inference,[],[18,20,2])).
% 0.79/0.93 cnf(45,plain,
% 0.79/0.93 (P2(f6(a1,a1),a1)+P2(f4(a1,a1),a1)),
% 0.79/0.93 inference(scs_inference,[],[30,24])).
% 0.79/0.93 cnf(156,plain,
% 0.79/0.93 (P2(f6(a1,a1),a1)),
% 0.79/0.93 inference(scs_inference,[],[45,21])).
% 0.79/0.93 cnf(299,plain,
% 0.79/0.93 ($false),
% 0.79/0.93 inference(scs_inference,[],[156,21]),
% 0.79/0.93 ['proof']).
% 0.79/0.93 % SZS output end Proof
% 0.79/0.93 % Total time :0.310000s
%------------------------------------------------------------------------------