TSTP Solution File: SET880+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET880+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 : n025.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 14:31:33 EDT 2023
% Result : Theorem 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET880+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 : n025.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 10:47:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % File :CSE---1.6
% 0.19/0.64 % Problem :theBenchmark
% 0.19/0.64 % Transform :cnf
% 0.19/0.64 % Format :tptp:raw
% 0.19/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.64
% 0.19/0.64 % Result :Theorem 0.030000s
% 0.19/0.64 % Output :CNFRefutation 0.030000s
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 % File : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.64 % Domain : Set theory
% 0.19/0.64 % Problem : difference(singleton(A),singleton(B)) = empty_set => A = B
% 0.19/0.64 % Version : [Urb06] axioms : Especial.
% 0.19/0.64 % English :
% 0.19/0.64
% 0.19/0.64 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.64 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.64 % Source : [Urb06]
% 0.19/0.64 % Names : zfmisc_1__t21_zfmisc_1 [Urb06]
% 0.19/0.64
% 0.19/0.64 % Status : Theorem
% 0.19/0.64 % Rating : 0.06 v7.4.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.0, 0.12 v3.7.0, 0.10 v3.5.0, 0.11 v3.3.0, 0.14 v3.2.0
% 0.19/0.64 % Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% 0.19/0.64 % Number of atoms : 12 ( 5 equ)
% 0.19/0.64 % Maximal formula atoms : 3 ( 1 avg)
% 0.19/0.64 % Number of connectives : 7 ( 2 ~; 0 |; 0 &)
% 0.19/0.64 % ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% 0.19/0.64 % Maximal formula depth : 6 ( 4 avg)
% 0.19/0.64 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.19/0.64 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.64 % Number of variables : 11 ( 9 !; 2 ?)
% 0.19/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.64
% 0.19/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.64 % library, www.mizar.org
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( in(A,B)
% 0.19/0.64 => ~ in(B,A) ) ).
% 0.19/0.64
% 0.19/0.64 fof(d1_tarski,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( B = singleton(A)
% 0.19/0.64 <=> ! [C] :
% 0.19/0.64 ( in(C,B)
% 0.19/0.64 <=> C = A ) ) ).
% 0.19/0.64
% 0.19/0.64 fof(fc1_xboole_0,axiom,
% 0.19/0.64 empty(empty_set) ).
% 0.19/0.64
% 0.19/0.64 fof(l36_zfmisc_1,axiom,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( set_difference(singleton(A),B) = empty_set
% 0.19/0.64 <=> in(A,B) ) ).
% 0.19/0.64
% 0.19/0.64 fof(rc1_xboole_0,axiom,
% 0.19/0.64 ? [A] : empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(rc2_xboole_0,axiom,
% 0.19/0.64 ? [A] : ~ empty(A) ).
% 0.19/0.64
% 0.19/0.64 fof(t21_zfmisc_1,conjecture,
% 0.19/0.64 ! [A,B] :
% 0.19/0.64 ( set_difference(singleton(A),singleton(B)) = empty_set
% 0.19/0.64 => A = B ) ).
% 0.19/0.64
% 0.19/0.64 %------------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:23(EqnAxiom:11)
% 0.19/0.64 %VarNum:40(SingletonVarNum:16)
% 0.19/0.64 %MaxLitNum:3
% 0.19/0.64 %MaxfuncDepth:2
% 0.19/0.64 %SharedTerms:13
% 0.19/0.64 %goalClause: 14 15
% 0.19/0.64 %singleGoalClaCount:2
% 0.19/0.64 [12]P1(a1)
% 0.19/0.64 [13]P1(a2)
% 0.19/0.64 [15]~E(a7,a4)
% 0.19/0.64 [16]~P1(a5)
% 0.19/0.64 [14]E(f8(f6(a4),f6(a7)),a1)
% 0.19/0.64 [20]~P2(x202,x201)+~P2(x201,x202)
% 0.19/0.64 [19]~P2(x191,x192)+E(f8(f6(x191),x192),a1)
% 0.19/0.64 [21]P2(x211,x212)+~E(f8(f6(x211),x212),a1)
% 0.19/0.64 [22]E(f3(x222,x221),x222)+P2(f3(x222,x221),x221)+E(x221,f6(x222))
% 0.19/0.64 [23]~E(f3(x232,x231),x232)+~P2(f3(x232,x231),x231)+E(x231,f6(x232))
% 0.19/0.64 [17]P2(x171,x172)+~E(x171,x173)+~E(x172,f6(x173))
% 0.19/0.64 [18]~P2(x181,x183)+E(x181,x182)+~E(x183,f6(x182))
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f6(x41),f6(x42))
% 0.19/0.64 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.64 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.64 [7]~E(x71,x72)+E(f8(x71,x73),f8(x72,x73))
% 0.19/0.64 [8]~E(x81,x82)+E(f8(x83,x81),f8(x83,x82))
% 0.19/0.64 [9]~P1(x91)+P1(x92)+~E(x91,x92)
% 0.19/0.64 [10]P2(x102,x103)+~E(x101,x102)+~P2(x101,x103)
% 0.19/0.64 [11]P2(x113,x112)+~E(x111,x112)+~P2(x113,x111)
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.65 cnf(25,plain,
% 0.19/0.65 (P2(a4,f6(a7))),
% 0.19/0.65 inference(scs_inference,[],[14,2,21])).
% 0.19/0.65 cnf(41,plain,
% 0.19/0.65 (~E(a4,a7)),
% 0.19/0.65 inference(scs_inference,[],[13,16,15,9,2])).
% 0.19/0.65 cnf(109,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[25,41,18]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.030000s
%------------------------------------------------------------------------------