TSTP Solution File: SET910+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET910+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 : n014.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 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET910+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n014.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 14:49:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % File :CSE---1.6
% 0.20/0.62 % Problem :theBenchmark
% 0.20/0.62 % Transform :cnf
% 0.20/0.62 % Format :tptp:raw
% 0.20/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.62
% 0.20/0.62 % Result :Theorem 0.000000s
% 0.20/0.62 % Output :CNFRefutation 0.000000s
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 % File : SET910+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.62 % Domain : Set theory
% 0.20/0.62 % Problem : intersection(A,singleton(B)) = singleton(B) => in(B,A)
% 0.20/0.62 % Version : [Urb06] axioms : Especial.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.62 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.62 % Source : [Urb06]
% 0.20/0.62 % Names : zfmisc_1__t51_zfmisc_1 [Urb06]
% 0.20/0.62
% 0.20/0.62 % Status : Theorem
% 0.20/0.62 % Rating : 0.00 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.13 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0
% 0.20/0.62 % Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% 0.20/0.62 % Number of atoms : 10 ( 4 equ)
% 0.20/0.62 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.62 % Number of connectives : 5 ( 2 ~; 0 |; 0 &)
% 0.20/0.62 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.20/0.62 % Maximal formula depth : 5 ( 3 avg)
% 0.20/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.62 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.62 % Number of variables : 12 ( 10 !; 2 ?)
% 0.20/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.62
% 0.20/0.62 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.62 % library, www.mizar.org
% 0.20/0.62 %------------------------------------------------------------------------------
% 0.20/0.62 fof(commutativity_k3_xboole_0,axiom,
% 0.20/0.62 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.20/0.62
% 0.20/0.62 fof(idempotence_k3_xboole_0,axiom,
% 0.20/0.62 ! [A,B] : set_intersection2(A,A) = A ).
% 0.20/0.62
% 0.20/0.62 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.62 ! [A,B] :
% 0.20/0.62 ( in(A,B)
% 0.20/0.62 => ~ in(B,A) ) ).
% 0.20/0.62
% 0.20/0.62 fof(rc1_xboole_0,axiom,
% 0.20/0.62 ? [A] : empty(A) ).
% 0.20/0.62
% 0.20/0.62 fof(rc2_xboole_0,axiom,
% 0.20/0.62 ? [A] : ~ empty(A) ).
% 0.20/0.63
% 0.20/0.63 fof(t51_zfmisc_1,conjecture,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( set_intersection2(A,singleton(B)) = singleton(B)
% 0.20/0.63 => in(B,A) ) ).
% 0.20/0.63
% 0.20/0.63 fof(l30_zfmisc_1,axiom,
% 0.20/0.63 ! [A,B] :
% 0.20/0.63 ( set_intersection2(A,singleton(B)) = singleton(B)
% 0.20/0.63 => in(B,A) ) ).
% 0.20/0.63
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark
% 0.20/0.63 % SZS output start Proof
% 0.20/0.63 %ClaNum:17(EqnAxiom:9)
% 0.20/0.63 %VarNum:16(SingletonVarNum:7)
% 0.20/0.63 %MaxLitNum:2
% 0.20/0.63 %MaxfuncDepth:2
% 0.20/0.63 %SharedTerms:10
% 0.20/0.63 %goalClause: 12 15
% 0.20/0.63 %singleGoalClaCount:2
% 0.20/0.63 [10]P1(a1)
% 0.20/0.63 [14]~P1(a4)
% 0.20/0.63 [15]~P2(a5,a3)
% 0.20/0.63 [12]E(f2(a3,f6(a5)),f6(a5))
% 0.20/0.63 [11]E(f2(x111,x111),x111)
% 0.20/0.63 [13]E(f2(x131,x132),f2(x132,x131))
% 0.20/0.63 [16]~P2(x162,x161)+~P2(x161,x162)
% 0.20/0.63 [17]P2(x171,x172)+~E(f2(x172,f6(x171)),f6(x171))
% 0.20/0.63 %EqnAxiom
% 0.20/0.63 [1]E(x11,x11)
% 0.20/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.63 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.20/0.63 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.20/0.63 [6]~E(x61,x62)+E(f6(x61),f6(x62))
% 0.20/0.63 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.63 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.20/0.63 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.20/0.63
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 cnf(18,plain,
% 0.20/0.63 ($false),
% 0.20/0.63 inference(scs_inference,[],[15,12,17]),
% 0.20/0.63 ['proof']).
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time :0.000000s
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