TSTP Solution File: SET925+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET925+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 14:31:43 EDT 2023
% Result : Theorem 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET925+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 15:33:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof:theBenchmark
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % File :CSE---1.6
% 0.19/0.60 % Problem :theBenchmark
% 0.19/0.60 % Transform :cnf
% 0.19/0.60 % Format :tptp:raw
% 0.19/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.60
% 0.19/0.60 % Result :Theorem 0.010000s
% 0.19/0.60 % Output :CNFRefutation 0.010000s
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 %------------------------------------------------------------------------------
% 0.19/0.60 % File : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.19/0.60 % Domain : Set theory
% 0.19/0.60 % Problem : difference(singleton(A),B) = empty_set <=> in(A,B)
% 0.19/0.60 % Version : [Urb06] axioms : Especial.
% 0.19/0.60 % English :
% 0.19/0.60
% 0.19/0.60 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.19/0.60 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.19/0.60 % Source : [Urb06]
% 0.19/0.60 % Names : zfmisc_1__t68_zfmisc_1 [Urb06]
% 0.19/0.60
% 0.19/0.60 % Status : Theorem
% 0.19/0.60 % Rating : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.07 v6.0.0, 0.04 v5.5.0, 0.00 v5.4.0, 0.04 v5.3.0, 0.11 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0
% 0.19/0.60 % Syntax : Number of formulae : 6 ( 3 unt; 0 def)
% 0.19/0.60 % Number of atoms : 9 ( 2 equ)
% 0.19/0.60 % Maximal formula atoms : 2 ( 1 avg)
% 0.19/0.60 % Number of connectives : 5 ( 2 ~; 0 |; 0 &)
% 0.19/0.60 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.60 % Maximal formula depth : 5 ( 3 avg)
% 0.19/0.60 % Maximal term depth : 3 ( 1 avg)
% 0.19/0.60 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.19/0.60 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.60 % Number of variables : 8 ( 6 !; 2 ?)
% 0.19/0.60 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.60
% 0.19/0.60 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.19/0.60 % library, www.mizar.org
% 0.19/0.60 %------------------------------------------------------------------------------
% 0.19/0.60 fof(antisymmetry_r2_hidden,axiom,
% 0.19/0.60 ! [A,B] :
% 0.19/0.60 ( in(A,B)
% 0.19/0.60 => ~ in(B,A) ) ).
% 0.19/0.60
% 0.19/0.60 fof(fc1_xboole_0,axiom,
% 0.19/0.60 empty(empty_set) ).
% 0.19/0.60
% 0.19/0.60 fof(rc1_xboole_0,axiom,
% 0.19/0.60 ? [A] : empty(A) ).
% 0.19/0.60
% 0.19/0.60 fof(rc2_xboole_0,axiom,
% 0.19/0.60 ? [A] : ~ empty(A) ).
% 0.19/0.60
% 0.19/0.60 fof(t68_zfmisc_1,conjecture,
% 0.19/0.60 ! [A,B] :
% 0.19/0.60 ( set_difference(singleton(A),B) = empty_set
% 0.19/0.60 <=> in(A,B) ) ).
% 0.19/0.60
% 0.19/0.60 fof(l36_zfmisc_1,axiom,
% 0.19/0.60 ! [A,B] :
% 0.19/0.60 ( set_difference(singleton(A),B) = empty_set
% 0.19/0.60 <=> in(A,B) ) ).
% 0.19/0.60
% 0.19/0.60 %------------------------------------------------------------------------------
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark
% 0.19/0.60 % SZS output start Proof
% 0.19/0.60 %ClaNum:17(EqnAxiom:9)
% 0.19/0.60 %VarNum:12(SingletonVarNum:6)
% 0.19/0.60 %MaxLitNum:2
% 0.19/0.60 %MaxfuncDepth:2
% 0.19/0.61 %SharedTerms:14
% 0.19/0.61 %goalClause: 13 14
% 0.19/0.61 [10]P1(a1)
% 0.19/0.61 [11]P1(a2)
% 0.19/0.61 [12]~P1(a3)
% 0.19/0.61 [13]P2(a4,a6)+E(f7(f5(a4),a6),a1)
% 0.19/0.61 [14]~P2(a4,a6)+~E(f7(f5(a4),a6),a1)
% 0.19/0.61 [16]~P2(x162,x161)+~P2(x161,x162)
% 0.19/0.61 [15]~P2(x151,x152)+E(f7(f5(x151),x152),a1)
% 0.19/0.61 [17]P2(x171,x172)+~E(f7(f5(x171),x172),a1)
% 0.19/0.61 %EqnAxiom
% 0.19/0.61 [1]E(x11,x11)
% 0.19/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.61 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.19/0.61 [5]~E(x51,x52)+E(f7(x51,x53),f7(x52,x53))
% 0.19/0.61 [6]~E(x61,x62)+E(f7(x63,x61),f7(x63,x62))
% 0.19/0.61 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.19/0.61 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.19/0.61 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.19/0.61
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 cnf(34,plain,
% 0.19/0.61 (~E(f7(f5(a4),a6),a1)),
% 0.19/0.61 inference(scs_inference,[],[14,17])).
% 0.19/0.61 cnf(35,plain,
% 0.19/0.61 (P2(a4,a6)),
% 0.19/0.61 inference(scs_inference,[],[34,13])).
% 0.19/0.61 cnf(37,plain,
% 0.19/0.61 (~P2(a4,a6)),
% 0.19/0.61 inference(scs_inference,[],[34,15])).
% 0.19/0.61 cnf(44,plain,
% 0.19/0.61 ($false),
% 0.19/0.61 inference(scs_inference,[],[37,35]),
% 0.19/0.61 ['proof']).
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time :0.010000s
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