TSTP Solution File: SET924+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET924+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 : n029.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 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET924+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
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:07:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 % File :CSE---1.6
% 0.20/0.63 % Problem :theBenchmark
% 0.20/0.63 % Transform :cnf
% 0.20/0.63 % Format :tptp:raw
% 0.20/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.63
% 0.20/0.63 % Result :Theorem 0.010000s
% 0.20/0.63 % Output :CNFRefutation 0.010000s
% 0.20/0.63 %-------------------------------------------
% 0.20/0.63 %------------------------------------------------------------------------------
% 0.20/0.63 % File : SET924+1 : TPTP v8.1.2. Released v3.2.0.
% 0.20/0.63 % Domain : Set theory
% 0.20/0.63 % Problem : difference(singleton(A),B) = singleton(A) <=> ~ in(A,B)
% 0.20/0.63 % Version : [Urb06] axioms : Especial.
% 0.20/0.63 % English :
% 0.20/0.63
% 0.20/0.63 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.20/0.63 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.20/0.63 % Source : [Urb06]
% 0.20/0.63 % Names : zfmisc_1__t67_zfmisc_1 [Urb06]
% 0.20/0.63
% 0.20/0.63 % Status : Theorem
% 0.20/0.63 % Rating : 0.03 v7.2.0, 0.00 v6.4.0, 0.04 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 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
% 0.20/0.63 % Syntax : Number of formulae : 5 ( 2 unt; 0 def)
% 0.20/0.63 % Number of atoms : 8 ( 2 equ)
% 0.20/0.63 % Maximal formula atoms : 2 ( 1 avg)
% 0.20/0.63 % Number of connectives : 7 ( 4 ~; 0 |; 0 &)
% 0.20/0.63 % ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.63 % Maximal formula depth : 5 ( 4 avg)
% 0.20/0.64 % Maximal term depth : 3 ( 1 avg)
% 0.20/0.64 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.20/0.64 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.20/0.64 % Number of variables : 8 ( 6 !; 2 ?)
% 0.20/0.64 % SPC : FOF_THM_RFO_SEQ
% 0.20/0.64
% 0.20/0.64 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.20/0.64 % library, www.mizar.org
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 fof(antisymmetry_r2_hidden,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( in(A,B)
% 0.20/0.64 => ~ in(B,A) ) ).
% 0.20/0.64
% 0.20/0.64 fof(rc1_xboole_0,axiom,
% 0.20/0.64 ? [A] : empty(A) ).
% 0.20/0.64
% 0.20/0.64 fof(rc2_xboole_0,axiom,
% 0.20/0.64 ? [A] : ~ empty(A) ).
% 0.20/0.64
% 0.20/0.64 fof(t67_zfmisc_1,conjecture,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( set_difference(singleton(A),B) = singleton(A)
% 0.20/0.64 <=> ~ in(A,B) ) ).
% 0.20/0.64
% 0.20/0.64 fof(l34_zfmisc_1,axiom,
% 0.20/0.64 ! [A,B] :
% 0.20/0.64 ( set_difference(singleton(A),B) = singleton(A)
% 0.20/0.64 <=> ~ in(A,B) ) ).
% 0.20/0.64
% 0.20/0.64 %------------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 %ClaNum:16(EqnAxiom:9)
% 0.20/0.64 %VarNum:14(SingletonVarNum:6)
% 0.20/0.64 %MaxLitNum:2
% 0.20/0.64 %MaxfuncDepth:2
% 0.20/0.64 %SharedTerms:12
% 0.20/0.64 %goalClause: 12 14
% 0.20/0.64 [10]P1(a1)
% 0.20/0.64 [11]~P1(a2)
% 0.20/0.64 [12]~P2(a3,a5)+E(f6(f4(a3),a5),f4(a3))
% 0.20/0.64 [14]P2(a3,a5)+~E(f6(f4(a3),a5),f4(a3))
% 0.20/0.64 [15]~P2(x152,x151)+~P2(x151,x152)
% 0.20/0.64 [13]P2(x131,x132)+E(f6(f4(x131),x132),f4(x131))
% 0.20/0.64 [16]~P2(x161,x162)+~E(f6(f4(x161),x162),f4(x161))
% 0.20/0.64 %EqnAxiom
% 0.20/0.64 [1]E(x11,x11)
% 0.20/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.64 [4]~E(x41,x42)+E(f4(x41),f4(x42))
% 0.20/0.64 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.20/0.64 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.20/0.64 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.20/0.64 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.20/0.64 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.20/0.64
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 cnf(28,plain,
% 0.20/0.64 (~E(f6(f4(a3),a5),f4(a3))),
% 0.20/0.64 inference(scs_inference,[],[14,16])).
% 0.20/0.64 cnf(29,plain,
% 0.20/0.64 (~P2(a3,a5)),
% 0.20/0.64 inference(scs_inference,[],[28,12])).
% 0.20/0.64 cnf(30,plain,
% 0.20/0.64 (P2(a3,a5)),
% 0.20/0.64 inference(scs_inference,[],[28,13])).
% 0.20/0.64 cnf(39,plain,
% 0.20/0.64 ($false),
% 0.20/0.64 inference(scs_inference,[],[30,29]),
% 0.20/0.64 ['proof']).
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time :0.010000s
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