TSTP Solution File: SEU162+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU162+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n028.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 16:18:01 EDT 2023
% Result : Theorem 0.56s 1.05s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU162+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n028.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 : Wed Aug 23 17:26:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.56/1.05 %-------------------------------------------
% 0.56/1.05 % File :CSE---1.6
% 0.56/1.05 % Problem :theBenchmark
% 0.56/1.05 % Transform :cnf
% 0.56/1.05 % Format :tptp:raw
% 0.56/1.05 % Command :java -jar mcs_scs.jar %d %s
% 0.56/1.05
% 0.56/1.05 % Result :Theorem 0.420000s
% 0.56/1.05 % Output :CNFRefutation 0.420000s
% 0.56/1.05 %-------------------------------------------
% 0.56/1.05 %------------------------------------------------------------------------------
% 0.56/1.05 % File : SEU162+3 : TPTP v8.1.2. Released v3.2.0.
% 0.56/1.05 % Domain : Set theory
% 0.56/1.05 % Problem : Basic properties of sets, theorem 65
% 0.56/1.05 % Version : [Urb06] axioms : Especial.
% 0.56/1.05 % English :
% 0.56/1.05
% 0.56/1.05 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.56/1.05 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.56/1.05 % Source : [Urb06]
% 0.56/1.05 % Names : zfmisc_1__t65_zfmisc_1 [Urb06]
% 0.56/1.05
% 0.56/1.05 % Status : Theorem
% 0.56/1.05 % Rating : 0.08 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.04 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.14 v3.2.0
% 0.56/1.05 % Syntax : Number of formulae : 8 ( 2 unt; 0 def)
% 0.56/1.05 % Number of atoms : 14 ( 2 equ)
% 0.56/1.05 % Maximal formula atoms : 2 ( 1 avg)
% 0.56/1.05 % Number of connectives : 11 ( 5 ~; 0 |; 1 &)
% 0.56/1.05 % ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% 0.56/1.05 % Maximal formula depth : 5 ( 4 avg)
% 0.56/1.05 % Maximal term depth : 3 ( 1 avg)
% 0.56/1.05 % Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% 0.56/1.05 % Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.56/1.05 % Number of variables : 14 ( 12 !; 2 ?)
% 0.56/1.05 % SPC : FOF_THM_RFO_SEQ
% 0.56/1.05
% 0.56/1.05 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.56/1.05 % library, www.mizar.org
% 0.56/1.05 %------------------------------------------------------------------------------
% 0.56/1.05 fof(antisymmetry_r2_hidden,axiom,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ( in(A,B)
% 0.56/1.05 => ~ in(B,A) ) ).
% 0.56/1.05
% 0.56/1.05 fof(l25_zfmisc_1,axiom,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ~ ( disjoint(singleton(A),B)
% 0.56/1.05 & in(A,B) ) ).
% 0.56/1.05
% 0.56/1.05 fof(l28_zfmisc_1,axiom,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ( ~ in(A,B)
% 0.56/1.05 => disjoint(singleton(A),B) ) ).
% 0.56/1.05
% 0.56/1.05 fof(rc1_xboole_0,axiom,
% 0.56/1.05 ? [A] : empty(A) ).
% 0.56/1.05
% 0.56/1.05 fof(rc2_xboole_0,axiom,
% 0.56/1.05 ? [A] : ~ empty(A) ).
% 0.56/1.05
% 0.56/1.05 fof(symmetry_r1_xboole_0,axiom,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ( disjoint(A,B)
% 0.56/1.05 => disjoint(B,A) ) ).
% 0.56/1.05
% 0.56/1.05 fof(t65_zfmisc_1,conjecture,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ( set_difference(A,singleton(B)) = A
% 0.56/1.05 <=> ~ in(B,A) ) ).
% 0.56/1.05
% 0.56/1.05 fof(t83_xboole_1,axiom,
% 0.56/1.05 ! [A,B] :
% 0.56/1.05 ( disjoint(A,B)
% 0.56/1.05 <=> set_difference(A,B) = A ) ).
% 0.56/1.05
% 0.56/1.05 %------------------------------------------------------------------------------
% 0.56/1.05 %-------------------------------------------
% 0.56/1.05 % Proof found
% 0.56/1.05 % SZS status Theorem for theBenchmark
% 0.56/1.05 % SZS output start Proof
% 0.56/1.05 %ClaNum:21(EqnAxiom:11)
% 0.56/1.05 %VarNum:26(SingletonVarNum:12)
% 0.56/1.05 %MaxLitNum:2
% 0.56/1.05 %MaxfuncDepth:2
% 0.56/1.05 %SharedTerms:12
% 0.56/1.05 %goalClause: 14 16
% 0.56/1.05 [12]P1(a1)
% 0.56/1.05 [13]~P1(a2)
% 0.56/1.05 [14]~P3(a4,a3)+E(f6(a3,f5(a4)),a3)
% 0.56/1.06 [16]P3(a4,a3)+~E(f6(a3,f5(a4)),a3)
% 0.56/1.06 [17]~P2(x172,x171)+P2(x171,x172)
% 0.56/1.06 [20]~P3(x202,x201)+~P3(x201,x202)
% 0.56/1.06 [15]P3(x151,x152)+P2(f5(x151),x152)
% 0.56/1.06 [18]~P2(x181,x182)+E(f6(x181,x182),x181)
% 0.56/1.06 [19]P2(x191,x192)+~E(f6(x191,x192),x191)
% 0.56/1.06 [21]~P3(x211,x212)+~P2(f5(x211),x212)
% 0.56/1.06 %EqnAxiom
% 0.56/1.06 [1]E(x11,x11)
% 0.56/1.06 [2]E(x22,x21)+~E(x21,x22)
% 0.56/1.06 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.56/1.06 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.56/1.06 [5]~E(x51,x52)+E(f6(x51,x53),f6(x52,x53))
% 0.56/1.06 [6]~E(x61,x62)+E(f6(x63,x61),f6(x63,x62))
% 0.56/1.06 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 0.56/1.06 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 0.56/1.06 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 0.56/1.06 [10]P3(x102,x103)+~E(x101,x102)+~P3(x101,x103)
% 0.56/1.06 [11]P3(x113,x112)+~E(x111,x112)+~P3(x113,x111)
% 0.56/1.06
% 0.56/1.06 %-------------------------------------------
% 0.56/1.06 cnf(25,plain,
% 0.56/1.06 (~P2(x251,x252)+E(f6(x252,x251),x252)),
% 0.56/1.06 inference(scs_inference,[],[17,18])).
% 0.56/1.06 cnf(26,plain,
% 0.56/1.06 (~P3(x261,x262)+P2(f5(x262),x261)),
% 0.56/1.06 inference(scs_inference,[],[20,15])).
% 0.56/1.06 cnf(32,plain,
% 0.56/1.06 (~P2(f5(a4),a3)+~E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[21,16])).
% 0.56/1.06 cnf(51,plain,
% 0.56/1.06 (P3(x511,a3)+~E(a4,x511)+~E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[10,16])).
% 0.56/1.06 cnf(57,plain,
% 0.56/1.06 (~E(x571,a4)+P3(x571,a3)+~E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[51,2])).
% 0.56/1.06 cnf(58,plain,
% 0.56/1.06 (~P3(a3,x581)+~E(x581,a4)+~E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[57,20])).
% 0.56/1.06 cnf(84,plain,
% 0.56/1.06 (E(x841,f6(x841,x842))+~P2(x841,x842)),
% 0.56/1.06 inference(scs_inference,[],[2,18])).
% 0.56/1.06 cnf(85,plain,
% 0.56/1.06 (E(f5(x851),f6(f5(x851),x852))+P3(x851,x852)),
% 0.56/1.06 inference(scs_inference,[],[84,15])).
% 0.56/1.06 cnf(92,plain,
% 0.56/1.06 (E(x921,f6(x921,x922))+~P2(x922,x921)),
% 0.56/1.06 inference(scs_inference,[],[2,25])).
% 0.56/1.06 cnf(93,plain,
% 0.56/1.06 (E(x931,f6(x931,f5(x932)))+P3(x932,x931)),
% 0.56/1.06 inference(scs_inference,[],[92,15])).
% 0.56/1.06 cnf(94,plain,
% 0.56/1.06 (E(a3,f6(a3,f5(a4)))+E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[93,14])).
% 0.56/1.06 cnf(139,plain,
% 0.56/1.06 (E(f6(a3,f5(a4)),a3)),
% 0.56/1.06 inference(scs_inference,[],[2,94])).
% 0.56/1.06 cnf(140,plain,
% 0.56/1.06 (P3(a4,a3)),
% 0.56/1.06 inference(scs_inference,[],[139,16])).
% 0.56/1.06 cnf(141,plain,
% 0.56/1.06 (~P2(f5(a4),a3)),
% 0.56/1.06 inference(scs_inference,[],[139,32])).
% 0.56/1.06 cnf(145,plain,
% 0.56/1.06 (~E(x1451,a4)+~P3(a3,x1451)),
% 0.56/1.06 inference(scs_inference,[],[139,58])).
% 0.56/1.06 cnf(154,plain,
% 0.56/1.06 (P2(a3,f5(a4))),
% 0.56/1.06 inference(scs_inference,[],[139,19])).
% 0.56/1.06 cnf(183,plain,
% 0.56/1.06 (~P3(a3,a4)),
% 0.56/1.06 inference(equality_inference,[],[145])).
% 0.56/1.06 cnf(209,plain,
% 0.56/1.06 ($false),
% 0.56/1.06 inference(scs_inference,[],[154,140,141,183,93,92,85,26,17]),
% 0.56/1.06 ['proof']).
% 0.56/1.06 % SZS output end Proof
% 0.56/1.06 % Total time :0.420000s
%------------------------------------------------------------------------------