TSTP Solution File: SET983+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET983+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 : n032.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 14:31:52 EDT 2023
% Result : Theorem 0.14s 0.51s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Aug 26 12:50:43 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.47 start to proof:theBenchmark
% 0.14/0.51 %-------------------------------------------
% 0.14/0.51 % File :CSE---1.6
% 0.14/0.51 % Problem :theBenchmark
% 0.14/0.51 % Transform :cnf
% 0.14/0.51 % Format :tptp:raw
% 0.14/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.14/0.51
% 0.14/0.51 % Result :Theorem 0.000000s
% 0.14/0.51 % Output :CNFRefutation 0.000000s
% 0.14/0.51 %-------------------------------------------
% 0.14/0.51 %------------------------------------------------------------------------------
% 0.14/0.51 % File : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.51 % Domain : Set theory
% 0.14/0.51 % Problem : Basic properties of sets, theorem 137
% 0.14/0.51 % Version : [Urb06] axioms : Especial.
% 0.14/0.51 % English :
% 0.14/0.51
% 0.14/0.51 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 0.14/0.51 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 0.14/0.51 % Source : [Urb06]
% 0.14/0.51 % Names : zfmisc_1__t137_zfmisc_1 [Urb06]
% 0.14/0.51
% 0.14/0.51 % Status : Theorem
% 0.14/0.51 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.2.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.17 v6.2.0, 0.28 v6.1.0, 0.30 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.21 v5.3.0, 0.30 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.0, 0.25 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0
% 0.14/0.51 % Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% 0.14/0.51 % Number of atoms : 14 ( 4 equ)
% 0.14/0.51 % Maximal formula atoms : 4 ( 1 avg)
% 0.14/0.51 % Number of connectives : 8 ( 2 ~; 0 |; 2 &)
% 0.14/0.51 % ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% 0.14/0.51 % Maximal formula depth : 8 ( 5 avg)
% 0.14/0.51 % Maximal term depth : 3 ( 1 avg)
% 0.14/0.51 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 0.14/0.51 % Number of functors : 2 ( 2 usr; 0 con; 2-2 aty)
% 0.14/0.51 % Number of variables : 21 ( 19 !; 2 ?)
% 0.14/0.51 % SPC : FOF_THM_RFO_SEQ
% 0.14/0.51
% 0.14/0.51 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.14/0.51 % library, www.mizar.org
% 0.14/0.51 %------------------------------------------------------------------------------
% 0.14/0.51 fof(antisymmetry_r2_hidden,axiom,
% 0.14/0.51 ! [A,B] :
% 0.14/0.51 ( in(A,B)
% 0.14/0.51 => ~ in(B,A) ) ).
% 0.14/0.51
% 0.14/0.51 fof(commutativity_k3_xboole_0,axiom,
% 0.14/0.51 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.14/0.51
% 0.14/0.51 fof(d3_xboole_0,axiom,
% 0.14/0.51 ! [A,B,C] :
% 0.14/0.51 ( C = set_intersection2(A,B)
% 0.14/0.51 <=> ! [D] :
% 0.14/0.51 ( in(D,C)
% 0.14/0.51 <=> ( in(D,A)
% 0.14/0.51 & in(D,B) ) ) ) ).
% 0.14/0.51
% 0.14/0.51 fof(idempotence_k3_xboole_0,axiom,
% 0.14/0.51 ! [A,B] : set_intersection2(A,A) = A ).
% 0.14/0.51
% 0.14/0.51 fof(rc1_xboole_0,axiom,
% 0.14/0.51 ? [A] : empty(A) ).
% 0.14/0.51
% 0.14/0.51 fof(rc2_xboole_0,axiom,
% 0.14/0.51 ? [A] : ~ empty(A) ).
% 0.14/0.51
% 0.14/0.51 fof(t123_zfmisc_1,axiom,
% 0.14/0.51 ! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)) ).
% 0.14/0.51
% 0.14/0.51 fof(t137_zfmisc_1,conjecture,
% 0.14/0.51 ! [A,B,C,D,E] :
% 0.14/0.51 ( ( in(A,cartesian_product2(B,C))
% 0.14/0.51 & in(A,cartesian_product2(D,E)) )
% 0.14/0.51 => in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ) ).
% 0.14/0.51
% 0.14/0.51 %------------------------------------------------------------------------------
% 0.14/0.51 %-------------------------------------------
% 0.14/0.51 % Proof found
% 0.14/0.51 % SZS status Theorem for theBenchmark
% 0.14/0.51 % SZS output start Proof
% 0.14/0.51 %ClaNum:28(EqnAxiom:13)
% 0.14/0.51 %VarNum:79(SingletonVarNum:30)
% 0.14/0.51 %MaxLitNum:4
% 0.14/0.51 %MaxfuncDepth:2
% 0.14/0.51 %SharedTerms:17
% 0.14/0.51 %goalClause: 17 18 21
% 0.14/0.51 %singleGoalClaCount:3
% 0.14/0.51 [14]P1(a1)
% 0.14/0.51 [20]~P1(a6)
% 0.14/0.51 [17]P2(a5,f2(a7,a8))
% 0.14/0.51 [18]P2(a5,f2(a9,a10))
% 0.14/0.51 [21]~P2(a5,f2(f4(a7,a9),f4(a8,a10)))
% 0.14/0.51 [15]E(f4(x151,x151),x151)
% 0.14/0.51 [16]E(f4(x161,x162),f4(x162,x161))
% 0.14/0.51 [19]E(f2(f4(x191,x192),f4(x193,x194)),f4(f2(x191,x193),f2(x192,x194)))
% 0.14/0.51 [22]~P2(x222,x221)+~P2(x221,x222)
% 0.14/0.51 [26]P2(f3(x262,x263,x261),x261)+P2(f3(x262,x263,x261),x263)+E(x261,f4(x262,x263))
% 0.14/0.51 [27]P2(f3(x272,x273,x271),x271)+P2(f3(x272,x273,x271),x272)+E(x271,f4(x272,x273))
% 0.14/0.51 [23]~P2(x231,x233)+P2(x231,x232)+~E(x233,f4(x234,x232))
% 0.14/0.51 [24]~P2(x241,x243)+P2(x241,x242)+~E(x243,f4(x242,x244))
% 0.14/0.51 [28]~P2(f3(x282,x283,x281),x281)+~P2(f3(x282,x283,x281),x283)+~P2(f3(x282,x283,x281),x282)+E(x281,f4(x282,x283))
% 0.14/0.51 [25]~P2(x251,x254)+~P2(x251,x253)+P2(x251,x252)+~E(x252,f4(x253,x254))
% 0.14/0.51 %EqnAxiom
% 0.14/0.52 [1]E(x11,x11)
% 0.14/0.52 [2]E(x22,x21)+~E(x21,x22)
% 0.14/0.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.14/0.52 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.14/0.52 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.14/0.52 [6]~E(x61,x62)+E(f3(x61,x63,x64),f3(x62,x63,x64))
% 0.14/0.52 [7]~E(x71,x72)+E(f3(x73,x71,x74),f3(x73,x72,x74))
% 0.14/0.52 [8]~E(x81,x82)+E(f3(x83,x84,x81),f3(x83,x84,x82))
% 0.14/0.52 [9]~E(x91,x92)+E(f2(x91,x93),f2(x92,x93))
% 0.14/0.52 [10]~E(x101,x102)+E(f2(x103,x101),f2(x103,x102))
% 0.14/0.52 [11]~P1(x111)+P1(x112)+~E(x111,x112)
% 0.14/0.52 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.14/0.52 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.14/0.52
% 0.14/0.52 %-------------------------------------------
% 0.14/0.52 cnf(32,plain,
% 0.14/0.52 (~E(f2(a7,a8),f2(f4(a7,a9),f4(a8,a10)))),
% 0.14/0.52 inference(scs_inference,[],[17,21,15,2,22,13])).
% 0.14/0.52 cnf(33,plain,
% 0.14/0.52 (P2(f4(a5,a5),f2(a7,a8))),
% 0.14/0.52 inference(scs_inference,[],[17,21,15,2,22,13,12])).
% 0.14/0.52 cnf(35,plain,
% 0.14/0.52 (E(f4(x351,x352),f4(x352,x351))),
% 0.14/0.52 inference(rename_variables,[],[16])).
% 0.14/0.52 cnf(38,plain,
% 0.14/0.52 (E(f4(x381,x382),f4(x382,x381))),
% 0.14/0.52 inference(rename_variables,[],[16])).
% 0.14/0.52 cnf(44,plain,
% 0.14/0.52 (E(f4(x441,x441),x441)),
% 0.14/0.52 inference(rename_variables,[],[15])).
% 0.14/0.52 cnf(45,plain,
% 0.14/0.52 (E(f2(f4(x451,x451),x452),f2(x451,x452))),
% 0.14/0.52 inference(scs_inference,[],[17,21,15,44,16,35,38,2,22,13,12,24,23,25,10,9])).
% 0.14/0.52 cnf(62,plain,
% 0.14/0.52 (E(f4(x621,x621),x621)),
% 0.14/0.52 inference(rename_variables,[],[15])).
% 0.14/0.52 cnf(68,plain,
% 0.14/0.52 (E(f2(f4(x681,x682),f4(x683,x684)),f4(f2(x682,x684),f2(x681,x683)))),
% 0.14/0.52 inference(scs_inference,[],[17,18,19,20,16,15,62,21,45,32,22,23,25,2,12,11,24,13,3])).
% 0.14/0.52 cnf(75,plain,
% 0.14/0.52 ($false),
% 0.14/0.52 inference(scs_inference,[],[18,21,68,33,17,22,25]),
% 0.14/0.52 ['proof']).
% 0.14/0.52 % SZS output end Proof
% 0.14/0.52 % Total time :0.000000s
%------------------------------------------------------------------------------