%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SET704+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 : Mon Jun 24 14:22:16 EDT 2024
% Result : Theorem 2.38s 2.49s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET704+4 : TPTP v8.2.0. Released v2.2.0.
% 0.04/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 14:49:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.49/0.56 start to proof:theBenchmark
% 2.38/2.48 %-------------------------------------------
% 2.38/2.48 % File :CSE---1.7
% 2.38/2.48 % Problem :theBenchmark
% 2.38/2.48 % Transform :cnf
% 2.38/2.48 % Format :tptp:raw
% 2.38/2.48 % Command :java -jar mcs_scs.jar %d %s
% 2.38/2.48
% 2.38/2.48 % Result :Theorem 1.870000s
% 2.38/2.48 % Output :CNFRefutation 1.870000s
% 2.38/2.48 %-------------------------------------------
% 2.38/2.49 %--------------------------------------------------------------------------
% 2.38/2.49 % File : SET704+4 : TPTP v8.2.0. Released v2.2.0.
% 2.38/2.49 % Domain : Set Theory (Naive)
% 2.38/2.49 % Problem : If X is a member of A, then product(A) is a subset of X
% 2.38/2.49 % Version : [Pas99] axioms.
% 2.38/2.49 % English :
% 2.38/2.49
% 2.38/2.49 % Refs : [Pas99] Pastre (1999), Email to G. Sutcliffe
% 2.38/2.49 % Source : [Pas99]
% 2.38/2.49 % Names :
% 2.38/2.49
% 2.38/2.49 % Status : Theorem
% 2.38/2.49 % Rating : 0.14 v8.2.0, 0.17 v7.5.0, 0.16 v7.4.0, 0.17 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.29 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.26 v5.5.0, 0.22 v5.4.0, 0.29 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.26 v4.0.0, 0.29 v3.7.0, 0.30 v3.5.0, 0.32 v3.4.0, 0.26 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1
% 2.38/2.49 % Syntax : Number of formulae : 12 ( 1 unt; 0 def)
% 2.38/2.49 % Number of atoms : 31 ( 3 equ)
% 2.38/2.49 % Maximal formula atoms : 3 ( 2 avg)
% 2.38/2.49 % Number of connectives : 21 ( 2 ~; 2 |; 4 &)
% 2.38/2.49 % ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% 2.38/2.49 % Maximal formula depth : 7 ( 5 avg)
% 2.38/2.49 % Maximal term depth : 2 ( 1 avg)
% 2.38/2.49 % Number of predicates : 4 ( 3 usr; 0 prp; 2-2 aty)
% 2.38/2.49 % Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% 2.38/2.49 % Number of variables : 30 ( 29 !; 1 ?)
% 2.38/2.49 % SPC : FOF_THM_RFO_SEQ
% 2.38/2.49
% 2.38/2.49 % Comments :
% 2.38/2.49 %--------------------------------------------------------------------------
% 2.38/2.49 %----Include set theory definitions
% 2.38/2.49 include('Axioms/SET006+0.ax').
% 2.38/2.49 %--------------------------------------------------------------------------
% 2.38/2.49 fof(thI42,conjecture,
% 2.38/2.49 ! [A,X] :
% 2.38/2.49 ( member(X,A)
% 2.38/2.49 => subset(product(A),X) ) ).
% 2.38/2.49
% 2.38/2.49 %--------------------------------------------------------------------------
% 2.38/2.49 %-------------------------------------------
% 2.38/2.49 % Proof found
% 2.38/2.49 % SZS status Theorem for theBenchmark
% 2.38/2.49 % SZS output start Proof
% 2.38/2.49 %ClaNum:58(EqnAxiom:27)
% 2.38/2.49 %VarNum:147(SingletonVarNum:72)
% 2.38/2.49 %MaxLitNum:3
% 2.38/2.49 %MaxfuncDepth:1
% 2.38/2.49 %SharedTerms:6
% 2.38/2.49 %goalClause: 28 30
% 2.38/2.49 %singleGoalClaCount:2
% 2.38/2.49 [28]P1(a1,a2)
% 2.38/2.49 [30]~P3(f8(a2),a1)
% 2.38/2.49 [29]~P1(x291,a3)
% 2.38/2.49 [33]~P2(x332,x331)+P3(x331,x332)
% 2.38/2.49 [34]~P2(x341,x342)+P3(x341,x342)
% 2.38/2.49 [31]~E(x311,x312)+P1(x311,f11(x312))
% 2.38/2.49 [32]E(x321,x322)+~P1(x321,f11(x322))
% 2.38/2.49 [35]~P3(x351,x352)+P1(x351,f9(x352))
% 2.38/2.49 [38]P3(x381,x382)+~P1(x381,f9(x382))
% 2.38/2.49 [39]P3(x391,x392)+P1(f5(x391,x392),x391)
% 2.38/2.49 [42]P1(f6(x421,x422),x422)+P1(x421,f8(x422))
% 2.38/2.49 [48]~P1(x481,f14(x482))+P1(x481,f7(x481,x482))
% 2.38/2.49 [49]~P1(x491,f14(x492))+P1(f7(x491,x492),x492)
% 2.38/2.49 [54]P3(x541,x542)+~P1(f5(x541,x542),x542)
% 2.38/2.49 [55]~P1(x551,f6(x551,x552))+P1(x551,f8(x552))
% 2.38/2.49 [36]~E(x361,x363)+P1(x361,f12(x362,x363))
% 2.38/2.49 [37]~E(x371,x372)+P1(x371,f12(x372,x373))
% 2.38/2.49 [43]~P1(x431,x433)+P1(x431,f13(x432,x433))
% 2.38/2.49 [44]~P1(x441,x442)+P1(x441,f13(x442,x443))
% 2.38/2.49 [51]P1(x511,x512)+~P1(x511,f10(x513,x512))
% 2.38/2.49 [52]P1(x521,x522)+~P1(x521,f10(x522,x523))
% 2.38/2.49 [53]P1(x531,x532)+~P1(x531,f4(x532,x533))
% 2.38/2.49 [57]~P1(x571,x572)+~P1(x571,f4(x573,x572))
% 2.38/2.49 [41]~P3(x412,x411)+~P3(x411,x412)+P2(x411,x412)
% 2.38/2.49 [40]~P1(x401,x403)+P1(x401,x402)+~P3(x403,x402)
% 2.38/2.49 [45]~P1(x453,x452)+~P1(x451,x453)+P1(x451,f14(x452))
% 2.38/2.49 [46]E(x461,x462)+E(x461,x463)+~P1(x461,f12(x463,x462))
% 2.38/2.49 [47]P1(x471,x472)+~P1(x472,x473)+~P1(x471,f8(x473))
% 2.38/2.49 [50]~P1(x501,x503)+P1(x501,x502)+P1(x501,f4(x503,x502))
% 2.38/2.49 [56]~P1(x561,x563)+~P1(x561,x562)+P1(x561,f10(x562,x563))
% 2.38/2.49 [58]P1(x581,x582)+P1(x581,x583)+~P1(x581,f13(x583,x582))
% 2.38/2.49 %EqnAxiom
% 2.38/2.49 [1]E(x11,x11)
% 2.38/2.49 [2]E(x22,x21)+~E(x21,x22)
% 2.38/2.49 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.38/2.49 [4]~E(x41,x42)+E(f8(x41),f8(x42))
% 2.38/2.49 [5]~E(x51,x52)+E(f11(x51),f11(x52))
% 2.38/2.49 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 2.38/2.49 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 2.38/2.49 [8]~E(x81,x82)+E(f9(x81),f9(x82))
% 2.38/2.49 [9]~E(x91,x92)+E(f12(x91,x93),f12(x92,x93))
% 2.38/2.49 [10]~E(x101,x102)+E(f12(x103,x101),f12(x103,x102))
% 2.38/2.49 [11]~E(x111,x112)+E(f4(x111,x113),f4(x112,x113))
% 2.38/2.49 [12]~E(x121,x122)+E(f4(x123,x121),f4(x123,x122))
% 2.38/2.49 [13]~E(x131,x132)+E(f5(x131,x133),f5(x132,x133))
% 2.38/2.49 [14]~E(x141,x142)+E(f5(x143,x141),f5(x143,x142))
% 2.38/2.49 [15]~E(x151,x152)+E(f14(x151),f14(x152))
% 2.38/2.49 [16]~E(x161,x162)+E(f13(x161,x163),f13(x162,x163))
% 2.38/2.49 [17]~E(x171,x172)+E(f13(x173,x171),f13(x173,x172))
% 2.38/2.49 [18]~E(x181,x182)+E(f10(x181,x183),f10(x182,x183))
% 2.38/2.49 [19]~E(x191,x192)+E(f10(x193,x191),f10(x193,x192))
% 2.38/2.49 [20]~E(x201,x202)+E(f7(x201,x203),f7(x202,x203))
% 2.38/2.49 [21]~E(x211,x212)+E(f7(x213,x211),f7(x213,x212))
% 2.38/2.49 [22]P1(x222,x223)+~E(x221,x222)+~P1(x221,x223)
% 2.38/2.49 [23]P1(x233,x232)+~E(x231,x232)+~P1(x233,x231)
% 2.38/2.49 [24]P3(x242,x243)+~E(x241,x242)+~P3(x241,x243)
% 2.38/2.49 [25]P3(x253,x252)+~E(x251,x252)+~P3(x253,x251)
% 2.38/2.49 [26]P2(x262,x263)+~E(x261,x262)+~P2(x261,x263)
% 2.38/2.49 [27]P2(x273,x272)+~E(x271,x272)+~P2(x273,x271)
% 2.38/2.49
% 2.38/2.49 %-------------------------------------------
% 2.38/2.49 cnf(60,plain,
% 2.38/2.49 (P1(x601,f12(x602,x601))),
% 2.38/2.49 inference(equality_inference,[],[36])).
% 2.38/2.49 cnf(67,plain,
% 2.38/2.49 (~P1(x671,a3)),
% 2.38/2.49 inference(rename_variables,[],[29])).
% 2.38/2.49 cnf(69,plain,
% 2.38/2.49 (~P1(x691,f14(a3))),
% 2.38/2.49 inference(scs_inference,[],[30,29,67,33,34,39,49])).
% 2.38/2.49 cnf(157,plain,
% 2.38/2.49 (~P1(f8(a2),f10(x1571,f9(a1)))),
% 2.38/2.49 inference(scs_inference,[],[30,51,38])).
% 2.38/2.49 cnf(158,plain,
% 2.38/2.49 (~P1(f8(a2),f9(a1))),
% 2.38/2.49 inference(scs_inference,[],[60,157,56])).
% 2.38/2.49 cnf(165,plain,
% 2.38/2.49 (~P1(f5(f8(a2),a1),f4(a1,x1651))),
% 2.38/2.49 inference(scs_inference,[],[30,53,54])).
% 2.38/2.49 cnf(166,plain,
% 2.38/2.49 (~P1(f5(f8(a2),a1),a1)),
% 2.38/2.49 inference(scs_inference,[],[69,165,50])).
% 2.38/2.49 cnf(588,plain,
% 2.38/2.49 (P1(f5(f8(a2),a1),f8(a2))),
% 2.38/2.49 inference(scs_inference,[],[158,35,39])).
% 2.38/2.49 cnf(589,plain,
% 2.38/2.49 ($false),
% 2.38/2.49 inference(scs_inference,[],[28,166,588,47]),
% 2.38/2.49 ['proof']).
% 2.38/2.49 % SZS output end Proof
% 2.38/2.49 % Total time :1.870000s
%------------------------------------------------------------------------------