TSTP Solution File: SEU121+2 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SEU121+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n009.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 16:17:34 EDT 2023
% Result : Theorem 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU121+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 16:16:06 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof:theBenchmark
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % File :CSE---1.6
% 0.21/0.65 % Problem :theBenchmark
% 0.21/0.65 % Transform :cnf
% 0.21/0.65 % Format :tptp:raw
% 0.21/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.65
% 0.21/0.65 % Result :Theorem 0.030000s
% 0.21/0.65 % Output :CNFRefutation 0.030000s
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 % File : SEU121+2 : TPTP v8.1.2. Released v3.3.0.
% 0.21/0.65 % Domain : Set theory
% 0.21/0.65 % Problem : MPTP chainy problem t1_xboole_1
% 0.21/0.65 % Version : [Urb07] axioms : Especial.
% 0.21/0.65 % English :
% 0.21/0.65
% 0.21/0.65 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% 0.21/0.65 % : [Urb07] Urban (2006), Email to G. Sutcliffe
% 0.21/0.65 % Source : [Urb07]
% 0.21/0.65 % Names : chainy-t1_xboole_1 [Urb07]
% 0.21/0.65
% 0.21/0.65 % Status : Theorem
% 0.21/0.65 % Rating : 0.08 v8.1.0, 0.03 v7.2.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.10 v6.0.0, 0.17 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.17 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0
% 0.21/0.65 % Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% 0.21/0.65 % Number of atoms : 43 ( 7 equ)
% 0.21/0.65 % Maximal formula atoms : 6 ( 2 avg)
% 0.21/0.65 % Number of connectives : 37 ( 14 ~; 0 |; 13 &)
% 0.21/0.65 % ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% 0.21/0.65 % Maximal formula depth : 9 ( 4 avg)
% 0.21/0.65 % Maximal term depth : 2 ( 1 avg)
% 0.21/0.65 % Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% 0.21/0.65 % Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% 0.21/0.65 % Number of variables : 39 ( 35 !; 4 ?)
% 0.21/0.65 % SPC : FOF_THM_RFO_SEQ
% 0.21/0.65
% 0.21/0.65 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 0.21/0.65 % library, www.mizar.org
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 fof(antisymmetry_r2_hidden,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( in(A,B)
% 0.21/0.65 => ~ in(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(commutativity_k3_xboole_0,axiom,
% 0.21/0.65 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
% 0.21/0.65
% 0.21/0.65 fof(d1_xboole_0,axiom,
% 0.21/0.65 ! [A] :
% 0.21/0.65 ( A = empty_set
% 0.21/0.65 <=> ! [B] : ~ in(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d3_tarski,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( subset(A,B)
% 0.21/0.65 <=> ! [C] :
% 0.21/0.65 ( in(C,A)
% 0.21/0.65 => in(C,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d3_xboole_0,axiom,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( C = set_intersection2(A,B)
% 0.21/0.65 <=> ! [D] :
% 0.21/0.65 ( in(D,C)
% 0.21/0.65 <=> ( in(D,A)
% 0.21/0.65 & in(D,B) ) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(d7_xboole_0,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( disjoint(A,B)
% 0.21/0.65 <=> set_intersection2(A,B) = empty_set ) ).
% 0.21/0.65
% 0.21/0.65 fof(dt_k1_xboole_0,axiom,
% 0.21/0.65 $true ).
% 0.21/0.65
% 0.21/0.65 fof(dt_k3_xboole_0,axiom,
% 0.21/0.65 $true ).
% 0.21/0.65
% 0.21/0.65 fof(fc1_xboole_0,axiom,
% 0.21/0.65 empty(empty_set) ).
% 0.21/0.65
% 0.21/0.65 fof(idempotence_k3_xboole_0,axiom,
% 0.21/0.65 ! [A,B] : set_intersection2(A,A) = A ).
% 0.21/0.65
% 0.21/0.65 fof(rc1_xboole_0,axiom,
% 0.21/0.65 ? [A] : empty(A) ).
% 0.21/0.65
% 0.21/0.65 fof(rc2_xboole_0,axiom,
% 0.21/0.65 ? [A] : ~ empty(A) ).
% 0.21/0.65
% 0.21/0.65 fof(reflexivity_r1_tarski,axiom,
% 0.21/0.65 ! [A,B] : subset(A,A) ).
% 0.21/0.65
% 0.21/0.65 fof(symmetry_r1_xboole_0,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( disjoint(A,B)
% 0.21/0.65 => disjoint(B,A) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t1_xboole_1,conjecture,
% 0.21/0.65 ! [A,B,C] :
% 0.21/0.65 ( ( subset(A,B)
% 0.21/0.65 & subset(B,C) )
% 0.21/0.65 => subset(A,C) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t3_xboole_0,lemma,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( ~ ( ~ disjoint(A,B)
% 0.21/0.65 & ! [C] :
% 0.21/0.65 ~ ( in(C,A)
% 0.21/0.65 & in(C,B) ) )
% 0.21/0.65 & ~ ( ? [C] :
% 0.21/0.65 ( in(C,A)
% 0.21/0.65 & in(C,B) )
% 0.21/0.65 & disjoint(A,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t4_xboole_0,lemma,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ( ~ ( ~ disjoint(A,B)
% 0.21/0.65 & ! [C] : ~ in(C,set_intersection2(A,B)) )
% 0.21/0.65 & ~ ( ? [C] : in(C,set_intersection2(A,B))
% 0.21/0.65 & disjoint(A,B) ) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t6_boole,axiom,
% 0.21/0.65 ! [A] :
% 0.21/0.65 ( empty(A)
% 0.21/0.65 => A = empty_set ) ).
% 0.21/0.65
% 0.21/0.65 fof(t7_boole,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ~ ( in(A,B)
% 0.21/0.65 & empty(B) ) ).
% 0.21/0.65
% 0.21/0.65 fof(t8_boole,axiom,
% 0.21/0.65 ! [A,B] :
% 0.21/0.65 ~ ( empty(A)
% 0.21/0.65 & A != B
% 0.21/0.65 & empty(B) ) ).
% 0.21/0.65
% 0.21/0.65 %------------------------------------------------------------------------------
% 0.21/0.65 %-------------------------------------------
% 0.21/0.65 % Proof found
% 0.21/0.65 % SZS status Theorem for theBenchmark
% 0.21/0.65 % SZS output start Proof
% 0.21/0.65 %ClaNum:54(EqnAxiom:22)
% 0.21/0.65 %VarNum:143(SingletonVarNum:60)
% 0.21/0.65 %MaxLitNum:4
% 0.21/0.65 %MaxfuncDepth:1
% 0.21/0.66 %SharedTerms:12
% 0.21/0.66 %goalClause: 25 26 31
% 0.21/0.66 %singleGoalClaCount:3
% 0.21/0.66 [23]P1(a1)
% 0.21/0.66 [24]P1(a2)
% 0.21/0.66 [25]P3(a7,a9)
% 0.21/0.66 [26]P3(a9,a10)
% 0.21/0.66 [30]~P1(a8)
% 0.21/0.66 [31]~P3(a7,a10)
% 0.21/0.66 [27]P3(x271,x271)
% 0.21/0.66 [28]E(f11(x281,x281),x281)
% 0.21/0.66 [29]E(f11(x291,x292),f11(x292,x291))
% 0.21/0.66 [32]~P1(x321)+E(x321,a1)
% 0.21/0.66 [34]P4(f3(x341),x341)+E(x341,a1)
% 0.21/0.66 [35]~P4(x352,x351)+~E(x351,a1)
% 0.21/0.66 [36]~P1(x361)+~P4(x362,x361)
% 0.21/0.66 [39]~P2(x392,x391)+P2(x391,x392)
% 0.21/0.66 [40]~P4(x402,x401)+~P4(x401,x402)
% 0.21/0.66 [37]~P2(x371,x372)+E(f11(x371,x372),a1)
% 0.21/0.66 [38]P2(x381,x382)+~E(f11(x381,x382),a1)
% 0.21/0.66 [41]P3(x411,x412)+P4(f5(x411,x412),x411)
% 0.21/0.66 [42]P2(x421,x422)+P4(f12(x421,x422),x422)
% 0.21/0.66 [43]P2(x431,x432)+P4(f12(x431,x432),x431)
% 0.21/0.66 [48]P3(x481,x482)+~P4(f5(x481,x482),x482)
% 0.21/0.66 [49]P2(x491,x492)+P4(f4(x491,x492),f11(x491,x492))
% 0.21/0.66 [51]~P2(x511,x512)+~P4(x513,f11(x511,x512))
% 0.21/0.66 [33]~P1(x332)+~P1(x331)+E(x331,x332)
% 0.21/0.66 [44]~P3(x443,x442)+P4(x441,x442)+~P4(x441,x443)
% 0.21/0.66 [47]~P2(x473,x472)+~P4(x471,x472)+~P4(x471,x473)
% 0.21/0.66 [52]P4(f6(x522,x523,x521),x521)+P4(f6(x522,x523,x521),x523)+E(x521,f11(x522,x523))
% 0.21/0.66 [53]P4(f6(x532,x533,x531),x531)+P4(f6(x532,x533,x531),x532)+E(x531,f11(x532,x533))
% 0.21/0.66 [45]~P4(x451,x453)+P4(x451,x452)+~E(x453,f11(x454,x452))
% 0.21/0.66 [46]~P4(x461,x463)+P4(x461,x462)+~E(x463,f11(x462,x464))
% 0.21/0.66 [54]~P4(f6(x542,x543,x541),x541)+~P4(f6(x542,x543,x541),x543)+~P4(f6(x542,x543,x541),x542)+E(x541,f11(x542,x543))
% 0.21/0.66 [50]~P4(x501,x504)+~P4(x501,x503)+P4(x501,x502)+~E(x502,f11(x503,x504))
% 0.21/0.66 %EqnAxiom
% 0.21/0.66 [1]E(x11,x11)
% 0.21/0.66 [2]E(x22,x21)+~E(x21,x22)
% 0.21/0.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.21/0.66 [4]~E(x41,x42)+E(f11(x41,x43),f11(x42,x43))
% 0.21/0.66 [5]~E(x51,x52)+E(f11(x53,x51),f11(x53,x52))
% 0.21/0.66 [6]~E(x61,x62)+E(f6(x61,x63,x64),f6(x62,x63,x64))
% 0.21/0.66 [7]~E(x71,x72)+E(f6(x73,x71,x74),f6(x73,x72,x74))
% 0.21/0.66 [8]~E(x81,x82)+E(f6(x83,x84,x81),f6(x83,x84,x82))
% 0.21/0.66 [9]~E(x91,x92)+E(f4(x91,x93),f4(x92,x93))
% 0.21/0.66 [10]~E(x101,x102)+E(f4(x103,x101),f4(x103,x102))
% 0.21/0.66 [11]~E(x111,x112)+E(f3(x111),f3(x112))
% 0.21/0.66 [12]~E(x121,x122)+E(f5(x121,x123),f5(x122,x123))
% 0.21/0.66 [13]~E(x131,x132)+E(f5(x133,x131),f5(x133,x132))
% 0.21/0.66 [14]~E(x141,x142)+E(f12(x141,x143),f12(x142,x143))
% 0.21/0.66 [15]~E(x151,x152)+E(f12(x153,x151),f12(x153,x152))
% 0.21/0.66 [16]~P1(x161)+P1(x162)+~E(x161,x162)
% 0.21/0.66 [17]P4(x172,x173)+~E(x171,x172)+~P4(x171,x173)
% 0.21/0.66 [18]P4(x183,x182)+~E(x181,x182)+~P4(x183,x181)
% 0.21/0.66 [19]P3(x192,x193)+~E(x191,x192)+~P3(x191,x193)
% 0.21/0.66 [20]P3(x203,x202)+~E(x201,x202)+~P3(x203,x201)
% 0.21/0.66 [21]P2(x212,x213)+~E(x211,x212)+~P2(x211,x213)
% 0.21/0.66 [22]P2(x223,x222)+~E(x221,x222)+~P2(x223,x221)
% 0.21/0.66
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 cnf(55,plain,
% 0.21/0.66 (E(x551,f11(x551,x551))),
% 0.21/0.66 inference(scs_inference,[],[28,2])).
% 0.21/0.66 cnf(56,plain,
% 0.21/0.66 (~P4(x561,a1)),
% 0.21/0.66 inference(scs_inference,[],[23,28,2,36])).
% 0.21/0.66 cnf(59,plain,
% 0.21/0.66 (E(f11(x591,x591),x591)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(66,plain,
% 0.21/0.66 (E(f11(x661,x661),x661)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(71,plain,
% 0.21/0.66 (E(f11(x711,x711),x711)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(73,plain,
% 0.21/0.66 (E(f11(x731,x731),x731)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(75,plain,
% 0.21/0.66 (E(f11(x751,x751),x751)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(78,plain,
% 0.21/0.66 (E(f11(x781,x781),x781)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(80,plain,
% 0.21/0.66 (E(a2,a1)),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,2,36,35,43,42,22,21,20,19,16,3,46,45,32])).
% 0.21/0.66 cnf(94,plain,
% 0.21/0.66 (~P4(x941,f11(a1,x942))),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,78,2,36,35,43,42,22,21,20,19,16,3,46,45,32,15,14,13,12,11,10,9,8,7,6,5,4,51])).
% 0.21/0.66 cnf(102,plain,
% 0.21/0.66 (~P4(x1021,f11(f11(a1,x1022),f11(a1,x1022)))),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,78,2,36,35,43,42,22,21,20,19,16,3,46,45,32,15,14,13,12,11,10,9,8,7,6,5,4,51,48,41,37,18])).
% 0.21/0.66 cnf(103,plain,
% 0.21/0.66 (E(f11(x1031,x1031),x1031)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(104,plain,
% 0.21/0.66 (~P4(f11(f5(a7,a10),f5(a7,a10)),a10)),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,78,103,2,36,35,43,42,22,21,20,19,16,3,46,45,32,15,14,13,12,11,10,9,8,7,6,5,4,51,48,41,37,18,17])).
% 0.21/0.66 cnf(106,plain,
% 0.21/0.66 (P4(f5(a7,a10),a9)),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,78,103,2,36,35,43,42,22,21,20,19,16,3,46,45,32,15,14,13,12,11,10,9,8,7,6,5,4,51,48,41,37,18,17,44])).
% 0.21/0.66 cnf(114,plain,
% 0.21/0.66 (~P2(a7,a7)),
% 0.21/0.66 inference(scs_inference,[],[25,27,31,23,24,30,28,59,66,71,73,75,78,103,2,36,35,43,42,22,21,20,19,16,3,46,45,32,15,14,13,12,11,10,9,8,7,6,5,4,51,48,41,37,18,17,44,53,50,40,47])).
% 0.21/0.66 cnf(128,plain,
% 0.21/0.66 (P4(f12(a7,a7),a7)),
% 0.21/0.66 inference(scs_inference,[],[114,106,49,38,36,35,40,32,43])).
% 0.21/0.66 cnf(134,plain,
% 0.21/0.66 (E(f11(x1341,x1341),x1341)),
% 0.21/0.66 inference(rename_variables,[],[28])).
% 0.21/0.66 cnf(135,plain,
% 0.21/0.66 (~P3(a7,f11(a10,a10))),
% 0.21/0.66 inference(scs_inference,[],[28,134,31,94,114,106,49,38,36,35,40,32,43,41,21,20])).
% 0.21/0.66 cnf(139,plain,
% 0.21/0.66 (~P4(x1391,f11(f11(a1,x1392),f11(a1,x1392)))),
% 0.21/0.66 inference(rename_variables,[],[102])).
% 0.21/0.66 cnf(143,plain,
% 0.21/0.66 (~P4(x1431,f11(f11(a1,x1432),f11(a1,x1432)))),
% 0.21/0.66 inference(rename_variables,[],[102])).
% 0.21/0.66 cnf(148,plain,
% 0.21/0.66 (P4(f11(f5(a7,a10),f5(a7,a10)),a9)),
% 0.21/0.66 inference(scs_inference,[],[26,23,30,28,134,31,55,102,139,143,94,56,114,106,49,38,36,35,40,32,43,41,21,20,19,16,44,53,50,17])).
% 0.21/0.66 cnf(186,plain,
% 0.21/0.66 ($false),
% 0.21/0.66 inference(scs_inference,[],[26,128,148,135,80,102,94,104,36,49,35,43,41,44]),
% 0.21/0.66 ['proof']).
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66 % Total time :0.030000s
%------------------------------------------------------------------------------