TSTP Solution File: SWV376+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n006.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 21:33:21 EDT 2023
% Result : Theorem 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 08:46:21 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 % File :CSE---1.6
% 0.19/0.69 % Problem :theBenchmark
% 0.19/0.69 % Transform :cnf
% 0.19/0.69 % Format :tptp:raw
% 0.19/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.69
% 0.19/0.69 % Result :Theorem 0.070000s
% 0.19/0.69 % Output :CNFRefutation 0.070000s
% 0.19/0.69 %-------------------------------------------
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 % File : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.19/0.69 % Domain : Software Verification
% 0.19/0.69 % Problem : Priority queue checker: lemma_not_ok_persistence
% 0.19/0.69 % Version : [dNP05] axioms.
% 0.19/0.69 % English :
% 0.19/0.69
% 0.19/0.69 % Refs : [Pis06] Piskac (2006), Email to Geoff Sutcliffe
% 0.19/0.69 % : [dNP05] de Nivelle & Piskac (2005), Verification of an Off-Lin
% 0.19/0.69 % Source : [Pis06]
% 0.19/0.69 % Names : cpq_l012 [Pis06]
% 0.19/0.69
% 0.19/0.69 % Status : Theorem
% 0.19/0.69 % Rating : 0.22 v7.4.0, 0.20 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.30 v7.0.0, 0.27 v6.4.0, 0.31 v6.3.0, 0.33 v6.2.0, 0.36 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.30 v5.4.0, 0.36 v5.3.0, 0.37 v5.2.0, 0.30 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.39 v4.0.0, 0.42 v3.7.0, 0.45 v3.5.0, 0.47 v3.3.0
% 0.19/0.69 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.19/0.69 % Number of atoms : 93 ( 29 equ)
% 0.19/0.69 % Maximal formula atoms : 6 ( 2 avg)
% 0.19/0.69 % Number of connectives : 70 ( 21 ~; 3 |; 12 &)
% 0.19/0.69 % ( 7 <=>; 27 =>; 0 <=; 0 <~>)
% 0.19/0.69 % Maximal formula depth : 11 ( 5 avg)
% 0.19/0.69 % Maximal term depth : 4 ( 1 avg)
% 0.19/0.69 % Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% 0.19/0.69 % Number of functors : 19 ( 19 usr; 3 con; 0-3 aty)
% 0.19/0.69 % Number of variables : 138 ( 138 !; 0 ?)
% 0.19/0.69 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.69
% 0.19/0.69 % Comments :
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 %----Include the axioms about priority queues and checked priority queues
% 0.19/0.69 include('Axioms/SWV007+0.ax').
% 0.19/0.69 include('Axioms/SWV007+2.ax').
% 0.19/0.69 include('Axioms/SWV007+3.ax').
% 0.19/0.69 %------------------------------------------------------------------------------
% 0.19/0.69 /*----
% 0.19/0.69 Explanation about induction
% 0.19/0.69 ===========================
% 0.19/0.69
% 0.19/0.69 In order to prove lemma_not_ok_persistence we use the following induction
% 0.19/0.69 principle: (the induction principle used in Coq)
% 0.19/0.69 =====================
% 0.19/0.69 let s/1 be the successor function defined on some set S and let =</2 be the
% 0.19/0.69 predicate that satisfies the following axioms:
% 0.19/0.69
% 0.19/0.69 1) x =< x
% 0.19/0.69 2) x =< y -> x =< s(y)
% 0.19/0.69
% 0.19/0.69 Note that our predicate succ_cpq/2 satisfies those two axioms
% 0.19/0.69
% 0.19/0.69 The induction principle: (V = for eVery
% 0.19/0.69
% 0.19/0.69 Vx ( (P(x) and Vy (x =< y -> (P(y) -> P(s(y)))) -> Vy (x=<y -> P(y)) )
% 0.19/0.69 ======================
% 0.19/0.69
% 0.19/0.69 Let P(x) == ~(ok(x)) and let =</2 == succ/2
% 0.19/0.69
% 0.19/0.69 Then, in order to confirm correctness of lemma_not_ok_persistence we have
% 0.19/0.69 to only verify "Vy (x =< y -> (P(y) -> P(s(y))))" part of the induction
% 0.19/0.69 principle, in other words we need to prove validity of:
% 0.19/0.69
% 0.19/0.69 all(CPQ1, all(CPQ2, succ_cpq(CPQ1, CPQ2) => ( ~(ok(CPQ2)) => ~(ok(s(CPQ2))) ) )), (1)
% 0.19/0.69
% 0.19/0.69 where s(CPQ2) is the immediate successor of CPQ2
% 0.19/0.69
% 0.19/0.69 all(CPQ2, ~(ok(CPQ2)) => ~(ok(s(CPQ2))) ) (2)
% 0.19/0.69
% 0.19/0.70 is a valid formula.
% 0.19/0.70
% 0.19/0.70 the validity of formula (2) is proved in lemma_not_ok_persistence_induction,
% 0.19/0.70 so here we have included it as a valid formula
% 0.19/0.70
% 0.19/0.70 lemma_not_ok_persistence_induction proves the validity of formula (1)
% 0.19/0.70 and thus, since (1) is valid we can conclude that the following formula holds:
% 0.19/0.70
% 0.19/0.70 Vx ( P(x) -> Vy (x=<y -> P(y)) )
% 0.19/0.70
% 0.19/0.70 or in our example:
% 0.19/0.70
% 0.19/0.70 all(CPQ, ~(ok(CPQ)) => all(CPQ1, succ(CPQ, CPQ1) => ~(ok(CPQ1)) ) )
% 0.19/0.70
% 0.19/0.70 which completes the inductive proof of lemma_not_ok_persistence
% 0.19/0.70 ----*/
% 0.19/0.70
% 0.19/0.70 %----induction axiom
% 0.19/0.70 fof(l12_induction,axiom,
% 0.19/0.70 ( ! [U,V,W,X,Y,Z] :
% 0.19/0.70 ( succ_cpq(triple(U,V,W),triple(X,Y,Z))
% 0.19/0.70 => ( ~ ok(triple(X,Y,Z))
% 0.19/0.70 => ~ ok(im_succ_cpq(triple(X,Y,Z))) ) )
% 0.19/0.70 => ! [X1,X2,X3] :
% 0.19/0.70 ( ~ ok(triple(X1,X2,X3))
% 0.19/0.70 => ! [X4,X5,X6] :
% 0.19/0.70 ( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
% 0.19/0.70 => ~ ok(triple(X4,X5,X6)) ) ) ) ).
% 0.19/0.70
% 0.19/0.70 %----lemma_not_ok_persistence_induction (cpq_l013.p .. cpq_l016.p)
% 0.19/0.70 fof(l12_l13,lemma,
% 0.19/0.70 ! [U,V,W] :
% 0.19/0.70 ( ~ ok(triple(U,V,W))
% 0.19/0.70 => ~ ok(im_succ_cpq(triple(U,V,W))) ) ).
% 0.19/0.70
% 0.19/0.70 %----lemma_not_ok_persistence (conjecture)
% 0.19/0.70 fof(l12_co,conjecture,
% 0.19/0.70 ! [U,V,W] :
% 0.19/0.70 ( ~ ok(triple(U,V,W))
% 0.19/0.70 => ! [X,Y,Z] :
% 0.19/0.70 ( succ_cpq(triple(U,V,W),triple(X,Y,Z))
% 0.19/0.70 => ~ ok(triple(X,Y,Z)) ) ) ).
% 0.19/0.70
% 0.19/0.70 %------------------------------------------------------------------------------
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark
% 0.19/0.70 % SZS output start Proof
% 0.19/0.70 %ClaNum:99(EqnAxiom:44)
% 0.19/0.70 %VarNum:341(SingletonVarNum:168)
% 0.19/0.70 %MaxLitNum:4
% 0.19/0.70 %MaxfuncDepth:3
% 0.19/0.70 %SharedTerms:27
% 0.19/0.70 %goalClause: 52 56 61
% 0.19/0.70 %singleGoalClaCount:3
% 0.19/0.70 [58]~P2(a1)
% 0.19/0.70 [52]P7(f29(a7,a8,a9))
% 0.19/0.70 [56]P6(f29(a12,a19,a20),f29(a7,a8,a9))
% 0.19/0.70 [61]~P7(f29(a12,a19,a20))
% 0.19/0.70 [46]P1(a2,x461)
% 0.19/0.70 [47]P1(x471,x471)
% 0.19/0.70 [48]P6(x481,x481)
% 0.19/0.70 [59]~P4(a1,x591)
% 0.19/0.70 [45]E(f4(a1,x451),a1)
% 0.19/0.70 [60]~P8(a1,x601,x602)
% 0.19/0.70 [54]P3(f29(x541,a1,x542))
% 0.19/0.70 [62]~P7(f29(x621,x622,a3))
% 0.19/0.70 [53]E(f10(f29(x531,a1,x532)),a2)
% 0.19/0.70 [55]E(f11(f29(x551,a1,x552)),f29(x551,a1,a3))
% 0.19/0.70 [49]P2(f6(x491,f5(x492,x493)))
% 0.19/0.70 [50]E(f26(f6(x501,f5(x502,x503)),x502),x501)
% 0.19/0.70 [51]E(f25(f6(x511,f5(x512,x513)),x512),x513)
% 0.19/0.70 [57]E(f29(f21(x571,x572),f6(x573,f5(x572,a2)),x574),f22(f29(x571,x573,x574),x572))
% 0.19/0.70 [63]P1(x632,x631)+P1(x631,x632)
% 0.19/0.70 [64]~P9(x641,x642)+P1(x641,x642)
% 0.19/0.70 [66]~P9(x662,x661)+~P1(x661,x662)
% 0.19/0.70 [65]~P6(x651,x652)+P6(x651,f11(x652))
% 0.19/0.70 [71]~P6(x711,x712)+P6(x711,f27(f11(x712),f10(x712)))
% 0.19/0.70 [69]~P6(x691,x692)+P6(x691,f22(x692,x693))
% 0.19/0.70 [70]~P6(x701,x702)+P6(x701,f27(x702,x703))
% 0.19/0.70 [73]E(x731,a3)+P7(f29(x732,x733,x731))
% 0.19/0.70 [75]E(x751,a1)+E(f10(f29(x752,x751,x753)),f23(x752))
% 0.19/0.70 [94]P7(f29(x941,x942,x943))+~P7(f24(f29(x941,x942,x943)))
% 0.19/0.70 [78]~P4(x782,x784)+P5(f29(x781,x782,x783),x784)
% 0.19/0.70 [84]P4(x841,x842)+~P5(f29(x843,x841,x844),x842)
% 0.19/0.70 [72]~E(x722,x724)+P4(f6(x721,f5(x722,x723)),x724)
% 0.19/0.70 [74]~P4(x741,x744)+P4(f6(x741,f5(x742,x743)),x744)
% 0.19/0.70 [83]P4(x832,x834)+E(f27(f29(x831,x832,x833),x834),f29(x831,x832,a3))
% 0.19/0.70 [80]~P1(x802,x804)+E(f6(f4(x801,x802),f5(x803,x804)),f4(f6(x801,f5(x803,x804)),x802))
% 0.19/0.70 [81]~P9(x813,x814)+E(f4(f6(x811,f5(x812,x813)),x814),f6(f4(x811,x814),f5(x812,x814)))
% 0.19/0.70 [85]~P8(x851,x854,x855)+P8(f6(x851,f5(x852,x853)),x854,x855)
% 0.19/0.70 [93]~P9(x931,x932)+~P3(f29(x933,f6(x934,f5(x931,x932)),x935))
% 0.19/0.70 [67]P9(x672,x671)+~P1(x672,x671)+P1(x671,x672)
% 0.19/0.70 [68]~P1(x681,x683)+P1(x681,x682)+~P1(x683,x682)
% 0.19/0.70 [86]P4(x861,f23(x862))+E(x861,a1)+E(f11(f29(x862,x861,x863)),f29(x862,f4(x861,f23(x862)),a3))
% 0.19/0.70 [79]E(x791,x792)+P4(x793,x792)+~P4(f6(x793,f5(x791,x794)),x792)
% 0.19/0.70 [89]~P4(x892,x894)+~P9(x894,f25(x892,x894))+E(f27(f29(x891,x892,x893),x894),f29(f28(x891,x894),f26(x892,x894),a3))
% 0.19/0.70 [90]~P4(x903,x902)+~P1(f25(x903,x902),x902)+E(f29(f28(x901,x902),f26(x903,x902),x904),f27(f29(x901,x903,x904),x902))
% 0.19/0.70 [76]~P4(x763,x762)+E(x761,x762)+E(f25(f6(x763,f5(x761,x764)),x762),f25(x763,x762))
% 0.19/0.70 [82]~P4(x823,x822)+E(x821,x822)+E(f26(f6(x823,f5(x821,x824)),x822),f6(f26(x823,x822),f5(x821,x824)))
% 0.19/0.70 [77]~E(x773,x775)+~E(x772,x774)+P8(f6(x771,f5(x772,x773)),x774,x775)
% 0.19/0.70 [87]E(x871,x872)+P8(x873,x874,x872)+~P8(f6(x873,f5(x875,x871)),x874,x872)
% 0.19/0.70 [88]E(x881,x882)+P8(x883,x882,x884)+~P8(f6(x883,f5(x881,x885)),x882,x884)
% 0.19/0.70 [95]~P1(x954,x953)+~P3(f29(x951,x952,x955))+P3(f29(x951,f6(x952,f5(x953,x954)),x955))
% 0.19/0.70 [96]~P1(x964,x965)+P3(f29(x961,x962,x963))+~P3(f29(x961,f6(x962,f5(x965,x964)),x963))
% 0.19/0.70 [91]~P4(x911,f23(x912))+E(x911,a1)+~P9(f23(x912),f25(x911,f23(x912)))+E(f11(f29(x912,x911,x913)),f29(x912,f4(x911,f23(x912)),a3))
% 0.19/0.70 [92]~P4(x921,f23(x922))+E(x921,a1)+~P1(f25(x921,f23(x922)),f23(x922))+E(f29(x922,f4(x921,f23(x922)),x923),f11(f29(x922,x921,x923)))
% 0.19/0.70 [97]~P6(f29(x971,x972,x973),f29(x974,x975,x976))+P7(f29(x971,x972,x973))+~P7(f29(x974,x975,x976))+~P7(f29(a13,a17,a18))
% 0.19/0.70 [99]~P6(f29(x991,x992,x993),f29(x994,x995,x996))+P6(f29(a14,a15,a16),f29(a13,a17,a18))+P7(f29(x991,x992,x993))+~P7(f29(x994,x995,x996))
% 0.19/0.70 [98]~P6(f29(x981,x982,x983),f29(x984,x985,x986))+P7(f29(x981,x982,x983))+~P7(f29(x984,x985,x986))+P7(f24(f29(a13,a17,a18)))
% 0.19/0.70 %EqnAxiom
% 0.19/0.70 [1]E(x11,x11)
% 0.19/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.70 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.19/0.70 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.19/0.70 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.19/0.70 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.19/0.70 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.19/0.70 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.19/0.70 [10]~E(x101,x102)+E(f29(x101,x103,x104),f29(x102,x103,x104))
% 0.19/0.70 [11]~E(x111,x112)+E(f29(x113,x111,x114),f29(x113,x112,x114))
% 0.19/0.70 [12]~E(x121,x122)+E(f29(x123,x124,x121),f29(x123,x124,x122))
% 0.19/0.70 [13]~E(x131,x132)+E(f11(x131),f11(x132))
% 0.19/0.70 [14]~E(x141,x142)+E(f26(x141,x143),f26(x142,x143))
% 0.19/0.70 [15]~E(x151,x152)+E(f26(x153,x151),f26(x153,x152))
% 0.19/0.70 [16]~E(x161,x162)+E(f25(x161,x163),f25(x162,x163))
% 0.19/0.70 [17]~E(x171,x172)+E(f25(x173,x171),f25(x173,x172))
% 0.19/0.70 [18]~E(x181,x182)+E(f27(x181,x183),f27(x182,x183))
% 0.19/0.70 [19]~E(x191,x192)+E(f27(x193,x191),f27(x193,x192))
% 0.19/0.70 [20]~E(x201,x202)+E(f10(x201),f10(x202))
% 0.19/0.70 [21]~E(x211,x212)+E(f23(x211),f23(x212))
% 0.19/0.70 [22]~E(x221,x222)+E(f28(x221,x223),f28(x222,x223))
% 0.19/0.70 [23]~E(x231,x232)+E(f28(x233,x231),f28(x233,x232))
% 0.19/0.70 [24]~E(x241,x242)+E(f22(x241,x243),f22(x242,x243))
% 0.19/0.70 [25]~E(x251,x252)+E(f22(x253,x251),f22(x253,x252))
% 0.19/0.70 [26]~E(x261,x262)+E(f24(x261),f24(x262))
% 0.19/0.70 [27]~E(x271,x272)+E(f21(x271,x273),f21(x272,x273))
% 0.19/0.70 [28]~E(x281,x282)+E(f21(x283,x281),f21(x283,x282))
% 0.19/0.70 [29]P1(x292,x293)+~E(x291,x292)+~P1(x291,x293)
% 0.19/0.70 [30]P1(x303,x302)+~E(x301,x302)+~P1(x303,x301)
% 0.19/0.70 [31]P6(x312,x313)+~E(x311,x312)+~P6(x311,x313)
% 0.19/0.70 [32]P6(x323,x322)+~E(x321,x322)+~P6(x323,x321)
% 0.19/0.70 [33]~P3(x331)+P3(x332)+~E(x331,x332)
% 0.19/0.70 [34]~P2(x341)+P2(x342)+~E(x341,x342)
% 0.19/0.70 [35]~P7(x351)+P7(x352)+~E(x351,x352)
% 0.19/0.70 [36]P9(x362,x363)+~E(x361,x362)+~P9(x361,x363)
% 0.19/0.70 [37]P9(x373,x372)+~E(x371,x372)+~P9(x373,x371)
% 0.19/0.70 [38]P4(x382,x383)+~E(x381,x382)+~P4(x381,x383)
% 0.19/0.70 [39]P4(x393,x392)+~E(x391,x392)+~P4(x393,x391)
% 0.19/0.70 [40]P8(x402,x403,x404)+~E(x401,x402)+~P8(x401,x403,x404)
% 0.19/0.70 [41]P8(x413,x412,x414)+~E(x411,x412)+~P8(x413,x411,x414)
% 0.19/0.70 [42]P8(x423,x424,x422)+~E(x421,x422)+~P8(x423,x424,x421)
% 0.19/0.70 [43]P5(x432,x433)+~E(x431,x432)+~P5(x431,x433)
% 0.19/0.70 [44]P5(x443,x442)+~E(x441,x442)+~P5(x443,x441)
% 0.19/0.70
% 0.19/0.70 %-------------------------------------------
% 0.19/0.70 cnf(106,plain,
% 0.19/0.70 (E(f11(f29(x1061,a1,x1062)),f29(x1061,a1,a3))),
% 0.19/0.70 inference(rename_variables,[],[55])).
% 0.19/0.70 cnf(110,plain,
% 0.19/0.70 (P6(x1101,x1101)),
% 0.19/0.70 inference(rename_variables,[],[48])).
% 0.19/0.70 cnf(112,plain,
% 0.19/0.70 (P6(x1121,x1121)),
% 0.19/0.70 inference(rename_variables,[],[48])).
% 0.19/0.70 cnf(114,plain,
% 0.19/0.70 (P1(x1141,x1141)),
% 0.19/0.70 inference(rename_variables,[],[47])).
% 0.19/0.70 cnf(116,plain,
% 0.19/0.70 (P1(x1161,x1161)),
% 0.19/0.70 inference(rename_variables,[],[47])).
% 0.19/0.70 cnf(118,plain,
% 0.19/0.70 (E(f26(f6(x1181,f5(x1182,x1183)),x1182),x1181)),
% 0.19/0.70 inference(rename_variables,[],[50])).
% 0.19/0.70 cnf(171,plain,
% 0.19/0.70 (P3(f29(x1711,f6(a1,f5(x1712,x1712)),x1713))),
% 0.19/0.70 inference(scs_inference,[],[52,47,114,116,48,110,112,60,59,58,61,56,45,54,62,55,106,50,118,2,66,73,35,34,32,31,30,29,3,99,84,72,70,69,65,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,71,83,80,94,43,40,38,37,36,77,95])).
% 0.19/0.70 cnf(173,plain,
% 0.19/0.70 (~P7(f29(a13,a17,a18))),
% 0.19/0.70 inference(scs_inference,[],[52,47,114,116,48,110,112,60,59,58,61,56,45,54,62,55,106,50,118,2,66,73,35,34,32,31,30,29,3,99,84,72,70,69,65,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,71,83,80,94,43,40,38,37,36,77,95,97])).
% 0.19/0.70 cnf(175,plain,
% 0.19/0.70 (P7(f24(f29(a13,a17,a18)))),
% 0.19/0.70 inference(scs_inference,[],[52,47,114,116,48,110,112,60,59,58,61,56,45,54,62,55,106,50,118,2,66,73,35,34,32,31,30,29,3,99,84,72,70,69,65,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,71,83,80,94,43,40,38,37,36,77,95,97,98])).
% 0.19/0.70 cnf(177,plain,
% 0.19/0.70 (P8(f6(x1771,f5(f4(a1,x1772),f4(a1,x1772))),a1,f4(a1,x1772))),
% 0.19/0.70 inference(scs_inference,[],[52,47,114,116,48,110,112,60,59,58,61,56,45,54,62,55,106,50,118,2,66,73,35,34,32,31,30,29,3,99,84,72,70,69,65,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,71,83,80,94,43,40,38,37,36,77,95,97,98,42])).
% 0.19/0.70 cnf(179,plain,
% 0.19/0.70 (P4(f6(x1791,f5(f4(a1,x1792),x1793)),f4(a1,x1792))),
% 0.19/0.70 inference(scs_inference,[],[52,47,114,116,48,110,112,60,59,58,61,56,45,54,62,55,106,50,118,2,66,73,35,34,32,31,30,29,3,99,84,72,70,69,65,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,71,83,80,94,43,40,38,37,36,77,95,97,98,42,41,39])).
% 0.19/0.70 cnf(192,plain,
% 0.19/0.70 ($false),
% 0.19/0.70 inference(scs_inference,[],[57,46,54,171,179,177,173,175,85,74,33,95,94]),
% 0.19/0.70 ['proof']).
% 0.19/0.70 % SZS output end Proof
% 0.19/0.70 % Total time :0.070000s
%------------------------------------------------------------------------------