%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWV385+1 : TPTP v8.2.0. Released v3.3.0.
% 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 16:47:03 EDT 2024
% Result : Theorem 0.53s 0.62s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV385+1 : TPTP v8.2.0. Released v3.3.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n022.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 20 14:31:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.53/0.57 start to proof:theBenchmark
% 0.53/0.62 %-------------------------------------------
% 0.53/0.62 % File :CSE---1.7
% 0.53/0.62 % Problem :theBenchmark
% 0.53/0.62 % Transform :cnf
% 0.53/0.62 % Format :tptp:raw
% 0.53/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.53/0.62
% 0.53/0.62 % Result :Theorem 0.010000s
% 0.53/0.62 % Output :CNFRefutation 0.010000s
% 0.53/0.62 %-------------------------------------------
% 0.53/0.62 %------------------------------------------------------------------------------
% 0.53/0.62 % File : SWV385+1 : TPTP v8.2.0. Released v3.3.0.
% 0.53/0.62 % Domain : Software Verification
% 0.53/0.62 % Problem : Priority queue checker: lemma_not_min_elem_not_check_induction02
% 0.53/0.62 % Version : [dNP05] axioms.
% 0.53/0.62 % English :
% 0.53/0.62
% 0.53/0.62 % Refs : [Pis06] Piskac (2006), Email to Geoff Sutcliffe
% 0.53/0.62 % : [dNP05] de Nivelle & Piskac (2005), Verification of an Off-Lin
% 0.53/0.62 % Source : [Pis06]
% 0.53/0.62 % Names : cpq_l021 [Pis06]
% 0.53/0.62
% 0.53/0.62 % Status : Theorem
% 0.53/0.62 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.1.0, 0.13 v7.0.0, 0.10 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.20 v6.1.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.18 v5.3.0, 0.19 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.4.0, 0.21 v3.3.0
% 0.53/0.62 % Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% 0.53/0.62 % Number of atoms : 91 ( 29 equ)
% 0.53/0.62 % Maximal formula atoms : 4 ( 2 avg)
% 0.53/0.62 % Number of connectives : 69 ( 22 ~; 6 |; 12 &)
% 0.53/0.62 % ( 7 <=>; 22 =>; 0 <=; 0 <~>)
% 0.53/0.62 % Maximal formula depth : 9 ( 5 avg)
% 0.53/0.62 % Maximal term depth : 4 ( 1 avg)
% 0.53/0.62 % Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% 0.53/0.62 % Number of functors : 19 ( 19 usr; 3 con; 0-3 aty)
% 0.53/0.62 % Number of variables : 126 ( 126 !; 0 ?)
% 0.53/0.62 % SPC : FOF_THM_RFO_SEQ
% 0.53/0.62
% 0.53/0.62 % Comments :
% 0.53/0.62 %------------------------------------------------------------------------------
% 0.53/0.62 %----Include the axioms about priority queues and checked priority queues
% 0.53/0.62 include('Axioms/SWV007+0.ax').
% 0.53/0.62 include('Axioms/SWV007+2.ax').
% 0.53/0.62 include('Axioms/SWV007+3.ax').
% 0.53/0.62 %------------------------------------------------------------------------------
% 0.53/0.62 %----lemma_not_ok_persistence_induction (cpq_l013.p .. cpq_l016.p)
% 0.53/0.62 fof(l21_li1316,lemma,
% 0.53/0.62 ! [U,V,W] :
% 0.53/0.62 ( ~ ok(triple(U,V,W))
% 0.53/0.62 => ~ ok(im_succ_cpq(triple(U,V,W))) ) ).
% 0.53/0.62
% 0.53/0.62 %----lemma_not_min_elem_not_check_ind_steps (cpq_l022.p .. cpq_l025.p)
% 0.53/0.62 fof(l21_li2225,lemma,
% 0.53/0.62 ! [U,V,W] :
% 0.53/0.62 ( ~ check_cpq(triple(U,V,W))
% 0.53/0.62 => ( ~ check_cpq(im_succ_cpq(triple(U,V,W)))
% 0.53/0.62 | ~ ok(im_succ_cpq(triple(U,V,W))) ) ) ).
% 0.53/0.62
% 0.53/0.62 %----lemma_not_min_elem_not_check_induction02 (conjecture)
% 0.53/0.62 fof(l21_co,conjecture,
% 0.53/0.62 ! [U,V,W] :
% 0.53/0.62 ( ( ~ check_cpq(triple(U,V,W))
% 0.53/0.62 | ~ ok(triple(U,V,W)) )
% 0.53/0.62 => ( ~ check_cpq(im_succ_cpq(triple(U,V,W)))
% 0.53/0.62 | ~ ok(im_succ_cpq(triple(U,V,W))) ) ) ).
% 0.53/0.62
% 0.53/0.62 %------------------------------------------------------------------------------
% 0.53/0.62 %-------------------------------------------
% 0.53/0.62 % Proof found
% 0.53/0.62 % SZS status Theorem for theBenchmark
% 0.53/0.62 % SZS output start Proof
% 0.53/0.62 %ClaNum:97(EqnAxiom:44)
% 0.53/0.62 %VarNum:314(SingletonVarNum:153)
% 0.53/0.62 %MaxLitNum:4
% 0.53/0.62 %MaxfuncDepth:3
% 0.53/0.62 %SharedTerms:13
% 0.53/0.62 %goalClause: 55 56 90
% 0.53/0.62 %singleGoalClaCount:2
% 0.53/0.62 [58]~P2(a1)
% 0.53/0.63 [55]P3(f12(f20(a9,a10,a11)))
% 0.53/0.63 [56]P7(f12(f20(a9,a10,a11)))
% 0.53/0.63 [46]P1(a2,x461)
% 0.53/0.63 [47]P1(x471,x471)
% 0.53/0.63 [48]P6(x481,x481)
% 0.53/0.63 [59]~P4(a1,x591)
% 0.53/0.63 [45]E(f4(a1,x451),a1)
% 0.53/0.63 [60]~P8(a1,x601,x602)
% 0.53/0.63 [53]P3(f20(x531,a1,x532))
% 0.53/0.63 [61]~P7(f20(x611,x612,a3))
% 0.53/0.63 [52]E(f7(f20(x521,a1,x522)),a2)
% 0.53/0.63 [54]E(f8(f20(x541,a1,x542)),f20(x541,a1,a3))
% 0.53/0.63 [49]P2(f6(x491,f5(x492,x493)))
% 0.53/0.63 [50]E(f17(f6(x501,f5(x502,x503)),x502),x501)
% 0.53/0.63 [51]E(f16(f6(x511,f5(x512,x513)),x512),x513)
% 0.53/0.63 [57]E(f20(f14(x571,x572),f6(x573,f5(x572,a2)),x574),f15(f20(x571,x573,x574),x572))
% 0.53/0.63 [90]~P7(f20(a9,a10,a11))+~P3(f20(a9,a10,a11))
% 0.53/0.63 [62]P1(x622,x621)+P1(x621,x622)
% 0.53/0.63 [63]~P9(x631,x632)+P1(x631,x632)
% 0.53/0.63 [65]~P9(x652,x651)+~P1(x651,x652)
% 0.53/0.63 [64]~P6(x641,x642)+P6(x641,f8(x642))
% 0.53/0.63 [70]~P6(x701,x702)+P6(x701,f18(f8(x702),f7(x702)))
% 0.53/0.63 [68]~P6(x681,x682)+P6(x681,f15(x682,x683))
% 0.53/0.63 [69]~P6(x691,x692)+P6(x691,f18(x692,x693))
% 0.53/0.63 [72]E(x721,a3)+P7(f20(x722,x723,x721))
% 0.53/0.63 [74]E(x741,a1)+E(f7(f20(x742,x741,x743)),f13(x742))
% 0.53/0.63 [94]P7(f20(x941,x942,x943))+~P7(f12(f20(x941,x942,x943)))
% 0.53/0.63 [77]~P4(x772,x774)+P5(f20(x771,x772,x773),x774)
% 0.53/0.63 [83]P4(x831,x832)+~P5(f20(x833,x831,x834),x832)
% 0.53/0.63 [71]~E(x712,x714)+P4(f6(x711,f5(x712,x713)),x714)
% 0.53/0.63 [73]~P4(x731,x734)+P4(f6(x731,f5(x732,x733)),x734)
% 0.53/0.63 [82]P4(x822,x824)+E(f18(f20(x821,x822,x823),x824),f20(x821,x822,a3))
% 0.53/0.63 [79]~P1(x792,x794)+E(f6(f4(x791,x792),f5(x793,x794)),f4(f6(x791,f5(x793,x794)),x792))
% 0.53/0.63 [80]~P9(x803,x804)+E(f4(f6(x801,f5(x802,x803)),x804),f6(f4(x801,x804),f5(x802,x804)))
% 0.53/0.63 [84]~P8(x841,x844,x845)+P8(f6(x841,f5(x842,x843)),x844,x845)
% 0.53/0.63 [93]~P9(x931,x932)+~P3(f20(x933,f6(x934,f5(x931,x932)),x935))
% 0.53/0.63 [66]P9(x662,x661)+~P1(x662,x661)+P1(x661,x662)
% 0.53/0.63 [67]~P1(x671,x673)+P1(x671,x672)+~P1(x673,x672)
% 0.53/0.63 [97]P3(f20(x971,x972,x973))+~P3(f12(f20(x971,x972,x973)))+~P7(f12(f20(x971,x972,x973)))
% 0.53/0.63 [85]P4(x851,f13(x852))+E(x851,a1)+E(f8(f20(x852,x851,x853)),f20(x852,f4(x851,f13(x852)),a3))
% 0.53/0.63 [78]E(x781,x782)+P4(x783,x782)+~P4(f6(x783,f5(x781,x784)),x782)
% 0.53/0.63 [88]~P4(x882,x884)+~P9(x884,f16(x882,x884))+E(f18(f20(x881,x882,x883),x884),f20(f19(x881,x884),f17(x882,x884),a3))
% 0.53/0.63 [89]~P4(x893,x892)+~P1(f16(x893,x892),x892)+E(f20(f19(x891,x892),f17(x893,x892),x894),f18(f20(x891,x893,x894),x892))
% 0.53/0.63 [75]~P4(x753,x752)+E(x751,x752)+E(f16(f6(x753,f5(x751,x754)),x752),f16(x753,x752))
% 0.53/0.63 [81]~P4(x813,x812)+E(x811,x812)+E(f17(f6(x813,f5(x811,x814)),x812),f6(f17(x813,x812),f5(x811,x814)))
% 0.53/0.63 [76]~E(x763,x765)+~E(x762,x764)+P8(f6(x761,f5(x762,x763)),x764,x765)
% 0.53/0.63 [86]E(x861,x862)+P8(x863,x864,x862)+~P8(f6(x863,f5(x865,x861)),x864,x862)
% 0.53/0.63 [87]E(x871,x872)+P8(x873,x872,x874)+~P8(f6(x873,f5(x871,x875)),x872,x874)
% 0.53/0.63 [95]~P1(x954,x953)+~P3(f20(x951,x952,x955))+P3(f20(x951,f6(x952,f5(x953,x954)),x955))
% 0.53/0.63 [96]~P1(x964,x965)+P3(f20(x961,x962,x963))+~P3(f20(x961,f6(x962,f5(x965,x964)),x963))
% 0.53/0.63 [91]~P4(x911,f13(x912))+E(x911,a1)+~P9(f13(x912),f16(x911,f13(x912)))+E(f8(f20(x912,x911,x913)),f20(x912,f4(x911,f13(x912)),a3))
% 0.53/0.63 [92]~P4(x921,f13(x922))+E(x921,a1)+~P1(f16(x921,f13(x922)),f13(x922))+E(f20(x922,f4(x921,f13(x922)),x923),f8(f20(x922,x921,x923)))
% 0.53/0.63 %EqnAxiom
% 0.53/0.63 [1]E(x11,x11)
% 0.53/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.53/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.53/0.63 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.53/0.63 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.53/0.63 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.53/0.63 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.53/0.63 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.53/0.63 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.53/0.63 [10]~E(x101,x102)+E(f20(x101,x103,x104),f20(x102,x103,x104))
% 0.53/0.63 [11]~E(x111,x112)+E(f20(x113,x111,x114),f20(x113,x112,x114))
% 0.53/0.63 [12]~E(x121,x122)+E(f20(x123,x124,x121),f20(x123,x124,x122))
% 0.53/0.63 [13]~E(x131,x132)+E(f13(x131),f13(x132))
% 0.53/0.63 [14]~E(x141,x142)+E(f17(x141,x143),f17(x142,x143))
% 0.53/0.63 [15]~E(x151,x152)+E(f17(x153,x151),f17(x153,x152))
% 0.53/0.63 [16]~E(x161,x162)+E(f18(x161,x163),f18(x162,x163))
% 0.53/0.63 [17]~E(x171,x172)+E(f18(x173,x171),f18(x173,x172))
% 0.53/0.63 [18]~E(x181,x182)+E(f16(x181,x183),f16(x182,x183))
% 0.53/0.63 [19]~E(x191,x192)+E(f16(x193,x191),f16(x193,x192))
% 0.53/0.63 [20]~E(x201,x202)+E(f12(x201),f12(x202))
% 0.53/0.63 [21]~E(x211,x212)+E(f19(x211,x213),f19(x212,x213))
% 0.53/0.63 [22]~E(x221,x222)+E(f19(x223,x221),f19(x223,x222))
% 0.53/0.63 [23]~E(x231,x232)+E(f7(x231),f7(x232))
% 0.53/0.63 [24]~E(x241,x242)+E(f8(x241),f8(x242))
% 0.53/0.63 [25]~E(x251,x252)+E(f14(x251,x253),f14(x252,x253))
% 0.53/0.63 [26]~E(x261,x262)+E(f14(x263,x261),f14(x263,x262))
% 0.53/0.63 [27]~E(x271,x272)+E(f15(x271,x273),f15(x272,x273))
% 0.53/0.63 [28]~E(x281,x282)+E(f15(x283,x281),f15(x283,x282))
% 0.53/0.63 [29]P1(x292,x293)+~E(x291,x292)+~P1(x291,x293)
% 0.53/0.63 [30]P1(x303,x302)+~E(x301,x302)+~P1(x303,x301)
% 0.53/0.63 [31]~P7(x311)+P7(x312)+~E(x311,x312)
% 0.53/0.63 [32]P6(x322,x323)+~E(x321,x322)+~P6(x321,x323)
% 0.53/0.63 [33]P6(x333,x332)+~E(x331,x332)+~P6(x333,x331)
% 0.53/0.63 [34]~P2(x341)+P2(x342)+~E(x341,x342)
% 0.53/0.63 [35]~P3(x351)+P3(x352)+~E(x351,x352)
% 0.53/0.63 [36]P5(x362,x363)+~E(x361,x362)+~P5(x361,x363)
% 0.53/0.63 [37]P5(x373,x372)+~E(x371,x372)+~P5(x373,x371)
% 0.53/0.63 [38]P9(x382,x383)+~E(x381,x382)+~P9(x381,x383)
% 0.53/0.63 [39]P9(x393,x392)+~E(x391,x392)+~P9(x393,x391)
% 0.53/0.63 [40]P8(x402,x403,x404)+~E(x401,x402)+~P8(x401,x403,x404)
% 0.53/0.63 [41]P8(x413,x412,x414)+~E(x411,x412)+~P8(x413,x411,x414)
% 0.53/0.63 [42]P8(x423,x424,x422)+~E(x421,x422)+~P8(x423,x424,x421)
% 0.53/0.63 [43]P4(x432,x433)+~E(x431,x432)+~P4(x431,x433)
% 0.53/0.63 [44]P4(x443,x442)+~E(x441,x442)+~P4(x443,x441)
% 0.53/0.63
% 0.53/0.63 %-------------------------------------------
% 0.53/0.63 cnf(98,plain,
% 0.53/0.63 (P4(f6(x982,f5(x981,x983)),x981)),
% 0.53/0.63 inference(equality_inference,[],[71])).
% 0.53/0.63 cnf(112,plain,
% 0.53/0.63 (P1(x1121,x1121)),
% 0.53/0.63 inference(rename_variables,[],[47])).
% 0.53/0.63 cnf(116,plain,
% 0.53/0.63 (P6(x1161,x1161)),
% 0.53/0.63 inference(rename_variables,[],[48])).
% 0.53/0.63 cnf(121,plain,
% 0.53/0.63 (P4(f6(x1211,f5(x1212,x1213)),x1212)),
% 0.53/0.63 inference(rename_variables,[],[98])).
% 0.53/0.63 cnf(124,plain,
% 0.53/0.63 ($false),
% 0.53/0.63 inference(scs_inference,[],[55,56,98,121,45,61,54,50,47,112,48,116,59,58,94,2,65,97,31,3,29,30,32,33,34,43,44,90]),
% 0.53/0.63 ['proof']).
% 0.53/0.63 % SZS output end Proof
% 0.53/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------