TSTP Solution File: NUN089+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 12:45:30 EDT 2023
% Result : Theorem 0.17s 0.67s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.31 % Computer : n006.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Sun Aug 27 08:57:52 EDT 2023
% 0.13/0.31 % CPUTime :
% 0.17/0.54 start to proof:theBenchmark
% 0.17/0.66 %-------------------------------------------
% 0.17/0.66 % File :CSE---1.6
% 0.17/0.66 % Problem :theBenchmark
% 0.17/0.66 % Transform :cnf
% 0.17/0.66 % Format :tptp:raw
% 0.17/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.17/0.66
% 0.17/0.66 % Result :Theorem 0.060000s
% 0.17/0.66 % Output :CNFRefutation 0.060000s
% 0.17/0.66 %-------------------------------------------
% 0.17/0.66 %------------------------------------------------------------------------------
% 0.17/0.66 % File : NUN089+1 : TPTP v8.1.2. Released v7.3.0.
% 0.17/0.66 % Domain : Number Theory
% 0.17/0.66 % Problem : Robinson arithmetic: 0 != 2
% 0.17/0.66 % Version : Especial.
% 0.17/0.66 % English :
% 0.17/0.66
% 0.17/0.66 % Refs : [BBJ03] Boolos et al. (2003), Computability and Logic
% 0.17/0.66 % : [Smi07] Smith (2007), An Introduction to Goedel's Theorems
% 0.17/0.66 % : [Lam18] Lampert (2018), Email to Geoff Sutcliffe
% 0.17/0.66 % Source : [Lam18]
% 0.17/0.66 % Names : zerounidtwo [Lam18]
% 0.17/0.66
% 0.17/0.66 % Status : Theorem
% 0.17/0.66 % Rating : 0.00 v7.3.0
% 0.17/0.66 % Syntax : Number of formulae : 19 ( 1 unt; 0 def)
% 0.17/0.66 % Number of atoms : 80 ( 0 equ)
% 0.17/0.66 % Maximal formula atoms : 7 ( 4 avg)
% 0.17/0.66 % Number of connectives : 100 ( 39 ~; 30 |; 31 &)
% 0.17/0.66 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.66 % Maximal formula depth : 13 ( 8 avg)
% 0.17/0.66 % Maximal term depth : 1 ( 1 avg)
% 0.17/0.66 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.17/0.66 % Number of functors : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.67 % Number of variables : 71 ( 51 !; 20 ?)
% 0.17/0.67 % SPC : FOF_THM_RFO_NEQ
% 0.17/0.67
% 0.17/0.67 % Comments : Translated to FOL without equality.
% 0.17/0.67 %------------------------------------------------------------------------------
% 0.17/0.67 include('Axioms/NUM009+0.ax').
% 0.17/0.67 %------------------------------------------------------------------------------
% 0.17/0.67 fof(zerounidtwo,conjecture,
% 0.17/0.67 ! [Y1] :
% 0.17/0.67 ( ! [Y2] :
% 0.17/0.67 ( ! [Y3] :
% 0.17/0.67 ( ~ r1(Y3)
% 0.17/0.67 | ~ r2(Y3,Y2) )
% 0.17/0.67 | ~ r2(Y2,Y1) )
% 0.17/0.67 | ! [Y4] :
% 0.17/0.67 ( ~ id(Y4,Y1)
% 0.17/0.67 | ~ r1(Y4) ) ) ).
% 0.17/0.67
% 0.17/0.67 %------------------------------------------------------------------------------
% 0.17/0.67 %-------------------------------------------
% 0.17/0.67 % Proof found
% 0.17/0.67 % SZS status Theorem for theBenchmark
% 0.17/0.67 % SZS output start Proof
% 0.17/0.67 %ClaNum:47(EqnAxiom:0)
% 0.17/0.67 %VarNum:201(SingletonVarNum:98)
% 0.17/0.67 %MaxLitNum:5
% 0.17/0.67 %MaxfuncDepth:1
% 0.17/0.67 %SharedTerms:10
% 0.17/0.67 %goalClause: 1 2 6 7 8
% 0.17/0.67 %singleGoalClaCount:5
% 0.17/0.67 [1]P1(a1)
% 0.17/0.67 [2]P1(a16)
% 0.17/0.67 [6]P2(a16,a10)
% 0.17/0.67 [7]P3(a15,a10)
% 0.17/0.67 [8]P3(a1,a15)
% 0.17/0.67 [9]P2(x91,x91)
% 0.17/0.67 [3]P1(f2(x31))
% 0.17/0.67 [4]P1(f7(x41))
% 0.17/0.67 [5]P1(f9(x51))
% 0.17/0.67 [10]P2(f3(x101),x101)
% 0.17/0.67 [11]P2(f8(x111),f9(x111))
% 0.17/0.67 [17]P4(x171,f2(x171),f3(x171))
% 0.17/0.67 [18]P5(x181,f7(x181),f8(x181))
% 0.17/0.67 [12]P3(x121,f17(x122,x121))
% 0.17/0.67 [13]P3(x131,f4(x132,x131))
% 0.17/0.67 [14]P2(f18(x141,x142),f19(x141,x142))
% 0.17/0.67 [15]P2(f5(x151,x152),f23(x151,x152))
% 0.17/0.67 [16]P3(f24(x161,x162),f19(x161,x162))
% 0.17/0.67 [19]P4(x191,x192,f24(x191,x192))
% 0.17/0.67 [20]P5(x201,x202,f6(x201,x202))
% 0.17/0.67 [21]P4(x211,f17(x211,x212),f18(x211,x212))
% 0.17/0.67 [22]P5(x221,f4(x221,x222),f5(x221,x222))
% 0.17/0.67 [23]P4(f6(x231,x232),x231,f23(x231,x232))
% 0.17/0.67 [24]~P1(x241)+P2(x241,a11)
% 0.17/0.67 [25]P1(x251)+~P2(x251,a11)
% 0.17/0.67 [26]P2(x261,f14(x261))+P1(f12(x261))
% 0.17/0.67 [30]P3(f13(x301),f14(x301))+P1(f12(x301))
% 0.17/0.67 [31]P2(x311,f14(x311))+P2(x311,f12(x311))
% 0.17/0.67 [34]P3(f13(x341),f14(x341))+P2(x341,f12(x341))
% 0.17/0.67 [29]~P2(x292,x291)+P2(x291,x292)
% 0.17/0.67 [32]~P3(x322,x321)+P2(x321,f20(x322))
% 0.17/0.67 [33]P3(x331,x332)+~P2(x332,f20(x331))
% 0.17/0.67 [40]P4(x401,x402,x403)+~P2(x403,f21(x401,x402))
% 0.17/0.67 [41]P5(x411,x412,x413)+~P2(x413,f22(x411,x412))
% 0.17/0.67 [42]~P4(x422,x423,x421)+P2(x421,f21(x422,x423))
% 0.17/0.67 [43]~P5(x432,x433,x431)+P2(x431,f22(x432,x433))
% 0.17/0.67 [27]~P2(x272,x271)+P1(x271)+~P1(x272)
% 0.17/0.67 [28]~P2(x281,x282)+P1(x281)+~P1(x282)
% 0.17/0.67 [35]~P1(x351)+~P2(x351,x352)+~P3(x353,x352)
% 0.17/0.67 [36]~P2(x361,x363)+P2(x361,x362)+~P2(x363,x362)
% 0.17/0.67 [37]~P3(x372,x374)+~P3(x371,x373)+P2(x371,x372)+~P2(x373,x374)
% 0.17/0.67 [38]~P3(x384,x383)+P3(x381,x382)+~P2(x383,x382)+~P2(x384,x381)
% 0.17/0.67 [39]~P3(x394,x393)+P3(x391,x392)+~P2(x392,x393)+~P2(x391,x394)
% 0.17/0.67 [44]~P4(x446,x445,x444)+P4(x441,x442,x443)+~P2(x444,x443)+~P2(x445,x442)+~P2(x446,x441)
% 0.17/0.67 [45]~P4(x456,x455,x454)+P4(x451,x452,x453)+~P2(x453,x454)+~P2(x452,x455)+~P2(x451,x456)
% 0.17/0.67 [46]~P5(x466,x465,x464)+P5(x461,x462,x463)+~P2(x464,x463)+~P2(x465,x462)+~P2(x466,x461)
% 0.17/0.67 [47]~P5(x476,x475,x474)+P5(x471,x472,x473)+~P2(x473,x474)+~P2(x472,x475)+~P2(x471,x476)
% 0.17/0.67 %EqnAxiom
% 0.17/0.67
% 0.17/0.67 %-------------------------------------------
% 0.17/0.67 cnf(48,plain,
% 0.17/0.67 (P1(a11)),
% 0.17/0.67 inference(scs_inference,[],[9,25])).
% 0.17/0.67 cnf(49,plain,
% 0.17/0.67 (P2(x491,x491)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(50,plain,
% 0.17/0.67 (P3(x501,f20(x501))),
% 0.17/0.67 inference(scs_inference,[],[9,49,25,33])).
% 0.17/0.67 cnf(51,plain,
% 0.17/0.67 (P2(x511,x511)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(54,plain,
% 0.17/0.67 (P2(x541,x541)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(57,plain,
% 0.17/0.67 (P2(x571,x571)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(59,plain,
% 0.17/0.67 (~P3(x591,a1)),
% 0.17/0.67 inference(scs_inference,[],[1,9,49,51,54,57,25,33,41,40,35])).
% 0.17/0.67 cnf(62,plain,
% 0.17/0.67 (P2(f3(x621),x621)),
% 0.17/0.67 inference(rename_variables,[],[10])).
% 0.17/0.67 cnf(63,plain,
% 0.17/0.67 (P2(x631,x631)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(66,plain,
% 0.17/0.67 (P2(f3(x661),x661)),
% 0.17/0.67 inference(rename_variables,[],[10])).
% 0.17/0.67 cnf(68,plain,
% 0.17/0.67 (P2(x681,x681)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(69,plain,
% 0.17/0.67 (P5(x691,x692,f6(x691,x692))),
% 0.17/0.67 inference(rename_variables,[],[20])).
% 0.17/0.67 cnf(72,plain,
% 0.17/0.67 (P2(f3(x721),x721)),
% 0.17/0.67 inference(rename_variables,[],[10])).
% 0.17/0.67 cnf(74,plain,
% 0.17/0.67 (P2(x741,x741)),
% 0.17/0.67 inference(rename_variables,[],[9])).
% 0.17/0.67 cnf(75,plain,
% 0.17/0.67 (P4(x751,x752,f24(x751,x752))),
% 0.17/0.67 inference(rename_variables,[],[19])).
% 0.17/0.67 cnf(81,plain,
% 0.17/0.68 (P2(a10,f20(a15))),
% 0.17/0.68 inference(scs_inference,[],[1,9,49,51,54,57,63,68,6,7,8,19,20,10,62,66,25,33,41,40,35,39,47,45,29,24,32])).
% 0.17/0.68 cnf(87,plain,
% 0.17/0.68 (~P2(a10,a1)),
% 0.17/0.68 inference(scs_inference,[],[1,9,49,51,54,57,63,68,74,6,7,8,19,75,20,69,10,62,66,25,33,41,40,35,39,47,45,29,24,32,43,42,38])).
% 0.17/0.68 cnf(88,plain,
% 0.17/0.68 (P2(x881,x881)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(94,plain,
% 0.17/0.68 (P2(x941,x941)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(103,plain,
% 0.17/0.68 (P1(a10)),
% 0.17/0.68 inference(scs_inference,[],[1,9,49,51,54,57,63,68,74,88,94,2,6,7,8,19,75,20,69,10,62,66,72,25,33,41,40,35,39,47,45,29,24,32,43,42,38,37,46,44,28,27])).
% 0.17/0.68 cnf(107,plain,
% 0.17/0.68 (~P2(a1,f20(x1071))),
% 0.17/0.68 inference(scs_inference,[],[59,87,29,33])).
% 0.17/0.68 cnf(113,plain,
% 0.17/0.68 (P3(x1131,f17(x1132,x1131))),
% 0.17/0.68 inference(rename_variables,[],[12])).
% 0.17/0.68 cnf(118,plain,
% 0.17/0.68 (P2(x1181,x1181)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(122,plain,
% 0.17/0.68 (P2(x1221,x1221)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(126,plain,
% 0.17/0.68 (P2(f8(x1261),f9(x1261))),
% 0.17/0.68 inference(rename_variables,[],[11])).
% 0.17/0.68 cnf(129,plain,
% 0.17/0.68 (~P2(f17(x1291,a10),f4(x1292,a1))),
% 0.17/0.68 inference(scs_inference,[],[12,113,13,5,18,11,9,118,122,19,20,6,59,87,29,33,28,39,47,45,46,37])).
% 0.17/0.68 cnf(133,plain,
% 0.17/0.68 (~P3(x1331,f9(a16))),
% 0.17/0.68 inference(scs_inference,[],[12,113,13,5,18,11,126,9,118,122,19,20,6,59,87,29,33,28,39,47,45,46,37,35])).
% 0.17/0.68 cnf(146,plain,
% 0.17/0.68 (P2(f3(x1461),x1461)),
% 0.17/0.68 inference(rename_variables,[],[10])).
% 0.17/0.68 cnf(150,plain,
% 0.17/0.68 (P2(x1501,x1501)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(151,plain,
% 0.17/0.68 (P2(f3(x1511),x1511)),
% 0.17/0.68 inference(rename_variables,[],[10])).
% 0.17/0.68 cnf(162,plain,
% 0.17/0.68 (~P1(f18(x1621,x1622))),
% 0.17/0.68 inference(scs_inference,[],[21,14,16,8,12,9,150,20,10,146,6,81,107,103,33,45,46,37,27,29,35])).
% 0.17/0.68 cnf(163,plain,
% 0.17/0.68 (P3(f24(x1631,x1632),f19(x1631,x1632))),
% 0.17/0.68 inference(rename_variables,[],[16])).
% 0.17/0.68 cnf(166,plain,
% 0.17/0.68 (~P3(x1661,f9(a16))),
% 0.17/0.68 inference(rename_variables,[],[133])).
% 0.17/0.68 cnf(167,plain,
% 0.17/0.68 (P2(f3(x1671),x1671)),
% 0.17/0.68 inference(rename_variables,[],[10])).
% 0.17/0.68 cnf(174,plain,
% 0.17/0.68 (P2(f18(x1741,x1742),f19(x1741,x1742))),
% 0.17/0.68 inference(rename_variables,[],[14])).
% 0.17/0.68 cnf(178,plain,
% 0.17/0.68 (~P1(f19(x1781,x1782))),
% 0.17/0.68 inference(scs_inference,[],[21,14,174,16,163,8,12,9,150,20,10,146,151,167,6,133,166,81,107,103,33,45,46,37,27,29,35,39,38,36,25,28])).
% 0.17/0.68 cnf(185,plain,
% 0.17/0.68 (P2(f3(x1851),x1851)),
% 0.17/0.68 inference(rename_variables,[],[10])).
% 0.17/0.68 cnf(189,plain,
% 0.17/0.68 (P2(x1891,x1891)),
% 0.17/0.68 inference(rename_variables,[],[9])).
% 0.17/0.68 cnf(196,plain,
% 0.17/0.68 (~P3(x1961,a16)),
% 0.17/0.68 inference(scs_inference,[],[2,15,19,9,189,10,185,129,25,45,28,29,35])).
% 0.17/0.68 cnf(222,plain,
% 0.17/0.68 (~P3(x2221,a16)),
% 0.17/0.68 inference(rename_variables,[],[196])).
% 0.17/0.68 cnf(232,plain,
% 0.17/0.68 (~P3(x2321,a16)),
% 0.17/0.68 inference(rename_variables,[],[196])).
% 0.17/0.68 cnf(239,plain,
% 0.17/0.68 (P2(f3(x2391),x2391)),
% 0.17/0.68 inference(rename_variables,[],[10])).
% 0.17/0.68 cnf(250,plain,
% 0.17/0.68 ($false),
% 0.17/0.68 inference(scs_inference,[],[6,50,48,3,22,23,16,10,239,162,178,196,222,232,81,28,39,25,29,35,38,43,42,41,32,40,24,33,36]),
% 0.17/0.68 ['proof']).
% 0.17/0.68 % SZS output end Proof
% 0.17/0.68 % Total time :0.060000s
%------------------------------------------------------------------------------