TSTP Solution File: GEO268+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : Wed Aug 30 22:44:08 EDT 2023
% Result : Theorem 4.37s 4.56s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 22:51:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 4.37/4.56 %-------------------------------------------
% 4.37/4.56 % File :CSE---1.6
% 4.37/4.56 % Problem :theBenchmark
% 4.37/4.56 % Transform :cnf
% 4.37/4.56 % Format :tptp:raw
% 4.37/4.56 % Command :java -jar mcs_scs.jar %d %s
% 4.37/4.56
% 4.37/4.56 % Result :Theorem 3.950000s
% 4.37/4.56 % Output :CNFRefutation 3.950000s
% 4.37/4.56 %-------------------------------------------
% 4.37/4.56 %------------------------------------------------------------------------------
% 4.37/4.56 % File : GEO268+3 : TPTP v8.1.2. Released v4.0.0.
% 4.37/4.56 % Domain : Geometry (Constructive)
% 4.37/4.56 % Problem : Equivalence of unequally directed opposite and reversed lines
% 4.37/4.56 % Version : [vPl98] axioms.
% 4.37/4.56 % English :
% 4.37/4.56
% 4.37/4.56 % Refs : [vPl98] von Plato (1998), A Constructive Theory of Ordered Aff
% 4.37/4.56 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 4.37/4.56 % : [Rat07] Raths (2007), Email to Geoff Sutcliffe
% 4.37/4.56 % Source : [Rat07]
% 4.37/4.56 % Names : Theorem 3.12 [vPl98]
% 4.37/4.56
% 4.37/4.56 % Status : Theorem
% 4.37/4.56 % Rating : 0.00 v7.5.0, 0.05 v7.4.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.2.0, 0.09 v6.1.0, 0.12 v6.0.0, 0.25 v5.5.0, 0.08 v5.4.0, 0.09 v5.3.0, 0.17 v5.2.0, 0.07 v5.0.0, 0.00 v4.0.1, 0.05 v4.0.0
% 4.37/4.56 % Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% 4.37/4.56 % Number of atoms : 111 ( 0 equ)
% 4.37/4.56 % Maximal formula atoms : 10 ( 3 avg)
% 4.37/4.56 % Number of connectives : 86 ( 12 ~; 22 |; 24 &)
% 4.37/4.56 % ( 11 <=>; 17 =>; 0 <=; 0 <~>)
% 4.37/4.56 % Maximal formula depth : 13 ( 5 avg)
% 4.37/4.56 % Maximal term depth : 3 ( 1 avg)
% 4.37/4.56 % Number of predicates : 18 ( 18 usr; 0 prp; 1-4 aty)
% 4.37/4.56 % Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% 4.37/4.56 % Number of variables : 83 ( 83 !; 0 ?)
% 4.37/4.56 % SPC : FOF_THM_RFO_NEQ
% 4.37/4.56
% 4.37/4.56 % Comments :
% 4.37/4.56 %------------------------------------------------------------------------------
% 4.37/4.56 include('Axioms/GEO009+0.ax').
% 4.37/4.56 %------------------------------------------------------------------------------
% 4.37/4.56 fof(con,conjecture,
% 4.37/4.56 ! [L,M] :
% 4.37/4.56 ( unequally_directed_lines(L,M)
% 4.37/4.56 <=> unequally_directed_opposite_lines(L,reverse_line(M)) ) ).
% 4.37/4.56
% 4.37/4.56 %------------------------------------------------------------------------------
% 4.37/4.56 %-------------------------------------------
% 4.37/4.56 % Proof found
% 4.37/4.56 % SZS status Theorem for theBenchmark
% 4.37/4.56 % SZS output start Proof
% 4.37/4.57 %ClaNum:68(EqnAxiom:0)
% 4.37/4.57 %VarNum:311(SingletonVarNum:129)
% 4.37/4.57 %MaxLitNum:10
% 4.37/4.57 %MaxfuncDepth:2
% 4.37/4.57 %SharedTerms:7
% 4.37/4.57 %goalClause: 12 20
% 4.37/4.57 [1]P1(x11,x11)
% 4.37/4.57 [5]~P2(x51,x51)
% 4.37/4.57 [6]~P3(x61,x61)
% 4.37/4.57 [9]~P3(x91,f6(x91))
% 4.37/4.57 [3]~P9(x31,x32)
% 4.37/4.57 [4]~P12(x41,x42)
% 4.37/4.57 [2]P1(f1(x21,x22),x21)
% 4.37/4.57 [10]~P4(x101,f1(x102,x101))
% 4.37/4.57 [12]P14(a2,a3)+P18(a2,f6(a3))
% 4.37/4.57 [20]~P14(a2,a3)+~P18(a2,f6(a3))
% 4.37/4.57 [11]~P13(x111)+P13(f6(x111))
% 4.37/4.57 [13]P10(x131,x132)+P18(x131,x132)
% 4.37/4.57 [14]P1(x141,x142)+P14(x141,x142)
% 4.37/4.57 [16]~P5(x161,x162)+P18(x161,x162)
% 4.37/4.57 [17]~P5(x171,x172)+P14(x171,x172)
% 4.37/4.57 [18]~P15(x181,x182)+P4(x181,x182)
% 4.37/4.57 [25]~P10(x251,x252)+~P18(x251,x252)
% 4.37/4.57 [26]~P1(x261,x262)+~P14(x261,x262)
% 4.37/4.57 [15]P14(x151,x152)+P14(x151,f6(x152))
% 4.37/4.57 [21]~P18(x211,x212)+P14(x211,f6(x212))
% 4.37/4.57 [22]~P15(x221,x222)+P9(x221,f6(x222))
% 4.37/4.57 [23]~P17(x231,x232)+P12(x231,f6(x232))
% 4.37/4.57 [27]P18(x271,x272)+~P14(x271,f6(x272))
% 4.37/4.57 [40]~P2(x401,x402)+~P4(x402,f4(x401,x402))
% 4.37/4.57 [41]~P2(x411,x412)+~P4(x411,f4(x411,x412))
% 4.37/4.57 [59]~P2(x591,x592)+P1(f4(x591,x592),f6(f4(x592,x591)))
% 4.37/4.57 [50]P2(x501,x502)+~P6(x503,x501,x502)
% 4.37/4.57 [51]P11(x511,x512)+~P6(x512,x513,x511)
% 4.37/4.57 [52]P11(x521,x522)+~P6(x522,x521,x523)
% 4.37/4.57 [60]~P6(x601,x602,x603)+P1(x601,f4(x602,x603))
% 4.37/4.57 [32]P9(x321,x322)+~P4(x321,x322)+P15(x321,x322)
% 4.37/4.57 [36]~P18(x361,x362)+~P14(x361,x362)+P5(x361,x362)
% 4.37/4.57 [24]~P16(x242)+~P13(x241)+P13(f1(x241,x242))
% 4.37/4.57 [57]~P14(x571,x572)+~P14(x571,f6(x572))+~P4(f5(x571,x572),x572)
% 4.37/4.57 [58]~P14(x581,x582)+~P14(x581,f6(x582))+~P4(f5(x581,x582),x581)
% 4.37/4.57 [30]~P14(x303,x301)+P14(x301,x302)+P14(x303,x302)
% 4.37/4.57 [34]~P2(x343,x341)+P2(x341,x342)+P2(x343,x342)
% 4.37/4.57 [35]~P3(x353,x351)+P3(x351,x352)+P3(x353,x352)
% 4.37/4.57 [53]~P8(x532,x533,x531)+P15(x531,x532)+P15(x533,x532)
% 4.37/4.57 [54]P9(x541,x542)+P15(x541,x542)+~P8(x542,x543,x541)
% 4.37/4.57 [55]P9(x551,x552)+P15(x551,x552)+~P8(x552,x551,x553)
% 4.37/4.57 [56]~P8(x562,x561,x563)+P9(x561,x562)+P9(x563,x562)
% 4.37/4.57 [63]~P6(x631,x633,x632)+~P6(x631,x634,x633)+P7(x631,x632,x633,x634)
% 4.37/4.57 [64]~P6(x641,x643,x644)+~P6(x641,x642,x643)+P7(x641,x642,x643,x644)
% 4.37/4.57 [65]~P7(x651,x652,x653,x654)+P6(x651,x652,x653)+P6(x651,x654,x653)
% 4.37/4.57 [66]P6(x661,x663,x662)+P6(x661,x662,x663)+~P7(x661,x664,x662,x663)
% 4.37/4.57 [67]P6(x671,x673,x672)+P6(x671,x672,x673)+~P7(x671,x672,x673,x674)
% 4.37/4.57 [68]~P7(x681,x684,x682,x683)+P6(x681,x682,x683)+P6(x681,x682,x684)
% 4.37/4.57 [37]~P16(x372)+~P16(x371)+~P2(x371,x372)+P13(f4(x371,x372))
% 4.37/4.57 [44]~P14(x441,x442)+P12(x441,x442)+P12(x441,f6(x442))+~P14(x441,f6(x442))
% 4.37/4.57 [42]~P14(x421,x423)+P14(x421,x422)+~P14(x421,f6(x423))+P14(x423,f6(x422))
% 4.37/4.57 [43]~P14(x433,x431)+P14(x431,x432)+~P14(x433,f6(x431))+P14(x433,f6(x432))
% 4.37/4.57 [46]~P13(x462)+~P13(x461)+~P14(x461,x462)+~P14(x461,f6(x462))+P16(f5(x461,x462))
% 4.37/4.57 [62]~P2(x622,x623)+~P11(x623,x621)+~P11(x622,x621)+P6(x621,x622,x623)+~P1(x621,f4(x622,x623))
% 4.37/4.57 [61]P9(x614,x613)+~P2(x614,x611)+~P3(x613,x612)+P9(x611,x612)+P9(x611,x613)+P9(x614,x612)+P9(x611,f6(x612))+P9(x611,f6(x613))+P9(x614,f6(x612))+P9(x614,f6(x613))
% 4.37/4.57 %EqnAxiom
% 4.37/4.57
% 4.37/4.57 %-------------------------------------------
% 4.37/4.57 cnf(72,plain,
% 4.37/4.57 (~P9(x721,x722)),
% 4.37/4.57 inference(rename_variables,[],[3])).
% 4.37/4.57 cnf(80,plain,
% 4.37/4.57 (~P14(x801,x801)),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,10,50,18,22,68,67,66,26])).
% 4.37/4.57 cnf(82,plain,
% 4.37/4.57 (P14(x821,f6(x821))),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,10,50,18,22,68,67,66,26,15])).
% 4.37/4.57 cnf(86,plain,
% 4.37/4.57 (P14(f6(x861),x861)),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,72,10,50,18,22,68,67,66,26,15,32,30])).
% 4.37/4.57 cnf(88,plain,
% 4.37/4.57 (~P14(f6(f6(x881)),x881)+P12(f6(f6(x881)),f6(x881))),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,72,4,10,50,18,22,68,67,66,26,15,32,30,44])).
% 4.37/4.57 cnf(93,plain,
% 4.37/4.57 (P1(f6(f6(x931)),x931)+P12(f6(f6(x931)),f6(x931))),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,72,4,10,50,18,22,68,67,66,26,15,32,30,44,17,14])).
% 4.37/4.57 cnf(95,plain,
% 4.37/4.57 (P18(f6(x951),f6(x951))+P12(f6(f6(x951)),f6(x951))),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,72,4,10,50,18,22,68,67,66,26,15,32,30,44,17,14,27])).
% 4.37/4.57 cnf(97,plain,
% 4.37/4.57 (~P18(f6(x971),x971)+P12(f6(f6(x971)),f6(x971))),
% 4.37/4.57 inference(scs_inference,[],[1,5,3,72,4,10,50,18,22,68,67,66,26,15,32,30,44,17,14,27,21])).
% 4.37/4.57 cnf(99,plain,
% 4.37/4.57 (~P3(f6(x991),x991)+P12(f6(f6(x992)),f6(x992))),
% 4.37/4.57 inference(scs_inference,[],[1,5,6,3,72,4,9,10,50,18,22,68,67,66,26,15,32,30,44,17,14,27,21,35])).
% 4.37/4.57 cnf(104,plain,
% 4.37/4.57 (~P12(x1041,x1042)),
% 4.37/4.57 inference(rename_variables,[],[4])).
% 4.37/4.57 cnf(106,plain,
% 4.37/4.57 (~P12(x1061,x1062)),
% 4.37/4.57 inference(rename_variables,[],[4])).
% 4.37/4.57 cnf(108,plain,
% 4.37/4.57 (~P12(x1081,x1082)),
% 4.37/4.57 inference(rename_variables,[],[4])).
% 4.37/4.57 cnf(110,plain,
% 4.37/4.57 (~P12(x1101,x1102)),
% 4.37/4.57 inference(rename_variables,[],[4])).
% 4.37/4.57 cnf(111,plain,
% 4.37/4.57 (~P14(f6(f6(x1111)),x1111)),
% 4.37/4.57 inference(scs_inference,[],[4,104,106,108,110,82,26,99,97,95,93,88])).
% 4.37/4.57 cnf(125,plain,
% 4.37/4.57 (~P14(f1(x1251,x1252),x1251)),
% 4.37/4.57 inference(scs_inference,[],[2,26])).
% 4.37/4.57 cnf(127,plain,
% 4.37/4.57 (P18(f6(f6(x1271)),x1271)),
% 4.37/4.57 inference(scs_inference,[],[2,86,26,27])).
% 4.37/4.57 cnf(130,plain,
% 4.37/4.57 (P14(f6(f1(x1301,x1302)),x1301)),
% 4.37/4.57 inference(scs_inference,[],[2,86,82,26,27,30])).
% 4.37/4.57 cnf(131,plain,
% 4.37/4.57 (P14(x1311,f6(x1311))),
% 4.37/4.57 inference(rename_variables,[],[82])).
% 4.37/4.57 cnf(133,plain,
% 4.37/4.57 (P12(x1331,f6(x1331))+~P14(x1331,f6(f6(x1331)))),
% 4.37/4.57 inference(scs_inference,[],[2,4,86,82,131,26,27,30,44])).
% 4.37/4.57 cnf(143,plain,
% 4.37/4.57 (~P14(x1431,f6(f6(x1431)))),
% 4.37/4.57 inference(scs_inference,[],[4,125,130,15,26,133])).
% 4.37/4.57 cnf(145,plain,
% 4.37/4.57 (~P14(f1(x1451,x1452),f6(f6(x1451)))),
% 4.37/4.57 inference(scs_inference,[],[4,125,130,80,15,26,133,42])).
% 4.37/4.57 cnf(148,plain,
% 4.37/4.57 (~P14(f6(f6(x1481)),f1(x1481,x1482))),
% 4.37/4.57 inference(scs_inference,[],[4,111,125,130,80,15,26,133,42,30])).
% 4.37/4.57 cnf(151,plain,
% 4.37/4.57 (P14(f6(x1511),f1(x1511,x1512))),
% 4.37/4.57 inference(scs_inference,[],[148,86,30])).
% 4.37/4.57 cnf(154,plain,
% 4.37/4.57 (~P18(x1541,f6(x1541))),
% 4.37/4.57 inference(scs_inference,[],[143,148,86,30,21])).
% 4.37/4.57 cnf(162,plain,
% 4.37/4.57 (P14(f6(f1(x1621,x1622)),f6(f6(x1621)))),
% 4.37/4.57 inference(scs_inference,[],[145,86,30])).
% 4.37/4.57 cnf(173,plain,
% 4.37/4.57 (~P14(f6(x1731),f6(f1(x1731,x1732)))),
% 4.37/4.57 inference(scs_inference,[],[154,145,151,127,86,80,125,30,16,25,13,46,43])).
% 4.37/4.57 cnf(181,plain,
% 4.37/4.57 (~P14(x1811,f1(x1811,x1812))),
% 4.37/4.57 inference(scs_inference,[],[80,162,148,125,27,15,30])).
% 4.37/4.57 cnf(350,plain,
% 4.37/4.57 (~P14(f1(f1(x3501,x3502),x3503),x3501)),
% 4.37/4.57 inference(scs_inference,[],[125,181,30])).
% 4.37/4.57 cnf(353,plain,
% 4.37/4.57 (P14(f1(f1(x3531,x3532),x3533),f6(x3531))),
% 4.37/4.57 inference(scs_inference,[],[125,181,30,15])).
% 4.37/4.57 cnf(355,plain,
% 4.37/4.57 (P18(f1(f1(x3551,x3552),x3553),x3551)),
% 4.37/4.57 inference(scs_inference,[],[125,181,30,15,27])).
% 4.37/4.57 cnf(364,plain,
% 4.37/4.57 (~P14(f1(f1(x3641,x3642),x3643),f6(f6(x3641)))),
% 4.37/4.57 inference(scs_inference,[],[125,350,353,355,173,25,14,26,42])).
% 4.37/4.57 cnf(489,plain,
% 4.37/4.57 (~P14(x4891,f1(f1(x4891,x4892),x4893))),
% 4.37/4.57 inference(scs_inference,[],[181,125,30])).
% 4.37/4.57 cnf(553,plain,
% 4.37/4.57 (~P1(a2,a3)+P18(a2,f6(a3))),
% 4.37/4.57 inference(scs_inference,[],[12,26])).
% 4.37/4.57 cnf(554,plain,
% 4.37/4.57 (P14(a2,f6(f6(a3)))+~P1(a2,a3)),
% 4.37/4.57 inference(scs_inference,[],[553,21])).
% 4.37/4.57 cnf(555,plain,
% 4.37/4.57 (~P1(a2,f6(f6(a3)))+~P1(a2,a3)),
% 4.37/4.57 inference(scs_inference,[],[554,26])).
% 4.37/4.57 cnf(556,plain,
% 4.37/4.57 (P14(a2,a3)+~P1(a2,f6(f6(a3)))),
% 4.37/4.57 inference(scs_inference,[],[555,14])).
% 4.37/4.57 cnf(557,plain,
% 4.37/4.57 (~P1(a2,f6(f6(a3)))+~P18(a2,f6(a3))),
% 4.37/4.57 inference(scs_inference,[],[556,20])).
% 4.37/4.57 cnf(558,plain,
% 4.37/4.57 (P10(a2,f6(a3))+~P1(a2,f6(f6(a3)))),
% 4.37/4.57 inference(scs_inference,[],[557,13])).
% 4.37/4.57 cnf(559,plain,
% 4.37/4.57 (P14(a2,f6(f6(a3)))+P10(a2,f6(a3))),
% 4.37/4.57 inference(scs_inference,[],[558,14])).
% 4.37/4.57 cnf(560,plain,
% 4.37/4.57 (P14(f6(f6(a3)),f1(f1(a2,x5601),x5602))+P10(a2,f6(a3))),
% 4.37/4.57 inference(scs_inference,[],[489,559,30])).
% 4.37/4.58 cnf(561,plain,
% 4.37/4.58 (~P1(f6(f6(a3)),f1(f1(a2,x5611),x5612))+P10(a2,f6(a3))),
% 4.37/4.58 inference(scs_inference,[],[560,26])).
% 4.37/4.58 cnf(562,plain,
% 4.37/4.58 (~P18(a2,f6(a3))+~P1(f6(f6(a3)),f1(f1(a2,x5621),x5622))),
% 4.37/4.58 inference(scs_inference,[],[561,25])).
% 4.37/4.58 cnf(575,plain,
% 4.37/4.58 (~P14(f6(f6(x5751)),f1(f1(x5751,x5752),x5753))),
% 4.37/4.58 inference(scs_inference,[],[364,80,30])).
% 4.37/4.58 cnf(590,plain,
% 4.37/4.58 (P14(a2,f6(f6(a3)))+P18(a2,f6(a3))),
% 4.37/4.58 inference(scs_inference,[],[143,12,30])).
% 4.37/4.58 cnf(591,plain,
% 4.37/4.58 (~P1(a2,f6(f6(a3)))+P18(a2,f6(a3))),
% 4.37/4.58 inference(scs_inference,[],[590,26])).
% 4.37/4.58 cnf(592,plain,
% 4.37/4.58 (~P1(a2,f6(f6(a3)))+~P14(a2,a3)),
% 4.37/4.58 inference(scs_inference,[],[591,20])).
% 4.37/4.58 cnf(593,plain,
% 4.37/4.58 (P14(a2,f6(f6(a3)))+~P14(a2,a3)),
% 4.37/4.58 inference(scs_inference,[],[592,14])).
% 4.37/4.58 cnf(594,plain,
% 4.37/4.58 (P18(a2,f6(a3))+~P14(a2,a3)),
% 4.37/4.58 inference(scs_inference,[],[593,27])).
% 4.37/4.58 cnf(612,plain,
% 4.37/4.58 (P18(a2,f6(a3))),
% 4.37/4.58 inference(scs_inference,[],[12,594])).
% 4.37/4.58 cnf(613,plain,
% 4.37/4.58 (~P14(a2,a3)),
% 4.37/4.58 inference(scs_inference,[],[612,20])).
% 4.37/4.58 cnf(615,plain,
% 4.37/4.58 (~P1(f6(f6(a3)),f1(f1(a2,x6151),x6152))),
% 4.37/4.58 inference(scs_inference,[],[612,562])).
% 4.37/4.58 cnf(619,plain,
% 4.37/4.58 (P14(a2,f6(f6(a3)))),
% 4.37/4.58 inference(scs_inference,[],[612,25,21])).
% 4.37/4.58 cnf(660,plain,
% 4.37/4.58 ($false),
% 4.37/4.58 inference(scs_inference,[],[619,615,613,575,612,143,80,4,15,44,27,36,14,26,30,43,42]),
% 4.37/4.58 ['proof']).
% 4.37/4.58 % SZS output end Proof
% 4.37/4.58 % Total time :3.950000s
%------------------------------------------------------------------------------