TSTP Solution File: GEO196+3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO196+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 : n028.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 22:43:33 EDT 2023
% Result : Theorem 1.52s 1.61s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 22:44:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 1.52/1.60 %-------------------------------------------
% 1.52/1.60 % File :CSE---1.6
% 1.52/1.60 % Problem :theBenchmark
% 1.52/1.60 % Transform :cnf
% 1.52/1.60 % Format :tptp:raw
% 1.52/1.60 % Command :java -jar mcs_scs.jar %d %s
% 1.52/1.60
% 1.52/1.60 % Result :Theorem 1.000000s
% 1.52/1.60 % Output :CNFRefutation 1.000000s
% 1.52/1.60 %-------------------------------------------
% 1.52/1.61 %------------------------------------------------------------------------------
% 1.52/1.61 % File : GEO196+3 : TPTP v8.1.2. Released v4.0.0.
% 1.52/1.61 % Domain : Geometry (Constructive)
% 1.52/1.61 % Problem : Symmetry of incidence
% 1.52/1.61 % Version : [vPl95] axioms.
% 1.52/1.61 % English : If the lines X and Y are convergent, U and V are convergent,
% 1.52/1.61 % and the intersection point of X and Y is incident with U and V,
% 1.52/1.61 % then the intersection point of U and V is incident with X and Y.
% 1.52/1.61
% 1.52/1.61 % Refs : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
% 1.52/1.61 % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% 1.52/1.61 % : [Rat07] Raths (2007), Email to Geoff Sutcliffe
% 1.52/1.61 % Source : [Rat07]
% 1.52/1.61 % Names : Theorem 4.11 [vPl95]
% 1.52/1.61
% 1.52/1.61 % Status : Theorem
% 1.52/1.61 % Rating : 0.00 v7.4.0, 0.06 v7.3.0, 0.00 v6.1.0, 0.08 v6.0.0, 0.00 v5.5.0, 0.17 v5.4.0, 0.22 v5.2.0, 0.36 v5.0.0, 0.30 v4.1.0, 0.39 v4.0.1, 0.37 v4.0.0
% 1.52/1.61 % Syntax : Number of formulae : 36 ( 7 unt; 0 def)
% 1.52/1.61 % Number of atoms : 99 ( 0 equ)
% 1.52/1.61 % Maximal formula atoms : 6 ( 2 avg)
% 1.52/1.61 % Number of connectives : 91 ( 28 ~; 19 |; 17 &)
% 1.52/1.61 % ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% 1.52/1.61 % Maximal formula depth : 9 ( 6 avg)
% 1.52/1.61 % Maximal term depth : 2 ( 1 avg)
% 1.52/1.61 % Number of predicates : 12 ( 12 usr; 0 prp; 1-2 aty)
% 1.52/1.61 % Number of functors : 4 ( 4 usr; 0 con; 2-2 aty)
% 1.52/1.61 % Number of variables : 85 ( 85 !; 0 ?)
% 1.52/1.61 % SPC : FOF_THM_RFO_NEQ
% 1.52/1.61
% 1.52/1.61 % Comments :
% 1.52/1.61 %------------------------------------------------------------------------------
% 1.52/1.61 include('Axioms/GEO006+0.ax').
% 1.52/1.61 include('Axioms/GEO006+1.ax').
% 1.52/1.61 include('Axioms/GEO006+2.ax').
% 1.52/1.61 include('Axioms/GEO006+3.ax').
% 1.52/1.61 include('Axioms/GEO006+4.ax').
% 1.52/1.61 include('Axioms/GEO006+5.ax').
% 1.52/1.61 include('Axioms/GEO006+6.ax').
% 1.52/1.61 %------------------------------------------------------------------------------
% 1.52/1.61 fof(con,conjecture,
% 1.52/1.61 ! [X,Y,U,V] :
% 1.52/1.61 ( ( convergent_lines(X,Y)
% 1.52/1.61 & convergent_lines(U,V)
% 1.52/1.61 & incident_point_and_line(intersection_point(X,Y),U)
% 1.52/1.61 & incident_point_and_line(intersection_point(X,Y),V) )
% 1.52/1.61 => ( incident_point_and_line(intersection_point(U,V),X)
% 1.52/1.61 & incident_point_and_line(intersection_point(U,V),Y) ) ) ).
% 1.52/1.61
% 1.52/1.61 %------------------------------------------------------------------------------
% 1.52/1.61 %-------------------------------------------
% 1.52/1.61 % Proof found
% 1.52/1.61 % SZS status Theorem for theBenchmark
% 1.52/1.61 % SZS output start Proof
% 1.52/1.61 %ClaNum:51(EqnAxiom:0)
% 1.52/1.61 %VarNum:218(SingletonVarNum:98)
% 1.52/1.61 %MaxLitNum:6
% 1.52/1.61 %MaxfuncDepth:1
% 1.52/1.61 %SharedTerms:12
% 1.52/1.61 %goalClause: 1 2 3 4 50
% 1.52/1.61 %singleGoalClaCount:4
% 1.52/1.61 [1]P1(a1,a2)
% 1.52/1.61 [2]P1(a3,a4)
% 1.52/1.61 [3]P3(f5(a1,a2),a3)
% 1.52/1.61 [4]P3(f5(a1,a2),a4)
% 1.52/1.61 [5]~P4(x51,x51)
% 1.52/1.61 [6]~P5(x61,x61)
% 1.52/1.61 [7]~P1(x71,x71)
% 1.52/1.61 [8]~P2(x81,f6(x82,x81))
% 1.52/1.61 [9]~P2(x91,f7(x92,x91))
% 1.52/1.61 [10]~P1(f6(x101,x102),x101)
% 1.52/1.61 [11]~P8(f7(x111,x112),x111)
% 1.52/1.61 [50]~P3(f5(a3,a4),a2)+~P3(f5(a3,a4),a1)
% 1.52/1.61 [12]P6(x121,x122)+P4(x121,x122)
% 1.52/1.61 [13]P7(x131,x132)+P5(x131,x132)
% 1.52/1.61 [15]P8(x151,x152)+P1(x151,x152)
% 1.52/1.61 [16]P9(x161,x162)+P1(x161,x162)
% 1.52/1.61 [17]P3(x171,x172)+P2(x171,x172)
% 1.52/1.61 [18]P10(x181,x182)+P8(x181,x182)
% 1.52/1.61 [19]~P5(x191,x192)+P1(x191,x192)
% 1.52/1.61 [22]~P6(x221,x222)+~P4(x221,x222)
% 1.52/1.61 [23]~P7(x231,x232)+~P5(x231,x232)
% 1.52/1.61 [24]~P9(x241,x242)+~P1(x241,x242)
% 1.52/1.61 [25]~P3(x251,x252)+~P2(x251,x252)
% 1.52/1.61 [26]~P10(x261,x262)+~P8(x261,x262)
% 1.52/1.61 [46]~P4(x461,x462)+~P2(x462,f8(x461,x462))
% 1.52/1.61 [47]~P4(x471,x472)+~P2(x471,f8(x471,x472))
% 1.52/1.61 [48]~P1(x481,x482)+~P2(f5(x481,x482),x482)
% 1.52/1.61 [49]~P1(x491,x492)+~P2(f5(x491,x492),x491)
% 1.52/1.61 [20]~P12(x202)+~P11(x201)+P11(f6(x201,x202))
% 1.52/1.61 [21]~P12(x212)+~P11(x211)+P11(f7(x211,x212))
% 1.52/1.61 [27]~P4(x273,x271)+P4(x271,x272)+P4(x273,x272)
% 1.52/1.61 [28]~P2(x281,x283)+P4(x281,x282)+P2(x282,x283)
% 1.52/1.61 [29]~P5(x293,x291)+P5(x291,x292)+P5(x293,x292)
% 1.52/1.61 [30]~P1(x303,x301)+P5(x301,x302)+P1(x303,x302)
% 1.52/1.61 [31]~P2(x313,x311)+P5(x311,x312)+P2(x313,x312)
% 1.52/1.61 [32]~P1(x323,x321)+P1(x321,x322)+P1(x323,x322)
% 1.52/1.61 [33]~P1(x333,x332)+P8(x331,x332)+P8(x331,x333)
% 1.52/1.61 [35]~P11(x352)+~P11(x351)+~P1(x351,x352)+P12(f5(x351,x352))
% 1.52/1.61 [36]~P12(x362)+~P12(x361)+~P4(x361,x362)+P11(f8(x361,x362))
% 1.52/1.61 [38]~P1(x381,x383)+~P8(x381,x383)+P1(x381,x382)+P8(x383,x382)
% 1.52/1.61 [39]~P1(x392,x393)+~P8(x392,x393)+P1(x391,x392)+P1(x391,x393)
% 1.52/1.61 [40]~P1(x402,x403)+~P8(x402,x403)+P1(x401,x402)+P8(x401,x403)
% 1.52/1.61 [41]~P1(x413,x411)+~P8(x413,x411)+P1(x411,x412)+P8(x413,x412)
% 1.52/1.61 [42]~P1(x423,x422)+~P8(x423,x422)+P1(x421,x422)+P8(x421,x423)
% 1.52/1.61 [43]~P1(x431,x433)+~P8(x431,x433)+P8(x431,x432)+P8(x433,x432)
% 1.52/1.61 [45]P8(x453,x454)+~P5(x453,x452)+P2(x451,x452)+P2(x451,x453)+P8(x452,x454)
% 1.52/1.61 [51]P2(x514,x513)+~P4(x514,x511)+~P5(x513,x512)+P2(x511,x512)+P2(x511,x513)+P2(x514,x512)
% 1.52/1.61 %EqnAxiom
% 1.52/1.61
% 1.52/1.61 %-------------------------------------------
% 1.52/1.62 cnf(53,plain,
% 1.52/1.62 (~P5(f6(x531,x532),x531)),
% 1.52/1.62 inference(scs_inference,[],[1,10,24,19])).
% 1.52/1.62 cnf(60,plain,
% 1.52/1.62 (P8(x601,x601)),
% 1.52/1.62 inference(scs_inference,[],[1,7,8,10,11,24,19,18,17,16,15])).
% 1.52/1.62 cnf(66,plain,
% 1.52/1.62 (P8(f7(a1,x661),a2)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,8,10,11,24,19,18,17,16,15,13,12,33])).
% 1.52/1.62 cnf(67,plain,
% 1.52/1.62 (~P8(f7(x671,x672),x671)),
% 1.52/1.62 inference(rename_variables,[],[11])).
% 1.52/1.62 cnf(69,plain,
% 1.52/1.62 (P1(a2,a1)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,8,10,11,24,19,18,17,16,15,13,12,33,32])).
% 1.52/1.62 cnf(70,plain,
% 1.52/1.62 (~P1(x701,x701)),
% 1.52/1.62 inference(rename_variables,[],[7])).
% 1.52/1.62 cnf(72,plain,
% 1.52/1.62 (P5(a2,a1)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,8,10,11,24,19,18,17,16,15,13,12,33,32,30])).
% 1.52/1.62 cnf(73,plain,
% 1.52/1.62 (~P1(x731,x731)),
% 1.52/1.62 inference(rename_variables,[],[7])).
% 1.52/1.62 cnf(75,plain,
% 1.52/1.62 (P5(a1,a2)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,8,10,11,24,19,18,17,16,15,13,12,33,32,30,29])).
% 1.52/1.62 cnf(77,plain,
% 1.52/1.62 (~P2(f5(a1,a2),a4)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,4,8,10,11,24,19,18,17,16,15,13,12,33,32,30,29,25])).
% 1.52/1.62 cnf(79,plain,
% 1.52/1.62 (~P2(f5(a1,a2),a1)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,4,8,10,11,24,19,18,17,16,15,13,12,33,32,30,29,25,49])).
% 1.52/1.62 cnf(81,plain,
% 1.52/1.62 (~P2(f5(a1,a2),a2)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,4,8,10,11,24,19,18,17,16,15,13,12,33,32,30,29,25,49,48])).
% 1.52/1.62 cnf(91,plain,
% 1.52/1.62 (~P8(a1,a2)+P8(a2,x911)+P8(a1,x911)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,4,8,10,11,67,24,19,18,17,16,15,13,12,33,32,30,29,25,49,48,42,26,23,31,43])).
% 1.52/1.62 cnf(95,plain,
% 1.52/1.62 (P8(x951,a4)+~P8(a3,a4)+P1(x951,a3)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,73,2,4,8,10,11,67,24,19,18,17,16,15,13,12,33,32,30,29,25,49,48,42,26,23,31,43,41,40])).
% 1.52/1.62 cnf(99,plain,
% 1.52/1.62 (P8(a4,x991)+~P8(a3,a4)+P1(a3,x991)),
% 1.52/1.62 inference(scs_inference,[],[1,5,6,7,70,73,2,4,8,10,11,67,24,19,18,17,16,15,13,12,33,32,30,29,25,49,48,42,26,23,31,43,41,40,39,38])).
% 1.52/1.62 cnf(103,plain,
% 1.52/1.62 (P8(f7(a2,x1031),a1)),
% 1.52/1.62 inference(scs_inference,[],[1,11,33])).
% 1.52/1.62 cnf(104,plain,
% 1.52/1.62 (~P8(f7(x1041,x1042),x1041)),
% 1.52/1.62 inference(rename_variables,[],[11])).
% 1.52/1.62 cnf(106,plain,
% 1.52/1.62 (P1(f7(x1061,x1062),x1061)),
% 1.52/1.62 inference(scs_inference,[],[1,11,104,33,15])).
% 1.52/1.62 cnf(109,plain,
% 1.52/1.62 (~P8(f7(x1091,x1092),x1091)),
% 1.52/1.62 inference(rename_variables,[],[11])).
% 1.52/1.62 cnf(111,plain,
% 1.52/1.62 (~P5(x1111,f6(x1111,x1112))),
% 1.52/1.62 inference(scs_inference,[],[1,11,104,6,53,33,15,95,29])).
% 1.52/1.62 cnf(112,plain,
% 1.52/1.62 (~P5(f6(x1121,x1122),x1121)),
% 1.52/1.62 inference(rename_variables,[],[53])).
% 1.52/1.62 cnf(114,plain,
% 1.52/1.62 (~P1(f6(x1141,x1142),f6(x1141,x1143))),
% 1.52/1.62 inference(scs_inference,[],[1,10,11,104,6,53,112,33,15,95,29,30])).
% 1.52/1.62 cnf(120,plain,
% 1.52/1.62 (P8(f7(a1,x1201),a2)),
% 1.52/1.62 inference(rename_variables,[],[66])).
% 1.52/1.62 cnf(121,plain,
% 1.52/1.62 (~P8(f7(x1211,x1212),x1211)),
% 1.52/1.62 inference(rename_variables,[],[11])).
% 1.52/1.62 cnf(124,plain,
% 1.52/1.62 (~P1(f6(x1241,x1242),x1241)),
% 1.52/1.62 inference(rename_variables,[],[10])).
% 1.52/1.62 cnf(132,plain,
% 1.52/1.62 (~P5(f7(a4,x1321),a3)+P2(x1321,a3)+P1(f7(a4,x1322),a3)),
% 1.52/1.62 inference(scs_inference,[],[1,10,124,9,11,104,109,121,6,7,53,112,66,120,33,15,95,29,30,35,43,40,39,38,45])).
% 1.52/1.62 cnf(139,plain,
% 1.52/1.62 (P1(f7(f6(x1391,x1392),x1393),x1391)),
% 1.52/1.62 inference(scs_inference,[],[10,106,32])).
% 1.52/1.62 cnf(142,plain,
% 1.52/1.62 (P8(f6(x1421,x1422),x1421)),
% 1.52/1.62 inference(scs_inference,[],[10,106,32,15])).
% 1.52/1.62 cnf(144,plain,
% 1.52/1.62 (P5(a4,a3)),
% 1.52/1.62 inference(scs_inference,[],[2,10,7,106,32,15,30])).
% 1.52/1.62 cnf(150,plain,
% 1.52/1.62 (P5(a3,a4)),
% 1.52/1.62 inference(scs_inference,[],[2,10,6,7,106,32,15,30,95,29])).
% 1.52/1.62 cnf(153,plain,
% 1.52/1.62 (P1(a4,a3)),
% 1.52/1.62 inference(scs_inference,[],[2,10,6,7,106,32,15,30,95,29,19])).
% 1.52/1.62 cnf(166,plain,
% 1.52/1.62 (P1(x1661,f7(f6(x1661,x1662),x1663))),
% 1.52/1.62 inference(scs_inference,[],[7,139,32])).
% 1.52/1.62 cnf(167,plain,
% 1.52/1.62 (~P1(x1671,x1671)),
% 1.52/1.62 inference(rename_variables,[],[7])).
% 1.52/1.62 cnf(169,plain,
% 1.52/1.62 (~P5(f6(x1691,x1692),f6(x1691,x1693))),
% 1.52/1.62 inference(scs_inference,[],[7,139,114,32,19])).
% 1.52/1.62 cnf(172,plain,
% 1.52/1.62 (~P1(x1721,x1721)),
% 1.52/1.62 inference(rename_variables,[],[7])).
% 1.52/1.62 cnf(174,plain,
% 1.52/1.62 (~P1(x1741,f6(x1741,x1742))),
% 1.52/1.62 inference(scs_inference,[],[7,167,172,10,139,114,53,32,19,39,30])).
% 1.52/1.62 cnf(189,plain,
% 1.52/1.62 (~P5(f6(f6(x1891,x1892),x1893),x1891)),
% 1.52/1.62 inference(scs_inference,[],[53,111,29])).
% 1.52/1.62 cnf(190,plain,
% 1.52/1.62 (~P5(f6(x1901,x1902),x1901)),
% 1.52/1.62 inference(rename_variables,[],[53])).
% 1.52/1.62 cnf(192,plain,
% 1.52/1.62 (P5(f7(f6(x1921,x1922),x1923),x1921)),
% 1.52/1.62 inference(scs_inference,[],[53,7,166,111,29,30])).
% 1.52/1.62 cnf(193,plain,
% 1.52/1.62 (~P1(x1931,x1931)),
% 1.52/1.62 inference(rename_variables,[],[7])).
% 1.52/1.62 cnf(202,plain,
% 1.52/1.62 (~P5(f6(x2021,x2022),x2021)),
% 1.52/1.62 inference(rename_variables,[],[53])).
% 1.52/1.62 cnf(204,plain,
% 1.52/1.62 (~P2(f5(a1,a2),a3)),
% 1.52/1.62 inference(scs_inference,[],[3,53,190,9,7,142,174,166,111,29,30,15,17,26,31,25])).
% 1.52/1.62 cnf(206,plain,
% 1.52/1.62 (~P2(f5(a2,a1),a2)),
% 1.52/1.62 inference(scs_inference,[],[3,53,190,9,7,142,174,166,69,111,29,30,15,17,26,31,25,49])).
% 1.52/1.62 cnf(208,plain,
% 1.52/1.62 (~P2(f5(a2,a1),a1)),
% 1.52/1.62 inference(scs_inference,[],[3,53,190,9,7,142,174,166,69,111,29,30,15,17,26,31,25,49,48])).
% 1.52/1.62 cnf(229,plain,
% 1.52/1.62 (P8(a3,x2291)+P8(a4,x2291)),
% 1.52/1.62 inference(scs_inference,[],[3,53,190,202,9,7,193,10,11,142,174,166,69,103,144,111,77,29,30,15,17,26,31,25,49,48,24,16,13,23,38,132,40,42,45])).
% 1.52/1.62 cnf(231,plain,
% 1.52/1.62 (P1(a3,f6(a4,x2311))),
% 1.52/1.62 inference(scs_inference,[],[153,174,32])).
% 1.52/1.62 cnf(234,plain,
% 1.52/1.62 (P5(x2341,f7(f6(x2341,x2342),x2343))),
% 1.52/1.62 inference(scs_inference,[],[6,192,153,174,32,29])).
% 1.52/1.62 cnf(255,plain,
% 1.52/1.62 (~P8(f7(x2551,x2552),x2551)),
% 1.52/1.62 inference(rename_variables,[],[11])).
% 1.52/1.62 cnf(257,plain,
% 1.52/1.62 (~P8(x2571,f7(f6(x2571,x2572),x2573))),
% 1.52/1.62 inference(scs_inference,[],[11,255,231,174,166,33,38])).
% 1.52/1.62 cnf(258,plain,
% 1.52/1.62 (~P1(x2581,f6(x2581,x2582))),
% 1.52/1.62 inference(rename_variables,[],[174])).
% 1.52/1.62 cnf(265,plain,
% 1.52/1.62 (P1(a3,f6(f6(a4,x2651),x2652))),
% 1.52/1.62 inference(scs_inference,[],[11,255,231,174,258,166,33,38,229,99,32])).
% 1.52/1.62 cnf(272,plain,
% 1.52/1.62 (~P2(x2721,f6(x2722,x2723))),
% 1.52/1.62 inference(scs_inference,[],[8,7,11,255,169,231,139,174,258,166,33,38,229,99,32,42,31])).
% 1.52/1.62 cnf(280,plain,
% 1.52/1.62 (P8(a4,f7(f6(a3,x2801),x2802))),
% 1.52/1.62 inference(scs_inference,[],[257,229])).
% 1.52/1.62 cnf(283,plain,
% 1.52/1.62 (P1(f6(f6(a4,x2831),x2832),a3)),
% 1.52/1.62 inference(scs_inference,[],[7,257,265,229,32])).
% 1.52/1.62 cnf(308,plain,
% 1.52/1.62 (~P2(f5(f7(x3081,x3082),x3081),f7(x3081,x3082))),
% 1.52/1.62 inference(scs_inference,[],[272,257,106,91,17,49])).
% 1.52/1.62 cnf(310,plain,
% 1.52/1.62 (~P2(f5(f7(x3101,x3102),x3101),x3101)),
% 1.52/1.62 inference(scs_inference,[],[272,257,106,91,17,49,48])).
% 1.52/1.62 cnf(318,plain,
% 1.52/1.62 (~P8(f7(f6(x3181,x3182),x3183),x3181)),
% 1.52/1.62 inference(scs_inference,[],[11,189,280,283,272,257,106,139,174,91,17,49,48,26,24,13,41])).
% 1.52/1.62 cnf(326,plain,
% 1.52/1.62 (~P1(x3261,f6(f6(x3261,x3262),x3263))),
% 1.52/1.62 inference(scs_inference,[],[7,11,189,280,283,272,234,257,106,139,114,174,91,17,49,48,26,24,13,41,23,16,30])).
% 1.52/1.62 cnf(346,plain,
% 1.52/1.62 (P5(a3,f6(a4,x3461))),
% 1.52/1.62 inference(scs_inference,[],[10,283,30])).
% 1.52/1.62 cnf(347,plain,
% 1.52/1.62 (~P1(f6(x3471,x3472),x3471)),
% 1.52/1.62 inference(rename_variables,[],[10])).
% 1.52/1.62 cnf(350,plain,
% 1.52/1.62 (~P8(x3501,f7(f6(x3501,x3502),x3503))),
% 1.52/1.62 inference(rename_variables,[],[257])).
% 1.52/1.62 cnf(357,plain,
% 1.52/1.62 (~P5(f6(x3571,x3572),f6(f6(x3571,x3573),x3574))),
% 1.52/1.62 inference(scs_inference,[],[53,10,318,206,72,283,208,189,257,350,231,30,45,18,43,29])).
% 1.52/1.62 cnf(360,plain,
% 1.52/1.62 (~P1(f6(f6(x3601,x3602),x3603),x3601)),
% 1.52/1.62 inference(scs_inference,[],[53,10,347,318,206,72,283,208,189,257,350,231,174,30,45,18,43,29,32])).
% 1.52/1.62 cnf(363,plain,
% 1.52/1.62 (P2(f5(f7(a4,x3631),a4),a3)+~P4(f5(f7(a4,x3631),a4),f5(a1,a2))),
% 1.52/1.62 inference(scs_inference,[],[53,10,347,310,318,204,206,150,72,283,208,189,257,350,77,231,174,30,45,18,43,29,32,51])).
% 1.52/1.62 cnf(375,plain,
% 1.52/1.62 (P5(f6(a4,x3751),a3)),
% 1.52/1.62 inference(scs_inference,[],[6,346,29])).
% 1.52/1.62 cnf(381,plain,
% 1.52/1.62 (P1(a1,f6(f6(a2,x3811),x3812))),
% 1.52/1.62 inference(scs_inference,[],[6,346,326,81,79,75,69,257,29,45,32])).
% 1.52/1.62 cnf(390,plain,
% 1.52/1.62 (P1(f6(a4,x3901),a3)),
% 1.52/1.62 inference(scs_inference,[],[6,10,346,326,81,79,75,318,69,257,29,45,32,33,39,19])).
% 1.52/1.62 cnf(407,plain,
% 1.52/1.62 (~P5(x4071,f6(f6(x4071,x4072),x4073))),
% 1.52/1.62 inference(scs_inference,[],[11,390,326,33,19])).
% 1.52/1.62 cnf(421,plain,
% 1.52/1.63 (P5(f6(a4,x4211),f6(f6(a3,x4212),x4213))),
% 1.52/1.63 inference(scs_inference,[],[407,375,29])).
% 1.52/1.63 cnf(422,plain,
% 1.52/1.63 (~P5(x4221,f6(f6(x4221,x4222),x4223))),
% 1.52/1.63 inference(rename_variables,[],[407])).
% 1.52/1.63 cnf(424,plain,
% 1.52/1.63 (P1(a1,f6(a2,x4241))),
% 1.52/1.63 inference(scs_inference,[],[53,407,375,381,29,30])).
% 1.52/1.63 cnf(425,plain,
% 1.52/1.63 (P1(a1,f6(f6(a2,x4251),x4252))),
% 1.52/1.63 inference(rename_variables,[],[381])).
% 1.52/1.63 cnf(428,plain,
% 1.52/1.63 (P1(f6(a4,x4281),f6(f6(a3,x4282),x4283))),
% 1.52/1.63 inference(scs_inference,[],[53,407,375,381,29,30,19])).
% 1.52/1.63 cnf(446,plain,
% 1.52/1.63 (~P8(f7(f6(x4461,x4462),x4463),f7(x4461,x4464))+~P1(f7(f6(x4461,x4462),x4463),f7(x4461,x4464))),
% 1.52/1.63 inference(scs_inference,[],[60,53,11,407,422,375,308,360,381,425,390,318,153,29,30,19,49,17,48,26,23,16,24,13,43])).
% 1.52/1.63 cnf(455,plain,
% 1.52/1.63 (~P1(f6(f6(x4551,x4552),x4553),f6(x4551,x4554))),
% 1.52/1.63 inference(scs_inference,[],[7,357,30])).
% 1.52/1.63 cnf(478,plain,
% 1.52/1.63 (~P5(f6(f6(x4781,x4782),x4783),f6(x4781,x4784))),
% 1.52/1.63 inference(scs_inference,[],[455,19])).
% 1.52/1.63 cnf(481,plain,
% 1.52/1.63 (P1(f6(a4,x4811),f6(f6(a3,x4812),x4813))),
% 1.52/1.63 inference(rename_variables,[],[428])).
% 1.52/1.63 cnf(482,plain,
% 1.52/1.63 (~P1(f6(x4821,x4822),x4821)),
% 1.52/1.63 inference(rename_variables,[],[10])).
% 1.52/1.63 cnf(484,plain,
% 1.52/1.63 (P5(f6(a4,x4841),f6(a3,x4842))),
% 1.52/1.63 inference(scs_inference,[],[53,10,455,421,428,19,32,29])).
% 1.52/1.63 cnf(487,plain,
% 1.52/1.63 (P5(f6(f6(a3,x4871),x4872),a4)),
% 1.52/1.63 inference(scs_inference,[],[53,10,482,455,421,428,481,19,32,29,30])).
% 1.52/1.63 cnf(511,plain,
% 1.52/1.63 (P8(f6(f6(x5111,x5112),x5113),f6(x5111,x5114))),
% 1.52/1.63 inference(scs_inference,[],[455,15])).
% 1.52/1.63 cnf(513,plain,
% 1.52/1.63 (P1(f6(f6(a3,x5131),x5132),a4)),
% 1.52/1.63 inference(scs_inference,[],[487,455,15,19])).
% 1.52/1.63 cnf(515,plain,
% 1.52/1.63 (~P1(f6(x5151,x5152),f6(f6(x5151,x5153),x5154))),
% 1.52/1.63 inference(scs_inference,[],[10,487,455,360,15,19,32])).
% 1.52/1.63 cnf(518,plain,
% 1.52/1.63 (P5(f6(a3,x5181),a4)),
% 1.52/1.63 inference(scs_inference,[],[53,10,484,487,455,360,15,19,32,29])).
% 1.52/1.63 cnf(522,plain,
% 1.52/1.63 (P1(a2,f6(f6(a1,x5221),x5222))),
% 1.52/1.63 inference(scs_inference,[],[53,10,484,487,407,455,360,69,15,19,32,29,30])).
% 1.52/1.63 cnf(546,plain,
% 1.52/1.63 (P1(a4,f6(a3,x5461))),
% 1.52/1.63 inference(scs_inference,[],[10,11,513,33,32])).
% 1.52/1.63 cnf(549,plain,
% 1.52/1.63 (~P2(f5(a1,f6(a2,x5491)),a1)),
% 1.52/1.63 inference(scs_inference,[],[10,11,513,424,33,32,49])).
% 1.52/1.63 cnf(594,plain,
% 1.52/1.63 (P1(f6(a3,x5941),a4)),
% 1.52/1.63 inference(scs_inference,[],[518,19])).
% 1.52/1.63 cnf(596,plain,
% 1.52/1.63 (P1(a2,f6(a1,x5961))),
% 1.52/1.63 inference(scs_inference,[],[10,522,518,19,32])).
% 1.52/1.63 cnf(617,plain,
% 1.52/1.63 (P5(a4,f6(a3,x6171))),
% 1.52/1.63 inference(scs_inference,[],[478,487,29])).
% 1.52/1.63 cnf(620,plain,
% 1.52/1.63 (P1(f6(a3,x6201),f6(a4,x6202))),
% 1.52/1.63 inference(scs_inference,[],[594,478,487,111,29,30])).
% 1.52/1.63 cnf(648,plain,
% 1.52/1.63 (P5(a2,f6(f6(a1,x6481),x6482))),
% 1.52/1.63 inference(scs_inference,[],[72,407,515,15,29])).
% 1.52/1.63 cnf(689,plain,
% 1.52/1.63 (P8(f7(f6(a1,x6891),x6892),a2)),
% 1.52/1.63 inference(scs_inference,[],[75,69,511,596,549,594,357,455,326,318,49,48,16,17,26,23,24,13,39,99,33])).
% 1.52/1.63 cnf(701,plain,
% 1.52/1.63 (P8(f6(x7011,x7012),f6(x7011,x7013))),
% 1.52/1.63 inference(scs_inference,[],[689,114,318,43,15])).
% 1.52/1.63 cnf(709,plain,
% 1.52/1.63 (P5(a1,f6(a2,x7091))),
% 1.52/1.63 inference(scs_inference,[],[66,69,546,326,174,257,41,43,30])).
% 1.52/1.63 cnf(715,plain,
% 1.52/1.63 (P1(f6(f6(a3,x7151),x7152),f6(a4,x7153))),
% 1.52/1.63 inference(scs_inference,[],[513,111,30])).
% 1.52/1.63 cnf(734,plain,
% 1.52/1.63 (P8(x7341,f6(f6(x7341,x7342),x7343))),
% 1.52/1.63 inference(scs_inference,[],[326,15])).
% 1.52/1.63 cnf(736,plain,
% 1.52/1.63 (P5(a2,f6(a1,x7361))),
% 1.52/1.63 inference(scs_inference,[],[648,478,326,15,29])).
% 1.52/1.63 cnf(767,plain,
% 1.52/1.63 (P1(f6(a3,x7671),f6(f6(a4,x7672),x7673))),
% 1.52/1.63 inference(scs_inference,[],[79,77,66,701,715,709,648,620,478,546,518,169,272,515,326,360,2,318,257,15,29,49,17,48,23,16,13,26,24,45,42,40,32])).
% 1.52/1.63 cnf(799,plain,
% 1.52/1.63 (P8(f7(f6(x7991,x7992),x7993),f7(x7991,x7994))),
% 1.52/1.63 inference(scs_inference,[],[69,106,174,318,35,99,33])).
% 1.52/1.63 cnf(826,plain,
% 1.52/1.63 (P5(f6(a3,x8261),f6(f6(a4,x8262),x8263))),
% 1.52/1.63 inference(scs_inference,[],[81,69,734,736,767,484,357,111,231,360,174,49,17,23,13,16,26,24,39,29])).
% 1.52/1.63 cnf(829,plain,
% 1.52/1.63 (~P1(f7(f6(x8291,x8292),x8293),f7(x8291,x8294))),
% 1.52/1.63 inference(scs_inference,[],[81,69,734,799,736,767,484,357,111,231,360,174,49,17,23,13,16,26,24,39,29,446])).
% 1.52/1.63 cnf(831,plain,
% 1.52/1.63 (~P5(f7(f6(x8311,x8312),x8313),f7(x8311,x8314))),
% 1.52/1.63 inference(scs_inference,[],[829,19])).
% 1.52/1.63 cnf(840,plain,
% 1.52/1.63 (~P1(f7(x8401,x8402),f7(f6(x8401,x8403),x8404))),
% 1.52/1.63 inference(scs_inference,[],[69,829,826,478,360,7,19,29,39,32])).
% 1.52/1.63 cnf(855,plain,
% 1.52/1.63 (~P2(x8551,f7(f6(x8552,x8553),x8554))),
% 1.52/1.63 inference(scs_inference,[],[831,9,31])).
% 1.52/1.63 cnf(895,plain,
% 1.52/1.63 (~P4(f5(a1,a2),f5(f7(a1,x8951),a1))),
% 1.52/1.63 inference(scs_inference,[],[79,855,310,192,9,51])).
% 1.52/1.63 cnf(939,plain,
% 1.52/1.63 (~P5(f7(x9391,x9392),f7(f6(x9391,x9393),x9394))),
% 1.52/1.63 inference(scs_inference,[],[895,308,5,428,840,114,27,28,12,30,19])).
% 1.52/1.63 cnf(947,plain,
% 1.52/1.63 (P5(f6(f6(a4,x9471),x9472),f6(a3,x9473))),
% 1.52/1.63 inference(scs_inference,[],[895,826,308,5,428,840,620,169,455,114,27,28,12,30,19,39,15,29])).
% 1.52/1.63 cnf(952,plain,
% 1.52/1.63 (~P2(x9521,x9522)),
% 1.52/1.63 inference(scs_inference,[],[81,895,855,826,308,234,5,428,840,620,310,407,169,455,272,114,9,27,28,12,30,19,39,15,29,51,31])).
% 1.52/1.63 cnf(969,plain,
% 1.52/1.63 (~P1(f7(x9691,x9692),f7(x9691,x9693))),
% 1.52/1.63 inference(scs_inference,[],[111,939,952,947,617,840,363,19,29,30])).
% 1.52/1.63 cnf(977,plain,
% 1.52/1.63 (~P5(f7(x9771,x9772),f7(x9771,x9773))),
% 1.52/1.63 inference(scs_inference,[],[969,19])).
% 1.52/1.63 cnf(983,plain,
% 1.52/1.63 (P3(x9831,x9832)),
% 1.52/1.63 inference(scs_inference,[],[150,977,952,13,23,17])).
% 1.52/1.63 cnf(1016,plain,
% 1.52/1.63 (~P3(f5(a3,a4),a1)),
% 1.52/1.63 inference(scs_inference,[],[983,50])).
% 1.52/1.63 cnf(1051,plain,
% 1.52/1.63 ($false),
% 1.52/1.63 inference(scs_inference,[],[1016,983]),
% 1.52/1.63 ['proof']).
% 1.52/1.63 % SZS output end Proof
% 1.52/1.63 % Total time :1.000000s
%------------------------------------------------------------------------------