TSTP Solution File: SET025-3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET025-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 14:28:00 EDT 2023
% Result : Unsatisfiable 0.56s 0.68s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET025-3 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n023.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 : Sat Aug 26 12:35:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.56/0.67 %-------------------------------------------
% 0.56/0.67 % File :CSE---1.6
% 0.56/0.68 % Problem :theBenchmark
% 0.56/0.68 % Transform :cnf
% 0.56/0.68 % Format :tptp:raw
% 0.56/0.68 % Command :java -jar mcs_scs.jar %d %s
% 0.56/0.68
% 0.56/0.68 % Result :Theorem 0.010000s
% 0.56/0.68 % Output :CNFRefutation 0.010000s
% 0.56/0.68 %-------------------------------------------
% 0.56/0.68 %--------------------------------------------------------------------------
% 0.56/0.68 % File : SET025-3 : TPTP v8.1.2. Released v1.0.0.
% 0.56/0.68 % Domain : Set Theory
% 0.56/0.68 % Problem : Ordered pairs are little sets
% 0.56/0.68 % Version : [BL+86] axioms : Augmented.
% 0.56/0.68 % English :
% 0.56/0.68
% 0.56/0.68 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.56/0.68 % Source : [BL+86]
% 0.56/0.68 % Names : Lemma 10 [BL+86]
% 0.56/0.68
% 0.56/0.68 % Status : Unsatisfiable
% 0.56/0.68 % Rating : 0.10 v8.1.0, 0.05 v7.5.0, 0.11 v7.4.0, 0.12 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.14 v6.0.0, 0.00 v5.5.0, 0.10 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.18 v4.0.0, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.08 v3.3.0, 0.07 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.5.0, 0.08 v2.4.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.11 v2.1.0, 0.22 v2.0.0
% 0.56/0.68 % Syntax : Number of clauses : 151 ( 12 unt; 20 nHn; 128 RR)
% 0.56/0.68 % Number of literals : 385 ( 56 equ; 218 neg)
% 0.56/0.68 % Maximal clause size : 8 ( 2 avg)
% 0.56/0.68 % Maximal term depth : 4 ( 1 avg)
% 0.56/0.68 % Number of predicates : 14 ( 13 usr; 0 prp; 1-5 aty)
% 0.56/0.68 % Number of functors : 61 ( 61 usr; 8 con; 0-5 aty)
% 0.56/0.68 % Number of variables : 340 ( 30 sgn)
% 0.56/0.68 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.56/0.68
% 0.56/0.68 % Comments :
% 0.56/0.68 %--------------------------------------------------------------------------
% 0.56/0.68 %----Include Godel's set axioms
% 0.56/0.68 include('Axioms/SET003-0.ax').
% 0.56/0.68 %--------------------------------------------------------------------------
% 0.56/0.68 %----Previously proved lemmas are added at each step
% 0.56/0.68 cnf(first_components_are_equal,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | ~ little_set(U)
% 0.56/0.68 | ordered_pair(X,Y) != ordered_pair(U,V)
% 0.56/0.68 | X = U ) ).
% 0.56/0.68
% 0.56/0.68 cnf(left_cancellation,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | ~ little_set(Y)
% 0.56/0.68 | non_ordered_pair(Z,X) != non_ordered_pair(Z,Y)
% 0.56/0.68 | X = Y ) ).
% 0.56/0.68
% 0.56/0.68 cnf(second_components_are_equal,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | ~ little_set(Y)
% 0.56/0.68 | ~ little_set(U)
% 0.56/0.68 | ~ little_set(V)
% 0.56/0.68 | ordered_pair(X,Y) != ordered_pair(U,V)
% 0.56/0.68 | Y = V ) ).
% 0.56/0.68
% 0.56/0.68 cnf(two_sets_equal,axiom,
% 0.56/0.68 ( ~ subset(X,Y)
% 0.56/0.68 | ~ subset(Y,X)
% 0.56/0.68 | X = Y ) ).
% 0.56/0.68
% 0.56/0.68 cnf(property_of_first,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | ~ little_set(Y)
% 0.56/0.68 | first(ordered_pair(X,Y)) = X ) ).
% 0.56/0.68
% 0.56/0.68 cnf(property_of_second,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | ~ little_set(Y)
% 0.56/0.68 | second(ordered_pair(X,Y)) = Y ) ).
% 0.56/0.68
% 0.56/0.68 cnf(first_component_is_small,axiom,
% 0.56/0.68 ( ~ ordered_pair_predicate(X)
% 0.56/0.68 | little_set(first(X)) ) ).
% 0.56/0.68
% 0.56/0.68 cnf(second_component_is_small,axiom,
% 0.56/0.68 ( ~ ordered_pair_predicate(X)
% 0.56/0.68 | little_set(second(X)) ) ).
% 0.56/0.68
% 0.56/0.68 cnf(property_of_singleton_sets,axiom,
% 0.56/0.68 ( ~ little_set(X)
% 0.56/0.68 | member(X,singleton_set(X)) ) ).
% 0.56/0.68
% 0.56/0.68 cnf(prove_ordered_pairs_are_small,negated_conjecture,
% 0.56/0.68 ~ little_set(ordered_pair(a,b)) ).
% 0.56/0.68
% 0.56/0.68 %--------------------------------------------------------------------------
% 0.56/0.68 %-------------------------------------------
% 0.56/0.68 % Proof found
% 0.56/0.68 % SZS status Theorem for theBenchmark
% 0.56/0.68 % SZS output start Proof
% 0.56/0.68 %ClaNum:259(EqnAxiom:114)
% 0.56/0.68 %VarNum:970(SingletonVarNum:329)
% 0.56/0.68 %MaxLitNum:8
% 0.56/0.68 %MaxfuncDepth:5
% 0.56/0.68 %SharedTerms:15
% 0.56/0.68 %goalClause: 120
% 0.56/0.68 %singleGoalClaCount:1
% 0.56/0.68 [115]P1(a1)
% 0.56/0.68 [116]P2(a2)
% 0.56/0.68 [117]P6(a3,a1)
% 0.56/0.68 [120]~P1(f48(f48(a4,a4),f48(a4,a5)))
% 0.56/0.68 [119]~P6(x1191,a3)
% 0.56/0.68 [118]P1(f48(x1181,x1182))
% 0.56/0.68 [121]~P2(x1211)+P8(x1211)
% 0.56/0.68 [122]~P2(x1221)+P12(x1221)
% 0.56/0.68 [123]~P9(x1231)+P2(x1231)
% 0.56/0.68 [136]~P1(x1361)+P6(x1361,a55)
% 0.56/0.68 [140]P10(x1401)+~P6(x1401,a14)
% 0.56/0.68 [141]P10(x1411)+~P6(x1411,a45)
% 0.56/0.68 [124]P12(x1241)+P1(f12(x1241))
% 0.56/0.68 [125]P12(x1251)+P1(f23(x1251))
% 0.56/0.68 [126]P12(x1261)+P1(f25(x1261))
% 0.56/0.68 [127]P12(x1271)+~E(f25(x1271),f23(x1271))
% 0.56/0.68 [128]~P10(x1281)+P1(f24(x1281))
% 0.56/0.68 [129]~P10(x1291)+P1(f29(x1291))
% 0.56/0.68 [130]~P10(x1301)+P1(f34(x1301))
% 0.56/0.68 [131]~P10(x1311)+P1(f50(x1311))
% 0.56/0.68 [132]~P1(x1321)+P1(f54(x1321))
% 0.56/0.68 [133]~P1(x1331)+P1(f51(x1331))
% 0.56/0.68 [134]~P9(x1341)+P2(f7(x1341))
% 0.56/0.68 [137]P8(x1371)+~P10(f13(x1371))
% 0.56/0.68 [138]P6(f26(x1381),x1381)+E(x1381,a3)
% 0.56/0.68 [139]P3(f26(x1391),x1391)+E(x1391,a3)
% 0.56/0.68 [142]P8(x1421)+P6(f13(x1421),x1421)
% 0.56/0.68 [148]~P6(x1481,a45)+E(f50(x1481),f34(x1481))
% 0.56/0.68 [159]~P6(x1591,a14)+P6(f34(x1591),f50(x1591))
% 0.56/0.68 [160]~P1(x1601)+P6(x1601,f48(x1601,x1601))
% 0.56/0.68 [213]~P10(x2131)+E(f48(f48(f24(x2131),f24(x2131)),f48(f24(x2131),f29(x2131))),x2131)
% 0.56/0.68 [233]P12(x2331)+P6(f48(f48(f12(x2331),f12(x2331)),f48(f12(x2331),f23(x2331))),x2331)
% 0.56/0.68 [234]P12(x2341)+P6(f48(f48(f12(x2341),f12(x2341)),f48(f12(x2341),f25(x2341))),x2341)
% 0.56/0.68 [240]~P6(x2401,a1)+P6(f8(f49(f8(x2401),f8(f48(x2401,x2401)))),a1)
% 0.56/0.68 [143]~P11(x1431,x1432)+~E(x1431,x1432)
% 0.56/0.68 [144]P1(x1441)+~P4(x1442,x1441)
% 0.56/0.68 [145]P1(x1451)+~P6(x1451,x1452)
% 0.56/0.68 [146]P1(x1461)+~P4(x1461,x1462)
% 0.56/0.68 [153]~P11(x1531,x1532)+P13(x1531,x1532)
% 0.56/0.68 [150]E(x1501,x1502)+P1(f15(x1501,x1502))
% 0.56/0.68 [152]P10(x1521)+~P6(x1521,f7(x1522))
% 0.56/0.68 [158]P13(x1581,x1582)+~P6(x1581,f51(x1582))
% 0.56/0.68 [165]P13(x1651,x1652)+P6(f16(x1651,x1652),x1651)
% 0.56/0.68 [166]P3(x1661,x1662)+P6(f27(x1661,x1662),x1662)
% 0.56/0.68 [167]P3(x1671,x1672)+P6(f27(x1671,x1672),x1671)
% 0.56/0.68 [168]~P6(x1681,x1682)+~P6(x1681,f8(x1682))
% 0.56/0.68 [171]~P6(x1711,f34(x1712))+P1(f35(x1711,x1712))
% 0.56/0.68 [172]~P6(x1721,f34(x1722))+P1(f40(x1721,x1722))
% 0.56/0.68 [173]~P6(x1731,f50(x1732))+P1(f41(x1731,x1732))
% 0.56/0.68 [174]~P6(x1741,f50(x1742))+P1(f42(x1741,x1742))
% 0.56/0.68 [175]~P6(x1751,f52(x1752))+P1(f43(x1751,x1752))
% 0.56/0.68 [176]~P6(x1761,f52(x1762))+P1(f17(x1761,x1762))
% 0.56/0.68 [177]~P6(x1771,f52(x1772))+P1(f18(x1771,x1772))
% 0.56/0.68 [178]~P6(x1781,f46(x1782))+P1(f19(x1781,x1782))
% 0.56/0.68 [179]~P6(x1791,f46(x1792))+P1(f20(x1791,x1792))
% 0.56/0.68 [180]~P6(x1801,f46(x1802))+P1(f21(x1801,x1802))
% 0.56/0.68 [181]~P6(x1811,f10(x1812))+P10(f44(x1811,x1812))
% 0.56/0.68 [182]~P6(x1821,f53(x1822))+P10(f31(x1821,x1822))
% 0.56/0.69 [192]~P6(x1921,f34(x1922))+P6(x1921,f35(x1921,x1922))
% 0.56/0.69 [193]~P6(x1931,f50(x1932))+P6(x1931,f42(x1931,x1932))
% 0.56/0.69 [194]~P6(x1941,f54(x1942))+P6(x1941,f22(x1941,x1942))
% 0.56/0.69 [195]~P6(x1951,f10(x1952))+P6(f44(x1951,x1952),x1952)
% 0.56/0.69 [196]~P6(x1961,f54(x1962))+P6(f22(x1961,x1962),x1962)
% 0.56/0.69 [197]~P6(x1971,f53(x1972))+P6(f31(x1971,x1972),x1972)
% 0.56/0.69 [200]P13(x2001,x2002)+~P6(f16(x2001,x2002),x2002)
% 0.56/0.69 [208]~P4(x2082,x2081)+P7(x2081,f11(x2082,x2082),x2082)
% 0.56/0.69 [183]~P6(x1831,f10(x1832))+E(f34(f44(x1831,x1832)),x1831)
% 0.56/0.69 [184]~P6(x1841,f53(x1842))+E(f50(f31(x1841,x1842)),x1841)
% 0.56/0.69 [235]~P6(x2351,f7(x2352))+P6(f48(f48(f50(x2351),f50(x2351)),f48(f50(x2351),f34(x2351))),x2352)
% 0.56/0.69 [238]~P6(x2381,f34(x2382))+E(f48(f48(f35(x2381,x2382),f35(x2381,x2382)),f48(f35(x2381,x2382),f40(x2381,x2382))),x2382)
% 0.56/0.69 [239]~P6(x2391,f50(x2392))+E(f48(f48(f41(x2391,x2392),f41(x2391,x2392)),f48(f41(x2391,x2392),f42(x2391,x2392))),x2392)
% 0.56/0.69 [245]~P6(x2451,f52(x2452))+E(f48(f48(f43(x2451,x2452),f43(x2451,x2452)),f48(f43(x2451,x2452),f48(f48(f17(x2451,x2452),f17(x2451,x2452)),f48(f17(x2451,x2452),f18(x2451,x2452))))),x2451)
% 0.56/0.69 [246]~P6(x2461,f46(x2462))+E(f48(f48(f19(x2461,x2462),f19(x2461,x2462)),f48(f19(x2461,x2462),f48(f48(f20(x2461,x2462),f20(x2461,x2462)),f48(f20(x2461,x2462),f21(x2461,x2462))))),x2461)
% 0.56/0.69 [254]~P6(x2541,f52(x2542))+P6(f48(f48(f17(x2541,x2542),f17(x2541,x2542)),f48(f17(x2541,x2542),f48(f48(f18(x2541,x2542),f18(x2541,x2542)),f48(f18(x2541,x2542),f43(x2541,x2542))))),x2542)
% 0.56/0.69 [255]~P6(x2551,f46(x2552))+P6(f48(f48(f19(x2551,x2552),f19(x2551,x2552)),f48(f19(x2551,x2552),f48(f48(f21(x2551,x2552),f21(x2551,x2552)),f48(f21(x2551,x2552),f20(x2551,x2552))))),x2552)
% 0.56/0.69 [205]P2(x2051)+~P7(x2051,x2052,x2053)
% 0.56/0.69 [188]P10(x1881)+~P6(x1881,f11(x1882,x1883))
% 0.56/0.69 [198]P6(x1981,x1982)+~P6(x1981,f49(x1983,x1982))
% 0.56/0.69 [199]P6(x1991,x1992)+~P6(x1991,f49(x1992,x1993))
% 0.56/0.69 [202]P6(f34(x2021),x2022)+~P6(x2021,f11(x2022,x2023))
% 0.56/0.69 [203]P6(f50(x2031),x2032)+~P6(x2031,f11(x2033,x2032))
% 0.56/0.69 [206]~P7(x2061,x2062,x2063)+E(f10(x2061),x2062)
% 0.56/0.69 [209]~P7(x2091,x2093,x2092)+P13(f53(x2091),x2092)
% 0.56/0.69 [221]~P6(x2211,f9(x2212,x2213))+P1(f32(x2211,x2212,x2213))
% 0.56/0.69 [222]~P6(x2221,f9(x2222,x2223))+P1(f36(x2221,x2222,x2223))
% 0.56/0.69 [223]~P6(x2231,f9(x2232,x2233))+P1(f37(x2231,x2232,x2233))
% 0.56/0.69 [224]~P6(x2241,f47(x2242,x2243))+P10(f28(x2241,x2242,x2243))
% 0.56/0.69 [225]~P6(x2251,f6(x2252,x2253))+P10(f33(x2251,x2252,x2253))
% 0.56/0.69 [229]~P6(x2291,f47(x2292,x2293))+P6(f28(x2291,x2292,x2293),x2293)
% 0.56/0.69 [230]~P6(x2301,f6(x2302,x2303))+P6(f33(x2301,x2302,x2303),x2302)
% 0.56/0.69 [226]~P6(x2261,f6(x2262,x2263))+E(f34(f33(x2261,x2262,x2263)),x2263)
% 0.56/0.69 [227]~P6(x2271,f47(x2272,x2273))+E(f50(f28(x2271,x2272,x2273)),x2271)
% 0.56/0.69 [236]~P6(x2361,f6(x2362,x2363))+P6(x2361,f50(f33(x2361,x2362,x2363)))
% 0.56/0.69 [237]~P6(x2371,f47(x2372,x2373))+P6(f34(f28(x2371,x2372,x2373)),x2372)
% 0.56/0.69 [244]~P6(x2441,f9(x2442,x2443))+E(f48(f48(f32(x2441,x2442,x2443),f32(x2441,x2442,x2443)),f48(f32(x2441,x2442,x2443),f36(x2441,x2442,x2443))),x2441)
% 0.56/0.69 [251]~P6(x2511,f9(x2512,x2513))+P6(f48(f48(f32(x2511,x2512,x2513),f32(x2511,x2512,x2513)),f48(f32(x2511,x2512,x2513),f37(x2511,x2512,x2513))),x2512)
% 0.56/0.69 [252]~P6(x2521,f9(x2522,x2523))+P6(f48(f48(f37(x2521,x2522,x2523),f37(x2521,x2522,x2523)),f48(f37(x2521,x2522,x2523),f36(x2521,x2522,x2523))),x2523)
% 0.56/0.69 [249]P4(x2491,x2492)+~P5(x2493,x2494,x2495,x2491,x2492)
% 0.56/0.69 [250]P4(x2501,x2502)+~P5(x2503,x2501,x2502,x2504,x2505)
% 0.56/0.69 [253]P7(x2531,x2532,x2533)+~P5(x2531,x2532,x2534,x2533,x2535)
% 0.56/0.69 [135]~P8(x1351)+~P12(x1351)+P2(x1351)
% 0.56/0.69 [147]~P2(x1471)+P9(x1471)+~P2(f7(x1471))
% 0.56/0.69 [149]~P1(x1491)+P6(f30(x1491),x1491)+E(x1491,a3)
% 0.56/0.69 [228]~P1(x2281)+E(x2281,a3)+P6(f48(f48(x2281,x2281),f48(x2281,f30(x2281))),a2)
% 0.56/0.69 [151]~P6(x1511,x1512)+P10(x1511)+~P8(x1512)
% 0.56/0.69 [154]P11(x1541,x1542)+~P13(x1541,x1542)+E(x1541,x1542)
% 0.56/0.69 [161]~P13(x1612,x1611)+~P13(x1611,x1612)+E(x1611,x1612)
% 0.56/0.69 [156]~P1(x1561)+P6(x1561,x1562)+P6(x1561,f8(x1562))
% 0.56/0.69 [157]~P1(x1571)+~P2(x1572)+P1(f47(x1571,x1572))
% 0.56/0.69 [162]~P1(x1621)+~P13(x1621,x1622)+P6(x1621,f51(x1622))
% 0.56/0.69 [201]E(x2011,x2012)+P6(f15(x2011,x2012),x2012)+P6(f15(x2011,x2012),x2011)
% 0.56/0.69 [215]E(x2151,x2152)+~P6(f15(x2151,x2152),x2152)+~P6(f15(x2151,x2152),x2151)
% 0.56/0.69 [216]~P1(x2162)+~P1(x2161)+E(f34(f48(f48(x2161,x2161),f48(x2161,x2162))),x2161)
% 0.56/0.69 [217]~P1(x2172)+~P1(x2171)+E(f50(f48(f48(x2171,x2171),f48(x2171,x2172))),x2172)
% 0.56/0.69 [169]~P13(x1693,x1692)+P6(x1691,x1692)+~P6(x1691,x1693)
% 0.56/0.69 [190]~P3(x1903,x1902)+~P6(x1901,x1902)+~P6(x1901,x1903)
% 0.56/0.69 [163]~E(x1631,x1633)+~P1(x1631)+P6(x1631,f48(x1632,x1633))
% 0.56/0.69 [164]~E(x1641,x1642)+~P1(x1641)+P6(x1641,f48(x1642,x1643))
% 0.56/0.69 [185]~P6(x1851,x1853)+~P6(x1853,x1852)+P6(x1851,f54(x1852))
% 0.56/0.69 [189]E(x1891,x1892)+E(x1891,x1893)+~P6(x1891,f48(x1893,x1892))
% 0.56/0.69 [204]~P6(x2041,x2043)+~P6(x2041,x2042)+P6(x2041,f49(x2042,x2043))
% 0.56/0.69 [155]~P1(x1551)+~P10(x1551)+~E(f50(x1551),f34(x1551))+P6(x1551,a45)
% 0.56/0.69 [191]~P1(x1911)+~P10(x1911)+~P6(f34(x1911),f50(x1911))+P6(x1911,a14)
% 0.56/0.69 [218]~P1(x2182)+~P1(x2181)+P4(x2181,x2182)+~P7(x2182,f11(x2181,x2181),x2181)
% 0.56/0.69 [241]~P1(x2411)+~P10(x2411)+P6(x2411,f7(x2412))+~P6(f48(f48(f50(x2411),f50(x2411)),f48(f50(x2411),f34(x2411))),x2412)
% 0.56/0.69 [170]~P1(x1702)+~P1(x1701)+E(x1701,x1702)+~E(f48(x1703,x1701),f48(x1703,x1702))
% 0.56/0.69 [207]~P2(x2071)+P7(x2071,x2072,x2073)+~E(f10(x2071),x2072)+~P13(f53(x2071),x2073)
% 0.56/0.69 [214]~P1(x2143)+~P1(x2142)+P10(x2141)+~E(x2141,f48(f48(x2142,x2142),f48(x2142,x2143)))
% 0.56/0.69 [231]~P1(x2312)+~P1(x2311)+E(x2311,x2312)+~E(f48(f48(x2311,x2311),f48(x2311,x2313)),f48(f48(x2312,x2312),f48(x2312,x2314)))
% 0.56/0.69 [256]~P6(x2563,x2566)+~P5(x2561,x2566,x2562,x2567,x2565)+~P6(x2564,x2566)+E(f6(x2561,f6(x2562,f48(f48(x2563,x2563),f48(x2563,x2564)))),f6(x2565,f48(f48(f6(x2561,x2563),f6(x2561,x2563)),f48(f6(x2561,x2563),f6(x2561,x2564)))))
% 0.56/0.69 [186]~P1(x1861)+~P10(x1863)+~P6(x1863,x1862)+P6(x1861,f10(x1862))+~E(x1861,f34(x1863))
% 0.56/0.69 [187]~P1(x1871)+~P10(x1873)+~P6(x1873,x1872)+P6(x1871,f53(x1872))+~E(x1871,f50(x1873))
% 0.56/0.69 [212]~P1(x2121)+~P10(x2121)+~P6(f34(x2121),x2122)+~P6(f50(x2121),x2123)+P6(x2121,f11(x2122,x2123))
% 0.56/0.69 [210]~P10(x2104)+~P6(x2104,x2102)+~P6(x2101,f50(x2104))+P6(x2101,f6(x2102,x2103))+~E(f34(x2104),x2103)
% 0.56/0.69 [219]~P1(x2194)+~P1(x2193)+~P6(x2191,x2193)+P6(x2191,f34(x2192))+~E(x2192,f48(f48(x2193,x2193),f48(x2193,x2194)))
% 0.56/0.69 [220]~P1(x2204)+~P1(x2203)+~P6(x2201,x2204)+P6(x2201,f50(x2202))+~E(x2202,f48(f48(x2203,x2203),f48(x2203,x2204)))
% 0.56/0.69 [257]~P4(x2574,x2575)+~P4(x2572,x2573)+~P7(x2571,x2572,x2574)+P5(x2571,x2572,x2573,x2574,x2575)+P6(f38(x2571,x2572,x2573,x2574,x2575),x2572)
% 0.56/0.69 [258]~P4(x2584,x2585)+~P4(x2582,x2583)+~P7(x2581,x2582,x2584)+P5(x2581,x2582,x2583,x2584,x2585)+P6(f39(x2581,x2582,x2583,x2584,x2585),x2582)
% 0.56/0.69 [259]~P4(x2594,x2595)+~P4(x2592,x2593)+~P7(x2591,x2592,x2594)+P5(x2591,x2592,x2593,x2594,x2595)+~E(f6(x2591,f6(x2593,f48(f48(f38(x2591,x2592,x2593,x2594,x2595),f38(x2591,x2592,x2593,x2594,x2595)),f48(f38(x2591,x2592,x2593,x2594,x2595),f39(x2591,x2592,x2593,x2594,x2595))))),f6(x2595,f48(f48(f6(x2591,f38(x2591,x2592,x2593,x2594,x2595)),f6(x2591,f38(x2591,x2592,x2593,x2594,x2595))),f48(f6(x2591,f38(x2591,x2592,x2593,x2594,x2595)),f6(x2591,f39(x2591,x2592,x2593,x2594,x2595))))))
% 0.56/0.69 [211]~P1(x2111)+~P10(x2114)+~P6(x2114,x2113)+~P6(f34(x2114),x2112)+P6(x2111,f47(x2112,x2113))+~E(f50(x2114),x2111)
% 0.56/0.69 [232]~P1(x2322)+~P1(x2324)+~P1(x2321)+~P1(x2323)+E(x2321,x2322)+~E(f48(f48(x2323,x2323),f48(x2323,x2321)),f48(f48(x2324,x2324),f48(x2324,x2322)))
% 0.56/0.69 [242]~P1(x2422)+~P1(x2421)+E(x2421,x2422)+~P1(x2423)+~P12(x2424)+~P6(f48(f48(x2423,x2423),f48(x2423,x2422)),x2424)+~P6(f48(f48(x2423,x2423),f48(x2423,x2421)),x2424)
% 0.56/0.69 [247]~P1(x2475)+~P1(x2474)+~P1(x2473)+~P1(x2471)+P6(x2471,f52(x2472))+~P6(f48(f48(x2474,x2474),f48(x2474,f48(f48(x2475,x2475),f48(x2475,x2473)))),x2472)+~E(x2471,f48(f48(x2473,x2473),f48(x2473,f48(f48(x2474,x2474),f48(x2474,x2475)))))
% 0.56/0.69 [248]~P1(x2485)+~P1(x2484)+~P1(x2483)+~P1(x2481)+P6(x2481,f46(x2482))+~P6(f48(f48(x2483,x2483),f48(x2483,f48(f48(x2485,x2485),f48(x2485,x2484)))),x2482)+~E(x2481,f48(f48(x2483,x2483),f48(x2483,f48(f48(x2484,x2484),f48(x2484,x2485)))))
% 0.56/0.69 [243]~P1(x2435)+~P1(x2434)+~P1(x2431)+~P1(x2436)+P6(x2431,f9(x2432,x2433))+~P6(f48(f48(x2436,x2436),f48(x2436,x2435)),x2433)+~P6(f48(f48(x2434,x2434),f48(x2434,x2436)),x2432)+~E(x2431,f48(f48(x2434,x2434),f48(x2434,x2435)))
% 0.56/0.69 %EqnAxiom
% 0.56/0.69 [1]E(x11,x11)
% 0.56/0.69 [2]E(x22,x21)+~E(x21,x22)
% 0.56/0.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.56/0.69 [4]~E(x41,x42)+E(f48(x41,x43),f48(x42,x43))
% 0.56/0.69 [5]~E(x51,x52)+E(f48(x53,x51),f48(x53,x52))
% 0.56/0.69 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.56/0.69 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.56/0.69 [8]~E(x81,x82)+E(f32(x81,x83,x84),f32(x82,x83,x84))
% 0.56/0.69 [9]~E(x91,x92)+E(f32(x93,x91,x94),f32(x93,x92,x94))
% 0.56/0.69 [10]~E(x101,x102)+E(f32(x103,x104,x101),f32(x103,x104,x102))
% 0.56/0.69 [11]~E(x111,x112)+E(f39(x111,x113,x114,x115,x116),f39(x112,x113,x114,x115,x116))
% 0.56/0.69 [12]~E(x121,x122)+E(f39(x123,x121,x124,x125,x126),f39(x123,x122,x124,x125,x126))
% 0.56/0.69 [13]~E(x131,x132)+E(f39(x133,x134,x131,x135,x136),f39(x133,x134,x132,x135,x136))
% 0.56/0.69 [14]~E(x141,x142)+E(f39(x143,x144,x145,x141,x146),f39(x143,x144,x145,x142,x146))
% 0.56/0.69 [15]~E(x151,x152)+E(f39(x153,x154,x155,x156,x151),f39(x153,x154,x155,x156,x152))
% 0.56/0.69 [16]~E(x161,x162)+E(f12(x161),f12(x162))
% 0.56/0.69 [17]~E(x171,x172)+E(f23(x171),f23(x172))
% 0.56/0.69 [18]~E(x181,x182)+E(f25(x181),f25(x182))
% 0.56/0.69 [19]~E(x191,x192)+E(f34(x191),f34(x192))
% 0.56/0.69 [20]~E(x201,x202)+E(f41(x201,x203),f41(x202,x203))
% 0.56/0.69 [21]~E(x211,x212)+E(f41(x213,x211),f41(x213,x212))
% 0.56/0.69 [22]~E(x221,x222)+E(f24(x221),f24(x222))
% 0.56/0.69 [23]~E(x231,x232)+E(f29(x231),f29(x232))
% 0.56/0.69 [24]~E(x241,x242)+E(f46(x241),f46(x242))
% 0.56/0.69 [25]~E(x251,x252)+E(f50(x251),f50(x252))
% 0.56/0.69 [26]~E(x261,x262)+E(f54(x261),f54(x262))
% 0.56/0.69 [27]~E(x271,x272)+E(f51(x271),f51(x272))
% 0.56/0.69 [28]~E(x281,x282)+E(f7(x281),f7(x282))
% 0.56/0.69 [29]~E(x291,x292)+E(f13(x291),f13(x292))
% 0.56/0.69 [30]~E(x301,x302)+E(f26(x301),f26(x302))
% 0.56/0.69 [31]~E(x311,x312)+E(f9(x311,x313),f9(x312,x313))
% 0.56/0.69 [32]~E(x321,x322)+E(f9(x323,x321),f9(x323,x322))
% 0.56/0.69 [33]~E(x331,x332)+E(f37(x331,x333,x334),f37(x332,x333,x334))
% 0.56/0.69 [34]~E(x341,x342)+E(f37(x343,x341,x344),f37(x343,x342,x344))
% 0.56/0.69 [35]~E(x351,x352)+E(f37(x353,x354,x351),f37(x353,x354,x352))
% 0.56/0.69 [36]~E(x361,x362)+E(f33(x361,x363,x364),f33(x362,x363,x364))
% 0.56/0.69 [37]~E(x371,x372)+E(f33(x373,x371,x374),f33(x373,x372,x374))
% 0.56/0.69 [38]~E(x381,x382)+E(f33(x383,x384,x381),f33(x383,x384,x382))
% 0.56/0.69 [39]~E(x391,x392)+E(f20(x391,x393),f20(x392,x393))
% 0.56/0.69 [40]~E(x401,x402)+E(f20(x403,x401),f20(x403,x402))
% 0.56/0.69 [41]~E(x411,x412)+E(f40(x411,x413),f40(x412,x413))
% 0.56/0.69 [42]~E(x421,x422)+E(f40(x423,x421),f40(x423,x422))
% 0.56/0.69 [43]~E(x431,x432)+E(f30(x431),f30(x432))
% 0.56/0.69 [44]~E(x441,x442)+E(f15(x441,x443),f15(x442,x443))
% 0.56/0.69 [45]~E(x451,x452)+E(f15(x453,x451),f15(x453,x452))
% 0.56/0.69 [46]~E(x461,x462)+E(f47(x461,x463),f47(x462,x463))
% 0.56/0.69 [47]~E(x471,x472)+E(f47(x473,x471),f47(x473,x472))
% 0.56/0.69 [48]~E(x481,x482)+E(f36(x481,x483,x484),f36(x482,x483,x484))
% 0.56/0.69 [49]~E(x491,x492)+E(f36(x493,x491,x494),f36(x493,x492,x494))
% 0.56/0.69 [50]~E(x501,x502)+E(f36(x503,x504,x501),f36(x503,x504,x502))
% 0.56/0.69 [51]~E(x511,x512)+E(f35(x511,x513),f35(x512,x513))
% 0.56/0.69 [52]~E(x521,x522)+E(f35(x523,x521),f35(x523,x522))
% 0.56/0.69 [53]~E(x531,x532)+E(f8(x531),f8(x532))
% 0.56/0.69 [54]~E(x541,x542)+E(f38(x541,x543,x544,x545,x546),f38(x542,x543,x544,x545,x546))
% 0.56/0.69 [55]~E(x551,x552)+E(f38(x553,x551,x554,x555,x556),f38(x553,x552,x554,x555,x556))
% 0.56/0.69 [56]~E(x561,x562)+E(f38(x563,x564,x561,x565,x566),f38(x563,x564,x562,x565,x566))
% 0.56/0.69 [57]~E(x571,x572)+E(f38(x573,x574,x575,x571,x576),f38(x573,x574,x575,x572,x576))
% 0.56/0.69 [58]~E(x581,x582)+E(f38(x583,x584,x585,x586,x581),f38(x583,x584,x585,x586,x582))
% 0.56/0.69 [59]~E(x591,x592)+E(f49(x591,x593),f49(x592,x593))
% 0.56/0.69 [60]~E(x601,x602)+E(f49(x603,x601),f49(x603,x602))
% 0.56/0.69 [61]~E(x611,x612)+E(f52(x611),f52(x612))
% 0.56/0.69 [62]~E(x621,x622)+E(f21(x621,x623),f21(x622,x623))
% 0.56/0.69 [63]~E(x631,x632)+E(f21(x633,x631),f21(x633,x632))
% 0.56/0.69 [64]~E(x641,x642)+E(f17(x641,x643),f17(x642,x643))
% 0.56/0.69 [65]~E(x651,x652)+E(f17(x653,x651),f17(x653,x652))
% 0.56/0.69 [66]~E(x661,x662)+E(f19(x661,x663),f19(x662,x663))
% 0.56/0.69 [67]~E(x671,x672)+E(f19(x673,x671),f19(x673,x672))
% 0.56/0.69 [68]~E(x681,x682)+E(f53(x681),f53(x682))
% 0.56/0.69 [69]~E(x691,x692)+E(f31(x691,x693),f31(x692,x693))
% 0.56/0.69 [70]~E(x701,x702)+E(f31(x703,x701),f31(x703,x702))
% 0.56/0.69 [71]~E(x711,x712)+E(f16(x711,x713),f16(x712,x713))
% 0.56/0.69 [72]~E(x721,x722)+E(f16(x723,x721),f16(x723,x722))
% 0.56/0.69 [73]~E(x731,x732)+E(f27(x731,x733),f27(x732,x733))
% 0.56/0.69 [74]~E(x741,x742)+E(f27(x743,x741),f27(x743,x742))
% 0.56/0.69 [75]~E(x751,x752)+E(f28(x751,x753,x754),f28(x752,x753,x754))
% 0.56/0.69 [76]~E(x761,x762)+E(f28(x763,x761,x764),f28(x763,x762,x764))
% 0.56/0.69 [77]~E(x771,x772)+E(f28(x773,x774,x771),f28(x773,x774,x772))
% 0.56/0.69 [78]~E(x781,x782)+E(f11(x781,x783),f11(x782,x783))
% 0.56/0.69 [79]~E(x791,x792)+E(f11(x793,x791),f11(x793,x792))
% 0.56/0.69 [80]~E(x801,x802)+E(f10(x801),f10(x802))
% 0.56/0.69 [81]~E(x811,x812)+E(f43(x811,x813),f43(x812,x813))
% 0.56/0.69 [82]~E(x821,x822)+E(f43(x823,x821),f43(x823,x822))
% 0.56/0.69 [83]~E(x831,x832)+E(f22(x831,x833),f22(x832,x833))
% 0.56/0.69 [84]~E(x841,x842)+E(f22(x843,x841),f22(x843,x842))
% 0.56/0.69 [85]~E(x851,x852)+E(f44(x851,x853),f44(x852,x853))
% 0.56/0.69 [86]~E(x861,x862)+E(f44(x863,x861),f44(x863,x862))
% 0.56/0.69 [87]~E(x871,x872)+E(f18(x871,x873),f18(x872,x873))
% 0.56/0.69 [88]~E(x881,x882)+E(f18(x883,x881),f18(x883,x882))
% 0.56/0.69 [89]~E(x891,x892)+E(f42(x891,x893),f42(x892,x893))
% 0.56/0.69 [90]~E(x901,x902)+E(f42(x903,x901),f42(x903,x902))
% 0.56/0.69 [91]~P1(x911)+P1(x912)+~E(x911,x912)
% 0.56/0.69 [92]~P2(x921)+P2(x922)+~E(x921,x922)
% 0.56/0.69 [93]P6(x932,x933)+~E(x931,x932)+~P6(x931,x933)
% 0.56/0.69 [94]P6(x943,x942)+~E(x941,x942)+~P6(x943,x941)
% 0.56/0.69 [95]P7(x952,x953,x954)+~E(x951,x952)+~P7(x951,x953,x954)
% 0.56/0.69 [96]P7(x963,x962,x964)+~E(x961,x962)+~P7(x963,x961,x964)
% 0.56/0.69 [97]P7(x973,x974,x972)+~E(x971,x972)+~P7(x973,x974,x971)
% 0.56/0.69 [98]~P10(x981)+P10(x982)+~E(x981,x982)
% 0.56/0.69 [99]P4(x992,x993)+~E(x991,x992)+~P4(x991,x993)
% 0.56/0.69 [100]P4(x1003,x1002)+~E(x1001,x1002)+~P4(x1003,x1001)
% 0.56/0.69 [101]~P8(x1011)+P8(x1012)+~E(x1011,x1012)
% 0.56/0.69 [102]~P12(x1021)+P12(x1022)+~E(x1021,x1022)
% 0.56/0.69 [103]P13(x1032,x1033)+~E(x1031,x1032)+~P13(x1031,x1033)
% 0.56/0.69 [104]P13(x1043,x1042)+~E(x1041,x1042)+~P13(x1043,x1041)
% 0.56/0.69 [105]P5(x1052,x1053,x1054,x1055,x1056)+~E(x1051,x1052)+~P5(x1051,x1053,x1054,x1055,x1056)
% 0.56/0.69 [106]P5(x1063,x1062,x1064,x1065,x1066)+~E(x1061,x1062)+~P5(x1063,x1061,x1064,x1065,x1066)
% 0.56/0.69 [107]P5(x1073,x1074,x1072,x1075,x1076)+~E(x1071,x1072)+~P5(x1073,x1074,x1071,x1075,x1076)
% 0.56/0.69 [108]P5(x1083,x1084,x1085,x1082,x1086)+~E(x1081,x1082)+~P5(x1083,x1084,x1085,x1081,x1086)
% 0.56/0.69 [109]P5(x1093,x1094,x1095,x1096,x1092)+~E(x1091,x1092)+~P5(x1093,x1094,x1095,x1096,x1091)
% 0.56/0.69 [110]P3(x1102,x1103)+~E(x1101,x1102)+~P3(x1101,x1103)
% 0.56/0.69 [111]P3(x1113,x1112)+~E(x1111,x1112)+~P3(x1113,x1111)
% 0.56/0.69 [112]~P9(x1121)+P9(x1122)+~E(x1121,x1122)
% 0.56/0.69 [113]P11(x1132,x1133)+~E(x1131,x1132)+~P11(x1131,x1133)
% 0.56/0.69 [114]P11(x1143,x1142)+~E(x1141,x1142)+~P11(x1143,x1141)
% 0.56/0.69
% 0.56/0.69 %-------------------------------------------
% 0.56/0.69 cnf(260,plain,
% 0.56/0.69 ($false),
% 0.56/0.69 inference(scs_inference,[],[120,118]),
% 0.56/0.69 ['proof']).
% 0.56/0.69 % SZS output end Proof
% 0.56/0.69 % Total time :0.010000s
%------------------------------------------------------------------------------