TSTP Solution File: GRP037-3 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP037-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : Thu Aug 31 00:10:42 EDT 2023
% Result : Unsatisfiable 0.53s 0.74s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % 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 02:59:40 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.53/0.74 %-------------------------------------------
% 0.53/0.74 % File :CSE---1.6
% 0.53/0.74 % Problem :theBenchmark
% 0.53/0.74 % Transform :cnf
% 0.53/0.74 % Format :tptp:raw
% 0.53/0.74 % Command :java -jar mcs_scs.jar %d %s
% 0.53/0.74
% 0.53/0.74 % Result :Theorem 0.150000s
% 0.53/0.74 % Output :CNFRefutation 0.150000s
% 0.53/0.74 %-------------------------------------------
% 0.53/0.74 %--------------------------------------------------------------------------
% 0.53/0.74 % File : GRP037-3 : TPTP v8.1.2. Released v1.0.0.
% 0.53/0.74 % Domain : Group Theory (Subgroups)
% 0.53/0.74 % Problem : In subgroups, the inverse of an element is unique
% 0.53/0.74 % Version : [Wos65] axioms.
% 0.53/0.74 % English :
% 0.53/0.74
% 0.53/0.74 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.53/0.74 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.53/0.74 % Source : [SPRFN]
% 0.53/0.74 % Names : Problem 17 [Wos65]
% 0.53/0.74 % : wos17 [WM76]
% 0.53/0.74
% 0.53/0.74 % Status : Unsatisfiable
% 0.53/0.74 % Rating : 0.00 v6.0.0, 0.11 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.25 v5.2.0, 0.12 v5.1.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.7.0, 0.00 v2.6.0, 0.14 v2.5.0, 0.00 v2.0.0
% 0.53/0.74 % Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 14 RR)
% 0.53/0.74 % Number of literals : 39 ( 4 equ; 21 neg)
% 0.53/0.74 % Maximal clause size : 4 ( 2 avg)
% 0.53/0.74 % Maximal term depth : 2 ( 1 avg)
% 0.53/0.74 % Number of predicates : 3 ( 2 usr; 0 prp; 1-3 aty)
% 0.53/0.74 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% 0.53/0.74 % Number of variables : 38 ( 0 sgn)
% 0.53/0.74 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.53/0.74
% 0.53/0.74 % Comments :
% 0.53/0.74 %--------------------------------------------------------------------------
% 0.53/0.74 %----Include group theory axioms
% 0.53/0.74 include('Axioms/GRP003-0.ax').
% 0.53/0.74 %----Include sub-group theory axioms
% 0.53/0.74 include('Axioms/GRP003-2.ax').
% 0.53/0.74 %--------------------------------------------------------------------------
% 0.53/0.74 cnf(another_left_identity,hypothesis,
% 0.53/0.74 ( ~ subgroup_member(A)
% 0.53/0.74 | product(another_identity,A,A) ) ).
% 0.53/0.74
% 0.53/0.74 cnf(another_right_identity,hypothesis,
% 0.53/0.74 ( ~ subgroup_member(A)
% 0.53/0.74 | product(A,another_identity,A) ) ).
% 0.53/0.74
% 0.53/0.74 cnf(another_right_inverse,hypothesis,
% 0.53/0.74 ( ~ subgroup_member(A)
% 0.53/0.74 | product(A,another_inverse(A),another_identity) ) ).
% 0.53/0.74
% 0.53/0.74 cnf(another_left_inverse,hypothesis,
% 0.53/0.74 ( ~ subgroup_member(A)
% 0.53/0.74 | product(another_inverse(A),A,another_identity) ) ).
% 0.53/0.74
% 0.53/0.74 cnf(another_inverse_in_subgroup,hypothesis,
% 0.53/0.74 ( ~ subgroup_member(A)
% 0.53/0.74 | subgroup_member(another_inverse(A)) ) ).
% 0.53/0.74
% 0.53/0.74 cnf(product_right_cancellation,hypothesis,
% 0.53/0.74 ( ~ product(A,B,C)
% 0.53/0.74 | ~ product(A,D,C)
% 0.53/0.74 | D = B ) ).
% 0.53/0.74
% 0.53/0.74 cnf(product_left_cancellation,hypothesis,
% 0.53/0.74 ( ~ product(A,B,C)
% 0.53/0.74 | ~ product(D,B,C)
% 0.53/0.74 | D = A ) ).
% 0.53/0.74
% 0.53/0.74 cnf(a_is_in_subgroup,hypothesis,
% 0.53/0.74 subgroup_member(a) ).
% 0.53/0.74
% 0.53/0.74 cnf(another_identity_in_subgroup,hypothesis,
% 0.53/0.74 subgroup_member(another_identity) ).
% 0.53/0.74
% 0.53/0.74 cnf(prove_two_inverses_are_equal,negated_conjecture,
% 0.53/0.74 inverse(a) != another_inverse(a) ).
% 0.53/0.74
% 0.53/0.74 %--------------------------------------------------------------------------
% 0.53/0.74 %-------------------------------------------
% 0.53/0.74 % Proof found
% 0.53/0.74 % SZS status Theorem for theBenchmark
% 0.53/0.74 % SZS output start Proof
% 0.53/0.74 %ClaNum:30(EqnAxiom:11)
% 0.53/0.74 %VarNum:80(SingletonVarNum:38)
% 0.53/0.74 %MaxLitNum:4
% 0.53/0.74 %MaxfuncDepth:1
% 0.53/0.74 %SharedTerms:8
% 0.53/0.74 %goalClause: 19
% 0.53/0.74 %singleGoalClaCount:1
% 0.53/0.74 [12]P1(a1)
% 0.53/0.74 [13]P1(a2)
% 0.53/0.74 [19]~E(f5(a2),f4(a2))
% 0.53/0.74 [14]P2(x141,a3,x141)
% 0.53/0.74 [15]P2(a3,x151,x151)
% 0.53/0.74 [16]P2(x161,f5(x161),a3)
% 0.53/0.74 [17]P2(f5(x171),x171,a3)
% 0.53/0.74 [18]P2(x181,x182,f6(x181,x182))
% 0.53/0.74 [21]~P1(x211)+P2(x211,a1,x211)
% 0.53/0.74 [22]~P1(x221)+P2(a1,x221,x221)
% 0.53/0.74 [20]~P1(x201)+P1(f4(x201))
% 0.53/0.74 [23]~P1(x231)+P2(x231,f4(x231),a1)
% 0.53/0.74 [24]~P1(x241)+P2(f4(x241),x241,a1)
% 0.53/0.74 [26]~P2(x263,x264,x261)+E(x261,x262)+~P2(x263,x264,x262)
% 0.53/0.74 [27]~P2(x273,x271,x274)+E(x271,x272)+~P2(x273,x272,x274)
% 0.53/0.74 [28]~P2(x281,x283,x284)+E(x281,x282)+~P2(x282,x283,x284)
% 0.53/0.74 [25]P1(x251)+~P1(x252)+~P1(x253)+~P2(x253,f5(x252),x251)
% 0.53/0.74 [29]~P2(x296,x294,x291)+P2(x291,x292,x293)+~P2(x294,x292,x295)+~P2(x296,x295,x293)
% 0.53/0.74 [30]~P2(x301,x306,x304)+P2(x301,x302,x303)+~P2(x304,x305,x303)+~P2(x306,x305,x302)
% 0.53/0.74 %EqnAxiom
% 0.53/0.74 [1]E(x11,x11)
% 0.53/0.74 [2]E(x22,x21)+~E(x21,x22)
% 0.53/0.74 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.53/0.74 [4]~E(x41,x42)+E(f5(x41),f5(x42))
% 0.53/0.74 [5]~E(x51,x52)+E(f4(x51),f4(x52))
% 0.53/0.74 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.53/0.74 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.53/0.74 [8]~P1(x81)+P1(x82)+~E(x81,x82)
% 0.53/0.74 [9]P2(x92,x93,x94)+~E(x91,x92)+~P2(x91,x93,x94)
% 0.53/0.74 [10]P2(x103,x102,x104)+~E(x101,x102)+~P2(x103,x101,x104)
% 0.53/0.74 [11]P2(x113,x114,x112)+~E(x111,x112)+~P2(x113,x114,x111)
% 0.53/0.74
% 0.53/0.74 %-------------------------------------------
% 0.53/0.75 cnf(31,plain,
% 0.53/0.75 (E(f6(x311,a3),x311)),
% 0.53/0.75 inference(scs_inference,[],[14,18,28])).
% 0.53/0.75 cnf(32,plain,
% 0.53/0.75 (P2(x321,x322,f6(x321,x322))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(33,plain,
% 0.53/0.75 (P2(x331,a3,x331)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(35,plain,
% 0.53/0.75 (E(f6(a3,x351),x351)),
% 0.53/0.75 inference(scs_inference,[],[14,15,18,32,28,27])).
% 0.53/0.75 cnf(36,plain,
% 0.53/0.75 (P2(x361,x362,f6(x361,x362))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(37,plain,
% 0.53/0.75 (P2(a3,x371,x371)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(39,plain,
% 0.53/0.75 (E(x391,f6(x391,a3))),
% 0.53/0.75 inference(scs_inference,[],[14,33,15,18,32,36,28,27,26])).
% 0.53/0.75 cnf(40,plain,
% 0.53/0.75 (P2(x401,x402,f6(x401,x402))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(42,plain,
% 0.53/0.75 (P2(x421,f6(a3,a3),x421)),
% 0.53/0.75 inference(scs_inference,[],[14,33,15,18,32,36,40,28,27,26,30])).
% 0.53/0.75 cnf(43,plain,
% 0.53/0.75 (P2(x431,x432,f6(x431,x432))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(46,plain,
% 0.53/0.75 (P2(x461,x462,f6(x461,x462))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(48,plain,
% 0.53/0.75 (~E(f4(a2),f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,18,32,36,40,43,28,27,26,30,25,2])).
% 0.53/0.75 cnf(51,plain,
% 0.53/0.75 (P2(a2,a1,a2)),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21])).
% 0.53/0.75 cnf(57,plain,
% 0.53/0.75 (P1(f4(a1))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20])).
% 0.53/0.75 cnf(59,plain,
% 0.53/0.75 (E(f6(x591,f6(x592,a3)),f6(x591,x592))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20,7])).
% 0.53/0.75 cnf(60,plain,
% 0.53/0.75 (E(f6(f6(x601,a3),x602),f6(x601,x602))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20,7,6])).
% 0.53/0.75 cnf(61,plain,
% 0.53/0.75 (E(f4(f6(x611,a3)),f4(x611))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20,7,6,5])).
% 0.53/0.75 cnf(63,plain,
% 0.53/0.75 (P1(f6(a1,a3))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20,7,6,5,4,8])).
% 0.53/0.75 cnf(64,plain,
% 0.53/0.75 (~E(f5(a2),f6(f4(a2),a3))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,15,12,13,18,32,36,40,43,28,27,26,30,25,2,22,21,24,23,20,7,6,5,4,8,3])).
% 0.53/0.75 cnf(66,plain,
% 0.53/0.75 (P2(x661,x662,f6(x661,x662))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(67,plain,
% 0.53/0.75 (P2(x671,a3,x671)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(68,plain,
% 0.53/0.75 (P2(a3,x681,x681)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(72,plain,
% 0.53/0.75 (P2(x721,x722,f6(f6(a3,x721),x722))),
% 0.53/0.75 inference(scs_inference,[],[19,14,33,67,15,37,68,12,13,18,32,36,40,43,46,66,28,27,26,30,25,2,22,21,24,23,20,7,6,5,4,8,3,29,11,10,9])).
% 0.53/0.75 cnf(73,plain,
% 0.53/0.75 (~P2(f4(a2),f5(f5(a2)),a3)),
% 0.53/0.75 inference(scs_inference,[],[19,16,28])).
% 0.53/0.75 cnf(74,plain,
% 0.53/0.75 (P2(x741,f5(x741),a3)),
% 0.53/0.75 inference(rename_variables,[],[16])).
% 0.53/0.75 cnf(76,plain,
% 0.53/0.75 (~P2(f5(a3),f5(a2),f4(a2))),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,17,28,29])).
% 0.53/0.75 cnf(77,plain,
% 0.53/0.75 (P2(x771,f5(x771),a3)),
% 0.53/0.75 inference(rename_variables,[],[16])).
% 0.53/0.75 cnf(78,plain,
% 0.53/0.75 (P2(f5(x781),x781,a3)),
% 0.53/0.75 inference(rename_variables,[],[17])).
% 0.53/0.75 cnf(82,plain,
% 0.53/0.75 (P2(a3,x821,x821)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(84,plain,
% 0.53/0.75 (P2(x841,a3,x841)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(85,plain,
% 0.53/0.75 (E(f6(f6(x851,a3),f6(x852,a3)),f6(x851,x852))),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,17,14,15,59,60,28,29,2,10,9,3])).
% 0.53/0.75 cnf(87,plain,
% 0.53/0.75 (~P2(a2,f4(a2),a3)),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,77,17,14,15,59,60,28,29,2,10,9,3,27])).
% 0.53/0.75 cnf(88,plain,
% 0.53/0.75 (P2(x881,f5(x881),a3)),
% 0.53/0.75 inference(rename_variables,[],[16])).
% 0.53/0.75 cnf(90,plain,
% 0.53/0.75 (~P2(f5(a2),a3,f4(a2))),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,77,17,14,84,15,59,60,28,29,2,10,9,3,27,26])).
% 0.53/0.75 cnf(93,plain,
% 0.53/0.75 (~P2(a3,f4(a2),f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,77,17,78,14,84,15,82,59,60,28,29,2,10,9,3,27,26,30])).
% 0.53/0.75 cnf(97,plain,
% 0.53/0.75 (P2(x971,f5(x971),f6(a3,a3))),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,77,88,17,78,14,84,15,82,59,60,39,28,29,2,10,9,3,27,26,30,11])).
% 0.53/0.75 cnf(99,plain,
% 0.53/0.75 (P1(a3)),
% 0.53/0.75 inference(scs_inference,[],[19,16,74,77,88,17,78,14,84,15,82,13,59,60,39,28,29,2,10,9,3,27,26,30,11,25])).
% 0.53/0.75 cnf(102,plain,
% 0.53/0.75 (~P2(f4(a2),x1021,f6(f5(a2),x1021))),
% 0.53/0.75 inference(scs_inference,[],[18,48,28])).
% 0.53/0.75 cnf(103,plain,
% 0.53/0.75 (P2(x1031,x1032,f6(x1031,x1032))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(105,plain,
% 0.53/0.75 (~P2(f4(a2),a3,f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[18,103,64,48,28,26])).
% 0.53/0.75 cnf(106,plain,
% 0.53/0.75 (P2(x1061,x1062,f6(x1061,x1062))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(109,plain,
% 0.53/0.75 (P2(x1091,x1092,f6(x1091,x1092))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(111,plain,
% 0.53/0.75 (~P2(f5(a2),f5(a3),f4(a2))),
% 0.53/0.75 inference(scs_inference,[],[18,103,106,17,14,13,64,48,90,28,26,25,30])).
% 0.53/0.75 cnf(112,plain,
% 0.53/0.75 (P2(x1121,a3,x1121)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(113,plain,
% 0.53/0.75 (P2(f5(x1131),x1131,a3)),
% 0.53/0.75 inference(rename_variables,[],[17])).
% 0.53/0.75 cnf(116,plain,
% 0.53/0.75 (P2(x1161,x1162,f6(x1161,x1162))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(120,plain,
% 0.53/0.75 (~E(f5(a2),f4(f6(a2,a3)))),
% 0.53/0.75 inference(scs_inference,[],[18,103,106,109,17,113,14,112,13,61,64,48,90,19,28,26,25,30,29,3])).
% 0.53/0.75 cnf(122,plain,
% 0.53/0.75 (~P2(x1221,f4(a2),f6(x1221,f5(a2)))),
% 0.53/0.75 inference(scs_inference,[],[18,103,106,109,116,17,113,14,112,13,61,64,48,90,19,28,26,25,30,29,3,27])).
% 0.53/0.75 cnf(126,plain,
% 0.53/0.75 (E(f6(x1261,a3),x1261)),
% 0.53/0.75 inference(rename_variables,[],[31])).
% 0.53/0.75 cnf(127,plain,
% 0.53/0.75 (~E(f6(f4(a2),a3),f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[31,18,103,106,109,116,17,113,14,112,13,61,64,48,76,90,19,28,26,25,30,29,3,27,9,2])).
% 0.53/0.75 cnf(128,plain,
% 0.53/0.75 (~P2(f5(a3),f5(a2),f6(f4(a2),a3))),
% 0.53/0.75 inference(scs_inference,[],[31,126,18,103,106,109,116,17,113,14,112,13,61,64,48,76,90,19,28,26,25,30,29,3,27,9,2,11])).
% 0.53/0.75 cnf(129,plain,
% 0.53/0.75 (E(f6(x1291,a3),x1291)),
% 0.53/0.75 inference(rename_variables,[],[31])).
% 0.53/0.75 cnf(130,plain,
% 0.53/0.75 (~P2(f5(a3),f6(f5(a2),a3),f4(a2))),
% 0.53/0.75 inference(scs_inference,[],[31,126,129,18,103,106,109,116,17,113,14,112,13,61,64,48,76,90,19,28,26,25,30,29,3,27,9,2,11,10])).
% 0.53/0.75 cnf(132,plain,
% 0.53/0.75 (E(x1321,f5(f5(x1321)))),
% 0.53/0.75 inference(scs_inference,[],[16,17,28])).
% 0.53/0.75 cnf(136,plain,
% 0.53/0.75 (P2(a3,x1361,x1361)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(137,plain,
% 0.53/0.75 (P2(x1371,f5(x1371),a3)),
% 0.53/0.75 inference(rename_variables,[],[16])).
% 0.53/0.75 cnf(141,plain,
% 0.53/0.75 (P2(a3,x1411,x1411)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(142,plain,
% 0.53/0.75 (P2(x1421,f5(x1421),a3)),
% 0.53/0.75 inference(rename_variables,[],[16])).
% 0.53/0.75 cnf(148,plain,
% 0.53/0.75 (~E(f6(f5(a2),a3),f4(a2))),
% 0.53/0.75 inference(scs_inference,[],[16,137,142,15,136,141,18,17,122,39,19,28,29,26,30,3])).
% 0.53/0.75 cnf(161,plain,
% 0.53/0.75 (~P2(f5(a2),a3,f6(f4(a2),a3))),
% 0.53/0.75 inference(scs_inference,[],[14,127,28])).
% 0.53/0.75 cnf(162,plain,
% 0.53/0.75 (P2(x1621,a3,x1621)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(164,plain,
% 0.53/0.75 (~P2(x1641,f6(f5(x1641),f4(a2)),f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[14,18,16,127,93,28,29])).
% 0.53/0.75 cnf(165,plain,
% 0.53/0.75 (P2(x1651,x1652,f6(x1651,x1652))),
% 0.53/0.75 inference(rename_variables,[],[18])).
% 0.53/0.75 cnf(167,plain,
% 0.53/0.75 (~P2(a3,f5(a2),f6(f4(a2),a3))),
% 0.53/0.75 inference(scs_inference,[],[14,15,18,16,127,93,28,29,27])).
% 0.53/0.75 cnf(168,plain,
% 0.53/0.75 (P2(a3,x1681,x1681)),
% 0.53/0.75 inference(rename_variables,[],[15])).
% 0.53/0.75 cnf(171,plain,
% 0.53/0.75 (P2(x1711,a3,x1711)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(173,plain,
% 0.53/0.75 (~P2(f4(a2),x1731,f6(f5(a2),f6(a3,x1731)))),
% 0.53/0.75 inference(scs_inference,[],[14,162,171,15,18,165,16,127,102,93,28,29,27,26,30])).
% 0.53/0.75 cnf(175,plain,
% 0.53/0.75 (P2(x1751,a3,x1751)),
% 0.53/0.75 inference(rename_variables,[],[14])).
% 0.53/0.75 cnf(176,plain,
% 0.53/0.75 (~P2(f4(a2),x1761,f6(f5(a2),x1761))),
% 0.53/0.75 inference(rename_variables,[],[102])).
% 0.53/0.75 cnf(179,plain,
% 0.53/0.75 (E(f6(a3,x1791),x1791)),
% 0.53/0.75 inference(rename_variables,[],[35])).
% 0.53/0.75 cnf(180,plain,
% 0.53/0.75 (~E(f4(a2),f6(f5(a2),a3))),
% 0.53/0.75 inference(scs_inference,[],[35,14,162,171,175,15,18,165,16,31,127,102,176,93,28,29,27,26,30,3,11])).
% 0.53/0.75 cnf(183,plain,
% 0.53/0.75 (P2(f5(f5(a3)),x1831,x1831)),
% 0.53/0.75 inference(scs_inference,[],[35,14,162,171,175,15,168,18,165,16,31,132,127,102,176,93,28,29,27,26,30,3,11,9])).
% 0.53/0.75 cnf(185,plain,
% 0.53/0.75 (~E(f4(f6(a2,a3)),f5(a2))),
% 0.53/0.75 inference(scs_inference,[],[35,14,162,171,175,15,168,18,165,16,31,132,127,102,176,120,93,28,29,27,26,30,3,11,9,2])).
% 0.53/0.75 cnf(186,plain,
% 0.53/0.75 (P2(x1861,x1862,f6(f6(a3,x1861),f6(a3,x1862)))),
% 0.53/0.76 inference(scs_inference,[],[35,179,14,162,171,175,15,168,18,165,16,31,132,72,127,102,176,120,93,28,29,27,26,30,3,11,9,2,10])).
% 0.53/0.76 cnf(188,plain,
% 0.53/0.76 (P2(f4(a2),a2,a1)),
% 0.53/0.76 inference(scs_inference,[],[13,35,179,14,162,171,175,15,168,18,165,16,31,132,72,127,102,176,120,93,28,29,27,26,30,3,11,9,2,10,24])).
% 0.53/0.76 cnf(198,plain,
% 0.53/0.76 (E(f4(f6(a3,x1981)),f4(x1981))),
% 0.53/0.76 inference(scs_inference,[],[13,35,179,14,162,171,175,15,168,18,165,16,31,132,72,127,102,176,120,57,93,28,29,27,26,30,3,11,9,2,10,24,23,21,22,20,5])).
% 0.53/0.76 cnf(199,plain,
% 0.53/0.76 (E(f6(x1991,f6(a3,x1992)),f6(x1991,x1992))),
% 0.53/0.76 inference(scs_inference,[],[13,35,179,14,162,171,175,15,168,18,165,16,31,132,72,127,102,176,120,57,93,28,29,27,26,30,3,11,9,2,10,24,23,21,22,20,5,7])).
% 0.53/0.76 cnf(202,plain,
% 0.53/0.76 (~P2(f6(f5(a2),a3),a3,f4(a2))),
% 0.53/0.76 inference(scs_inference,[],[14,148,28])).
% 0.53/0.76 cnf(203,plain,
% 0.53/0.76 (P2(x2031,a3,x2031)),
% 0.53/0.76 inference(rename_variables,[],[14])).
% 0.53/0.76 cnf(205,plain,
% 0.53/0.76 (P1(f5(f5(a2)))),
% 0.53/0.76 inference(scs_inference,[],[13,14,148,132,28,8])).
% 0.53/0.76 cnf(207,plain,
% 0.53/0.76 (~P2(a3,f4(a2),f6(f5(a2),a3))),
% 0.53/0.76 inference(scs_inference,[],[13,17,14,15,130,148,132,28,8,30])).
% 0.53/0.76 cnf(208,plain,
% 0.53/0.76 (P2(f5(x2081),x2081,a3)),
% 0.53/0.76 inference(rename_variables,[],[17])).
% 0.53/0.76 cnf(213,plain,
% 0.53/0.76 (P2(x2131,a3,x2131)),
% 0.53/0.76 inference(rename_variables,[],[14])).
% 0.53/0.76 cnf(221,plain,
% 0.53/0.76 (~E(f4(a2),f6(f5(a2),f6(a3,a3)))),
% 0.53/0.76 inference(scs_inference,[],[13,17,208,14,203,213,15,130,199,180,148,173,185,132,48,28,8,30,29,27,26,3])).
% 0.53/0.76 cnf(225,plain,
% 0.53/0.76 (E(x2251,f6(a3,x2251))),
% 0.53/0.76 inference(scs_inference,[],[13,35,17,208,14,203,213,15,130,199,180,148,164,173,185,132,48,28,8,30,29,27,26,3,9,2])).
% 0.53/0.76 cnf(227,plain,
% 0.53/0.76 (E(f6(a3,x2271),x2271)),
% 0.53/0.76 inference(rename_variables,[],[35])).
% 0.53/0.76 cnf(228,plain,
% 0.53/0.76 (~P2(f4(a2),f6(a3,a3),f5(a2))),
% 0.53/0.76 inference(scs_inference,[],[13,35,227,17,208,14,203,213,15,130,199,180,148,164,105,173,185,132,48,28,8,30,29,27,26,3,9,2,11,10])).
% 0.53/0.76 cnf(233,plain,
% 0.53/0.76 (E(f6(f6(a3,x2331),f6(a3,a3)),x2331)),
% 0.53/0.76 inference(scs_inference,[],[14,97,186,205,25,28])).
% 0.53/0.76 cnf(235,plain,
% 0.53/0.76 (P2(x2351,a3,x2351)),
% 0.53/0.76 inference(rename_variables,[],[14])).
% 0.53/0.76 cnf(238,plain,
% 0.53/0.76 (P2(x2381,f5(x2381),a3)),
% 0.53/0.76 inference(rename_variables,[],[16])).
% 0.53/0.76 cnf(241,plain,
% 0.53/0.76 (P2(x2411,f5(x2411),a3)),
% 0.53/0.76 inference(rename_variables,[],[16])).
% 0.53/0.76 cnf(242,plain,
% 0.53/0.76 (P2(x2421,x2422,f6(x2421,x2422))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(245,plain,
% 0.53/0.76 (P2(x2451,a3,x2451)),
% 0.53/0.76 inference(rename_variables,[],[14])).
% 0.53/0.76 cnf(248,plain,
% 0.53/0.76 (P2(x2481,f5(a3),x2481)),
% 0.53/0.76 inference(scs_inference,[],[14,235,245,18,16,238,241,17,97,186,202,205,25,28,27,26,30,29])).
% 0.53/0.76 cnf(251,plain,
% 0.53/0.76 (P2(f6(x2511,a3),a3,x2511)),
% 0.53/0.76 inference(scs_inference,[],[14,235,245,39,18,16,238,241,17,97,186,202,205,25,28,27,26,30,29,9])).
% 0.53/0.76 cnf(253,plain,
% 0.53/0.76 (~E(f6(f5(a2),f6(a3,a3)),f4(a2))),
% 0.53/0.76 inference(scs_inference,[],[14,235,245,39,18,16,238,241,17,97,186,202,205,221,25,28,27,26,30,29,9,2])).
% 0.53/0.76 cnf(256,plain,
% 0.53/0.76 (P2(x2561,x2562,f6(x2561,f6(a3,x2562)))),
% 0.53/0.76 inference(scs_inference,[],[14,235,245,39,35,18,242,16,238,241,17,97,186,202,205,221,25,28,27,26,30,29,9,2,11,10])).
% 0.53/0.76 cnf(267,plain,
% 0.53/0.76 (P2(x2671,a3,x2671)),
% 0.53/0.76 inference(rename_variables,[],[14])).
% 0.53/0.76 cnf(268,plain,
% 0.53/0.76 (P2(a3,x2681,x2681)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(271,plain,
% 0.53/0.76 (P2(a3,x2711,x2711)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(277,plain,
% 0.53/0.76 (~E(f6(f4(a2),f6(a3,a3)),f5(a2))),
% 0.53/0.76 inference(scs_inference,[],[14,267,15,268,18,17,233,183,228,253,120,28,30,27,26,2,11])).
% 0.53/0.76 cnf(279,plain,
% 0.53/0.76 (P2(f6(a3,a3),x2791,x2791)),
% 0.53/0.76 inference(scs_inference,[],[14,267,39,15,268,271,18,17,233,183,228,253,120,28,30,27,26,2,11,9])).
% 0.53/0.76 cnf(280,plain,
% 0.53/0.76 (E(x2801,f6(x2801,a3))),
% 0.53/0.76 inference(rename_variables,[],[39])).
% 0.53/0.76 cnf(283,plain,
% 0.53/0.76 (P2(x2831,f6(x2832,a3),f6(x2831,f6(a3,x2832)))),
% 0.53/0.76 inference(scs_inference,[],[14,267,39,280,15,268,271,18,17,256,233,183,228,225,253,120,28,30,27,26,2,11,9,3,10])).
% 0.53/0.76 cnf(288,plain,
% 0.53/0.76 (P2(x2881,f6(a3,a3),x2881)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(291,plain,
% 0.53/0.76 (P2(x2911,f6(a3,a3),x2911)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(292,plain,
% 0.53/0.76 (P2(a3,x2921,x2921)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(296,plain,
% 0.53/0.76 (P2(a3,x2961,x2961)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(299,plain,
% 0.53/0.76 (P2(a3,x2991,x2991)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(304,plain,
% 0.53/0.76 (~E(f5(a2),f6(f4(a2),f6(a3,a3)))),
% 0.53/0.76 inference(scs_inference,[],[15,292,296,299,42,288,291,207,277,73,28,29,30,27,26,2])).
% 0.53/0.76 cnf(306,plain,
% 0.53/0.76 (E(f6(x3061,a3),x3061)),
% 0.53/0.76 inference(rename_variables,[],[31])).
% 0.53/0.76 cnf(307,plain,
% 0.53/0.76 (~P2(f6(a3,a3),f4(a2),f6(f5(a2),a3))),
% 0.53/0.76 inference(scs_inference,[],[15,292,296,299,42,288,291,31,306,111,207,277,73,28,29,30,27,26,2,11,9])).
% 0.53/0.76 cnf(326,plain,
% 0.53/0.76 (P2(x3261,x3262,f6(x3261,x3262))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(327,plain,
% 0.53/0.76 (P2(x3271,f6(a3,a3),x3271)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(334,plain,
% 0.53/0.76 (P2(x3341,f6(a3,a3),x3341)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(337,plain,
% 0.53/0.76 (P2(a3,x3371,x3371)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(338,plain,
% 0.53/0.76 (P2(x3381,f6(a3,a3),x3381)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(342,plain,
% 0.53/0.76 (P2(a3,x3421,x3421)),
% 0.53/0.76 inference(rename_variables,[],[15])).
% 0.53/0.76 cnf(347,plain,
% 0.53/0.76 (P2(x3471,f6(a3,a3),f6(x3471,a3))),
% 0.53/0.76 inference(scs_inference,[],[15,337,342,42,327,334,338,31,18,326,35,17,85,283,51,167,87,28,29,26,30,27,2,11,9])).
% 0.53/0.76 cnf(355,plain,
% 0.53/0.76 (E(x3551,f6(x3551,a3))),
% 0.53/0.76 inference(rename_variables,[],[39])).
% 0.53/0.76 cnf(356,plain,
% 0.53/0.76 (~P2(f4(a2),a2,f5(a3))),
% 0.53/0.76 inference(scs_inference,[],[16,39,18,17,128,304,63,28,8,29])).
% 0.53/0.76 cnf(357,plain,
% 0.53/0.76 (P2(x3571,f5(x3571),a3)),
% 0.53/0.76 inference(rename_variables,[],[16])).
% 0.53/0.76 cnf(364,plain,
% 0.53/0.76 (P2(x3641,f6(a3,a3),x3641)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(366,plain,
% 0.53/0.76 (~P2(f6(f5(a2),a3),f6(a3,a3),f4(a2))),
% 0.53/0.76 inference(scs_inference,[],[16,357,42,364,39,18,17,279,128,307,304,63,28,8,29,27,26,30])).
% 0.53/0.76 cnf(368,plain,
% 0.53/0.76 (P2(f6(a3,a3),x3681,x3681)),
% 0.53/0.76 inference(rename_variables,[],[279])).
% 0.53/0.76 cnf(370,plain,
% 0.53/0.76 (P2(f6(f6(a3,a3),a3),x3701,x3701)),
% 0.53/0.76 inference(scs_inference,[],[16,357,42,364,39,355,18,17,279,368,128,307,304,63,28,8,29,27,26,30,9])).
% 0.53/0.76 cnf(377,plain,
% 0.53/0.76 (~P2(f5(a2),f5(f4(a2)),a3)),
% 0.53/0.76 inference(scs_inference,[],[16,19,28])).
% 0.53/0.76 cnf(378,plain,
% 0.53/0.76 (P2(x3781,f5(x3781),a3)),
% 0.53/0.76 inference(rename_variables,[],[16])).
% 0.53/0.76 cnf(380,plain,
% 0.53/0.76 (P2(x3801,f5(f6(a3,a3)),f6(x3801,a3))),
% 0.53/0.76 inference(scs_inference,[],[16,378,42,18,19,28,29])).
% 0.53/0.76 cnf(381,plain,
% 0.53/0.76 (P2(x3811,f5(x3811),a3)),
% 0.53/0.76 inference(rename_variables,[],[16])).
% 0.53/0.76 cnf(382,plain,
% 0.53/0.76 (P2(x3821,x3822,f6(x3821,x3822))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(385,plain,
% 0.53/0.76 (P2(x3851,f6(a3,a3),x3851)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(394,plain,
% 0.53/0.76 (~P2(f5(a2),f6(a3,a3),f6(f4(a2),a3))),
% 0.53/0.76 inference(scs_inference,[],[16,378,381,42,385,31,18,382,251,161,221,185,19,28,29,26,30,27,10])).
% 0.53/0.76 cnf(405,plain,
% 0.53/0.76 (P2(x4051,x4052,f6(x4051,x4052))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(409,plain,
% 0.53/0.76 (P2(f5(x4091),x4091,a3)),
% 0.53/0.76 inference(rename_variables,[],[17])).
% 0.53/0.76 cnf(412,plain,
% 0.53/0.76 (P2(x4121,f6(a3,a3),x4121)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(413,plain,
% 0.53/0.76 (P2(f5(x4131),x4131,a3)),
% 0.53/0.76 inference(rename_variables,[],[17])).
% 0.53/0.76 cnf(417,plain,
% 0.53/0.76 (P2(x4171,x4172,f6(x4171,x4172))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(420,plain,
% 0.53/0.76 (P2(x4201,x4202,f6(x4201,x4202))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(428,plain,
% 0.53/0.76 (~E(f6(a3,f5(a2)),f4(a2))),
% 0.53/0.76 inference(scs_inference,[],[17,409,413,48,42,412,35,18,405,417,420,370,380,93,99,25,28,29,27,26,30,3,2])).
% 0.53/0.76 cnf(430,plain,
% 0.53/0.76 (E(x4301,f6(x4301,a3))),
% 0.53/0.76 inference(rename_variables,[],[39])).
% 0.53/0.76 cnf(432,plain,
% 0.53/0.76 (E(x4321,f6(x4321,a3))),
% 0.53/0.76 inference(rename_variables,[],[39])).
% 0.53/0.76 cnf(433,plain,
% 0.53/0.76 (P2(f5(x4331),x4331,f6(a3,a3))),
% 0.53/0.76 inference(scs_inference,[],[17,409,413,48,42,412,39,430,432,35,18,405,417,420,370,380,93,99,25,28,29,27,26,30,3,2,10,9,11])).
% 0.53/0.76 cnf(450,plain,
% 0.53/0.76 (P2(f5(x4501),x4501,a3)),
% 0.53/0.76 inference(rename_variables,[],[17])).
% 0.53/0.76 cnf(464,plain,
% 0.53/0.76 (P2(f5(x4641),x4641,a3)),
% 0.53/0.76 inference(rename_variables,[],[17])).
% 0.53/0.76 cnf(467,plain,
% 0.53/0.76 (~E(a2,f5(f4(a2)))),
% 0.53/0.76 inference(scs_inference,[],[17,450,464,48,42,18,433,366,198,347,394,428,377,279,64,28,26,30,29,27,2,10])).
% 0.53/0.76 cnf(471,plain,
% 0.53/0.76 (~E(a1,f5(a3))),
% 0.53/0.76 inference(scs_inference,[],[17,450,464,48,42,39,18,433,366,198,347,394,428,188,377,356,279,64,28,26,30,29,27,2,10,9,11])).
% 0.53/0.76 cnf(475,plain,
% 0.53/0.76 (P2(x4751,x4752,f6(x4751,x4752))),
% 0.53/0.76 inference(rename_variables,[],[18])).
% 0.53/0.76 cnf(477,plain,
% 0.53/0.76 (~P2(x4771,a1,f6(x4771,f5(a3)))),
% 0.53/0.76 inference(scs_inference,[],[18,475,471,28,27])).
% 0.53/0.76 cnf(535,plain,
% 0.53/0.76 (P2(x5351,f6(a3,a3),x5351)),
% 0.53/0.76 inference(rename_variables,[],[42])).
% 0.53/0.76 cnf(542,plain,
% 0.53/0.76 ($false),
% 0.53/0.76 inference(scs_inference,[],[51,42,535,477,467,97,248,471,28,26,30,29,27]),
% 0.53/0.76 ['proof']).
% 0.53/0.76 % SZS output end Proof
% 0.53/0.76 % Total time :0.150000s
%------------------------------------------------------------------------------