TSTP Solution File: GRP029-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP029-1 : 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 : n021.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 00:10:40 EDT 2023
% Result : Unsatisfiable 0.55s 0.88s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP029-1 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n021.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 02:31:14 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.55/0.87 %-------------------------------------------
% 0.55/0.87 % File :CSE---1.6
% 0.55/0.87 % Problem :theBenchmark
% 0.55/0.87 % Transform :cnf
% 0.55/0.87 % Format :tptp:raw
% 0.55/0.87 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.87
% 0.55/0.87 % Result :Theorem 0.270000s
% 0.55/0.87 % Output :CNFRefutation 0.270000s
% 0.55/0.87 %-------------------------------------------
% 0.55/0.87 %--------------------------------------------------------------------------
% 0.55/0.88 % File : GRP029-1 : TPTP v8.1.2. Released v1.0.0.
% 0.55/0.88 % Domain : Group Theory (Semigroups)
% 0.55/0.88 % Problem : In semigroups, left id and inverse => right id exists
% 0.55/0.88 % Version : [MOW76] axioms :
% 0.55/0.88 % Incomplete > Augmented > Complete.
% 0.55/0.88 % English : If there are a left identity and left inverse, then there
% 0.55/0.88 % is a right identity element.
% 0.55/0.88
% 0.55/0.88 % Refs : [Wos65] Wos (1965), Unpublished Note
% 0.55/0.88 % : [MOW76] McCharen et al. (1976), Problems and Experiments for a
% 0.55/0.88 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.55/0.88 % Source : [SPRFN]
% 0.55/0.88 % Names : Problem 1 [Wos65]
% 0.55/0.88 % : wos1 [WM76]
% 0.55/0.88 % : G5 [MOW76]
% 0.55/0.88 % : ident2.ver1.in [ANL]
% 0.55/0.88
% 0.55/0.88 % Status : Unsatisfiable
% 0.55/0.88 % Rating : 0.00 v6.0.0, 0.11 v5.5.0, 0.06 v5.4.0, 0.07 v5.3.0, 0.17 v5.2.0, 0.12 v5.1.0, 0.29 v5.0.0, 0.14 v4.1.0, 0.11 v4.0.1, 0.17 v3.7.0, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v2.0.0
% 0.55/0.88 % Syntax : Number of clauses : 7 ( 4 unt; 0 nHn; 4 RR)
% 0.55/0.88 % Number of literals : 15 ( 1 equ; 9 neg)
% 0.55/0.88 % Maximal clause size : 4 ( 2 avg)
% 0.55/0.88 % Maximal term depth : 2 ( 1 avg)
% 0.55/0.88 % Number of predicates : 2 ( 1 usr; 0 prp; 2-3 aty)
% 0.55/0.88 % Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% 0.55/0.88 % Number of variables : 21 ( 0 sgn)
% 0.55/0.88 % SPC : CNF_UNS_RFO_SEQ_HRN
% 0.55/0.88
% 0.55/0.88 % Comments : This may also be viewed as a group theory problem, to prove
% 0.55/0.88 % that the right identity axiom is dependant on the rest of the
% 0.55/0.88 % axiom set; i.e., each element has a right identity. Note that
% 0.55/0.88 % this is a corollary to proving that the right identity axiom
% 0.55/0.88 % is dependant on the rest of the axiom set, but also that the
% 0.55/0.88 % proof is different due to the introduction of a skolem
% 0.55/0.88 % function for the right identity of each element of the group.
% 0.55/0.88 % : The inverse_substitution substitution axioms are missing
% 0.55/0.88 % in the [MOW76] presentation.
% 0.55/0.88 %--------------------------------------------------------------------------
% 0.55/0.88 %----Include semi-group axioms
% 0.55/0.88 include('Axioms/GRP002-0.ax').
% 0.55/0.88 %--------------------------------------------------------------------------
% 0.55/0.88 cnf(left_identity,axiom,
% 0.55/0.88 product(identity,A,A) ).
% 0.55/0.88
% 0.55/0.88 cnf(left_inverse,axiom,
% 0.55/0.88 product(inverse(A),A,identity) ).
% 0.55/0.88
% 0.55/0.88 cnf(prove_there_is_a_right_identity,negated_conjecture,
% 0.55/0.88 ~ product(not_right_identity(A),A,not_right_identity(A)) ).
% 0.55/0.88
% 0.55/0.88 %--------------------------------------------------------------------------
% 0.55/0.88 %-------------------------------------------
% 0.55/0.88 % Proof found
% 0.55/0.88 % SZS status Theorem for theBenchmark
% 0.55/0.88 % SZS output start Proof
% 0.55/0.88 %ClaNum:17(EqnAxiom:10)
% 0.55/0.88 %VarNum:43(SingletonVarNum:21)
% 0.55/0.88 %MaxLitNum:4
% 0.55/0.88 %MaxfuncDepth:1
% 0.55/0.88 %SharedTerms:1
% 0.55/0.88 %goalClause: 14
% 0.55/0.88 %singleGoalClaCount:1
% 0.55/0.88 [11]P1(a1,x111,x111)
% 0.55/0.88 [12]P1(f2(x121),x121,a1)
% 0.55/0.88 [14]~P1(f4(x141),x141,f4(x141))
% 0.55/0.88 [13]P1(x131,x132,f3(x131,x132))
% 0.55/0.88 [15]~P1(x153,x154,x151)+E(x151,x152)+~P1(x153,x154,x152)
% 0.55/0.88 [16]~P1(x166,x164,x161)+P1(x161,x162,x163)+~P1(x164,x162,x165)+~P1(x166,x165,x163)
% 0.55/0.88 [17]~P1(x171,x176,x174)+P1(x171,x172,x173)+~P1(x174,x175,x173)+~P1(x176,x175,x172)
% 0.55/0.88 %EqnAxiom
% 0.55/0.88 [1]E(x11,x11)
% 0.55/0.88 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.88 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.88 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.55/0.88 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.55/0.88 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.55/0.88 [7]~E(x71,x72)+E(f4(x71),f4(x72))
% 0.55/0.88 [8]P1(x82,x83,x84)+~E(x81,x82)+~P1(x81,x83,x84)
% 0.55/0.88 [9]P1(x93,x92,x94)+~E(x91,x92)+~P1(x93,x91,x94)
% 0.55/0.88 [10]P1(x103,x104,x102)+~E(x101,x102)+~P1(x103,x104,x101)
% 0.55/0.88
% 0.55/0.88 %-------------------------------------------
% 0.55/0.88 cnf(18,plain,
% 0.55/0.88 (~E(f3(f4(x181),x181),f4(x181))),
% 0.55/0.88 inference(scs_inference,[],[14,13,10])).
% 0.55/0.88 cnf(19,plain,
% 0.55/0.88 (P1(x191,x192,f3(x191,x192))),
% 0.55/0.88 inference(rename_variables,[],[13])).
% 0.55/0.88 cnf(20,plain,
% 0.55/0.88 (E(x201,f3(a1,x201))),
% 0.55/0.88 inference(scs_inference,[],[14,11,13,19,10,15])).
% 0.55/0.88 cnf(21,plain,
% 0.55/0.88 (P1(x211,x212,f3(x211,x212))),
% 0.55/0.88 inference(rename_variables,[],[13])).
% 0.55/0.88 cnf(23,plain,
% 0.55/0.88 (P1(a1,f3(a1,a1),a1)),
% 0.55/0.88 inference(scs_inference,[],[14,11,13,19,21,10,15,17])).
% 0.55/0.88 cnf(24,plain,
% 0.55/0.88 (P1(x241,x242,f3(x241,x242))),
% 0.55/0.88 inference(rename_variables,[],[13])).
% 0.55/0.88 cnf(26,plain,
% 0.55/0.88 (P1(a1,x261,x261)),
% 0.55/0.88 inference(rename_variables,[],[11])).
% 0.55/0.88 cnf(28,plain,
% 0.55/0.88 (P1(f3(f2(x281),a1),x281,a1)),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16])).
% 0.55/0.88 cnf(32,plain,
% 0.55/0.88 (~E(f4(x321),f3(f4(x321),x321))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2])).
% 0.55/0.88 cnf(33,plain,
% 0.55/0.88 (E(f4(a1),f4(f3(a1,a1)))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2,7])).
% 0.55/0.88 cnf(34,plain,
% 0.55/0.88 (E(f3(x341,a1),f3(x341,f3(a1,a1)))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2,7,6])).
% 0.55/0.88 cnf(35,plain,
% 0.55/0.88 (E(f3(a1,x351),f3(f3(a1,a1),x351))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2,7,6,5])).
% 0.55/0.88 cnf(39,plain,
% 0.55/0.88 (P1(a1,f4(f3(a1,a1)),f4(a1))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2,7,6,5,4,8,9])).
% 0.55/0.88 cnf(41,plain,
% 0.55/0.88 (E(a1,f3(a1,f3(a1,a1)))),
% 0.55/0.88 inference(scs_inference,[],[14,11,26,13,19,21,24,12,10,15,17,16,2,7,6,5,4,8,9,3])).
% 0.55/0.88 cnf(43,plain,
% 0.55/0.88 (P1(x431,x432,f3(x431,x432))),
% 0.55/0.88 inference(rename_variables,[],[13])).
% 0.55/0.88 cnf(44,plain,
% 0.55/0.88 (~P1(f4(x441),x441,f4(x441))),
% 0.55/0.88 inference(rename_variables,[],[14])).
% 0.55/0.89 cnf(46,plain,
% 0.55/0.89 (~P1(a1,f3(f4(x461),x461),f4(x461))),
% 0.55/0.89 inference(scs_inference,[],[14,44,13,43,12,11,17,16])).
% 0.55/0.89 cnf(48,plain,
% 0.55/0.89 (~P1(f4(x481),x481,f4(x481))),
% 0.55/0.89 inference(rename_variables,[],[14])).
% 0.55/0.89 cnf(49,plain,
% 0.55/0.89 (P1(x491,x492,f3(x491,x492))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(53,plain,
% 0.55/0.89 (P1(f3(a1,x531),x532,f3(x531,x532))),
% 0.55/0.89 inference(scs_inference,[],[14,44,48,13,43,49,12,11,20,33,17,16,10,8])).
% 0.55/0.89 cnf(54,plain,
% 0.55/0.89 (E(x541,f3(a1,x541))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(55,plain,
% 0.55/0.89 (E(x551,f3(f3(a1,a1),x551))),
% 0.55/0.89 inference(scs_inference,[],[14,44,48,13,43,49,12,11,20,54,35,33,17,16,10,8,3])).
% 0.55/0.89 cnf(57,plain,
% 0.55/0.89 (E(a1,f3(f2(x571),x571))),
% 0.55/0.89 inference(scs_inference,[],[14,44,48,13,43,49,12,11,20,54,35,33,17,16,10,8,3,15])).
% 0.55/0.89 cnf(59,plain,
% 0.55/0.89 (P1(x591,x592,f3(x591,x592))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(61,plain,
% 0.55/0.89 (E(f3(a1,x611),x611)),
% 0.55/0.89 inference(scs_inference,[],[14,44,48,13,43,49,12,11,20,54,35,33,17,16,10,8,3,15,2])).
% 0.55/0.89 cnf(62,plain,
% 0.55/0.89 (P1(x621,f3(a1,x622),f3(x621,x622))),
% 0.55/0.89 inference(scs_inference,[],[14,44,48,13,43,49,59,12,11,20,54,35,33,17,16,10,8,3,15,2,9])).
% 0.55/0.89 cnf(64,plain,
% 0.55/0.89 (~P1(f3(a1,a1),f4(x641),f3(f4(x641),x641))),
% 0.55/0.89 inference(scs_inference,[],[11,23,46,17])).
% 0.55/0.89 cnf(65,plain,
% 0.55/0.89 (P1(a1,x651,x651)),
% 0.55/0.89 inference(rename_variables,[],[11])).
% 0.55/0.89 cnf(67,plain,
% 0.55/0.89 (~P1(f2(a1),f3(f4(x671),x671),f4(x671))),
% 0.55/0.89 inference(scs_inference,[],[11,65,12,23,46,17,16])).
% 0.55/0.89 cnf(68,plain,
% 0.55/0.89 (P1(a1,x681,x681)),
% 0.55/0.89 inference(rename_variables,[],[11])).
% 0.55/0.89 cnf(72,plain,
% 0.55/0.89 (E(x721,f3(f3(a1,a1),x721))),
% 0.55/0.89 inference(rename_variables,[],[55])).
% 0.55/0.89 cnf(73,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),x731),x732,f3(x731,x732))),
% 0.55/0.89 inference(scs_inference,[],[11,65,68,13,12,55,72,23,46,17,16,10,8])).
% 0.55/0.89 cnf(75,plain,
% 0.55/0.89 (~P1(a1,f4(x751),f3(f4(x751),x751))),
% 0.55/0.89 inference(scs_inference,[],[11,65,68,18,13,12,55,72,23,46,17,16,10,8,15])).
% 0.55/0.89 cnf(78,plain,
% 0.55/0.89 (E(f3(f3(a1,a1),x781),x781)),
% 0.55/0.89 inference(scs_inference,[],[11,65,68,18,13,12,55,72,23,46,17,16,10,8,15,2])).
% 0.55/0.89 cnf(79,plain,
% 0.55/0.89 (P1(x791,f3(a1,x792),f3(f3(x791,a1),x792))),
% 0.55/0.89 inference(scs_inference,[],[11,13,62,17])).
% 0.55/0.89 cnf(81,plain,
% 0.55/0.89 (P1(a1,x811,x811)),
% 0.55/0.89 inference(rename_variables,[],[11])).
% 0.55/0.89 cnf(82,plain,
% 0.55/0.89 (P1(x821,x822,f3(x821,x822))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(84,plain,
% 0.55/0.89 (~E(f3(f4(a1),f3(a1,a1)),f4(a1))),
% 0.55/0.89 inference(scs_inference,[],[11,18,13,62,34,17,3])).
% 0.55/0.89 cnf(87,plain,
% 0.55/0.89 (P1(f3(a1,f2(x871)),x871,a1)),
% 0.55/0.89 inference(scs_inference,[],[11,81,18,13,82,12,62,34,17,3,16])).
% 0.55/0.89 cnf(89,plain,
% 0.55/0.89 (P1(x891,x892,f3(x891,x892))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(91,plain,
% 0.55/0.89 (P1(f2(x911),x911,f3(a1,f3(a1,a1)))),
% 0.55/0.89 inference(scs_inference,[],[11,81,18,13,82,12,62,34,41,17,3,16,10])).
% 0.55/0.89 cnf(93,plain,
% 0.55/0.89 (E(f3(f3(a1,a1),x931),x931)),
% 0.55/0.89 inference(rename_variables,[],[78])).
% 0.55/0.89 cnf(94,plain,
% 0.55/0.89 (~P1(f4(x941),f3(f3(a1,a1),x941),f4(x941))),
% 0.55/0.89 inference(scs_inference,[],[11,81,18,13,82,12,78,93,62,34,41,14,17,3,16,10,8,9])).
% 0.55/0.89 cnf(96,plain,
% 0.55/0.89 (E(f3(f2(x961),x961),a1)),
% 0.55/0.89 inference(scs_inference,[],[11,81,18,13,82,89,12,78,93,62,34,41,14,17,3,16,10,8,9,15])).
% 0.55/0.89 cnf(100,plain,
% 0.55/0.89 (P1(f2(a1),f3(a1,x1001),f3(a1,x1001))),
% 0.55/0.89 inference(scs_inference,[],[12,13,17])).
% 0.55/0.89 cnf(101,plain,
% 0.55/0.89 (P1(x1011,x1012,f3(x1011,x1012))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(102,plain,
% 0.55/0.89 (P1(f2(x1021),x1021,a1)),
% 0.55/0.89 inference(rename_variables,[],[12])).
% 0.55/0.89 cnf(103,plain,
% 0.55/0.89 (P1(x1031,x1032,f3(x1031,x1032))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(105,plain,
% 0.55/0.89 (P1(a1,x1051,f3(f2(x1052),f3(x1052,x1051)))),
% 0.55/0.89 inference(scs_inference,[],[12,102,13,103,101,17,16])).
% 0.55/0.89 cnf(106,plain,
% 0.55/0.89 (P1(x1061,x1062,f3(x1061,x1062))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(107,plain,
% 0.55/0.89 (P1(f2(x1071),x1071,a1)),
% 0.55/0.89 inference(rename_variables,[],[12])).
% 0.55/0.89 cnf(112,plain,
% 0.55/0.89 (E(f3(f2(x1121),x1121),f3(a1,a1))),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,13,103,101,91,96,17,16,15,3])).
% 0.55/0.89 cnf(113,plain,
% 0.55/0.89 (E(x1131,f3(a1,x1131))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(115,plain,
% 0.55/0.89 (E(f3(a1,x1151),x1151)),
% 0.55/0.89 inference(rename_variables,[],[61])).
% 0.55/0.89 cnf(116,plain,
% 0.55/0.89 (~E(f4(a1),f3(f4(a1),f3(a1,a1)))),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,13,103,101,91,61,84,96,14,17,16,15,3,10,2])).
% 0.55/0.89 cnf(117,plain,
% 0.55/0.89 (P1(x1171,x1172,f3(f3(a1,x1171),x1172))),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,13,103,106,101,91,61,115,84,96,14,17,16,15,3,10,2,8])).
% 0.55/0.89 cnf(119,plain,
% 0.55/0.89 (P1(f2(x1191),f3(a1,x1191),a1)),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,113,13,103,106,101,91,61,115,84,96,14,17,16,15,3,10,2,8,9])).
% 0.55/0.89 cnf(120,plain,
% 0.55/0.89 (E(x1201,f3(a1,x1201))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(121,plain,
% 0.55/0.89 (E(f3(x1211,x1212),f3(x1211,f3(a1,x1212)))),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,113,120,13,103,106,101,91,61,115,84,96,14,17,16,15,3,10,2,8,9,6])).
% 0.55/0.89 cnf(122,plain,
% 0.55/0.89 (E(f2(x1221),f2(f3(a1,x1221)))),
% 0.55/0.89 inference(scs_inference,[],[12,102,107,20,113,120,13,103,106,101,91,61,115,84,96,14,17,16,15,3,10,2,8,9,6,4])).
% 0.55/0.89 cnf(128,plain,
% 0.55/0.89 (P1(f3(a1,x1281),x1282,f3(x1281,x1282))),
% 0.55/0.89 inference(rename_variables,[],[53])).
% 0.55/0.89 cnf(130,plain,
% 0.55/0.89 (~P1(f4(a1),f3(a1,a1),f4(a1))),
% 0.55/0.89 inference(scs_inference,[],[13,53,67,100,116,17,15])).
% 0.55/0.89 cnf(133,plain,
% 0.55/0.89 (E(x1331,f3(f3(a1,a1),f3(a1,x1331)))),
% 0.55/0.89 inference(scs_inference,[],[20,13,53,67,100,116,55,17,15,3])).
% 0.55/0.89 cnf(135,plain,
% 0.55/0.89 (P1(f2(x1351),x1351,f3(a1,a1))),
% 0.55/0.89 inference(scs_inference,[],[12,20,13,53,67,100,116,55,17,15,3,10])).
% 0.55/0.89 cnf(136,plain,
% 0.55/0.89 (E(x1361,f3(a1,x1361))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(138,plain,
% 0.55/0.89 (E(x1381,f3(a1,x1381))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(139,plain,
% 0.55/0.89 (E(f3(a1,a1),f3(f2(x1391),x1391))),
% 0.55/0.89 inference(scs_inference,[],[12,20,136,13,112,53,128,67,100,116,55,17,15,3,10,8,2])).
% 0.55/0.89 cnf(140,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),x1401),f3(a1,x1402),f3(x1401,x1402))),
% 0.55/0.89 inference(scs_inference,[],[12,20,136,138,13,73,112,53,128,67,100,116,55,17,15,3,10,8,2,9])).
% 0.55/0.89 cnf(147,plain,
% 0.55/0.89 (P1(x1471,x1472,f3(x1471,x1472))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(149,plain,
% 0.55/0.89 (E(f3(a1,x1491),f3(f2(x1492),f3(x1492,x1491)))),
% 0.55/0.89 inference(scs_inference,[],[13,147,75,105,39,17,15])).
% 0.55/0.89 cnf(151,plain,
% 0.55/0.89 (P1(x1511,x1512,f3(x1511,x1512))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(153,plain,
% 0.55/0.89 (P1(f3(a1,a1),a1,a1)),
% 0.55/0.89 inference(scs_inference,[],[13,147,151,23,75,105,39,17,15,16])).
% 0.55/0.89 cnf(165,plain,
% 0.55/0.89 (P1(x1651,x1652,f3(x1651,x1652))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(168,plain,
% 0.55/0.89 (P1(f3(x1681,a1),f3(a1,a1),f3(x1681,a1))),
% 0.55/0.89 inference(scs_inference,[],[13,165,23,135,11,17,16])).
% 0.55/0.89 cnf(170,plain,
% 0.55/0.89 (P1(x1701,x1702,f3(x1701,x1702))),
% 0.55/0.89 inference(rename_variables,[],[13])).
% 0.55/0.89 cnf(172,plain,
% 0.55/0.89 (E(f3(f3(a1,x1721),x1722),f3(x1721,x1722))),
% 0.55/0.89 inference(scs_inference,[],[13,165,170,23,135,117,11,17,16,15])).
% 0.55/0.89 cnf(175,plain,
% 0.55/0.89 (~P1(f4(a1),f3(a1,a1),f3(a1,f4(a1)))),
% 0.55/0.89 inference(scs_inference,[],[13,165,170,23,135,117,130,61,11,17,16,15,10])).
% 0.55/0.89 cnf(177,plain,
% 0.55/0.89 (P1(x1771,f3(f3(a1,a1),f3(a1,x1772)),f3(x1771,x1772))),
% 0.55/0.89 inference(scs_inference,[],[13,165,170,23,135,117,133,130,61,11,17,16,15,10,9])).
% 0.55/0.89 cnf(178,plain,
% 0.55/0.89 (E(x1781,f3(f3(a1,a1),f3(a1,x1781)))),
% 0.55/0.89 inference(rename_variables,[],[133])).
% 0.55/0.89 cnf(179,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),f3(a1,x1791)),x1792,f3(x1791,x1792))),
% 0.55/0.89 inference(scs_inference,[],[13,165,170,23,135,117,133,178,130,61,11,17,16,15,10,9,8])).
% 0.55/0.89 cnf(183,plain,
% 0.55/0.89 (P1(f3(f2(x1831),a1),x1831,a1)),
% 0.55/0.89 inference(rename_variables,[],[28])).
% 0.55/0.89 cnf(184,plain,
% 0.55/0.89 (P1(x1841,f3(f3(a1,a1),f3(a1,x1842)),f3(x1841,x1842))),
% 0.55/0.89 inference(rename_variables,[],[177])).
% 0.55/0.89 cnf(188,plain,
% 0.55/0.89 (P1(x1881,f3(f3(a1,a1),f3(a1,x1882)),f3(x1881,x1882))),
% 0.55/0.89 inference(rename_variables,[],[177])).
% 0.55/0.89 cnf(193,plain,
% 0.55/0.89 (P1(x1931,f3(f3(a1,a1),f3(a1,x1932)),f3(x1931,x1932))),
% 0.55/0.89 inference(rename_variables,[],[177])).
% 0.55/0.89 cnf(195,plain,
% 0.55/0.89 (P1(f3(a1,x1951),f3(f3(a1,a1),f3(a1,x1952)),f3(x1951,x1952))),
% 0.55/0.89 inference(scs_inference,[],[28,32,177,184,188,193,172,119,135,17,16,15,10])).
% 0.55/0.89 cnf(200,plain,
% 0.55/0.89 (P1(f3(a1,a1),f3(a1,a1),a1)),
% 0.55/0.89 inference(scs_inference,[],[28,183,23,20,32,177,184,188,193,172,119,135,17,16,15,10,9,8])).
% 0.55/0.89 cnf(201,plain,
% 0.55/0.89 (E(x2011,f3(a1,x2011))),
% 0.55/0.89 inference(rename_variables,[],[20])).
% 0.55/0.89 cnf(202,plain,
% 0.55/0.89 (E(f3(x2021,f3(a1,x2022)),f3(x2021,x2022))),
% 0.55/0.89 inference(scs_inference,[],[28,183,23,20,32,177,184,188,193,172,119,135,61,17,16,15,10,9,8,6])).
% 0.55/0.89 cnf(206,plain,
% 0.55/0.89 (E(x2061,f3(f2(x2062),f3(x2062,x2061)))),
% 0.55/0.89 inference(scs_inference,[],[28,183,23,20,201,32,177,184,188,193,172,149,119,135,61,17,16,15,10,9,8,6,4,7,2,3])).
% 0.55/0.89 cnf(208,plain,
% 0.55/0.89 (~P1(f3(a1,a1),f3(f4(x2081),x2081),f4(x2081))),
% 0.55/0.89 inference(scs_inference,[],[23,75,11,17])).
% 0.55/0.89 cnf(226,plain,
% 0.55/0.89 (E(f3(f2(x2261),f3(x2261,x2262)),x2262)),
% 0.55/0.89 inference(scs_inference,[],[206,2])).
% 0.55/0.89 cnf(227,plain,
% 0.55/0.89 (~P1(f3(a1,a1),f4(x2271),f3(f4(x2271),f3(a1,x2271)))),
% 0.55/0.89 inference(scs_inference,[],[206,64,202,2,10])).
% 0.55/0.89 cnf(229,plain,
% 0.55/0.89 (E(f3(x2291,f3(a1,x2292)),f3(x2291,x2292))),
% 0.55/0.89 inference(rename_variables,[],[202])).
% 0.55/0.89 cnf(230,plain,
% 0.55/0.89 (~P1(f3(a1,a1),f3(f4(x2301),f3(a1,x2301)),f4(x2301))),
% 0.55/0.89 inference(scs_inference,[],[206,208,64,202,229,2,10,9])).
% 0.55/0.89 cnf(233,plain,
% 0.55/0.89 (P1(f3(f2(x2331),x2331),f3(a1,a1),a1)),
% 0.55/0.89 inference(scs_inference,[],[23,206,208,64,202,229,57,2,10,9,8])).
% 0.55/0.89 cnf(241,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),f3(a1,x2411)),x2412,f3(x2411,x2412))),
% 0.55/0.89 inference(rename_variables,[],[179])).
% 0.55/0.89 cnf(245,plain,
% 0.55/0.89 (P1(a1,x2451,x2451)),
% 0.55/0.89 inference(rename_variables,[],[11])).
% 0.55/0.89 cnf(252,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),f3(a1,x2521)),f3(a1,x2522),f3(x2521,x2522))),
% 0.55/0.89 inference(scs_inference,[],[20,227,230,179,241,122,79,195,11,245,13,17,10,8,16,9])).
% 0.55/0.89 cnf(268,plain,
% 0.55/0.89 (P1(a1,f3(f3(a1,a1),f3(a1,a1)),a1)),
% 0.55/0.89 inference(scs_inference,[],[23,200,233,133,195,17,8,16])).
% 0.55/0.89 cnf(273,plain,
% 0.55/0.89 (E(f3(f2(a1),x2731),x2731)),
% 0.55/0.89 inference(scs_inference,[],[23,226,200,175,233,121,172,133,195,17,8,16,10,3])).
% 0.55/0.89 cnf(277,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),f3(a1,x2771)),f3(a1,x2772),f3(x2771,x2772))),
% 0.55/0.89 inference(rename_variables,[],[252])).
% 0.55/0.89 cnf(283,plain,
% 0.55/0.89 (P1(f3(x2831,a1),a1,f3(x2831,a1))),
% 0.55/0.89 inference(scs_inference,[],[153,252,277,179,168,18,17,15,16])).
% 0.55/0.89 cnf(287,plain,
% 0.55/0.89 (E(x2871,f3(f2(a1),x2871))),
% 0.55/0.89 inference(scs_inference,[],[153,273,252,277,179,168,18,17,15,16,2])).
% 0.55/0.89 cnf(296,plain,
% 0.55/0.89 (P1(f3(f2(x2961),f3(a1,a1)),x2961,a1)),
% 0.55/0.89 inference(scs_inference,[],[28,32,283,121,15,8])).
% 0.55/0.89 cnf(300,plain,
% 0.55/0.89 (E(x3001,f3(f2(a1),x3001))),
% 0.55/0.89 inference(rename_variables,[],[287])).
% 0.55/0.89 cnf(301,plain,
% 0.55/0.89 (P1(f3(a1,a1),f3(f2(a1),f3(a1,a1)),a1)),
% 0.55/0.89 inference(scs_inference,[],[287,300,200,100,8,9])).
% 0.55/0.89 cnf(314,plain,
% 0.55/0.89 (P1(f3(f3(a1,a1),f2(x3141)),f3(a1,x3141),f3(a1,a1))),
% 0.55/0.89 inference(scs_inference,[],[39,301,296,112,140,133,61,17,8,2,10])).
% 0.55/0.89 cnf(324,plain,
% 0.55/0.89 (P1(f3(x3241,a1),a1,f3(x3241,a1))),
% 0.55/0.89 inference(rename_variables,[],[283])).
% 0.55/0.89 cnf(326,plain,
% 0.55/0.89 (~P1(x3261,a1,f4(f3(a1,a1)))),
% 0.55/0.89 inference(scs_inference,[],[39,41,94,314,268,87,139,283,324,73,17,15,8,9,16])).
% 0.55/0.89 cnf(331,plain,
% 0.55/0.89 ($false),
% 0.55/0.89 inference(scs_inference,[],[326,296,87,11,17]),
% 0.55/0.89 ['proof']).
% 0.55/0.89 % SZS output end Proof
% 0.55/0.89 % Total time :0.270000s
%------------------------------------------------------------------------------