TSTP Solution File: MSC008-2.002 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : MSC008-2.002 : 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 : n022.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 09:20:43 EDT 2023
% Result : Unsatisfiable 2.40s 2.47s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MSC008-2.002 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 13:45:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 2.40/2.46 %-------------------------------------------
% 2.40/2.46 % File :CSE---1.6
% 2.40/2.46 % Problem :theBenchmark
% 2.40/2.46 % Transform :cnf
% 2.40/2.46 % Format :tptp:raw
% 2.40/2.46 % Command :java -jar mcs_scs.jar %d %s
% 2.40/2.46
% 2.40/2.46 % Result :Theorem 1.830000s
% 2.40/2.46 % Output :CNFRefutation 1.830000s
% 2.40/2.46 %-------------------------------------------
% 2.40/2.46 %--------------------------------------------------------------------------
% 2.40/2.46 % File : MSC008-2.002 : TPTP v8.1.2. Released v1.0.0.
% 2.40/2.46 % Domain : Miscellaneous
% 2.40/2.46 % Problem : The inconstructability of a Graeco-Latin Square
% 2.40/2.46 % Version : Especial.
% 2.40/2.46 % Theorem formulation : Buggy; A 2x2 square.
% 2.40/2.46 % English : The constructibility of Graeco-Latin squares of order 4t+2.
% 2.40/2.46 % This is impossible for t=0,1, but possible for all other
% 2.40/2.46 % cases.
% 2.40/2.46
% 2.40/2.46 % Refs : [Rob63] Robinson (1963), Theorem Proving on the Computer
% 2.40/2.46 % Source : [SPRFN]
% 2.40/2.46 % Names : LATINSQ [SPRFN]
% 2.40/2.46 % : - [Rob63]
% 2.40/2.46
% 2.40/2.46 % Status : Unsatisfiable
% 2.40/2.46 % Rating : 0.00 v6.2.0, 0.12 v6.1.0, 0.00 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.00 v2.4.0, 0.00 v2.1.0, 0.00 v2.0.0
% 2.40/2.46 % Syntax : Number of clauses : 16 ( 2 unt; 7 nHn; 9 RR)
% 2.40/2.46 % Number of literals : 40 ( 0 equ; 18 neg)
% 2.40/2.46 % Maximal clause size : 6 ( 2 avg)
% 2.40/2.46 % Maximal term depth : 1 ( 1 avg)
% 2.40/2.46 % Number of predicates : 3 ( 3 usr; 0 prp; 2-3 aty)
% 2.40/2.46 % Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% 2.40/2.46 % Number of variables : 45 ( 0 sgn)
% 2.40/2.46 % SPC : CNF_UNS_EPR_NEQ_NHN
% 2.40/2.46
% 2.40/2.46 % Comments : This uses the form of the theorem given in [Rob63], which fails
% 2.40/2.46 % to capture the intended semantics. The error is that the clauses
% 2.40/2.46 % with type "theorem" insist that two squares with the same Greek
% 2.40/2.46 % and Latin elements be in the same row OR the same column. What
% 2.40/2.46 % is required that the two squares be the same (i.e., there cannot
% 2.40/2.46 % be two such squares) so that they are in the same row AND the
% 2.40/2.46 % same column.
% 2.40/2.46 %--------------------------------------------------------------------------
% 2.40/2.46 cnf(p1_is_not_p2,axiom,
% 2.40/2.46 ~ eq(p1,p2) ).
% 2.40/2.46
% 2.40/2.46 cnf(reflexivity,axiom,
% 2.40/2.46 eq(A,A) ).
% 2.40/2.46
% 2.40/2.46 cnf(symmetry,axiom,
% 2.40/2.46 ( ~ eq(A,B)
% 2.40/2.46 | eq(B,A) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(latin_element_is_unique,axiom,
% 2.40/2.46 ( ~ latin(A,B,C)
% 2.40/2.46 | ~ latin(A,B,D)
% 2.40/2.46 | eq(D,C) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(latin_column_is_unique,axiom,
% 2.40/2.46 ( ~ latin(A,B,C)
% 2.40/2.46 | ~ latin(A,D,C)
% 2.40/2.46 | eq(D,B) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(latin_row_is_unique,axiom,
% 2.40/2.46 ( ~ latin(A,B,C)
% 2.40/2.46 | ~ latin(D,B,C)
% 2.40/2.46 | eq(D,A) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(greek_element_is_unique,axiom,
% 2.40/2.46 ( ~ greek(A,B,C)
% 2.40/2.46 | ~ greek(A,B,D)
% 2.40/2.46 | eq(D,C) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(greek_column_is_unique,axiom,
% 2.40/2.46 ( ~ greek(A,B,C)
% 2.40/2.46 | ~ greek(A,D,C)
% 2.40/2.46 | eq(D,B) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(greek_row_is_unique,axiom,
% 2.40/2.46 ( ~ greek(A,B,C)
% 2.40/2.46 | ~ greek(D,B,C)
% 2.40/2.46 | eq(D,A) ) ).
% 2.40/2.46
% 2.40/2.46 cnf(latin_cell_element,axiom,
% 2.40/2.46 ( latin(E,F,p1)
% 2.40/2.46 | latin(E,F,p2) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(latin_column_required,axiom,
% 2.40/2.47 ( latin(G,p1,H)
% 2.40/2.47 | latin(G,p2,H) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(latin_row_required,axiom,
% 2.40/2.47 ( latin(p1,I,J)
% 2.40/2.47 | latin(p2,I,J) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(greek_cell_element,axiom,
% 2.40/2.47 ( greek(K,L,p1)
% 2.40/2.47 | greek(K,L,p2) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(greek_column_required,axiom,
% 2.40/2.47 ( greek(M,p1,N)
% 2.40/2.47 | greek(M,p2,N) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(greek_row_required,axiom,
% 2.40/2.47 ( greek(p1,O,P)
% 2.40/2.47 | greek(p2,O,P) ) ).
% 2.40/2.47
% 2.40/2.47 cnf(no_two_same,negated_conjecture,
% 2.40/2.47 ( ~ greek(A,B,C)
% 2.40/2.47 | ~ latin(A,B,D)
% 2.40/2.47 | ~ greek(E,F,C)
% 2.40/2.47 | ~ latin(E,F,D)
% 2.40/2.47 | eq(F,B)
% 2.40/2.47 | eq(E,A) ) ).
% 2.40/2.47
% 2.40/2.47 %----This is the fixed version. Original is wrong I think
% 2.40/2.47 %input_clause(no_two_same1,hypothesis,
% 2.40/2.47 % [--greek(A,B,C),
% 2.40/2.47 % --latin(A,B,D),
% 2.40/2.47 % --greek(E,F,C),
% 2.40/2.47 % --latin(E,F,D),
% 2.40/2.47 % ++eq(F,B)]).
% 2.40/2.47 %input_clause(no_two_same2,negated_conjecture,
% 2.40/2.47 % [--greek(A,B,C),
% 2.40/2.47 % --latin(A,B,D),
% 2.40/2.47 % --greek(E,F,C),
% 2.40/2.47 % --latin(E,F,D),
% 2.40/2.47 % ++eq(E,A)]).
% 2.40/2.47 %--------------------------------------------------------------------------
% 2.40/2.47 %-------------------------------------------
% 2.40/2.47 % Proof found
% 2.40/2.47 % SZS status Theorem for theBenchmark
% 2.40/2.47 % SZS output start Proof
% 2.40/2.47 %ClaNum:16(EqnAxiom:0)
% 2.40/2.47 %VarNum:94(SingletonVarNum:45)
% 2.40/2.47 %MaxLitNum:6
% 2.40/2.47 %MaxfuncDepth:0
% 2.40/2.47 %SharedTerms:3
% 2.40/2.47 %goalClause: 16
% 2.40/2.47 [2]~P1(a1,a2)
% 2.40/2.47 [1]P1(x11,x11)
% 2.40/2.47 [3]~P1(x32,x31)+P1(x31,x32)
% 2.40/2.47 [4]P2(x41,x42,a2)+P2(x41,x42,a1)
% 2.40/2.47 [5]P3(x51,x52,a2)+P3(x51,x52,a1)
% 2.40/2.47 [6]P2(x61,a2,x62)+P2(x61,a1,x62)
% 2.40/2.47 [7]P3(x71,a2,x72)+P3(x71,a1,x72)
% 2.40/2.47 [8]P2(a2,x81,x82)+P2(a1,x81,x82)
% 2.40/2.47 [9]P3(a2,x91,x92)+P3(a1,x91,x92)
% 2.40/2.47 [10]~P2(x103,x104,x102)+P1(x101,x102)+~P2(x103,x104,x101)
% 2.40/2.47 [11]~P3(x113,x114,x112)+P1(x111,x112)+~P3(x113,x114,x111)
% 2.40/2.47 [12]~P2(x123,x122,x124)+P1(x121,x122)+~P2(x123,x121,x124)
% 2.40/2.47 [13]~P3(x133,x132,x134)+P1(x131,x132)+~P3(x133,x131,x134)
% 2.40/2.47 [14]~P2(x142,x143,x144)+P1(x141,x142)+~P2(x141,x143,x144)
% 2.40/2.47 [15]~P3(x152,x153,x154)+P1(x151,x152)+~P3(x151,x153,x154)
% 2.40/2.47 [16]~P2(x164,x162,x165)+~P3(x164,x162,x166)+P1(x161,x162)+~P2(x163,x161,x165)+P1(x163,x164)+~P3(x163,x161,x166)
% 2.40/2.47 %EqnAxiom
% 2.40/2.47
% 2.40/2.47 %-------------------------------------------
% 2.40/2.47 cnf(18,plain,
% 2.40/2.47 (~P3(a1,x181,x182)+~P3(a2,x181,x182)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15])).
% 2.40/2.47 cnf(19,plain,
% 2.40/2.47 (~P2(a1,x191,x192)+~P2(a2,x191,x192)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15,14])).
% 2.40/2.47 cnf(21,plain,
% 2.40/2.47 (~P3(x211,a1,x212)+~P3(x211,a2,x212)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15,14,13])).
% 2.40/2.47 cnf(23,plain,
% 2.40/2.47 (~P2(x231,a1,x232)+~P2(x231,a2,x232)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15,14,13,12])).
% 2.40/2.47 cnf(25,plain,
% 2.40/2.47 (~P3(x251,x252,a1)+~P3(x251,x252,a2)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15,14,13,12,11])).
% 2.40/2.47 cnf(27,plain,
% 2.40/2.47 (~P2(x271,x272,a1)+~P2(x271,x272,a2)),
% 2.40/2.47 inference(scs_inference,[],[2,3,15,14,13,12,11,10])).
% 2.40/2.47 cnf(29,plain,
% 2.40/2.47 (~P3(a1,a1,x291)+~P2(a2,a2,x292)+~P3(a2,a2,x291)+~P2(a1,a1,x292)),
% 2.40/2.47 inference(scs_inference,[],[2,16])).
% 2.40/2.47 cnf(30,plain,
% 2.40/2.47 (~P2(a2,x301,a1)+P2(a1,x301,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,19])).
% 2.40/2.47 cnf(31,plain,
% 2.40/2.47 (~P3(a2,x311,a1)+P3(a1,x311,a2)),
% 2.40/2.47 inference(scs_inference,[],[5,18])).
% 2.40/2.47 cnf(34,plain,
% 2.40/2.47 (P2(a2,x341,a2)+~P2(a1,x341,a1)),
% 2.40/2.47 inference(scs_inference,[],[8,27])).
% 2.40/2.47 cnf(35,plain,
% 2.40/2.47 (~P3(a1,x351,a2)+P3(a2,x351,a1)),
% 2.40/2.47 inference(scs_inference,[],[9,25])).
% 2.40/2.47 cnf(36,plain,
% 2.40/2.47 (~P2(a1,a2,a2)+~P2(a2,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[30,23])).
% 2.40/2.47 cnf(38,plain,
% 2.40/2.47 (P2(a1,a1,a1)+P2(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[34,6])).
% 2.40/2.47 cnf(39,plain,
% 2.40/2.47 (P2(a2,a1,a2)+~P2(a1,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[36,4])).
% 2.40/2.47 cnf(40,plain,
% 2.40/2.47 (~P2(a2,a1,a1)+P2(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[38,19])).
% 2.40/2.47 cnf(41,plain,
% 2.40/2.47 (P2(a1,a2,a1)+P2(a2,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[39,4])).
% 2.40/2.47 cnf(43,plain,
% 2.40/2.47 (~P2(a2,a2,a2)+P2(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[41,23])).
% 2.40/2.47 cnf(44,plain,
% 2.40/2.47 (~P2(a2,a1,a1)+P2(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[43,40])).
% 2.40/2.47 cnf(45,plain,
% 2.40/2.47 (P2(a1,x451,a1)+~P2(a2,x451,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,19])).
% 2.40/2.47 cnf(47,plain,
% 2.40/2.47 (~P2(x471,a2,a1)+P2(x471,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,23])).
% 2.40/2.47 cnf(48,plain,
% 2.40/2.47 (~P2(a2,a1,a2)+~P2(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[47,19])).
% 2.40/2.47 cnf(51,plain,
% 2.40/2.47 (P2(a2,x511,a1)+~P2(a1,x511,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,19])).
% 2.40/2.47 cnf(52,plain,
% 2.40/2.47 (P2(a1,a1,a2)+P2(a2,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[51,6])).
% 2.40/2.47 cnf(53,plain,
% 2.40/2.47 (P2(a1,a1,a2)+~P2(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[52,27])).
% 2.40/2.47 cnf(54,plain,
% 2.40/2.47 (~P2(a2,a2,a2)+~P2(a1,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[53,27])).
% 2.40/2.47 cnf(55,plain,
% 2.40/2.47 (~P2(a2,a2,a2)+P2(a2,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[54,8])).
% 2.40/2.47 cnf(56,plain,
% 2.40/2.47 (P2(a2,a1,a1)+P2(a1,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[55,8])).
% 2.40/2.47 cnf(60,plain,
% 2.40/2.47 (P2(x601,a2,a2)+~P2(x601,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[4,23])).
% 2.40/2.47 cnf(61,plain,
% 2.40/2.47 (~P2(a1,a1,a2)+P2(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[60,51])).
% 2.40/2.47 cnf(62,plain,
% 2.40/2.47 (~P2(a1,a1,a2)+~P2(a2,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[61,27])).
% 2.40/2.47 cnf(65,plain,
% 2.40/2.47 (P2(x651,a1,a1)+~P2(x651,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,23])).
% 2.40/2.47 cnf(66,plain,
% 2.40/2.47 (P2(a1,a1,a1)+~P2(a2,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[65,30])).
% 2.40/2.47 cnf(67,plain,
% 2.40/2.47 (~P3(a2,a2,x671)+~P3(a1,a1,x671)+~P2(a2,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[66,29])).
% 2.40/2.47 cnf(77,plain,
% 2.40/2.47 (P2(x771,a2,a1)+~P2(x771,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,23])).
% 2.40/2.47 cnf(78,plain,
% 2.40/2.47 (~P2(a1,a1,a1)+P2(a2,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[77,34])).
% 2.40/2.47 cnf(85,plain,
% 2.40/2.47 (P2(a1,a1,a1)+~P3(a2,a2,x851)+~P3(a1,a1,x851)+~P2(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[4,29])).
% 2.40/2.47 cnf(86,plain,
% 2.40/2.47 (P3(a1,x861,a1)+~P3(a2,x861,a2)),
% 2.40/2.47 inference(scs_inference,[],[5,18])).
% 2.40/2.47 cnf(87,plain,
% 2.40/2.47 (P3(a2,a1,a2)+P3(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[86,7])).
% 2.40/2.47 cnf(88,plain,
% 2.40/2.47 (~P3(a1,a1,a1)+P3(a2,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[87,21])).
% 2.40/2.47 cnf(89,plain,
% 2.40/2.47 (~P3(a2,a2,a2)+~P3(a1,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[88,21])).
% 2.40/2.47 cnf(90,plain,
% 2.40/2.47 (P3(a2,a1,a1)+~P3(a2,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[89,9])).
% 2.40/2.47 cnf(91,plain,
% 2.40/2.47 (P3(a1,a2,a2)+P3(a2,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[90,9])).
% 2.40/2.47 cnf(92,plain,
% 2.40/2.47 (~P3(a2,a1,a2)+P3(a1,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[91,25])).
% 2.40/2.47 cnf(93,plain,
% 2.40/2.47 (P3(a2,a2,a1)+~P3(a2,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[92,35])).
% 2.40/2.47 cnf(94,plain,
% 2.40/2.47 (~P3(a1,a2,a1)+~P3(a2,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[93,18])).
% 2.40/2.47 cnf(95,plain,
% 2.40/2.47 (P3(a2,a1,a1)+~P3(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[94,5])).
% 2.40/2.47 cnf(96,plain,
% 2.40/2.47 (P3(a1,a1,a2)+~P3(a1,a2,a1)),
% 2.40/2.47 inference(scs_inference,[],[95,31])).
% 2.40/2.47 cnf(97,plain,
% 2.40/2.47 (~P3(a2,a2,a2)+P3(a1,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[96,86])).
% 2.40/2.47 cnf(98,plain,
% 2.40/2.47 (P3(a2,a2,a1)+P3(a1,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[97,5])).
% 2.40/2.47 cnf(109,plain,
% 2.40/2.47 (P3(x1091,a1,a1)+~P3(x1091,a2,a2)),
% 2.40/2.47 inference(scs_inference,[],[5,21])).
% 2.40/2.47 cnf(110,plain,
% 2.40/2.47 (P3(a2,a2,a2)+P3(a1,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[109,9])).
% 2.40/2.47 cnf(145,plain,
% 2.40/2.47 (P3(a2,a2,a1)+~P3(a1,a1,a1)),
% 2.40/2.47 inference(scs_inference,[],[5,89])).
% 2.40/2.47 cnf(148,plain,
% 2.40/2.47 (~P3(x1481,a2,a1)+P3(x1481,a1,a2)),
% 2.40/2.47 inference(scs_inference,[],[5,21])).
% 2.40/2.48 cnf(149,plain,
% 2.40/2.48 (~P3(a1,a1,a2)+~P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[148,18])).
% 2.40/2.48 cnf(150,plain,
% 2.40/2.48 (~P3(a2,a2,a1)+P3(a1,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[149,5])).
% 2.40/2.48 cnf(151,plain,
% 2.40/2.48 (~P2(a2,a2,a1)+~P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[150,67])).
% 2.40/2.48 cnf(152,plain,
% 2.40/2.48 (~P3(a2,a2,a1)+P2(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[151,4])).
% 2.40/2.48 cnf(161,plain,
% 2.40/2.48 (P3(x1611,a2,a2)+~P3(x1611,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[5,21])).
% 2.40/2.48 cnf(162,plain,
% 2.40/2.48 (~P2(a2,a2,a1)+~P3(a2,a1,a1)+~P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[161,67])).
% 2.40/2.48 cnf(163,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P3(a1,a1,a2)+P2(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[162,4])).
% 2.40/2.48 cnf(164,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P3(a1,a1,a2)+~P2(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[163,19])).
% 2.40/2.48 cnf(165,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P3(a1,a1,a2)+P2(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[164,6])).
% 2.40/2.48 cnf(166,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P3(a1,a1,a2)+~P2(a1,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[165,27])).
% 2.40/2.48 cnf(167,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P3(a1,a1,a2)+P2(a2,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[166,8])).
% 2.40/2.48 cnf(168,plain,
% 2.40/2.48 (P2(a1,a2,a1)+~P3(a2,a1,a1)+~P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[167,44])).
% 2.40/2.48 cnf(169,plain,
% 2.40/2.48 (~P3(a2,a1,a1)+~P2(a2,a1,a2)+~P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[168,48])).
% 2.40/2.48 cnf(170,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+~P3(a1,a1,a2)+P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[169,7])).
% 2.40/2.48 cnf(323,plain,
% 2.40/2.48 (P3(a2,a2,a1)+~P2(a2,a1,a2)+P3(a1,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[5,170])).
% 2.40/2.48 cnf(324,plain,
% 2.40/2.48 (P3(a2,a2,a1)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[323,145])).
% 2.40/2.48 cnf(325,plain,
% 2.40/2.48 (~P3(a1,a1,a2)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[324,149])).
% 2.40/2.48 cnf(326,plain,
% 2.40/2.48 (~P3(a2,a2,a2)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[325,97])).
% 2.40/2.48 cnf(327,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+P3(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[326,9])).
% 2.40/2.48 cnf(328,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+P3(a1,a1,a1)),
% 2.40/2.48 inference(scs_inference,[],[327,109])).
% 2.40/2.48 cnf(329,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+~P3(a1,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[328,21])).
% 2.40/2.48 cnf(330,plain,
% 2.40/2.48 (~P2(a1,a2,a2)+~P3(a1,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[329,39])).
% 2.40/2.48 cnf(338,plain,
% 2.40/2.48 (~P2(a1,a2,a2)+P3(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[5,330])).
% 2.40/2.48 cnf(339,plain,
% 2.40/2.48 (~P2(a1,a2,a2)+P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[338,35])).
% 2.40/2.48 cnf(340,plain,
% 2.40/2.48 (P3(a1,a1,a1)+~P2(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[339,150])).
% 2.40/2.48 cnf(341,plain,
% 2.40/2.48 (~P2(a1,a2,a2)+~P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[340,25])).
% 2.40/2.48 cnf(342,plain,
% 2.40/2.48 (~P2(a1,a2,a2)+~P3(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[341,97])).
% 2.40/2.48 cnf(343,plain,
% 2.40/2.48 (~P3(a2,a2,a2)+~P2(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[342,30])).
% 2.40/2.48 cnf(344,plain,
% 2.40/2.48 (~P2(a1,a1,a1)+~P3(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[343,78])).
% 2.40/2.48 cnf(345,plain,
% 2.40/2.48 (P2(a2,a2,a2)+~P3(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[344,38])).
% 2.40/2.48 cnf(346,plain,
% 2.40/2.48 (~P3(a2,a2,a2)+P2(a1,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[345,45])).
% 2.40/2.48 cnf(347,plain,
% 2.40/2.48 (P3(a1,a1,a1)+P2(a1,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[346,110])).
% 2.40/2.48 cnf(348,plain,
% 2.40/2.48 (P2(a1,a2,a1)+P3(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[347,161])).
% 2.40/2.48 cnf(349,plain,
% 2.40/2.48 (P2(a1,a2,a1)+P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[348,35])).
% 2.40/2.48 cnf(350,plain,
% 2.40/2.48 (P2(a2,a2,a2)+P2(a1,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[349,152])).
% 2.40/2.48 cnf(351,plain,
% 2.40/2.48 (P2(a1,a2,a1)+~P2(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[350,27])).
% 2.40/2.48 cnf(352,plain,
% 2.40/2.48 (P2(a1,a2,a1)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[351,77])).
% 2.40/2.48 cnf(353,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+P2(a2,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[352,34])).
% 2.40/2.48 cnf(354,plain,
% 2.40/2.48 (P2(a1,a1,a2)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[353,53])).
% 2.40/2.48 cnf(355,plain,
% 2.40/2.48 (~P2(a2,a2,a1)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[354,62])).
% 2.40/2.48 cnf(356,plain,
% 2.40/2.48 (~P2(a1,a1,a1)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[355,78])).
% 2.40/2.48 cnf(357,plain,
% 2.40/2.48 (~P2(a2,a1,a2)+~P2(a1,a2,a2)),
% 2.40/2.48 inference(scs_inference,[],[356,65])).
% 2.40/2.48 cnf(358,plain,
% 2.40/2.48 (P2(a2,a1,a1)+~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[357,56])).
% 2.40/2.48 cnf(359,plain,
% 2.40/2.48 (~P2(a2,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[358,27])).
% 2.40/2.48 cnf(374,plain,
% 2.40/2.48 (~P3(a1,a1,x3741)+~P3(a2,a2,x3741)),
% 2.40/2.48 inference(scs_inference,[],[359,47,34,8,6,4,85])).
% 2.40/2.48 cnf(375,plain,
% 2.40/2.48 (~P3(a2,a2,a1)),
% 2.40/2.48 inference(scs_inference,[],[359,47,34,8,6,4,85,150])).
% 2.40/2.48 cnf(378,plain,
% 2.40/2.48 (P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[375,98])).
% 2.40/2.48 cnf(383,plain,
% 2.40/2.48 (~P3(a1,a1,a2)),
% 2.40/2.48 inference(scs_inference,[],[375,374,5])).
% 2.40/2.48 cnf(384,plain,
% 2.40/2.48 ($false),
% 2.40/2.48 inference(scs_inference,[],[378,383]),
% 2.40/2.48 ['proof']).
% 2.40/2.48 % SZS output end Proof
% 2.40/2.48 % Total time :1.830000s
%------------------------------------------------------------------------------