TSTP Solution File: GRP124-7.004 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n007.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 00:11:02 EDT 2023
% Result : Unsatisfiable 1.60s 1.67s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 23:10:43 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.50/0.56 start to proof:theBenchmark
% 1.60/1.66 %-------------------------------------------
% 1.60/1.66 % File :CSE---1.6
% 1.60/1.66 % Problem :theBenchmark
% 1.60/1.66 % Transform :cnf
% 1.60/1.66 % Format :tptp:raw
% 1.60/1.66 % Command :java -jar mcs_scs.jar %d %s
% 1.60/1.66
% 1.60/1.66 % Result :Theorem 1.060000s
% 1.60/1.66 % Output :CNFRefutation 1.060000s
% 1.60/1.66 %-------------------------------------------
% 1.60/1.66 %--------------------------------------------------------------------------
% 1.60/1.66 % File : GRP124-7.004 : TPTP v8.1.2. Released v1.2.0.
% 1.60/1.66 % Domain : Group Theory (Quasigroups)
% 1.60/1.66 % Problem : (3,1,2) conjugate orthogonality
% 1.60/1.66 % Version : [Sla93] axioms : Augmented.
% 1.60/1.66 % Theorem formulation : Uses a second group.
% 1.60/1.66 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 1.60/1.66 % Generate the multiplication table for the specified quasi-
% 1.60/1.66 % group with 4 elements.
% 1.60/1.66
% 1.60/1.66 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 1.60/1.66 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 1.60/1.66 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 1.60/1.66 % Source : [TPTP]
% 1.60/1.66 % Names :
% 1.60/1.66
% 1.60/1.66 % Status : Unsatisfiable
% 1.60/1.66 % Rating : 0.00 v2.1.0
% 1.60/1.66 % Syntax : Number of clauses : 37 ( 27 unt; 2 nHn; 35 RR)
% 1.60/1.66 % Number of literals : 63 ( 0 equ; 33 neg)
% 1.60/1.66 % Maximal clause size : 6 ( 1 avg)
% 1.60/1.66 % Maximal term depth : 1 ( 1 avg)
% 1.60/1.66 % Number of predicates : 7 ( 7 usr; 0 prp; 1-3 aty)
% 1.60/1.66 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 1.60/1.66 % Number of variables : 37 ( 0 sgn)
% 1.60/1.66 % SPC : CNF_UNS_EPR_NEQ_NHN
% 1.60/1.66
% 1.60/1.66 % Comments : [SFS93]'s axiomatization has been modified for this.
% 1.60/1.66 % : Substitution axioms are not needed, as any positive equality
% 1.60/1.67 % literals should resolve on negative ones directly.
% 1.60/1.67 % : Version 7 has simple isomorphism avoidance (as mentioned in
% 1.60/1.67 % [FSB93])
% 1.60/1.67 % : tptp2X: -f tptp -s4 GRP124-7.g
% 1.60/1.67 %--------------------------------------------------------------------------
% 1.60/1.67 cnf(e_1_then_e_2,axiom,
% 1.60/1.67 next(e_1,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_2_then_e_3,axiom,
% 1.60/1.67 next(e_2,e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_then_e_4,axiom,
% 1.60/1.67 next(e_3,e_4) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_2_greater_e_1,axiom,
% 1.60/1.67 greater(e_2,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_greater_e_1,axiom,
% 1.60/1.67 greater(e_3,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_greater_e_1,axiom,
% 1.60/1.67 greater(e_4,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_greater_e_2,axiom,
% 1.60/1.67 greater(e_3,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_greater_e_2,axiom,
% 1.60/1.67 greater(e_4,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_greater_e_3,axiom,
% 1.60/1.67 greater(e_4,e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(no_redundancy,axiom,
% 1.60/1.67 ( ~ product(X,e_1,Y)
% 1.60/1.67 | ~ next(X,X1)
% 1.60/1.67 | ~ greater(Y,X1) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(element_1,axiom,
% 1.60/1.67 group_element(e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(element_2,axiom,
% 1.60/1.67 group_element(e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(element_3,axiom,
% 1.60/1.67 group_element(e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(element_4,axiom,
% 1.60/1.67 group_element(e_4) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_1_is_not_e_2,axiom,
% 1.60/1.67 ~ equalish(e_1,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_1_is_not_e_3,axiom,
% 1.60/1.67 ~ equalish(e_1,e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_1_is_not_e_4,axiom,
% 1.60/1.67 ~ equalish(e_1,e_4) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_2_is_not_e_1,axiom,
% 1.60/1.67 ~ equalish(e_2,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_2_is_not_e_3,axiom,
% 1.60/1.67 ~ equalish(e_2,e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_2_is_not_e_4,axiom,
% 1.60/1.67 ~ equalish(e_2,e_4) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_is_not_e_1,axiom,
% 1.60/1.67 ~ equalish(e_3,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_is_not_e_2,axiom,
% 1.60/1.67 ~ equalish(e_3,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_3_is_not_e_4,axiom,
% 1.60/1.67 ~ equalish(e_3,e_4) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_is_not_e_1,axiom,
% 1.60/1.67 ~ equalish(e_4,e_1) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_is_not_e_2,axiom,
% 1.60/1.67 ~ equalish(e_4,e_2) ).
% 1.60/1.67
% 1.60/1.67 cnf(e_4_is_not_e_3,axiom,
% 1.60/1.67 ~ equalish(e_4,e_3) ).
% 1.60/1.67
% 1.60/1.67 cnf(product1_total_function1,axiom,
% 1.60/1.67 ( ~ group_element(X)
% 1.60/1.67 | ~ group_element(Y)
% 1.60/1.67 | product1(X,Y,e_1)
% 1.60/1.67 | product1(X,Y,e_2)
% 1.60/1.67 | product1(X,Y,e_3)
% 1.60/1.67 | product1(X,Y,e_4) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product1_total_function2,axiom,
% 1.60/1.67 ( ~ product1(X,Y,W)
% 1.60/1.67 | ~ product1(X,Y,Z)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product1_right_cancellation,axiom,
% 1.60/1.67 ( ~ product1(X,W,Y)
% 1.60/1.67 | ~ product1(X,Z,Y)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product1_left_cancellation,axiom,
% 1.60/1.67 ( ~ product1(W,Y,X)
% 1.60/1.67 | ~ product1(Z,Y,X)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product1_idempotence,axiom,
% 1.60/1.67 product1(X,X,X) ).
% 1.60/1.67
% 1.60/1.67 cnf(product2_total_function1,axiom,
% 1.60/1.67 ( ~ group_element(X)
% 1.60/1.67 | ~ group_element(Y)
% 1.60/1.67 | product2(X,Y,e_1)
% 1.60/1.67 | product2(X,Y,e_2)
% 1.60/1.67 | product2(X,Y,e_3)
% 1.60/1.67 | product2(X,Y,e_4) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product2_total_function2,axiom,
% 1.60/1.67 ( ~ product2(X,Y,W)
% 1.60/1.67 | ~ product2(X,Y,Z)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product2_right_cancellation,axiom,
% 1.60/1.67 ( ~ product2(X,W,Y)
% 1.60/1.67 | ~ product2(X,Z,Y)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product2_left_cancellation,axiom,
% 1.60/1.67 ( ~ product2(W,Y,X)
% 1.60/1.67 | ~ product2(Z,Y,X)
% 1.60/1.67 | equalish(W,Z) ) ).
% 1.60/1.67
% 1.60/1.67 cnf(product2_idempotence,axiom,
% 1.60/1.67 product2(X,X,X) ).
% 1.60/1.67
% 1.60/1.67 cnf(qg2a,negated_conjecture,
% 1.60/1.67 ( ~ product1(X,Y,Z1)
% 1.60/1.67 | ~ product1(Z1,X,Z2)
% 1.60/1.67 | product2(Z2,Y,X) ) ).
% 1.60/1.67
% 1.60/1.67 %--------------------------------------------------------------------------
% 1.60/1.67 %-------------------------------------------
% 1.60/1.67 % Proof found
% 1.60/1.67 % SZS status Theorem for theBenchmark
% 1.60/1.67 % SZS output start Proof
% 1.60/1.67 %ClaNum:37(EqnAxiom:0)
% 1.60/1.67 %VarNum:89(SingletonVarNum:37)
% 1.60/1.67 %MaxLitNum:6
% 1.60/1.67 %MaxfuncDepth:0
% 1.60/1.67 %SharedTerms:29
% 1.60/1.67 %goalClause: 35
% 1.60/1.67 [1]P1(a1)
% 1.60/1.67 [2]P1(a2)
% 1.60/1.67 [3]P1(a3)
% 1.60/1.67 [4]P1(a4)
% 1.60/1.67 [5]P4(a1,a2)
% 1.60/1.67 [6]P4(a2,a3)
% 1.60/1.67 [7]P4(a3,a4)
% 1.60/1.67 [8]P2(a2,a1)
% 1.60/1.67 [9]P2(a3,a1)
% 1.60/1.67 [10]P2(a3,a2)
% 1.60/1.67 [11]P2(a4,a1)
% 1.60/1.67 [12]P2(a4,a2)
% 1.60/1.67 [13]P2(a4,a3)
% 1.60/1.67 [16]~P3(a1,a2)
% 1.60/1.67 [17]~P3(a1,a3)
% 1.60/1.67 [18]~P3(a1,a4)
% 1.60/1.67 [19]~P3(a2,a1)
% 1.60/1.67 [20]~P3(a2,a3)
% 1.60/1.67 [21]~P3(a2,a4)
% 1.60/1.67 [22]~P3(a3,a1)
% 1.60/1.67 [23]~P3(a3,a2)
% 1.60/1.67 [24]~P3(a3,a4)
% 1.60/1.67 [25]~P3(a4,a1)
% 1.60/1.67 [26]~P3(a4,a2)
% 1.60/1.67 [27]~P3(a4,a3)
% 1.60/1.67 [14]P5(x141,x141,x141)
% 1.60/1.67 [15]P7(x151,x151,x151)
% 1.60/1.67 [28]~P4(x281,x282)+~P2(x283,x282)+~P6(x281,a1,x283)
% 1.60/1.67 [29]~P5(x293,x294,x291)+P3(x291,x292)+~P5(x293,x294,x292)
% 1.60/1.67 [30]~P7(x303,x304,x301)+P3(x301,x302)+~P7(x303,x304,x302)
% 1.60/1.67 [31]~P5(x313,x311,x314)+P3(x311,x312)+~P5(x313,x312,x314)
% 1.60/1.67 [32]~P7(x323,x321,x324)+P3(x321,x322)+~P7(x323,x322,x324)
% 1.60/1.67 [33]~P5(x331,x333,x334)+P3(x331,x332)+~P5(x332,x333,x334)
% 1.60/1.67 [34]~P7(x341,x343,x344)+P3(x341,x342)+~P7(x342,x343,x344)
% 1.60/1.67 [35]~P5(x353,x352,x354)+P7(x351,x352,x353)+~P5(x354,x353,x351)
% 1.60/1.67 [36]~P1(x362)+~P1(x361)+P5(x361,x362,a2)+P5(x361,x362,a3)+P5(x361,x362,a4)+P5(x361,x362,a1)
% 1.60/1.67 [37]~P1(x372)+~P1(x371)+P7(x371,x372,a2)+P7(x371,x372,a3)+P7(x371,x372,a4)+P7(x371,x372,a1)
% 1.60/1.67 %EqnAxiom
% 1.60/1.67
% 1.60/1.67 %-------------------------------------------
% 1.60/1.67 cnf(39,plain,
% 1.60/1.67 (~P5(a2,a1,a1)),
% 1.60/1.67 inference(scs_inference,[],[14,15,16,34,33])).
% 1.60/1.67 cnf(40,plain,
% 1.60/1.67 (P5(x401,x401,x401)),
% 1.60/1.67 inference(rename_variables,[],[14])).
% 1.60/1.67 cnf(42,plain,
% 1.60/1.67 (~P7(a1,a2,a1)),
% 1.60/1.67 inference(scs_inference,[],[14,15,16,34,33,32])).
% 1.60/1.67 cnf(43,plain,
% 1.60/1.67 (P7(x431,x431,x431)),
% 1.60/1.67 inference(rename_variables,[],[15])).
% 1.60/1.67 cnf(45,plain,
% 1.60/1.67 (~P5(a1,a2,a1)),
% 1.60/1.67 inference(scs_inference,[],[14,40,15,16,34,33,32,31])).
% 1.60/1.67 cnf(46,plain,
% 1.60/1.67 (P5(x461,x461,x461)),
% 1.60/1.67 inference(rename_variables,[],[14])).
% 1.60/1.67 cnf(48,plain,
% 1.60/1.67 (~P7(a1,a1,a2)),
% 1.60/1.67 inference(scs_inference,[],[14,40,15,43,16,34,33,32,31,30])).
% 1.60/1.67 cnf(54,plain,
% 1.60/1.67 (~P5(x541,a2,a1)+~P5(a2,a1,x541)),
% 1.60/1.67 inference(scs_inference,[],[14,40,46,15,43,16,34,33,32,31,30,29,35])).
% 1.60/1.67 cnf(56,plain,
% 1.60/1.67 (~P5(a1,a3,a3)),
% 1.60/1.67 inference(scs_inference,[],[17,14,33])).
% 1.60/1.67 cnf(57,plain,
% 1.60/1.67 (P5(x571,x571,x571)),
% 1.60/1.67 inference(rename_variables,[],[14])).
% 1.60/1.67 cnf(59,plain,
% 1.60/1.67 (~P5(a3,a1,a3)),
% 1.60/1.67 inference(scs_inference,[],[17,14,57,33,31])).
% 1.60/1.67 cnf(60,plain,
% 1.60/1.67 (P5(x601,x601,x601)),
% 1.60/1.67 inference(rename_variables,[],[14])).
% 1.60/1.67 cnf(62,plain,
% 1.60/1.67 (~P7(a3,a3,a1)),
% 1.60/1.67 inference(scs_inference,[],[17,14,57,15,33,31,30])).
% 1.60/1.67 cnf(63,plain,
% 1.60/1.67 (P7(x631,x631,x631)),
% 1.60/1.67 inference(rename_variables,[],[15])).
% 1.60/1.67 cnf(68,plain,
% 1.60/1.67 (~P7(a3,a1,a1)),
% 1.60/1.67 inference(scs_inference,[],[17,14,57,60,15,63,33,31,30,29,34])).
% 1.60/1.67 cnf(69,plain,
% 1.60/1.67 (P7(x691,x691,x691)),
% 1.60/1.67 inference(rename_variables,[],[15])).
% 1.60/1.67 cnf(71,plain,
% 1.60/1.67 (~P7(a3,a1,a3)),
% 1.60/1.67 inference(scs_inference,[],[17,14,57,60,15,63,69,33,31,30,29,34,32])).
% 1.60/1.67 cnf(76,plain,
% 1.60/1.67 (P5(a1,a2,a4)+P5(a1,a2,a2)+P5(a1,a2,a3)),
% 1.60/1.67 inference(scs_inference,[],[1,2,17,14,57,60,15,63,69,45,42,33,31,30,29,34,32,37,36])).
% 1.60/1.67 cnf(78,plain,
% 1.60/1.68 (~P5(a2,x781,a1)+P7(a4,x781,a2)+P5(a1,a2,a2)+P5(a1,a2,a3)),
% 1.60/1.68 inference(scs_inference,[],[1,2,17,14,57,60,15,63,69,45,42,33,31,30,29,34,32,37,36,35])).
% 1.60/1.68 cnf(86,plain,
% 1.60/1.68 (~P7(a1,a4,a4)),
% 1.60/1.68 inference(scs_inference,[],[18,14,15,68,31,35,34])).
% 1.60/1.68 cnf(91,plain,
% 1.60/1.68 (P5(a1,a3,a2)+P5(a1,a3,a1)+P5(a1,a3,a4)),
% 1.60/1.68 inference(scs_inference,[],[3,18,14,15,56,68,71,1,31,35,34,37,36])).
% 1.60/1.68 cnf(97,plain,
% 1.60/1.68 (P5(x971,x971,x971)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(107,plain,
% 1.60/1.68 (P5(a2,a1,a4)+P5(a2,a1,a3)),
% 1.60/1.68 inference(scs_inference,[],[2,19,39,14,97,15,86,42,1,29,35,31,34,37,36])).
% 1.60/1.68 cnf(112,plain,
% 1.60/1.68 (P5(x1121,x1121,x1121)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(114,plain,
% 1.60/1.68 (~P7(a2,a3,a3)),
% 1.60/1.68 inference(scs_inference,[],[20,15,14,33,29,34])).
% 1.60/1.68 cnf(117,plain,
% 1.60/1.68 (~P5(a3,a2,a3)),
% 1.60/1.68 inference(scs_inference,[],[20,15,14,112,33,29,34,31])).
% 1.60/1.68 cnf(126,plain,
% 1.60/1.68 (P5(x1261,x1261,x1261)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(128,plain,
% 1.60/1.68 (~P5(a4,a2,a2)),
% 1.60/1.68 inference(scs_inference,[],[21,15,14,126,32,29,33])).
% 1.60/1.68 cnf(134,plain,
% 1.60/1.68 (~P7(a1,a1,a3)),
% 1.60/1.68 inference(scs_inference,[],[22,15,30])).
% 1.60/1.68 cnf(142,plain,
% 1.60/1.68 (P5(a3,a1,a4)+P5(a3,a1,a2)),
% 1.60/1.68 inference(scs_inference,[],[22,15,14,59,3,1,30,29,33,36])).
% 1.60/1.68 cnf(157,plain,
% 1.60/1.68 (P5(x1571,x1571,x1571)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(159,plain,
% 1.60/1.68 (~P7(a1,a4,a1)),
% 1.60/1.68 inference(scs_inference,[],[14,25,15,30,29,32])).
% 1.60/1.68 cnf(164,plain,
% 1.60/1.68 (~P5(a4,a1,a4)),
% 1.60/1.68 inference(scs_inference,[],[14,157,25,15,4,86,1,30,29,32,37,31])).
% 1.60/1.68 cnf(177,plain,
% 1.60/1.68 (~P5(a2,a4,a2)),
% 1.60/1.68 inference(scs_inference,[],[14,26,31])).
% 1.60/1.68 cnf(178,plain,
% 1.60/1.68 (P5(x1781,x1781,x1781)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(180,plain,
% 1.60/1.68 (~P7(a4,a4,a2)),
% 1.60/1.68 inference(scs_inference,[],[14,26,15,31,30])).
% 1.60/1.68 cnf(181,plain,
% 1.60/1.68 (P7(x1811,x1811,x1811)),
% 1.60/1.68 inference(rename_variables,[],[15])).
% 1.60/1.68 cnf(185,plain,
% 1.60/1.68 (~P7(a4,a2,a2)),
% 1.60/1.68 inference(scs_inference,[],[14,178,26,15,181,31,30,29,34])).
% 1.60/1.68 cnf(186,plain,
% 1.60/1.68 (P7(x1861,x1861,x1861)),
% 1.60/1.68 inference(rename_variables,[],[15])).
% 1.60/1.68 cnf(188,plain,
% 1.60/1.68 (~P5(a4,a3,a3)),
% 1.60/1.68 inference(scs_inference,[],[14,178,26,27,15,181,31,30,29,34,33])).
% 1.60/1.68 cnf(191,plain,
% 1.60/1.68 (~P7(a4,a2,a4)),
% 1.60/1.68 inference(scs_inference,[],[14,178,26,27,15,181,186,31,30,29,34,33,32])).
% 1.60/1.68 cnf(194,plain,
% 1.60/1.68 (~P7(a2,a2,a3)),
% 1.60/1.68 inference(scs_inference,[],[15,23,30])).
% 1.60/1.68 cnf(195,plain,
% 1.60/1.68 (P7(x1951,x1951,x1951)),
% 1.60/1.68 inference(rename_variables,[],[15])).
% 1.60/1.68 cnf(204,plain,
% 1.60/1.68 (P5(a4,a3,a2)+P5(a4,a3,a4)+P5(a4,a3,a1)),
% 1.60/1.68 inference(scs_inference,[],[15,195,23,188,114,4,3,2,14,30,34,29,37,36])).
% 1.60/1.68 cnf(206,plain,
% 1.60/1.68 (~P5(a2,a4,x2061)+P7(x2061,a3,a4)+P5(a4,a3,a4)+P5(a4,a3,a1)),
% 1.60/1.68 inference(scs_inference,[],[15,195,23,188,114,4,3,2,14,30,34,29,37,36,35])).
% 1.60/1.68 cnf(211,plain,
% 1.60/1.68 (~P7(a4,a3,a3)),
% 1.60/1.68 inference(scs_inference,[],[15,24,14,31,34])).
% 1.60/1.68 cnf(221,plain,
% 1.60/1.68 (~P5(a2,a1,a4)+P5(a4,a2,a3)+P5(a4,a2,a4)),
% 1.60/1.68 inference(scs_inference,[],[15,48,24,128,191,185,4,2,14,31,34,29,37,36,35])).
% 1.60/1.68 cnf(224,plain,
% 1.60/1.68 (~P5(a1,a4,a1)),
% 1.60/1.68 inference(scs_inference,[],[159,14,35])).
% 1.60/1.68 cnf(225,plain,
% 1.60/1.68 (P5(x2251,x2251,x2251)),
% 1.60/1.68 inference(rename_variables,[],[14])).
% 1.60/1.68 cnf(232,plain,
% 1.60/1.68 (~P5(a4,a3,a4)),
% 1.60/1.68 inference(scs_inference,[],[27,19,159,15,14,225,35,32,34,31])).
% 1.60/1.68 cnf(236,plain,
% 1.66/1.68 (P5(a1,a2,a3)+P5(a1,a2,a2)+~P5(a2,a4,a1)),
% 1.66/1.68 inference(scs_inference,[],[27,19,180,159,15,14,225,35,32,34,31,204,78])).
% 1.66/1.68 cnf(240,plain,
% 1.66/1.68 (P5(a4,a3,a1)+P7(x2401,a3,a4)+~P5(a2,a4,x2401)),
% 1.66/1.68 inference(scs_inference,[],[232,206])).
% 1.66/1.68 cnf(252,plain,
% 1.66/1.68 (~P7(a1,a3,a1)),
% 1.66/1.68 inference(scs_inference,[],[17,15,30,32])).
% 1.66/1.68 cnf(255,plain,
% 1.66/1.68 (~P5(a4,a1,a1)),
% 1.66/1.68 inference(scs_inference,[],[17,18,15,14,30,32,33])).
% 1.66/1.68 cnf(265,plain,
% 1.66/1.68 (P5(a4,a1,a3)+P5(a4,a1,a2)),
% 1.66/1.68 inference(scs_inference,[],[164,255,4,1,14,31,36])).
% 1.66/1.68 cnf(273,plain,
% 1.66/1.68 (~P7(a1,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[18,15,32,30])).
% 1.66/1.68 cnf(274,plain,
% 1.66/1.68 (P7(x2741,x2741,x2741)),
% 1.66/1.68 inference(rename_variables,[],[15])).
% 1.66/1.68 cnf(276,plain,
% 1.66/1.68 (~P5(x2761,a1,a3)+~P5(a1,a3,x2761)),
% 1.66/1.68 inference(scs_inference,[],[18,62,15,32,30,35])).
% 1.66/1.68 cnf(281,plain,
% 1.66/1.68 (~P5(a2,a1,a3)+P5(a1,a3,a1)+P5(a1,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[18,62,15,274,32,30,35,34,91])).
% 1.66/1.68 cnf(283,plain,
% 1.66/1.68 (~P7(a2,a4,a4)),
% 1.66/1.68 inference(scs_inference,[],[21,15,34])).
% 1.66/1.68 cnf(284,plain,
% 1.66/1.68 (P7(x2841,x2841,x2841)),
% 1.66/1.68 inference(rename_variables,[],[15])).
% 1.66/1.68 cnf(286,plain,
% 1.66/1.68 (~P7(a4,a4,a1)),
% 1.66/1.68 inference(scs_inference,[],[18,21,15,284,34,30])).
% 1.66/1.68 cnf(287,plain,
% 1.66/1.68 (P7(x2871,x2871,x2871)),
% 1.66/1.68 inference(rename_variables,[],[15])).
% 1.66/1.68 cnf(291,plain,
% 1.66/1.68 (~P7(a4,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[18,27,21,14,15,284,287,34,30,33,32])).
% 1.66/1.68 cnf(313,plain,
% 1.66/1.68 (~P5(a1,a3,a1)),
% 1.66/1.68 inference(scs_inference,[],[211,252,291,3,4,14,31,37,35])).
% 1.66/1.68 cnf(320,plain,
% 1.66/1.68 (P5(a1,a3,a4)+P5(a1,a3,a2)),
% 1.66/1.68 inference(scs_inference,[],[313,91])).
% 1.66/1.68 cnf(322,plain,
% 1.66/1.68 (~P5(a2,a1,a3)+P5(a1,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[313,281])).
% 1.66/1.68 cnf(325,plain,
% 1.66/1.68 (~P5(a2,a3,a2)),
% 1.66/1.68 inference(scs_inference,[],[20,14,29,31])).
% 1.66/1.68 cnf(328,plain,
% 1.66/1.68 (~P7(a3,a3,a2)),
% 1.66/1.68 inference(scs_inference,[],[20,15,14,29,31,30])).
% 1.66/1.68 cnf(340,plain,
% 1.66/1.68 (~P5(a2,a3,a4)+~P5(a2,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[20,21,328,15,14,32,31,221,34,35])).
% 1.66/1.68 cnf(351,plain,
% 1.66/1.68 (P7(x3511,x3511,x3511)),
% 1.66/1.68 inference(rename_variables,[],[15])).
% 1.66/1.68 cnf(358,plain,
% 1.66/1.68 (P5(a3,a2,a1)+P5(a3,a2,a2)+P5(a3,a2,a4)),
% 1.66/1.68 inference(scs_inference,[],[21,24,117,283,3,2,4,15,351,14,33,34,32,37,36])).
% 1.66/1.68 cnf(360,plain,
% 1.66/1.68 (~P5(a1,a3,a2)+P5(a3,a2,a2)+P5(a3,a2,a4)),
% 1.66/1.68 inference(scs_inference,[],[21,24,117,194,283,3,2,4,15,351,14,33,34,32,37,36,35])).
% 1.66/1.68 cnf(365,plain,
% 1.66/1.68 (~P5(a2,a4,a4)),
% 1.66/1.68 inference(scs_inference,[],[21,14,29,33])).
% 1.66/1.68 cnf(379,plain,
% 1.66/1.68 (~P5(a2,a3,a3)),
% 1.66/1.68 inference(scs_inference,[],[23,15,14,34,33])).
% 1.66/1.68 cnf(403,plain,
% 1.66/1.68 (~P5(x4031,a3,a1)+~P5(a3,a1,x4031)),
% 1.66/1.68 inference(scs_inference,[],[134,15,30,35])).
% 1.66/1.68 cnf(405,plain,
% 1.66/1.68 (~P5(a1,a4,a4)),
% 1.66/1.68 inference(scs_inference,[],[25,134,15,14,30,35,33])).
% 1.66/1.68 cnf(410,plain,
% 1.66/1.68 (~P7(a3,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[24,15,30])).
% 1.66/1.68 cnf(411,plain,
% 1.66/1.68 (P7(x4111,x4111,x4111)),
% 1.66/1.68 inference(rename_variables,[],[15])).
% 1.66/1.68 cnf(415,plain,
% 1.66/1.68 (P5(a2,a4,a1)+P5(a2,a4,a3)),
% 1.66/1.68 inference(scs_inference,[],[24,365,177,2,4,15,411,30,32,36])).
% 1.66/1.68 cnf(427,plain,
% 1.66/1.68 (P5(a1,a4,a2)+P5(a1,a4,a3)),
% 1.66/1.68 inference(scs_inference,[],[405,224,4,1,14,33,36])).
% 1.66/1.68 cnf(443,plain,
% 1.66/1.68 (~P5(a2,a1,a3)+P5(a3,a2,a4)),
% 1.66/1.68 inference(scs_inference,[],[25,48,23,18,15,14,30,33,360,358,29,32,35])).
% 1.66/1.68 cnf(447,plain,
% 1.66/1.68 (P5(a2,a3,a4)+P5(a2,a3,a1)),
% 1.66/1.68 inference(scs_inference,[],[325,379,3,2,15,32,36])).
% 1.66/1.68 cnf(483,plain,
% 1.66/1.68 (P5(a4,a3,a1)+~P5(a2,a4,a3)),
% 1.66/1.68 inference(scs_inference,[],[410,16,15,14,32,33,236,76,240])).
% 1.66/1.68 cnf(493,plain,
% 1.66/1.68 (P5(a3,a1,a4)+~P5(a2,a3,a1)),
% 1.66/1.68 inference(scs_inference,[],[142,403])).
% 1.66/1.68 cnf(499,plain,
% 1.66/1.68 (~P5(x4991,a1,a4)+~P5(a1,a4,x4991)),
% 1.66/1.68 inference(scs_inference,[],[286,14,31,35])).
% 1.66/1.68 cnf(532,plain,
% 1.66/1.68 (P5(a1,a3,a2)+~P5(a4,a1,a3)),
% 1.66/1.68 inference(scs_inference,[],[320,276])).
% 1.66/1.68 cnf(536,plain,
% 1.66/1.68 (P5(a2,a1,a4)+P5(a1,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[322,107])).
% 1.66/1.68 cnf(558,plain,
% 1.66/1.68 (P5(a4,a3,a1)+P5(a2,a4,a1)),
% 1.66/1.68 inference(scs_inference,[],[415,483])).
% 1.66/1.68 cnf(565,plain,
% 1.66/1.68 (P5(a1,a4,a2)+~P5(a3,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[427,499])).
% 1.66/1.68 cnf(580,plain,
% 1.66/1.68 (P5(a2,a3,a4)+~P5(a3,a1,a2)),
% 1.66/1.68 inference(scs_inference,[],[447,403])).
% 1.66/1.68 cnf(614,plain,
% 1.66/1.68 (~P5(a4,a1,a3)+~P5(a2,a1,a3)),
% 1.66/1.68 inference(scs_inference,[],[532,276])).
% 1.66/1.68 cnf(638,plain,
% 1.66/1.68 (~P5(a3,a1,a4)+~P5(a2,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[565,499])).
% 1.66/1.68 cnf(647,plain,
% 1.66/1.68 (~P5(a2,a1,a4)+~P5(a3,a1,a2)),
% 1.66/1.68 inference(scs_inference,[],[580,340])).
% 1.66/1.68 cnf(670,plain,
% 1.66/1.68 (P5(a2,a1,a4)+~P5(a4,a1,a3)),
% 1.66/1.68 inference(scs_inference,[],[614,107])).
% 1.66/1.68 cnf(684,plain,
% 1.66/1.68 (~P5(x6841,a4,a1)+~P5(a4,a1,x6841)),
% 1.66/1.68 inference(scs_inference,[],[273,35])).
% 1.66/1.68 cnf(691,plain,
% 1.66/1.68 (P5(a3,a1,a2)+~P5(a2,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[638,142])).
% 1.66/1.68 cnf(698,plain,
% 1.66/1.68 (~P5(a2,a1,a4)),
% 1.66/1.68 inference(scs_inference,[],[647,691])).
% 1.66/1.68 cnf(699,plain,
% 1.66/1.68 (P5(a2,a1,a3)),
% 1.66/1.68 inference(scs_inference,[],[698,107])).
% 1.66/1.68 cnf(700,plain,
% 1.66/1.68 (P5(a1,a3,a4)),
% 1.66/1.68 inference(scs_inference,[],[698,536])).
% 1.66/1.68 cnf(701,plain,
% 1.66/1.68 (~P5(a4,a1,a3)),
% 1.66/1.68 inference(scs_inference,[],[698,670])).
% 1.66/1.68 cnf(704,plain,
% 1.66/1.68 (P5(a4,a1,a2)),
% 1.66/1.68 inference(scs_inference,[],[701,265])).
% 1.66/1.68 cnf(707,plain,
% 1.66/1.68 (P5(a3,a2,a4)),
% 1.66/1.68 inference(scs_inference,[],[699,443])).
% 1.66/1.68 cnf(738,plain,
% 1.66/1.68 ($false),
% 1.66/1.68 inference(scs_inference,[],[707,699,700,704,20,27,19,16,276,54,35,31,34,30,33,684,558,493,447]),
% 1.66/1.68 ['proof']).
% 1.66/1.68 % SZS output end Proof
% 1.66/1.68 % Total time :1.060000s
%------------------------------------------------------------------------------