TSTP Solution File: GRP124-3.004 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP124-3.004 : 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 : n001.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 00:11:01 EDT 2023
% Result : Unsatisfiable 39.53s 39.65s
% Output : CNFRefutation 39.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.17/0.33 % Computer : n001.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon Aug 28 21:18:51 EDT 2023
% 0.20/0.33 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 39.53/39.64 %-------------------------------------------
% 39.53/39.64 % File :CSE---1.6
% 39.53/39.64 % Problem :theBenchmark
% 39.53/39.64 % Transform :cnf
% 39.53/39.64 % Format :tptp:raw
% 39.53/39.64 % Command :java -jar mcs_scs.jar %d %s
% 39.53/39.64
% 39.53/39.64 % Result :Theorem 38.960000s
% 39.53/39.64 % Output :CNFRefutation 38.960000s
% 39.53/39.64 %-------------------------------------------
% 39.53/39.64 %--------------------------------------------------------------------------
% 39.53/39.64 % File : GRP124-3.004 : TPTP v8.1.2. Released v1.2.0.
% 39.53/39.64 % Domain : Group Theory (Quasigroups)
% 39.53/39.64 % Problem : (3,1,2) conjugate orthogonality
% 39.53/39.64 % Version : [Sla93] axioms : Augmented.
% 39.53/39.64 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 39.53/39.64 % Generate the multiplication table for the specified quasi-
% 39.53/39.64 % group with 4 elements.
% 39.53/39.64
% 39.53/39.64 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 39.53/39.64 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 39.53/39.64 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 39.53/39.64 % Source : [TPTP]
% 39.53/39.64 % Names :
% 39.53/39.64
% 39.53/39.64 % Status : Unsatisfiable
% 39.53/39.64 % Rating : 0.00 v2.1.0
% 39.53/39.64 % Syntax : Number of clauses : 44 ( 32 unt; 2 nHn; 43 RR)
% 39.53/39.64 % Number of literals : 85 ( 0 equ; 49 neg)
% 39.53/39.64 % Maximal clause size : 6 ( 1 avg)
% 39.53/39.64 % Maximal term depth : 1 ( 1 avg)
% 39.53/39.64 % Number of predicates : 6 ( 6 usr; 0 prp; 1-3 aty)
% 39.53/39.65 % Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% 39.53/39.65 % Number of variables : 47 ( 0 sgn)
% 39.53/39.65 % SPC : CNF_UNS_EPR_NEQ_NHN
% 39.53/39.65
% 39.53/39.65 % Comments : [SFS93]'s axiomatization has been modified for this.
% 39.53/39.65 % : Substitution axioms are not needed, as any positive equality
% 39.53/39.65 % literals should resolve on negative ones directly.
% 39.53/39.65 % : As in GRP123-1, either one of qg2_1 or qg2_2 may be used, as
% 39.53/39.65 % each implies the other in this scenario, with the help of
% 39.53/39.65 % cancellation. The dependence cannot be proved, so both have
% 39.53/39.65 % been left in here.
% 39.53/39.65 % : Version 3 has complex isomorphism avoidance (mentioned in
% 39.53/39.65 % [SFS95]
% 39.53/39.65 % : tptp2X: -f tptp -s4 GRP124-3.g
% 39.53/39.65 %--------------------------------------------------------------------------
% 39.53/39.65 cnf(e_0_then_e_1,axiom,
% 39.53/39.65 next(e_0,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_1_then_e_2,axiom,
% 39.53/39.65 next(e_1,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_then_e_3,axiom,
% 39.53/39.65 next(e_2,e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_then_e_4,axiom,
% 39.53/39.65 next(e_3,e_4) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_1_greater_e_0,axiom,
% 39.53/39.65 greater(e_1,e_0) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_greater_e_0,axiom,
% 39.53/39.65 greater(e_2,e_0) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_greater_e_0,axiom,
% 39.53/39.65 greater(e_3,e_0) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_greater_e_0,axiom,
% 39.53/39.65 greater(e_4,e_0) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_greater_e_1,axiom,
% 39.53/39.65 greater(e_2,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_greater_e_1,axiom,
% 39.53/39.65 greater(e_3,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_greater_e_1,axiom,
% 39.53/39.65 greater(e_4,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_greater_e_2,axiom,
% 39.53/39.65 greater(e_3,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_greater_e_2,axiom,
% 39.53/39.65 greater(e_4,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_greater_e_3,axiom,
% 39.53/39.65 greater(e_4,e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle1,axiom,
% 39.53/39.65 ( ~ cycle(X,Y)
% 39.53/39.65 | ~ cycle(X,Z)
% 39.53/39.65 | equalish(Y,Z) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle2,axiom,
% 39.53/39.65 ( ~ group_element(X)
% 39.53/39.65 | cycle(X,e_0)
% 39.53/39.65 | cycle(X,e_1)
% 39.53/39.65 | cycle(X,e_2)
% 39.53/39.65 | cycle(X,e_3) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle3,axiom,
% 39.53/39.65 cycle(e_4,e_0) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle4,axiom,
% 39.53/39.65 ( ~ cycle(X,Y)
% 39.53/39.65 | ~ cycle(W,Z)
% 39.53/39.65 | ~ next(X,W)
% 39.53/39.65 | ~ greater(Y,e_0)
% 39.53/39.65 | ~ next(Z,Z1)
% 39.53/39.65 | equalish(Y,Z1) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle5,axiom,
% 39.53/39.65 ( ~ cycle(X,Z1)
% 39.53/39.65 | ~ cycle(Y,e_0)
% 39.53/39.65 | ~ cycle(W,Z2)
% 39.53/39.65 | ~ next(Y,W)
% 39.53/39.65 | ~ greater(Y,X)
% 39.53/39.65 | ~ greater(Z1,Z2) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle6,axiom,
% 39.53/39.65 ( ~ cycle(X,e_0)
% 39.53/39.65 | ~ product(X,e_1,Y)
% 39.53/39.65 | ~ greater(Y,X) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(cycle7,axiom,
% 39.53/39.65 ( ~ cycle(X,Y)
% 39.53/39.65 | ~ product(X,e_1,Z)
% 39.53/39.65 | ~ greater(Y,e_0)
% 39.53/39.65 | ~ next(X,X1)
% 39.53/39.65 | equalish(Z,X1) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(element_1,axiom,
% 39.53/39.65 group_element(e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(element_2,axiom,
% 39.53/39.65 group_element(e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(element_3,axiom,
% 39.53/39.65 group_element(e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(element_4,axiom,
% 39.53/39.65 group_element(e_4) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_1_is_not_e_2,axiom,
% 39.53/39.65 ~ equalish(e_1,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_1_is_not_e_3,axiom,
% 39.53/39.65 ~ equalish(e_1,e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_1_is_not_e_4,axiom,
% 39.53/39.65 ~ equalish(e_1,e_4) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_is_not_e_1,axiom,
% 39.53/39.65 ~ equalish(e_2,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_is_not_e_3,axiom,
% 39.53/39.65 ~ equalish(e_2,e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_2_is_not_e_4,axiom,
% 39.53/39.65 ~ equalish(e_2,e_4) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_is_not_e_1,axiom,
% 39.53/39.65 ~ equalish(e_3,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_is_not_e_2,axiom,
% 39.53/39.65 ~ equalish(e_3,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_3_is_not_e_4,axiom,
% 39.53/39.65 ~ equalish(e_3,e_4) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_is_not_e_1,axiom,
% 39.53/39.65 ~ equalish(e_4,e_1) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_is_not_e_2,axiom,
% 39.53/39.65 ~ equalish(e_4,e_2) ).
% 39.53/39.65
% 39.53/39.65 cnf(e_4_is_not_e_3,axiom,
% 39.53/39.65 ~ equalish(e_4,e_3) ).
% 39.53/39.65
% 39.53/39.65 cnf(product_total_function1,axiom,
% 39.53/39.65 ( ~ group_element(X)
% 39.53/39.65 | ~ group_element(Y)
% 39.53/39.65 | product(X,Y,e_1)
% 39.53/39.65 | product(X,Y,e_2)
% 39.53/39.65 | product(X,Y,e_3)
% 39.53/39.65 | product(X,Y,e_4) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(product_total_function2,axiom,
% 39.53/39.65 ( ~ product(X,Y,W)
% 39.53/39.65 | ~ product(X,Y,Z)
% 39.53/39.65 | equalish(W,Z) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(product_right_cancellation,axiom,
% 39.53/39.65 ( ~ product(X,W,Y)
% 39.53/39.65 | ~ product(X,Z,Y)
% 39.53/39.65 | equalish(W,Z) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(product_left_cancellation,axiom,
% 39.53/39.65 ( ~ product(W,Y,X)
% 39.53/39.65 | ~ product(Z,Y,X)
% 39.53/39.65 | equalish(W,Z) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(product_idempotence,axiom,
% 39.53/39.65 product(X,X,X) ).
% 39.53/39.65
% 39.53/39.65 cnf(qg2_1,negated_conjecture,
% 39.53/39.65 ( ~ product(X1,Y1,Z1)
% 39.53/39.65 | ~ product(X2,Y2,Z1)
% 39.53/39.65 | ~ product(Z2,X1,Y1)
% 39.53/39.65 | ~ product(Z2,X2,Y2)
% 39.53/39.65 | equalish(X1,X2) ) ).
% 39.53/39.65
% 39.53/39.65 cnf(qg2_2,negated_conjecture,
% 39.53/39.65 ( ~ product(X1,Y1,Z1)
% 39.53/39.65 | ~ product(X2,Y2,Z1)
% 39.53/39.65 | ~ product(Z2,X1,Y1)
% 39.53/39.65 | ~ product(Z2,X2,Y2)
% 39.53/39.65 | equalish(Y1,Y2) ) ).
% 39.53/39.65
% 39.53/39.65 %--------------------------------------------------------------------------
% 39.53/39.65 %-------------------------------------------
% 39.53/39.65 % Proof found
% 39.53/39.65 % SZS status Theorem for theBenchmark
% 39.53/39.65 % SZS output start Proof
% 39.53/39.65 %ClaNum:44(EqnAxiom:0)
% 39.53/39.65 %VarNum:112(SingletonVarNum:47)
% 39.53/39.65 %MaxLitNum:6
% 39.53/39.65 %MaxfuncDepth:0
% 39.53/39.65 %SharedTerms:36
% 39.53/39.65 %goalClause: 43 44
% 39.53/39.65 [1]P1(a1)
% 39.53/39.65 [2]P1(a3)
% 39.53/39.65 [3]P1(a4)
% 39.53/39.65 [4]P1(a5)
% 39.53/39.65 [5]P5(a2,a1)
% 39.53/39.65 [6]P5(a1,a3)
% 39.53/39.65 [7]P5(a3,a4)
% 39.53/39.65 [8]P5(a4,a5)
% 39.53/39.65 [9]P2(a1,a2)
% 39.53/39.65 [10]P2(a3,a2)
% 39.53/39.65 [11]P2(a3,a1)
% 39.53/39.65 [12]P2(a4,a2)
% 39.53/39.65 [13]P2(a4,a1)
% 39.53/39.65 [14]P2(a4,a3)
% 39.53/39.65 [15]P2(a5,a2)
% 39.53/39.65 [16]P2(a5,a1)
% 39.53/39.65 [17]P2(a5,a3)
% 39.53/39.65 [18]P2(a5,a4)
% 39.53/39.65 [19]P3(a5,a2)
% 39.53/39.65 [21]~P4(a1,a3)
% 39.53/39.65 [22]~P4(a1,a4)
% 39.53/39.65 [23]~P4(a1,a5)
% 39.53/39.65 [24]~P4(a3,a1)
% 39.53/39.65 [25]~P4(a3,a4)
% 39.53/39.66 [26]~P4(a3,a5)
% 39.53/39.66 [27]~P4(a4,a1)
% 39.53/39.66 [28]~P4(a4,a3)
% 39.53/39.66 [29]~P4(a4,a5)
% 39.53/39.66 [30]~P4(a5,a1)
% 39.53/39.66 [31]~P4(a5,a3)
% 39.53/39.66 [32]~P4(a5,a4)
% 39.53/39.66 [20]P6(x201,x201,x201)
% 39.53/39.66 [36]~P2(x361,x362)+~P6(x362,a1,x361)+~P3(x362,a2)
% 39.53/39.66 [34]~P3(x343,x341)+P4(x341,x342)+~P3(x343,x342)
% 39.53/39.66 [39]~P6(x393,x394,x391)+P4(x391,x392)+~P6(x393,x394,x392)
% 39.53/39.66 [40]~P6(x403,x401,x404)+P4(x401,x402)+~P6(x403,x402,x404)
% 39.53/39.66 [41]~P6(x411,x413,x414)+P4(x411,x412)+~P6(x412,x413,x414)
% 39.53/39.66 [33]~P1(x331)+P3(x331,a1)+P3(x331,a3)+P3(x331,a4)+P3(x331,a2)
% 39.53/39.66 [38]P4(x381,x382)+~P5(x383,x382)+~P3(x383,x384)+~P6(x383,a1,x381)+~P2(x384,a2)
% 39.53/39.66 [43]~P6(x435,x431,x436)+P4(x431,x432)+~P6(x433,x434,x432)+~P6(x433,x435,x431)+~P6(x434,x432,x436)
% 39.53/39.66 [44]~P6(x441,x445,x446)+P4(x441,x442)+~P6(x443,x442,x444)+~P6(x443,x441,x445)+~P6(x442,x444,x446)
% 39.53/39.66 [42]~P1(x422)+~P1(x421)+P6(x421,x422,a3)+P6(x421,x422,a4)+P6(x421,x422,a5)+P6(x421,x422,a1)
% 39.53/39.66 [35]~P3(x355,x353)+~P3(x354,x351)+P4(x351,x352)+~P5(x353,x352)+~P5(x354,x355)+~P2(x351,a2)
% 39.53/39.66 [37]~P3(x372,x375)+~P3(x373,x374)+~P5(x371,x372)+~P2(x371,x373)+~P2(x374,x375)+~P3(x371,a2)
% 39.53/39.66 %EqnAxiom
% 39.53/39.66
% 39.53/39.66 %-------------------------------------------
% 39.53/39.68 cnf(46,plain,
% 39.53/39.68 (~P3(a1,a1)),
% 39.53/39.68 inference(scs_inference,[],[20,6,9,21,41,38])).
% 39.53/39.68 cnf(47,plain,
% 39.53/39.68 (P6(x471,x471,x471)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(48,plain,
% 39.53/39.68 (~P6(a1,a3,a1)),
% 39.53/39.68 inference(scs_inference,[],[20,47,6,9,21,41,38,40])).
% 39.53/39.68 cnf(49,plain,
% 39.53/39.68 (P6(x491,x491,x491)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(52,plain,
% 39.53/39.68 (P6(x521,x521,x521)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(55,plain,
% 39.53/39.68 (P6(x551,x551,x551)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(59,plain,
% 39.53/39.68 (~P6(a3,x591,a1)+~P6(a1,a3,x591)),
% 39.53/39.68 inference(scs_inference,[],[20,47,49,52,55,6,9,21,41,38,40,39,36,34,44])).
% 39.53/39.68 cnf(72,plain,
% 39.53/39.68 (~P6(a4,a1,a1)),
% 39.53/39.68 inference(scs_inference,[],[22,20,41])).
% 39.53/39.68 cnf(73,plain,
% 39.53/39.68 (P6(x731,x731,x731)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(78,plain,
% 39.53/39.68 (P6(x781,x781,x781)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(80,plain,
% 39.53/39.68 (~P6(a4,a1,a4)),
% 39.53/39.68 inference(scs_inference,[],[22,19,20,73,78,41,34,39,40])).
% 39.53/39.68 cnf(81,plain,
% 39.53/39.68 (P6(x811,x811,x811)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(87,plain,
% 39.53/39.68 (~P3(a1,a3)),
% 39.53/39.68 inference(scs_inference,[],[10,22,19,6,20,73,78,81,21,41,34,39,40,44,36,38])).
% 39.53/39.68 cnf(94,plain,
% 39.53/39.68 (P6(a1,a3,a4)+P6(a1,a3,a5)+P6(a1,a3,a3)),
% 39.53/39.68 inference(scs_inference,[],[1,10,22,23,5,2,8,19,6,20,73,78,81,9,21,48,41,34,39,40,44,36,38,37,35,42])).
% 39.53/39.68 cnf(96,plain,
% 39.53/39.68 (~P6(a3,a1,a1)),
% 39.53/39.68 inference(scs_inference,[],[24,20,41])).
% 39.53/39.68 cnf(97,plain,
% 39.53/39.68 (P6(x971,x971,x971)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(104,plain,
% 39.53/39.68 (P3(a1,a4)+P3(a1,a2)),
% 39.53/39.68 inference(scs_inference,[],[46,15,24,6,20,97,21,87,1,41,43,38,33])).
% 39.53/39.68 cnf(126,plain,
% 39.53/39.68 (P6(a4,a1,a5)+P6(a4,a1,a3)),
% 39.53/39.68 inference(scs_inference,[],[3,25,20,19,72,80,1,41,36,43,42])).
% 39.53/39.68 cnf(138,plain,
% 39.53/39.68 (~P6(a5,a3,a3)),
% 39.53/39.68 inference(scs_inference,[],[26,20,19,34,40,41])).
% 39.53/39.68 cnf(139,plain,
% 39.53/39.68 (P6(x1391,x1391,x1391)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(144,plain,
% 39.53/39.68 (P3(a4,a2)+P3(a4,a3)+P3(a4,a4)+P3(a4,a1)),
% 39.53/39.68 inference(scs_inference,[],[3,26,20,139,19,34,40,41,36,33])).
% 39.53/39.68 cnf(156,plain,
% 39.53/39.68 (P6(x1561,x1561,x1561)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(165,plain,
% 39.53/39.68 (P6(a4,a3,a5)+P6(a4,a3,a1)),
% 39.53/39.68 inference(scs_inference,[],[3,14,27,28,20,156,2,39,41,40,36,34,42])).
% 39.53/39.68 cnf(178,plain,
% 39.53/39.68 (P6(x1781,x1781,x1781)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(185,plain,
% 39.53/39.68 (P6(x1851,x1851,x1851)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(187,plain,
% 39.53/39.68 (~P6(a5,a4,a4)),
% 39.53/39.68 inference(scs_inference,[],[29,15,23,20,178,185,19,39,34,44,38,41])).
% 39.53/39.68 cnf(198,plain,
% 39.53/39.68 (P6(x1981,x1981,x1981)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(202,plain,
% 39.53/39.68 (~P6(a5,a1,a1)),
% 39.53/39.68 inference(scs_inference,[],[30,20,198,39,40,41])).
% 39.53/39.68 cnf(215,plain,
% 39.53/39.68 (~P6(a3,a5,a3)),
% 39.53/39.68 inference(scs_inference,[],[31,20,39,40])).
% 39.53/39.68 cnf(216,plain,
% 39.53/39.68 (P6(x2161,x2161,x2161)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(219,plain,
% 39.53/39.68 (P6(x2191,x2191,x2191)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(221,plain,
% 39.53/39.68 (P3(a1,a2)),
% 39.53/39.68 inference(scs_inference,[],[31,12,6,21,20,216,39,40,38,104])).
% 39.53/39.68 cnf(222,plain,
% 39.53/39.68 (~P6(a3,x2221,a5)+~P6(a5,a3,x2221)),
% 39.53/39.68 inference(scs_inference,[],[31,12,6,21,20,216,219,39,40,38,104,44])).
% 39.53/39.68 cnf(224,plain,
% 39.53/39.68 (P6(x2241,x2241,x2241)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(229,plain,
% 39.53/39.68 (~P3(a2,a4)),
% 39.53/39.68 inference(scs_inference,[],[5,31,27,12,6,21,20,216,219,224,39,40,38,104,44,36,35])).
% 39.53/39.68 cnf(238,plain,
% 39.53/39.68 (P6(x2381,x2381,x2381)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(243,plain,
% 39.53/39.68 (P6(x2431,x2431,x2431)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(245,plain,
% 39.53/39.68 (~P6(a5,a4,a5)),
% 39.53/39.68 inference(scs_inference,[],[32,20,238,243,221,39,43,36,40])).
% 39.53/39.68 cnf(246,plain,
% 39.53/39.68 (P6(x2461,x2461,x2461)),
% 39.53/39.68 inference(rename_variables,[],[20])).
% 39.53/39.68 cnf(248,plain,
% 39.53/39.68 (~P3(a2,a3)),
% 39.53/39.68 inference(scs_inference,[],[5,32,24,10,20,238,243,221,39,43,36,40,35])).
% 39.53/39.68 cnf(253,plain,
% 39.53/39.68 (P6(a5,a3,a1)+P6(a5,a3,a5)+P6(a5,a3,a4)),
% 39.53/39.68 inference(scs_inference,[],[5,32,23,24,10,20,238,243,246,221,138,4,2,39,43,36,40,35,38,42])).
% 39.53/39.68 cnf(258,plain,
% 39.63/39.68 (P6(x2581,x2581,x2581)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(269,plain,
% 39.63/39.68 (P6(a3,a5,a1)+P6(a3,a5,a5)+P6(a3,a5,a4)),
% 39.63/39.68 inference(scs_inference,[],[13,26,15,23,20,258,19,215,4,221,2,39,34,44,36,38,42])).
% 39.63/39.68 cnf(278,plain,
% 39.63/39.68 (P6(x2781,x2781,x2781)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(280,plain,
% 39.63/39.68 (~P6(a3,a4,a4)),
% 39.63/39.68 inference(scs_inference,[],[28,20,278,221,39,36,41])).
% 39.63/39.68 cnf(293,plain,
% 39.63/39.68 (P6(x2931,x2931,x2931)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(296,plain,
% 39.63/39.68 (P6(x2961,x2961,x2961)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(299,plain,
% 39.63/39.68 (P6(x2991,x2991,x2991)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(301,plain,
% 39.63/39.68 (~P3(a4,a4)),
% 39.63/39.68 inference(scs_inference,[],[26,27,12,8,21,20,293,296,19,221,6,5,40,41,38,36,35])).
% 39.63/39.68 cnf(303,plain,
% 39.63/39.68 (P6(a3,a5,a1)+P6(a3,a5,a4)),
% 39.63/39.68 inference(scs_inference,[],[26,27,12,8,21,20,293,296,19,221,6,5,40,41,38,36,35,269])).
% 39.63/39.68 cnf(309,plain,
% 39.63/39.68 (P6(a1,a3,a4)+P6(a1,a3,a3)+P6(a3,a5,a4)),
% 39.63/39.68 inference(scs_inference,[],[25,26,27,12,8,21,20,293,296,299,19,221,6,5,40,41,38,36,35,269,39,59,94])).
% 39.63/39.68 cnf(316,plain,
% 39.63/39.68 (P3(a4,a3)+P3(a4,a1)+P3(a4,a2)),
% 39.63/39.68 inference(scs_inference,[],[301,144])).
% 39.63/39.68 cnf(320,plain,
% 39.63/39.68 (~P6(a4,a5,a4)),
% 39.63/39.68 inference(scs_inference,[],[32,20,39,40])).
% 39.63/39.68 cnf(321,plain,
% 39.63/39.68 (P6(x3211,x3211,x3211)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(328,plain,
% 39.63/39.68 (P3(a4,a1)+P3(a4,a2)),
% 39.63/39.68 inference(scs_inference,[],[32,24,10,8,21,20,321,19,6,221,5,39,40,38,35,316])).
% 39.63/39.68 cnf(346,plain,
% 39.63/39.68 (P6(x3461,x3461,x3461)),
% 39.63/39.68 inference(rename_variables,[],[20])).
% 39.63/39.68 cnf(353,plain,
% 39.63/39.68 (P6(a5,a4,a3)+P6(a5,a4,a1)),
% 39.63/39.68 inference(scs_inference,[],[23,30,15,20,346,187,245,4,3,221,5,44,40,35,39,42])).
% 39.63/39.68 cnf(406,plain,
% 39.63/39.69 (P6(x4061,x4061,x4061)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(408,plain,
% 39.63/39.69 (~P6(a3,a5,x4081)+~P6(a5,x4081,a3)),
% 39.63/39.69 inference(scs_inference,[],[31,20,406,43,39,44])).
% 39.63/39.69 cnf(411,plain,
% 39.63/39.69 (~P6(a5,a4,a3)+P6(a3,a5,a1)),
% 39.63/39.69 inference(scs_inference,[],[31,20,406,43,39,44,303])).
% 39.63/39.69 cnf(412,plain,
% 39.63/39.69 (~P6(a5,a4,a3)+P6(a1,a3,a4)+P6(a1,a3,a3)),
% 39.63/39.69 inference(scs_inference,[],[31,20,406,43,39,44,303,309])).
% 39.63/39.69 cnf(427,plain,
% 39.63/39.69 (P6(x4271,x4271,x4271)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(429,plain,
% 39.63/39.69 (~P6(a4,a5,x4291)+~P6(a5,x4291,a4)),
% 39.63/39.69 inference(scs_inference,[],[32,19,20,427,221,34,43,36,44])).
% 39.63/39.69 cnf(441,plain,
% 39.63/39.69 (~P6(a5,x4411,a3)+~P6(x4411,a3,a5)),
% 39.63/39.69 inference(scs_inference,[],[26,20,248,229,41,34,33,43])).
% 39.63/39.69 cnf(445,plain,
% 39.63/39.69 (P6(a3,a1,a3)+P6(a3,a1,a5)+P6(a3,a1,a4)),
% 39.63/39.69 inference(scs_inference,[],[96,26,20,248,229,1,2,41,34,33,43,42])).
% 39.63/39.69 cnf(461,plain,
% 39.63/39.69 (~P6(a1,a3,a3)),
% 39.63/39.69 inference(scs_inference,[],[24,19,20,34,39,41])).
% 39.63/39.69 cnf(462,plain,
% 39.63/39.69 (P6(x4621,x4621,x4621)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(464,plain,
% 39.63/39.69 (~P6(a1,x4641,a4)+~P6(x4641,a4,a1)),
% 39.63/39.69 inference(scs_inference,[],[24,27,19,20,462,34,39,41,43])).
% 39.63/39.69 cnf(468,plain,
% 39.63/39.69 (~P6(a3,a4,a1)+P6(a3,a5,a4)),
% 39.63/39.69 inference(scs_inference,[],[24,27,19,20,462,34,39,41,43,309])).
% 39.63/39.69 cnf(484,plain,
% 39.63/39.69 (~P6(a5,a4,a3)+P6(a1,a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[461,412])).
% 39.63/39.69 cnf(487,plain,
% 39.63/39.69 (~P6(a4,a5,a5)),
% 39.63/39.69 inference(scs_inference,[],[29,20,44,41])).
% 39.63/39.69 cnf(490,plain,
% 39.63/39.69 (~P6(a4,a1,a5)+~P3(a4,a2)),
% 39.63/39.69 inference(scs_inference,[],[18,29,20,44,41,36])).
% 39.63/39.69 cnf(501,plain,
% 39.63/39.69 (P6(x5011,x5011,x5011)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(508,plain,
% 39.63/39.69 (P6(a3,a4,a3)+P6(a3,a4,a1)+P6(a3,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[25,21,20,501,280,3,2,6,221,40,38,36,34,42])).
% 39.63/39.69 cnf(515,plain,
% 39.63/39.69 (P6(x5151,x5151,x5151)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(518,plain,
% 39.63/39.69 (P6(x5181,x5181,x5181)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(522,plain,
% 39.63/39.69 (~P6(a5,a3,a5)),
% 39.63/39.69 inference(scs_inference,[],[12,32,26,24,20,515,518,7,221,43,36,39,38,40])).
% 39.63/39.69 cnf(527,plain,
% 39.63/39.69 (P6(a5,a3,a4)+P6(a5,a3,a1)),
% 39.63/39.69 inference(scs_inference,[],[522,253])).
% 39.63/39.69 cnf(532,plain,
% 39.63/39.69 (P6(a4,a5,a3)+P6(a4,a5,a1)),
% 39.63/39.69 inference(scs_inference,[],[30,15,19,20,320,487,4,3,8,5,44,35,42])).
% 39.63/39.69 cnf(534,plain,
% 39.63/39.69 (P6(a4,a5,a1)+~P6(a5,a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[30,15,19,20,320,487,4,3,8,5,44,35,42,429])).
% 39.63/39.69 cnf(601,plain,
% 39.63/39.69 (P6(x6011,x6011,x6011)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(604,plain,
% 39.63/39.69 (P6(x6041,x6041,x6041)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(606,plain,
% 39.63/39.69 (~P6(a5,x6061,a4)+~P6(x6061,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[29,21,20,601,604,6,221,39,38,36,43])).
% 39.63/39.69 cnf(608,plain,
% 39.63/39.69 (P6(x6081,x6081,x6081)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(610,plain,
% 39.63/39.69 (~P6(a1,a4,a1)),
% 39.63/39.69 inference(scs_inference,[],[29,22,21,20,601,604,608,6,221,39,38,36,43,40])).
% 39.63/39.69 cnf(613,plain,
% 39.63/39.69 (~P6(a1,a4,a5)+P6(a5,a1,a3)+P6(a5,a1,a5)),
% 39.63/39.69 inference(scs_inference,[],[29,22,21,20,601,604,608,202,4,1,6,221,39,38,36,43,40,42])).
% 39.63/39.69 cnf(629,plain,
% 39.63/39.69 (~P3(a4,a1)+~P3(a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[15,26,28,19,20,12,7,6,221,44,36,37,38,35])).
% 39.63/39.69 cnf(662,plain,
% 39.63/39.69 (P6(x6621,x6621,x6621)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(665,plain,
% 39.63/39.69 (P6(x6651,x6651,x6651)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(669,plain,
% 39.63/39.69 (~P6(a4,x6691,a3)+~P6(a3,a4,x6691)),
% 39.63/39.69 inference(scs_inference,[],[25,23,21,20,662,665,6,15,221,40,38,36,34,44])).
% 39.63/39.69 cnf(680,plain,
% 39.63/39.69 (P6(x6801,x6801,x6801)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(682,plain,
% 39.63/39.69 (~P6(a3,a4,a3)),
% 39.63/39.69 inference(scs_inference,[],[28,21,20,680,6,221,43,38,40])).
% 39.63/39.69 cnf(683,plain,
% 39.63/39.69 (P6(x6831,x6831,x6831)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(685,plain,
% 39.63/39.69 (~P6(a1,a4,a4)),
% 39.63/39.69 inference(scs_inference,[],[28,27,21,20,680,683,6,221,43,38,40,41])).
% 39.63/39.69 cnf(694,plain,
% 39.63/39.69 (P6(a3,a4,a5)+P6(a3,a4,a1)),
% 39.63/39.69 inference(scs_inference,[],[682,508])).
% 39.63/39.69 cnf(710,plain,
% 39.63/39.69 (~P6(a4,x7101,a1)+~P6(x7101,a1,a4)),
% 39.63/39.69 inference(scs_inference,[],[22,19,20,34,41,43])).
% 39.63/39.69 cnf(725,plain,
% 39.63/39.69 (P3(a4,a2)+~P3(a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[328,629])).
% 39.63/39.69 cnf(799,plain,
% 39.63/39.69 (P6(x7991,x7991,x7991)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(802,plain,
% 39.63/39.69 (P6(x8021,x8021,x8021)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(806,plain,
% 39.63/39.69 (~P6(a3,a1,x8061)+~P6(a1,x8061,a3)),
% 39.63/39.69 inference(scs_inference,[],[21,29,221,6,20,799,802,40,38,36,34,44])).
% 39.63/39.69 cnf(807,plain,
% 39.63/39.69 (P6(x8071,x8071,x8071)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(809,plain,
% 39.63/39.69 (~P6(a3,x8091,a1)+~P6(x8091,a1,a3)),
% 39.63/39.69 inference(scs_inference,[],[21,29,221,6,20,799,802,807,40,38,36,34,44,43])).
% 39.63/39.69 cnf(826,plain,
% 39.63/39.69 (P6(x8261,x8261,x8261)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(828,plain,
% 39.63/39.69 (~P6(a3,a1,a3)),
% 39.63/39.69 inference(scs_inference,[],[24,221,20,826,34,36,40])).
% 39.63/39.69 cnf(829,plain,
% 39.63/39.69 (P6(x8291,x8291,x8291)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(833,plain,
% 39.63/39.69 (P6(x8331,x8331,x8331)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(841,plain,
% 39.63/39.69 (~P6(a3,a4,a5)+~P6(a1,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[22,96,24,26,221,2,1,20,826,829,833,34,36,40,44,534,532,39,42,43])).
% 39.63/39.69 cnf(850,plain,
% 39.63/39.69 (P6(a3,a1,a5)+P6(a3,a1,a4)),
% 39.63/39.69 inference(scs_inference,[],[828,445])).
% 39.63/39.69 cnf(867,plain,
% 39.63/39.69 (~P6(a5,a1,a5)),
% 39.63/39.69 inference(scs_inference,[],[23,20,40])).
% 39.63/39.69 cnf(890,plain,
% 39.63/39.69 (~P6(a1,a4,a5)+P6(a5,a1,a3)),
% 39.63/39.69 inference(scs_inference,[],[867,613])).
% 39.63/39.69 cnf(979,plain,
% 39.63/39.69 (P6(x9791,x9791,x9791)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(984,plain,
% 39.63/39.69 (P6(a1,a4,a3)+P6(a1,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[221,685,610,3,1,21,6,20,979,34,38,36,42])).
% 39.63/39.69 cnf(1001,plain,
% 39.63/39.69 (~P6(a5,a3,a1)+~P6(a1,a4,a3)),
% 39.63/39.69 inference(scs_inference,[],[30,20,44,43,850,806])).
% 39.63/39.69 cnf(1010,plain,
% 39.63/39.69 (~P6(a5,a3,a1)+P6(a5,a4,a1)),
% 39.63/39.69 inference(scs_inference,[],[187,245,248,229,30,4,3,20,44,43,850,806,710,165,441,33,42])).
% 39.63/39.69 cnf(1026,plain,
% 39.63/39.69 (P6(x10261,x10261,x10261)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(1032,plain,
% 39.63/39.69 (~P6(a4,a1,a5)+~P6(a5,a3,a1)),
% 39.63/39.69 inference(scs_inference,[],[32,221,20,1026,34,43,36,44,1010])).
% 39.63/39.69 cnf(1077,plain,
% 39.63/39.69 (P6(x10771,x10771,x10771)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(1084,plain,
% 39.63/39.69 (~P6(a1,a3,a5)+P6(a1,a4,a3)),
% 39.63/39.69 inference(scs_inference,[],[30,221,610,685,3,1,20,1077,43,36,44,890,42])).
% 39.63/39.69 cnf(2779,plain,
% 39.63/39.69 (~P6(a4,a1,a5)+~P3(a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[490,725])).
% 39.63/39.69 cnf(6090,plain,
% 39.63/39.69 (P6(a5,a3,a1)+~P6(a3,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[222,527])).
% 39.63/39.69 cnf(7352,plain,
% 39.63/39.69 (P6(a3,a4,a1)+~P6(a5,a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[606,694])).
% 39.63/39.69 cnf(9351,plain,
% 39.63/39.69 (P6(a1,a4,a3)+~P6(a3,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[841,984])).
% 39.63/39.69 cnf(11210,plain,
% 39.63/39.69 (~P6(a1,a3,a5)+~P6(a3,a1,a4)),
% 39.63/39.69 inference(scs_inference,[],[1084,806])).
% 39.63/39.69 cnf(11837,plain,
% 39.63/39.69 (P6(a3,a5,a4)+~P6(a5,a3,a4)),
% 39.63/39.69 inference(scs_inference,[],[7352,468])).
% 39.63/39.69 cnf(13385,plain,
% 39.63/39.69 (~P6(a5,a3,a1)+~P6(a3,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[9351,1001])).
% 39.63/39.69 cnf(14696,plain,
% 39.63/39.69 (~P6(a1,a3,a5)+P6(a3,a1,a5)),
% 39.63/39.69 inference(scs_inference,[],[1,2,96,828,11210,42])).
% 39.63/39.69 cnf(14835,plain,
% 39.63/39.69 (P6(x148351,x148351,x148351)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(14841,plain,
% 39.63/39.69 (~P6(a4,x148411,x148412)+~P6(a3,x148411,x148412)),
% 39.63/39.69 inference(scs_inference,[],[15,20,14835,6,19,21,25,221,34,36,44,38,41])).
% 39.63/39.69 cnf(15526,plain,
% 39.63/39.69 (~P6(a5,a3,a4)+~P6(a5,a4,a3)),
% 39.63/39.69 inference(scs_inference,[],[11837,408])).
% 39.63/39.69 cnf(20365,plain,
% 39.63/39.69 (~P6(a3,a4,a5)),
% 39.63/39.69 inference(scs_inference,[],[13385,6090])).
% 39.63/39.69 cnf(20366,plain,
% 39.63/39.69 (P6(a3,a4,a1)),
% 39.63/39.69 inference(scs_inference,[],[20365,694])).
% 39.63/39.69 cnf(20376,plain,
% 39.63/39.69 (P6(a3,a5,a4)),
% 39.63/39.69 inference(scs_inference,[],[20366,468])).
% 39.63/39.69 cnf(20389,plain,
% 39.63/39.69 (P6(x203891,x203891,x203891)),
% 39.63/39.69 inference(rename_variables,[],[20])).
% 39.63/39.69 cnf(20422,plain,
% 39.63/39.69 (~P6(a3,a5,a4)),
% 39.63/39.69 inference(scs_inference,[],[828,20366,1,25,18,2,26,22,9,21,19,8,6,20,20389,96,221,29,669,126,38,41,36,1032,14841,464,527,353,34,328,42,35,44,43,15526,14696,2779,484,806,411,809,408])).
% 39.63/39.69 cnf(20434,plain,
% 39.63/39.69 ($false),
% 39.63/39.69 inference(scs_inference,[],[20376,20422]),
% 39.63/39.69 ['proof']).
% 39.63/39.70 % SZS output end Proof
% 39.63/39.70 % Total time :38.960000s
%------------------------------------------------------------------------------