TSTP Solution File: GRP124-9.004 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n013.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 00:11:03 EDT 2023
% Result : Unsatisfiable 2.11s 2.20s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:02:01 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 2.11/2.19 %-------------------------------------------
% 2.11/2.19 % File :CSE---1.6
% 2.11/2.19 % Problem :theBenchmark
% 2.11/2.19 % Transform :cnf
% 2.11/2.19 % Format :tptp:raw
% 2.11/2.19 % Command :java -jar mcs_scs.jar %d %s
% 2.11/2.19
% 2.11/2.19 % Result :Theorem 1.570000s
% 2.11/2.19 % Output :CNFRefutation 1.570000s
% 2.11/2.19 %-------------------------------------------
% 2.11/2.19 %--------------------------------------------------------------------------
% 2.11/2.19 % File : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 2.11/2.19 % Domain : Group Theory (Quasigroups)
% 2.11/2.19 % Problem : (3,1,2) conjugate orthogonality
% 2.11/2.19 % Version : [Sla93] axioms : Augmented.
% 2.11/2.19 % Theorem formulation : Uses a second group.
% 2.11/2.19 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 2.11/2.19 % Generate the multiplication table for the specified quasi-
% 2.11/2.19 % group with 4 elements.
% 2.11/2.19
% 2.11/2.19 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 2.11/2.19 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 2.11/2.19 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 2.11/2.19 % Source : [TPTP]
% 2.11/2.19 % Names :
% 2.11/2.19
% 2.11/2.19 % Status : Unsatisfiable
% 2.11/2.19 % Rating : 0.00 v2.1.0
% 2.11/2.19 % Syntax : Number of clauses : 29 ( 18 unt; 4 nHn; 27 RR)
% 2.11/2.19 % Number of literals : 63 ( 0 equ; 34 neg)
% 2.11/2.19 % Maximal clause size : 6 ( 2 avg)
% 2.11/2.19 % Maximal term depth : 1 ( 1 avg)
% 2.11/2.19 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 2.11/2.19 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 2.11/2.19 % Number of variables : 38 ( 0 sgn)
% 2.11/2.19 % SPC : CNF_UNS_EPR_NEQ_NHN
% 2.11/2.19
% 2.11/2.19 % Comments : [SFS93]'s axiomatization has been modified for this.
% 2.11/2.19 % : Substitution axioms are not needed, as any positive equality
% 2.11/2.19 % literals should resolve on negative ones directly.
% 2.11/2.19 % : Version 9 has surjectivity and rotation
% 2.11/2.19 % : tptp2X: -f tptp -s4 GRP124-9.g
% 2.11/2.19 % Bugfixes : v1.2.1 - Clauses row_surjectivity and column_surjectivity fixed.
% 2.11/2.19 %--------------------------------------------------------------------------
% 2.11/2.19 cnf(row_surjectivity,axiom,
% 2.11/2.19 ( ~ group_element(X)
% 2.11/2.19 | ~ group_element(Y)
% 2.11/2.19 | product(e_1,X,Y)
% 2.11/2.19 | product(e_2,X,Y)
% 2.11/2.19 | product(e_3,X,Y)
% 2.11/2.19 | product(e_4,X,Y) ) ).
% 2.11/2.19
% 2.11/2.19 cnf(column_surjectivity,axiom,
% 2.11/2.19 ( ~ group_element(X)
% 2.11/2.19 | ~ group_element(Y)
% 2.11/2.19 | product(X,e_1,Y)
% 2.11/2.19 | product(X,e_2,Y)
% 2.11/2.19 | product(X,e_3,Y)
% 2.11/2.19 | product(X,e_4,Y) ) ).
% 2.11/2.19
% 2.11/2.19 cnf(element_1,axiom,
% 2.11/2.19 group_element(e_1) ).
% 2.11/2.19
% 2.11/2.19 cnf(element_2,axiom,
% 2.11/2.19 group_element(e_2) ).
% 2.11/2.19
% 2.11/2.19 cnf(element_3,axiom,
% 2.11/2.19 group_element(e_3) ).
% 2.11/2.19
% 2.11/2.19 cnf(element_4,axiom,
% 2.11/2.19 group_element(e_4) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_1_is_not_e_2,axiom,
% 2.11/2.19 ~ equalish(e_1,e_2) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_1_is_not_e_3,axiom,
% 2.11/2.19 ~ equalish(e_1,e_3) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_1_is_not_e_4,axiom,
% 2.11/2.19 ~ equalish(e_1,e_4) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_2_is_not_e_1,axiom,
% 2.11/2.19 ~ equalish(e_2,e_1) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_2_is_not_e_3,axiom,
% 2.11/2.19 ~ equalish(e_2,e_3) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_2_is_not_e_4,axiom,
% 2.11/2.19 ~ equalish(e_2,e_4) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_3_is_not_e_1,axiom,
% 2.11/2.19 ~ equalish(e_3,e_1) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_3_is_not_e_2,axiom,
% 2.11/2.19 ~ equalish(e_3,e_2) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_3_is_not_e_4,axiom,
% 2.11/2.19 ~ equalish(e_3,e_4) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_4_is_not_e_1,axiom,
% 2.11/2.19 ~ equalish(e_4,e_1) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_4_is_not_e_2,axiom,
% 2.11/2.19 ~ equalish(e_4,e_2) ).
% 2.11/2.19
% 2.11/2.19 cnf(e_4_is_not_e_3,axiom,
% 2.11/2.19 ~ equalish(e_4,e_3) ).
% 2.11/2.19
% 2.11/2.19 cnf(product1_total_function1,axiom,
% 2.11/2.19 ( ~ group_element(X)
% 2.11/2.19 | ~ group_element(Y)
% 2.11/2.19 | product1(X,Y,e_1)
% 2.11/2.19 | product1(X,Y,e_2)
% 2.11/2.19 | product1(X,Y,e_3)
% 2.11/2.19 | product1(X,Y,e_4) ) ).
% 2.11/2.19
% 2.11/2.19 cnf(product1_total_function2,axiom,
% 2.11/2.19 ( ~ product1(X,Y,W)
% 2.11/2.19 | ~ product1(X,Y,Z)
% 2.11/2.19 | equalish(W,Z) ) ).
% 2.11/2.19
% 2.11/2.19 cnf(product1_right_cancellation,axiom,
% 2.11/2.20 ( ~ product1(X,W,Y)
% 2.11/2.20 | ~ product1(X,Z,Y)
% 2.11/2.20 | equalish(W,Z) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product1_left_cancellation,axiom,
% 2.11/2.20 ( ~ product1(W,Y,X)
% 2.11/2.20 | ~ product1(Z,Y,X)
% 2.11/2.20 | equalish(W,Z) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product1_idempotence,axiom,
% 2.11/2.20 product1(X,X,X) ).
% 2.11/2.20
% 2.11/2.20 cnf(product2_total_function1,axiom,
% 2.11/2.20 ( ~ group_element(X)
% 2.11/2.20 | ~ group_element(Y)
% 2.11/2.20 | product2(X,Y,e_1)
% 2.11/2.20 | product2(X,Y,e_2)
% 2.11/2.20 | product2(X,Y,e_3)
% 2.11/2.20 | product2(X,Y,e_4) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product2_total_function2,axiom,
% 2.11/2.20 ( ~ product2(X,Y,W)
% 2.11/2.20 | ~ product2(X,Y,Z)
% 2.11/2.20 | equalish(W,Z) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product2_right_cancellation,axiom,
% 2.11/2.20 ( ~ product2(X,W,Y)
% 2.11/2.20 | ~ product2(X,Z,Y)
% 2.11/2.20 | equalish(W,Z) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product2_left_cancellation,axiom,
% 2.11/2.20 ( ~ product2(W,Y,X)
% 2.11/2.20 | ~ product2(Z,Y,X)
% 2.11/2.20 | equalish(W,Z) ) ).
% 2.11/2.20
% 2.11/2.20 cnf(product2_idempotence,axiom,
% 2.11/2.20 product2(X,X,X) ).
% 2.11/2.20
% 2.11/2.20 cnf(qg2a,negated_conjecture,
% 2.11/2.20 ( ~ product1(X,Y,Z1)
% 2.11/2.20 | ~ product1(Z1,X,Z2)
% 2.11/2.20 | product2(Z2,Y,X) ) ).
% 2.11/2.20
% 2.11/2.20 %--------------------------------------------------------------------------
% 2.11/2.20 %-------------------------------------------
% 2.11/2.20 % Proof found
% 2.11/2.20 % SZS status Theorem for theBenchmark
% 2.11/2.20 % SZS output start Proof
% 2.11/2.20 %ClaNum:29(EqnAxiom:0)
% 2.11/2.20 %VarNum:103(SingletonVarNum:38)
% 2.11/2.20 %MaxLitNum:6
% 2.11/2.20 %MaxfuncDepth:0
% 2.11/2.20 %SharedTerms:20
% 2.11/2.20 %goalClause: 25
% 2.11/2.20 [1]P1(a1)
% 2.11/2.20 [2]P1(a2)
% 2.11/2.20 [3]P1(a3)
% 2.11/2.20 [4]P1(a4)
% 2.11/2.20 [7]~P2(a1,a2)
% 2.11/2.20 [8]~P2(a1,a3)
% 2.11/2.20 [9]~P2(a1,a4)
% 2.11/2.20 [10]~P2(a2,a1)
% 2.11/2.20 [11]~P2(a2,a3)
% 2.11/2.20 [12]~P2(a2,a4)
% 2.11/2.20 [13]~P2(a3,a1)
% 2.11/2.20 [14]~P2(a3,a2)
% 2.11/2.20 [15]~P2(a3,a4)
% 2.11/2.20 [16]~P2(a4,a1)
% 2.11/2.20 [17]~P2(a4,a2)
% 2.11/2.20 [18]~P2(a4,a3)
% 2.11/2.20 [5]P3(x51,x51,x51)
% 2.11/2.20 [6]P5(x61,x61,x61)
% 2.11/2.20 [19]~P3(x193,x194,x191)+P2(x191,x192)+~P3(x193,x194,x192)
% 2.11/2.20 [20]~P5(x203,x204,x201)+P2(x201,x202)+~P5(x203,x204,x202)
% 2.11/2.20 [21]~P3(x213,x211,x214)+P2(x211,x212)+~P3(x213,x212,x214)
% 2.11/2.20 [22]~P5(x223,x221,x224)+P2(x221,x222)+~P5(x223,x222,x224)
% 2.11/2.20 [23]~P3(x231,x233,x234)+P2(x231,x232)+~P3(x232,x233,x234)
% 2.11/2.20 [24]~P5(x241,x243,x244)+P2(x241,x242)+~P5(x242,x243,x244)
% 2.11/2.20 [25]~P3(x253,x252,x254)+P5(x251,x252,x253)+~P3(x254,x253,x251)
% 2.11/2.20 [26]~P1(x262)+~P1(x261)+P3(x261,x262,a2)+P3(x261,x262,a3)+P3(x261,x262,a4)+P3(x261,x262,a1)
% 2.11/2.20 [27]~P1(x272)+~P1(x271)+P5(x271,x272,a2)+P5(x271,x272,a3)+P5(x271,x272,a4)+P5(x271,x272,a1)
% 2.11/2.20 [28]~P1(x282)+~P1(x281)+P4(x281,a2,x282)+P4(x281,a3,x282)+P4(x281,a4,x282)+P4(x281,a1,x282)
% 2.11/2.20 [29]~P1(x292)+~P1(x291)+P4(a2,x291,x292)+P4(a3,x291,x292)+P4(a4,x291,x292)+P4(a1,x291,x292)
% 2.11/2.20 %EqnAxiom
% 2.11/2.20
% 2.11/2.20 %-------------------------------------------
% 2.11/2.20 cnf(31,plain,
% 2.11/2.20 (~P3(a2,a1,a1)),
% 2.11/2.20 inference(scs_inference,[],[5,6,7,24,23])).
% 2.11/2.20 cnf(32,plain,
% 2.11/2.20 (P3(x321,x321,x321)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(35,plain,
% 2.11/2.20 (P5(x351,x351,x351)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(38,plain,
% 2.11/2.20 (P3(x381,x381,x381)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(46,plain,
% 2.11/2.20 (~P3(x461,a2,a1)+~P3(a2,a1,x461)),
% 2.11/2.20 inference(scs_inference,[],[5,32,38,6,35,7,24,23,22,21,20,19,25])).
% 2.11/2.20 cnf(48,plain,
% 2.11/2.20 (~P3(a1,a3,a3)),
% 2.11/2.20 inference(scs_inference,[],[8,5,23])).
% 2.11/2.20 cnf(49,plain,
% 2.11/2.20 (P3(x491,x491,x491)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(54,plain,
% 2.11/2.20 (~P5(a3,a1,a1)),
% 2.11/2.20 inference(scs_inference,[],[8,5,49,6,23,21,24])).
% 2.11/2.20 cnf(55,plain,
% 2.11/2.20 (P5(x551,x551,x551)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(58,plain,
% 2.11/2.20 (P5(x581,x581,x581)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(60,plain,
% 2.11/2.20 (~P5(a3,a3,a1)),
% 2.11/2.20 inference(scs_inference,[],[8,5,49,6,55,58,23,21,24,22,20])).
% 2.11/2.20 cnf(78,plain,
% 2.11/2.20 (~P5(a1,a4,a4)),
% 2.11/2.20 inference(scs_inference,[],[9,5,6,54,21,25,24])).
% 2.11/2.20 cnf(88,plain,
% 2.11/2.20 (P3(x881,x881,x881)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(93,plain,
% 2.11/2.20 (~P5(a1,a2,a2)),
% 2.11/2.20 inference(scs_inference,[],[10,5,88,6,78,23,21,25,24])).
% 2.11/2.20 cnf(96,plain,
% 2.11/2.20 (P3(a2,a1,a4)+P3(a2,a1,a3)),
% 2.11/2.20 inference(scs_inference,[],[2,10,31,5,88,6,78,1,23,21,25,24,26])).
% 2.11/2.20 cnf(102,plain,
% 2.11/2.20 (~P3(a3,a2,a3)),
% 2.11/2.20 inference(scs_inference,[],[11,6,5,22,21])).
% 2.11/2.20 cnf(103,plain,
% 2.11/2.20 (P3(x1031,x1031,x1031)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(105,plain,
% 2.11/2.20 (~P3(a3,a2,a2)),
% 2.11/2.20 inference(scs_inference,[],[11,6,5,103,22,21,23])).
% 2.11/2.20 cnf(120,plain,
% 2.11/2.20 (P3(x1201,x1201,x1201)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(125,plain,
% 2.11/2.20 (P3(a2,a4,a1)+P3(a2,a4,a3)+P3(a2,a4,a2)),
% 2.11/2.20 inference(scs_inference,[],[12,4,5,120,6,2,20,22,23,19,26])).
% 2.11/2.20 cnf(130,plain,
% 2.11/2.20 (P3(x1301,x1301,x1301)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(135,plain,
% 2.11/2.20 (P5(x1351,x1351,x1351)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(137,plain,
% 2.11/2.20 (~P5(a3,a3,a2)),
% 2.11/2.20 inference(scs_inference,[],[13,14,5,130,6,135,19,21,22,20])).
% 2.11/2.20 cnf(140,plain,
% 2.11/2.20 (~P3(a3,a4,a3)),
% 2.11/2.20 inference(scs_inference,[],[15,5,21])).
% 2.11/2.20 cnf(150,plain,
% 2.11/2.20 (~P5(a1,a1,a4)),
% 2.11/2.20 inference(scs_inference,[],[5,16,6,19,20])).
% 2.11/2.20 cnf(151,plain,
% 2.11/2.20 (P5(x1511,x1511,x1511)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(154,plain,
% 2.11/2.20 (P3(x1541,x1541,x1541)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(157,plain,
% 2.11/2.20 (P3(x1571,x1571,x1571)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(159,plain,
% 2.11/2.20 (~P5(a4,a1,a4)),
% 2.11/2.20 inference(scs_inference,[],[5,154,16,6,151,93,19,20,25,21,22])).
% 2.11/2.20 cnf(160,plain,
% 2.11/2.20 (P5(x1601,x1601,x1601)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(165,plain,
% 2.11/2.20 (P3(a1,a4,a3)+P3(a1,a4,a2)),
% 2.11/2.20 inference(scs_inference,[],[5,154,157,16,6,151,93,4,1,19,20,25,21,22,23,26])).
% 2.11/2.20 cnf(167,plain,
% 2.11/2.20 (~P5(a4,a1,a1)),
% 2.11/2.20 inference(scs_inference,[],[5,154,157,16,6,151,160,93,4,1,19,20,25,21,22,23,26,24])).
% 2.11/2.20 cnf(174,plain,
% 2.11/2.20 (~P5(a4,a4,a2)),
% 2.11/2.20 inference(scs_inference,[],[17,6,24,20])).
% 2.11/2.20 cnf(175,plain,
% 2.11/2.20 (P5(x1751,x1751,x1751)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(178,plain,
% 2.11/2.20 (P3(x1781,x1781,x1781)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(183,plain,
% 2.11/2.20 (~P3(a4,a2,a2)),
% 2.11/2.20 inference(scs_inference,[],[5,178,17,18,6,175,24,20,19,22,23])).
% 2.11/2.20 cnf(204,plain,
% 2.11/2.20 (P3(x2041,x2041,x2041)),
% 2.11/2.20 inference(rename_variables,[],[5])).
% 2.11/2.20 cnf(206,plain,
% 2.11/2.20 (~P3(a4,a3,a4)),
% 2.11/2.20 inference(scs_inference,[],[6,18,167,5,204,20,25,21])).
% 2.11/2.20 cnf(209,plain,
% 2.11/2.20 (P3(a3,a2,a1)+P3(a3,a2,a4)),
% 2.11/2.20 inference(scs_inference,[],[6,18,167,102,105,3,2,5,204,20,25,21,26])).
% 2.11/2.20 cnf(217,plain,
% 2.11/2.20 (P5(x2171,x2171,x2171)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(222,plain,
% 2.11/2.20 (~P3(a4,a1,a4)),
% 2.11/2.20 inference(scs_inference,[],[7,159,5,6,217,22,24,20,25])).
% 2.11/2.20 cnf(230,plain,
% 2.11/2.20 (P5(x2301,x2301,x2301)),
% 2.11/2.20 inference(rename_variables,[],[6])).
% 2.11/2.20 cnf(234,plain,
% 2.11/2.20 (~P5(a3,a3,a4)),
% 2.11/2.20 inference(scs_inference,[],[14,15,5,6,230,24,19,20])).
% 2.11/2.20 cnf(260,plain,
% 2.11/2.20 (~P3(a4,a1,a3)+P3(a1,a3,a2)),
% 2.11/2.20 inference(scs_inference,[],[8,48,60,3,1,6,5,22,21,26,25])).
% 2.11/2.20 cnf(264,plain,
% 2.11/2.20 (~P3(a4,a2,a4)),
% 2.11/2.20 inference(scs_inference,[],[12,6,5,24,21])).
% 2.11/2.20 cnf(274,plain,
% 2.11/2.20 (P3(a4,a2,a3)+P3(a4,a2,a1)),
% 2.11/2.20 inference(scs_inference,[],[183,264,4,2,5,19,26])).
% 2.11/2.20 cnf(292,plain,
% 2.11/2.20 (~P3(a2,a4,a2)),
% 2.11/2.20 inference(scs_inference,[],[17,6,5,24,21])).
% 2.11/2.20 cnf(295,plain,
% 2.11/2.20 (P3(a2,a4,a3)+P3(a2,a4,a1)),
% 2.11/2.20 inference(scs_inference,[],[292,125])).
% 2.11/2.20 cnf(298,plain,
% 2.11/2.20 (~P3(a4,a3,a3)),
% 2.11/2.20 inference(scs_inference,[],[15,6,5,20,23])).
% 2.11/2.20 cnf(305,plain,
% 2.11/2.20 (~P5(a4,a3,a3)),
% 2.11/2.20 inference(scs_inference,[],[60,18,5,6,23,25,24])).
% 2.11/2.20 cnf(308,plain,
% 2.11/2.20 (~P3(a1,a3,a2)+P3(a2,a1,a4)),
% 2.11/2.20 inference(scs_inference,[],[60,18,5,6,23,25,24,96])).
% 2.11/2.20 cnf(315,plain,
% 2.11/2.20 (~P3(a4,x3151,a3)+P5(a2,x3151,a4)+P3(a3,a4,a1)+P3(a3,a4,a4)),
% 2.11/2.20 inference(scs_inference,[],[140,4,3,6,22,26,25])).
% 2.11/2.20 cnf(334,plain,
% 2.11/2.20 (~P5(a4,a3,a4)),
% 2.11/2.20 inference(scs_inference,[],[18,6,5,21,22])).
% 2.11/2.20 cnf(345,plain,
% 2.11/2.20 (~P3(a2,a3,a2)),
% 2.11/2.20 inference(scs_inference,[],[11,5,6,24,21])).
% 2.11/2.20 cnf(357,plain,
% 2.11/2.20 (~P5(a4,a4,a3)),
% 2.11/2.20 inference(scs_inference,[],[18,5,6,23,20])).
% 2.11/2.20 cnf(362,plain,
% 2.11/2.20 (~P3(a3,a4,a4)),
% 2.11/2.20 inference(scs_inference,[],[15,5,21,23])).
% 2.11/2.20 cnf(373,plain,
% 2.11/2.20 (P3(a3,a4,a1)+P5(a2,x3731,a4)+~P3(a4,x3731,a3)),
% 2.11/2.20 inference(scs_inference,[],[362,315])).
% 2.11/2.20 cnf(381,plain,
% 2.11/2.20 (P3(a4,a1,a2)+P3(a4,a1,a3)),
% 2.11/2.21 inference(scs_inference,[],[222,305,334,9,4,3,1,6,5,22,23,27,26])).
% 2.11/2.21 cnf(387,plain,
% 2.11/2.21 (~P3(a2,a4,a1)+P3(a2,a3,a4)+P3(a2,a3,a3)),
% 2.11/2.21 inference(scs_inference,[],[18,345,3,2,6,20,26,21])).
% 2.11/2.21 cnf(391,plain,
% 2.11/2.21 (~P3(x3911,a4,a3)+~P3(a4,a3,x3911)),
% 2.11/2.21 inference(scs_inference,[],[234,6,24,25])).
% 2.11/2.21 cnf(401,plain,
% 2.11/2.21 (P5(x4011,x4011,x4011)),
% 2.11/2.21 inference(rename_variables,[],[6])).
% 2.11/2.21 cnf(403,plain,
% 2.11/2.21 (~P5(a2,a2,a4)),
% 2.11/2.21 inference(scs_inference,[],[10,12,5,6,401,23,22,20])).
% 2.11/2.21 cnf(409,plain,
% 2.11/2.21 (P3(a3,a4,a1)+~P3(a4,a2,a3)),
% 2.11/2.21 inference(scs_inference,[],[403,6,22,373])).
% 2.11/2.21 cnf(414,plain,
% 2.11/2.21 (~P3(a3,a2,a1)+~P3(a4,a2,a3)),
% 2.11/2.21 inference(scs_inference,[],[17,18,403,6,22,373,24,21])).
% 2.11/2.21 cnf(427,plain,
% 2.11/2.21 (P3(a4,a3,a2)+P3(a4,a3,a1)),
% 2.11/2.21 inference(scs_inference,[],[206,298,4,3,6,20,26])).
% 2.11/2.21 cnf(446,plain,
% 2.11/2.21 (~P3(a2,a3,a3)),
% 2.11/2.21 inference(scs_inference,[],[14,5,6,24,23])).
% 2.11/2.21 cnf(452,plain,
% 2.11/2.21 (~P3(a2,a4,a1)+P3(a2,a3,a4)),
% 2.11/2.21 inference(scs_inference,[],[446,387])).
% 2.11/2.21 cnf(486,plain,
% 2.11/2.21 (~P3(x4861,a2,a3)+~P3(a2,a3,x4861)),
% 2.11/2.21 inference(scs_inference,[],[137,5,19,25])).
% 2.11/2.21 cnf(498,plain,
% 2.11/2.21 (P3(a2,a1,a4)+~P3(a4,a1,a3)),
% 2.11/2.21 inference(scs_inference,[],[260,308])).
% 2.11/2.21 cnf(507,plain,
% 2.11/2.21 (~P3(x5071,a4,a1)+~P3(a4,a1,x5071)),
% 2.11/2.21 inference(scs_inference,[],[150,5,19,25])).
% 2.11/2.21 cnf(523,plain,
% 2.11/2.21 (P3(a2,a1,a4)+P3(a4,a1,a2)),
% 2.11/2.21 inference(scs_inference,[],[381,498])).
% 2.11/2.21 cnf(526,plain,
% 2.11/2.21 (~P3(x5261,a2,a4)+~P3(a2,a4,x5261)),
% 2.11/2.21 inference(scs_inference,[],[174,6,22,25])).
% 2.11/2.21 cnf(528,plain,
% 2.11/2.21 (P3(a4,a3,a1)+~P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[391,427])).
% 2.11/2.21 cnf(543,plain,
% 2.11/2.21 (P3(a4,a2,a1)+~P3(a3,a2,a1)),
% 2.11/2.21 inference(scs_inference,[],[414,274])).
% 2.11/2.21 cnf(545,plain,
% 2.11/2.21 (~P3(x5451,a4,a2)+~P3(a4,a2,x5451)),
% 2.11/2.21 inference(scs_inference,[],[403,25])).
% 2.11/2.21 cnf(559,plain,
% 2.11/2.21 (P3(a2,a3,a4)+P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[452,295])).
% 2.11/2.21 cnf(568,plain,
% 2.11/2.21 (~P3(x5681,a3,a4)+~P3(a3,a4,x5681)),
% 2.11/2.21 inference(scs_inference,[],[357,6,22,25])).
% 2.11/2.21 cnf(591,plain,
% 2.11/2.21 (P3(a4,a1,a2)+~P3(a4,a2,a1)),
% 2.11/2.21 inference(scs_inference,[],[523,46])).
% 2.11/2.21 cnf(597,plain,
% 2.11/2.21 (~P3(a1,a4,a3)+~P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[528,391])).
% 2.11/2.21 cnf(625,plain,
% 2.11/2.21 (P3(a2,a4,a3)+~P3(a4,a2,a3)),
% 2.11/2.21 inference(scs_inference,[],[559,486])).
% 2.11/2.21 cnf(651,plain,
% 2.11/2.21 (~P3(a4,a2,a1)+~P3(a2,a4,a1)),
% 2.11/2.21 inference(scs_inference,[],[591,507])).
% 2.11/2.21 cnf(657,plain,
% 2.11/2.21 (P3(a1,a4,a2)+~P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[597,165])).
% 2.11/2.21 cnf(699,plain,
% 2.11/2.21 (P3(a2,a4,a3)+~P3(a4,a2,a1)),
% 2.11/2.21 inference(scs_inference,[],[651,295])).
% 2.11/2.21 cnf(705,plain,
% 2.11/2.21 (~P3(a4,a2,a1)+~P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[657,545])).
% 2.11/2.21 cnf(746,plain,
% 2.11/2.21 (~P3(a4,a2,a1)),
% 2.11/2.21 inference(scs_inference,[],[699,705])).
% 2.11/2.21 cnf(747,plain,
% 2.11/2.21 (P3(a4,a2,a3)),
% 2.11/2.21 inference(scs_inference,[],[746,274])).
% 2.11/2.21 cnf(748,plain,
% 2.11/2.21 (~P3(a3,a2,a1)),
% 2.11/2.21 inference(scs_inference,[],[746,543])).
% 2.11/2.21 cnf(753,plain,
% 2.11/2.21 (P3(a3,a2,a4)),
% 2.11/2.21 inference(scs_inference,[],[748,209])).
% 2.11/2.21 cnf(754,plain,
% 2.11/2.21 (P3(a3,a4,a1)),
% 2.11/2.21 inference(scs_inference,[],[747,409])).
% 2.11/2.21 cnf(764,plain,
% 2.11/2.21 (P3(a2,a4,a3)),
% 2.11/2.21 inference(scs_inference,[],[747,625])).
% 2.20/2.21 cnf(789,plain,
% 2.20/2.21 ($false),
% 2.20/2.21 inference(scs_inference,[],[754,753,764,568,526]),
% 2.20/2.21 ['proof']).
% 2.20/2.21 % SZS output end Proof
% 2.20/2.21 % Total time :1.570000s
%------------------------------------------------------------------------------