TSTP Solution File: GRP127-1.004 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n015.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 00:11:06 EDT 2023
% Result : Unsatisfiable 1.08s 1.15s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Mon Aug 28 20:05:10 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 1.00/1.14 %-------------------------------------------
% 1.00/1.14 % File :CSE---1.6
% 1.00/1.14 % Problem :theBenchmark
% 1.00/1.14 % Transform :cnf
% 1.00/1.14 % Format :tptp:raw
% 1.00/1.14 % Command :java -jar mcs_scs.jar %d %s
% 1.00/1.14
% 1.00/1.14 % Result :Theorem 0.520000s
% 1.00/1.14 % Output :CNFRefutation 0.520000s
% 1.00/1.14 %-------------------------------------------
% 1.08/1.14 %--------------------------------------------------------------------------
% 1.08/1.14 % File : GRP127-1.004 : TPTP v8.1.2. Released v1.2.0.
% 1.08/1.14 % Domain : Group Theory (Quasigroups)
% 1.08/1.14 % Problem : ((b.a).b).b) = a
% 1.08/1.14 % Version : [Sla93] axioms.
% 1.08/1.14 % English : Generate the multiplication table for the specified quasi-
% 1.08/1.14 % group with 4 elements.
% 1.08/1.14
% 1.08/1.14 % Refs : [Ben89] Bennett (1989), Quasigroup Identities and Mendelsohn D
% 1.08/1.14 % : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 1.08/1.14 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 1.08/1.14 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 1.08/1.14 % Source : [Sla93]
% 1.08/1.14 % Names : QG5 [Sla93]
% 1.08/1.14 % : QG5 [FSB93]
% 1.08/1.14 % : QG5 [SFS95]
% 1.08/1.14 % : Bennett QG5 [TPTP]
% 1.08/1.14
% 1.08/1.14 % Status : Unsatisfiable
% 1.08/1.14 % Rating : 0.00 v2.1.0
% 1.08/1.14 % Syntax : Number of clauses : 22 ( 17 unt; 1 nHn; 21 RR)
% 1.08/1.14 % Number of literals : 35 ( 0 equ; 22 neg)
% 1.08/1.14 % Maximal clause size : 6 ( 1 avg)
% 1.08/1.14 % Maximal term depth : 1 ( 1 avg)
% 1.08/1.14 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 1.08/1.14 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 1.08/1.14 % Number of variables : 19 ( 0 sgn)
% 1.08/1.14 % SPC : CNF_UNS_EPR_NEQ_NHN
% 1.08/1.14
% 1.08/1.14 % Comments : [SFS93]'s axiomatization has been modified for this.
% 1.08/1.14 % : Substitution axioms are not needed, as any positive equality
% 1.08/1.14 % literals should resolve on negative ones directly.
% 1.08/1.14 % : This problem is extensively investigated in [Ben89].
% 1.08/1.14 % : tptp2X: -f tptp -s4 GRP127-1.g
% 1.08/1.14 %--------------------------------------------------------------------------
% 1.08/1.14 cnf(element_1,axiom,
% 1.08/1.14 group_element(e_1) ).
% 1.08/1.14
% 1.08/1.14 cnf(element_2,axiom,
% 1.08/1.14 group_element(e_2) ).
% 1.08/1.14
% 1.08/1.14 cnf(element_3,axiom,
% 1.08/1.14 group_element(e_3) ).
% 1.08/1.14
% 1.08/1.14 cnf(element_4,axiom,
% 1.08/1.14 group_element(e_4) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_1_is_not_e_2,axiom,
% 1.08/1.14 ~ equalish(e_1,e_2) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_1_is_not_e_3,axiom,
% 1.08/1.14 ~ equalish(e_1,e_3) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_1_is_not_e_4,axiom,
% 1.08/1.14 ~ equalish(e_1,e_4) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_2_is_not_e_1,axiom,
% 1.08/1.14 ~ equalish(e_2,e_1) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_2_is_not_e_3,axiom,
% 1.08/1.14 ~ equalish(e_2,e_3) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_2_is_not_e_4,axiom,
% 1.08/1.14 ~ equalish(e_2,e_4) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_3_is_not_e_1,axiom,
% 1.08/1.14 ~ equalish(e_3,e_1) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_3_is_not_e_2,axiom,
% 1.08/1.14 ~ equalish(e_3,e_2) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_3_is_not_e_4,axiom,
% 1.08/1.14 ~ equalish(e_3,e_4) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_4_is_not_e_1,axiom,
% 1.08/1.14 ~ equalish(e_4,e_1) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_4_is_not_e_2,axiom,
% 1.08/1.14 ~ equalish(e_4,e_2) ).
% 1.08/1.14
% 1.08/1.14 cnf(e_4_is_not_e_3,axiom,
% 1.08/1.14 ~ equalish(e_4,e_3) ).
% 1.08/1.14
% 1.08/1.14 cnf(product_total_function1,axiom,
% 1.08/1.14 ( ~ group_element(X)
% 1.08/1.14 | ~ group_element(Y)
% 1.08/1.14 | product(X,Y,e_1)
% 1.08/1.14 | product(X,Y,e_2)
% 1.08/1.14 | product(X,Y,e_3)
% 1.08/1.14 | product(X,Y,e_4) ) ).
% 1.08/1.14
% 1.08/1.14 cnf(product_total_function2,axiom,
% 1.08/1.14 ( ~ product(X,Y,W)
% 1.08/1.14 | ~ product(X,Y,Z)
% 1.08/1.14 | equalish(W,Z) ) ).
% 1.08/1.14
% 1.08/1.14 cnf(product_right_cancellation,axiom,
% 1.08/1.14 ( ~ product(X,W,Y)
% 1.08/1.14 | ~ product(X,Z,Y)
% 1.08/1.14 | equalish(W,Z) ) ).
% 1.08/1.14
% 1.08/1.14 cnf(product_left_cancellation,axiom,
% 1.08/1.14 ( ~ product(W,Y,X)
% 1.08/1.14 | ~ product(Z,Y,X)
% 1.08/1.15 | equalish(W,Z) ) ).
% 1.08/1.15
% 1.08/1.15 cnf(product_idempotence,axiom,
% 1.08/1.15 product(X,X,X) ).
% 1.08/1.15
% 1.08/1.15 cnf(qg3,negated_conjecture,
% 1.08/1.15 ( ~ product(Y,X,Z1)
% 1.08/1.15 | ~ product(Z1,Y,Z2)
% 1.08/1.15 | product(Z2,Y,X) ) ).
% 1.08/1.15
% 1.08/1.15 %--------------------------------------------------------------------------
% 1.08/1.15 %-------------------------------------------
% 1.08/1.15 % Proof found
% 1.08/1.15 % SZS status Theorem for theBenchmark
% 1.08/1.15 % SZS output start Proof
% 1.08/1.15 %ClaNum:22(EqnAxiom:0)
% 1.08/1.15 %VarNum:46(SingletonVarNum:19)
% 1.08/1.15 %MaxLitNum:6
% 1.08/1.15 %MaxfuncDepth:0
% 1.08/1.15 %SharedTerms:20
% 1.08/1.15 %goalClause: 21
% 1.08/1.15 [1]P1(a1)
% 1.08/1.15 [2]P1(a2)
% 1.08/1.15 [3]P1(a3)
% 1.08/1.15 [4]P1(a4)
% 1.08/1.15 [6]~P2(a1,a2)
% 1.08/1.15 [7]~P2(a1,a3)
% 1.08/1.15 [8]~P2(a1,a4)
% 1.08/1.15 [9]~P2(a2,a1)
% 1.08/1.15 [10]~P2(a2,a3)
% 1.08/1.15 [11]~P2(a2,a4)
% 1.08/1.15 [12]~P2(a3,a1)
% 1.08/1.15 [13]~P2(a3,a2)
% 1.08/1.15 [14]~P2(a3,a4)
% 1.08/1.15 [15]~P2(a4,a1)
% 1.08/1.15 [16]~P2(a4,a2)
% 1.08/1.15 [17]~P2(a4,a3)
% 1.08/1.15 [5]P3(x51,x51,x51)
% 1.08/1.15 [18]~P3(x183,x184,x181)+P2(x181,x182)+~P3(x183,x184,x182)
% 1.08/1.15 [19]~P3(x193,x191,x194)+P2(x191,x192)+~P3(x193,x192,x194)
% 1.08/1.15 [20]~P3(x201,x203,x204)+P2(x201,x202)+~P3(x202,x203,x204)
% 1.08/1.15 [21]~P3(x212,x213,x214)+P3(x211,x212,x213)+~P3(x214,x212,x211)
% 1.08/1.15 [22]~P1(x222)+~P1(x221)+P3(x221,x222,a2)+P3(x221,x222,a3)+P3(x221,x222,a4)+P3(x221,x222,a1)
% 1.08/1.15 %EqnAxiom
% 1.08/1.15
% 1.08/1.15 %-------------------------------------------
% 1.08/1.15 cnf(24,plain,
% 1.08/1.15 (~P3(a1,a2,a1)),
% 1.08/1.15 inference(scs_inference,[],[5,6,20,19])).
% 1.08/1.15 cnf(25,plain,
% 1.08/1.15 (P3(x251,x251,x251)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(30,plain,
% 1.08/1.15 (~P3(x301,a2,a1)+~P3(a2,a1,x301)),
% 1.08/1.15 inference(scs_inference,[],[5,25,6,20,19,18,21])).
% 1.08/1.15 cnf(32,plain,
% 1.08/1.15 (~P3(a3,a1,a3)),
% 1.08/1.15 inference(scs_inference,[],[7,5,19])).
% 1.08/1.15 cnf(33,plain,
% 1.08/1.15 (P3(x331,x331,x331)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(36,plain,
% 1.08/1.15 (P3(x361,x361,x361)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(38,plain,
% 1.08/1.15 (~P3(a3,a1,a1)),
% 1.08/1.15 inference(scs_inference,[],[7,5,33,36,19,18,20])).
% 1.08/1.15 cnf(43,plain,
% 1.08/1.15 (~P3(a2,x431,a1)+P3(a4,a2,x431)+P3(a1,a2,a3)+P3(a1,a2,a2)),
% 1.08/1.15 inference(scs_inference,[],[1,2,7,5,33,36,24,19,18,20,22,21])).
% 1.08/1.15 cnf(45,plain,
% 1.08/1.15 (~P3(a1,a1,a3)),
% 1.08/1.15 inference(scs_inference,[],[5,38,21])).
% 1.08/1.15 cnf(46,plain,
% 1.08/1.15 (P3(x461,x461,x461)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(50,plain,
% 1.08/1.15 (~P3(a1,a4,a4)),
% 1.08/1.15 inference(scs_inference,[],[8,5,46,38,21,18,20])).
% 1.08/1.15 cnf(53,plain,
% 1.08/1.15 (P3(a3,a1,a2)+P3(a3,a1,a4)),
% 1.08/1.15 inference(scs_inference,[],[3,8,5,46,32,38,1,21,18,20,22])).
% 1.08/1.15 cnf(56,plain,
% 1.08/1.15 (~P3(a2,a2,a1)),
% 1.08/1.15 inference(scs_inference,[],[9,5,18])).
% 1.08/1.15 cnf(57,plain,
% 1.08/1.15 (P3(x571,x571,x571)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(61,plain,
% 1.08/1.15 (~P3(a1,a3,a1)),
% 1.08/1.15 inference(scs_inference,[],[9,5,57,45,18,19,21])).
% 1.08/1.15 cnf(62,plain,
% 1.08/1.15 (P3(x621,x621,x621)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(64,plain,
% 1.08/1.15 (~P3(a1,a2,a2)),
% 1.08/1.15 inference(scs_inference,[],[9,5,57,62,45,18,19,21,20])).
% 1.08/1.15 cnf(70,plain,
% 1.08/1.15 (P3(a1,a2,a3)+P3(a4,a2,x701)+~P3(a2,x701,a1)),
% 1.08/1.15 inference(scs_inference,[],[64,43])).
% 1.08/1.15 cnf(71,plain,
% 1.08/1.15 (~P3(a2,a3,a2)),
% 1.08/1.15 inference(scs_inference,[],[10,5,19])).
% 1.08/1.15 cnf(72,plain,
% 1.08/1.15 (P3(x721,x721,x721)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(74,plain,
% 1.08/1.15 (~P3(a2,a3,a3)),
% 1.08/1.15 inference(scs_inference,[],[10,5,72,19,20])).
% 1.08/1.15 cnf(75,plain,
% 1.08/1.15 (P3(x751,x751,x751)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(77,plain,
% 1.08/1.15 (~P3(a3,a3,a2)),
% 1.08/1.15 inference(scs_inference,[],[10,5,72,75,19,20,18])).
% 1.08/1.15 cnf(86,plain,
% 1.08/1.15 (~P3(a4,a2,a4)),
% 1.08/1.15 inference(scs_inference,[],[11,5,20,19])).
% 1.08/1.15 cnf(93,plain,
% 1.08/1.15 (~P3(a1,a4,x931)+P3(x931,a4,a2)+P3(a4,a2,a3)+P3(a4,a2,a2)),
% 1.08/1.15 inference(scs_inference,[],[11,4,5,2,20,19,70,22,21])).
% 1.08/1.15 cnf(98,plain,
% 1.08/1.15 (P3(x981,x981,x981)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(103,plain,
% 1.08/1.15 (P3(a1,a3,a2)+P3(a1,a3,a4)),
% 1.08/1.15 inference(scs_inference,[],[12,5,98,56,61,3,1,18,21,20,22])).
% 1.08/1.15 cnf(108,plain,
% 1.08/1.15 (~P3(a3,a2,a2)),
% 1.08/1.15 inference(scs_inference,[],[13,5,19,20])).
% 1.08/1.15 cnf(109,plain,
% 1.08/1.15 (P3(x1091,x1091,x1091)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(111,plain,
% 1.08/1.15 (P3(a2,a3,a4)+P3(a2,a3,a1)),
% 1.08/1.15 inference(scs_inference,[],[13,5,71,74,3,2,19,20,22])).
% 1.08/1.15 cnf(116,plain,
% 1.08/1.15 (~P3(a3,x1161,a2)+P3(a4,a3,x1161)+P3(a2,a3,a1)),
% 1.08/1.15 inference(scs_inference,[],[13,14,5,109,71,74,3,2,19,20,22,18,21])).
% 1.08/1.15 cnf(120,plain,
% 1.08/1.15 (~P3(a4,a1,a4)),
% 1.08/1.15 inference(scs_inference,[],[5,15,18,19])).
% 1.08/1.15 cnf(125,plain,
% 1.08/1.15 (~P3(a2,a4,a2)),
% 1.08/1.15 inference(scs_inference,[],[5,16,20,19])).
% 1.08/1.15 cnf(131,plain,
% 1.08/1.15 (~P3(a3,a2,a3)),
% 1.08/1.15 inference(scs_inference,[],[77,5,21])).
% 1.08/1.15 cnf(145,plain,
% 1.08/1.15 (~P3(a2,a4,a4)),
% 1.08/1.15 inference(scs_inference,[],[11,5,20])).
% 1.08/1.15 cnf(146,plain,
% 1.08/1.15 (P3(x1461,x1461,x1461)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(150,plain,
% 1.08/1.15 (~P3(a1,a4,a1)),
% 1.08/1.15 inference(scs_inference,[],[8,11,5,146,20,18,19])).
% 1.08/1.15 cnf(159,plain,
% 1.08/1.15 (P3(a4,a2,a2)+P3(a4,a2,a3)+~P3(a1,a4,a2)),
% 1.08/1.15 inference(scs_inference,[],[125,5,19,93])).
% 1.08/1.15 cnf(163,plain,
% 1.08/1.15 (~P3(a3,a1,a4)+P3(a4,a2,a2)+P3(a4,a2,a3)),
% 1.08/1.15 inference(scs_inference,[],[150,125,120,50,4,1,5,19,93,22,21])).
% 1.08/1.15 cnf(169,plain,
% 1.08/1.15 (~P3(a4,a1,a2)+P3(a2,a4,a3)),
% 1.08/1.15 inference(scs_inference,[],[145,125,150,4,2,5,20,22,21])).
% 1.08/1.15 cnf(176,plain,
% 1.08/1.15 (P3(a2,a4,a3)+P3(a4,a3,x1761)+~P3(a3,x1761,a2)),
% 1.08/1.15 inference(scs_inference,[],[12,14,145,125,150,4,2,5,20,22,21,18,19,111,116])).
% 1.08/1.15 cnf(181,plain,
% 1.08/1.15 (P3(x1811,x1811,x1811)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(184,plain,
% 1.08/1.15 (P3(x1841,x1841,x1841)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(186,plain,
% 1.08/1.15 (~P3(a4,a3,a4)),
% 1.08/1.15 inference(scs_inference,[],[8,17,50,5,181,184,21,18,19])).
% 1.08/1.15 cnf(187,plain,
% 1.08/1.15 (P3(x1871,x1871,x1871)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(192,plain,
% 1.08/1.15 (P3(a2,a4,a3)+~P3(a3,a4,a2)),
% 1.08/1.15 inference(scs_inference,[],[8,17,50,5,181,184,187,21,18,19,20,176])).
% 1.08/1.15 cnf(194,plain,
% 1.08/1.15 (P3(a2,a3,a1)+~P3(a3,a4,a2)),
% 1.08/1.15 inference(scs_inference,[],[8,17,50,5,181,184,187,21,18,19,20,176,116])).
% 1.08/1.15 cnf(196,plain,
% 1.08/1.15 (P3(a4,a1,a3)+P3(a4,a1,a2)),
% 1.08/1.15 inference(scs_inference,[],[8,17,50,120,4,1,5,181,184,187,21,18,19,20,176,116,22])).
% 1.08/1.15 cnf(200,plain,
% 1.08/1.15 (~P3(a3,a4,a4)),
% 1.08/1.15 inference(scs_inference,[],[14,5,18,20])).
% 1.08/1.15 cnf(203,plain,
% 1.08/1.15 (P3(a3,a2,a4)+P3(a3,a2,a1)),
% 1.08/1.15 inference(scs_inference,[],[14,108,131,3,2,5,18,20,22])).
% 1.08/1.15 cnf(210,plain,
% 1.08/1.15 (P3(x2101,x2101,x2101)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(214,plain,
% 1.08/1.15 (~P3(x2141,a1,a3)+~P3(a1,a3,x2141)),
% 1.08/1.15 inference(scs_inference,[],[13,32,5,210,18,20,21])).
% 1.08/1.15 cnf(220,plain,
% 1.08/1.15 (~P3(a3,a4,a3)),
% 1.08/1.15 inference(scs_inference,[],[14,5,19])).
% 1.08/1.15 cnf(221,plain,
% 1.08/1.15 (P3(x2211,x2211,x2211)),
% 1.08/1.15 inference(rename_variables,[],[5])).
% 1.08/1.15 cnf(230,plain,
% 1.08/1.15 (P3(a4,a3,a2)+P3(a4,a3,a3)+P3(a4,a3,a1)),
% 1.08/1.15 inference(scs_inference,[],[11,14,186,3,4,5,221,19,18,20,163,159,22])).
% 1.08/1.15 cnf(239,plain,
% 1.08/1.15 (P3(a3,a4,a2)+P3(a3,a4,a1)),
% 1.08/1.15 inference(scs_inference,[],[200,220,3,4,5,19,22])).
% 1.08/1.15 cnf(241,plain,
% 1.08/1.15 (~P3(a4,a3,a3)),
% 1.08/1.15 inference(scs_inference,[],[17,200,220,3,4,5,19,22,20])).
% 1.08/1.15 cnf(244,plain,
% 1.08/1.15 (P3(a4,a3,a1)+P3(a4,a3,a2)),
% 1.08/1.15 inference(scs_inference,[],[17,200,220,3,4,5,19,22,20,230])).
% 1.08/1.15 cnf(256,plain,
% 1.08/1.15 (~P3(x2561,a3,a1)+~P3(a3,a1,x2561)),
% 1.08/1.15 inference(scs_inference,[],[61,5,18,21])).
% 1.08/1.15 cnf(267,plain,
% 1.08/1.15 (P3(a1,a3,a2)+~P3(a4,a1,a3)),
% 1.08/1.15 inference(scs_inference,[],[103,214])).
% 1.08/1.15 cnf(270,plain,
% 1.08/1.15 (~P3(a3,a2,a4)+~P3(a4,a1,a2)),
% 1.08/1.15 inference(scs_inference,[],[86,169,21])).
% 1.08/1.15 cnf(284,plain,
% 1.08/1.15 (~P3(a3,a4,a2)+~P3(a3,a1,a2)),
% 1.08/1.15 inference(scs_inference,[],[194,256])).
% 1.08/1.15 cnf(298,plain,
% 1.08/1.15 (~P3(a4,a1,a3)+P3(a3,a4,a2)),
% 1.08/1.15 inference(scs_inference,[],[150,239,21])).
% 1.08/1.15 cnf(299,plain,
% 1.08/1.15 (P3(a4,a3,a2)+~P3(a3,a1,a4)),
% 1.08/1.15 inference(scs_inference,[],[244,256])).
% 1.08/1.15 cnf(300,plain,
% 1.08/1.15 (~P3(x3001,a3,a2)+~P3(a3,a2,x3001)),
% 1.08/1.15 inference(scs_inference,[],[71,21])).
% 1.08/1.15 cnf(303,plain,
% 1.08/1.15 (~P3(a3,a2,a1)+P3(a1,a3,a4)),
% 1.08/1.15 inference(scs_inference,[],[71,21,267,103])).
% 1.08/1.15 cnf(314,plain,
% 1.08/1.15 (P3(a3,a2,a1)+~P3(a4,a1,a2)),
% 1.08/1.15 inference(scs_inference,[],[270,203])).
% 1.08/1.15 cnf(318,plain,
% 1.08/1.15 (~P3(x3181,a2,a4)+~P3(a2,a4,x3181)),
% 1.08/1.15 inference(scs_inference,[],[86,21])).
% 1.08/1.15 cnf(323,plain,
% 1.08/1.15 (P3(a3,a4,a1)+~P3(a3,a1,a2)),
% 1.08/1.15 inference(scs_inference,[],[284,239])).
% 1.08/1.16 cnf(333,plain,
% 1.08/1.16 (~P3(x3331,a4,a3)+~P3(a4,a3,x3331)),
% 1.08/1.16 inference(scs_inference,[],[220,21])).
% 1.08/1.16 cnf(335,plain,
% 1.08/1.16 (P3(a2,a4,a3)+~P3(a4,a1,a3)),
% 1.08/1.16 inference(scs_inference,[],[298,192])).
% 1.08/1.16 cnf(340,plain,
% 1.08/1.16 (P3(a3,a2,a4)+P3(a1,a3,a4)),
% 1.08/1.16 inference(scs_inference,[],[303,203])).
% 1.08/1.16 cnf(348,plain,
% 1.08/1.16 (~P3(x3481,a3,a4)+~P3(a3,a4,x3481)),
% 1.08/1.16 inference(scs_inference,[],[186,21])).
% 1.08/1.16 cnf(355,plain,
% 1.08/1.16 (~P3(a3,a1,a2)+~P3(a1,a3,a4)),
% 1.08/1.16 inference(scs_inference,[],[323,348])).
% 1.08/1.16 cnf(363,plain,
% 1.08/1.16 (~P3(x3631,a4,a1)+~P3(a4,a1,x3631)),
% 1.08/1.16 inference(scs_inference,[],[150,21])).
% 1.08/1.16 cnf(368,plain,
% 1.08/1.16 (~P3(a4,a1,a3)+~P3(a3,a2,a4)),
% 1.08/1.16 inference(scs_inference,[],[335,318])).
% 1.08/1.16 cnf(373,plain,
% 1.08/1.16 (P3(a1,a3,a4)+~P3(a4,a1,a3)),
% 1.08/1.16 inference(scs_inference,[],[340,368])).
% 1.08/1.16 cnf(387,plain,
% 1.08/1.16 (P3(a1,a3,a2)+~P3(a3,a1,a2)),
% 1.08/1.16 inference(scs_inference,[],[355,103])).
% 1.08/1.16 cnf(402,plain,
% 1.08/1.16 (~P3(a4,a1,a3)),
% 1.08/1.16 inference(scs_inference,[],[373,214])).
% 1.08/1.16 cnf(403,plain,
% 1.08/1.16 (P3(a4,a1,a2)),
% 1.08/1.16 inference(scs_inference,[],[402,196])).
% 1.08/1.16 cnf(406,plain,
% 1.08/1.16 (P3(a2,a4,a3)),
% 1.08/1.16 inference(scs_inference,[],[403,169])).
% 1.08/1.16 cnf(408,plain,
% 1.08/1.16 (P3(a3,a2,a1)),
% 1.08/1.16 inference(scs_inference,[],[403,314])).
% 1.08/1.16 cnf(436,plain,
% 1.08/1.16 ($false),
% 1.08/1.16 inference(scs_inference,[],[10,3,4,408,406,403,241,186,363,333,300,299,53,30,22,21,19,387]),
% 1.08/1.16 ['proof']).
% 1.08/1.16 % SZS output end Proof
% 1.08/1.16 % Total time :0.520000s
%------------------------------------------------------------------------------