TSTP Solution File: GRP127-4.004 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n032.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 00:11:07 EDT 2023
% Result : Unsatisfiable 0.12s 0.57s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.08/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Tue Aug 29 02:15:31 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.12/0.45 start to proof:theBenchmark
% 0.12/0.56 %-------------------------------------------
% 0.12/0.56 % File :CSE---1.6
% 0.12/0.56 % Problem :theBenchmark
% 0.12/0.56 % Transform :cnf
% 0.12/0.56 % Format :tptp:raw
% 0.12/0.56 % Command :java -jar mcs_scs.jar %d %s
% 0.12/0.56
% 0.12/0.56 % Result :Theorem 0.060000s
% 0.12/0.56 % Output :CNFRefutation 0.060000s
% 0.12/0.56 %-------------------------------------------
% 0.12/0.56 %--------------------------------------------------------------------------
% 0.12/0.56 % File : GRP127-4.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.56 % Domain : Group Theory (Quasigroups)
% 0.12/0.56 % Problem : ((b.a).b).b) = a
% 0.12/0.56 % Version : [Sla93] axioms : Augmented.
% 0.12/0.56 % English : Generate the multiplication table for the specified quasi-
% 0.12/0.56 % group with 4 elements.
% 0.12/0.56
% 0.12/0.56 % Refs : [Ben89] Bennett (1989), Quasigroup Identities and Mendelsohn D
% 0.12/0.56 % : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.12/0.56 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.12/0.56 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.12/0.56 % Source : [TPTP]
% 0.12/0.56 % Names :
% 0.12/0.56
% 0.12/0.56 % Status : Unsatisfiable
% 0.12/0.56 % Rating : 0.00 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.00 v2.1.0
% 0.12/0.56 % Syntax : Number of clauses : 26 ( 17 unt; 3 nHn; 25 RR)
% 0.12/0.56 % Number of literals : 53 ( 0 equ; 30 neg)
% 0.12/0.56 % Maximal clause size : 6 ( 2 avg)
% 0.12/0.56 % Maximal term depth : 1 ( 1 avg)
% 0.12/0.56 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 0.12/0.56 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.12/0.56 % Number of variables : 31 ( 0 sgn)
% 0.12/0.56 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.12/0.56
% 0.12/0.56 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.12/0.56 % : Substitution axioms are not needed, as any positive equality
% 0.12/0.56 % literals should resolve on negative ones directly.
% 0.12/0.56 % : This problem is extensively investigated in [Ben89].
% 0.12/0.56 % : Version 4 has surjectivity and rotation
% 0.12/0.56 % : tptp2X: -f tptp -s4 GRP127-4.g
% 0.12/0.56 % Bugfixes : v1.2.1 - Clauses row_surjectivity and column_surjectivity fixed.
% 0.12/0.56 %--------------------------------------------------------------------------
% 0.12/0.56 cnf(row_surjectivity,axiom,
% 0.12/0.56 ( ~ group_element(X)
% 0.12/0.56 | ~ group_element(Y)
% 0.12/0.56 | product(e_1,X,Y)
% 0.12/0.56 | product(e_2,X,Y)
% 0.12/0.56 | product(e_3,X,Y)
% 0.12/0.56 | product(e_4,X,Y) ) ).
% 0.12/0.56
% 0.12/0.56 cnf(column_surjectivity,axiom,
% 0.12/0.56 ( ~ group_element(X)
% 0.12/0.56 | ~ group_element(Y)
% 0.12/0.56 | product(X,e_1,Y)
% 0.12/0.56 | product(X,e_2,Y)
% 0.12/0.56 | product(X,e_3,Y)
% 0.12/0.56 | product(X,e_4,Y) ) ).
% 0.12/0.56
% 0.12/0.56 cnf(qg3_1,negated_conjecture,
% 0.12/0.56 ( product(Y,X,Z1)
% 0.12/0.56 | ~ product(Z2,Y,X)
% 0.12/0.56 | ~ product(Z1,Y,Z2) ) ).
% 0.12/0.56
% 0.12/0.56 cnf(qg3_2,negated_conjecture,
% 0.12/0.56 ( product(Z1,Y,Z2)
% 0.12/0.56 | ~ product(Z2,Y,X)
% 0.12/0.56 | ~ product(Y,X,Z1) ) ).
% 0.12/0.56
% 0.12/0.56 cnf(element_1,axiom,
% 0.12/0.56 group_element(e_1) ).
% 0.12/0.56
% 0.12/0.56 cnf(element_2,axiom,
% 0.12/0.56 group_element(e_2) ).
% 0.12/0.56
% 0.12/0.56 cnf(element_3,axiom,
% 0.12/0.56 group_element(e_3) ).
% 0.12/0.56
% 0.12/0.56 cnf(element_4,axiom,
% 0.12/0.56 group_element(e_4) ).
% 0.12/0.56
% 0.12/0.56 cnf(e_1_is_not_e_2,axiom,
% 0.12/0.56 ~ equalish(e_1,e_2) ).
% 0.12/0.56
% 0.12/0.56 cnf(e_1_is_not_e_3,axiom,
% 0.12/0.56 ~ equalish(e_1,e_3) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_1_is_not_e_4,axiom,
% 0.12/0.57 ~ equalish(e_1,e_4) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_2_is_not_e_1,axiom,
% 0.12/0.57 ~ equalish(e_2,e_1) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_2_is_not_e_3,axiom,
% 0.12/0.57 ~ equalish(e_2,e_3) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_2_is_not_e_4,axiom,
% 0.12/0.57 ~ equalish(e_2,e_4) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_3_is_not_e_1,axiom,
% 0.12/0.57 ~ equalish(e_3,e_1) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_3_is_not_e_2,axiom,
% 0.12/0.57 ~ equalish(e_3,e_2) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_3_is_not_e_4,axiom,
% 0.12/0.57 ~ equalish(e_3,e_4) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_4_is_not_e_1,axiom,
% 0.12/0.57 ~ equalish(e_4,e_1) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_4_is_not_e_2,axiom,
% 0.12/0.57 ~ equalish(e_4,e_2) ).
% 0.12/0.57
% 0.12/0.57 cnf(e_4_is_not_e_3,axiom,
% 0.12/0.57 ~ equalish(e_4,e_3) ).
% 0.12/0.57
% 0.12/0.57 cnf(product_total_function1,axiom,
% 0.12/0.57 ( ~ group_element(X)
% 0.12/0.57 | ~ group_element(Y)
% 0.12/0.57 | product(X,Y,e_1)
% 0.12/0.57 | product(X,Y,e_2)
% 0.12/0.57 | product(X,Y,e_3)
% 0.12/0.57 | product(X,Y,e_4) ) ).
% 0.12/0.57
% 0.12/0.57 cnf(product_total_function2,axiom,
% 0.12/0.57 ( ~ product(X,Y,W)
% 0.12/0.57 | ~ product(X,Y,Z)
% 0.12/0.57 | equalish(W,Z) ) ).
% 0.12/0.57
% 0.12/0.57 cnf(product_right_cancellation,axiom,
% 0.12/0.57 ( ~ product(X,W,Y)
% 0.12/0.57 | ~ product(X,Z,Y)
% 0.12/0.57 | equalish(W,Z) ) ).
% 0.12/0.57
% 0.12/0.57 cnf(product_left_cancellation,axiom,
% 0.12/0.57 ( ~ product(W,Y,X)
% 0.12/0.57 | ~ product(Z,Y,X)
% 0.12/0.57 | equalish(W,Z) ) ).
% 0.12/0.57
% 0.12/0.57 cnf(product_idempotence,axiom,
% 0.12/0.57 product(X,X,X) ).
% 0.12/0.57
% 0.12/0.57 cnf(qg3,negated_conjecture,
% 0.12/0.57 ( ~ product(Y,X,Z1)
% 0.12/0.57 | ~ product(Z1,Y,Z2)
% 0.12/0.57 | product(Z2,Y,X) ) ).
% 0.12/0.57
% 0.12/0.57 %--------------------------------------------------------------------------
% 0.12/0.57 %-------------------------------------------
% 0.12/0.57 % Proof found
% 0.12/0.57 % SZS status Theorem for theBenchmark
% 0.12/0.57 % SZS output start Proof
% 0.12/0.57 %ClaNum:26(EqnAxiom:0)
% 0.12/0.57 %VarNum:84(SingletonVarNum:31)
% 0.12/0.57 %MaxLitNum:6
% 0.12/0.57 %MaxfuncDepth:0
% 0.12/0.57 %SharedTerms:20
% 0.12/0.57 %goalClause: 21 22 23
% 0.12/0.57 [1]P1(a1)
% 0.12/0.57 [2]P1(a2)
% 0.12/0.57 [3]P1(a3)
% 0.12/0.57 [4]P1(a4)
% 0.12/0.57 [6]~P2(a1,a2)
% 0.12/0.57 [7]~P2(a1,a3)
% 0.12/0.57 [8]~P2(a1,a4)
% 0.12/0.57 [9]~P2(a2,a1)
% 0.12/0.57 [10]~P2(a2,a3)
% 0.12/0.57 [11]~P2(a2,a4)
% 0.12/0.57 [12]~P2(a3,a1)
% 0.12/0.57 [13]~P2(a3,a2)
% 0.12/0.57 [14]~P2(a3,a4)
% 0.12/0.57 [15]~P2(a4,a1)
% 0.12/0.57 [16]~P2(a4,a2)
% 0.12/0.57 [17]~P2(a4,a3)
% 0.12/0.57 [5]P3(x51,x51,x51)
% 0.12/0.57 [18]~P3(x183,x184,x181)+P2(x181,x182)+~P3(x183,x184,x182)
% 0.12/0.57 [19]~P3(x193,x191,x194)+P2(x191,x192)+~P3(x193,x192,x194)
% 0.12/0.57 [20]~P3(x201,x203,x204)+P2(x201,x202)+~P3(x202,x203,x204)
% 0.12/0.57 [21]~P3(x212,x213,x214)+P3(x211,x212,x213)+~P3(x214,x212,x211)
% 0.12/0.57 [22]~P3(x223,x221,x224)+P3(x221,x222,x223)+~P3(x224,x221,x222)
% 0.12/0.57 [23]~P3(x232,x234,x231)+P3(x231,x232,x233)+~P3(x233,x232,x234)
% 0.12/0.57 [24]~P1(x242)+~P1(x241)+P3(x241,x242,a2)+P3(x241,x242,a3)+P3(x241,x242,a4)+P3(x241,x242,a1)
% 0.12/0.57 [25]~P1(x252)+~P1(x251)+P3(x251,a2,x252)+P3(x251,a3,x252)+P3(x251,a4,x252)+P3(x251,a1,x252)
% 0.12/0.57 [26]~P1(x262)+~P1(x261)+P3(a2,x261,x262)+P3(a3,x261,x262)+P3(a4,x261,x262)+P3(a1,x261,x262)
% 0.12/0.57 %EqnAxiom
% 0.12/0.57
% 0.12/0.57 %-------------------------------------------
% 0.12/0.57 cnf(28,plain,
% 0.12/0.57 (~P3(a1,a2,a1)),
% 0.12/0.57 inference(scs_inference,[],[5,6,20,19])).
% 0.12/0.57 cnf(29,plain,
% 0.12/0.57 (P3(x291,x291,x291)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(31,plain,
% 0.12/0.57 (~P3(a1,a1,a2)),
% 0.12/0.57 inference(scs_inference,[],[5,29,6,20,19,18])).
% 0.12/0.57 cnf(32,plain,
% 0.12/0.57 (P3(x321,x321,x321)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(34,plain,
% 0.12/0.57 (~P3(a1,a2,x341)+~P3(a2,x341,a1)),
% 0.12/0.57 inference(scs_inference,[],[5,29,6,20,19,18,23])).
% 0.12/0.57 cnf(36,plain,
% 0.12/0.57 (~P3(a2,a1,a1)),
% 0.12/0.57 inference(scs_inference,[],[5,29,32,6,20,19,18,23,22])).
% 0.12/0.57 cnf(45,plain,
% 0.12/0.57 (~P3(a3,a1,a1)),
% 0.12/0.57 inference(scs_inference,[],[7,5,20])).
% 0.12/0.57 cnf(46,plain,
% 0.12/0.57 (P3(x461,x461,x461)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(48,plain,
% 0.12/0.57 (~P3(a3,a3,a1)),
% 0.12/0.57 inference(scs_inference,[],[7,5,46,20,18])).
% 0.12/0.57 cnf(49,plain,
% 0.12/0.57 (P3(x491,x491,x491)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(51,plain,
% 0.12/0.57 (~P3(a3,a1,a3)),
% 0.12/0.57 inference(scs_inference,[],[7,5,46,49,20,18,19])).
% 0.12/0.57 cnf(54,plain,
% 0.12/0.57 (P3(a1,a4,a2)+P3(a1,a3,a2)+P3(a1,a2,a2)),
% 0.12/0.57 inference(scs_inference,[],[1,7,2,5,46,49,31,20,18,19,25])).
% 0.12/0.57 cnf(56,plain,
% 0.12/0.57 (P3(a1,a2,a3)+P3(a1,a2,a4)+P3(a1,a2,a2)),
% 0.12/0.57 inference(scs_inference,[],[1,7,2,5,46,49,31,28,20,18,19,25,24])).
% 0.12/0.57 cnf(60,plain,
% 0.12/0.57 (~P3(a4,a2,x601)+P3(x601,a4,a1)+P3(a1,a3,a2)+P3(a1,a2,a2)),
% 0.12/0.57 inference(scs_inference,[],[1,7,2,5,46,49,31,28,20,18,19,25,24,26,23])).
% 0.12/0.57 cnf(64,plain,
% 0.12/0.57 (~P3(a4,a1,a1)+P3(a2,a4,a1)+P3(a1,a3,a2)+P3(a1,a2,a2)),
% 0.12/0.57 inference(scs_inference,[],[1,7,2,5,46,49,31,28,20,18,19,25,24,26,23,22,21])).
% 0.12/0.57 cnf(66,plain,
% 0.12/0.57 (~P3(a1,a4,a4)),
% 0.12/0.57 inference(scs_inference,[],[8,5,20])).
% 0.12/0.57 cnf(67,plain,
% 0.12/0.57 (P3(x671,x671,x671)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(69,plain,
% 0.12/0.57 (~P3(a1,a3,a3)),
% 0.12/0.57 inference(scs_inference,[],[8,5,67,48,20,23])).
% 0.12/0.57 cnf(70,plain,
% 0.12/0.57 (P3(x701,x701,x701)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(74,plain,
% 0.12/0.57 (P3(a3,a1,a2)+P3(a3,a1,a4)),
% 0.12/0.57 inference(scs_inference,[],[3,8,5,67,70,45,48,51,1,20,23,18,24])).
% 0.12/0.57 cnf(76,plain,
% 0.12/0.57 (~P3(a2,a1,a3)+P3(a3,a1,a4)),
% 0.12/0.57 inference(scs_inference,[],[3,8,5,67,70,45,48,51,1,20,23,18,24,22])).
% 0.12/0.57 cnf(80,plain,
% 0.12/0.57 (P3(a3,a2,a1)+P3(a3,a1,a4)+P3(a3,a4,a1)),
% 0.12/0.57 inference(scs_inference,[],[3,8,5,67,70,45,48,51,1,20,23,18,24,22,21,25])).
% 0.12/0.57 cnf(87,plain,
% 0.12/0.57 (~P3(a4,a4,a1)),
% 0.12/0.57 inference(scs_inference,[],[5,66,19,21])).
% 0.12/0.57 cnf(88,plain,
% 0.12/0.57 (P3(x881,x881,x881)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(90,plain,
% 0.12/0.57 (~P3(a1,a1,a3)),
% 0.12/0.57 inference(scs_inference,[],[5,88,66,45,19,21,23])).
% 0.12/0.57 cnf(91,plain,
% 0.12/0.57 (P3(x911,x911,x911)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(93,plain,
% 0.12/0.57 (~P3(a2,a2,a1)),
% 0.12/0.57 inference(scs_inference,[],[9,5,88,91,66,45,19,21,23,18])).
% 0.12/0.57 cnf(94,plain,
% 0.12/0.57 (P3(x941,x941,x941)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(103,plain,
% 0.12/0.57 (P3(a2,a1,a3)+P3(a3,a2,a1)+P3(a3,a4,a1)),
% 0.12/0.57 inference(scs_inference,[],[9,3,5,88,91,94,66,45,51,1,19,21,23,18,26,22,20,80])).
% 0.12/0.57 cnf(104,plain,
% 0.12/0.57 (P3(a1,a2,a3)+P3(a2,a1,a3)+P3(a1,a2,a4)),
% 0.12/0.57 inference(scs_inference,[],[9,3,5,88,91,94,66,45,51,1,19,21,23,18,26,22,20,80,56])).
% 0.12/0.57 cnf(105,plain,
% 0.12/0.57 (P3(a1,a3,a2)+P3(a2,a1,a3)+P3(a1,a4,a2)),
% 0.12/0.57 inference(scs_inference,[],[9,3,5,88,91,94,66,45,51,1,19,21,23,18,26,22,20,80,56,54])).
% 0.12/0.57 cnf(106,plain,
% 0.12/0.57 (P3(a2,a4,a1)+P3(a2,a1,a3)+P3(a2,a3,a1)),
% 0.12/0.57 inference(scs_inference,[],[2,9,3,5,88,91,94,66,36,45,51,1,19,21,23,18,26,22,20,80,56,54,25])).
% 0.12/0.57 cnf(111,plain,
% 0.12/0.57 (~P3(a2,a3,a2)),
% 0.12/0.57 inference(scs_inference,[],[10,5,19])).
% 0.12/0.57 cnf(112,plain,
% 0.12/0.57 (P3(x1121,x1121,x1121)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(114,plain,
% 0.12/0.57 (~P3(a3,a3,a2)),
% 0.12/0.57 inference(scs_inference,[],[10,5,112,19,18])).
% 0.12/0.57 cnf(115,plain,
% 0.12/0.57 (P3(x1151,x1151,x1151)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(117,plain,
% 0.12/0.57 (~P3(a2,a3,a3)),
% 0.12/0.57 inference(scs_inference,[],[10,5,112,115,19,18,20])).
% 0.12/0.57 cnf(120,plain,
% 0.12/0.57 (P3(a1,a4,a3)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,5,112,115,69,90,1,19,18,20,25])).
% 0.12/0.57 cnf(122,plain,
% 0.12/0.57 (~P3(a3,a1,a4)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,5,112,115,69,90,51,1,19,18,20,25,23])).
% 0.12/0.57 cnf(124,plain,
% 0.12/0.57 (P3(a1,a2,a3)+~P3(a2,a1,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,5,112,115,69,90,51,1,19,18,20,25,23,76])).
% 0.12/0.57 cnf(125,plain,
% 0.12/0.57 (P3(a3,a1,a2)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,5,112,115,69,90,51,1,19,18,20,25,23,76,74])).
% 0.12/0.57 cnf(128,plain,
% 0.12/0.57 (P3(a1,a2,a4)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,5,112,115,69,90,51,1,19,18,20,25,23,76,74,106,105,104])).
% 0.12/0.57 cnf(136,plain,
% 0.12/0.57 (P3(a2,a1,a4)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,28,5,112,115,69,87,90,93,36,51,2,1,19,18,20,25,23,76,74,106,105,104,103,60,24,26,21])).
% 0.12/0.57 cnf(138,plain,
% 0.12/0.57 (P3(a4,a1,a1)+P3(a3,a2,a1)+P3(a1,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[3,10,28,5,112,115,69,87,90,93,36,51,2,1,19,18,20,25,23,76,74,106,105,104,103,60,24,26,21,22])).
% 0.12/0.57 cnf(140,plain,
% 0.12/0.57 (~P3(a4,a2,a4)),
% 0.12/0.57 inference(scs_inference,[],[11,5,19])).
% 0.12/0.57 cnf(141,plain,
% 0.12/0.57 (P3(x1411,x1411,x1411)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(145,plain,
% 0.12/0.57 (P3(a2,a3,a4)+P3(a2,a3,a1)),
% 0.12/0.57 inference(scs_inference,[],[3,11,5,141,117,111,2,19,18,24])).
% 0.12/0.57 cnf(147,plain,
% 0.12/0.57 (~P3(a3,a4,a2)+P3(a2,a3,a1)),
% 0.12/0.57 inference(scs_inference,[],[3,11,5,141,117,111,2,19,18,24,23])).
% 0.12/0.57 cnf(151,plain,
% 0.12/0.57 (P3(a1,a3,a4)+P3(a2,a3,a1)+P3(a1,a2,a4)+P3(a1,a1,a4)),
% 0.12/0.57 inference(scs_inference,[],[3,4,11,5,141,117,111,66,2,1,19,18,24,23,26,25])).
% 0.12/0.57 cnf(153,plain,
% 0.12/0.57 (P3(a2,a4,a2)+P3(a2,a3,a1)+P3(a3,a2,a4)+P3(a1,a2,a4)),
% 0.12/0.57 inference(scs_inference,[],[3,4,11,5,141,117,111,66,2,1,19,18,24,23,26,25,22])).
% 0.12/0.57 cnf(158,plain,
% 0.12/0.57 (~P3(a3,a2,a3)),
% 0.12/0.57 inference(scs_inference,[],[5,114,21])).
% 0.12/0.57 cnf(159,plain,
% 0.12/0.57 (P3(x1591,x1591,x1591)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(163,plain,
% 0.12/0.57 (~P3(a4,a4,a2)),
% 0.12/0.57 inference(scs_inference,[],[5,159,114,140,21,20,22])).
% 0.12/0.57 cnf(164,plain,
% 0.12/0.57 (P3(x1641,x1641,x1641)),
% 0.12/0.57 inference(rename_variables,[],[5])).
% 0.12/0.57 cnf(166,plain,
% 0.12/0.57 (~P3(a1,a2,a2)),
% 0.12/0.57 inference(scs_inference,[],[5,159,164,114,140,93,21,20,22,23])).
% 0.12/0.57 cnf(167,plain,
% 0.12/0.58 (P3(x1671,x1671,x1671)),
% 0.12/0.58 inference(rename_variables,[],[5])).
% 0.12/0.58 cnf(169,plain,
% 0.12/0.58 (~P3(a2,a2,a3)),
% 0.12/0.58 inference(scs_inference,[],[13,5,159,164,167,114,140,93,21,20,22,23,18])).
% 0.12/0.58 cnf(177,plain,
% 0.12/0.58 (P3(a1,a3,a2)+P3(a1,a4,a2)),
% 0.12/0.58 inference(scs_inference,[],[166,54])).
% 0.12/0.58 cnf(180,plain,
% 0.12/0.58 (P3(a1,a3,a2)+P3(a2,a4,a1)+~P3(a4,a1,a1)),
% 0.12/0.58 inference(scs_inference,[],[166,64])).
% 0.12/0.58 cnf(185,plain,
% 0.12/0.58 (~P3(a4,a3,a3)),
% 0.12/0.58 inference(scs_inference,[],[14,5,158,169,3,2,19,26,20])).
% 0.12/0.58 cnf(198,plain,
% 0.12/0.58 (P3(x1981,x1981,x1981)),
% 0.12/0.58 inference(rename_variables,[],[5])).
% 0.12/0.58 cnf(225,plain,
% 0.12/0.58 (P3(a2,a4,a1)),
% 0.12/0.58 inference(scs_inference,[],[5,198,15,36,45,28,158,169,140,93,4,3,2,1,19,18,25,22,23,177,136,128,125,124,122,120,34,180,138,21])).
% 0.12/0.58 cnf(230,plain,
% 0.12/0.58 (P3(a1,a2,a3)),
% 0.12/0.58 inference(scs_inference,[],[28,225,166,2,1,34,24])).
% 0.12/0.58 cnf(232,plain,
% 0.12/0.58 (~P3(a2,a4,a2)),
% 0.12/0.58 inference(scs_inference,[],[5,16,28,225,166,2,1,34,24,19])).
% 0.12/0.58 cnf(233,plain,
% 0.12/0.58 (P3(x2331,x2331,x2331)),
% 0.12/0.58 inference(rename_variables,[],[5])).
% 0.12/0.58 cnf(238,plain,
% 0.12/0.58 (P3(x2381,x2381,x2381)),
% 0.12/0.58 inference(rename_variables,[],[5])).
% 0.12/0.58 cnf(249,plain,
% 0.12/0.58 (P3(a4,a2,a1)),
% 0.12/0.58 inference(scs_inference,[],[5,233,238,16,36,28,225,185,166,93,2,1,34,24,19,20,21,18,22,23,153,151,26])).
% 0.12/0.58 cnf(253,plain,
% 0.12/0.58 (~P3(a3,a4,a2)),
% 0.12/0.58 inference(scs_inference,[],[5,233,238,16,36,45,28,225,185,166,48,93,3,2,1,34,24,19,20,21,18,22,23,153,151,26,25,147])).
% 0.12/0.58 cnf(254,plain,
% 0.12/0.58 (P3(a2,a3,a4)),
% 0.12/0.58 inference(scs_inference,[],[5,233,238,16,36,45,28,225,185,166,48,93,3,2,1,34,24,19,20,21,18,22,23,153,151,26,25,147,145])).
% 0.12/0.58 cnf(264,plain,
% 0.12/0.58 ($false),
% 0.12/0.58 inference(scs_inference,[],[11,230,254,249,232,253,163,4,2,19,20,26,21]),
% 0.12/0.58 ['proof']).
% 0.12/0.58 % SZS output end Proof
% 0.12/0.58 % Total time :0.060000s
%------------------------------------------------------------------------------