TSTP Solution File: GRP124-1.004 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP124-1.004 : 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 : n023.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 1.94s 2.03s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 23:31:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 1.94/2.02 %-------------------------------------------
% 1.94/2.02 % File :CSE---1.6
% 1.94/2.02 % Problem :theBenchmark
% 1.94/2.02 % Transform :cnf
% 1.94/2.02 % Format :tptp:raw
% 1.94/2.02 % Command :java -jar mcs_scs.jar %d %s
% 1.94/2.02
% 1.94/2.02 % Result :Theorem 1.400000s
% 1.94/2.02 % Output :CNFRefutation 1.400000s
% 1.94/2.02 %-------------------------------------------
% 1.94/2.02 %--------------------------------------------------------------------------
% 1.94/2.02 % File : GRP124-1.004 : TPTP v8.1.2. Released v1.2.0.
% 1.94/2.02 % Domain : Group Theory (Quasigroups)
% 1.94/2.02 % Problem : (3,1,2) conjugate orthogonality
% 1.94/2.02 % Version : [Sla93] axioms.
% 1.94/2.02 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 1.94/2.02 % Generate the multiplication table for the specified quasi-
% 1.94/2.02 % group with 4 elements.
% 1.94/2.02
% 1.94/2.02 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 1.94/2.02 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 1.94/2.02 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 1.94/2.02 % Source : [Sla93]
% 1.94/2.02 % Names : QG2 [Sla93]
% 1.94/2.02 % : QG2 [FSB93]
% 1.94/2.02 % : QG2 [SFS95]
% 1.94/2.02 % : Bennett QG2 [TPTP]
% 1.94/2.02
% 1.94/2.02 % Status : Unsatisfiable
% 1.94/2.02 % Rating : 0.00 v2.1.0
% 1.94/2.02 % Syntax : Number of clauses : 23 ( 17 unt; 1 nHn; 22 RR)
% 1.94/2.02 % Number of literals : 42 ( 0 equ; 28 neg)
% 1.94/2.02 % Maximal clause size : 6 ( 1 avg)
% 1.94/2.02 % Maximal term depth : 1 ( 1 avg)
% 1.94/2.02 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 1.94/2.02 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 1.94/2.02 % Number of variables : 27 ( 0 sgn)
% 1.94/2.02 % SPC : CNF_UNS_EPR_NEQ_NHN
% 1.94/2.02
% 1.94/2.02 % Comments : [SFS93]'s axiomatization has been modified for this.
% 1.94/2.02 % : Substitution axioms are not needed, as any positive equality
% 1.94/2.02 % literals should resolve on negative ones directly.
% 1.94/2.02 % : As in GRP123-1, either one of qg2_1 or qg2_2 may be used, as
% 1.94/2.02 % each implies the other in this scenario, with the help of
% 1.94/2.02 % cancellation. The dependence cannot be proved, so both have
% 1.94/2.02 % been left in here.
% 1.94/2.02 % : tptp2X: -f tptp -s4 GRP124-1.g
% 1.94/2.02 %--------------------------------------------------------------------------
% 1.94/2.02 cnf(element_1,axiom,
% 1.94/2.02 group_element(e_1) ).
% 1.94/2.02
% 1.94/2.02 cnf(element_2,axiom,
% 1.94/2.02 group_element(e_2) ).
% 1.94/2.02
% 1.94/2.02 cnf(element_3,axiom,
% 1.94/2.02 group_element(e_3) ).
% 1.94/2.02
% 1.94/2.02 cnf(element_4,axiom,
% 1.94/2.02 group_element(e_4) ).
% 1.94/2.02
% 1.94/2.02 cnf(e_1_is_not_e_2,axiom,
% 1.94/2.02 ~ equalish(e_1,e_2) ).
% 1.94/2.02
% 1.94/2.02 cnf(e_1_is_not_e_3,axiom,
% 1.94/2.02 ~ equalish(e_1,e_3) ).
% 1.94/2.02
% 1.94/2.02 cnf(e_1_is_not_e_4,axiom,
% 1.94/2.02 ~ equalish(e_1,e_4) ).
% 1.94/2.02
% 1.94/2.03 cnf(e_2_is_not_e_1,axiom,
% 1.94/2.03 ~ equalish(e_2,e_1) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_2_is_not_e_3,axiom,
% 1.94/2.03 ~ equalish(e_2,e_3) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_2_is_not_e_4,axiom,
% 1.94/2.03 ~ equalish(e_2,e_4) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_3_is_not_e_1,axiom,
% 1.94/2.03 ~ equalish(e_3,e_1) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_3_is_not_e_2,axiom,
% 1.94/2.03 ~ equalish(e_3,e_2) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_3_is_not_e_4,axiom,
% 1.94/2.03 ~ equalish(e_3,e_4) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_4_is_not_e_1,axiom,
% 1.94/2.03 ~ equalish(e_4,e_1) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_4_is_not_e_2,axiom,
% 1.94/2.03 ~ equalish(e_4,e_2) ).
% 1.94/2.03
% 1.94/2.03 cnf(e_4_is_not_e_3,axiom,
% 1.94/2.03 ~ equalish(e_4,e_3) ).
% 1.94/2.03
% 1.94/2.03 cnf(product_total_function1,axiom,
% 1.94/2.03 ( ~ group_element(X)
% 1.94/2.03 | ~ group_element(Y)
% 1.94/2.03 | product(X,Y,e_1)
% 1.94/2.03 | product(X,Y,e_2)
% 1.94/2.03 | product(X,Y,e_3)
% 1.94/2.03 | product(X,Y,e_4) ) ).
% 1.94/2.03
% 1.94/2.03 cnf(product_total_function2,axiom,
% 1.94/2.03 ( ~ product(X,Y,W)
% 1.94/2.03 | ~ product(X,Y,Z)
% 1.94/2.03 | equalish(W,Z) ) ).
% 1.94/2.03
% 1.94/2.03 cnf(product_right_cancellation,axiom,
% 1.94/2.03 ( ~ product(X,W,Y)
% 1.94/2.03 | ~ product(X,Z,Y)
% 1.94/2.03 | equalish(W,Z) ) ).
% 1.94/2.03
% 1.94/2.03 cnf(product_left_cancellation,axiom,
% 1.94/2.03 ( ~ product(W,Y,X)
% 1.94/2.03 | ~ product(Z,Y,X)
% 1.94/2.03 | equalish(W,Z) ) ).
% 1.94/2.03
% 1.94/2.03 cnf(product_idempotence,axiom,
% 1.94/2.03 product(X,X,X) ).
% 1.94/2.03
% 1.94/2.03 cnf(qg2_1,negated_conjecture,
% 1.94/2.03 ( ~ product(X1,Y1,Z1)
% 1.94/2.03 | ~ product(X2,Y2,Z1)
% 1.94/2.03 | ~ product(Z2,X1,Y1)
% 1.94/2.03 | ~ product(Z2,X2,Y2)
% 1.94/2.03 | equalish(X1,X2) ) ).
% 1.94/2.03
% 1.94/2.03 cnf(qg2_2,negated_conjecture,
% 1.94/2.03 ( ~ product(X1,Y1,Z1)
% 1.94/2.03 | ~ product(X2,Y2,Z1)
% 1.94/2.03 | ~ product(Z2,X1,Y1)
% 1.94/2.03 | ~ product(Z2,X2,Y2)
% 1.94/2.03 | equalish(Y1,Y2) ) ).
% 1.94/2.03
% 1.94/2.03 %--------------------------------------------------------------------------
% 1.94/2.03 %-------------------------------------------
% 1.94/2.03 % Proof found
% 1.94/2.03 % SZS status Theorem for theBenchmark
% 1.94/2.03 % SZS output start Proof
% 1.94/2.03 %ClaNum:23(EqnAxiom:0)
% 1.94/2.03 %VarNum:65(SingletonVarNum:27)
% 1.94/2.03 %MaxLitNum:6
% 1.94/2.03 %MaxfuncDepth:0
% 1.94/2.03 %SharedTerms:20
% 1.94/2.03 %goalClause: 22 23
% 1.94/2.03 [1]P1(a1)
% 1.94/2.03 [2]P1(a2)
% 1.94/2.03 [3]P1(a3)
% 1.94/2.03 [4]P1(a4)
% 1.94/2.03 [6]~P2(a1,a2)
% 1.94/2.03 [7]~P2(a1,a3)
% 1.94/2.03 [8]~P2(a1,a4)
% 1.94/2.03 [9]~P2(a2,a1)
% 1.94/2.03 [10]~P2(a2,a3)
% 1.94/2.03 [11]~P2(a2,a4)
% 1.94/2.03 [12]~P2(a3,a1)
% 1.94/2.03 [13]~P2(a3,a2)
% 1.94/2.03 [14]~P2(a3,a4)
% 1.94/2.03 [15]~P2(a4,a1)
% 1.94/2.03 [16]~P2(a4,a2)
% 1.94/2.03 [17]~P2(a4,a3)
% 1.94/2.03 [5]P3(x51,x51,x51)
% 1.94/2.03 [18]~P3(x183,x184,x181)+P2(x181,x182)+~P3(x183,x184,x182)
% 1.94/2.03 [19]~P3(x193,x191,x194)+P2(x191,x192)+~P3(x193,x192,x194)
% 1.94/2.03 [20]~P3(x201,x203,x204)+P2(x201,x202)+~P3(x202,x203,x204)
% 1.94/2.03 [22]~P3(x225,x221,x226)+P2(x221,x222)+~P3(x223,x224,x222)+~P3(x223,x225,x221)+~P3(x224,x222,x226)
% 1.94/2.03 [23]~P3(x231,x235,x236)+P2(x231,x232)+~P3(x233,x232,x234)+~P3(x233,x231,x235)+~P3(x232,x234,x236)
% 1.94/2.03 [21]~P1(x212)+~P1(x211)+P3(x211,x212,a2)+P3(x211,x212,a3)+P3(x211,x212,a4)+P3(x211,x212,a1)
% 1.94/2.03 %EqnAxiom
% 1.94/2.03
% 1.94/2.03 %-------------------------------------------
% 1.94/2.03 cnf(25,plain,
% 1.94/2.03 (~P3(a1,a2,a1)),
% 1.94/2.03 inference(scs_inference,[],[5,6,20,19])).
% 1.94/2.03 cnf(26,plain,
% 1.94/2.03 (P3(x261,x261,x261)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(29,plain,
% 1.94/2.03 (P3(x291,x291,x291)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(31,plain,
% 1.94/2.03 (~P3(a2,x311,a1)+~P3(a1,a2,x311)),
% 1.94/2.03 inference(scs_inference,[],[5,26,29,6,20,19,18,23])).
% 1.94/2.03 cnf(32,plain,
% 1.94/2.03 (P3(x321,x321,x321)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(34,plain,
% 1.94/2.03 (~P3(x341,a2,a1)+~P3(a1,x341,a2)),
% 1.94/2.03 inference(scs_inference,[],[5,26,29,32,6,20,19,18,23,22])).
% 1.94/2.03 cnf(39,plain,
% 1.94/2.03 (~P3(a3,a1,a1)),
% 1.94/2.03 inference(scs_inference,[],[7,5,20])).
% 1.94/2.03 cnf(40,plain,
% 1.94/2.03 (P3(x401,x401,x401)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(42,plain,
% 1.94/2.03 (~P3(a3,a1,a3)),
% 1.94/2.03 inference(scs_inference,[],[7,5,40,20,19])).
% 1.94/2.03 cnf(43,plain,
% 1.94/2.03 (P3(x431,x431,x431)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(46,plain,
% 1.94/2.03 (P3(x461,x461,x461)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(50,plain,
% 1.94/2.03 (P3(a1,a2,a3)+P3(a1,a2,a2)+P3(a1,a2,a4)),
% 1.94/2.03 inference(scs_inference,[],[1,7,2,5,40,43,46,25,20,19,18,22,21])).
% 1.94/2.03 cnf(53,plain,
% 1.94/2.03 (~P3(a1,a4,a4)),
% 1.94/2.03 inference(scs_inference,[],[8,5,20])).
% 1.94/2.03 cnf(54,plain,
% 1.94/2.03 (P3(x541,x541,x541)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(58,plain,
% 1.94/2.03 (P3(a3,a1,a2)+P3(a3,a1,a4)),
% 1.94/2.03 inference(scs_inference,[],[3,8,5,54,39,42,1,20,23,21])).
% 1.94/2.03 cnf(66,plain,
% 1.94/2.03 (~P3(a3,a2,x661)+~P3(a2,x661,a3)),
% 1.94/2.03 inference(scs_inference,[],[10,5,20,23])).
% 1.94/2.03 cnf(70,plain,
% 1.94/2.03 (~P3(a4,a2,a2)),
% 1.94/2.03 inference(scs_inference,[],[11,5,20])).
% 1.94/2.03 cnf(77,plain,
% 1.94/2.03 (~P3(a3,a2,a2)),
% 1.94/2.03 inference(scs_inference,[],[13,5,18,20])).
% 1.94/2.03 cnf(78,plain,
% 1.94/2.03 (P3(x781,x781,x781)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(80,plain,
% 1.94/2.03 (~P3(a3,a2,a3)),
% 1.94/2.03 inference(scs_inference,[],[13,5,78,18,20,19])).
% 1.94/2.03 cnf(83,plain,
% 1.94/2.03 (P3(a4,a2,a1)+P3(a4,a2,a4)+P3(a4,a2,a3)),
% 1.94/2.03 inference(scs_inference,[],[4,13,5,78,70,2,18,20,19,21])).
% 1.94/2.03 cnf(90,plain,
% 1.94/2.03 (P3(x901,x901,x901)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(92,plain,
% 1.94/2.03 (~P3(a1,a3,a3)),
% 1.94/2.03 inference(scs_inference,[],[12,14,5,90,23,18,20])).
% 1.94/2.03 cnf(97,plain,
% 1.94/2.03 (~P3(a4,a1,a1)),
% 1.94/2.03 inference(scs_inference,[],[15,5,22,20])).
% 1.94/2.03 cnf(110,plain,
% 1.94/2.03 (~P3(x1101,a2,a4)+~P3(a4,x1101,a2)),
% 1.94/2.03 inference(scs_inference,[],[5,16,18,22])).
% 1.94/2.03 cnf(121,plain,
% 1.94/2.03 (P3(x1211,x1211,x1211)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(125,plain,
% 1.94/2.03 (~P3(a3,x1251,a4)+~P3(a4,a3,x1251)),
% 1.94/2.03 inference(scs_inference,[],[6,17,5,121,18,19,23])).
% 1.94/2.03 cnf(129,plain,
% 1.94/2.03 (~P3(a4,a3,a1)+P3(a3,a1,a2)),
% 1.94/2.03 inference(scs_inference,[],[6,17,42,39,3,1,5,121,18,19,23,21])).
% 1.94/2.03 cnf(132,plain,
% 1.94/2.03 (P3(x1321,x1321,x1321)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(136,plain,
% 1.94/2.03 (~P3(a2,a1,a2)),
% 1.94/2.03 inference(scs_inference,[],[9,10,5,132,18,22,19])).
% 1.94/2.03 cnf(137,plain,
% 1.94/2.03 (P3(x1371,x1371,x1371)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(139,plain,
% 1.94/2.03 (~P3(a2,a1,a1)),
% 1.94/2.03 inference(scs_inference,[],[6,9,10,5,132,137,18,22,19,20])).
% 1.94/2.03 cnf(142,plain,
% 1.94/2.03 (P3(a3,a2,a1)+P3(a3,a2,a4)),
% 1.94/2.03 inference(scs_inference,[],[6,9,10,77,80,3,2,5,132,137,18,22,19,20,21])).
% 1.94/2.03 cnf(144,plain,
% 1.94/2.03 (P3(a3,a2,a4)+~P3(a2,a1,a3)),
% 1.94/2.03 inference(scs_inference,[],[6,9,10,77,80,3,2,5,132,137,18,22,19,20,21,66])).
% 1.94/2.03 cnf(148,plain,
% 1.94/2.03 (~P3(a2,a4,a4)),
% 1.94/2.03 inference(scs_inference,[],[11,5,18,20])).
% 1.94/2.03 cnf(163,plain,
% 1.94/2.03 (~P3(a1,a4,a1)),
% 1.94/2.03 inference(scs_inference,[],[8,5,22,19])).
% 1.94/2.03 cnf(171,plain,
% 1.94/2.03 (P3(a1,a2,a2)+P3(a1,a2,a4)+~P3(a2,a3,a1)),
% 1.94/2.03 inference(scs_inference,[],[31,50])).
% 1.94/2.03 cnf(175,plain,
% 1.94/2.03 (P3(x1751,x1751,x1751)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(178,plain,
% 1.94/2.03 (P3(x1781,x1781,x1781)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(180,plain,
% 1.94/2.03 (~P3(a1,a2,a2)),
% 1.94/2.03 inference(scs_inference,[],[9,14,5,175,178,18,19,22,20])).
% 1.94/2.03 cnf(187,plain,
% 1.94/2.03 (P3(a1,a2,a4)+~P3(a2,a3,a1)),
% 1.94/2.03 inference(scs_inference,[],[180,171])).
% 1.94/2.03 cnf(202,plain,
% 1.94/2.03 (P3(x2021,x2021,x2021)),
% 1.94/2.03 inference(rename_variables,[],[5])).
% 1.94/2.03 cnf(209,plain,
% 1.94/2.03 (~P3(a2,a3,a1)+P3(a3,a1,a4)),
% 1.94/2.03 inference(scs_inference,[],[10,15,5,202,19,18,23,129,58])).
% 1.94/2.03 cnf(215,plain,
% 1.94/2.03 (~P3(a2,a3,a2)),
% 1.94/2.03 inference(scs_inference,[],[10,5,18,19])).
% 1.94/2.03 cnf(219,plain,
% 1.94/2.04 (P3(x2191,x2191,x2191)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(223,plain,
% 1.94/2.04 (~P3(a4,a2,a4)),
% 1.94/2.04 inference(scs_inference,[],[11,5,219,18,22,19])).
% 1.94/2.04 cnf(226,plain,
% 1.94/2.04 (P3(a4,a2,a3)+P3(a4,a2,a1)),
% 1.94/2.04 inference(scs_inference,[],[11,5,219,18,22,19,83])).
% 1.94/2.04 cnf(227,plain,
% 1.94/2.04 (P3(a2,a3,a1)+P3(a2,a3,a3)+P3(a2,a3,a4)),
% 1.94/2.04 inference(scs_inference,[],[11,215,3,2,5,219,18,22,19,83,21])).
% 1.94/2.04 cnf(233,plain,
% 1.94/2.04 (P3(x2331,x2331,x2331)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(235,plain,
% 1.94/2.04 (~P3(a3,a4,a4)),
% 1.94/2.04 inference(scs_inference,[],[11,14,5,233,23,18,20])).
% 1.94/2.04 cnf(244,plain,
% 1.94/2.04 (P3(x2441,x2441,x2441)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(246,plain,
% 1.94/2.04 (~P3(a1,a3,a1)),
% 1.94/2.04 inference(scs_inference,[],[12,5,244,22,23,19])).
% 1.94/2.04 cnf(252,plain,
% 1.94/2.04 (~P3(a2,a4,x2521)+~P3(a4,x2521,a2)),
% 1.94/2.04 inference(scs_inference,[],[16,5,18,23])).
% 1.94/2.04 cnf(260,plain,
% 1.94/2.04 (P3(x2601,x2601,x2601)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(267,plain,
% 1.94/2.04 (~P3(a3,a1,a2)+P3(a1,a2,a4)),
% 1.94/2.04 inference(scs_inference,[],[13,25,180,2,1,5,260,18,20,22,21])).
% 1.94/2.04 cnf(288,plain,
% 1.94/2.04 (P3(x2881,x2881,x2881)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(290,plain,
% 1.94/2.04 (~P3(a3,a4,a3)),
% 1.94/2.04 inference(scs_inference,[],[14,13,5,288,18,20,19])).
% 1.94/2.04 cnf(291,plain,
% 1.94/2.04 (P3(x2911,x2911,x2911)),
% 1.94/2.04 inference(rename_variables,[],[5])).
% 1.94/2.04 cnf(294,plain,
% 1.94/2.04 (~P3(a4,a2,a3)+P3(a2,a3,a1)),
% 1.94/2.04 inference(scs_inference,[],[14,13,5,288,291,18,20,19,227,22])).
% 1.94/2.04 cnf(305,plain,
% 1.94/2.04 (~P3(a2,a4,a2)),
% 1.94/2.04 inference(scs_inference,[],[16,5,23,19])).
% 1.94/2.04 cnf(310,plain,
% 1.94/2.04 (P3(a1,a3,a4)+~P3(a3,a2,a1)),
% 1.94/2.04 inference(scs_inference,[],[92,16,246,3,1,5,23,19,21,34])).
% 1.94/2.04 cnf(318,plain,
% 1.94/2.04 (P3(a2,a4,a1)+P3(a2,a4,a3)),
% 1.94/2.04 inference(scs_inference,[],[305,148,8,4,2,5,23,18,21])).
% 1.94/2.04 cnf(327,plain,
% 1.94/2.04 (~P3(a3,a4,x3271)+~P3(a4,x3271,a3)),
% 1.94/2.04 inference(scs_inference,[],[17,5,18,23])).
% 1.94/2.04 cnf(330,plain,
% 1.94/2.04 (~P3(a3,a4,a2)+P3(a4,a2,a1)),
% 1.94/2.04 inference(scs_inference,[],[17,70,223,4,2,5,18,23,21])).
% 1.94/2.04 cnf(332,plain,
% 1.94/2.04 (~P3(a3,a4,a2)+~P3(a1,a4,a2)),
% 1.94/2.04 inference(scs_inference,[],[17,70,223,4,2,5,18,23,21,34])).
% 1.94/2.04 cnf(334,plain,
% 1.94/2.04 (~P3(a3,a2,a1)+~P3(a3,a4,a2)),
% 1.94/2.04 inference(scs_inference,[],[17,70,223,4,2,5,18,23,21,34,20])).
% 1.94/2.04 cnf(342,plain,
% 1.94/2.04 (P3(a4,a1,a2)+P3(a4,a1,a3)),
% 1.94/2.04 inference(scs_inference,[],[97,8,4,1,5,22,19,21])).
% 1.94/2.04 cnf(367,plain,
% 1.94/2.04 (~P3(a4,a3,a1)+~P3(a3,a4,a2)),
% 1.94/2.04 inference(scs_inference,[],[53,163,7,4,1,5,23,22,21,332])).
% 1.94/2.04 cnf(388,plain,
% 1.94/2.04 (~P3(a1,a2,a4)+P3(a3,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[235,290,9,7,3,4,5,23,21,367,334,330,327,142,125,332,66,18,20])).
% 1.94/2.04 cnf(412,plain,
% 1.94/2.04 (~P3(a2,a1,a3)+~P3(a2,a4,a3)),
% 1.94/2.04 inference(scs_inference,[],[144,66])).
% 1.94/2.04 cnf(419,plain,
% 1.94/2.04 (~P3(a1,a3,a2)+P3(a2,a1,a4)),
% 1.94/2.04 inference(scs_inference,[],[136,139,10,2,1,5,23,22,21])).
% 1.94/2.04 cnf(421,plain,
% 1.94/2.04 (~P3(a3,a1,a4)+~P3(a1,a3,a2)),
% 1.94/2.04 inference(scs_inference,[],[136,139,10,2,1,5,23,22,21,20])).
% 1.94/2.04 cnf(436,plain,
% 1.94/2.04 (~P3(a4,a2,a1)+P3(a2,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[136,139,16,2,1,5,22,23,21,419,412,318])).
% 1.94/2.04 cnf(456,plain,
% 1.94/2.04 (~P3(a4,a1,a3)+P3(a3,a1,a2)),
% 1.94/2.04 inference(scs_inference,[],[92,246,15,3,1,5,22,23,21,421,310,209,58])).
% 1.94/2.04 cnf(470,plain,
% 1.94/2.04 (~P3(a4,a1,a3)+~P3(a1,a2,a4)),
% 1.94/2.04 inference(scs_inference,[],[12,5,23,22,388])).
% 1.94/2.04 cnf(556,plain,
% 1.94/2.04 (P3(a4,a1,a3)+~P3(a2,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[252,342])).
% 1.94/2.04 cnf(565,plain,
% 1.94/2.04 (P3(a1,a2,a4)+~P3(a4,a2,a3)),
% 1.94/2.04 inference(scs_inference,[],[294,187])).
% 1.94/2.04 cnf(644,plain,
% 1.94/2.04 (P3(a3,a1,a2)+~P3(a2,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[456,556])).
% 1.94/2.04 cnf(653,plain,
% 1.94/2.04 (P3(a4,a1,a2)+~P3(a1,a2,a4)),
% 1.94/2.04 inference(scs_inference,[],[470,342])).
% 1.94/2.04 cnf(782,plain,
% 1.94/2.04 (P3(a1,a2,a4)+~P3(a2,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[644,267])).
% 1.94/2.04 cnf(791,plain,
% 1.94/2.04 (~P3(a1,a2,a4)),
% 1.94/2.04 inference(scs_inference,[],[653,110])).
% 1.94/2.04 cnf(795,plain,
% 1.94/2.04 (~P3(a4,a2,a3)),
% 1.94/2.04 inference(scs_inference,[],[791,565])).
% 1.94/2.04 cnf(796,plain,
% 1.94/2.04 (~P3(a2,a4,a1)),
% 1.94/2.04 inference(scs_inference,[],[791,782])).
% 1.94/2.04 cnf(802,plain,
% 1.94/2.04 (P3(a4,a2,a1)),
% 1.94/2.04 inference(scs_inference,[],[795,226])).
% 1.94/2.04 cnf(808,plain,
% 1.94/2.04 (~P3(a4,a2,a1)),
% 1.94/2.04 inference(scs_inference,[],[796,436])).
% 1.94/2.04 cnf(821,plain,
% 1.94/2.04 ($false),
% 1.94/2.04 inference(scs_inference,[],[802,808]),
% 1.94/2.04 ['proof']).
% 1.94/2.04 % SZS output end Proof
% 1.94/2.04 % Total time :1.400000s
%------------------------------------------------------------------------------