TSTP Solution File: GRP124-6.004 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP124-6.004 : 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 : n014.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 00:11:02 EDT 2023
% Result : Unsatisfiable 1.95s 2.02s
% Output : CNFRefutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP124-6.004 : 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 : n014.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:31:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof:theBenchmark
% 1.95/2.01 %-------------------------------------------
% 1.95/2.01 % File :CSE---1.6
% 1.95/2.01 % Problem :theBenchmark
% 1.95/2.01 % Transform :cnf
% 1.95/2.01 % Format :tptp:raw
% 1.95/2.01 % Command :java -jar mcs_scs.jar %d %s
% 1.95/2.01
% 1.95/2.01 % Result :Theorem 1.370000s
% 1.95/2.01 % Output :CNFRefutation 1.370000s
% 1.95/2.01 %-------------------------------------------
% 1.95/2.01 %--------------------------------------------------------------------------
% 1.95/2.01 % File : GRP124-6.004 : TPTP v8.1.2. Released v1.2.0.
% 1.95/2.01 % Domain : Group Theory (Quasigroups)
% 1.95/2.01 % Problem : (3,1,2) conjugate orthogonality
% 1.95/2.01 % Version : [Sla93] axioms.
% 1.95/2.01 % Theorem formulation : Uses a second group.
% 1.95/2.01 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*a=b iff ab=c.
% 1.95/2.01 % Generate the multiplication table for the specified quasi-
% 1.95/2.01 % group with 4 elements.
% 1.95/2.01
% 1.95/2.01 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 1.95/2.01 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 1.95/2.01 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 1.95/2.01 % Source : [Sla93]
% 1.95/2.01 % Names : QG2a [Sla93]
% 1.95/2.01
% 1.95/2.01 % Status : Unsatisfiable
% 1.95/2.01 % Rating : 0.00 v2.1.0
% 1.95/2.01 % Syntax : Number of clauses : 27 ( 18 unt; 2 nHn; 25 RR)
% 1.95/2.01 % Number of literals : 51 ( 0 equ; 30 neg)
% 1.95/2.01 % Maximal clause size : 6 ( 1 avg)
% 1.95/2.01 % Maximal term depth : 1 ( 1 avg)
% 1.95/2.01 % Number of predicates : 4 ( 4 usr; 0 prp; 1-3 aty)
% 1.95/2.01 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 1.95/2.01 % Number of variables : 34 ( 0 sgn)
% 1.95/2.01 % SPC : CNF_UNS_EPR_NEQ_NHN
% 1.95/2.01
% 1.95/2.01 % Comments : [SFS93]'s axiomatization has been modified for this.
% 1.95/2.01 % : Substitution axioms are not needed, as any positive equality
% 1.95/2.01 % literals should resolve on negative ones directly.
% 1.95/2.01 % : tptp2X: -f tptp -s4 GRP124-6.g
% 1.95/2.01 %--------------------------------------------------------------------------
% 1.95/2.01 cnf(element_1,axiom,
% 1.95/2.01 group_element(e_1) ).
% 1.95/2.01
% 1.95/2.01 cnf(element_2,axiom,
% 1.95/2.01 group_element(e_2) ).
% 1.95/2.01
% 1.95/2.01 cnf(element_3,axiom,
% 1.95/2.01 group_element(e_3) ).
% 1.95/2.01
% 1.95/2.01 cnf(element_4,axiom,
% 1.95/2.01 group_element(e_4) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_1_is_not_e_2,axiom,
% 1.95/2.01 ~ equalish(e_1,e_2) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_1_is_not_e_3,axiom,
% 1.95/2.01 ~ equalish(e_1,e_3) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_1_is_not_e_4,axiom,
% 1.95/2.01 ~ equalish(e_1,e_4) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_2_is_not_e_1,axiom,
% 1.95/2.01 ~ equalish(e_2,e_1) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_2_is_not_e_3,axiom,
% 1.95/2.01 ~ equalish(e_2,e_3) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_2_is_not_e_4,axiom,
% 1.95/2.01 ~ equalish(e_2,e_4) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_3_is_not_e_1,axiom,
% 1.95/2.01 ~ equalish(e_3,e_1) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_3_is_not_e_2,axiom,
% 1.95/2.01 ~ equalish(e_3,e_2) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_3_is_not_e_4,axiom,
% 1.95/2.01 ~ equalish(e_3,e_4) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_4_is_not_e_1,axiom,
% 1.95/2.01 ~ equalish(e_4,e_1) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_4_is_not_e_2,axiom,
% 1.95/2.01 ~ equalish(e_4,e_2) ).
% 1.95/2.01
% 1.95/2.01 cnf(e_4_is_not_e_3,axiom,
% 1.95/2.01 ~ equalish(e_4,e_3) ).
% 1.95/2.01
% 1.95/2.01 cnf(product1_total_function1,axiom,
% 1.95/2.01 ( ~ group_element(X)
% 1.95/2.01 | ~ group_element(Y)
% 1.95/2.01 | product1(X,Y,e_1)
% 1.95/2.01 | product1(X,Y,e_2)
% 1.95/2.01 | product1(X,Y,e_3)
% 1.95/2.01 | product1(X,Y,e_4) ) ).
% 1.95/2.01
% 1.95/2.01 cnf(product1_total_function2,axiom,
% 1.95/2.01 ( ~ product1(X,Y,W)
% 1.95/2.01 | ~ product1(X,Y,Z)
% 1.95/2.01 | equalish(W,Z) ) ).
% 1.95/2.01
% 1.95/2.01 cnf(product1_right_cancellation,axiom,
% 1.95/2.01 ( ~ product1(X,W,Y)
% 1.95/2.01 | ~ product1(X,Z,Y)
% 1.95/2.01 | equalish(W,Z) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product1_left_cancellation,axiom,
% 1.95/2.02 ( ~ product1(W,Y,X)
% 1.95/2.02 | ~ product1(Z,Y,X)
% 1.95/2.02 | equalish(W,Z) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product1_idempotence,axiom,
% 1.95/2.02 product1(X,X,X) ).
% 1.95/2.02
% 1.95/2.02 cnf(product2_total_function1,axiom,
% 1.95/2.02 ( ~ group_element(X)
% 1.95/2.02 | ~ group_element(Y)
% 1.95/2.02 | product2(X,Y,e_1)
% 1.95/2.02 | product2(X,Y,e_2)
% 1.95/2.02 | product2(X,Y,e_3)
% 1.95/2.02 | product2(X,Y,e_4) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product2_total_function2,axiom,
% 1.95/2.02 ( ~ product2(X,Y,W)
% 1.95/2.02 | ~ product2(X,Y,Z)
% 1.95/2.02 | equalish(W,Z) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product2_right_cancellation,axiom,
% 1.95/2.02 ( ~ product2(X,W,Y)
% 1.95/2.02 | ~ product2(X,Z,Y)
% 1.95/2.02 | equalish(W,Z) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product2_left_cancellation,axiom,
% 1.95/2.02 ( ~ product2(W,Y,X)
% 1.95/2.02 | ~ product2(Z,Y,X)
% 1.95/2.02 | equalish(W,Z) ) ).
% 1.95/2.02
% 1.95/2.02 cnf(product2_idempotence,axiom,
% 1.95/2.02 product2(X,X,X) ).
% 1.95/2.02
% 1.95/2.02 cnf(qg2a,negated_conjecture,
% 1.95/2.02 ( ~ product1(X,Y,Z1)
% 1.95/2.02 | ~ product1(Z1,X,Z2)
% 1.95/2.02 | product2(Z2,Y,X) ) ).
% 1.95/2.02
% 1.95/2.02 %--------------------------------------------------------------------------
% 1.95/2.02 %-------------------------------------------
% 1.95/2.02 % Proof found
% 1.95/2.02 % SZS status Theorem for theBenchmark
% 1.95/2.02 % SZS output start Proof
% 1.95/2.02 %ClaNum:27(EqnAxiom:0)
% 1.95/2.02 %VarNum:83(SingletonVarNum:34)
% 1.95/2.02 %MaxLitNum:6
% 1.95/2.02 %MaxfuncDepth:0
% 1.95/2.02 %SharedTerms:20
% 1.95/2.02 %goalClause: 25
% 1.95/2.02 [1]P1(a1)
% 1.95/2.02 [2]P1(a2)
% 1.95/2.02 [3]P1(a3)
% 1.95/2.02 [4]P1(a4)
% 1.95/2.02 [7]~P2(a1,a2)
% 1.95/2.02 [8]~P2(a1,a3)
% 1.95/2.02 [9]~P2(a1,a4)
% 1.95/2.02 [10]~P2(a2,a1)
% 1.95/2.02 [11]~P2(a2,a3)
% 1.95/2.02 [12]~P2(a2,a4)
% 1.95/2.02 [13]~P2(a3,a1)
% 1.95/2.02 [14]~P2(a3,a2)
% 1.95/2.02 [15]~P2(a3,a4)
% 1.95/2.02 [16]~P2(a4,a1)
% 1.95/2.02 [17]~P2(a4,a2)
% 1.95/2.02 [18]~P2(a4,a3)
% 1.95/2.02 [5]P3(x51,x51,x51)
% 1.95/2.02 [6]P4(x61,x61,x61)
% 1.95/2.02 [19]~P3(x193,x194,x191)+P2(x191,x192)+~P3(x193,x194,x192)
% 1.95/2.02 [20]~P4(x203,x204,x201)+P2(x201,x202)+~P4(x203,x204,x202)
% 1.95/2.02 [21]~P3(x213,x211,x214)+P2(x211,x212)+~P3(x213,x212,x214)
% 1.95/2.02 [22]~P4(x223,x221,x224)+P2(x221,x222)+~P4(x223,x222,x224)
% 1.95/2.02 [23]~P3(x231,x233,x234)+P2(x231,x232)+~P3(x232,x233,x234)
% 1.95/2.02 [24]~P4(x241,x243,x244)+P2(x241,x242)+~P4(x242,x243,x244)
% 1.95/2.02 [25]~P3(x253,x252,x254)+P4(x251,x252,x253)+~P3(x254,x253,x251)
% 1.95/2.02 [26]~P1(x262)+~P1(x261)+P3(x261,x262,a2)+P3(x261,x262,a3)+P3(x261,x262,a4)+P3(x261,x262,a1)
% 1.95/2.02 [27]~P1(x272)+~P1(x271)+P4(x271,x272,a2)+P4(x271,x272,a3)+P4(x271,x272,a4)+P4(x271,x272,a1)
% 1.95/2.02 %EqnAxiom
% 1.95/2.02
% 1.95/2.02 %-------------------------------------------
% 1.95/2.02 cnf(29,plain,
% 1.95/2.02 (~P3(a2,a1,a1)),
% 1.95/2.02 inference(scs_inference,[],[5,6,7,24,23])).
% 1.95/2.02 cnf(30,plain,
% 1.95/2.02 (P3(x301,x301,x301)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(32,plain,
% 1.95/2.02 (~P4(a1,a2,a1)),
% 1.95/2.02 inference(scs_inference,[],[5,6,7,24,23,22])).
% 1.95/2.02 cnf(33,plain,
% 1.95/2.02 (P4(x331,x331,x331)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(35,plain,
% 1.95/2.02 (~P3(a1,a2,a1)),
% 1.95/2.02 inference(scs_inference,[],[5,30,6,7,24,23,22,21])).
% 1.95/2.02 cnf(36,plain,
% 1.95/2.02 (P3(x361,x361,x361)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(38,plain,
% 1.95/2.02 (~P4(a1,a1,a2)),
% 1.95/2.02 inference(scs_inference,[],[5,30,6,33,7,24,23,22,21,20])).
% 1.95/2.02 cnf(44,plain,
% 1.95/2.02 (~P3(x441,a2,a1)+~P3(a2,a1,x441)),
% 1.95/2.02 inference(scs_inference,[],[5,30,36,6,33,7,24,23,22,21,20,19,25])).
% 1.95/2.02 cnf(46,plain,
% 1.95/2.02 (~P3(a1,a3,a3)),
% 1.95/2.02 inference(scs_inference,[],[8,5,23])).
% 1.95/2.02 cnf(47,plain,
% 1.95/2.02 (P3(x471,x471,x471)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(49,plain,
% 1.95/2.02 (~P3(a3,a1,a3)),
% 1.95/2.02 inference(scs_inference,[],[8,5,47,23,21])).
% 1.95/2.02 cnf(50,plain,
% 1.95/2.02 (P3(x501,x501,x501)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(52,plain,
% 1.95/2.02 (~P4(a3,a3,a1)),
% 1.95/2.02 inference(scs_inference,[],[8,5,47,6,23,21,20])).
% 1.95/2.02 cnf(53,plain,
% 1.95/2.02 (P4(x531,x531,x531)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(58,plain,
% 1.95/2.02 (~P4(a3,a1,a1)),
% 1.95/2.02 inference(scs_inference,[],[8,5,47,50,6,53,23,21,20,19,24])).
% 1.95/2.02 cnf(59,plain,
% 1.95/2.02 (P4(x591,x591,x591)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(61,plain,
% 1.95/2.02 (~P4(a3,a1,a3)),
% 1.95/2.02 inference(scs_inference,[],[8,5,47,50,6,53,59,23,21,20,19,24,22])).
% 1.95/2.02 cnf(66,plain,
% 1.95/2.02 (P3(a1,a2,a4)+P3(a1,a2,a2)+P3(a1,a2,a3)),
% 1.95/2.02 inference(scs_inference,[],[1,2,8,5,47,50,6,53,59,35,32,23,21,20,19,24,22,27,26])).
% 1.95/2.02 cnf(73,plain,
% 1.95/2.02 (~P4(a1,a4,a4)),
% 1.95/2.02 inference(scs_inference,[],[9,5,6,21,24])).
% 1.95/2.02 cnf(81,plain,
% 1.95/2.02 (P3(a1,a3,a2)+P3(a1,a3,a1)+P3(a1,a3,a4)),
% 1.95/2.02 inference(scs_inference,[],[3,9,5,6,46,58,61,1,21,24,25,27,26])).
% 1.95/2.02 cnf(87,plain,
% 1.95/2.02 (P3(x871,x871,x871)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(97,plain,
% 1.95/2.02 (P3(a2,a1,a4)+P3(a2,a1,a3)),
% 1.95/2.02 inference(scs_inference,[],[2,10,29,5,87,6,73,32,1,19,21,25,24,27,26])).
% 1.95/2.02 cnf(102,plain,
% 1.95/2.02 (P3(x1021,x1021,x1021)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(104,plain,
% 1.95/2.02 (~P4(a2,a3,a3)),
% 1.95/2.02 inference(scs_inference,[],[11,6,5,23,19,24])).
% 1.95/2.02 cnf(107,plain,
% 1.95/2.02 (~P3(a3,a2,a3)),
% 1.95/2.02 inference(scs_inference,[],[11,6,5,102,23,19,24,21])).
% 1.95/2.02 cnf(110,plain,
% 1.95/2.02 (P4(a1,a4,a1)+P4(a1,a4,a3)+P4(a1,a4,a2)),
% 1.95/2.02 inference(scs_inference,[],[4,11,6,5,102,73,1,23,19,24,21,27])).
% 1.95/2.02 cnf(116,plain,
% 1.95/2.02 (P3(x1161,x1161,x1161)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(118,plain,
% 1.95/2.02 (~P3(a4,a2,a2)),
% 1.95/2.02 inference(scs_inference,[],[12,6,5,116,22,19,23])).
% 1.95/2.02 cnf(124,plain,
% 1.95/2.02 (~P4(a1,a1,a3)),
% 1.95/2.02 inference(scs_inference,[],[13,6,20])).
% 1.95/2.02 cnf(125,plain,
% 1.95/2.02 (P4(x1251,x1251,x1251)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(132,plain,
% 1.95/2.02 (P3(a3,a1,a4)+P3(a3,a1,a2)),
% 1.95/2.02 inference(scs_inference,[],[13,6,5,49,3,1,20,19,23,26])).
% 1.95/2.02 cnf(134,plain,
% 1.95/2.02 (~P4(a3,a2,a3)),
% 1.95/2.02 inference(scs_inference,[],[13,14,6,125,5,49,3,1,20,19,23,26,22])).
% 1.95/2.02 cnf(147,plain,
% 1.95/2.02 (P3(x1471,x1471,x1471)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(150,plain,
% 1.95/2.02 (P3(x1501,x1501,x1501)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(152,plain,
% 1.95/2.02 (~P3(a1,a4,a4)),
% 1.95/2.02 inference(scs_inference,[],[5,147,150,16,6,22,19,21,23])).
% 1.95/2.02 cnf(155,plain,
% 1.95/2.02 (P3(a4,a1,a3)+P3(a4,a1,a2)+P3(a4,a1,a1)),
% 1.95/2.02 inference(scs_inference,[],[5,147,150,16,6,4,1,22,19,21,23,26])).
% 1.95/2.02 cnf(157,plain,
% 1.95/2.02 (~P4(a4,a1,a1)),
% 1.95/2.02 inference(scs_inference,[],[5,147,150,16,6,4,1,22,19,21,23,26,24])).
% 1.95/2.02 cnf(168,plain,
% 1.95/2.02 (~P3(a2,a4,a2)),
% 1.95/2.02 inference(scs_inference,[],[5,17,6,20,22,21])).
% 1.95/2.02 cnf(169,plain,
% 1.95/2.02 (P3(x1691,x1691,x1691)),
% 1.95/2.02 inference(rename_variables,[],[5])).
% 1.95/2.02 cnf(171,plain,
% 1.95/2.02 (~P3(a4,a3,a3)),
% 1.95/2.02 inference(scs_inference,[],[5,169,17,18,6,20,22,21,23])).
% 1.95/2.02 cnf(176,plain,
% 1.95/2.02 (~P4(a1,a1,a4)),
% 1.95/2.02 inference(scs_inference,[],[6,9,24,20])).
% 1.95/2.02 cnf(177,plain,
% 1.95/2.02 (P4(x1771,x1771,x1771)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(185,plain,
% 1.95/2.02 (P3(a4,a3,a2)+P3(a4,a3,a4)+P3(a4,a3,a1)),
% 1.95/2.02 inference(scs_inference,[],[6,177,9,171,157,4,3,1,24,20,22,110,27,26])).
% 1.95/2.02 cnf(187,plain,
% 1.95/2.02 (~P3(a2,a4,x1871)+P4(x1871,a3,a4)+P3(a4,a3,a4)+P3(a4,a3,a1)),
% 1.95/2.02 inference(scs_inference,[],[6,177,9,171,157,4,3,1,24,20,22,110,27,26,25])).
% 1.95/2.02 cnf(191,plain,
% 1.95/2.02 (~P4(a2,a2,a3)),
% 1.95/2.02 inference(scs_inference,[],[6,14,5,19,20])).
% 1.95/2.02 cnf(192,plain,
% 1.95/2.02 (P4(x1921,x1921,x1921)),
% 1.95/2.02 inference(rename_variables,[],[6])).
% 1.95/2.02 cnf(201,plain,
% 1.95/2.02 (~P3(a2,a1,a4)+P3(a4,a2,a3)+P3(a4,a2,a4)),
% 1.95/2.02 inference(scs_inference,[],[6,192,38,14,118,134,2,4,3,5,19,20,24,27,26,25])).
% 1.95/2.02 cnf(212,plain,
% 1.95/2.02 (~P4(a2,a1,a1)),
% 1.95/2.02 inference(scs_inference,[],[7,104,6,5,20,25,24])).
% 1.95/2.02 cnf(223,plain,
% 1.95/2.02 (~P4(a3,a3,a4)),
% 1.95/2.02 inference(scs_inference,[],[15,6,22,20])).
% 1.95/2.02 cnf(226,plain,
% 1.95/2.02 (P3(a4,a3,a4)+P3(a4,a3,a1)+~P3(a2,a4,a3)),
% 1.95/2.02 inference(scs_inference,[],[15,6,22,20,187])).
% 1.95/2.02 cnf(228,plain,
% 1.95/2.02 (~P3(a1,a2,a2)),
% 1.95/2.02 inference(scs_inference,[],[7,15,6,5,22,20,187,23])).
% 1.95/2.02 cnf(231,plain,
% 1.95/2.02 (P3(a1,a2,a3)+P3(a1,a2,a4)),
% 1.95/2.02 inference(scs_inference,[],[228,66])).
% 1.95/2.03 cnf(235,plain,
% 1.95/2.03 (~P4(a1,a3,a1)),
% 1.95/2.03 inference(scs_inference,[],[8,5,6,19,22])).
% 1.95/2.03 cnf(240,plain,
% 1.95/2.03 (~P4(a4,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[15,5,6,23,22])).
% 1.95/2.03 cnf(250,plain,
% 1.95/2.03 (P3(x2501,x2501,x2501)),
% 1.95/2.03 inference(rename_variables,[],[5])).
% 1.95/2.03 cnf(254,plain,
% 1.95/2.03 (P3(a1,a3,a2)+P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[235,5,250,25,21,81])).
% 1.95/2.03 cnf(259,plain,
% 1.95/2.03 (~P4(a4,a1,a4)+P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[9,10,235,152,4,1,6,5,250,25,21,81,23,26,22])).
% 1.95/2.03 cnf(265,plain,
% 1.95/2.03 (P3(x2651,x2651,x2651)),
% 1.95/2.03 inference(rename_variables,[],[5])).
% 1.95/2.03 cnf(270,plain,
% 1.95/2.03 (P3(a4,a1,a2)+P3(a4,a1,a3)),
% 1.95/2.03 inference(scs_inference,[],[9,6,5,265,20,21,23,155])).
% 1.95/2.03 cnf(271,plain,
% 1.95/2.03 (P3(a1,a4,a3)+P3(a1,a4,a2)),
% 1.95/2.03 inference(scs_inference,[],[9,152,4,1,6,5,265,20,21,23,155,26])).
% 1.95/2.03 cnf(273,plain,
% 1.95/2.03 (~P3(a4,a3,a1)+P3(a1,a4,a2)),
% 1.95/2.03 inference(scs_inference,[],[9,223,152,4,1,6,5,265,20,21,23,155,26,25])).
% 1.95/2.03 cnf(296,plain,
% 1.95/2.03 (~P3(a4,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[240,5,25])).
% 1.95/2.03 cnf(297,plain,
% 1.95/2.03 (P3(x2971,x2971,x2971)),
% 1.95/2.03 inference(rename_variables,[],[5])).
% 1.95/2.03 cnf(305,plain,
% 1.95/2.03 (P3(a4,a3,a1)+~P3(a2,a4,a3)),
% 1.95/2.03 inference(scs_inference,[],[12,240,5,297,25,19,21,201,226])).
% 1.95/2.03 cnf(311,plain,
% 1.95/2.03 (P3(a4,a3,a1)+P3(a4,a3,a2)),
% 1.95/2.03 inference(scs_inference,[],[296,185])).
% 1.95/2.03 cnf(319,plain,
% 1.95/2.03 (P3(a3,a2,a2)+P3(a3,a2,a4)+P3(a3,a2,a1)),
% 1.95/2.03 inference(scs_inference,[],[15,107,3,2,6,24,22,26])).
% 1.95/2.03 cnf(324,plain,
% 1.95/2.03 (P4(x3241,x3241,x3241)),
% 1.95/2.03 inference(rename_variables,[],[6])).
% 1.95/2.03 cnf(328,plain,
% 1.95/2.03 (~P3(a2,a4,a4)),
% 1.95/2.03 inference(scs_inference,[],[12,5,6,324,24,22,23])).
% 1.95/2.03 cnf(331,plain,
% 1.95/2.03 (~P4(a4,a4,a2)),
% 1.95/2.03 inference(scs_inference,[],[12,5,6,324,24,22,23,20])).
% 1.95/2.03 cnf(357,plain,
% 1.95/2.03 (~P3(a3,a2,a2)),
% 1.95/2.03 inference(scs_inference,[],[14,5,23])).
% 1.95/2.03 cnf(361,plain,
% 1.95/2.03 (P4(x3611,x3611,x3611)),
% 1.95/2.03 inference(rename_variables,[],[6])).
% 1.95/2.03 cnf(365,plain,
% 1.95/2.03 (~P3(x3651,a1,a3)+~P3(a1,a3,x3651)),
% 1.95/2.03 inference(scs_inference,[],[14,52,15,5,6,361,23,20,24,25])).
% 1.95/2.03 cnf(368,plain,
% 1.95/2.03 (~P3(a4,a1,a3)+P3(a1,a3,a2)),
% 1.95/2.03 inference(scs_inference,[],[14,52,15,5,6,361,23,20,24,25,259,254])).
% 1.95/2.03 cnf(373,plain,
% 1.95/2.03 (P3(a3,a2,a4)+P3(a3,a2,a1)),
% 1.95/2.03 inference(scs_inference,[],[357,319])).
% 1.95/2.03 cnf(389,plain,
% 1.95/2.03 (P3(a2,a4,a1)+P3(a2,a4,a3)),
% 1.95/2.03 inference(scs_inference,[],[328,168,4,2,5,23,26])).
% 1.95/2.03 cnf(400,plain,
% 1.95/2.03 (~P4(a4,a4,a1)),
% 1.95/2.03 inference(scs_inference,[],[16,6,20])).
% 1.95/2.03 cnf(405,plain,
% 1.95/2.03 (~P4(a2,a2,a1)),
% 1.95/2.03 inference(scs_inference,[],[7,6,20])).
% 1.95/2.03 cnf(417,plain,
% 1.95/2.03 (P4(x4171,x4171,x4171)),
% 1.95/2.03 inference(rename_variables,[],[6])).
% 1.95/2.03 cnf(424,plain,
% 1.95/2.03 (~P3(x4241,a1,a4)+~P3(a1,a4,x4241)),
% 1.95/2.03 inference(scs_inference,[],[400,212,7,12,2,1,6,417,20,22,24,27,25])).
% 1.95/2.03 cnf(448,plain,
% 1.95/2.03 (~P3(x4481,a1,a2)+~P3(a1,a2,x4481)),
% 1.95/2.03 inference(scs_inference,[],[405,25])).
% 1.95/2.03 cnf(460,plain,
% 1.95/2.03 (P3(a3,a1,a4)+~P3(a1,a2,a3)),
% 1.95/2.03 inference(scs_inference,[],[132,448])).
% 1.95/2.03 cnf(465,plain,
% 1.95/2.03 (~P3(x4651,a3,a1)+~P3(a3,a1,x4651)),
% 1.95/2.03 inference(scs_inference,[],[124,25])).
% 1.95/2.03 cnf(467,plain,
% 1.95/2.03 (P3(a1,a2,a4)+P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[231,460])).
% 1.95/2.03 cnf(470,plain,
% 1.95/2.03 (P3(a4,a1,a2)+~P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[270,365])).
% 1.95/2.03 cnf(473,plain,
% 1.95/2.03 (P3(a1,a4,a3)+~P3(a2,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[271,424])).
% 1.95/2.03 cnf(476,plain,
% 1.95/2.03 (~P3(a4,a3,a1)+~P3(a2,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[273,424])).
% 1.95/2.03 cnf(485,plain,
% 1.95/2.03 (P3(a2,a4,a1)+P3(a4,a3,a1)),
% 1.95/2.03 inference(scs_inference,[],[305,389])).
% 1.95/2.03 cnf(488,plain,
% 1.95/2.03 (P3(a4,a3,a2)+~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[311,465])).
% 1.95/2.03 cnf(506,plain,
% 1.95/2.03 (~P3(x5061,a4,a1)+~P3(a4,a1,x5061)),
% 1.95/2.03 inference(scs_inference,[],[176,25])).
% 1.95/2.03 cnf(508,plain,
% 1.95/2.03 (P3(a1,a3,a2)+P3(a4,a1,a2)),
% 1.95/2.03 inference(scs_inference,[],[368,270])).
% 1.95/2.03 cnf(533,plain,
% 1.95/2.03 (P3(a3,a1,a4)+~P3(a4,a1,a2)),
% 1.95/2.03 inference(scs_inference,[],[467,448])).
% 1.95/2.03 cnf(536,plain,
% 1.95/2.03 (~P3(a2,a4,a1)+~P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[470,506])).
% 1.95/2.03 cnf(539,plain,
% 1.95/2.03 (~P3(a2,a1,a4)+~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[473,424])).
% 1.95/2.03 cnf(542,plain,
% 1.95/2.03 (P3(a2,a1,a3)+~P3(a4,a3,a1)),
% 1.95/2.03 inference(scs_inference,[],[476,97])).
% 1.95/2.03 cnf(543,plain,
% 1.95/2.03 (~P3(x5431,a3,a2)+~P3(a3,a2,x5431)),
% 1.95/2.03 inference(scs_inference,[],[191,25])).
% 1.95/2.03 cnf(565,plain,
% 1.95/2.03 (P3(a4,a1,a2)+~P3(a2,a1,a3)),
% 1.95/2.03 inference(scs_inference,[],[508,365])).
% 1.95/2.03 cnf(579,plain,
% 1.95/2.03 (~P3(x5791,a2,a4)+~P3(a2,a4,x5791)),
% 1.95/2.03 inference(scs_inference,[],[331,25])).
% 1.95/2.03 cnf(583,plain,
% 1.95/2.03 (P3(a2,a4,a3)+~P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[536,389])).
% 1.95/2.03 cnf(586,plain,
% 1.95/2.03 (P3(a2,a1,a3)+~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[539,97])).
% 1.95/2.03 cnf(589,plain,
% 1.95/2.03 (~P3(a4,a3,a1)+~P3(a3,a2,a1)),
% 1.95/2.03 inference(scs_inference,[],[542,44])).
% 1.95/2.03 cnf(617,plain,
% 1.95/2.03 (P3(a4,a3,a1)+~P3(a1,a2,a4)),
% 1.95/2.03 inference(scs_inference,[],[579,485])).
% 1.95/2.03 cnf(620,plain,
% 1.95/2.03 (P3(a4,a3,a1)+~P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[583,305])).
% 1.95/2.03 cnf(623,plain,
% 1.95/2.03 (~P3(a3,a1,a4)+~P3(a1,a3,a2)),
% 1.95/2.03 inference(scs_inference,[],[586,365])).
% 1.95/2.03 cnf(626,plain,
% 1.95/2.03 (P3(a3,a2,a4)+~P3(a4,a3,a1)),
% 1.95/2.03 inference(scs_inference,[],[589,373])).
% 1.95/2.03 cnf(648,plain,
% 1.95/2.03 (~P3(a2,a1,a4)+~P3(a1,a2,a4)),
% 1.95/2.03 inference(scs_inference,[],[617,476])).
% 1.95/2.03 cnf(651,plain,
% 1.95/2.03 (P3(a3,a2,a4)+~P3(a1,a3,a4)),
% 1.95/2.03 inference(scs_inference,[],[620,626])).
% 1.95/2.03 cnf(652,plain,
% 1.95/2.03 (P3(a1,a3,a4)+~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[623,254])).
% 1.95/2.03 cnf(674,plain,
% 1.95/2.03 (P3(a2,a1,a3)+~P3(a1,a2,a4)),
% 1.95/2.03 inference(scs_inference,[],[648,97])).
% 1.95/2.03 cnf(677,plain,
% 1.95/2.03 (~P3(a1,a3,a4)+~P3(a4,a3,a2)),
% 1.95/2.03 inference(scs_inference,[],[651,543])).
% 1.95/2.03 cnf(700,plain,
% 1.95/2.03 (~P3(a1,a3,a4)+~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[677,488])).
% 1.95/2.03 cnf(719,plain,
% 1.95/2.03 (~P3(a3,a1,a4)),
% 1.95/2.03 inference(scs_inference,[],[700,652])).
% 1.95/2.03 cnf(722,plain,
% 1.95/2.03 (P3(a1,a2,a4)),
% 1.95/2.03 inference(scs_inference,[],[719,467])).
% 1.95/2.03 cnf(723,plain,
% 1.95/2.03 (~P3(a4,a1,a2)),
% 1.95/2.03 inference(scs_inference,[],[719,533])).
% 1.95/2.03 cnf(746,plain,
% 1.95/2.03 (~P3(a2,a1,a3)),
% 1.95/2.03 inference(scs_inference,[],[723,565])).
% 1.95/2.03 cnf(760,plain,
% 1.95/2.03 (P3(a2,a1,a3)),
% 1.95/2.03 inference(scs_inference,[],[722,674])).
% 1.95/2.03 cnf(763,plain,
% 1.95/2.03 ($false),
% 1.95/2.03 inference(scs_inference,[],[760,746]),
% 1.95/2.03 ['proof']).
% 1.95/2.03 % SZS output end Proof
% 1.95/2.03 % Total time :1.370000s
%------------------------------------------------------------------------------