TSTP Solution File: GRP128-4.003 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP128-4.003 : 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 : n008.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 00:11:08 EDT 2023
% Result : Unsatisfiable 1.32s 1.49s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 02:27:02 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 1.32/1.49 %-------------------------------------------
% 1.32/1.49 % File :CSE---1.6
% 1.32/1.49 % Problem :theBenchmark
% 1.32/1.49 % Transform :cnf
% 1.32/1.49 % Format :tptp:raw
% 1.32/1.49 % Command :java -jar mcs_scs.jar %d %s
% 1.32/1.49
% 1.32/1.49 % Result :Theorem 0.850000s
% 1.32/1.49 % Output :CNFRefutation 0.850000s
% 1.32/1.49 %-------------------------------------------
% 1.32/1.49 %--------------------------------------------------------------------------
% 1.32/1.49 % File : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 1.32/1.49 % Domain : Group Theory (Quasigroups)
% 1.32/1.49 % Problem : (a.b).b = a.(a.b)
% 1.32/1.49 % Version : [Sla93] axioms : Augmented.
% 1.32/1.49 % English : Generate the multiplication table for the specified quasi-
% 1.32/1.49 % group with 3 elements.
% 1.32/1.49
% 1.32/1.49 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 1.32/1.49 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 1.32/1.49 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 1.32/1.49 % Source : [TPTP]
% 1.32/1.49 % Names :
% 1.32/1.49
% 1.32/1.49 % Status : Unsatisfiable
% 1.32/1.49 % Rating : 0.00 v2.1.0
% 1.32/1.49 % Syntax : Number of clauses : 18 ( 9 unt; 3 nHn; 18 RR)
% 1.32/1.49 % Number of literals : 42 ( 0 equ; 24 neg)
% 1.32/1.49 % Maximal clause size : 5 ( 2 avg)
% 1.32/1.49 % Maximal term depth : 1 ( 1 avg)
% 1.32/1.49 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 1.32/1.49 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 1.32/1.49 % Number of variables : 30 ( 0 sgn)
% 1.32/1.49 % SPC : CNF_UNS_EPR_NEQ_NHN
% 1.32/1.49
% 1.32/1.49 % Comments : [SFS93]'s axiomatization has been modified for this.
% 1.32/1.49 % : Substitution axioms are not needed, as any positive equality
% 1.32/1.49 % literals should resolve on negative ones directly.
% 1.32/1.49 % : Version 4 has surjectivity and rotation
% 1.32/1.49 % : tptp2X: -f tptp -s3 GRP128-4.g
% 1.32/1.49 % Bugfixes : v1.2.1 - Clauses row_surjectivity and column_surjectivity fixed.
% 1.32/1.49 %--------------------------------------------------------------------------
% 1.32/1.49 cnf(row_surjectivity,axiom,
% 1.32/1.49 ( ~ group_element(X)
% 1.32/1.49 | ~ group_element(Y)
% 1.32/1.49 | product(e_1,X,Y)
% 1.32/1.49 | product(e_2,X,Y)
% 1.32/1.49 | product(e_3,X,Y) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(column_surjectivity,axiom,
% 1.32/1.49 ( ~ group_element(X)
% 1.32/1.49 | ~ group_element(Y)
% 1.32/1.49 | product(X,e_1,Y)
% 1.32/1.49 | product(X,e_2,Y)
% 1.32/1.49 | product(X,e_3,Y) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(qg3_1,negated_conjecture,
% 1.32/1.49 ( product(X,Y,Z1)
% 1.32/1.49 | ~ product(X,Z1,Z2)
% 1.32/1.49 | ~ product(Z1,Y,Z2) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(qg3_2,negated_conjecture,
% 1.32/1.49 ( product(Z1,Y,Z2)
% 1.32/1.49 | ~ product(X,Z1,Z2)
% 1.32/1.49 | ~ product(X,Y,Z1) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(element_1,axiom,
% 1.32/1.49 group_element(e_1) ).
% 1.32/1.49
% 1.32/1.49 cnf(element_2,axiom,
% 1.32/1.49 group_element(e_2) ).
% 1.32/1.49
% 1.32/1.49 cnf(element_3,axiom,
% 1.32/1.49 group_element(e_3) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_1_is_not_e_2,axiom,
% 1.32/1.49 ~ equalish(e_1,e_2) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_1_is_not_e_3,axiom,
% 1.32/1.49 ~ equalish(e_1,e_3) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_2_is_not_e_1,axiom,
% 1.32/1.49 ~ equalish(e_2,e_1) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_2_is_not_e_3,axiom,
% 1.32/1.49 ~ equalish(e_2,e_3) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_3_is_not_e_1,axiom,
% 1.32/1.49 ~ equalish(e_3,e_1) ).
% 1.32/1.49
% 1.32/1.49 cnf(e_3_is_not_e_2,axiom,
% 1.32/1.49 ~ equalish(e_3,e_2) ).
% 1.32/1.49
% 1.32/1.49 cnf(product_total_function1,axiom,
% 1.32/1.49 ( ~ group_element(X)
% 1.32/1.49 | ~ group_element(Y)
% 1.32/1.49 | product(X,Y,e_1)
% 1.32/1.49 | product(X,Y,e_2)
% 1.32/1.49 | product(X,Y,e_3) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(product_total_function2,axiom,
% 1.32/1.49 ( ~ product(X,Y,W)
% 1.32/1.49 | ~ product(X,Y,Z)
% 1.32/1.49 | equalish(W,Z) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(product_right_cancellation,axiom,
% 1.32/1.49 ( ~ product(X,W,Y)
% 1.32/1.49 | ~ product(X,Z,Y)
% 1.32/1.49 | equalish(W,Z) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(product_left_cancellation,axiom,
% 1.32/1.49 ( ~ product(W,Y,X)
% 1.32/1.49 | ~ product(Z,Y,X)
% 1.32/1.49 | equalish(W,Z) ) ).
% 1.32/1.49
% 1.32/1.49 cnf(qg3,negated_conjecture,
% 1.32/1.49 ( ~ product(X,Y,Z1)
% 1.32/1.49 | ~ product(Z1,Y,Z2)
% 1.32/1.49 | product(X,Z1,Z2) ) ).
% 1.32/1.49
% 1.32/1.49 %--------------------------------------------------------------------------
% 1.32/1.49 %-------------------------------------------
% 1.32/1.49 % Proof found
% 1.32/1.49 % SZS status Theorem for theBenchmark
% 1.32/1.49 % SZS output start Proof
% 1.32/1.49 %ClaNum:18(EqnAxiom:0)
% 1.32/1.49 %VarNum:75(SingletonVarNum:30)
% 1.32/1.49 %MaxLitNum:5
% 1.32/1.49 %MaxfuncDepth:0
% 1.32/1.49 %SharedTerms:12
% 1.32/1.49 %goalClause: 16 17 18
% 1.32/1.50 [1]P1(a1)
% 1.32/1.50 [2]P1(a2)
% 1.32/1.50 [3]P1(a3)
% 1.32/1.50 [4]~P2(a1,a2)
% 1.32/1.50 [5]~P2(a1,a3)
% 1.32/1.50 [6]~P2(a2,a1)
% 1.32/1.50 [7]~P2(a2,a3)
% 1.32/1.50 [8]~P2(a3,a1)
% 1.32/1.50 [9]~P2(a3,a2)
% 1.32/1.50 [13]~P3(x133,x134,x131)+P2(x131,x132)+~P3(x133,x134,x132)
% 1.32/1.50 [14]~P3(x143,x141,x144)+P2(x141,x142)+~P3(x143,x142,x144)
% 1.32/1.50 [15]~P3(x151,x153,x154)+P2(x151,x152)+~P3(x152,x153,x154)
% 1.32/1.50 [16]~P3(x161,x164,x162)+P3(x161,x162,x163)+~P3(x162,x164,x163)
% 1.32/1.50 [17]~P3(x174,x171,x173)+P3(x171,x172,x173)+~P3(x174,x172,x171)
% 1.32/1.50 [18]~P3(x181,x183,x184)+P3(x181,x182,x183)+~P3(x183,x182,x184)
% 1.32/1.50 [10]~P1(x102)+~P1(x101)+P3(x101,x102,a2)+P3(x101,x102,a3)+P3(x101,x102,a1)
% 1.32/1.50 [11]~P1(x112)+~P1(x111)+P3(x111,a2,x112)+P3(x111,a3,x112)+P3(x111,a1,x112)
% 1.32/1.50 [12]~P1(x122)+~P1(x121)+P3(a2,x121,x122)+P3(a3,x121,x122)+P3(a1,x121,x122)
% 1.32/1.50 %EqnAxiom
% 1.32/1.50
% 1.32/1.50 %-------------------------------------------
% 1.32/1.50 cnf(19,plain,
% 1.32/1.50 (~P3(a2,x191,x192)+~P3(a1,x191,x192)),
% 1.32/1.50 inference(scs_inference,[],[4,15])).
% 1.32/1.50 cnf(20,plain,
% 1.32/1.50 (~P3(x201,a2,x202)+~P3(x201,a1,x202)),
% 1.32/1.50 inference(scs_inference,[],[4,15,14])).
% 1.32/1.50 cnf(21,plain,
% 1.32/1.50 (~P3(x211,x212,a2)+~P3(x211,x212,a1)),
% 1.32/1.50 inference(scs_inference,[],[4,15,14,13])).
% 1.32/1.50 cnf(24,plain,
% 1.32/1.50 (P3(a2,a2,a2)+P3(a2,a1,a2)+P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[2,12,11])).
% 1.32/1.50 cnf(25,plain,
% 1.32/1.50 (P3(a2,a2,a2)+P3(a2,a2,a1)+P3(a2,a2,a3)),
% 1.32/1.50 inference(scs_inference,[],[2,12,11,10])).
% 1.32/1.50 cnf(29,plain,
% 1.32/1.50 (~P3(x291,a1,x292)+~P3(x291,x292,x293)+~P3(x292,a2,x293)),
% 1.32/1.50 inference(scs_inference,[],[20,17])).
% 1.32/1.50 cnf(41,plain,
% 1.32/1.50 (~P3(a1,x411,x412)+~P3(x413,a1,x412)+~P3(x413,x411,a2)),
% 1.32/1.50 inference(scs_inference,[],[21,18])).
% 1.32/1.50 cnf(42,plain,
% 1.32/1.50 (~P3(x421,x422,a3)+~P3(x421,x422,a2)),
% 1.32/1.50 inference(scs_inference,[],[7,13])).
% 1.32/1.50 cnf(44,plain,
% 1.32/1.50 (~P3(a2,a2,a3)+P3(a2,a1,a2)+P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[7,13,25,24])).
% 1.32/1.50 cnf(58,plain,
% 1.32/1.50 (~P3(x581,a2,x582)+~P3(x581,x582,x583)+~P3(x582,a3,x583)),
% 1.32/1.50 inference(scs_inference,[],[9,14,17])).
% 1.32/1.50 cnf(60,plain,
% 1.32/1.50 (~P3(a2,a3,a3)+P3(a2,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[9,14,17,25,18])).
% 1.32/1.50 cnf(63,plain,
% 1.32/1.50 (~P3(x631,x632,a2)+~P3(x633,x632,x631)+~P3(x633,x631,a3)),
% 1.32/1.50 inference(scs_inference,[],[42,16])).
% 1.32/1.50 cnf(67,plain,
% 1.32/1.50 (P3(a1,a1,a1)+P3(a1,a1,a3)+P3(a1,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[1,10])).
% 1.32/1.50 cnf(71,plain,
% 1.32/1.50 (~P3(a3,a1,a1)+P3(a1,a1,a3)+P3(a1,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[1,5,10,13,14,15])).
% 1.32/1.50 cnf(85,plain,
% 1.32/1.50 (~P3(a2,a3,a3)+~P3(a2,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[29,60])).
% 1.32/1.50 cnf(97,plain,
% 1.32/1.50 (~P3(x971,x972,a3)+~P3(x971,x972,a1)),
% 1.32/1.50 inference(scs_inference,[],[5,13])).
% 1.32/1.50 cnf(98,plain,
% 1.32/1.50 (~P3(a2,x981,x982)+~P3(a3,x981,x982)),
% 1.32/1.50 inference(scs_inference,[],[5,9,13,15])).
% 1.32/1.50 cnf(105,plain,
% 1.32/1.50 (~P3(a2,a2,a3)+P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[63,44])).
% 1.32/1.50 cnf(106,plain,
% 1.32/1.50 (~P3(a3,a2,x1061)+~P3(a2,a3,x1061)+P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[105,18])).
% 1.32/1.50 cnf(110,plain,
% 1.32/1.50 (P3(a1,a1,a2)+~P3(a3,a1,a1)+~P3(a2,a1,a3)),
% 1.32/1.50 inference(scs_inference,[],[71,19])).
% 1.32/1.50 cnf(119,plain,
% 1.32/1.50 (~P3(a2,a1,a3)+~P3(a3,a1,a1)),
% 1.32/1.50 inference(scs_inference,[],[110,41])).
% 1.32/1.50 cnf(137,plain,
% 1.32/1.50 (P3(a1,a1,a1)+P3(a1,a1,a2)+~P3(a2,a1,a3)),
% 1.32/1.50 inference(scs_inference,[],[19,67])).
% 1.32/1.50 cnf(138,plain,
% 1.32/1.50 (P3(a1,a1,a2)+~P3(a2,a1,a3)+~P3(a1,a2,a1)),
% 1.32/1.50 inference(scs_inference,[],[137,20])).
% 1.32/1.50 cnf(139,plain,
% 1.32/1.50 (~P3(a1,a2,a1)+~P3(a2,a1,a3)),
% 1.32/1.50 inference(scs_inference,[],[138,41])).
% 1.32/1.50 cnf(156,plain,
% 1.32/1.50 (~P3(x1561,x1562,a1)+~P3(x1561,a1,x1563)+~P3(a2,x1562,x1563)),
% 1.32/1.50 inference(scs_inference,[],[19,17])).
% 1.32/1.50 cnf(183,plain,
% 1.32/1.50 (P3(a1,a2,a3)+P3(a1,a2,a1)+~P3(a2,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[2,1,19,10])).
% 1.32/1.50 cnf(184,plain,
% 1.32/1.50 (~P3(a2,a2,a2)+~P3(a2,a1,a3)+P3(a1,a2,a3)),
% 1.32/1.50 inference(scs_inference,[],[183,139])).
% 1.32/1.50 cnf(185,plain,
% 1.32/1.50 (~P3(a2,x1851,a2)+~P3(a2,a1,a3)+P3(a1,a2,a3)),
% 1.32/1.50 inference(scs_inference,[],[184,16])).
% 1.32/1.50 cnf(198,plain,
% 1.32/1.50 (~P3(x1981,x1982,a2)+~P3(x1981,a2,x1983)+~P3(a1,x1982,x1983)),
% 1.32/1.50 inference(scs_inference,[],[19,17])).
% 1.32/1.50 cnf(215,plain,
% 1.32/1.50 (P3(a1,a2,a2)+P3(a1,a1,a2)+~P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[2,1,19,11])).
% 1.32/1.50 cnf(216,plain,
% 1.32/1.50 (P3(a1,a1,a2)+~P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[215,198])).
% 1.32/1.50 cnf(217,plain,
% 1.32/1.50 (~P3(a2,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[216,41])).
% 1.32/1.50 cnf(218,plain,
% 1.32/1.50 (P3(a2,a2,a2)+P3(a2,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[217,24])).
% 1.32/1.50 cnf(219,plain,
% 1.32/1.50 (~P3(a2,a2,a3)),
% 1.32/1.50 inference(scs_inference,[],[217,105])).
% 1.32/1.50 cnf(220,plain,
% 1.32/1.50 (~P3(a2,a3,x2201)+~P3(a3,a2,x2201)),
% 1.32/1.50 inference(scs_inference,[],[217,106])).
% 1.32/1.50 cnf(225,plain,
% 1.32/1.50 (~P3(a2,a3,a3)+P3(a1,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[217,2,3,16,12])).
% 1.32/1.50 cnf(246,plain,
% 1.32/1.50 (P3(a2,a1,a2)+~P3(a1,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[218,198])).
% 1.32/1.50 cnf(247,plain,
% 1.32/1.50 (P3(a2,a3,a3)+P3(a2,a3,a1)),
% 1.32/1.50 inference(scs_inference,[],[217,3,2,10])).
% 1.32/1.50 cnf(287,plain,
% 1.32/1.50 (P3(a2,a3,a1)+P3(a1,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[225,247])).
% 1.32/1.50 cnf(298,plain,
% 1.32/1.50 (~P3(a1,a3,a1)+P3(a3,a3,a2)),
% 1.32/1.50 inference(scs_inference,[],[2,6,9,217,3,12,18,14,13])).
% 1.32/1.50 cnf(301,plain,
% 1.32/1.50 (~P3(a1,a2,a2)+~P3(a2,a1,a3)),
% 1.32/1.50 inference(scs_inference,[],[246,42])).
% 1.32/1.50 cnf(313,plain,
% 1.32/1.50 (~P3(a2,a1,a2)+P3(a2,a3,a3)),
% 1.32/1.50 inference(scs_inference,[],[3,6,219,8,2,11,14,13,15,301,119,97,42])).
% 1.32/1.50 cnf(315,plain,
% 1.32/1.50 (P3(a1,a2,a3)+P3(a2,a3,a3)+~P3(a2,x3151,a2)),
% 1.32/1.50 inference(scs_inference,[],[3,6,219,8,2,11,14,13,15,301,119,97,42,185])).
% 1.32/1.50 cnf(320,plain,
% 1.32/1.50 (~P3(a3,a1,a2)+P3(a2,a3,a3)),
% 1.32/1.50 inference(scs_inference,[],[3,6,219,217,8,2,11,14,13,15,301,119,97,42,185,58,17,16])).
% 1.32/1.50 cnf(335,plain,
% 1.32/1.50 (P3(a1,a3,a2)+~P3(a3,a2,a1)),
% 1.32/1.50 inference(scs_inference,[],[287,220])).
% 1.32/1.50 cnf(342,plain,
% 1.32/1.50 (~P3(a1,a3,a1)+~P3(a3,a3,a3)),
% 1.32/1.50 inference(scs_inference,[],[298,42])).
% 1.32/1.50 cnf(349,plain,
% 1.32/1.50 (~P3(a2,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[313,85])).
% 1.32/1.50 cnf(352,plain,
% 1.32/1.50 (P3(a2,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[349,218])).
% 1.32/1.50 cnf(353,plain,
% 1.32/1.50 (~P3(a1,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[349,246])).
% 1.32/1.50 cnf(400,plain,
% 1.32/1.50 (P3(a2,a3,a3)+P3(a1,a2,a3)),
% 1.32/1.50 inference(scs_inference,[],[352,315])).
% 1.32/1.50 cnf(402,plain,
% 1.32/1.50 (~P3(a3,a2,a2)),
% 1.32/1.50 inference(scs_inference,[],[352,98])).
% 1.32/1.50 cnf(412,plain,
% 1.32/1.50 (~P3(a3,a2,a3)+~P3(a2,a1,a1)),
% 1.32/1.50 inference(scs_inference,[],[8,352,353,1,2,98,14,41,10,18,15])).
% 1.32/1.50 cnf(439,plain,
% 1.32/1.50 (~P3(a3,a1,a2)),
% 1.32/1.50 inference(scs_inference,[],[7,352,6,219,402,1,3,2,13,15,156,10,18,12,14,412,400,320])).
% 1.32/1.50 cnf(458,plain,
% 1.32/1.50 ($false),
% 1.32/1.50 inference(scs_inference,[],[5,352,439,402,3,2,11,18,13,15,342,335,225,63]),
% 1.32/1.50 ['proof']).
% 1.32/1.50 % SZS output end Proof
% 1.32/1.50 % Total time :0.850000s
%------------------------------------------------------------------------------