TSTP Solution File: GRP123-4.003 by CSE---1.6

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE---1.6
% Problem  : GRP123-4.003 : 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 : 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 00:10:59 EDT 2023

% Result   : Unsatisfiable 0.54s 0.64s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP123-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34  % Computer : n023.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 22:46:25 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.48/0.57  start to proof:theBenchmark
% 0.48/0.63  %-------------------------------------------
% 0.48/0.63  % File        :CSE---1.6
% 0.48/0.63  % Problem     :theBenchmark
% 0.48/0.63  % Transform   :cnf
% 0.48/0.63  % Format      :tptp:raw
% 0.48/0.63  % Command     :java -jar mcs_scs.jar %d %s
% 0.48/0.63  
% 0.48/0.63  % Result      :Theorem 0.010000s
% 0.48/0.63  % Output      :CNFRefutation 0.010000s
% 0.48/0.63  %-------------------------------------------
% 0.48/0.63  %--------------------------------------------------------------------------
% 0.48/0.63  % File     : GRP123-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.48/0.63  % Domain   : Group Theory (Quasigroups)
% 0.48/0.63  % Problem  : (3,2,1) conjugate orthogonality
% 0.48/0.63  % Version  : [Sla93] axioms : Augmented.
% 0.48/0.63  % English  : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.48/0.63  %            Generate the multiplication table for the specified quasi-
% 0.48/0.63  %            group with 3 elements.
% 0.48/0.63  
% 0.48/0.63  % Refs     : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.48/0.63  %          : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.48/0.63  %          : [Zha94] Zhang (1994), Email to G. Sutcliffe
% 0.48/0.63  %          : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.48/0.63  % Source   : [TPTP]
% 0.48/0.63  % Names    :
% 0.48/0.63  
% 0.48/0.63  % Status   : Unsatisfiable
% 0.48/0.63  % Rating   : 0.00 v2.1.0
% 0.48/0.63  % Syntax   : Number of clauses     :   18 (  10 unt;   3 nHn;  17 RR)
% 0.48/0.63  %            Number of literals    :   44 (   0 equ;  26 neg)
% 0.48/0.63  %            Maximal clause size   :    5 (   2 avg)
% 0.48/0.63  %            Maximal term depth    :    1 (   1 avg)
% 0.48/0.63  %            Number of predicates  :    3 (   3 usr;   0 prp; 1-3 aty)
% 0.48/0.63  %            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
% 0.48/0.63  %            Number of variables   :   31 (   0 sgn)
% 0.48/0.63  % SPC      : CNF_UNS_EPR_NEQ_NHN
% 0.48/0.63  
% 0.48/0.63  % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.48/0.63  %          : Substitution axioms are not needed, as any positive equality
% 0.48/0.64  %            literals should resolve on negative ones directly.
% 0.48/0.64  %          : [Zha94] has pointed out that either one of qg1_1
% 0.48/0.64  %            or qg1_2 may be used, as each implies the other in this
% 0.48/0.64  %            scenario, with the help of cancellation. The dependence
% 0.48/0.64  %            cannot be proved, so both have been left in here.
% 0.48/0.64  %          : Version 4 has surjectivity and rotation
% 0.48/0.64  %          : tptp2X: -f tptp -s3 GRP123-4.g
% 0.48/0.64  % Bugfixes : v1.2.1 - Clauses row_surjectivity and column_surjectivity fixed.
% 0.48/0.64  %--------------------------------------------------------------------------
% 0.48/0.64  cnf(row_surjectivity,axiom,
% 0.48/0.64      ( ~ group_element(X)
% 0.48/0.64      | ~ group_element(Y)
% 0.48/0.64      | product(e_1,X,Y)
% 0.48/0.64      | product(e_2,X,Y)
% 0.48/0.64      | product(e_3,X,Y) ) ).
% 0.48/0.64  
% 0.48/0.64  cnf(column_surjectivity,axiom,
% 0.48/0.64      ( ~ group_element(X)
% 0.48/0.64      | ~ group_element(Y)
% 0.48/0.64      | product(X,e_1,Y)
% 0.48/0.64      | product(X,e_2,Y)
% 0.48/0.64      | product(X,e_3,Y) ) ).
% 0.48/0.64  
% 0.48/0.64  cnf(element_1,axiom,
% 0.48/0.64      group_element(e_1) ).
% 0.48/0.64  
% 0.48/0.64  cnf(element_2,axiom,
% 0.48/0.64      group_element(e_2) ).
% 0.48/0.64  
% 0.48/0.64  cnf(element_3,axiom,
% 0.48/0.64      group_element(e_3) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_1_is_not_e_2,axiom,
% 0.48/0.64      ~ equalish(e_1,e_2) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_1_is_not_e_3,axiom,
% 0.48/0.64      ~ equalish(e_1,e_3) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_2_is_not_e_1,axiom,
% 0.48/0.64      ~ equalish(e_2,e_1) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_2_is_not_e_3,axiom,
% 0.48/0.64      ~ equalish(e_2,e_3) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_3_is_not_e_1,axiom,
% 0.48/0.64      ~ equalish(e_3,e_1) ).
% 0.48/0.64  
% 0.48/0.64  cnf(e_3_is_not_e_2,axiom,
% 0.48/0.64      ~ equalish(e_3,e_2) ).
% 0.48/0.64  
% 0.48/0.64  cnf(product_total_function1,axiom,
% 0.54/0.64      ( ~ group_element(X)
% 0.54/0.64      | ~ group_element(Y)
% 0.54/0.64      | product(X,Y,e_1)
% 0.54/0.64      | product(X,Y,e_2)
% 0.54/0.64      | product(X,Y,e_3) ) ).
% 0.54/0.64  
% 0.54/0.64  cnf(product_total_function2,axiom,
% 0.54/0.64      ( ~ product(X,Y,W)
% 0.54/0.64      | ~ product(X,Y,Z)
% 0.54/0.64      | equalish(W,Z) ) ).
% 0.54/0.64  
% 0.54/0.64  cnf(product_right_cancellation,axiom,
% 0.54/0.64      ( ~ product(X,W,Y)
% 0.54/0.64      | ~ product(X,Z,Y)
% 0.54/0.64      | equalish(W,Z) ) ).
% 0.54/0.64  
% 0.54/0.64  cnf(product_left_cancellation,axiom,
% 0.54/0.64      ( ~ product(W,Y,X)
% 0.54/0.64      | ~ product(Z,Y,X)
% 0.54/0.64      | equalish(W,Z) ) ).
% 0.54/0.64  
% 0.54/0.64  cnf(product_idempotence,axiom,
% 0.54/0.64      product(X,X,X) ).
% 0.54/0.64  
% 0.54/0.64  cnf(qg1_1,negated_conjecture,
% 0.54/0.64      ( ~ product(X1,Y1,Z1)
% 0.54/0.64      | ~ product(X2,Y2,Z1)
% 0.54/0.64      | ~ product(Z2,Y1,X1)
% 0.54/0.64      | ~ product(Z2,Y2,X2)
% 0.54/0.64      | equalish(X1,X2) ) ).
% 0.54/0.64  
% 0.54/0.64  cnf(qg1_2,negated_conjecture,
% 0.54/0.64      ( ~ product(X1,Y1,Z1)
% 0.54/0.64      | ~ product(X2,Y2,Z1)
% 0.54/0.64      | ~ product(Z2,Y1,X1)
% 0.54/0.64      | ~ product(Z2,Y2,X2)
% 0.54/0.64      | equalish(Y1,Y2) ) ).
% 0.54/0.64  
% 0.54/0.64  %--------------------------------------------------------------------------
% 0.54/0.64  %-------------------------------------------
% 0.54/0.64  % Proof found
% 0.54/0.64  % SZS status Theorem for theBenchmark
% 0.54/0.64  % SZS output start Proof
% 0.54/0.64  %ClaNum:18(EqnAxiom:0)
% 0.54/0.64  %VarNum:79(SingletonVarNum:31)
% 0.54/0.64  %MaxLitNum:5
% 0.54/0.64  %MaxfuncDepth:0
% 0.54/0.64  %SharedTerms:12
% 0.54/0.64  %goalClause: 17 18
% 0.54/0.64  [1]P1(a1)
% 0.54/0.64  [2]P1(a2)
% 0.54/0.64  [3]P1(a3)
% 0.54/0.64  [5]~P2(a1,a2)
% 0.54/0.64  [6]~P2(a1,a3)
% 0.54/0.64  [7]~P2(a2,a1)
% 0.54/0.64  [8]~P2(a2,a3)
% 0.54/0.64  [9]~P2(a3,a1)
% 0.54/0.64  [10]~P2(a3,a2)
% 0.54/0.64  [4]P3(x41,x41,x41)
% 0.54/0.64  [14]~P3(x143,x144,x141)+P2(x141,x142)+~P3(x143,x144,x142)
% 0.54/0.64  [15]~P3(x153,x151,x154)+P2(x151,x152)+~P3(x153,x152,x154)
% 0.54/0.64  [16]~P3(x161,x163,x164)+P2(x161,x162)+~P3(x162,x163,x164)
% 0.54/0.64  [11]~P1(x112)+~P1(x111)+P3(x111,x112,a2)+P3(x111,x112,a3)+P3(x111,x112,a1)
% 0.54/0.64  [12]~P1(x122)+~P1(x121)+P3(x121,a2,x122)+P3(x121,a3,x122)+P3(x121,a1,x122)
% 0.54/0.64  [13]~P1(x132)+~P1(x131)+P3(a2,x131,x132)+P3(a3,x131,x132)+P3(a1,x131,x132)
% 0.54/0.64  [17]~P3(x175,x171,x176)+P2(x171,x172)+~P3(x173,x172,x174)+~P3(x173,x171,x175)+~P3(x174,x172,x176)
% 0.54/0.64  [18]~P3(x181,x185,x186)+P2(x181,x182)+~P3(x183,x184,x182)+~P3(x183,x185,x181)+~P3(x182,x184,x186)
% 0.54/0.64  %EqnAxiom
% 0.54/0.64  
% 0.54/0.64  %-------------------------------------------
% 0.54/0.64  cnf(20,plain,
% 0.54/0.64     (~P3(a1,a2,a1)),
% 0.54/0.64     inference(scs_inference,[],[4,5,16,15])).
% 0.54/0.64  cnf(21,plain,
% 0.54/0.64     (P3(x211,x211,x211)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(24,plain,
% 0.54/0.64     (P3(x241,x241,x241)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(27,plain,
% 0.54/0.64     (P3(x271,x271,x271)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(29,plain,
% 0.54/0.64     (~P3(x291,a2,a1)+~P3(a1,a2,x291)),
% 0.54/0.64     inference(scs_inference,[],[4,21,24,27,5,16,15,14,18,17])).
% 0.54/0.64  cnf(37,plain,
% 0.54/0.64     (P3(x371,x371,x371)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(39,plain,
% 0.54/0.64     (~P3(a3,a1,a3)),
% 0.54/0.64     inference(scs_inference,[],[6,4,37,16,15])).
% 0.54/0.64  cnf(40,plain,
% 0.54/0.64     (P3(x401,x401,x401)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(43,plain,
% 0.54/0.64     (P3(x431,x431,x431)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(47,plain,
% 0.54/0.64     (P3(a3,a2,a1)),
% 0.54/0.64     inference(scs_inference,[],[1,3,6,4,37,40,16,15,14,13,12])).
% 0.54/0.64  cnf(51,plain,
% 0.54/0.64     (P3(a3,a1,a2)),
% 0.54/0.64     inference(scs_inference,[],[1,3,6,4,37,40,43,16,15,14,13,12,18,11])).
% 0.54/0.64  cnf(56,plain,
% 0.54/0.64     (P3(x561,x561,x561)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(60,plain,
% 0.54/0.64     (P3(a1,a2,a2)),
% 0.54/0.64     inference(scs_inference,[],[2,7,20,4,56,47,1,29,16,18,11])).
% 0.54/0.64  cnf(73,plain,
% 0.54/0.64     (P3(x731,x731,x731)),
% 0.54/0.64     inference(rename_variables,[],[4])).
% 0.54/0.64  cnf(80,plain,
% 0.54/0.64     ($false),
% 0.54/0.64     inference(scs_inference,[],[8,7,4,73,3,51,39,60,1,17,16,18,13]),
% 0.54/0.64     ['proof']).
% 0.54/0.64  % SZS output end Proof
% 0.54/0.64  % Total time :0.010000s
%------------------------------------------------------------------------------