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