TSTP Solution File: GRP123-9.003 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n010.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 00:11:00 EDT 2023
% Result : Unsatisfiable 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n010.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 19:49:34 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 % File :CSE---1.6
% 0.20/0.65 % Problem :theBenchmark
% 0.20/0.65 % Transform :cnf
% 0.20/0.65 % Format :tptp:raw
% 0.20/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.65
% 0.20/0.65 % Result :Theorem 0.030000s
% 0.20/0.65 % Output :CNFRefutation 0.030000s
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 % File : GRP123-9.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.20/0.65 % Domain : Group Theory (Quasigroups)
% 0.20/0.65 % Problem : (3,2,1) conjugate orthogonality
% 0.20/0.65 % Version : [Sla93] axioms : Augmented.
% 0.20/0.65 % Theorem formulation : Uses a second group.
% 0.20/0.65 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.20/0.65 % Generate the multiplication table for the specified quasi-
% 0.20/0.65 % group with 3 elements.
% 0.20/0.65
% 0.20/0.65 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.20/0.65 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.20/0.65 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.20/0.65 % Source : [TPTP]
% 0.20/0.65 % Names :
% 0.20/0.65
% 0.20/0.65 % Status : Unsatisfiable
% 0.20/0.65 % Rating : 0.00 v2.1.0
% 0.20/0.65 % Syntax : Number of clauses : 22 ( 11 unt; 4 nHn; 20 RR)
% 0.20/0.65 % Number of literals : 52 ( 0 equ; 28 neg)
% 0.20/0.65 % Maximal clause size : 5 ( 2 avg)
% 0.20/0.65 % Maximal term depth : 1 ( 1 avg)
% 0.20/0.65 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.20/0.65 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.20/0.65 % Number of variables : 38 ( 0 sgn)
% 0.20/0.65 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.20/0.65
% 0.20/0.65 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.20/0.65 % : Substitution axioms are not needed, as any positive equality
% 0.20/0.65 % literals should resolve on negative ones directly.
% 0.20/0.65 % : Version 9 has surjectivity and rotation
% 0.20/0.65 % : tptp2X: -f tptp -s3 GRP123-9.g
% 0.20/0.65 % Bugfixes : v1.2.1 - Clauses row_surjectivity and column_surjectivity fixed.
% 0.20/0.65 %--------------------------------------------------------------------------
% 0.20/0.65 cnf(row_surjectivity,axiom,
% 0.20/0.65 ( ~ group_element(X)
% 0.20/0.65 | ~ group_element(Y)
% 0.20/0.65 | product(e_1,X,Y)
% 0.20/0.65 | product(e_2,X,Y)
% 0.20/0.65 | product(e_3,X,Y) ) ).
% 0.20/0.65
% 0.20/0.65 cnf(column_surjectivity,axiom,
% 0.20/0.65 ( ~ group_element(X)
% 0.20/0.65 | ~ group_element(Y)
% 0.20/0.65 | product(X,e_1,Y)
% 0.20/0.65 | product(X,e_2,Y)
% 0.20/0.65 | product(X,e_3,Y) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(element_1,axiom,
% 0.20/0.66 group_element(e_1) ).
% 0.20/0.66
% 0.20/0.66 cnf(element_2,axiom,
% 0.20/0.66 group_element(e_2) ).
% 0.20/0.66
% 0.20/0.66 cnf(element_3,axiom,
% 0.20/0.66 group_element(e_3) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_1_is_not_e_2,axiom,
% 0.20/0.66 ~ equalish(e_1,e_2) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_1_is_not_e_3,axiom,
% 0.20/0.66 ~ equalish(e_1,e_3) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_2_is_not_e_1,axiom,
% 0.20/0.66 ~ equalish(e_2,e_1) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_2_is_not_e_3,axiom,
% 0.20/0.66 ~ equalish(e_2,e_3) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_3_is_not_e_1,axiom,
% 0.20/0.66 ~ equalish(e_3,e_1) ).
% 0.20/0.66
% 0.20/0.66 cnf(e_3_is_not_e_2,axiom,
% 0.20/0.66 ~ equalish(e_3,e_2) ).
% 0.20/0.66
% 0.20/0.66 cnf(product1_total_function1,axiom,
% 0.20/0.66 ( ~ group_element(X)
% 0.20/0.66 | ~ group_element(Y)
% 0.20/0.66 | product1(X,Y,e_1)
% 0.20/0.66 | product1(X,Y,e_2)
% 0.20/0.66 | product1(X,Y,e_3) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product1_total_function2,axiom,
% 0.20/0.66 ( ~ product1(X,Y,W)
% 0.20/0.66 | ~ product1(X,Y,Z)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product1_right_cancellation,axiom,
% 0.20/0.66 ( ~ product1(X,W,Y)
% 0.20/0.66 | ~ product1(X,Z,Y)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product1_left_cancellation,axiom,
% 0.20/0.66 ( ~ product1(W,Y,X)
% 0.20/0.66 | ~ product1(Z,Y,X)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product1_idempotence,axiom,
% 0.20/0.66 product1(X,X,X) ).
% 0.20/0.66
% 0.20/0.66 cnf(product2_total_function1,axiom,
% 0.20/0.66 ( ~ group_element(X)
% 0.20/0.66 | ~ group_element(Y)
% 0.20/0.66 | product2(X,Y,e_1)
% 0.20/0.66 | product2(X,Y,e_2)
% 0.20/0.66 | product2(X,Y,e_3) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product2_total_function2,axiom,
% 0.20/0.66 ( ~ product2(X,Y,W)
% 0.20/0.66 | ~ product2(X,Y,Z)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product2_right_cancellation,axiom,
% 0.20/0.66 ( ~ product2(X,W,Y)
% 0.20/0.66 | ~ product2(X,Z,Y)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product2_left_cancellation,axiom,
% 0.20/0.66 ( ~ product2(W,Y,X)
% 0.20/0.66 | ~ product2(Z,Y,X)
% 0.20/0.66 | equalish(W,Z) ) ).
% 0.20/0.66
% 0.20/0.66 cnf(product2_idempotence,axiom,
% 0.20/0.66 product2(X,X,X) ).
% 0.20/0.66
% 0.20/0.66 cnf(qg1a,negated_conjecture,
% 0.20/0.66 ( ~ product1(X,Y,Z1)
% 0.20/0.66 | ~ product1(Z1,Y,Z2)
% 0.20/0.66 | product2(Z2,X,Y) ) ).
% 0.20/0.66
% 0.20/0.66 %--------------------------------------------------------------------------
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 % Proof found
% 0.20/0.66 % SZS status Theorem for theBenchmark
% 0.20/0.66 % SZS output start Proof
% 0.20/0.66 %ClaNum:22(EqnAxiom:0)
% 0.20/0.66 %VarNum:95(SingletonVarNum:38)
% 0.20/0.66 %MaxLitNum:5
% 0.20/0.66 %MaxfuncDepth:0
% 0.20/0.66 %SharedTerms:12
% 0.20/0.66 %goalClause: 22
% 0.20/0.66 [1]P1(a1)
% 0.20/0.66 [2]P1(a2)
% 0.20/0.66 [3]P1(a3)
% 0.20/0.66 [6]~P2(a1,a2)
% 0.20/0.66 [7]~P2(a1,a3)
% 0.20/0.66 [8]~P2(a2,a1)
% 0.20/0.66 [9]~P2(a2,a3)
% 0.20/0.66 [10]~P2(a3,a1)
% 0.20/0.66 [11]~P2(a3,a2)
% 0.20/0.66 [4]P3(x41,x41,x41)
% 0.20/0.66 [5]P5(x51,x51,x51)
% 0.20/0.66 [16]~P3(x163,x164,x161)+P2(x161,x162)+~P3(x163,x164,x162)
% 0.20/0.66 [17]~P5(x173,x174,x171)+P2(x171,x172)+~P5(x173,x174,x172)
% 0.20/0.66 [18]~P3(x183,x181,x184)+P2(x181,x182)+~P3(x183,x182,x184)
% 0.20/0.66 [19]~P5(x193,x191,x194)+P2(x191,x192)+~P5(x193,x192,x194)
% 0.20/0.66 [20]~P3(x201,x203,x204)+P2(x201,x202)+~P3(x202,x203,x204)
% 0.20/0.66 [21]~P5(x211,x213,x214)+P2(x211,x212)+~P5(x212,x213,x214)
% 0.20/0.66 [22]~P3(x222,x223,x224)+P5(x221,x222,x223)+~P3(x224,x223,x221)
% 0.20/0.66 [12]~P1(x122)+~P1(x121)+P3(x121,x122,a2)+P3(x121,x122,a3)+P3(x121,x122,a1)
% 0.20/0.66 [13]~P1(x132)+~P1(x131)+P5(x131,x132,a2)+P5(x131,x132,a3)+P5(x131,x132,a1)
% 0.20/0.66 [14]~P1(x142)+~P1(x141)+P4(x141,a2,x142)+P4(x141,a3,x142)+P4(x141,a1,x142)
% 0.20/0.66 [15]~P1(x152)+~P1(x151)+P4(a2,x151,x152)+P4(a3,x151,x152)+P4(a1,x151,x152)
% 0.20/0.66 %EqnAxiom
% 0.20/0.66
% 0.20/0.66 %-------------------------------------------
% 0.20/0.66 cnf(25,plain,
% 0.20/0.66 (P3(x251,x251,x251)),
% 0.20/0.66 inference(rename_variables,[],[4])).
% 0.20/0.66 cnf(28,plain,
% 0.20/0.66 (P5(x281,x281,x281)),
% 0.20/0.66 inference(rename_variables,[],[5])).
% 0.20/0.66 cnf(31,plain,
% 0.20/0.66 (P3(x311,x311,x311)),
% 0.20/0.66 inference(rename_variables,[],[4])).
% 0.20/0.66 cnf(43,plain,
% 0.20/0.66 (P3(a2,a1,a3)+P3(a2,a1,a2)),
% 0.20/0.66 inference(scs_inference,[],[1,4,25,31,5,28,2,6,21,20,19,18,17,16,22,13,12])).
% 0.20/0.66 cnf(46,plain,
% 0.20/0.66 (P5(x461,x461,x461)),
% 0.20/0.66 inference(rename_variables,[],[5])).
% 0.20/0.66 cnf(48,plain,
% 0.20/0.66 (~P3(a3,a1,a3)),
% 0.20/0.66 inference(scs_inference,[],[7,4,5,21,18])).
% 0.20/0.66 cnf(49,plain,
% 0.20/0.66 (P3(x491,x491,x491)),
% 0.20/0.66 inference(rename_variables,[],[4])).
% 0.20/0.66 cnf(52,plain,
% 0.20/0.66 (P3(x521,x521,x521)),
% 0.20/0.66 inference(rename_variables,[],[4])).
% 0.20/0.66 cnf(58,plain,
% 0.20/0.66 (P5(x581,x581,x581)),
% 0.20/0.66 inference(rename_variables,[],[5])).
% 0.20/0.66 cnf(60,plain,
% 0.20/0.66 (~P5(a3,a3,a1)),
% 0.20/0.66 inference(scs_inference,[],[7,4,49,52,5,46,58,21,18,16,20,19,17])).
% 0.20/0.66 cnf(82,plain,
% 0.20/0.66 (~P3(a3,a2,a2)),
% 0.20/0.66 inference(scs_inference,[],[9,4,5,21,20])).
% 0.20/0.66 cnf(85,plain,
% 0.20/0.66 (P3(a3,a1,a2)+P3(a3,a1,a1)),
% 0.20/0.66 inference(scs_inference,[],[9,3,4,5,48,1,21,20,12])).
% 0.20/0.66 cnf(87,plain,
% 0.20/0.66 (~P3(a2,a1,a3)+P3(a3,a1,a1)),
% 0.20/0.66 inference(scs_inference,[],[9,3,4,5,48,60,1,21,20,12,22])).
% 0.20/0.66 cnf(89,plain,
% 0.20/0.66 (P3(a2,a1,a2)+P3(a3,a1,a1)),
% 0.20/0.66 inference(scs_inference,[],[9,3,4,5,48,60,1,21,20,12,22,43])).
% 0.20/0.66 cnf(104,plain,
% 0.20/0.66 (P5(a2,a2,a1)),
% 0.20/0.66 inference(scs_inference,[],[3,10,4,5,82,2,18,21,20,89,87,85,12,22])).
% 0.20/0.66 cnf(135,plain,
% 0.20/0.66 ($false),
% 0.20/0.66 inference(scs_inference,[],[8,5,104,17]),
% 0.20/0.66 ['proof']).
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time :0.030000s
%------------------------------------------------------------------------------