TSTP Solution File: GRP123-3.003 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-3.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n019.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 00:10:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP123-3.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon Aug 28 22:08:28 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.54 start to proof:theBenchmark
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % File :CSE---1.6
% 0.19/0.63 % Problem :theBenchmark
% 0.19/0.63 % Transform :cnf
% 0.19/0.63 % Format :tptp:raw
% 0.19/0.63 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.63
% 0.19/0.63 % Result :Theorem 0.020000s
% 0.19/0.63 % Output :CNFRefutation 0.020000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.64 % File : GRP123-3.003 : TPTP v8.1.2. Released v1.2.0.
% 0.19/0.64 % Domain : Group Theory (Quasigroups)
% 0.19/0.64 % Problem : (3,2,1) conjugate orthogonality
% 0.19/0.64 % Version : [Sla93] axioms : Augmented.
% 0.19/0.64 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.19/0.64 % Generate the multiplication table for the specified quasi-
% 0.19/0.64 % group with 3 elements.
% 0.19/0.64
% 0.19/0.64 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.19/0.64 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.19/0.64 % : [Zha94] Zhang (1994), Email to G. Sutcliffe
% 0.19/0.64 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.19/0.64 % Source : [TPTP]
% 0.19/0.64 % Names :
% 0.19/0.64
% 0.19/0.64 % Status : Unsatisfiable
% 0.19/0.64 % Rating : 0.00 v2.1.0
% 0.19/0.64 % Syntax : Number of clauses : 32 ( 20 unt; 2 nHn; 31 RR)
% 0.19/0.64 % Number of literals : 71 ( 0 equ; 43 neg)
% 0.19/0.64 % Maximal clause size : 6 ( 2 avg)
% 0.19/0.64 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.64 % Number of predicates : 6 ( 6 usr; 0 prp; 1-3 aty)
% 0.19/0.64 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% 0.19/0.64 % Number of variables : 47 ( 0 sgn)
% 0.19/0.64 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.19/0.64
% 0.19/0.64 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.19/0.64 % : Substitution axioms are not needed, as any positive equality
% 0.19/0.64 % literals should resolve on negative ones directly.
% 0.19/0.64 % : [Zha94] has pointed out that either one of qg1_1
% 0.19/0.64 % or qg1_2 may be used, as each implies the other in this
% 0.19/0.64 % scenario, with the help of cancellation. The dependence
% 0.19/0.64 % cannot be proved, so both have been left in here.
% 0.19/0.64 % : Version 3 has complex isomorphism avoidance (mentioned in
% 0.19/0.64 % [SFS95]
% 0.19/0.64 % : tptp2X: -f tptp -s3 GRP123-3.g
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 cnf(e_0_then_e_1,axiom,
% 0.19/0.64 next(e_0,e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_1_then_e_2,axiom,
% 0.19/0.64 next(e_1,e_2) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_2_then_e_3,axiom,
% 0.19/0.64 next(e_2,e_3) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_1_greater_e_0,axiom,
% 0.19/0.64 greater(e_1,e_0) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_2_greater_e_0,axiom,
% 0.19/0.64 greater(e_2,e_0) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_3_greater_e_0,axiom,
% 0.19/0.64 greater(e_3,e_0) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_2_greater_e_1,axiom,
% 0.19/0.64 greater(e_2,e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_3_greater_e_1,axiom,
% 0.19/0.64 greater(e_3,e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_3_greater_e_2,axiom,
% 0.19/0.64 greater(e_3,e_2) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle1,axiom,
% 0.19/0.64 ( ~ cycle(X,Y)
% 0.19/0.64 | ~ cycle(X,Z)
% 0.19/0.64 | equalish(Y,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle2,axiom,
% 0.19/0.64 ( ~ group_element(X)
% 0.19/0.64 | cycle(X,e_0)
% 0.19/0.64 | cycle(X,e_1)
% 0.19/0.64 | cycle(X,e_2) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle3,axiom,
% 0.19/0.64 cycle(e_3,e_0) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle4,axiom,
% 0.19/0.64 ( ~ cycle(X,Y)
% 0.19/0.64 | ~ cycle(W,Z)
% 0.19/0.64 | ~ next(X,W)
% 0.19/0.64 | ~ greater(Y,e_0)
% 0.19/0.64 | ~ next(Z,Z1)
% 0.19/0.64 | equalish(Y,Z1) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle5,axiom,
% 0.19/0.64 ( ~ cycle(X,Z1)
% 0.19/0.64 | ~ cycle(Y,e_0)
% 0.19/0.64 | ~ cycle(W,Z2)
% 0.19/0.64 | ~ next(Y,W)
% 0.19/0.64 | ~ greater(Y,X)
% 0.19/0.64 | ~ greater(Z1,Z2) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle6,axiom,
% 0.19/0.64 ( ~ cycle(X,e_0)
% 0.19/0.64 | ~ product(X,e_1,Y)
% 0.19/0.64 | ~ greater(Y,X) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(cycle7,axiom,
% 0.19/0.64 ( ~ cycle(X,Y)
% 0.19/0.64 | ~ product(X,e_1,Z)
% 0.19/0.64 | ~ greater(Y,e_0)
% 0.19/0.64 | ~ next(X,X1)
% 0.19/0.64 | equalish(Z,X1) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(element_1,axiom,
% 0.19/0.64 group_element(e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(element_2,axiom,
% 0.19/0.64 group_element(e_2) ).
% 0.19/0.64
% 0.19/0.64 cnf(element_3,axiom,
% 0.19/0.64 group_element(e_3) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_1_is_not_e_2,axiom,
% 0.19/0.64 ~ equalish(e_1,e_2) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_1_is_not_e_3,axiom,
% 0.19/0.64 ~ equalish(e_1,e_3) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_2_is_not_e_1,axiom,
% 0.19/0.64 ~ equalish(e_2,e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_2_is_not_e_3,axiom,
% 0.19/0.64 ~ equalish(e_2,e_3) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_3_is_not_e_1,axiom,
% 0.19/0.64 ~ equalish(e_3,e_1) ).
% 0.19/0.64
% 0.19/0.64 cnf(e_3_is_not_e_2,axiom,
% 0.19/0.64 ~ equalish(e_3,e_2) ).
% 0.19/0.64
% 0.19/0.64 cnf(product_total_function1,axiom,
% 0.19/0.64 ( ~ group_element(X)
% 0.19/0.64 | ~ group_element(Y)
% 0.19/0.64 | product(X,Y,e_1)
% 0.19/0.64 | product(X,Y,e_2)
% 0.19/0.64 | product(X,Y,e_3) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product_total_function2,axiom,
% 0.19/0.64 ( ~ product(X,Y,W)
% 0.19/0.64 | ~ product(X,Y,Z)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product_right_cancellation,axiom,
% 0.19/0.64 ( ~ product(X,W,Y)
% 0.19/0.64 | ~ product(X,Z,Y)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product_left_cancellation,axiom,
% 0.19/0.64 ( ~ product(W,Y,X)
% 0.19/0.64 | ~ product(Z,Y,X)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product_idempotence,axiom,
% 0.19/0.64 product(X,X,X) ).
% 0.19/0.64
% 0.19/0.64 cnf(qg1_1,negated_conjecture,
% 0.19/0.64 ( ~ product(X1,Y1,Z1)
% 0.19/0.64 | ~ product(X2,Y2,Z1)
% 0.19/0.64 | ~ product(Z2,Y1,X1)
% 0.19/0.64 | ~ product(Z2,Y2,X2)
% 0.19/0.64 | equalish(X1,X2) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(qg1_2,negated_conjecture,
% 0.19/0.64 ( ~ product(X1,Y1,Z1)
% 0.19/0.64 | ~ product(X2,Y2,Z1)
% 0.19/0.64 | ~ product(Z2,Y1,X1)
% 0.19/0.64 | ~ product(Z2,Y2,X2)
% 0.19/0.64 | equalish(Y1,Y2) ) ).
% 0.19/0.64
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:32(EqnAxiom:0)
% 0.19/0.64 %VarNum:109(SingletonVarNum:47)
% 0.19/0.64 %MaxLitNum:6
% 0.19/0.64 %MaxfuncDepth:0
% 0.19/0.64 %SharedTerms:23
% 0.19/0.64 %goalClause: 31 32
% 0.19/0.64 [1]P1(a1)
% 0.19/0.64 [2]P1(a3)
% 0.19/0.64 [3]P1(a4)
% 0.19/0.64 [4]P5(a2,a1)
% 0.19/0.64 [5]P5(a1,a3)
% 0.19/0.64 [6]P5(a3,a4)
% 0.19/0.64 [7]P2(a1,a2)
% 0.19/0.64 [8]P2(a3,a2)
% 0.19/0.64 [9]P2(a3,a1)
% 0.19/0.64 [10]P2(a4,a2)
% 0.19/0.64 [11]P2(a4,a1)
% 0.19/0.64 [12]P2(a4,a3)
% 0.19/0.64 [13]P3(a4,a2)
% 0.19/0.64 [15]~P4(a1,a3)
% 0.19/0.64 [16]~P4(a1,a4)
% 0.19/0.64 [17]~P4(a3,a1)
% 0.19/0.64 [18]~P4(a3,a4)
% 0.19/0.64 [19]~P4(a4,a1)
% 0.19/0.64 [20]~P4(a4,a3)
% 0.19/0.64 [14]P6(x141,x141,x141)
% 0.19/0.64 [24]~P2(x241,x242)+~P6(x242,a1,x241)+~P3(x242,a2)
% 0.19/0.64 [22]~P3(x223,x221)+P4(x221,x222)+~P3(x223,x222)
% 0.19/0.64 [28]~P6(x283,x284,x281)+P4(x281,x282)+~P6(x283,x284,x282)
% 0.19/0.64 [29]~P6(x293,x291,x294)+P4(x291,x292)+~P6(x293,x292,x294)
% 0.19/0.64 [30]~P6(x301,x303,x304)+P4(x301,x302)+~P6(x302,x303,x304)
% 0.19/0.64 [21]~P1(x211)+P3(x211,a1)+P3(x211,a3)+P3(x211,a2)
% 0.19/0.64 [27]~P1(x272)+~P1(x271)+P6(x271,x272,a3)+P6(x271,x272,a4)+P6(x271,x272,a1)
% 0.19/0.64 [26]P4(x261,x262)+~P5(x263,x262)+~P3(x263,x264)+~P6(x263,a1,x261)+~P2(x264,a2)
% 0.19/0.64 [31]~P6(x315,x311,x316)+P4(x311,x312)+~P6(x313,x312,x314)+~P6(x313,x311,x315)+~P6(x314,x312,x316)
% 0.19/0.64 [32]~P6(x321,x325,x326)+P4(x321,x322)+~P6(x323,x324,x322)+~P6(x323,x325,x321)+~P6(x322,x324,x326)
% 0.19/0.64 [23]~P3(x235,x233)+~P3(x234,x231)+P4(x231,x232)+~P5(x233,x232)+~P5(x234,x235)+~P2(x231,a2)
% 0.19/0.64 [25]~P3(x252,x255)+~P3(x253,x254)+~P5(x251,x252)+~P2(x251,x253)+~P2(x254,x255)+~P3(x251,a2)
% 0.19/0.64 %EqnAxiom
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(34,plain,
% 0.19/0.64 (~P3(a1,a1)),
% 0.19/0.64 inference(scs_inference,[],[14,5,7,15,30,26])).
% 0.19/0.64 cnf(59,plain,
% 0.19/0.64 (P6(x591,x591,x591)),
% 0.19/0.64 inference(rename_variables,[],[14])).
% 0.19/0.64 cnf(64,plain,
% 0.19/0.64 (P6(x641,x641,x641)),
% 0.19/0.64 inference(rename_variables,[],[14])).
% 0.19/0.64 cnf(69,plain,
% 0.19/0.64 (P6(a4,a1,a3)),
% 0.19/0.64 inference(scs_inference,[],[1,3,16,13,14,59,64,30,22,29,28,27])).
% 0.19/0.64 cnf(81,plain,
% 0.19/0.64 (~P6(a3,a1,a1)),
% 0.19/0.64 inference(scs_inference,[],[17,14,30])).
% 0.19/0.64 cnf(82,plain,
% 0.19/0.64 (P6(x821,x821,x821)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(87,plain,
% 0.19/0.65 (P6(x871,x871,x871)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(91,plain,
% 0.19/0.65 (P3(a1,a2)),
% 0.19/0.65 inference(scs_inference,[],[34,17,8,5,14,82,87,13,15,1,30,22,26,32,21])).
% 0.19/0.65 cnf(93,plain,
% 0.19/0.65 (~P6(a4,a3,a3)+~P6(a3,a1,a3)),
% 0.19/0.65 inference(scs_inference,[],[34,17,8,5,14,82,87,13,15,69,1,30,22,26,32,21,31])).
% 0.19/0.65 cnf(110,plain,
% 0.19/0.65 (P6(x1101,x1101,x1101)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(113,plain,
% 0.19/0.65 (P6(x1131,x1131,x1131)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(118,plain,
% 0.19/0.65 (P6(a3,a1,a3)),
% 0.19/0.65 inference(scs_inference,[],[2,17,14,110,113,16,81,91,69,1,30,31,24,26,27])).
% 0.19/0.65 cnf(128,plain,
% 0.19/0.65 (~P6(a4,a3,a3)),
% 0.19/0.65 inference(scs_inference,[],[118,93])).
% 0.19/0.65 cnf(130,plain,
% 0.19/0.65 (P6(x1301,x1301,x1301)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(136,plain,
% 0.19/0.65 (~P6(a1,x1361,a4)+~P6(a4,x1361,a1)),
% 0.19/0.65 inference(scs_inference,[],[19,14,130,13,69,30,31,24,32])).
% 0.19/0.65 cnf(161,plain,
% 0.19/0.65 (P6(x1611,x1611,x1611)),
% 0.19/0.65 inference(rename_variables,[],[14])).
% 0.19/0.65 cnf(170,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[20,18,14,161,118,128,3,69,2,91,31,29,27,24,136,30]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.020000s
%------------------------------------------------------------------------------