TSTP Solution File: GRP123-7.003 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-7.003 : 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 : n028.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 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n028.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 21:41:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 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 0.030000s
% 0.19/0.63 % Output :CNFRefutation 0.030000s
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 % File : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.19/0.63 % Domain : Group Theory (Quasigroups)
% 0.19/0.63 % Problem : (3,2,1) conjugate orthogonality
% 0.19/0.63 % Version : [Sla93] axioms : Augmented.
% 0.19/0.63 % Theorem formulation : Uses a second group.
% 0.19/0.63 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.19/0.63 % Generate the multiplication table for the specified quasi-
% 0.19/0.63 % group with 3 elements.
% 0.19/0.63
% 0.19/0.63 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.19/0.63 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.19/0.63 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.19/0.63 % Source : [TPTP]
% 0.19/0.63 % Names :
% 0.19/0.63
% 0.19/0.63 % Status : Unsatisfiable
% 0.19/0.63 % Rating : 0.00 v2.1.0
% 0.19/0.63 % Syntax : Number of clauses : 26 ( 16 unt; 2 nHn; 24 RR)
% 0.19/0.63 % Number of literals : 50 ( 0 equ; 27 neg)
% 0.19/0.63 % Maximal clause size : 5 ( 1 avg)
% 0.19/0.63 % Maximal term depth : 1 ( 1 avg)
% 0.19/0.63 % Number of predicates : 7 ( 7 usr; 0 prp; 1-3 aty)
% 0.19/0.63 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.19/0.63 % Number of variables : 37 ( 0 sgn)
% 0.19/0.63 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.19/0.63
% 0.19/0.63 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.19/0.63 % : Substitution axioms are not needed, as any positive equality
% 0.19/0.63 % literals should resolve on negative ones directly.
% 0.19/0.63 % : Version 7 has simple isomorphism avoidance (as mentioned in
% 0.19/0.63 % [FSB93])
% 0.19/0.63 % : tptp2X: -f tptp -s3 GRP123-7.g
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 cnf(e_1_then_e_2,axiom,
% 0.19/0.63 next(e_1,e_2) ).
% 0.19/0.63
% 0.19/0.63 cnf(e_2_then_e_3,axiom,
% 0.19/0.63 next(e_2,e_3) ).
% 0.19/0.63
% 0.19/0.63 cnf(e_2_greater_e_1,axiom,
% 0.19/0.63 greater(e_2,e_1) ).
% 0.19/0.63
% 0.19/0.63 cnf(e_3_greater_e_1,axiom,
% 0.19/0.63 greater(e_3,e_1) ).
% 0.19/0.63
% 0.19/0.63 cnf(e_3_greater_e_2,axiom,
% 0.19/0.63 greater(e_3,e_2) ).
% 0.19/0.63
% 0.19/0.63 cnf(no_redundancy,axiom,
% 0.19/0.63 ( ~ product(X,e_1,Y)
% 0.19/0.63 | ~ next(X,X1)
% 0.19/0.64 | ~ greater(Y,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(product1_total_function1,axiom,
% 0.19/0.64 ( ~ group_element(X)
% 0.19/0.64 | ~ group_element(Y)
% 0.19/0.64 | product1(X,Y,e_1)
% 0.19/0.64 | product1(X,Y,e_2)
% 0.19/0.64 | product1(X,Y,e_3) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product1_total_function2,axiom,
% 0.19/0.64 ( ~ product1(X,Y,W)
% 0.19/0.64 | ~ product1(X,Y,Z)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product1_right_cancellation,axiom,
% 0.19/0.64 ( ~ product1(X,W,Y)
% 0.19/0.64 | ~ product1(X,Z,Y)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product1_left_cancellation,axiom,
% 0.19/0.64 ( ~ product1(W,Y,X)
% 0.19/0.64 | ~ product1(Z,Y,X)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product1_idempotence,axiom,
% 0.19/0.64 product1(X,X,X) ).
% 0.19/0.64
% 0.19/0.64 cnf(product2_total_function1,axiom,
% 0.19/0.64 ( ~ group_element(X)
% 0.19/0.64 | ~ group_element(Y)
% 0.19/0.64 | product2(X,Y,e_1)
% 0.19/0.64 | product2(X,Y,e_2)
% 0.19/0.64 | product2(X,Y,e_3) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product2_total_function2,axiom,
% 0.19/0.64 ( ~ product2(X,Y,W)
% 0.19/0.64 | ~ product2(X,Y,Z)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product2_right_cancellation,axiom,
% 0.19/0.64 ( ~ product2(X,W,Y)
% 0.19/0.64 | ~ product2(X,Z,Y)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product2_left_cancellation,axiom,
% 0.19/0.64 ( ~ product2(W,Y,X)
% 0.19/0.64 | ~ product2(Z,Y,X)
% 0.19/0.64 | equalish(W,Z) ) ).
% 0.19/0.64
% 0.19/0.64 cnf(product2_idempotence,axiom,
% 0.19/0.64 product2(X,X,X) ).
% 0.19/0.64
% 0.19/0.64 cnf(qg1a,negated_conjecture,
% 0.19/0.64 ( ~ product1(X,Y,Z1)
% 0.19/0.64 | ~ product1(Z1,Y,Z2)
% 0.19/0.64 | product2(Z2,X,Y) ) ).
% 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:26(EqnAxiom:0)
% 0.19/0.64 %VarNum:85(SingletonVarNum:37)
% 0.19/0.64 %MaxLitNum:5
% 0.19/0.64 %MaxfuncDepth:0
% 0.19/0.64 %SharedTerms:17
% 0.19/0.64 %goalClause: 26
% 0.19/0.64 [1]P1(a1)
% 0.19/0.64 [2]P1(a2)
% 0.19/0.64 [3]P1(a3)
% 0.19/0.64 [4]P4(a1,a2)
% 0.19/0.64 [5]P4(a2,a3)
% 0.19/0.64 [6]P2(a2,a1)
% 0.19/0.64 [7]P2(a3,a1)
% 0.19/0.64 [8]P2(a3,a2)
% 0.19/0.64 [11]~P3(a1,a2)
% 0.19/0.64 [12]~P3(a1,a3)
% 0.19/0.64 [13]~P3(a2,a1)
% 0.19/0.64 [14]~P3(a2,a3)
% 0.19/0.64 [15]~P3(a3,a1)
% 0.19/0.64 [16]~P3(a3,a2)
% 0.19/0.64 [9]P5(x91,x91,x91)
% 0.19/0.64 [10]P7(x101,x101,x101)
% 0.19/0.64 [17]~P4(x171,x172)+~P2(x173,x172)+~P6(x171,a1,x173)
% 0.19/0.64 [20]~P5(x203,x204,x201)+P3(x201,x202)+~P5(x203,x204,x202)
% 0.19/0.64 [21]~P7(x213,x214,x211)+P3(x211,x212)+~P7(x213,x214,x212)
% 0.19/0.64 [22]~P5(x223,x221,x224)+P3(x221,x222)+~P5(x223,x222,x224)
% 0.19/0.64 [23]~P7(x233,x231,x234)+P3(x231,x232)+~P7(x233,x232,x234)
% 0.19/0.64 [24]~P5(x241,x243,x244)+P3(x241,x242)+~P5(x242,x243,x244)
% 0.19/0.64 [25]~P7(x251,x253,x254)+P3(x251,x252)+~P7(x252,x253,x254)
% 0.19/0.64 [26]~P5(x262,x263,x264)+P7(x261,x262,x263)+~P5(x264,x263,x261)
% 0.19/0.64 [18]~P1(x182)+~P1(x181)+P5(x181,x182,a2)+P5(x181,x182,a3)+P5(x181,x182,a1)
% 0.19/0.64 [19]~P1(x192)+~P1(x191)+P7(x191,x192,a2)+P7(x191,x192,a3)+P7(x191,x192,a1)
% 0.19/0.64 %EqnAxiom
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 cnf(50,plain,
% 0.19/0.64 (P7(x501,x501,x501)),
% 0.19/0.64 inference(rename_variables,[],[10])).
% 0.19/0.64 cnf(52,plain,
% 0.19/0.64 (~P5(a3,a1,a3)),
% 0.19/0.64 inference(scs_inference,[],[12,9,10,23,22])).
% 0.19/0.64 cnf(53,plain,
% 0.19/0.64 (P5(x531,x531,x531)),
% 0.19/0.64 inference(rename_variables,[],[9])).
% 0.19/0.64 cnf(56,plain,
% 0.19/0.64 (P7(x561,x561,x561)),
% 0.19/0.64 inference(rename_variables,[],[10])).
% 0.19/0.64 cnf(58,plain,
% 0.19/0.64 (~P7(a3,a1,a1)),
% 0.19/0.64 inference(scs_inference,[],[12,9,10,50,56,23,22,21,25])).
% 0.19/0.64 cnf(61,plain,
% 0.19/0.64 (~P5(a1,a3,a3)),
% 0.19/0.64 inference(scs_inference,[],[12,9,53,10,50,56,23,22,21,25,24])).
% 0.19/0.64 cnf(84,plain,
% 0.19/0.64 (~P7(a2,a2,a3)),
% 0.19/0.64 inference(scs_inference,[],[14,9,10,24,21])).
% 0.19/0.64 cnf(85,plain,
% 0.19/0.64 (P7(x851,x851,x851)),
% 0.19/0.64 inference(rename_variables,[],[10])).
% 0.19/0.64 cnf(92,plain,
% 0.19/0.64 (~P7(a3,a2,a2)),
% 0.19/0.64 inference(scs_inference,[],[14,3,9,10,85,52,58,1,24,21,26,18,25])).
% 0.19/0.64 cnf(98,plain,
% 0.19/0.64 (P7(x981,x981,x981)),
% 0.19/0.64 inference(rename_variables,[],[10])).
% 0.19/0.64 cnf(105,plain,
% 0.19/0.64 (~P5(a2,a3,a3)),
% 0.19/0.64 inference(scs_inference,[],[3,15,16,14,9,10,98,92,2,23,25,21,19,24])).
% 0.19/0.64 cnf(139,plain,
% 0.19/0.64 (~P5(a2,a3,a2)),
% 0.19/0.64 inference(scs_inference,[],[9,15,11,61,3,1,20,22,18,24])).
% 0.19/0.64 cnf(141,plain,
% 0.19/0.64 (~P5(a2,a3,a1)),
% 0.19/0.64 inference(scs_inference,[],[9,15,11,61,84,3,1,20,22,18,24,26])).
% 0.19/0.64 cnf(143,plain,
% 0.19/0.64 ($false),
% 0.19/0.64 inference(scs_inference,[],[105,141,139,2,3,18]),
% 0.19/0.64 ['proof']).
% 0.19/0.64 % SZS output end Proof
% 0.19/0.64 % Total time :0.030000s
%------------------------------------------------------------------------------