TSTP Solution File: GRP123-6.003 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n029.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 0.45s 0.62s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 22:09:26 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.45/0.55 start to proof:theBenchmark
% 0.45/0.62 %-------------------------------------------
% 0.45/0.62 % File :CSE---1.6
% 0.45/0.62 % Problem :theBenchmark
% 0.45/0.62 % Transform :cnf
% 0.45/0.62 % Format :tptp:raw
% 0.45/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.45/0.62
% 0.45/0.62 % Result :Theorem 0.010000s
% 0.45/0.62 % Output :CNFRefutation 0.010000s
% 0.45/0.62 %-------------------------------------------
% 0.45/0.62 %--------------------------------------------------------------------------
% 0.45/0.62 % File : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% 0.45/0.62 % Domain : Group Theory (Quasigroups)
% 0.45/0.62 % Problem : (3,2,1) conjugate orthogonality
% 0.45/0.62 % Version : [Sla93] axioms.
% 0.45/0.62 % Theorem formulation : Uses a second group.
% 0.45/0.62 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c
% 0.45/0.62 % Generate the multiplication table for the specified quasi-
% 0.45/0.62 % group with 3 elements.
% 0.45/0.62
% 0.45/0.62 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.45/0.62 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.45/0.62 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.45/0.62 % Source : [Sla93]
% 0.45/0.62 % Names : QG1a [Sla93]
% 0.45/0.62
% 0.45/0.62 % Status : Unsatisfiable
% 0.45/0.62 % Rating : 0.00 v2.1.0
% 0.45/0.62 % Syntax : Number of clauses : 20 ( 11 unt; 2 nHn; 18 RR)
% 0.45/0.62 % Number of literals : 42 ( 0 equ; 24 neg)
% 0.45/0.62 % Maximal clause size : 5 ( 2 avg)
% 0.45/0.62 % Maximal term depth : 1 ( 1 avg)
% 0.45/0.62 % Number of predicates : 4 ( 4 usr; 0 prp; 1-3 aty)
% 0.45/0.62 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.45/0.62 % Number of variables : 34 ( 0 sgn)
% 0.45/0.62 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.45/0.62
% 0.45/0.62 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.45/0.62 % : Substitution axioms are not needed, as any positive equality
% 0.45/0.62 % literals should resolve on negative ones directly.
% 0.45/0.62 % : tptp2X: -f tptp -s3 GRP123-6.g
% 0.45/0.62 %--------------------------------------------------------------------------
% 0.45/0.62 cnf(element_1,axiom,
% 0.45/0.62 group_element(e_1) ).
% 0.45/0.62
% 0.45/0.62 cnf(element_2,axiom,
% 0.45/0.62 group_element(e_2) ).
% 0.45/0.62
% 0.45/0.62 cnf(element_3,axiom,
% 0.45/0.62 group_element(e_3) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_1_is_not_e_2,axiom,
% 0.45/0.62 ~ equalish(e_1,e_2) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_1_is_not_e_3,axiom,
% 0.45/0.62 ~ equalish(e_1,e_3) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_2_is_not_e_1,axiom,
% 0.45/0.62 ~ equalish(e_2,e_1) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_2_is_not_e_3,axiom,
% 0.45/0.62 ~ equalish(e_2,e_3) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_3_is_not_e_1,axiom,
% 0.45/0.62 ~ equalish(e_3,e_1) ).
% 0.45/0.62
% 0.45/0.62 cnf(e_3_is_not_e_2,axiom,
% 0.45/0.62 ~ equalish(e_3,e_2) ).
% 0.45/0.62
% 0.45/0.62 cnf(product1_total_function1,axiom,
% 0.45/0.62 ( ~ group_element(X)
% 0.45/0.62 | ~ group_element(Y)
% 0.45/0.62 | product1(X,Y,e_1)
% 0.45/0.62 | product1(X,Y,e_2)
% 0.45/0.62 | product1(X,Y,e_3) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product1_total_function2,axiom,
% 0.45/0.62 ( ~ product1(X,Y,W)
% 0.45/0.62 | ~ product1(X,Y,Z)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product1_right_cancellation,axiom,
% 0.45/0.62 ( ~ product1(X,W,Y)
% 0.45/0.62 | ~ product1(X,Z,Y)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product1_left_cancellation,axiom,
% 0.45/0.62 ( ~ product1(W,Y,X)
% 0.45/0.62 | ~ product1(Z,Y,X)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product1_idempotence,axiom,
% 0.45/0.62 product1(X,X,X) ).
% 0.45/0.62
% 0.45/0.62 cnf(product2_total_function1,axiom,
% 0.45/0.62 ( ~ group_element(X)
% 0.45/0.62 | ~ group_element(Y)
% 0.45/0.62 | product2(X,Y,e_1)
% 0.45/0.62 | product2(X,Y,e_2)
% 0.45/0.62 | product2(X,Y,e_3) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product2_total_function2,axiom,
% 0.45/0.62 ( ~ product2(X,Y,W)
% 0.45/0.62 | ~ product2(X,Y,Z)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product2_right_cancellation,axiom,
% 0.45/0.62 ( ~ product2(X,W,Y)
% 0.45/0.62 | ~ product2(X,Z,Y)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product2_left_cancellation,axiom,
% 0.45/0.62 ( ~ product2(W,Y,X)
% 0.45/0.62 | ~ product2(Z,Y,X)
% 0.45/0.62 | equalish(W,Z) ) ).
% 0.45/0.62
% 0.45/0.62 cnf(product2_idempotence,axiom,
% 0.45/0.62 product2(X,X,X) ).
% 0.45/0.62
% 0.45/0.62 cnf(qg1a,negated_conjecture,
% 0.45/0.62 ( ~ product1(X,Y,Z1)
% 0.45/0.62 | ~ product1(Z1,Y,Z2)
% 0.45/0.62 | product2(Z2,X,Y) ) ).
% 0.45/0.62
% 0.45/0.62 %--------------------------------------------------------------------------
% 0.45/0.62 %-------------------------------------------
% 0.45/0.62 % Proof found
% 0.45/0.62 % SZS status Theorem for theBenchmark
% 0.45/0.62 % SZS output start Proof
% 0.45/0.62 %ClaNum:20(EqnAxiom:0)
% 0.45/0.62 %VarNum:79(SingletonVarNum:34)
% 0.45/0.62 %MaxLitNum:5
% 0.45/0.62 %MaxfuncDepth:0
% 0.45/0.62 %SharedTerms:12
% 0.45/0.62 %goalClause: 20
% 0.45/0.62 [1]P1(a1)
% 0.45/0.62 [2]P1(a2)
% 0.45/0.62 [3]P1(a3)
% 0.45/0.62 [6]~P2(a1,a2)
% 0.45/0.63 [7]~P2(a1,a3)
% 0.45/0.63 [8]~P2(a2,a1)
% 0.45/0.63 [9]~P2(a2,a3)
% 0.45/0.63 [10]~P2(a3,a1)
% 0.45/0.63 [11]~P2(a3,a2)
% 0.45/0.63 [4]P3(x41,x41,x41)
% 0.45/0.63 [5]P4(x51,x51,x51)
% 0.45/0.63 [14]~P3(x143,x144,x141)+P2(x141,x142)+~P3(x143,x144,x142)
% 0.45/0.63 [15]~P4(x153,x154,x151)+P2(x151,x152)+~P4(x153,x154,x152)
% 0.45/0.63 [16]~P3(x163,x161,x164)+P2(x161,x162)+~P3(x163,x162,x164)
% 0.45/0.63 [17]~P4(x173,x171,x174)+P2(x171,x172)+~P4(x173,x172,x174)
% 0.45/0.63 [18]~P3(x181,x183,x184)+P2(x181,x182)+~P3(x182,x183,x184)
% 0.45/0.63 [19]~P4(x191,x193,x194)+P2(x191,x192)+~P4(x192,x193,x194)
% 0.45/0.63 [20]~P3(x202,x203,x204)+P4(x201,x202,x203)+~P3(x204,x203,x201)
% 0.45/0.63 [12]~P1(x122)+~P1(x121)+P3(x121,x122,a2)+P3(x121,x122,a3)+P3(x121,x122,a1)
% 0.45/0.63 [13]~P1(x132)+~P1(x131)+P4(x131,x132,a2)+P4(x131,x132,a3)+P4(x131,x132,a1)
% 0.45/0.63 %EqnAxiom
% 0.45/0.63
% 0.45/0.63 %-------------------------------------------
% 0.45/0.63 cnf(44,plain,
% 0.45/0.63 (P3(x441,x441,x441)),
% 0.45/0.63 inference(rename_variables,[],[4])).
% 0.45/0.63 cnf(47,plain,
% 0.45/0.63 (P3(x471,x471,x471)),
% 0.45/0.63 inference(rename_variables,[],[4])).
% 0.45/0.63 cnf(49,plain,
% 0.45/0.63 (~P4(a3,a1,a1)),
% 0.45/0.63 inference(scs_inference,[],[7,4,44,5,18,16,19])).
% 0.45/0.63 cnf(50,plain,
% 0.45/0.63 (P4(x501,x501,x501)),
% 0.45/0.63 inference(rename_variables,[],[5])).
% 0.45/0.63 cnf(52,plain,
% 0.45/0.63 (~P4(a3,a1,a3)),
% 0.45/0.63 inference(scs_inference,[],[7,4,44,5,50,18,16,19,17])).
% 0.45/0.63 cnf(53,plain,
% 0.45/0.63 (P4(x531,x531,x531)),
% 0.45/0.63 inference(rename_variables,[],[5])).
% 0.45/0.63 cnf(61,plain,
% 0.45/0.63 (P3(a1,a3,a2)+P3(a1,a3,a1)),
% 0.45/0.63 inference(scs_inference,[],[1,3,7,4,44,47,5,50,53,18,16,19,17,15,14,12])).
% 0.45/0.63 cnf(63,plain,
% 0.45/0.63 (~P3(a2,a3,a3)+P3(a1,a3,a1)),
% 0.45/0.63 inference(scs_inference,[],[1,3,7,4,44,47,5,50,53,18,16,19,17,15,14,12,20])).
% 0.45/0.63 cnf(72,plain,
% 0.45/0.63 (~P4(a2,a1,a1)),
% 0.45/0.63 inference(scs_inference,[],[8,4,3,5,49,52,1,16,13,19])).
% 0.45/0.63 cnf(81,plain,
% 0.45/0.63 (~P3(a2,a3,a2)),
% 0.45/0.63 inference(scs_inference,[],[9,4,18,16])).
% 0.45/0.63 cnf(97,plain,
% 0.45/0.63 (P3(x971,x971,x971)),
% 0.45/0.63 inference(rename_variables,[],[4])).
% 0.45/0.63 cnf(111,plain,
% 0.45/0.63 (P4(a1,a1,a3)),
% 0.45/0.63 inference(scs_inference,[],[3,10,8,9,5,4,97,72,81,2,1,17,16,19,63,61,12,18,13,20])).
% 0.45/0.63 cnf(124,plain,
% 0.45/0.63 (P4(x1241,x1241,x1241)),
% 0.45/0.63 inference(rename_variables,[],[5])).
% 0.45/0.63 cnf(128,plain,
% 0.45/0.63 ($false),
% 0.45/0.63 inference(scs_inference,[],[4,10,5,124,111,17,16,15]),
% 0.45/0.63 ['proof']).
% 0.45/0.63 % SZS output end Proof
% 0.45/0.63 % Total time :0.010000s
%------------------------------------------------------------------------------