TSTP Solution File: GRP006-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP006-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n004.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 00:10:32 EDT 2023
% Result : Unsatisfiable 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:16:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.56 start to proof:theBenchmark
% 0.21/0.61 %-------------------------------------------
% 0.21/0.61 % File :CSE---1.6
% 0.21/0.61 % Problem :theBenchmark
% 0.21/0.61 % Transform :cnf
% 0.21/0.61 % Format :tptp:raw
% 0.21/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.61
% 0.21/0.61 % Result :Theorem 0.000000s
% 0.21/0.61 % Output :CNFRefutation 0.000000s
% 0.21/0.61 %-------------------------------------------
% 0.21/0.61 %--------------------------------------------------------------------------
% 0.21/0.61 % File : GRP006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.21/0.61 % Domain : Group Theory
% 0.21/0.61 % Problem : Inverse is in this group
% 0.21/0.61 % Version : [Cha70] axioms : Incomplete.
% 0.21/0.61 % English : If S is a non-empty subset of a group such that if X, Y belong
% 0.21/0.61 % to S, the XY^-1 belongs to S, then S contains X^-1 whenever it
% 0.21/0.61 % contains X.
% 0.21/0.61
% 0.21/0.61 % Refs : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% 0.21/0.61 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% 0.21/0.61 % Source : [Cha70]
% 0.21/0.61 % Names : Example 6 [Cha70]
% 0.21/0.61 % : Example 6 [CL73]
% 0.21/0.61 % : EX6 [SPRFN]
% 0.21/0.61
% 0.21/0.61 % Status : Unsatisfiable
% 0.21/0.61 % Rating : 0.00 v5.4.0, 0.06 v5.3.0, 0.10 v5.2.0, 0.00 v2.0.0
% 0.21/0.61 % Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 5 RR)
% 0.21/0.61 % Number of literals : 18 ( 0 equ; 10 neg)
% 0.21/0.61 % Maximal clause size : 4 ( 2 avg)
% 0.21/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.21/0.61 % Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty)
% 0.21/0.61 % Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% 0.21/0.61 % Number of variables : 19 ( 0 sgn)
% 0.21/0.61 % SPC : CNF_UNS_RFO_NEQ_HRN
% 0.21/0.61
% 0.21/0.61 % Comments :
% 0.21/0.61 %--------------------------------------------------------------------------
% 0.21/0.61 cnf(left_identity,axiom,
% 0.21/0.61 product(identity,X,X) ).
% 0.21/0.61
% 0.21/0.61 cnf(right_identity,axiom,
% 0.21/0.61 product(X,identity,X) ).
% 0.21/0.61
% 0.21/0.61 cnf(right_inverse,axiom,
% 0.21/0.61 product(X,inverse(X),identity) ).
% 0.21/0.61
% 0.21/0.61 cnf(left_inverse,axiom,
% 0.21/0.61 product(inverse(X),X,identity) ).
% 0.21/0.61
% 0.21/0.61 cnf(condition,axiom,
% 0.21/0.61 ( ~ an_element(X)
% 0.21/0.61 | ~ an_element(Y)
% 0.21/0.61 | ~ product(X,inverse(Y),Z)
% 0.21/0.61 | an_element(Z) ) ).
% 0.21/0.61
% 0.21/0.61 cnf(associativity1,axiom,
% 0.21/0.61 ( ~ product(X,Y,U)
% 0.21/0.61 | ~ product(Y,Z,V)
% 0.21/0.61 | ~ product(U,Z,W)
% 0.21/0.61 | product(X,V,W) ) ).
% 0.21/0.61
% 0.21/0.61 cnf(associativity2,axiom,
% 0.21/0.61 ( ~ product(X,Y,U)
% 0.21/0.61 | ~ product(Y,Z,V)
% 0.21/0.61 | ~ product(X,V,W)
% 0.21/0.61 | product(U,Z,W) ) ).
% 0.21/0.61
% 0.21/0.61 cnf(element_of_set,hypothesis,
% 0.21/0.61 an_element(the_element) ).
% 0.21/0.61
% 0.21/0.62 cnf(prove_b_inverse_is_in_set,negated_conjecture,
% 0.21/0.62 ~ an_element(inverse(the_element)) ).
% 0.21/0.62
% 0.21/0.62 %--------------------------------------------------------------------------
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 %ClaNum:9(EqnAxiom:0)
% 0.21/0.62 %VarNum:38(SingletonVarNum:19)
% 0.21/0.62 %MaxLitNum:4
% 0.21/0.62 %MaxfuncDepth:1
% 0.21/0.62 %SharedTerms:5
% 0.21/0.62 %goalClause: 6
% 0.21/0.62 %singleGoalClaCount:1
% 0.21/0.62 [1]P1(a1)
% 0.21/0.62 [6]~P1(f3(a1))
% 0.21/0.62 [2]P2(x21,a2,x21)
% 0.21/0.62 [3]P2(a2,x31,x31)
% 0.21/0.62 [4]P2(x41,f3(x41),a2)
% 0.21/0.62 [5]P2(f3(x51),x51,a2)
% 0.21/0.62 [7]P1(x71)+~P1(x72)+~P1(x73)+~P2(x73,f3(x72),x71)
% 0.21/0.62 [8]~P2(x86,x84,x81)+P2(x81,x82,x83)+~P2(x84,x82,x85)+~P2(x86,x85,x83)
% 0.21/0.62 [9]~P2(x91,x96,x94)+P2(x91,x92,x93)+~P2(x94,x95,x93)+~P2(x96,x95,x92)
% 0.21/0.62 %EqnAxiom
% 0.21/0.62
% 0.21/0.62 %-------------------------------------------
% 0.21/0.62 cnf(12,plain,
% 0.21/0.62 (P2(a2,x121,x121)),
% 0.21/0.62 inference(rename_variables,[],[3])).
% 0.21/0.62 cnf(15,plain,
% 0.21/0.62 (~P1(a2)),
% 0.21/0.62 inference(scs_inference,[],[6,2,3,12,1,5,9,7])).
% 0.21/0.62 cnf(19,plain,
% 0.21/0.62 (P2(x191,f3(x191),a2)),
% 0.21/0.62 inference(rename_variables,[],[4])).
% 0.21/0.62 cnf(23,plain,
% 0.21/0.62 (~P2(f3(a1),f3(a1),f3(a1))),
% 0.21/0.62 inference(scs_inference,[],[6,4,19,2,3,1,8,7,9])).
% 0.21/0.62 cnf(31,plain,
% 0.21/0.62 ($false),
% 0.21/0.62 inference(scs_inference,[],[1,4,3,23,15,9,7]),
% 0.21/0.62 ['proof']).
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time :0.000000s
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