%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP004-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n023.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 : Mon Jun 24 06:38:25 EDT 2024 % Result : Unsatisfiable 0.54s 0.61s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : GRP004-1 : TPTP v8.2.0. Released v1.0.0. % 0.11/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.11/0.32 % Computer : n023.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Jun 20 07:50:09 EDT 2024 % 0.11/0.33 % CPUTime : % 0.18/0.56 start to proof:theBenchmark % 0.18/0.60 %------------------------------------------- % 0.18/0.60 % File :CSE---1.7 % 0.18/0.60 % Problem :theBenchmark % 0.18/0.60 % Transform :cnf % 0.18/0.60 % Format :tptp:raw % 0.18/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.18/0.60 % 0.18/0.60 % Result :Theorem 0.010000s % 0.18/0.60 % Output :CNFRefutation 0.010000s % 0.18/0.60 %------------------------------------------- % 0.18/0.60 %-------------------------------------------------------------------------- % 0.18/0.60 % File : GRP004-1 : TPTP v8.2.0. Released v1.0.0. % 0.18/0.60 % Domain : Group Theory % 0.18/0.60 % Problem : Left inverse and identity => Right inverse exists % 0.18/0.60 % Version : [Cha70] axioms : Incomplete. % 0.18/0.60 % English : In a group with left inverses and left identity every element % 0.18/0.60 % has a right inverse. % 0.18/0.60 % 0.18/0.60 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore % 0.18/0.60 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th % 0.18/0.60 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo % 0.18/0.60 % Source : [Cha70] % 0.18/0.60 % Names : Example 3 [Luc68] % 0.18/0.60 % : Example 4 [Cha70] % 0.18/0.60 % : Example 4 [CL73] % 0.18/0.60 % : EX4 [SPRFN] % 0.18/0.60 % 0.18/0.60 % Status : Unsatisfiable % 0.18/0.60 % Rating : 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v5.4.0, 0.11 v5.3.0, 0.10 v5.2.0, 0.00 v2.1.0, 0.00 v2.0.0 % 0.18/0.60 % Syntax : Number of clauses : 5 ( 3 unt; 0 nHn; 3 RR) % 0.18/0.60 % Number of literals : 11 ( 0 equ; 7 neg) % 0.18/0.60 % Maximal clause size : 4 ( 2 avg) % 0.54/0.60 % Maximal term depth : 2 ( 1 avg) % 0.54/0.60 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty) % 0.54/0.60 % Number of functors : 3 ( 3 usr; 2 con; 0-1 aty) % 0.54/0.60 % Number of variables : 15 ( 1 sgn) % 0.54/0.60 % SPC : CNF_UNS_RFO_NEQ_HRN % 0.54/0.60 % 0.54/0.60 % Comments : [Luc68] is actually the right to left version. % 0.54/0.60 %-------------------------------------------------------------------------- % 0.54/0.60 cnf(left_inverse,axiom, % 0.54/0.60 product(inverse(X),X,identity) ). % 0.54/0.60 % 0.54/0.60 cnf(left_identity,axiom, % 0.54/0.60 product(identity,X,X) ). % 0.54/0.60 % 0.54/0.60 cnf(associativity1,axiom, % 0.54/0.60 ( ~ product(X,Y,U) % 0.54/0.61 | ~ product(Y,Z,V) % 0.54/0.61 | ~ product(U,Z,W) % 0.54/0.61 | product(X,V,W) ) ). % 0.54/0.61 % 0.54/0.61 cnf(associativity2,axiom, % 0.54/0.61 ( ~ product(X,Y,U) % 0.54/0.61 | ~ product(Y,Z,V) % 0.54/0.61 | ~ product(X,V,W) % 0.54/0.61 | product(U,Z,W) ) ). % 0.54/0.61 % 0.54/0.61 cnf(prove_there_is_a_right_inverse,negated_conjecture, % 0.54/0.61 ~ product(a,X,identity) ). % 0.54/0.61 % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % Proof found % 0.54/0.61 % SZS status Theorem for theBenchmark % 0.54/0.61 % SZS output start Proof % 0.54/0.61 %ClaNum:5(EqnAxiom:0) % 0.54/0.61 %VarNum:29(SingletonVarNum:15) % 0.54/0.61 %MaxLitNum:4 % 0.54/0.61 %MaxfuncDepth:1 % 0.54/0.61 %SharedTerms:2 % 0.54/0.61 %goalClause: 3 % 0.54/0.61 %singleGoalClaCount:1 % 0.54/0.61 [1]P1(a1,x11,x11) % 0.54/0.61 [3]~P1(a2,x31,a1) % 0.54/0.61 [2]P1(f3(x21),x21,a1) % 0.54/0.61 [4]~P1(x46,x44,x41)+P1(x41,x42,x43)+~P1(x44,x42,x45)+~P1(x46,x45,x43) % 0.54/0.61 [5]~P1(x51,x56,x54)+P1(x51,x52,x53)+~P1(x54,x55,x53)+~P1(x56,x55,x52) % 0.54/0.61 %EqnAxiom % 0.54/0.61 % 0.54/0.61 %------------------------------------------- % 0.54/0.61 cnf(6,plain, % 0.54/0.61 (P1(f3(a1),x61,x61)), % 0.54/0.61 inference(scs_inference,[],[2,1,5])). % 0.54/0.61 cnf(10,plain, % 0.54/0.61 (P1(f3(x101),x101,a1)), % 0.54/0.61 inference(rename_variables,[],[2])). % 0.54/0.61 cnf(11,plain, % 0.54/0.61 (P1(f3(x111),x111,a1)), % 0.54/0.61 inference(rename_variables,[],[2])). % 0.54/0.61 cnf(14,plain, % 0.54/0.61 (P1(f3(f3(x141)),a1,x141)), % 0.54/0.61 inference(scs_inference,[],[2,11,10,6,1,4,5])). % 0.54/0.61 cnf(46,plain, % 0.54/0.61 ($false), % 0.54/0.61 inference(scs_inference,[],[14,3,2,1,4]), % 0.54/0.61 ['proof']). % 0.54/0.61 % SZS output end Proof % 0.54/0.61 % Total time :0.010000s %------------------------------------------------------------------------------