%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP001-5 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n001.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 06:38:24 EDT 2024 % Result : Unsatisfiable 0.53s 0.63s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP001-5 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n001.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % 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 08:23:39 EDT 2024 % 0.11/0.33 % CPUTime : % 0.53/0.57 start to proof:theBenchmark % 0.53/0.62 %------------------------------------------- % 0.53/0.62 % File :CSE---1.7 % 0.53/0.62 % Problem :theBenchmark % 0.53/0.62 % Transform :cnf % 0.53/0.62 % Format :tptp:raw % 0.53/0.62 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.63 % 0.53/0.63 % Result :Theorem 0.020000s % 0.53/0.63 % Output :CNFRefutation 0.020000s % 0.53/0.63 %------------------------------------------- % 0.53/0.63 %------------------------------------------------------------------------------ % 0.53/0.63 % File : GRP001-5 : TPTP v8.2.0. Released v1.0.0. % 0.53/0.63 % Domain : Group Theory % 0.53/0.63 % Problem : X^2 = identity => commutativity % 0.53/0.63 % Version : [Cha70] axioms : Incomplete. % 0.53/0.63 % English : If the square of every element is the identity, the system % 0.53/0.63 % is commutative. % 0.53/0.63 % 0.53/0.63 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore % 0.53/0.63 % : [Lov69] Loveland (1969), Theorem-provers Combining Model Elimi % 0.53/0.63 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th % 0.53/0.63 % : [MRS72] Michie et al. (1972), G-deduction % 0.53/0.63 % : [RR+72] Reboh et al. (1972), Study of automatic theorem provin % 0.53/0.63 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo % 0.53/0.63 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S % 0.53/0.63 % Source : [Cha70] % 0.53/0.63 % Names : Example 4 [Luc68] % 0.53/0.63 % : Example 1 [Lov69] % 0.53/0.63 % : Example 2 [Cha70] % 0.53/0.63 % : ROB2 [MRS72] % 0.53/0.63 % : GROUP2 [RR+72] % 0.53/0.63 % : Example 2 [CL73] % 0.53/0.63 % : GROUP2 [WM76] % 0.53/0.63 % : ROB2 [WM76] % 0.53/0.63 % : EX2 [SPRFN] % 0.53/0.63 % 0.53/0.63 % Status : Unsatisfiable % 0.53/0.63 % Rating : 0.00 v2.2.0, 0.11 v2.1.0, 0.00 v2.0.0 % 0.53/0.63 % Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 4 RR) % 0.53/0.63 % Number of literals : 13 ( 0 equ; 7 neg) % 0.53/0.63 % Maximal clause size : 4 ( 1 avg) % 0.53/0.63 % Maximal term depth : 1 ( 1 avg) % 0.53/0.63 % Number of predicates : 1 ( 1 usr; 0 prp; 3-3 aty) % 0.53/0.63 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 0.53/0.63 % Number of variables : 15 ( 0 sgn) % 0.53/0.63 % SPC : CNF_UNS_EPR_NEQ_HRN % 0.53/0.63 % 0.53/0.63 % Comments : In this format it is essentially a monoid problem. % 0.53/0.63 %------------------------------------------------------------------------------ % 0.53/0.63 cnf(left_identity,axiom, % 0.53/0.63 product(identity,X,X) ). % 0.53/0.63 % 0.53/0.63 cnf(right_identity,axiom, % 0.53/0.63 product(X,identity,X) ). % 0.53/0.63 % 0.53/0.63 cnf(associativity1,axiom, % 0.53/0.63 ( ~ product(X,Y,U) % 0.53/0.63 | ~ product(Y,Z,V) % 0.53/0.63 | ~ product(U,Z,W) % 0.53/0.63 | product(X,V,W) ) ). % 0.53/0.63 % 0.53/0.63 cnf(associativity2,axiom, % 0.53/0.63 ( ~ product(X,Y,U) % 0.53/0.63 | ~ product(Y,Z,V) % 0.53/0.63 | ~ product(X,V,W) % 0.53/0.63 | product(U,Z,W) ) ). % 0.53/0.63 % 0.53/0.63 cnf(square_element,hypothesis, % 0.53/0.63 product(X,X,identity) ). % 0.53/0.63 % 0.53/0.63 cnf(a_times_b_is_c,hypothesis, % 0.53/0.63 product(a,b,c) ). % 0.53/0.63 % 0.53/0.63 cnf(prove_b_times_a_is_c,negated_conjecture, % 0.53/0.63 ~ product(b,a,c) ). % 0.53/0.63 % 0.53/0.63 %------------------------------------------------------------------------------ % 0.53/0.63 %------------------------------------------- % 0.53/0.63 % Proof found % 0.53/0.63 % SZS status Theorem for theBenchmark % 0.53/0.63 % SZS output start Proof % 0.53/0.63 %ClaNum:7(EqnAxiom:0) % 0.53/0.63 %VarNum:30(SingletonVarNum:15) % 0.56/0.63 %MaxLitNum:4 % 0.56/0.63 %MaxfuncDepth:0 % 0.56/0.63 %SharedTerms:6 % 0.56/0.63 %goalClause: 5 % 0.56/0.63 %singleGoalClaCount:1 % 0.56/0.63 [1]P1(a1,a2,a3) % 0.56/0.63 [5]~P1(a2,a1,a3) % 0.56/0.63 [2]P1(x21,x21,a4) % 0.56/0.63 [3]P1(x31,a4,x31) % 0.56/0.63 [4]P1(a4,x41,x41) % 0.56/0.63 [6]~P1(x66,x64,x61)+P1(x61,x62,x63)+~P1(x64,x62,x65)+~P1(x66,x65,x63) % 0.56/0.63 [7]~P1(x71,x76,x74)+P1(x71,x72,x73)+~P1(x74,x75,x73)+~P1(x76,x75,x72) % 0.56/0.63 %EqnAxiom % 0.56/0.63 % 0.56/0.63 %------------------------------------------- % 0.56/0.63 cnf(8,plain, % 0.56/0.63 (P1(a1,a3,a2)), % 0.56/0.63 inference(scs_inference,[],[2,4,1,7])). % 0.56/0.63 cnf(12,plain, % 0.56/0.63 (P1(a3,a2,a1)), % 0.56/0.63 inference(scs_inference,[],[1,3,2,6])). % 0.56/0.63 cnf(27,plain, % 0.56/0.63 (~P1(a2,a3,a1)), % 0.56/0.63 inference(scs_inference,[],[5,12,1,7])). % 0.56/0.63 cnf(39,plain, % 0.56/0.63 (~P1(a3,a1,a2)), % 0.56/0.63 inference(scs_inference,[],[8,12,27,6])). % 0.56/0.63 cnf(47,plain, % 0.56/0.63 ($false), % 0.56/0.63 inference(scs_inference,[],[39,12,2,4,7]), % 0.56/0.63 ['proof']). % 0.56/0.63 % SZS output end Proof % 0.56/0.63 % Total time :0.020000s %------------------------------------------------------------------------------