%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM016-2 : 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 : n019.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 12:22:58 EDT 2024 % Result : Unsatisfiable 0.19s 0.60s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM016-2 : TPTP v8.2.0. Released v1.0.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.32 % Computer : n019.cluster.edu % 0.12/0.32 % Model : x86_64 x86_64 % 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.32 % Memory : 8042.1875MB % 0.12/0.32 % 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 : Sat Jun 22 23:47:39 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.19/0.60 %------------------------------------------- % 0.19/0.60 % File :CSE---1.7 % 0.19/0.60 % Problem :theBenchmark % 0.19/0.60 % Transform :cnf % 0.19/0.60 % Format :tptp:raw % 0.19/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.19/0.60 % 0.19/0.60 % Result :Theorem 0.000000s % 0.19/0.60 % Output :CNFRefutation 0.000000s % 0.19/0.60 %------------------------------------------- % 0.19/0.60 %-------------------------------------------------------------------------- % 0.19/0.60 % File : NUM016-2 : TPTP v8.2.0. Released v1.0.0. % 0.19/0.60 % Domain : Number Theory % 0.19/0.60 % Problem : There exist infinitely many primes % 0.19/0.60 % Version : [Cha70] axioms : Incomplete. % 0.19/0.60 % English : % 0.19/0.60 % 0.19/0.60 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore % 0.19/0.60 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th % 0.19/0.60 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo % 0.19/0.60 % Source : [Cha70] % 0.19/0.60 % Names : Example 8a [Luc68] % 0.19/0.60 % : Example 9 [Cha70] % 0.19/0.60 % : Example 9 [CL73] % 0.19/0.60 % 0.19/0.60 % Status : Unsatisfiable % 0.19/0.60 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0 % 0.19/0.60 % Syntax : Number of clauses : 8 ( 2 unt; 3 nHn; 4 RR) % 0.19/0.60 % Number of literals : 15 ( 0 equ; 6 neg) % 0.19/0.60 % Maximal clause size : 3 ( 1 avg) % 0.19/0.60 % Maximal term depth : 2 ( 1 avg) % 0.19/0.60 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty) % 0.19/0.60 % Number of functors : 3 ( 3 usr; 1 con; 0-1 aty) % 0.19/0.60 % Number of variables : 10 ( 0 sgn) % 0.19/0.60 % SPC : CNF_UNS_RFO_NEQ_NHN % 0.19/0.60 % 0.19/0.60 % Comments : % 0.19/0.60 %-------------------------------------------------------------------------- % 0.19/0.60 cnf(nothing_is_less_than_itself,axiom, % 0.19/0.60 ~ less(X,X) ). % 0.19/0.60 % 0.19/0.60 cnf(numbers_are_different,axiom, % 0.19/0.60 ( ~ less(X,Y) % 0.19/0.60 | ~ less(Y,X) ) ). % 0.19/0.60 % 0.19/0.60 cnf(a_prime_is_less_than_the_next_one,axiom, % 0.19/0.60 less(X,factorial_plus_one(X)) ). % 0.19/0.60 % 0.19/0.60 cnf(divisor_is_smaller,axiom, % 0.19/0.60 ( ~ divides(X,factorial_plus_one(Y)) % 0.19/0.60 | less(Y,X) ) ). % 0.19/0.60 % 0.19/0.60 cnf(division_by_prime_divisor,axiom, % 0.19/0.60 ( prime(X) % 0.19/0.60 | divides(prime_divisor(X),X) ) ). % 0.19/0.60 % 0.19/0.60 cnf(prime_divsiors,axiom, % 0.19/0.60 ( prime(X) % 0.19/0.60 | prime(prime_divisor(X)) ) ). % 0.19/0.60 % 0.19/0.60 cnf(smaller_prime_divisors,axiom, % 0.19/0.60 ( prime(X) % 0.19/0.60 | less(prime_divisor(X),X) ) ). % 0.19/0.60 % 0.19/0.60 cnf(prove_there_is_another_prime,negated_conjecture, % 0.19/0.60 ( ~ prime(X) % 0.19/0.60 | ~ less(a,X) % 0.19/0.60 | less(factorial_plus_one(a),X) ) ). % 0.19/0.60 % 0.19/0.60 %-------------------------------------------------------------------------- % 0.19/0.60 %------------------------------------------- % 0.19/0.60 % Proof found % 0.19/0.60 % SZS status Theorem for theBenchmark % 0.19/0.60 % SZS output start Proof % 0.19/0.60 %ClaNum:8(EqnAxiom:0) % 0.19/0.60 %VarNum:23(SingletonVarNum:10) % 0.54/0.60 %MaxLitNum:3 % 0.54/0.60 %MaxfuncDepth:1 % 0.54/0.60 %SharedTerms:2 % 0.54/0.60 %goalClause: 6 % 0.54/0.60 [2]~P1(x21,x21) % 0.54/0.60 [1]P1(x11,f1(x11)) % 0.54/0.60 [3]P3(x31)+P3(f3(x31)) % 0.54/0.60 [4]P3(x41)+P1(f3(x41),x41) % 0.54/0.60 [5]P3(x51)+P2(f3(x51),x51) % 0.54/0.60 [7]~P1(x72,x71)+~P1(x71,x72) % 0.54/0.60 [8]P1(x81,x82)+~P2(x82,f1(x81)) % 0.54/0.60 [6]~P3(x61)+~P1(a2,x61)+P1(f1(a2),x61) % 0.54/0.60 %EqnAxiom % 0.54/0.60 % 0.54/0.60 %------------------------------------------- % 0.54/0.61 cnf(11,plain, % 0.54/0.61 (~P3(f1(a2))), % 0.54/0.61 inference(scs_inference,[],[1,2,7,6])). % 0.54/0.61 cnf(15,plain, % 0.54/0.61 (P3(f3(f1(a2)))), % 0.54/0.61 inference(scs_inference,[],[2,1,3,6])). % 0.54/0.61 cnf(16,plain, % 0.54/0.61 (~P1(f1(a2),f3(f1(a2)))), % 0.54/0.61 inference(scs_inference,[],[11,4,7])). % 0.54/0.61 cnf(17,plain, % 0.54/0.61 (~P1(a2,f3(f1(a2)))), % 0.54/0.61 inference(scs_inference,[],[16,15,6])). % 0.54/0.61 cnf(19,plain, % 0.54/0.61 ($false), % 0.54/0.61 inference(scs_inference,[],[11,17,5,8]), % 0.54/0.61 ['proof']). % 0.54/0.61 % SZS output end Proof % 0.54/0.61 % Total time :0.000000s %------------------------------------------------------------------------------