%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : NUM016-1 : 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 : n021.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 0.49s 0.60s % Output : CNFRefutation 0.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM016-1 : TPTP v8.2.0. Released v1.0.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n021.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Jun 22 21:20:54 EDT 2024 % 0.13/0.33 % CPUTime : % 0.49/0.56 start to proof:theBenchmark % 0.49/0.60 %------------------------------------------- % 0.49/0.60 % File :CSE---1.7 % 0.49/0.60 % Problem :theBenchmark % 0.49/0.60 % Transform :cnf % 0.49/0.60 % Format :tptp:raw % 0.49/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.49/0.60 % 0.49/0.60 % Result :Theorem 0.000000s % 0.49/0.60 % Output :CNFRefutation 0.000000s % 0.49/0.60 %------------------------------------------- % 0.49/0.60 %-------------------------------------------------------------------------- % 0.49/0.60 % File : NUM016-1 : TPTP v8.2.0. Released v1.0.0. % 0.49/0.60 % Domain : Number Theory % 0.49/0.60 % Problem : There exist infinitely many primes % 0.49/0.60 % Version : [LS74] axioms. % 0.49/0.60 % English : % 0.49/0.60 % 0.49/0.60 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore % 0.49/0.60 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th % 0.49/0.60 % : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol % 0.49/0.60 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S % 0.49/0.60 % Source : [SPRFN] % 0.49/0.60 % Names : Example 8b [Luc68] % 0.49/0.60 % : ls17 [LS74] % 0.49/0.60 % : Problem 17 [LS74] % 0.49/0.60 % : ls17 [WM76] % 0.49/0.60 % 0.49/0.60 % Status : Unsatisfiable % 0.49/0.60 % Rating : 0.00 v7.1.0, 0.17 v7.0.0, 0.12 v6.3.0, 0.14 v6.2.0, 0.00 v5.4.0, 0.10 v5.3.0, 0.00 v2.0.0 % 0.49/0.60 % Syntax : Number of clauses : 12 ( 4 unt; 3 nHn; 7 RR) % 0.49/0.60 % Number of literals : 22 ( 0 equ; 10 neg) % 0.49/0.60 % Maximal clause size : 3 ( 1 avg) % 0.49/0.60 % Maximal term depth : 2 ( 1 avg) % 0.49/0.60 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty) % 0.49/0.60 % Number of functors : 3 ( 3 usr; 1 con; 0-1 aty) % 0.49/0.60 % Number of variables : 16 ( 0 sgn) % 0.49/0.60 % SPC : CNF_UNS_RFO_NEQ_NHN % 0.49/0.60 % 0.49/0.60 % Comments : These axioms are the same as in [Luc68] % 0.49/0.60 %-------------------------------------------------------------------------- % 0.49/0.60 cnf(nothing_is_less_than_itself,axiom, % 0.49/0.60 ~ less(X,X) ). % 0.49/0.60 % 0.49/0.60 cnf(numbers_are_different,axiom, % 0.49/0.60 ( ~ less(X,Y) % 0.49/0.60 | ~ less(Y,X) ) ). % 0.49/0.60 % 0.49/0.60 cnf(everything_divides_itself,axiom, % 0.49/0.60 divides(X,X) ). % 0.49/0.60 % 0.49/0.60 cnf(transitivity_of_divides,axiom, % 0.49/0.60 ( ~ divides(X,Y) % 0.49/0.60 | ~ divides(Y,Z) % 0.49/0.60 | divides(X,Z) ) ). % 0.49/0.60 % 0.49/0.60 cnf(small_divides_large,axiom, % 0.49/0.60 ( ~ divides(X,Y) % 0.49/0.60 | ~ less(Y,X) ) ). % 0.49/0.60 % 0.49/0.60 cnf(a_prime_is_less_than_the_next_one,axiom, % 0.49/0.60 less(X,factorial_plus_one(X)) ). % 0.49/0.60 % 0.49/0.60 cnf(divisor_is_smaller,axiom, % 0.49/0.60 ( ~ divides(X,factorial_plus_one(Y)) % 0.49/0.60 | less(Y,X) ) ). % 0.49/0.60 % 0.49/0.60 cnf(division_by_prime_divisor,axiom, % 0.49/0.60 ( prime(X) % 0.49/0.60 | divides(prime_divisor(X),X) ) ). % 0.49/0.60 % 0.49/0.60 cnf(prime_divsiors,axiom, % 0.49/0.60 ( prime(X) % 0.49/0.60 | prime(prime_divisor(X)) ) ). % 0.49/0.60 % 0.49/0.60 cnf(smaller_prime_divisors,axiom, % 0.49/0.60 ( prime(X) % 0.49/0.60 | less(prime_divisor(X),X) ) ). % 0.49/0.60 % 0.49/0.60 cnf(a_is_prime,hypothesis, % 0.49/0.60 prime(a) ). % 0.49/0.60 % 0.49/0.60 cnf(prove_there_is_another_prime,negated_conjecture, % 0.49/0.60 ( ~ prime(X) % 0.49/0.60 | ~ less(a,X) % 0.49/0.60 | less(factorial_plus_one(a),X) ) ). % 0.49/0.60 % 0.49/0.60 %-------------------------------------------------------------------------- % 0.49/0.60 %------------------------------------------- % 0.49/0.60 % Proof found % 0.49/0.60 % SZS status Theorem for theBenchmark % 0.49/0.60 % SZS output start Proof % 0.49/0.60 %ClaNum:12(EqnAxiom:0) % 0.49/0.60 %VarNum:35(SingletonVarNum:16) % 0.49/0.60 %MaxLitNum:3 % 0.49/0.61 %MaxfuncDepth:1 % 0.49/0.61 %SharedTerms:3 % 0.49/0.61 %goalClause: 8 % 0.49/0.61 [1]P1(a1) % 0.49/0.61 [2]P2(x21,x21) % 0.49/0.61 [4]~P3(x41,x41) % 0.49/0.61 [3]P3(x31,f2(x31)) % 0.49/0.61 [5]P1(x51)+P1(f3(x51)) % 0.49/0.61 [6]P1(x61)+P3(f3(x61),x61) % 0.49/0.61 [7]P1(x71)+P2(f3(x71),x71) % 0.49/0.61 [9]~P3(x92,x91)+~P3(x91,x92) % 0.49/0.61 [10]~P2(x102,x101)+~P3(x101,x102) % 0.49/0.61 [11]P3(x111,x112)+~P2(x112,f2(x111)) % 0.49/0.61 [8]~P1(x81)+~P3(a1,x81)+P3(f2(a1),x81) % 0.49/0.61 [12]~P2(x121,x123)+P2(x121,x122)+~P2(x123,x122) % 0.49/0.61 %EqnAxiom % 0.49/0.61 % 0.49/0.61 %------------------------------------------- % 0.49/0.61 cnf(17,plain, % 0.49/0.61 (~P1(f2(a1))), % 0.49/0.61 inference(scs_inference,[],[4,3,9,10,8])). % 0.49/0.61 cnf(21,plain, % 0.49/0.61 (~P3(a1,f3(f2(a1)))+P3(f2(a1),f3(f2(a1)))), % 0.49/0.61 inference(scs_inference,[],[17,5,8])). % 0.49/0.61 cnf(22,plain, % 0.49/0.61 (~P3(f2(a1),f3(f2(a1)))), % 0.49/0.61 inference(scs_inference,[],[17,6,9])). % 0.49/0.61 cnf(23,plain, % 0.49/0.61 (~P3(a1,f3(f2(a1)))), % 0.49/0.61 inference(scs_inference,[],[22,21])). % 0.49/0.61 cnf(24,plain, % 0.49/0.61 (P2(f3(f2(a1)),f2(a1))), % 0.49/0.61 inference(scs_inference,[],[4,3,7,8])). % 0.49/0.61 cnf(25,plain, % 0.49/0.61 ($false), % 0.49/0.61 inference(scs_inference,[],[23,24,11]), % 0.49/0.61 ['proof']). % 0.49/0.61 % SZS output end Proof % 0.49/0.61 % Total time :0.000000s %------------------------------------------------------------------------------