TSTP Solution File: NUM016-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 10:20:16 EDT 2023
% Result : Unsatisfiable 0.55s 0.61s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 10:40:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.000000s
% 0.19/0.61 % Output :CNFRefutation 0.000000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 % File : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.61 % Domain : Number Theory
% 0.19/0.61 % Problem : There exist infinitely many primes
% 0.19/0.61 % Version : [LS74] axioms.
% 0.19/0.61 % English :
% 0.19/0.61
% 0.19/0.61 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 0.19/0.61 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% 0.19/0.61 % : [LS74] Lawrence & Starkey (1974), Experimental Tests of Resol
% 0.19/0.61 % : [WM76] Wilson & Minker (1976), Resolution, Refinements, and S
% 0.19/0.61 % Source : [SPRFN]
% 0.19/0.61 % Names : Example 8b [Luc68]
% 0.19/0.61 % : ls17 [LS74]
% 0.19/0.61 % : Problem 17 [LS74]
% 0.19/0.61 % : ls17 [WM76]
% 0.19/0.61
% 0.19/0.61 % Status : Unsatisfiable
% 0.19/0.61 % 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
% 0.19/0.61 % Syntax : Number of clauses : 12 ( 4 unt; 3 nHn; 7 RR)
% 0.19/0.61 % Number of literals : 22 ( 0 equ; 10 neg)
% 0.19/0.61 % Maximal clause size : 3 ( 1 avg)
% 0.19/0.61 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.61 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty)
% 0.19/0.61 % Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.19/0.61 % Number of variables : 16 ( 0 sgn)
% 0.19/0.61 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.19/0.61
% 0.19/0.61 % Comments : These axioms are the same as in [Luc68]
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.19/0.61 cnf(nothing_is_less_than_itself,axiom,
% 0.19/0.61 ~ less(X,X) ).
% 0.19/0.61
% 0.19/0.61 cnf(numbers_are_different,axiom,
% 0.19/0.61 ( ~ less(X,Y)
% 0.19/0.61 | ~ less(Y,X) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(everything_divides_itself,axiom,
% 0.19/0.61 divides(X,X) ).
% 0.19/0.61
% 0.19/0.61 cnf(transitivity_of_divides,axiom,
% 0.19/0.61 ( ~ divides(X,Y)
% 0.19/0.61 | ~ divides(Y,Z)
% 0.19/0.61 | divides(X,Z) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(small_divides_large,axiom,
% 0.19/0.61 ( ~ divides(X,Y)
% 0.19/0.61 | ~ less(Y,X) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(a_prime_is_less_than_the_next_one,axiom,
% 0.19/0.61 less(X,factorial_plus_one(X)) ).
% 0.19/0.61
% 0.19/0.61 cnf(divisor_is_smaller,axiom,
% 0.19/0.61 ( ~ divides(X,factorial_plus_one(Y))
% 0.19/0.61 | less(Y,X) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(division_by_prime_divisor,axiom,
% 0.19/0.61 ( prime(X)
% 0.19/0.61 | divides(prime_divisor(X),X) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(prime_divsiors,axiom,
% 0.19/0.61 ( prime(X)
% 0.19/0.61 | prime(prime_divisor(X)) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(smaller_prime_divisors,axiom,
% 0.19/0.61 ( prime(X)
% 0.19/0.61 | less(prime_divisor(X),X) ) ).
% 0.19/0.61
% 0.19/0.61 cnf(a_is_prime,hypothesis,
% 0.19/0.61 prime(a) ).
% 0.19/0.61
% 0.19/0.61 cnf(prove_there_is_another_prime,negated_conjecture,
% 0.19/0.61 ( ~ prime(X)
% 0.19/0.61 | ~ less(a,X)
% 0.19/0.61 | less(factorial_plus_one(a),X) ) ).
% 0.19/0.61
% 0.19/0.61 %--------------------------------------------------------------------------
% 0.55/0.61 %-------------------------------------------
% 0.55/0.61 % Proof found
% 0.55/0.61 % SZS status Theorem for theBenchmark
% 0.55/0.61 % SZS output start Proof
% 0.55/0.61 %ClaNum:12(EqnAxiom:0)
% 0.55/0.61 %VarNum:35(SingletonVarNum:16)
% 0.55/0.61 %MaxLitNum:3
% 0.55/0.61 %MaxfuncDepth:1
% 0.55/0.61 %SharedTerms:3
% 0.55/0.61 %goalClause: 8
% 0.55/0.61 [1]P1(a1)
% 0.55/0.61 [2]P2(x21,x21)
% 0.55/0.61 [4]~P3(x41,x41)
% 0.55/0.61 [3]P3(x31,f2(x31))
% 0.55/0.61 [5]P1(x51)+P1(f3(x51))
% 0.55/0.61 [6]P1(x61)+P3(f3(x61),x61)
% 0.55/0.61 [7]P1(x71)+P2(f3(x71),x71)
% 0.55/0.61 [9]~P3(x92,x91)+~P3(x91,x92)
% 0.55/0.61 [10]~P2(x102,x101)+~P3(x101,x102)
% 0.55/0.61 [11]P3(x111,x112)+~P2(x112,f2(x111))
% 0.55/0.61 [8]~P1(x81)+~P3(a1,x81)+P3(f2(a1),x81)
% 0.55/0.61 [12]~P2(x121,x123)+P2(x121,x122)+~P2(x123,x122)
% 0.55/0.61 %EqnAxiom
% 0.55/0.61
% 0.55/0.61 %-------------------------------------------
% 0.55/0.61 cnf(16,plain,
% 0.55/0.61 (~P3(x161,x161)),
% 0.55/0.61 inference(rename_variables,[],[4])).
% 0.55/0.61 cnf(21,plain,
% 0.55/0.61 (P2(f3(f2(a1)),f2(a1))),
% 0.55/0.61 inference(scs_inference,[],[4,16,3,10,9,8,11,7])).
% 0.55/0.61 cnf(23,plain,
% 0.55/0.61 (P3(f3(f2(a1)),f2(a1))),
% 0.55/0.61 inference(scs_inference,[],[4,16,3,10,9,8,11,7,6])).
% 0.55/0.61 cnf(25,plain,
% 0.55/0.61 (P1(f3(f2(a1)))),
% 0.55/0.61 inference(scs_inference,[],[4,16,3,10,9,8,11,7,6,5])).
% 0.55/0.61 cnf(31,plain,
% 0.55/0.61 ($false),
% 0.55/0.61 inference(scs_inference,[],[25,21,23,9,11,8]),
% 0.55/0.61 ['proof']).
% 0.55/0.61 % SZS output end Proof
% 0.55/0.61 % Total time :0.000000s
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