TSTP Solution File: NUM016-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : NUM016-2 : 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 : n014.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 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 13:00:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.20/0.61 %-------------------------------------------
% 0.20/0.61 % File :CSE---1.6
% 0.20/0.61 % Problem :theBenchmark
% 0.20/0.61 % Transform :cnf
% 0.20/0.61 % Format :tptp:raw
% 0.20/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.61
% 0.20/0.61 % Result :Theorem 0.000000s
% 0.20/0.61 % Output :CNFRefutation 0.000000s
% 0.20/0.61 %-------------------------------------------
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 % File : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.20/0.62 % Domain : Number Theory
% 0.20/0.62 % Problem : There exist infinitely many primes
% 0.20/0.62 % Version : [Cha70] axioms : Incomplete.
% 0.20/0.62 % English :
% 0.20/0.62
% 0.20/0.62 % Refs : [Luc68] Luckham (1968), Some Tree-paring Strategies for Theore
% 0.20/0.62 % : [Cha70] Chang (1970), The Unit Proof and the Input Proof in Th
% 0.20/0.62 % : [CL73] Chang & Lee (1973), Symbolic Logic and Mechanical Theo
% 0.20/0.62 % Source : [Cha70]
% 0.20/0.62 % Names : Example 8a [Luc68]
% 0.20/0.62 % : Example 9 [Cha70]
% 0.20/0.62 % : Example 9 [CL73]
% 0.20/0.62
% 0.20/0.62 % Status : Unsatisfiable
% 0.20/0.62 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% 0.20/0.62 % Syntax : Number of clauses : 8 ( 2 unt; 3 nHn; 4 RR)
% 0.20/0.62 % Number of literals : 15 ( 0 equ; 6 neg)
% 0.20/0.62 % Maximal clause size : 3 ( 1 avg)
% 0.20/0.62 % Maximal term depth : 2 ( 1 avg)
% 0.20/0.62 % Number of predicates : 3 ( 3 usr; 0 prp; 1-2 aty)
% 0.20/0.62 % Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.20/0.62 % Number of variables : 10 ( 0 sgn)
% 0.20/0.62 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.20/0.62
% 0.20/0.62 % Comments :
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 cnf(nothing_is_less_than_itself,axiom,
% 0.20/0.62 ~ less(X,X) ).
% 0.20/0.62
% 0.20/0.62 cnf(numbers_are_different,axiom,
% 0.20/0.62 ( ~ less(X,Y)
% 0.20/0.62 | ~ less(Y,X) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(a_prime_is_less_than_the_next_one,axiom,
% 0.20/0.62 less(X,factorial_plus_one(X)) ).
% 0.20/0.62
% 0.20/0.62 cnf(divisor_is_smaller,axiom,
% 0.20/0.62 ( ~ divides(X,factorial_plus_one(Y))
% 0.20/0.62 | less(Y,X) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(division_by_prime_divisor,axiom,
% 0.20/0.62 ( prime(X)
% 0.20/0.62 | divides(prime_divisor(X),X) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(prime_divsiors,axiom,
% 0.20/0.62 ( prime(X)
% 0.20/0.62 | prime(prime_divisor(X)) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(smaller_prime_divisors,axiom,
% 0.20/0.62 ( prime(X)
% 0.20/0.62 | less(prime_divisor(X),X) ) ).
% 0.20/0.62
% 0.20/0.62 cnf(prove_there_is_another_prime,negated_conjecture,
% 0.20/0.62 ( ~ prime(X)
% 0.20/0.62 | ~ less(a,X)
% 0.20/0.62 | less(factorial_plus_one(a),X) ) ).
% 0.20/0.62
% 0.20/0.62 %--------------------------------------------------------------------------
% 0.20/0.62 %-------------------------------------------
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark
% 0.20/0.62 % SZS output start Proof
% 0.20/0.62 %ClaNum:8(EqnAxiom:0)
% 0.20/0.62 %VarNum:23(SingletonVarNum:10)
% 0.20/0.62 %MaxLitNum:3
% 0.20/0.62 %MaxfuncDepth:1
% 0.20/0.62 %SharedTerms:2
% 0.20/0.62 %goalClause: 6
% 0.20/0.62 [2]~P1(x21,x21)
% 0.20/0.62 [1]P1(x11,f1(x11))
% 0.20/0.62 [3]P3(x31)+P3(f3(x31))
% 0.20/0.62 [4]P3(x41)+P1(f3(x41),x41)
% 0.20/0.62 [5]P3(x51)+P2(f3(x51),x51)
% 0.20/0.62 [7]~P1(x72,x71)+~P1(x71,x72)
% 0.20/0.62 [8]P1(x81,x82)+~P2(x82,f1(x81))
% 0.20/0.62 [6]~P3(x61)+~P1(a2,x61)+P1(f1(a2),x61)
% 0.20/0.62 %EqnAxiom
% 0.20/0.62
% 0.20/0.62 %-------------------------------------------
% 0.20/0.63 cnf(11,plain,
% 0.20/0.63 (~P1(x111,x111)),
% 0.20/0.63 inference(rename_variables,[],[2])).
% 0.20/0.63 cnf(16,plain,
% 0.20/0.63 (P2(f3(f1(a2)),f1(a2))),
% 0.20/0.63 inference(scs_inference,[],[1,2,11,7,6,8,5])).
% 0.20/0.63 cnf(18,plain,
% 0.20/0.63 (P1(f3(f1(a2)),f1(a2))),
% 0.20/0.63 inference(scs_inference,[],[1,2,11,7,6,8,5,4])).
% 0.20/0.63 cnf(20,plain,
% 0.20/0.63 (P3(f3(f1(a2)))),
% 0.20/0.63 inference(scs_inference,[],[1,2,11,7,6,8,5,4,3])).
% 0.20/0.63 cnf(26,plain,
% 0.20/0.63 ($false),
% 0.20/0.63 inference(scs_inference,[],[20,16,18,7,8,6]),
% 0.20/0.63 ['proof']).
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time :0.000000s
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