%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:51:39 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 26 ( 16 unt; 2 nHn; 26 RR)
% Number of literals : 42 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('NUM001-1.ax',transitivity_of_less) ).
cnf(smaller_number,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('NUM001-1.ax',smaller_number) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
file('NUM001-1.ax',less_lemma) ).
cnf(divides_only_less_or_equal,axiom,
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
file('NUM001-2.ax',divides_only_less_or_equal) ).
cnf(transitivity,axiom,
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
file('theBenchmark.p',transitivity) ).
cnf(a_less_than_b,hypothesis,
less(a,b),
file('theBenchmark.p',a_less_than_b) ).
cnf(b_divides_d,hypothesis,
divides(b,d),
file('theBenchmark.p',b_divides_d) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d),
file('theBenchmark.p',prove_a_less_than_d) ).
cnf(t1,plain,
~ less(a,d),
inference(start,[status(thm),parent(0:0)],[prove_a_less_than_d]) ).
cnf(t2,plain,
( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d)
| less(a,d) ),
inference(extension,[status(thm),parent(t1:1)],[smaller_number]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b)
| ~ equalish(b,d)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),d) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( less(b,d)
| ~ divides(b,d)
| equalish(b,d) ),
inference(extension,[status(thm),parent(t4:2)],[divides_only_less_or_equal]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
divides(b,d),
inference(extension,[status(thm),parent(t6:2)],[b_divides_d]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ less(a,b)
| less(a,d)
| ~ less(b,d) ),
inference(extension,[status(thm),parent(t6:3)],[transitivity_of_less]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t10:2)],[t10:2,t1:1]) ).
cnf(t13,plain,
less(a,b),
inference(extension,[status(thm),parent(t10:3)],[a_less_than_b]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t10:3]) ).
cnf(t15,plain,
( ~ less(a,b)
| equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b) ),
inference(extension,[status(thm),parent(t4:3)],[less_lemma]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t4:3]) ).
cnf(t17,plain,
less(a,b),
inference(extension,[status(thm),parent(t15:2)],[a_less_than_b]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 17:36:19 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------