%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 08:16:03 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.35s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 12 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 29 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(divides_only_less_or_equal,axiom,
! [VAR_0,VAR_1] :
( equalish(VAR_0,VAR_1)
| less(VAR_0,VAR_1)
| ~ divides(VAR_0,VAR_1) ),
file('theBenchmark.p',divides_only_less_or_equal) ).
cnf(c_2,plain,
( equalish(A,B)
| less(A,B)
| ~ divides(A,B) ),
inference(clausify,[status(thm)],[divides_only_less_or_equal]) ).
fof(b_divides_d,axiom,
divides(b,d),
file('theBenchmark.p',b_divides_d) ).
cnf(c_4,plain,
divides(b,d),
inference(clausify,[status(thm)],[b_divides_d]) ).
cnf(c_5,plain,
( equalish(b,d)
| less(b,d) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
fof(prove_a_less_than_d,axiom,
~ less(a,d),
file('theBenchmark.p',prove_a_less_than_d) ).
cnf(c_6,plain,
~ less(a,d),
inference(clausify,[status(thm)],[prove_a_less_than_d]) ).
fof(a_less_than_b,axiom,
less(a,b),
file('theBenchmark.p',a_less_than_b) ).
cnf(c_7,plain,
less(a,b),
inference(clausify,[status(thm)],[a_less_than_b]) ).
fof(transitivity,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(VAR_2,VAR_1)
| ~ equalish(VAR_2,VAR_0)
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity) ).
cnf(c_8,plain,
( equalish(C,B)
| ~ equalish(C,A)
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity]) ).
fof(less_lemma,axiom,
! [VAR_0,VAR_1] :
( equalish(add(successor(predecessor_of_1st_minus_2nd(VAR_1,VAR_0)),VAR_0),VAR_1)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',less_lemma) ).
cnf(c_9,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[less_lemma]) ).
fof(smaller_number,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less(VAR_1,VAR_2)
| ~ equalish(add(successor(VAR_0),VAR_1),VAR_2) ),
file('theBenchmark.p',smaller_number) ).
cnf(c_10,plain,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
inference(clausify,[status(thm)],[smaller_number]) ).
fof(transitivity_of_less,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less(VAR_2,VAR_1)
| ~ less(VAR_2,VAR_0)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(c_11,plain,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
cnf(c_14,plain,
equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),b),
inference(resolve,[status(thm)],[c_9,c_7]) ).
cnf(c_16,plain,
~ equalish(add(successor(A),a),d),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_28,plain,
( less(a,A)
| ~ less(b,A) ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_21,plain,
~ less(b,d),
inference(resolve,[status(thm)],[c_28,c_6]) ).
cnf(c_24,plain,
equalish(b,d),
inference(resolve,[status(thm)],[c_21,c_5]) ).
cnf(c_29,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(b,a)),a),A)
| ~ equalish(b,A) ),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_30,plain,
~ equalish(b,d),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n005.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 01:54:01 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 937350 was started by sandbox on n005,
% 0.07/0.34 % Sat Sep 26 01:54:01 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 0.07/0.35
% 0.07/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.35
% 0.07/0.35 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.07/0.35 % Length of proof is 14.
% 0.07/0.35 % Level of proof is 3.
% 0.07/0.35 % Maximum clause weight is 31.000.
% 0.07/0.35 % Given clauses 9.
% 0.07/0.35
% 0.07/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------