%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 08:16:04 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 24 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_7,plain,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_less]) ).
fof(equality_preserved_over_times,axiom,
! [VAR_0,VAR_1,VAR_2] :
( equalish(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2))
| ~ equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',equality_preserved_over_times) ).
cnf(c_13,plain,
( equalish(multiply(A,C),multiply(B,C))
| ~ equalish(A,B) ),
inference(clausify,[status(thm)],[equality_preserved_over_times]) ).
fof(not_less_and_equal,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_0,VAR_1)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',not_less_and_equal) ).
cnf(c_14,plain,
( ~ equalish(A,B)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[not_less_and_equal]) ).
fof(numbers_either_less_or_equal,axiom,
! [VAR_0,VAR_1] :
( less(VAR_1,VAR_0)
| equalish(VAR_1,VAR_0)
| less(VAR_0,VAR_1) ),
file('theBenchmark.p',numbers_either_less_or_equal) ).
cnf(c_15,plain,
( less(B,A)
| equalish(B,A)
| less(A,B) ),
inference(clausify,[status(thm)],[numbers_either_less_or_equal]) ).
fof(number_not_less_than_itself,axiom,
! [VAR_0] : ~ less(VAR_0,VAR_0),
file('theBenchmark.p',number_not_less_than_itself) ).
cnf(c_16,plain,
~ less(A,A),
inference(clausify,[status(thm)],[number_not_less_than_itself]) ).
fof(multiply_lemma,axiom,
! [VAR_0,VAR_1,VAR_2] :
( less(multiply(VAR_0,VAR_2),multiply(VAR_1,VAR_2))
| equalish(VAR_2,n0)
| ~ less(VAR_0,VAR_1) ),
file('theBenchmark.p',multiply_lemma) ).
cnf(c_18,plain,
( less(multiply(A,C),multiply(B,C))
| equalish(C,n0)
| ~ less(A,B) ),
inference(clausify,[status(thm)],[multiply_lemma]) ).
fof(b_not_less_than_a,axiom,
~ less(b,a),
file('theBenchmark.p',b_not_less_than_a) ).
cnf(c_19,plain,
~ less(b,a),
inference(clausify,[status(thm)],[b_not_less_than_a]) ).
fof(b_times_c_less_than_a_times_c,axiom,
less(multiply(b,c),multiply(a,c)),
file('theBenchmark.p',b_times_c_less_than_a_times_c) ).
cnf(c_20,plain,
less(multiply(b,c),multiply(a,c)),
inference(clausify,[status(thm)],[b_times_c_less_than_a_times_c]) ).
fof(prove_c_is_0,axiom,
~ equalish(c,n0),
file('theBenchmark.p',prove_c_is_0) ).
cnf(c_21,plain,
~ equalish(c,n0),
inference(clausify,[status(thm)],[prove_c_is_0]) ).
cnf(c_70,plain,
( equalish(b,a)
| less(a,b) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_74,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolve,[status(thm)],[c_20,c_14]) ).
cnf(c_562,plain,
( less(multiply(b,c),A)
| ~ less(multiply(a,c),A) ),
inference(resolve,[status(thm)],[c_7,c_20]) ).
cnf(c_78,plain,
~ less(multiply(a,c),multiply(b,c)),
inference(resolve,[status(thm)],[c_562,c_16]) ).
cnf(c_307,plain,
~ equalish(b,a),
inference(resolve,[status(thm)],[c_13,c_74]) ).
cnf(c_320,plain,
less(a,b),
inference(resolve,[status(thm)],[c_307,c_70]) ).
cnf(c_563,plain,
( less(multiply(A,c),multiply(B,c))
| ~ less(A,B) ),
inference(resolve,[status(thm)],[c_18,c_21]) ).
cnf(c_564,plain,
~ less(a,b),
inference(resolve,[status(thm)],[c_563,c_78]) ).
cnf(c_561,plain,
$false,
inference(resolve,[status(thm)],[c_320,c_564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 01:56:08 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 1758112 was started by sandbox on n003,
% 0.11/0.36 % Sat Sep 26 01:56:08 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.41
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.41
% 0.11/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.11/0.41 % Length of proof is 15.
% 0.11/0.41 % Level of proof is 4.
% 0.11/0.41 % Maximum clause weight is 23.000.
% 0.11/0.41 % Given clauses 108.
% 0.11/0.41
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------