%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD061-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:11:40 AM UTC 2026
% Result : Unsatisfiable 18.11s 2.75s
% Output : CNFRefutation 18.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| equalish(add(VAR_0,VAR_1),add(VAR_1,VAR_0)) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_4,plain,
( ~ defined(B)
| ~ defined(A)
| equalish(add(A,B),add(B,A)) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(well_definedness_of_addition,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| defined(add(VAR_0,VAR_1)) ),
file('theBenchmark.p',well_definedness_of_addition) ).
cnf(c_10,plain,
( ~ defined(B)
| ~ defined(A)
| defined(add(A,B)) ),
inference(clausify,[status(thm)],[well_definedness_of_addition]) ).
fof(transitivity_of_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_2,VAR_1)
| ~ less_or_equal(VAR_0,VAR_2)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_order_relation) ).
cnf(c_17,plain,
( ~ less_or_equal(C,B)
| ~ less_or_equal(A,C)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[transitivity_of_order_relation]) ).
fof(totality_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ defined(VAR_1)
| ~ defined(VAR_0)
| less_or_equal(VAR_1,VAR_0)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',totality_of_order_relation) ).
cnf(c_18,plain,
( ~ defined(B)
| ~ defined(A)
| less_or_equal(B,A)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[totality_of_order_relation]) ).
fof(compatibility_of_order_relation_and_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ less_or_equal(VAR_0,VAR_2)
| ~ defined(VAR_1)
| less_or_equal(add(VAR_0,VAR_1),add(VAR_2,VAR_1)) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_19,plain,
( ~ less_or_equal(A,C)
| ~ defined(B)
| less_or_equal(add(A,B),add(C,B)) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(compatibility_of_equality_and_order_relation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_0)
| ~ less_or_equal(VAR_2,VAR_1)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_equality_and_order_relation) ).
cnf(c_26,plain,
( ~ equalish(C,A)
| ~ less_or_equal(C,B)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_equality_and_order_relation]) ).
fof(b_is_defined,axiom,
defined(b),
file('theBenchmark.p',b_is_defined) ).
cnf(c_29,plain,
defined(b),
inference(clausify,[status(thm)],[b_is_defined]) ).
fof(c_is_defined,axiom,
defined(c),
file('theBenchmark.p',c_is_defined) ).
cnf(c_30,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(less_or_equal_5,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_32,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(less_or_equal_6,axiom,
less_or_equal(c,d),
file('theBenchmark.p',less_or_equal_6) ).
cnf(c_33,plain,
less_or_equal(c,d),
inference(clausify,[status(thm)],[less_or_equal_6]) ).
fof(not_less_or_equal_7,axiom,
~ less_or_equal(add(a,c),add(d,b)),
file('theBenchmark.p',not_less_or_equal_7) ).
cnf(c_34,plain,
~ less_or_equal(add(a,c),add(d,b)),
inference(clausify,[status(thm)],[not_less_or_equal_7]) ).
cnf(c_18626,plain,
( ~ defined(A)
| ~ defined(A)
| less_or_equal(A,A) ),
inference(factor,[status(thm)],[c_18]) ).
cnf(c_49,plain,
( ~ defined(A)
| less_or_equal(A,A) ),
inference(copy,[status(thm)],[c_18626]) ).
cnf(c_174,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,b),add(B,b)) ),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_180,plain,
( ~ defined(A)
| defined(add(A,b)) ),
inference(resolve,[status(thm)],[c_29,c_10]) ).
cnf(c_192,plain,
( ~ defined(A)
| equalish(add(A,b),add(b,A)) ),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_212,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,c),add(B,c)) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_10349,plain,
defined(add(c,b)),
inference(resolve,[status(thm)],[c_180,c_30]) ).
cnf(c_10633,plain,
less_or_equal(add(c,b),add(c,b)),
inference(resolve,[status(thm)],[c_10349,c_49]) ).
cnf(c_16302,plain,
less_or_equal(add(c,b),add(d,b)),
inference(resolve,[status(thm)],[c_174,c_33]) ).
cnf(c_18627,plain,
( ~ less_or_equal(A,add(d,b))
| ~ less_or_equal(add(a,c),A) ),
inference(resolve,[status(thm)],[c_17,c_34]) ).
cnf(c_16947,plain,
~ less_or_equal(add(a,c),add(c,b)),
inference(resolve,[status(thm)],[c_18627,c_16302]) ).
cnf(c_17078,plain,
equalish(add(c,b),add(b,c)),
inference(resolve,[status(thm)],[c_192,c_30]) ).
cnf(c_18554,plain,
less_or_equal(add(a,c),add(b,c)),
inference(resolve,[status(thm)],[c_212,c_32]) ).
cnf(c_18628,plain,
( ~ less_or_equal(A,add(c,b))
| ~ less_or_equal(add(a,c),A) ),
inference(resolve,[status(thm)],[c_17,c_16947]) ).
cnf(c_18618,plain,
~ less_or_equal(add(b,c),add(c,b)),
inference(resolve,[status(thm)],[c_18628,c_18554]) ).
cnf(c_18629,plain,
( ~ equalish(A,add(b,c))
| ~ less_or_equal(A,add(c,b)) ),
inference(resolve,[status(thm)],[c_26,c_18618]) ).
cnf(c_18630,plain,
~ less_or_equal(add(c,b),add(c,b)),
inference(resolve,[status(thm)],[c_18629,c_17078]) ).
cnf(c_18625,plain,
$false,
inference(resolve,[status(thm)],[c_10633,c_18630]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD061-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 02:32:06 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 4028810 was started by sandbox on n013,
% 0.08/0.35 % Sun Sep 27 02:32:06 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 18.11/2.75
% 18.11/2.75 % given #500 (T,wt=17): 1570 less_or_equal(add(additive_identity,additive_identity),add(additive_identity,additive_identity)). [resolve(368,a,49,b)].
% 18.11/2.75
% 18.11/2.75 % given #1000 (T,wt=18): 1081 less_or_equal(multiplicative_identity,additive_inverse(d)) | less_or_equal(additive_inverse(d),multiplicative_identity). [resolve(255,a,118,c)].
% 18.11/2.75
% 18.11/2.75 % SZS status Unsatisfiable for theBenchmark
% 18.11/2.75
% 18.11/2.75 % Proof 1 at 1.67 (+ 0.59) seconds.
% 18.11/2.75 % Length of proof is 24.
% 18.11/2.75 % Level of proof is 5.
% 18.11/2.75 % Maximum clause weight is 22.000.
% 18.11/2.75 % Given clauses 1048.
% 18.11/2.75
% 18.11/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------