%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD055-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:11:38 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 13 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(symmetry_of_equality,axiom,
! [VAR_0,VAR_1] :
( ~ equalish(VAR_1,VAR_0)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',symmetry_of_equality) ).
cnf(c_22,plain,
( ~ equalish(B,A)
| equalish(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_equality]) ).
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(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_4,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_4) ).
cnf(c_31,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_4]) ).
fof(b_equals_c_5,axiom,
equalish(b,c),
file('theBenchmark.p',b_equals_c_5) ).
cnf(c_32,plain,
equalish(b,c),
inference(clausify,[status(thm)],[b_equals_c_5]) ).
fof(not_less_or_equal_6,axiom,
~ less_or_equal(a,c),
file('theBenchmark.p',not_less_or_equal_6) ).
cnf(c_33,plain,
~ less_or_equal(a,c),
inference(clausify,[status(thm)],[not_less_or_equal_6]) ).
cnf(c_197,plain,
( ~ defined(A)
| less_or_equal(c,A)
| less_or_equal(A,c) ),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_383,plain,
( ~ defined(c)
| less_or_equal(c,c) ),
inference(factor,[status(thm)],[c_197]) ).
cnf(c_221,plain,
less_or_equal(c,c),
inference(resolve,[status(thm)],[c_30,c_383]) ).
cnf(c_241,plain,
equalish(c,b),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_384,plain,
( ~ less_or_equal(A,c)
| ~ less_or_equal(a,A) ),
inference(resolve,[status(thm)],[c_17,c_33]) ).
cnf(c_242,plain,
~ less_or_equal(b,c),
inference(resolve,[status(thm)],[c_384,c_31]) ).
cnf(c_385,plain,
( ~ equalish(A,b)
| ~ less_or_equal(A,c) ),
inference(resolve,[status(thm)],[c_26,c_242]) ).
cnf(c_386,plain,
~ equalish(c,b),
inference(resolve,[status(thm)],[c_385,c_221]) ).
cnf(c_382,plain,
$false,
inference(resolve,[status(thm)],[c_241,c_386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD055-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 02:31:30 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 2596773 was started by sandbox2 on n006,
% 0.07/0.35 % Sun Sep 27 02:31:30 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 13.
% 0.13/0.38 % Level of proof is 3.
% 0.13/0.38 % Maximum clause weight is 15.000.
% 0.13/0.38 % Given clauses 70.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------