%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD070-2 : 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 : n011.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 07:11:43 AM UTC 2026
% Result : Unsatisfiable 7.41s 1.45s
% Output : CNFRefutation 7.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 56 ( 28 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 95 ( 51 ~; 44 |; 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 : 48 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| equalish(add(additive_identity,VAR_0),VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_2,plain,
( ~ defined(A)
| equalish(add(additive_identity,A),A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_11,plain,
defined(additive_identity),
inference(clausify,[status(thm)],[well_definedness_of_additive_identity]) ).
fof(antisymmetry_of_order_relation,axiom,
! [VAR_0,VAR_1] :
( ~ less_or_equal(VAR_1,VAR_0)
| ~ less_or_equal(VAR_0,VAR_1)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',antisymmetry_of_order_relation) ).
cnf(c_16,plain,
( ~ less_or_equal(B,A)
| ~ less_or_equal(A,B)
| equalish(A,B) ),
inference(clausify,[status(thm)],[antisymmetry_of_order_relation]) ).
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(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(transitivity_of_equality,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ equalish(VAR_2,VAR_1)
| ~ equalish(VAR_0,VAR_2)
| equalish(VAR_0,VAR_1) ),
file('theBenchmark.p',transitivity_of_equality) ).
cnf(c_23,plain,
( ~ equalish(C,B)
| ~ equalish(A,C)
| equalish(A,B) ),
inference(clausify,[status(thm)],[transitivity_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(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(add_equals_c_4,axiom,
equalish(add(a,b),c),
file('theBenchmark.p',add_equals_c_4) ).
cnf(c_31,plain,
equalish(add(a,b),c),
inference(clausify,[status(thm)],[add_equals_c_4]) ).
fof(less_or_equal_5,axiom,
less_or_equal(additive_identity,a),
file('theBenchmark.p',less_or_equal_5) ).
cnf(c_32,plain,
less_or_equal(additive_identity,a),
inference(clausify,[status(thm)],[less_or_equal_5]) ).
fof(less_or_equal_6,axiom,
less_or_equal(additive_identity,b),
file('theBenchmark.p',less_or_equal_6) ).
cnf(c_33,plain,
less_or_equal(additive_identity,b),
inference(clausify,[status(thm)],[less_or_equal_6]) ).
fof(not_less_or_equal_7,axiom,
~ less_or_equal(additive_identity,c),
file('theBenchmark.p',not_less_or_equal_7) ).
cnf(c_34,plain,
~ less_or_equal(additive_identity,c),
inference(clausify,[status(thm)],[not_less_or_equal_7]) ).
cnf(c_119,plain,
( ~ defined(A)
| less_or_equal(A,additive_identity)
| less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_18,c_11]) ).
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_195,plain,
equalish(add(additive_identity,b),b),
inference(resolve,[status(thm)],[c_29,c_2]) ).
cnf(c_213,plain,
( ~ defined(A)
| less_or_equal(c,A)
| less_or_equal(A,c) ),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_9695,plain,
( ~ defined(c)
| less_or_equal(c,c) ),
inference(factor,[status(thm)],[c_213]) ).
cnf(c_237,plain,
less_or_equal(c,c),
inference(resolve,[status(thm)],[c_30,c_9695]) ).
cnf(c_252,plain,
equalish(c,add(a,b)),
inference(resolve,[status(thm)],[c_31,c_22]) ).
cnf(c_265,plain,
( ~ less_or_equal(A,additive_identity)
| less_or_equal(A,b) ),
inference(resolve,[status(thm)],[c_33,c_17]) ).
cnf(c_9696,plain,
( ~ less_or_equal(A,c)
| ~ less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_17,c_34]) ).
cnf(c_269,plain,
~ less_or_equal(b,c),
inference(resolve,[status(thm)],[c_9696,c_33]) ).
cnf(c_9697,plain,
( ~ equalish(A,b)
| ~ less_or_equal(A,c) ),
inference(resolve,[status(thm)],[c_26,c_269]) ).
cnf(c_413,plain,
~ equalish(c,b),
inference(resolve,[status(thm)],[c_9697,c_237]) ).
cnf(c_418,plain,
~ equalish(b,c),
inference(resolve,[status(thm)],[c_22,c_413]) ).
cnf(c_9698,plain,
( ~ equalish(A,c)
| ~ equalish(b,A) ),
inference(resolve,[status(thm)],[c_23,c_418]) ).
cnf(c_442,plain,
~ equalish(b,add(a,b)),
inference(resolve,[status(thm)],[c_9698,c_31]) ).
cnf(c_9699,plain,
( less_or_equal(c,additive_identity)
| less_or_equal(additive_identity,c) ),
inference(resolve,[status(thm)],[c_119,c_30]) ).
cnf(c_730,plain,
less_or_equal(c,additive_identity),
inference(resolve,[status(thm)],[c_34,c_9699]) ).
cnf(c_731,plain,
less_or_equal(c,b),
inference(resolve,[status(thm)],[c_730,c_265]) ).
cnf(c_737,plain,
( ~ equalish(c,A)
| less_or_equal(A,b) ),
inference(resolve,[status(thm)],[c_731,c_26]) ).
cnf(c_6705,plain,
less_or_equal(add(a,b),b),
inference(resolve,[status(thm)],[c_252,c_737]) ).
cnf(c_9700,plain,
( ~ less_or_equal(b,add(a,b))
| equalish(b,add(a,b)) ),
inference(resolve,[status(thm)],[c_6705,c_16]) ).
cnf(c_8914,plain,
~ less_or_equal(b,add(a,b)),
inference(resolve,[status(thm)],[c_442,c_9700]) ).
cnf(c_9701,plain,
( ~ equalish(A,b)
| ~ less_or_equal(A,add(a,b)) ),
inference(resolve,[status(thm)],[c_26,c_8914]) ).
cnf(c_9022,plain,
~ less_or_equal(add(additive_identity,b),add(a,b)),
inference(resolve,[status(thm)],[c_9701,c_195]) ).
cnf(c_9702,plain,
less_or_equal(add(additive_identity,b),add(a,b)),
inference(resolve,[status(thm)],[c_174,c_32]) ).
cnf(c_9694,plain,
$false,
inference(resolve,[status(thm)],[c_9022,c_9702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 02:34:29 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2017313 was started by sandbox on n011,
% 0.19/0.45 % Sun Sep 27 02:34:29 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 7.41/1.45
% 7.41/1.45 % SZS status Unsatisfiable for theBenchmark
% 7.41/1.45
% 7.41/1.45 % Proof 1 at 0.70 (+ 0.26) seconds.
% 7.41/1.45 % Length of proof is 33.
% 7.41/1.45 % Level of proof is 8.
% 7.41/1.45 % Maximum clause weight is 22.000.
% 7.41/1.45 % Given clauses 464.
% 7.41/1.45
% 7.41/1.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------