%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD060-2 : 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 : n007.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 19.95s 2.96s
% Output : CNFRefutation 19.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 31 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 105 ( 57 ~; 48 |; 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 : 53 ( 0 sgn 20 !; 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(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(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_28,plain,
defined(a),
inference(clausify,[status(thm)],[a_is_defined]) ).
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(u_is_defined,axiom,
defined(u),
file('theBenchmark.p',u_is_defined) ).
cnf(c_30,plain,
defined(u),
inference(clausify,[status(thm)],[u_is_defined]) ).
fof(v_is_defined,axiom,
defined(v),
file('theBenchmark.p',v_is_defined) ).
cnf(c_31,plain,
defined(v),
inference(clausify,[status(thm)],[v_is_defined]) ).
fof(add_equals_u_5,axiom,
equalish(add(a,a),u),
file('theBenchmark.p',add_equals_u_5) ).
cnf(c_32,plain,
equalish(add(a,a),u),
inference(clausify,[status(thm)],[add_equals_u_5]) ).
fof(add_equals_v_6,axiom,
equalish(add(b,b),v),
file('theBenchmark.p',add_equals_v_6) ).
cnf(c_33,plain,
equalish(add(b,b),v),
inference(clausify,[status(thm)],[add_equals_v_6]) ).
fof(less_or_equal_7,axiom,
less_or_equal(a,b),
file('theBenchmark.p',less_or_equal_7) ).
cnf(c_34,plain,
less_or_equal(a,b),
inference(clausify,[status(thm)],[less_or_equal_7]) ).
fof(not_less_or_equal_8,axiom,
~ less_or_equal(u,v),
file('theBenchmark.p',not_less_or_equal_8) ).
cnf(c_35,plain,
~ less_or_equal(u,v),
inference(clausify,[status(thm)],[not_less_or_equal_8]) ).
cnf(c_137,plain,
( ~ less_or_equal(A,B)
| less_or_equal(add(A,a),add(B,a)) ),
inference(resolve,[status(thm)],[c_28,c_19]) ).
cnf(c_156,plain,
( ~ defined(A)
| equalish(add(a,A),add(A,a)) ),
inference(resolve,[status(thm)],[c_28,c_4]) ).
cnf(c_175,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_214,plain,
( ~ defined(A)
| less_or_equal(u,A)
| less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_30,c_18]) ).
cnf(c_252,plain,
( ~ defined(A)
| less_or_equal(v,A)
| less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_31,c_18]) ).
cnf(c_16474,plain,
( ~ defined(v)
| less_or_equal(v,v) ),
inference(factor,[status(thm)],[c_252]) ).
cnf(c_276,plain,
less_or_equal(v,v),
inference(resolve,[status(thm)],[c_31,c_16474]) ).
cnf(c_297,plain,
equalish(v,add(b,b)),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_16475,plain,
( ~ equalish(A,u)
| ~ less_or_equal(A,v) ),
inference(resolve,[status(thm)],[c_26,c_35]) ).
cnf(c_439,plain,
~ equalish(v,u),
inference(resolve,[status(thm)],[c_16475,c_276]) ).
cnf(c_450,plain,
~ equalish(u,v),
inference(resolve,[status(thm)],[c_22,c_439]) ).
cnf(c_16476,plain,
( ~ equalish(A,v)
| ~ equalish(u,A) ),
inference(resolve,[status(thm)],[c_23,c_450]) ).
cnf(c_451,plain,
~ equalish(u,add(b,b)),
inference(resolve,[status(thm)],[c_16476,c_33]) ).
cnf(c_16477,plain,
( less_or_equal(u,v)
| less_or_equal(v,u) ),
inference(resolve,[status(thm)],[c_214,c_31]) ).
cnf(c_944,plain,
less_or_equal(v,u),
inference(resolve,[status(thm)],[c_35,c_16477]) ).
cnf(c_945,plain,
( ~ equalish(v,A)
| less_or_equal(A,u) ),
inference(resolve,[status(thm)],[c_944,c_26]) ).
cnf(c_6789,plain,
less_or_equal(add(b,b),u),
inference(resolve,[status(thm)],[c_297,c_945]) ).
cnf(c_16478,plain,
( ~ less_or_equal(u,add(b,b))
| equalish(u,add(b,b)) ),
inference(resolve,[status(thm)],[c_6789,c_16]) ).
cnf(c_7469,plain,
~ less_or_equal(u,add(b,b)),
inference(resolve,[status(thm)],[c_451,c_16478]) ).
cnf(c_16479,plain,
( ~ equalish(A,u)
| ~ less_or_equal(A,add(b,b)) ),
inference(resolve,[status(thm)],[c_26,c_7469]) ).
cnf(c_7531,plain,
~ less_or_equal(add(a,a),add(b,b)),
inference(resolve,[status(thm)],[c_16479,c_32]) ).
cnf(c_13468,plain,
less_or_equal(add(a,a),add(b,a)),
inference(resolve,[status(thm)],[c_137,c_34]) ).
cnf(c_14332,plain,
equalish(add(a,b),add(b,a)),
inference(resolve,[status(thm)],[c_156,c_29]) ).
cnf(c_15516,plain,
less_or_equal(add(a,b),add(b,b)),
inference(resolve,[status(thm)],[c_175,c_34]) ).
cnf(c_16480,plain,
( ~ less_or_equal(A,add(b,b))
| ~ less_or_equal(add(a,a),A) ),
inference(resolve,[status(thm)],[c_17,c_7531]) ).
cnf(c_16254,plain,
~ less_or_equal(add(b,a),add(b,b)),
inference(resolve,[status(thm)],[c_16480,c_13468]) ).
cnf(c_16481,plain,
( ~ equalish(A,add(b,a))
| ~ less_or_equal(A,add(b,b)) ),
inference(resolve,[status(thm)],[c_26,c_16254]) ).
cnf(c_16482,plain,
~ less_or_equal(add(a,b),add(b,b)),
inference(resolve,[status(thm)],[c_16481,c_14332]) ).
cnf(c_16473,plain,
$false,
inference(resolve,[status(thm)],[c_15516,c_16482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 02:30:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1020258 was started by sandbox2 on n007,
% 0.09/0.37 % Sun Sep 27 02:30:40 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 19.95/2.96
% 19.95/2.96 % given #500 (W,wt=16): 11613 defined(multiplicative_inverse(v)) | equalish(additive_identity,v). [resolve(253,b,22,b)].
% 19.95/2.96
% 19.95/2.96 % SZS status Unsatisfiable for theBenchmark
% 19.95/2.96
% 19.95/2.96 % Proof 1 at 1.84 (+ 0.70) seconds.
% 19.95/2.96 % Length of proof is 36.
% 19.95/2.96 % Level of proof is 9.
% 19.95/2.96 % Maximum clause weight is 22.000.
% 19.95/2.96 % Given clauses 943.
% 19.95/2.96
% 19.95/2.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------