%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : FLD066-3 : 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 : n010.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 07:11:41 AM UTC 2026
% Result : Unsatisfiable 2.01s 0.75s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 31 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 125 ( 69 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 74 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_addition_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_4,VAR_5,VAR_2)
| ~ sum(VAR_3,VAR_5,VAR_1)
| ~ sum(VAR_0,VAR_3,VAR_4)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_1) ).
cnf(c_1,plain,
( ~ sum(E,F,C)
| ~ sum(D,F,B)
| ~ sum(A,D,E)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_1]) ).
fof(associativity_addition_2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ sum(VAR_3,VAR_5,VAR_2)
| ~ sum(VAR_4,VAR_1,VAR_5)
| ~ sum(VAR_3,VAR_4,VAR_0)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_addition_2) ).
cnf(c_2,plain,
( ~ sum(D,F,C)
| ~ sum(E,B,F)
| ~ sum(D,E,A)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[associativity_addition_2]) ).
fof(existence_of_identity_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_identity,VAR_0,VAR_0) ),
file('theBenchmark.p',existence_of_identity_addition) ).
cnf(c_3,plain,
( ~ defined(A)
| sum(additive_identity,A,A) ),
inference(clausify,[status(thm)],[existence_of_identity_addition]) ).
fof(existence_of_inverse_addition,axiom,
! [VAR_0] :
( ~ defined(VAR_0)
| sum(additive_inverse(VAR_0),VAR_0,additive_identity) ),
file('theBenchmark.p',existence_of_inverse_addition) ).
cnf(c_4,plain,
( ~ defined(A)
| sum(additive_inverse(A),A,additive_identity) ),
inference(clausify,[status(thm)],[existence_of_inverse_addition]) ).
fof(commutativity_addition,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ sum(VAR_1,VAR_0,VAR_2)
| sum(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_addition) ).
cnf(c_5,plain,
( ~ sum(B,A,C)
| sum(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_addition]) ).
fof(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('theBenchmark.p',well_definedness_of_additive_identity) ).
cnf(c_14,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)
| sum(additive_identity,VAR_0,VAR_1) ),
file('theBenchmark.p',antisymmetry_of_order_relation) ).
cnf(c_21,plain,
( ~ less_or_equal(B,A)
| ~ less_or_equal(A,B)
| sum(additive_identity,A,B) ),
inference(clausify,[status(thm)],[antisymmetry_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_23,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,VAR_3,VAR_4] :
( ~ sum(VAR_3,VAR_4,VAR_1)
| ~ sum(VAR_2,VAR_4,VAR_0)
| ~ less_or_equal(VAR_2,VAR_3)
| less_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',compatibility_of_order_relation_and_addition) ).
cnf(c_24,plain,
( ~ sum(D,E,B)
| ~ sum(C,E,A)
| ~ less_or_equal(C,D)
| less_or_equal(A,B) ),
inference(clausify,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
fof(a_is_defined,axiom,
defined(a),
file('theBenchmark.p',a_is_defined) ).
cnf(c_27,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_28,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_29,plain,
defined(c),
inference(clausify,[status(thm)],[c_is_defined]) ).
fof(sum_6,axiom,
sum(a,c,u),
file('theBenchmark.p',sum_6) ).
cnf(c_32,plain,
sum(a,c,u),
inference(clausify,[status(thm)],[sum_6]) ).
fof(sum_7,axiom,
sum(b,c,v),
file('theBenchmark.p',sum_7) ).
cnf(c_33,plain,
sum(b,c,v),
inference(clausify,[status(thm)],[sum_7]) ).
fof(less_or_equal_8,axiom,
less_or_equal(u,v),
file('theBenchmark.p',less_or_equal_8) ).
cnf(c_34,plain,
less_or_equal(u,v),
inference(clausify,[status(thm)],[less_or_equal_8]) ).
fof(not_less_or_equal_9,axiom,
~ less_or_equal(a,b),
file('theBenchmark.p',not_less_or_equal_9) ).
cnf(c_35,plain,
~ less_or_equal(a,b),
inference(clausify,[status(thm)],[not_less_or_equal_9]) ).
cnf(c_87,plain,
( ~ defined(A)
| less_or_equal(A,additive_identity)
| less_or_equal(additive_identity,A) ),
inference(resolve,[status(thm)],[c_23,c_14]) ).
cnf(c_2125,plain,
( ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(factor,[status(thm)],[c_87]) ).
cnf(c_89,plain,
less_or_equal(additive_identity,additive_identity),
inference(resolve,[status(thm)],[c_14,c_2125]) ).
cnf(c_90,plain,
( ~ defined(A)
| less_or_equal(a,A)
| less_or_equal(A,a) ),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_104,plain,
sum(additive_identity,a,a),
inference(resolve,[status(thm)],[c_27,c_3]) ).
cnf(c_120,plain,
sum(additive_identity,b,b),
inference(resolve,[status(thm)],[c_28,c_3]) ).
cnf(c_135,plain,
sum(additive_inverse(c),c,additive_identity),
inference(resolve,[status(thm)],[c_29,c_4]) ).
cnf(c_136,plain,
sum(additive_identity,c,c),
inference(resolve,[status(thm)],[c_29,c_3]) ).
cnf(c_172,plain,
sum(c,a,u),
inference(resolve,[status(thm)],[c_32,c_5]) ).
cnf(c_181,plain,
sum(c,b,v),
inference(resolve,[status(thm)],[c_33,c_5]) ).
cnf(c_191,plain,
( ~ less_or_equal(v,u)
| sum(additive_identity,u,v) ),
inference(resolve,[status(thm)],[c_34,c_21]) ).
cnf(c_2126,plain,
( ~ sum(B,C,b)
| ~ sum(A,C,a)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_35]) ).
cnf(c_2127,plain,
( ~ sum(additive_identity,A,b)
| ~ sum(additive_identity,A,a) ),
inference(resolve,[status(thm)],[c_2126,c_89]) ).
cnf(c_431,plain,
~ sum(additive_identity,b,a),
inference(resolve,[status(thm)],[c_2127,c_120]) ).
cnf(c_2128,plain,
( less_or_equal(a,b)
| less_or_equal(b,a) ),
inference(resolve,[status(thm)],[c_90,c_28]) ).
cnf(c_985,plain,
less_or_equal(b,a),
inference(resolve,[status(thm)],[c_35,c_2128]) ).
cnf(c_2129,plain,
( ~ sum(A,C,a)
| ~ sum(B,b,C)
| ~ sum(A,B,additive_identity) ),
inference(resolve,[status(thm)],[c_2,c_431]) ).
cnf(c_2130,plain,
( ~ sum(additive_inverse(c),A,a)
| ~ sum(c,b,A) ),
inference(resolve,[status(thm)],[c_2129,c_135]) ).
cnf(c_2081,plain,
~ sum(additive_inverse(c),v,a),
inference(resolve,[status(thm)],[c_2130,c_181]) ).
cnf(c_2131,plain,
( ~ sum(B,C,a)
| ~ sum(A,C,v)
| ~ sum(additive_inverse(c),A,B) ),
inference(resolve,[status(thm)],[c_1,c_2081]) ).
cnf(c_2132,plain,
( ~ sum(additive_identity,A,a)
| ~ sum(c,A,v) ),
inference(resolve,[status(thm)],[c_2131,c_135]) ).
cnf(c_2117,plain,
~ sum(c,a,v),
inference(resolve,[status(thm)],[c_2132,c_104]) ).
cnf(c_2133,plain,
( ~ sum(A,C,v)
| ~ sum(B,a,C)
| ~ sum(A,B,c) ),
inference(resolve,[status(thm)],[c_2,c_2117]) ).
cnf(c_2134,plain,
( ~ sum(additive_identity,A,v)
| ~ sum(c,a,A) ),
inference(resolve,[status(thm)],[c_2133,c_136]) ).
cnf(c_2121,plain,
~ sum(additive_identity,u,v),
inference(resolve,[status(thm)],[c_2134,c_172]) ).
cnf(c_2123,plain,
~ less_or_equal(v,u),
inference(resolve,[status(thm)],[c_2121,c_191]) ).
cnf(c_2135,plain,
( ~ sum(B,C,u)
| ~ sum(A,C,v)
| ~ less_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_24,c_2123]) ).
cnf(c_2136,plain,
( ~ sum(A,c,u)
| ~ less_or_equal(b,A) ),
inference(resolve,[status(thm)],[c_2135,c_33]) ).
cnf(c_2137,plain,
~ less_or_equal(b,a),
inference(resolve,[status(thm)],[c_2136,c_32]) ).
cnf(c_2124,plain,
$false,
inference(resolve,[status(thm)],[c_985,c_2137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n010.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sun Sep 27 02:34:31 UTC 2026
% 0.21/0.46 % CPUTime :
% 0.21/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.46 % Process 551692 was started by sandbox on n010,
% 0.21/0.46 % Sun Sep 27 02:34:31 2026
% 0.21/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.21/0.47
% 0.21/0.47 % From the command line: assign(max_seconds, 300).
% 2.01/0.75
% 2.01/0.75 % SZS status Unsatisfiable for theBenchmark
% 2.01/0.75
% 2.01/0.75 % Proof 1 at 0.21 (+ 0.06) seconds.
% 2.01/0.75 % Length of proof is 33.
% 2.01/0.75 % Level of proof is 8.
% 2.01/0.75 % Maximum clause weight is 21.000.
% 2.01/0.75 % Given clauses 379.
% 2.01/0.75
% 2.01/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------