%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD006-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 01:14:53 PM UTC 2026
% Result : Unsatisfiable 7.04s 1.42s
% Output : Proof 7.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 47 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 18 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 30 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f4_nnf,plain,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t16,plain,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t41,plain,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f3,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f3_nnf,plain,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t14,plain,
ifeq(defined(X1),true,sum(additive_inverse(X1),X1,additive_identity),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t52,plain,
ifeq(defined(X1),true,sum(additive_inverse(X1),X1,additive_identity),true) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f13,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f13_nnf,plain,
defined(additive_identity),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
defined(additive_identity),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(t0,plain,
defined(additive_identity) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t66,plain,
defined(additive_identity) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t70,plain,
true = ifeq(true,true,sum(additive_inverse(additive_identity),additive_identity,additive_identity),true),
inference(cp,[status(thm)],[t52,t66]) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t7]) ).
cnf(t365,plain,
true = sum(additive_inverse(additive_identity),additive_identity,additive_identity),
inference(step,[status(thm)],[t70,t34]) ).
cnf(t326,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t365]) ).
cnf(t327,plain,
true = ifeq(true,true,sum(additive_identity,additive_inverse(additive_identity),additive_identity),true),
inference(cp,[status(thm)],[t41,t326]) ).
cnf(t366,plain,
true = sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(step,[status(thm)],[t327,t34]) ).
cnf(f26,negated_conjecture,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_1) ).
fof(f26_nnf,plain,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ sum(additive_identity,additive_inverse(additive_identity),additive_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(t8,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity) = false,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t121,plain,
sum(additive_identity,additive_inverse(additive_identity),additive_identity) = false,
inference(orient,[status(thm)],[t8]) ).
cnf(t367,plain,
true = false,
inference(step,[status(thm)],[t366,t121]) ).
cnf(t343,plain,
false = true,
inference(orient,[status(thm)],[t367]) ).
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_identities) ).
fof(f25_nnf,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c26]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t343]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD006-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 10:29:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.04/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.04/1.42 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------