%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD019-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:14:56 PM UTC 2026
% Result : Unsatisfiable 15.41s 2.63s
% Output : Proof 15.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 36 unt; 0 def)
% Number of atoms : 68 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f28_nnf,plain,
~ sum(additive_identity,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ sum(additive_identity,a,additive_identity),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t129,plain,
ifeq(sum(additive_identity,a,additive_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f2,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f2_nnf,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(defined(X0),true,sum(additive_identity,X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f13,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/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(hi13,axiom,
defined(additive_identity) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h10,plain,
sum(additive_identity,additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi13]) ).
cnf(f3,axiom,
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox2/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(hi3,axiom,
ifeq(defined(X0),true,sum(additive_inverse(X0),X0,additive_identity),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f26,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f26_nnf,plain,
defined(a),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
defined(a),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi25,axiom,
defined(a) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h61,plain,
sum(additive_inverse(a),a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi25]) ).
cnf(f1,axiom,
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f1_nnf,plain,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f27,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_2) ).
fof(f27_nnf,plain,
sum(additive_identity,additive_inverse(a),additive_identity),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
sum(additive_identity,additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi26,negated_conjecture,
sum(additive_identity,additive_inverse(a),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t29,plain,
sum(additive_identity,a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi26,h61,h10]) ).
cnf(t284,plain,
sum(additive_identity,a,additive_identity) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t1749,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t129,t284]) ).
cnf(t39,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t39]) ).
cnf(t1750,plain,
false = true,
inference(step,[status(thm)],[t1749,t258]) ).
cnf(t1746,plain,
false = true,
inference(orient,[status(thm)],[t1750]) ).
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/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,c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1746]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD019-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 10:40:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.41/2.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.41/2.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------