%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:15:06 PM UTC 2026
% Result : Unsatisfiable 15.51s 2.57s
% Output : Proof 15.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 32 unt; 0 def)
% Number of atoms : 80 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 38 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(h46,plain,
sum(additive_inverse(a),a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi25]) ).
cnf(f4,axiom,
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/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(hi4,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h392,plain,
sum(a,additive_inverse(a),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi4,h46]) ).
cnf(f14,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f14_nnf,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(defined(X0),true,defined(additive_inverse(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h39,plain,
defined(additive_inverse(a)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi25]) ).
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(h110,plain,
sum(additive_identity,additive_inverse(a),additive_inverse(a)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h39]) ).
cnf(f23,axiom,
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
fof(f23_nnf,plain,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [U,V,X,Y,Z] :
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,axiom,
ifeq(less_or_equal(X0,X1),true,ifeq(sum(X0,X2,X3),true,ifeq(sum(X1,X2,X4),true,less_or_equal(X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(f27,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
fof(f27_nnf,plain,
less_or_equal(additive_identity,a),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi26,negated_conjecture,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h546,plain,
less_or_equal(additive_inverse(a),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi26,h110,h392]) ).
cnf(f28,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
fof(f28_nnf,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi28,negated_conjecture,
ifeq(less_or_equal(additive_inverse(a),additive_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi28,h546]) ).
cnf(t3840,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,t3840]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD064-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 11:01:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.51/2.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.51/2.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------