%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD059-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:15:05 PM UTC 2026
% Result : Unsatisfiable 8.87s 2.04s
% Output : Proof 8.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 35 unt; 0 def)
% Number of atoms : 83 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 45 ~; 32 |; 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 : 61 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f27,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/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(t7,plain,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t3677,plain,
less_or_equal(additive_identity,a) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f18,axiom,
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_addition) ).
fof(f18_nnf,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| sum(X,Y,add(X,Y)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(defined(X0),true,ifeq(defined(X1),true,sum(X0,X1,add(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f26,hypothesis,
defined(a),
file('/export/starexec/sandbox/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(h38,plain,
sum(a,a,add(a,a)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi25,hi25]) ).
cnf(f2,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/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(h56,plain,
sum(additive_identity,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi25]) ).
cnf(f23,axiom,
( ~ sum(Y,Z,V)
| ~ sum(X,Z,U)
| ~ less_or_equal(X,Y)
| less_or_equal(U,V) ),
file('/export/starexec/sandbox/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(hi26,negated_conjecture,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h1480,plain,
less_or_equal(a,add(a,a)) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi26,h56,h38]) ).
cnf(f21,axiom,
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
fof(f21_nnf,plain,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(less_or_equal(X0,X1),true,ifeq(less_or_equal(X1,X2),true,less_or_equal(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t45,plain,
less_or_equal(additive_identity,add(a,a)) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi26,h1480]) ).
cnf(t3690,plain,
less_or_equal(additive_identity,add(a,a)) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t41,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t41]) ).
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(f28,negated_conjecture,
~ less_or_equal(additive_identity,add(a,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_3) ).
fof(f28_nnf,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ less_or_equal(additive_identity,add(a,a)),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c28]) ).
cnf(g0_0,plain,
true != ifeq(less_or_equal(additive_identity,add(a,a)),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(less_or_equal(additive_identity,add(a,a)),true,false,less_or_equal(additive_identity,a)),
inference(rw,[status(thm)],[g0_0,t3677]) ).
cnf(g0_2,plain,
true != ifeq(less_or_equal(additive_identity,add(a,a)),less_or_equal(additive_identity,add(a,a)),false,less_or_equal(additive_identity,a)),
inference(rw,[status(thm)],[g0_1,t3690]) ).
cnf(g0_3,plain,
true != false,
inference(rw,[status(thm)],[g0_2,t256]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 11:00:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.87/2.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.87/2.04 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------