%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD060-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 195.64s 25.28s
% Output : Proof 195.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 84 ( 60 unt; 0 def)
% Number of atoms : 132 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 58 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 100 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f27,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f27_nnf,plain,
defined(b),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi26,axiom,
defined(b) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h56,plain,
sum(a,b,add(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi25,hi26]) ).
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(f30,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_5) ).
fof(f30_nnf,plain,
less_or_equal(a,b),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi29,negated_conjecture,
less_or_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(f32,negated_conjecture,
sum(b,b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
fof(f32_nnf,plain,
sum(b,b,v),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
sum(b,b,v),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi31,negated_conjecture,
sum(b,b,v) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h2731,plain,
less_or_equal(add(a,b),v) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi29,h56,hi31]) ).
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(hi4,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2732,plain,
sum(b,a,add(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h56]) ).
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(f28,hypothesis,
defined(u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_is_defined) ).
fof(f28_nnf,plain,
defined(u),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(u),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,axiom,
defined(u) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h119,plain,
sum(additive_identity,u,u) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi27]) ).
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(hi13,axiom,
defined(additive_identity) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h31,plain,
sum(additive_identity,a,add(additive_identity,a)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi13,hi25]) ).
cnf(f1,axiom,
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/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(f31,negated_conjecture,
sum(a,a,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f31_nnf,plain,
sum(a,a,u),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
sum(a,a,u),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi30,negated_conjecture,
sum(a,a,u) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h2695,plain,
sum(add(additive_identity,a),a,u) = true,
inference(hyper_resolution,[status(thm)],[hi1,h31,hi30,h119]) ).
cnf(h79,plain,
sum(additive_identity,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi26]) ).
cnf(h1207,plain,
sum(b,additive_identity,b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h79]) ).
cnf(h2693,plain,
sum(a,additive_identity,add(additive_identity,a)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h31]) ).
cnf(h2929,plain,
less_or_equal(add(additive_identity,a),b) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi29,h2693,h1207]) ).
cnf(h2945,plain,
less_or_equal(u,add(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi23,h2929,h2695,h2732]) ).
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(h2946,plain,
less_or_equal(u,v) = true,
inference(hyper_resolution,[status(thm)],[hi21,h2945,h2731]) ).
cnf(f33,negated_conjecture,
~ less_or_equal(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_8) ).
fof(f33_nnf,plain,
~ less_or_equal(u,v),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ less_or_equal(u,v),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
~ less_or_equal(u,v),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi33,negated_conjecture,
ifeq(less_or_equal(u,v),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi33,h2946]) ).
cnf(t3818,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c33]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3818]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD060-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n020.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 11:00:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 195.64/25.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.64/25.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------