%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD066-3 : 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 01:15:07 PM UTC 2026
% Result : Unsatisfiable 7.99s 1.60s
% Output : Proof 7.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 55 unt; 0 def)
% Number of atoms : 111 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 49 ~; 36 |; 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 : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 86 ( 2 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(h79,plain,
sum(additive_identity,b,b) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi26]) ).
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(h1474,plain,
sum(b,additive_identity,b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h79]) ).
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(hi3,axiom,
ifeq(defined(X0),true,sum(additive_inverse(X0),X0,additive_identity),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f28,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f28_nnf,plain,
defined(c),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(c),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,axiom,
defined(c) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h118,plain,
sum(additive_inverse(c),c,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi27]) ).
cnf(h3610,plain,
sum(c,additive_inverse(c),additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi4,h118]) ).
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(f32,negated_conjecture,
sum(b,c,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
fof(f32_nnf,plain,
sum(b,c,v),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
sum(b,c,v),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi31,negated_conjecture,
sum(b,c,v) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h3924,plain,
sum(v,additive_inverse(c),b) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi31,h3610,h1474]) ).
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(h47,plain,
sum(additive_identity,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi25]) ).
cnf(h1066,plain,
sum(a,additive_identity,a) = true,
inference(hyper_resolution,[status(thm)],[hi4,h47]) ).
cnf(f31,negated_conjecture,
sum(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f31_nnf,plain,
sum(a,c,u),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
sum(a,c,u),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi30,negated_conjecture,
sum(a,c,u) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(h3925,plain,
sum(u,additive_inverse(c),a) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi30,h3610,h1066]) ).
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(f33,negated_conjecture,
less_or_equal(u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_8) ).
fof(f33_nnf,plain,
less_or_equal(u,v),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
less_or_equal(u,v),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi32,negated_conjecture,
less_or_equal(u,v) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(t9,plain,
less_or_equal(a,b) = true,
inference(hyper_resolution,[status(thm)],[hi23,hi32,h3925,h3924]) ).
cnf(t3978,plain,
less_or_equal(a,b) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t93,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t93]) ).
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(f34,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_9) ).
fof(f34_nnf,plain,
~ less_or_equal(a,b),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
~ less_or_equal(a,b),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
~ less_or_equal(a,b),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c34]) ).
cnf(g0_0,plain,
true != ifeq(less_or_equal(a,b),true,false,true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(less_or_equal(a,b),true,false,less_or_equal(a,b)),
inference(rw,[status(thm)],[g0_0,t3978]) ).
cnf(g0_2,plain,
true != ifeq(true,true,false,less_or_equal(a,b)),
inference(rw,[status(thm)],[g0_1,t3978]) ).
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
% 0.00/0.02 % Problem : FLD066-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 11:03:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.99/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.99/1.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------