%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD020-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 5.47s 1.18s
% Output : Proof 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 32 unt; 0 def)
% Number of atoms : 64 ( 17 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 : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f29,negated_conjecture,
~ sum(additive_identity,m,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_4) ).
fof(f29_nnf,plain,
~ sum(additive_identity,m,additive_identity),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ sum(additive_identity,m,additive_identity),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
~ sum(additive_identity,m,additive_identity),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t233,plain,
ifeq(sum(additive_identity,m,additive_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
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(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(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/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(f28,negated_conjecture,
sum(m,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_3) ).
fof(f28_nnf,plain,
sum(m,a,a),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
sum(m,a,a),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,negated_conjecture,
sum(m,a,a) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h188,plain,
sum(a,m,a) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi27]) ).
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(t49,plain,
sum(additive_identity,m,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi1,h46,h188,h46]) ).
cnf(t431,plain,
sum(additive_identity,m,additive_identity) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t3477,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t233,t431]) ).
cnf(t79,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t79]) ).
cnf(t3478,plain,
false = true,
inference(step,[status(thm)],[t3477,t256]) ).
cnf(t3474,plain,
false = true,
inference(orient,[status(thm)],[t3478]) ).
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,c29]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3474]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD020-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 10:38:38 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.47/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.47/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------