%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 01:14:55 PM UTC 2026
% Result : Unsatisfiable 15.47s 2.41s
% Output : Proof 15.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 59 unt; 0 def)
% Number of atoms : 107 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 42 ~; 32 |; 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 : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 76 ( 2 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f34,negated_conjecture,
~ sum(additive_identity,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_9) ).
fof(f34_nnf,plain,
~ sum(additive_identity,u,v),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
~ sum(additive_identity,u,v),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
~ sum(additive_identity,u,v),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t233,plain,
ifeq(sum(additive_identity,u,v),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
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(v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_is_defined) ).
fof(f28_nnf,plain,
defined(v),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
defined(v),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,axiom,
defined(v) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h119,plain,
sum(additive_identity,v,v) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi27]) ).
cnf(f29,hypothesis,
defined(q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_is_defined) ).
fof(f29_nnf,plain,
defined(q),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
defined(q),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi28,axiom,
defined(q) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h167,plain,
sum(additive_identity,q,q) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi28]) ).
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(h7,plain,
sum(additive_identity,additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi13]) ).
cnf(f0,axiom,
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f0_nnf,plain,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X2,X3,X5),true,sum(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f33,negated_conjecture,
sum(additive_identity,q,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_8) ).
fof(f33_nnf,plain,
sum(additive_identity,q,r),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
sum(additive_identity,q,r),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi32,negated_conjecture,
sum(additive_identity,q,r) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h2641,plain,
sum(additive_identity,r,q) = true,
inference(hyper_resolution,[status(thm)],[hi0,h7,hi32,h167]) ).
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(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(a,v,r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_7) ).
fof(f32_nnf,plain,
sum(a,v,r),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
sum(a,v,r),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi31,negated_conjecture,
sum(a,v,r) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h3606,plain,
sum(a,v,q) = true,
inference(hyper_resolution,[status(thm)],[hi1,h47,hi31,h2641]) ).
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(h46,plain,
sum(additive_inverse(a),a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi25]) ).
cnf(h3620,plain,
sum(additive_inverse(a),q,v) = true,
inference(hyper_resolution,[status(thm)],[hi0,h46,h3606,h119]) ).
cnf(f31,negated_conjecture,
sum(a,u,q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
fof(f31_nnf,plain,
sum(a,u,q),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
sum(a,u,q),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi30,negated_conjecture,
sum(a,u,q) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t92,plain,
sum(additive_identity,u,v) = true,
inference(hyper_resolution,[status(thm)],[hi1,h46,hi30,h3620]) ).
cnf(t307,plain,
sum(additive_identity,u,v) = true,
inference(orient,[status(thm)],[t92]) ).
cnf(t1876,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t233,t307]) ).
cnf(t104,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t104]) ).
cnf(t1877,plain,
false = true,
inference(step,[status(thm)],[t1876,t256]) ).
cnf(t1873,plain,
false = true,
inference(orient,[status(thm)],[t1877]) ).
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,c34]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1873]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD016-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n008.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 10:37:39 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.47/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.47/2.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------