%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD039-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 01:15:00 PM UTC 2026
% Result : Unsatisfiable 12.94s 12.08s
% Output : Proof 12.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 35 unt; 0 def)
% Number of atoms : 59 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 26 ~; 16 |; 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 : 6 ( 6 usr; 5 con; 0-4 aty)
% Number of variables : 41 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/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(t123,plain,
ifeq(sum(additive_identity,additive_identity,multiplicative_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(f2,axiom,
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/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(f16,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f16_nnf,plain,
defined(multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
defined(multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h31,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi16]) ).
cnf(f13,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/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(h10,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/sandbox2/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(f28,negated_conjecture,
sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f28_nnf,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi26,negated_conjecture,
sum(additive_identity,multiplicative_identity,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t33,plain,
sum(additive_identity,additive_identity,multiplicative_identity) = true,
inference(hyper_resolution,[status(thm)],[hi0,h10,hi26,h31]) ).
cnf(t291,plain,
sum(additive_identity,additive_identity,multiplicative_identity) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t1747,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t123,t291]) ).
cnf(t43,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t43]) ).
cnf(t1748,plain,
false = true,
inference(step,[status(thm)],[t1747,t258]) ).
cnf(t1743,plain,
false = true,
inference(orient,[status(thm)],[t1748]) ).
cnf(f27,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
fof(f27_nnf,plain,
~ sum(additive_identity,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ sum(additive_identity,a,additive_identity),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c25,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1743]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD039-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/10.38 % Computer : n015.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.39 % DateTime : Fri Sep 25 10:51:22 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.94/12.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.94/12.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------