%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:14:52 PM UTC 2026
% Result : Unsatisfiable 173.88s 23.29s
% Output : Proof 173.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 49 unt; 0 def)
% Number of atoms : 93 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 34 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f22,axiom,
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
fof(f22_nnf,plain,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t21,plain,
ifeq(equalish(X1,X2),true,ifeq(equalish(X2,X3),true,equalish(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t56,plain,
ifeq(equalish(X1,X2),true,ifeq(equalish(X2,X3),true,equalish(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(f27,negated_conjecture,
~ equalish(additive_inverse(additive_identity),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_not_equal_to_additive_identity_1) ).
fof(f27_nnf,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ equalish(additive_inverse(additive_identity),additive_identity),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t7,plain,
equalish(additive_inverse(additive_identity),additive_identity) = false,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t138,plain,
equalish(additive_inverse(additive_identity),additive_identity) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t145,plain,
true = ifeq(equalish(additive_inverse(additive_identity),X1),true,ifeq(equalish(X1,additive_identity),true,false,true),true),
inference(cp,[status(thm)],[t56,t138]) ).
cnf(t215436,plain,
ifeq(equalish(additive_inverse(additive_identity),X1),true,ifeq(equalish(X1,additive_identity),true,false,true),true) = true,
inference(orient,[status(thm)],[t145]) ).
cnf(f21,axiom,
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
fof(f21_nnf,plain,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t13,plain,
ifeq(equalish(X1,X2),true,equalish(X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t57,plain,
ifeq(equalish(X1,X2),true,equalish(X2,X1),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f1,axiom,
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f1_nnf,plain,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t14,plain,
ifeq(defined(X1),true,equalish(add(additive_identity,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t52,plain,
ifeq(defined(X1),true,equalish(add(additive_identity,X1),X1),true) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f11,axiom,
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f11_nnf,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t10,plain,
ifeq(defined(X1),true,defined(additive_inverse(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t49,plain,
ifeq(defined(X1),true,defined(additive_inverse(X1)),true) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f10,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f10_nnf,plain,
defined(additive_identity),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
defined(additive_identity),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t0,plain,
defined(additive_identity) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t65,plain,
defined(additive_identity) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t67,plain,
true = ifeq(true,true,defined(additive_inverse(additive_identity)),true),
inference(cp,[status(thm)],[t49,t65]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t215471,plain,
true = defined(additive_inverse(additive_identity)),
inference(step,[status(thm)],[t67,t35]) ).
cnf(t159,plain,
defined(additive_inverse(additive_identity)) = true,
inference(orient,[status(thm)],[t215471]) ).
cnf(t163,plain,
true = ifeq(true,true,equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),true),
inference(cp,[status(thm)],[t52,t159]) ).
cnf(t215501,plain,
true = equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)),
inference(step,[status(thm)],[t163,t35]) ).
cnf(t644,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_inverse(additive_identity)) = true,
inference(orient,[status(thm)],[t215501]) ).
cnf(t645,plain,
true = ifeq(true,true,equalish(additive_inverse(additive_identity),add(additive_identity,additive_inverse(additive_identity))),true),
inference(cp,[status(thm)],[t57,t644]) ).
cnf(t215511,plain,
true = equalish(additive_inverse(additive_identity),add(additive_identity,additive_inverse(additive_identity))),
inference(step,[status(thm)],[t645,t35]) ).
cnf(t796,plain,
equalish(additive_inverse(additive_identity),add(additive_identity,additive_inverse(additive_identity))) = true,
inference(orient,[status(thm)],[t215511]) ).
cnf(t215437,plain,
true = ifeq(true,true,ifeq(equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),true,false,true),true),
inference(cp,[status(thm)],[t215436,t796]) ).
cnf(t218070,plain,
true = ifeq(equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),true,false,true),
inference(step,[status(thm)],[t215437,t35]) ).
cnf(f2,axiom,
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f2_nnf,plain,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t16,plain,
ifeq(defined(X1),true,equalish(add(X1,additive_inverse(X1)),additive_identity),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t51,plain,
ifeq(defined(X1),true,equalish(add(X1,additive_inverse(X1)),additive_identity),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t73,plain,
true = ifeq(true,true,equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),true),
inference(cp,[status(thm)],[t51,t65]) ).
cnf(t215492,plain,
true = equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity),
inference(step,[status(thm)],[t73,t35]) ).
cnf(t501,plain,
equalish(add(additive_identity,additive_inverse(additive_identity)),additive_identity) = true,
inference(orient,[status(thm)],[t215492]) ).
cnf(t218071,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t218070,t501]) ).
cnf(t218072,plain,
true = false,
inference(step,[status(thm)],[t218071,t35]) ).
cnf(t215446,plain,
false = true,
inference(orient,[status(thm)],[t218072]) ).
cnf(f26,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
fof(f26_nnf,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ equalish(additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c26,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t215446]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD006-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.37 % Computer : n005.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 10:34:02 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 173.88/23.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 173.88/23.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------