%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD058-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 01:15:05 PM UTC 2026
% Result : Unsatisfiable 8.02s 1.54s
% Output : Proof 8.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 38 unt; 0 def)
% Number of atoms : 82 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 66 ( 38 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 56 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f31,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_not_equal_to_additive_identity_5) ).
fof(f31_nnf,plain,
~ equalish(a,additive_identity),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ equalish(a,additive_identity),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t148,plain,
ifeq(equalish(a,additive_identity),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f21,axiom,
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox/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(hi21,axiom,
ifeq(equalish(X0,X1),true,equalish(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(f32,negated_conjecture,
equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_equals_additive_identity_6) ).
fof(f32_nnf,plain,
equalish(b,additive_identity),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
equalish(b,additive_identity),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi30,negated_conjecture,
equalish(b,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h50,plain,
equalish(additive_identity,b) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi30]) ).
cnf(f25,axiom,
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
fof(f25_nnf,plain,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(hi25,axiom,
ifeq(less_or_equal(X0,X1),true,ifeq(equalish(X0,X2),true,less_or_equal(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f29_nnf,plain,
less_or_equal(additive_identity,a),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi28,negated_conjecture,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(h127,plain,
less_or_equal(b,a) = true,
inference(hyper_resolution,[status(thm)],[hi25,hi28,h50]) ).
cnf(f15,axiom,
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
fof(f15_nnf,plain,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(less_or_equal(X0,X1),true,ifeq(less_or_equal(X1,X0),true,equalish(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f30,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f30_nnf,plain,
less_or_equal(a,b),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
less_or_equal(a,b),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(hi29,negated_conjecture,
less_or_equal(a,b) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h129,plain,
equalish(a,b) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi29,h127]) ).
cnf(f22,axiom,
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox/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(hi22,axiom,
ifeq(equalish(X0,X1),true,ifeq(equalish(X1,X2),true,equalish(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t11,plain,
equalish(a,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi22,h129,hi30]) ).
cnf(t292,plain,
equalish(a,additive_identity) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t3577,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t148,t292]) ).
cnf(t143,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t174,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t143]) ).
cnf(t3578,plain,
false = true,
inference(step,[status(thm)],[t3577,t174]) ).
cnf(t3573,plain,
false = true,
inference(orient,[status(thm)],[t3578]) ).
cnf(f26,axiom,
~ equalish(additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/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,c31]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3573]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD058-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 10:57:49 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.02/1.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.02/1.54 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------