%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD056-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:15:04 PM UTC 2026
% Result : Unsatisfiable 10.30s 1.93s
% Output : Proof 10.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 48 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 20 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f22,axiom,
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_order_relation) ).
fof(f22_nnf,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t26,plain,
ifeq(defined(X1),true,ifeq(defined(X2),true,or(less_or_equal(X1,X2),less_or_equal(X2,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t50,plain,
ifeq(defined(X1),true,ifeq(defined(X2),true,or(less_or_equal(X1,X2),less_or_equal(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t26]) ).
cnf(f27,negated_conjecture,
~ less_or_equal(a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_2) ).
fof(f27_nnf,plain,
~ less_or_equal(a,a),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
~ less_or_equal(a,a),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
~ less_or_equal(a,a),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(t3,plain,
less_or_equal(a,a) = false,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t139,plain,
less_or_equal(a,a) = false,
inference(orient,[status(thm)],[t3]) ).
cnf(t147,plain,
true = ifeq(defined(a),true,ifeq(defined(a),true,or(false,less_or_equal(a,a)),true),true),
inference(cp,[status(thm)],[t50,t139]) ).
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(t0,plain,
defined(a) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t84,plain,
defined(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t159,plain,
true = ifeq(true,true,ifeq(defined(a),true,or(false,less_or_equal(a,a)),true),true),
inference(step,[status(thm)],[t147,t84]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t160,plain,
true = ifeq(defined(a),true,or(false,less_or_equal(a,a)),true),
inference(step,[status(thm)],[t159,t35]) ).
cnf(t161,plain,
true = ifeq(true,true,or(false,less_or_equal(a,a)),true),
inference(step,[status(thm)],[t160,t84]) ).
cnf(t162,plain,
true = or(false,less_or_equal(a,a)),
inference(step,[status(thm)],[t161,t35]) ).
cnf(t6,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t37,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t163,plain,
true = less_or_equal(a,a),
inference(step,[status(thm)],[t162,t37]) ).
cnf(t164,plain,
true = false,
inference(step,[status(thm)],[t163,t139]) ).
cnf(t150,plain,
false = true,
inference(orient,[status(thm)],[t164]) ).
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,c27]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD056-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 11:00:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.30/1.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.30/1.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------