%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD071-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:15:08 PM UTC 2026
% Result : Unsatisfiable 12.70s 2.07s
% Output : Proof 12.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 33 unt; 0 def)
% Number of atoms : 45 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 18 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 18 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,axiom,
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
fof(f19_nnf,plain,
! [Y,Z] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Y,Z] :
( ~ less_or_equal(additive_identity,Z)
| ~ less_or_equal(additive_identity,Y)
| less_or_equal(additive_identity,multiply(Y,Z)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ less_or_equal(additive_identity,X1)
| ~ less_or_equal(additive_identity,X0)
| less_or_equal(additive_identity,multiply(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t32,plain,
ifeq(less_or_equal(additive_identity,X1),true,ifeq(less_or_equal(additive_identity,X2),true,less_or_equal(additive_identity,multiply(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t67,plain,
ifeq(less_or_equal(additive_identity,X1),true,ifeq(less_or_equal(additive_identity,X2),true,less_or_equal(additive_identity,multiply(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(f31,negated_conjecture,
~ less_or_equal(additive_identity,multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
fof(f31_nnf,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t12,plain,
less_or_equal(additive_identity,multiply(a,b)) = false,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t228,plain,
less_or_equal(additive_identity,multiply(a,b)) = false,
inference(orient,[status(thm)],[t12]) ).
cnf(t238,plain,
true = ifeq(less_or_equal(additive_identity,a),true,ifeq(less_or_equal(additive_identity,b),true,false,true),true),
inference(cp,[status(thm)],[t67,t228]) ).
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(t5,plain,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t189,plain,
less_or_equal(additive_identity,a) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t252,plain,
true = ifeq(true,true,ifeq(less_or_equal(additive_identity,b),true,false,true),true),
inference(step,[status(thm)],[t238,t189]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t39,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t253,plain,
true = ifeq(less_or_equal(additive_identity,b),true,false,true),
inference(step,[status(thm)],[t252,t39]) ).
cnf(f30,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f30_nnf,plain,
less_or_equal(additive_identity,b),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(t6,plain,
less_or_equal(additive_identity,b) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t202,plain,
less_or_equal(additive_identity,b) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t254,plain,
true = ifeq(true,true,false,true),
inference(step,[status(thm)],[t253,t202]) ).
cnf(t255,plain,
true = false,
inference(step,[status(thm)],[t254,t39]) ).
cnf(t243,plain,
false = true,
inference(orient,[status(thm)],[t255]) ).
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,t243]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD071-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 11:06:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.70/2.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.70/2.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------