%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 01:15:09 PM UTC 2026
% Result : Unsatisfiable 14.38s 2.30s
% Output : Proof 14.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 31 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,negated_conjecture,
~ less_or_equal(additive_identity,multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_5) ).
fof(f30_nnf,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
~ less_or_equal(additive_identity,multiply(a,b)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t235,plain,
ifeq(less_or_equal(additive_identity,multiply(a,b)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(f19,axiom,
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality_of_multiplication) ).
fof(f19_nnf,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(defined(X0),true,ifeq(defined(X1),true,product(X0,X1,multiply(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
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(hi25,axiom,
defined(a) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(f27,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f27_nnf,plain,
defined(b),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
defined(b),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi26,axiom,
defined(b) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h65,plain,
product(a,b,multiply(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi25,hi26]) ).
cnf(f24,axiom,
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
fof(f24_nnf,plain,
! [Z,X,Y] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [Z,X,Y] :
( ~ product(X,Y,Z)
| ~ less_or_equal(additive_identity,Y)
| ~ less_or_equal(additive_identity,X)
| less_or_equal(additive_identity,Z) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ product(X1,X2,X0)
| ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(additive_identity,X1)
| less_or_equal(additive_identity,X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(less_or_equal(additive_identity,X0),true,ifeq(less_or_equal(additive_identity,X1),true,ifeq(product(X0,X1,X2),true,less_or_equal(additive_identity,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(f28,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f28_nnf,plain,
less_or_equal(additive_identity,a),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi27,negated_conjecture,
less_or_equal(additive_identity,a) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f29,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f29_nnf,plain,
less_or_equal(additive_identity,b),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(hi28,negated_conjecture,
less_or_equal(additive_identity,b) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t46,plain,
less_or_equal(additive_identity,multiply(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi24,hi27,hi28,h65]) ).
cnf(t457,plain,
less_or_equal(additive_identity,multiply(a,b)) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t3592,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t235,t457]) ).
cnf(t38,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t38]) ).
cnf(t3593,plain,
false = true,
inference(step,[status(thm)],[t3592,t256]) ).
cnf(t3588,plain,
false = true,
inference(orient,[status(thm)],[t3593]) ).
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,c30]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3588]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD071-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n011.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 11:04:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.38/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.38/2.30 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------