%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:51:09 PM UTC 2026
% Result : Unsatisfiable 48.04s 6.67s
% Output : Proof 48.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 21 unt; 0 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 142 ( 65 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 88 ( 2 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( product(X,X,additive_identity)
| product(X,multiplicative_inverse(X),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
fof(f5_nnf,plain,
! [X] :
( product(X,X,additive_identity)
| product(X,multiplicative_inverse(X),multiplicative_identity) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( product(X,X,additive_identity)
| product(X,multiplicative_inverse(X),multiplicative_identity) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( product(X0,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f8,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p32,plain,
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(f10,axiom,
( product(X,X,additive_identity)
| ~ product(Y,Y,additive_identity)
| ~ product(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
fof(f10_nnf,plain,
! [Y,Z,X] :
( product(X,X,additive_identity)
| ~ product(Y,Y,additive_identity)
| ~ product(Y,Z,X) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y,Z,X] :
( product(X,X,additive_identity)
| ~ product(Y,Y,additive_identity)
| ~ product(Y,Z,X) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X2,X2,additive_identity)
| ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p79,plain,
( product(multiplicative_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_inverse(X0),multiplicative_inverse(X0),additive_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[status(thm)],[p32,c10]) ).
cnf(f9,axiom,
( greater_than_0(additive_inverse(X))
| product(X,X,additive_identity)
| greater_than_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
fof(f9_nnf,plain,
! [X] :
( greater_than_0(additive_inverse(X))
| product(X,X,additive_identity)
| greater_than_0(X) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] :
( greater_than_0(additive_inverse(X))
| product(X,X,additive_identity)
| greater_than_0(X) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( greater_than_0(additive_inverse(X0))
| product(X0,X0,additive_identity)
| greater_than_0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p225,plain,
( greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| greater_than_0(multiplicative_inverse(X0))
| product(multiplicative_identity,multiplicative_identity,additive_identity)
| product(X0,X0,additive_identity) ),
inference(resolution,[status(thm)],[p79,c9]) ).
cnf(f7,axiom,
( ~ product(X,X,additive_identity)
| ~ greater_than_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
fof(f7_nnf,plain,
! [X] :
( ~ product(X,X,additive_identity)
| ~ greater_than_0(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] :
( ~ product(X,X,additive_identity)
| ~ greater_than_0(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f12,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
fof(f12_nnf,plain,
greater_than_0(a),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
greater_than_0(a),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p17,plain,
~ product(a,a,additive_identity),
inference(resolution,[status(thm)],[c7,c12]) ).
cnf(p866,plain,
( greater_than_0(additive_inverse(multiplicative_inverse(a)))
| greater_than_0(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[p225,p17]) ).
cnf(f4,axiom,
( product(X,additive_inverse(Y),additive_inverse(Z))
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( product(X,additive_inverse(Y),additive_inverse(Z))
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( product(X,additive_inverse(Y),additive_inverse(Z))
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p33,plain,
( product(X0,additive_inverse(multiplicative_inverse(X0)),additive_inverse(multiplicative_identity))
| product(X0,X0,additive_identity) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(f11,axiom,
( greater_than_0(X)
| ~ greater_than_0(Z)
| ~ greater_than_0(Y)
| ~ product(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
fof(f11_nnf,plain,
! [Y,Z,X] :
( greater_than_0(X)
| ~ greater_than_0(Z)
| ~ greater_than_0(Y)
| ~ product(Y,Z,X) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Y,Z,X] :
( greater_than_0(X)
| ~ greater_than_0(Z)
| ~ greater_than_0(Y)
| ~ product(Y,Z,X) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p90,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(additive_inverse(multiplicative_inverse(X0)))
| ~ greater_than_0(X0)
| product(X0,X0,additive_identity) ),
inference(resolution,[status(thm)],[p33,c11]) ).
cnf(p265,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| ~ greater_than_0(additive_inverse(multiplicative_inverse(a)))
| product(a,a,additive_identity) ),
inference(resolution,[status(thm)],[p90,c12]) ).
cnf(p913,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| product(a,a,additive_identity)
| greater_than_0(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[p866,p265]) ).
cnf(p2369,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(multiplicative_inverse(a))
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[p913,p17]) ).
cnf(f1,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
fof(f1_nnf,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p2370,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[p2369,c1]) ).
cnf(f13,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
fof(f13_nnf,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p2371,plain,
greater_than_0(additive_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[p2370,c13]) ).
cnf(p58,plain,
( greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(f2,axiom,
( product(additive_inverse(X),additive_inverse(Y),Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_of_inverses1) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( product(additive_inverse(X),additive_inverse(Y),Z)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( product(additive_inverse(X),additive_inverse(Y),Z)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( product(additive_inverse(X0),additive_inverse(X1),X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(f0,axiom,
product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f0_nnf,plain,
! [X] : product(X,multiplicative_identity,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(X,multiplicative_identity,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p14,plain,
product(additive_inverse(X0),additive_inverse(multiplicative_identity),X0),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(p103,plain,
( greater_than_0(multiplicative_identity)
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[p58,p14]) ).
cnf(p38,plain,
( greater_than_0(additive_inverse(multiplicative_identity))
| greater_than_0(multiplicative_identity) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(p115,plain,
( greater_than_0(multiplicative_identity)
| greater_than_0(multiplicative_identity) ),
inference(resolution,[status(thm)],[p103,p38]) ).
cnf(p116,plain,
greater_than_0(multiplicative_identity),
inference(factoring,[status(thm)],[p115]) ).
cnf(f6,axiom,
( ~ greater_than_0(additive_inverse(X))
| ~ greater_than_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
fof(f6_nnf,plain,
! [X] :
( ~ greater_than_0(additive_inverse(X))
| ~ greater_than_0(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( ~ greater_than_0(additive_inverse(X))
| ~ greater_than_0(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ greater_than_0(additive_inverse(X0))
| ~ greater_than_0(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p117,plain,
~ greater_than_0(additive_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[p116,c6]) ).
cnf(p2419,plain,
$false,
inference(resolution,[status(thm)],[p2371,p117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:30:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 48.04/6.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.04/6.67 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------