%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD032-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 12:21:58 PM UTC 2026
% Result : Unsatisfiable 6.33s 1.30s
% Output : CNFRefutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 123 ( 66 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ equalish(a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
equalish(multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ equalish(a,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(multiply(X0,X1),multiply(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f53,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f64,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f65,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
equalish(multiplicative_inverse(a),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ equalish(a,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f88,plain,
! [X0] :
( ~ equalish(X0,multiplicative_identity)
| ~ equalish(a,X0) ),
inference(resolution,[status(thm)],[f66,f77]) ).
fof(f96,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| ~ equalish(a,X1)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f88,f66]) ).
fof(f117,plain,
! [X0,X1] :
( ~ equalish(X1,a)
| ~ equalish(X1,X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f96,f64]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ equalish(X2,a)
| ~ equalish(X1,X2)
| ~ equalish(X1,X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f117,f66]) ).
fof(f204,plain,
! [X0,X1] :
( ~ defined(a)
| ~ equalish(X1,multiply(multiplicative_identity,a))
| ~ equalish(X1,X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f133,f40]) ).
fof(f209,plain,
! [X0,X1] :
( ~ equalish(X1,multiply(multiplicative_identity,a))
| ~ equalish(X1,X0)
| ~ equalish(X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f74]) ).
fof(f634,plain,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(multiply(X0,a),multiply(X1,a)) ),
inference(resolution,[status(thm)],[f70,f74]) ).
fof(f1020,plain,
! [X0,X1] :
( ~ equalish(multiply(X0,a),X1)
| ~ equalish(X1,multiplicative_identity)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f634,f209]) ).
fof(f1100,plain,
! [X0] :
( ~ defined(a)
| ~ defined(X0)
| ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ equalish(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1020,f43]) ).
fof(f1104,plain,
! [X0] :
( ~ defined(X0)
| ~ equalish(multiply(a,X0),multiplicative_identity)
| ~ equalish(X0,multiplicative_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f1100,f74]) ).
fof(f1109,plain,
( equalish(a,additive_identity)
| ~ defined(a)
| ~ defined(multiplicative_inverse(a))
| ~ equalish(multiplicative_inverse(a),multiplicative_identity) ),
inference(resolution,[status(thm)],[f1104,f41]) ).
fof(f1112,plain,
( equalish(a,additive_identity)
| ~ defined(a)
| ~ defined(multiplicative_inverse(a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1109,f76]) ).
fof(f1113,plain,
( equalish(a,additive_identity)
| ~ defined(a) ),
inference(forward_subsumption_resolution,[status(thm)],[f1112,f53]) ).
fof(f1114,plain,
equalish(a,additive_identity),
inference(resolution,[status(thm)],[f1113,f74]) ).
fof(f1115,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1114,f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD032-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 15:39:03 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 6.33/1.30 % Refutation found
% 6.33/1.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.33/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.23/1.35 % Elapsed time: 0.967567 seconds
% 4.23/1.35 % CPU time: 7.327956 seconds
% 4.23/1.35 % Total memory used: 74.439 MB
% 4.23/1.35 % Net memory used: 66.616 MB
%------------------------------------------------------------------------------