%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:04:45 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.60s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 48 unt; 0 def)
% Number of atoms : 74 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] : sum(add(A,B),B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] : add(A,additive_identity) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] : add(A,A) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A] : multiply(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
multiply(b,a) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] : sum(A,B,add(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] : product(a,multiply(b,A),multiply(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
product(add(a,b),b,add(c,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
product(add(a,b),a,add(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f64,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f84,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
! [X0,X1] : sum(add(X0,X1),X1,X0),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f91,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f92,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f93,plain,
! [X0] : multiply(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f94,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f95,plain,
multiply(b,a) = d,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f96,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f102,plain,
! [X0,X1] : product(a,multiply(b,X0),multiply(X1,X0)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f123,plain,
product(add(a,b),b,add(c,b)),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f126,plain,
product(add(a,b),a,add(a,d)),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f130,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f168,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ sum(add(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f85,f89]) ).
fof(f297,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f168,f96]) ).
fof(f298,plain,
! [X0,X1] : add(add(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[f168,f64]) ).
fof(f325,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(paramodulation,[status(thm)],[f298,f297]) ).
fof(f335,plain,
product(add(a,b),b,add(b,c)),
inference(backward_demodulation,[status(thm)],[f325,f123]) ).
fof(f372,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f87,f63]) ).
fof(f429,plain,
! [X0,X1,X2] :
( X1 = multiply(X2,X0)
| ~ product(a,multiply(b,X0),X1) ),
inference(resolution,[status(thm)],[f102,f87]) ).
fof(f474,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X2,X1),
inference(resolution,[status(thm)],[f429,f102]) ).
fof(f482,plain,
! [X0] : d = multiply(X0,a),
inference(paramodulation,[status(thm)],[f95,f474]) ).
fof(f483,plain,
! [X0] : c = multiply(X0,b),
inference(paramodulation,[status(thm)],[f94,f474]) ).
fof(f486,plain,
! [X0,X1] : X0 = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f93,f474]) ).
fof(f551,plain,
c = b,
inference(backward_demodulation,[status(thm)],[f486,f483]) ).
fof(f552,plain,
d = a,
inference(backward_demodulation,[status(thm)],[f486,f482]) ).
fof(f553,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,X1,X2) ),
inference(backward_demodulation,[status(thm)],[f486,f372]) ).
fof(f614,plain,
b != d,
inference(backward_demodulation,[status(thm)],[f551,f130]) ).
fof(f625,plain,
product(add(a,b),b,add(b,b)),
inference(backward_demodulation,[status(thm)],[f551,f335]) ).
fof(f644,plain,
product(add(a,b),a,add(a,a)),
inference(backward_demodulation,[status(thm)],[f552,f126]) ).
fof(f649,plain,
b != a,
inference(forward_demodulation,[status(thm)],[f552,f614]) ).
fof(f657,plain,
product(add(a,b),b,additive_identity),
inference(forward_demodulation,[status(thm)],[f92,f625]) ).
fof(f671,plain,
product(add(a,b),a,additive_identity),
inference(forward_demodulation,[status(thm)],[f92,f644]) ).
fof(f678,plain,
additive_identity = b,
inference(resolution,[status(thm)],[f657,f553]) ).
fof(f681,plain,
additive_identity != a,
inference(backward_demodulation,[status(thm)],[f678,f649]) ).
fof(f683,plain,
product(add(a,additive_identity),a,additive_identity),
inference(backward_demodulation,[status(thm)],[f678,f671]) ).
fof(f690,plain,
product(a,a,additive_identity),
inference(forward_demodulation,[status(thm)],[f91,f683]) ).
fof(f691,plain,
additive_identity = a,
inference(resolution,[status(thm)],[f690,f553]) ).
fof(f693,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f691,f681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n020.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 04:15:48 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.54 % Drodi V4.1.1
% 0.15/0.60 % Refutation found
% 0.15/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.65/0.64 % Elapsed time: 0.095097 seconds
% 0.65/0.64 % CPU time: 0.475841 seconds
% 0.65/0.64 % Total memory used: 71.260 MB
% 0.65/0.64 % Net memory used: 70.677 MB
%------------------------------------------------------------------------------