%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 11:49:25 AM UTC 2026
% Result : Unsatisfiable 3.15s 0.86s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 64 ( 42 unt; 0 def)
% Number of atoms : 99 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 37 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 135 ( 135 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : m(A,A,B) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : m(A,B,B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : v(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : u(A,A,B) = u(A,B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : u(A,A,B) = u(B,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : v(A,B) = v(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] : u(A,A,B) = v(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8))
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( r(u(X0,X3,X6),u(X1,X4,X7),u(X2,X5,X8))
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( r(v(X0,X3),v(X1,X4),v(X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
r(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
r(a,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
r(b,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ r(a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : m(X0,X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
! [X0,X1] : m(X0,X1,X1) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : v(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1] : u(X0,X0,X1) = u(X0,X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f21,plain,
! [X0,X1] : u(X0,X0,X1) = u(X1,X0,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] : v(X0,X1) = v(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1] : u(X0,X0,X1) = v(X0,X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8))
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( r(u(X0,X3,X6),u(X1,X4,X7),u(X2,X5,X8))
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(v(X0,X3),v(X1,X4),v(X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
r(a,a,b),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
r(a,b,a),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
r(b,a,a),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
~ r(a,a,a),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0,X1] : v(X0,X1) = u(X0,X1,X0),
inference(backward_demodulation,[status(thm)],[f23,f20]) ).
fof(f43,plain,
! [X0,X1] : v(X0,X1) = u(X1,X0,X0),
inference(forward_demodulation,[status(thm)],[f23,f21]) ).
fof(f48,plain,
! [X0,X1,X2] :
( r(v(b,X0),v(a,X1),v(a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f26,f29]) ).
fof(f49,plain,
! [X0,X1,X2] :
( r(v(a,X0),v(b,X1),v(a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f26,f28]) ).
fof(f52,plain,
r(v(b,a),v(a,b),v(a,a)),
inference(resolution,[status(thm)],[f48,f28]) ).
fof(f53,plain,
r(v(b,a),v(a,a),v(a,b)),
inference(resolution,[status(thm)],[f48,f27]) ).
fof(f57,plain,
r(v(b,a),v(a,b),a),
inference(forward_demodulation,[status(thm)],[f19,f52]) ).
fof(f58,plain,
r(v(b,a),a,v(a,b)),
inference(forward_demodulation,[status(thm)],[f19,f53]) ).
fof(f66,plain,
r(v(a,b),a,v(a,b)),
inference(paramodulation,[status(thm)],[f22,f58]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(m(v(b,a),X0,X3),m(a,X1,X4),m(v(a,b),X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f58]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(m(v(b,a),X0,X3),m(v(a,b),X1,X4),m(a,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f57]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(u(b,X0,X3),u(a,X1,X4),u(a,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f29]) ).
fof(f95,plain,
r(v(a,a),v(b,a),v(a,b)),
inference(resolution,[status(thm)],[f49,f27]) ).
fof(f102,plain,
r(a,v(b,a),v(a,b)),
inference(forward_demodulation,[status(thm)],[f19,f95]) ).
fof(f117,plain,
r(a,v(a,b),v(a,b)),
inference(paramodulation,[status(thm)],[f22,f102]) ).
fof(f481,plain,
! [X0,X1,X2] :
( r(u(b,a,X0),u(a,b,X1),u(a,a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f81,f28]) ).
fof(f504,plain,
! [X0,X1,X2] :
( r(u(b,a,X0),u(a,b,X1),v(a,X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f23,f481]) ).
fof(f1434,plain,
r(u(b,a,a),u(a,b,a),v(a,b)),
inference(resolution,[status(thm)],[f504,f27]) ).
fof(f1490,plain,
r(v(a,b),u(a,b,a),v(a,b)),
inference(forward_demodulation,[status(thm)],[f43,f1434]) ).
fof(f1491,plain,
r(v(a,b),v(a,b),v(a,b)),
inference(forward_demodulation,[status(thm)],[f39,f1490]) ).
fof(f2993,plain,
! [X0,X1,X2] :
( r(m(v(b,a),v(a,b),X0),m(a,a,X1),m(v(a,b),v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f73,f66]) ).
fof(f3046,plain,
! [X0,X1,X2] :
( r(m(v(b,a),v(a,b),X0),X1,m(v(a,b),v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f2993]) ).
fof(f3047,plain,
! [X0,X1,X2] :
( r(m(v(b,a),v(a,b),X0),X1,X2)
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f3046]) ).
fof(f3820,plain,
r(m(v(b,a),v(a,b),v(a,b)),v(a,b),v(a,b)),
inference(resolution,[status(thm)],[f3047,f1491]) ).
fof(f3873,plain,
r(v(b,a),v(a,b),v(a,b)),
inference(forward_demodulation,[status(thm)],[f17,f3820]) ).
fof(f4230,plain,
! [X0,X1,X2] :
( r(m(v(b,a),v(b,a),X0),m(v(a,b),v(a,b),X1),m(a,v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3873,f74]) ).
fof(f4231,plain,
! [X0,X1,X2] :
( r(m(v(b,a),v(b,a),X0),m(a,v(a,b),X1),m(v(a,b),v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3873,f73]) ).
fof(f4264,plain,
! [X0,X1,X2] :
( r(X0,m(v(a,b),v(a,b),X1),m(a,v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f4230]) ).
fof(f4265,plain,
! [X0,X1,X2] :
( r(X0,X1,m(a,v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f4264]) ).
fof(f4266,plain,
! [X0,X1,X2] :
( r(X0,m(a,v(a,b),X1),m(v(a,b),v(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f4231]) ).
fof(f4267,plain,
! [X0,X1,X2] :
( r(X0,m(a,v(a,b),X1),X2)
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f16,f4266]) ).
fof(f4348,plain,
r(a,v(a,b),m(a,v(a,b),v(a,b))),
inference(resolution,[status(thm)],[f4265,f117]) ).
fof(f4368,plain,
r(a,v(a,b),a),
inference(forward_demodulation,[status(thm)],[f17,f4348]) ).
fof(f7121,plain,
r(a,m(a,v(a,b),v(a,b)),a),
inference(resolution,[status(thm)],[f4267,f4368]) ).
fof(f7150,plain,
r(a,a,a),
inference(forward_demodulation,[status(thm)],[f17,f7121]) ).
fof(f7151,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7150,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG440-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.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
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Mon Sep 21 13:21:04 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 3.15/0.86 % Refutation found
% 3.15/0.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.15/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.15/0.89 % Elapsed time: 0.514325 seconds
% 3.15/0.89 % CPU time: 3.709304 seconds
% 3.15/0.89 % Total memory used: 97.770 MB
% 3.15/0.89 % Net memory used: 93.864 MB
%------------------------------------------------------------------------------