%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG441-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 230.73s 29.71s
% Output : CNFRefutation 230.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 47 unt; 0 def)
% Number of atoms : 122 ( 19 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 96 ( 49 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 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; 0-4 aty)
% Number of variables : 177 ( 177 !; 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(f3,axiom,
! [A] : u(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : u(A,B) = u(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : v(A,A,A,B) = v(A,A,B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : v(A,A,B,A) = v(A,B,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] : v(A,B,A,A) = v(B,A,A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : u(A,B) = v(A,A,A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( r(u(X0,X3),u(X1,X4),u(X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11))
| ~ r(X9,X10,X11)
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
r(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
r(a,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
r(b,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ r(a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] : m(X0,X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] : m(X0,X1,X1) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : u(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : u(X0,X1) = u(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1] : v(X0,X0,X0,X1) = v(X0,X0,X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] : v(X0,X0,X1,X0) = v(X0,X1,X0,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1] : v(X0,X1,X0,X0) = v(X1,X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1] : u(X0,X1) = v(X0,X0,X0,X1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,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)],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(u(X0,X3),u(X1,X4),u(X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11))
| ~ r(X9,X10,X11)
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
r(a,a,b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
r(a,b,a),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
r(b,a,a),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
~ r(a,a,a),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
! [X0,X1] : u(X0,X1) = v(X0,X0,X1,X0),
inference(backward_demodulation,[status(thm)],[f25,f22]) ).
fof(f45,plain,
! [X0,X1] : u(X0,X1) = v(X0,X1,X0,X0),
inference(backward_demodulation,[status(thm)],[f41,f23]) ).
fof(f52,plain,
! [X0,X1] : u(X0,X1) = v(X1,X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f45,f24]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(m(a,X0,X3),m(a,X1,X4),m(b,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f26,f29]) ).
fof(f62,plain,
! [X0,X1,X2] :
( r(u(b,X0),u(a,X1),u(a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f31]) ).
fof(f63,plain,
! [X0,X1,X2] :
( r(u(a,X0),u(b,X1),u(a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f27,f30]) ).
fof(f66,plain,
r(u(b,a),u(a,b),u(a,a)),
inference(resolution,[status(thm)],[f62,f30]) ).
fof(f71,plain,
r(u(a,b),u(a,b),u(a,a)),
inference(forward_demodulation,[status(thm)],[f21,f66]) ).
fof(f72,plain,
r(u(a,b),u(a,b),a),
inference(forward_demodulation,[status(thm)],[f19,f71]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(m(u(a,b),X0,X3),m(u(a,b),X1,X4),m(a,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f72,f26]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( r(v(b,X0,X3,X6),v(a,X1,X4,X7),v(a,X2,X5,X8))
| ~ r(X6,X7,X8)
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f31]) ).
fof(f92,plain,
r(u(a,a),u(b,a),u(a,b)),
inference(resolution,[status(thm)],[f63,f29]) ).
fof(f100,plain,
r(a,u(b,a),u(a,b)),
inference(forward_demodulation,[status(thm)],[f19,f92]) ).
fof(f101,plain,
r(a,u(a,b),u(a,b)),
inference(forward_demodulation,[status(thm)],[f21,f100]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(m(a,X0,X3),m(u(a,b),X1,X4),m(u(a,b),X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f101,f26]) ).
fof(f265,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(v(b,b,X0,X3),v(a,a,X1,X4),v(a,a,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f80,f31]) ).
fof(f267,plain,
! [X0,X1,X2,X3,X4,X5] :
( r(v(b,a,X0,X3),v(a,b,X1,X4),v(a,a,X2,X5))
| ~ r(X3,X4,X5)
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f80,f30]) ).
fof(f775,plain,
! [X0,X1,X2] :
( r(v(b,b,a,X0),v(a,a,b,X1),v(a,a,a,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f265,f30]) ).
fof(f776,plain,
! [X0,X1,X2] :
( r(v(b,b,a,X0),v(a,a,a,X1),v(a,a,b,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f265,f29]) ).
fof(f797,plain,
! [X0,X1,X2] :
( r(v(b,b,a,X0),v(a,a,b,X1),u(a,X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f25,f775]) ).
fof(f798,plain,
! [X0,X1,X2] :
( r(v(b,b,a,X0),u(a,X1),v(a,a,b,X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f25,f776]) ).
fof(f897,plain,
! [X0,X1,X2] :
( r(v(b,a,a,X0),v(a,b,a,X1),v(a,a,b,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f267,f29]) ).
fof(f14105,plain,
r(v(b,b,a,a),v(a,a,b,a),u(a,b)),
inference(resolution,[status(thm)],[f797,f29]) ).
fof(f14252,plain,
r(v(b,b,a,a),u(a,b),u(a,b)),
inference(forward_demodulation,[status(thm)],[f41,f14105]) ).
fof(f14712,plain,
r(v(b,b,a,a),u(a,a),v(a,a,b,b)),
inference(resolution,[status(thm)],[f798,f29]) ).
fof(f14863,plain,
r(v(b,b,a,a),a,v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f19,f14712]) ).
fof(f14981,plain,
! [X0,X1,X2] :
( r(m(a,v(b,b,a,a),X0),m(u(a,b),u(a,b),X1),m(u(a,b),u(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f14252,f106]) ).
fof(f15031,plain,
! [X0,X1,X2] :
( r(m(a,v(b,b,a,a),X0),X1,m(u(a,b),u(a,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f14981]) ).
fof(f15032,plain,
! [X0,X1,X2] :
( r(m(a,v(b,b,a,a),X0),X1,X2)
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f15031]) ).
fof(f17102,plain,
r(m(a,v(b,b,a,a),v(b,b,a,a)),a,v(a,a,b,b)),
inference(resolution,[status(thm)],[f15032,f14863]) ).
fof(f17270,plain,
r(a,a,v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f18,f17102]) ).
fof(f17334,plain,
! [X0,X1,X2] :
( r(m(a,a,X0),m(a,a,X1),m(b,v(a,a,b,b),X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f17270,f61]) ).
fof(f17380,plain,
! [X0,X1,X2] :
( r(X0,m(a,a,X1),m(b,v(a,a,b,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f17334]) ).
fof(f17381,plain,
! [X0,X1,X2] :
( r(X0,X1,m(b,v(a,a,b,b),X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f17380]) ).
fof(f17560,plain,
r(v(b,a,a,a),v(a,b,a,a),v(a,a,b,b)),
inference(resolution,[status(thm)],[f897,f29]) ).
fof(f17694,plain,
r(u(a,b),v(a,b,a,a),v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f52,f17560]) ).
fof(f17695,plain,
r(u(a,b),u(a,b),v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f45,f17694]) ).
fof(f33648,plain,
r(u(a,b),u(a,b),m(b,v(a,a,b,b),v(a,a,b,b))),
inference(resolution,[status(thm)],[f17695,f17381]) ).
fof(f33737,plain,
r(u(a,b),u(a,b),b),
inference(forward_demodulation,[status(thm)],[f18,f33648]) ).
fof(f34169,plain,
! [X0,X1,X2] :
( r(m(u(a,b),u(a,b),X0),m(u(a,b),u(a,b),X1),m(a,b,X2))
| ~ r(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33737,f77]) ).
fof(f34223,plain,
! [X0,X1,X2] :
( r(X0,m(u(a,b),u(a,b),X1),m(a,b,X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f34169]) ).
fof(f34224,plain,
! [X0,X1,X2] :
( r(X0,X1,m(a,b,X2))
| ~ r(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f34223]) ).
fof(f40317,plain,
r(a,a,m(a,b,b)),
inference(resolution,[status(thm)],[f34224,f29]) ).
fof(f40376,plain,
r(a,a,a),
inference(forward_demodulation,[status(thm)],[f18,f40317]) ).
fof(f40377,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f40376,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG441-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n001.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 13:26:44 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 230.73/29.71 % Refutation found
% 230.73/29.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 230.73/29.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 218.45/29.75 % Elapsed time: 29.304508 seconds
% 218.45/29.75 % CPU time: 231.626340 seconds
% 218.45/29.75 % Total memory used: 274.222 MB
% 218.45/29.75 % Net memory used: 237.252 MB
%------------------------------------------------------------------------------