TSTP Solution File: ALG441-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG441-1 : TPTP v8.1.2. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:11:36 EDT 2024
% Result : Unsatisfiable 39.20s 5.30s
% Output : CNFRefutation 39.20s
% 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(X0,X1,X2)
| ~ r(X3,X4,X5)
| ~ r(X6,X7,X8)
| r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(u(X0,X3),u(X1,X4),u(X2,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| ~ r(X6,X7,X8)
| ~ r(X9,X10,X11)
| r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11)) ),
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(esa)],[f1]) ).
fof(f18,plain,
! [X0,X1] : m(X0,X1,X1) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f19,plain,
! [X0] : u(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f21,plain,
! [X0,X1] : u(X0,X1) = u(X1,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [X0,X1] : v(X0,X0,X0,X1) = v(X0,X0,X1,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [X0,X1] : v(X0,X0,X1,X0) = v(X0,X1,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f24,plain,
! [X0,X1] : v(X0,X1,X0,X0) = v(X1,X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f25,plain,
! [X0,X1] : u(X0,X1) = v(X0,X0,X0,X1),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| ~ r(X6,X7,X8)
| r(m(X0,X3,X6),m(X1,X4,X7),m(X2,X5,X8)) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(u(X0,X3),u(X1,X4),u(X2,X5)) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| ~ r(X6,X7,X8)
| ~ r(X9,X10,X11)
| r(v(X0,X3,X6,X9),v(X1,X4,X7,X10),v(X2,X5,X8,X11)) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
r(a,a,b),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f30,plain,
r(a,b,a),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f31,plain,
r(b,a,a),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f32,plain,
~ r(a,a,a),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f34,plain,
! [X0,X1] : u(X0,X1) = v(X0,X0,X1,X0),
inference(forward_demodulation,[status(thm)],[f25,f22]) ).
fof(f35,plain,
! [X0,X1] : u(X0,X1) = v(X0,X1,X0,X0),
inference(forward_demodulation,[status(thm)],[f34,f23]) ).
fof(f36,plain,
! [X0,X1] : u(X0,X1) = v(X1,X0,X0,X0),
inference(forward_demodulation,[status(thm)],[f35,f24]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(u(b,X0),u(a,X1),u(a,X2)) ),
inference(resolution,[status(thm)],[f27,f31]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(u(a,X0),u(b,X1),u(a,X2)) ),
inference(resolution,[status(thm)],[f27,f30]) ).
fof(f44,plain,
r(u(b,a),u(a,b),u(a,a)),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f45,plain,
r(u(a,b),u(a,b),u(a,a)),
inference(forward_demodulation,[status(thm)],[f21,f44]) ).
fof(f46,plain,
r(u(a,b),u(a,b),a),
inference(forward_demodulation,[status(thm)],[f19,f45]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(m(u(a,b),X0,X3),m(u(a,b),X1,X4),m(a,X2,X5)) ),
inference(resolution,[status(thm)],[f26,f46]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(m(a,X0,X3),m(a,X1,X4),m(b,X2,X5)) ),
inference(resolution,[status(thm)],[f26,f29]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| ~ r(X6,X7,X8)
| r(v(b,X0,X3,X6),v(a,X1,X4,X7),v(a,X2,X5,X8)) ),
inference(resolution,[status(thm)],[f28,f31]) ).
fof(f77,plain,
r(u(a,a),u(b,a),u(a,b)),
inference(resolution,[status(thm)],[f38,f29]) ).
fof(f78,plain,
r(a,u(b,a),u(a,b)),
inference(forward_demodulation,[status(thm)],[f19,f77]) ).
fof(f79,plain,
r(a,u(a,b),u(a,b)),
inference(forward_demodulation,[status(thm)],[f21,f78]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(m(a,X0,X3),m(u(a,b),X1,X4),m(u(a,b),X2,X5)) ),
inference(resolution,[status(thm)],[f79,f26]) ).
fof(f297,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(v(b,b,X0,X3),v(a,a,X1,X4),v(a,a,X2,X5)) ),
inference(resolution,[status(thm)],[f58,f31]) ).
fof(f301,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ r(X0,X1,X2)
| ~ r(X3,X4,X5)
| r(v(b,a,X0,X3),v(a,b,X1,X4),v(a,a,X2,X5)) ),
inference(resolution,[status(thm)],[f58,f30]) ).
fof(f1177,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(v(b,b,a,X0),v(a,a,b,X1),v(a,a,a,X2)) ),
inference(resolution,[status(thm)],[f297,f30]) ).
fof(f1178,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(v(b,b,a,X0),v(a,a,b,X1),u(a,X2)) ),
inference(forward_demodulation,[status(thm)],[f25,f1177]) ).
fof(f1179,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(v(b,b,a,X0),v(a,a,a,X1),v(a,a,b,X2)) ),
inference(resolution,[status(thm)],[f297,f29]) ).
fof(f1180,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(v(b,b,a,X0),u(a,X1),v(a,a,b,X2)) ),
inference(forward_demodulation,[status(thm)],[f25,f1179]) ).
fof(f1228,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(v(b,a,a,X0),v(a,b,a,X1),v(a,a,b,X2)) ),
inference(resolution,[status(thm)],[f301,f29]) ).
fof(f23422,plain,
r(v(b,b,a,a),v(a,a,b,a),u(a,b)),
inference(resolution,[status(thm)],[f1178,f29]) ).
fof(f23423,plain,
r(v(b,b,a,a),u(a,b),u(a,b)),
inference(forward_demodulation,[status(thm)],[f34,f23422]) ).
fof(f23851,plain,
r(v(b,b,a,a),u(a,a),v(a,a,b,b)),
inference(resolution,[status(thm)],[f1180,f29]) ).
fof(f23852,plain,
r(v(b,b,a,a),a,v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f19,f23851]) ).
fof(f24362,plain,
! [X0,X1,X2] :
( ~ r(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)) ),
inference(resolution,[status(thm)],[f23423,f83]) ).
fof(f24363,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(m(a,v(b,b,a,a),X0),X1,m(u(a,b),u(a,b),X2)) ),
inference(forward_demodulation,[status(thm)],[f17,f24362]) ).
fof(f24364,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(m(a,v(b,b,a,a),X0),X1,X2) ),
inference(forward_demodulation,[status(thm)],[f17,f24363]) ).
fof(f26317,plain,
r(m(a,v(b,b,a,a),v(b,b,a,a)),a,v(a,a,b,b)),
inference(resolution,[status(thm)],[f24364,f23852]) ).
fof(f26318,plain,
r(a,a,v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f18,f26317]) ).
fof(f26655,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(m(a,a,X0),m(a,a,X1),m(b,v(a,a,b,b),X2)) ),
inference(resolution,[status(thm)],[f26318,f56]) ).
fof(f26656,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(X0,m(a,a,X1),m(b,v(a,a,b,b),X2)) ),
inference(forward_demodulation,[status(thm)],[f17,f26655]) ).
fof(f26657,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(X0,X1,m(b,v(a,a,b,b),X2)) ),
inference(forward_demodulation,[status(thm)],[f17,f26656]) ).
fof(f29155,plain,
r(v(b,a,a,a),v(a,b,a,a),v(a,a,b,b)),
inference(resolution,[status(thm)],[f1228,f29]) ).
fof(f29156,plain,
r(u(a,b),v(a,b,a,a),v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f36,f29155]) ).
fof(f29157,plain,
r(u(a,b),u(a,b),v(a,a,b,b)),
inference(forward_demodulation,[status(thm)],[f35,f29156]) ).
fof(f43858,plain,
r(u(a,b),u(a,b),m(b,v(a,a,b,b),v(a,a,b,b))),
inference(resolution,[status(thm)],[f29157,f26657]) ).
fof(f43859,plain,
r(u(a,b),u(a,b),b),
inference(forward_demodulation,[status(thm)],[f18,f43858]) ).
fof(f44068,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(m(u(a,b),u(a,b),X0),m(u(a,b),u(a,b),X1),m(a,b,X2)) ),
inference(resolution,[status(thm)],[f43859,f53]) ).
fof(f44069,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(X0,m(u(a,b),u(a,b),X1),m(a,b,X2)) ),
inference(forward_demodulation,[status(thm)],[f17,f44068]) ).
fof(f44070,plain,
! [X0,X1,X2] :
( ~ r(X0,X1,X2)
| r(X0,X1,m(a,b,X2)) ),
inference(forward_demodulation,[status(thm)],[f17,f44069]) ).
fof(f49083,plain,
r(a,a,m(a,b,b)),
inference(resolution,[status(thm)],[f44070,f29]) ).
fof(f49084,plain,
r(a,a,a),
inference(forward_demodulation,[status(thm)],[f18,f49083]) ).
fof(f49085,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f49084,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : ALG441-1 : TPTP v8.1.2. Released v5.4.0.
% 0.08/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n012.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 23:21:26 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 39.20/5.30 % Refutation found
% 39.20/5.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 39.20/5.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 39.79/5.39 % Elapsed time: 5.063807 seconds
% 39.79/5.39 % CPU time: 39.792656 seconds
% 39.79/5.39 % Total memory used: 258.102 MB
% 39.79/5.39 % Net memory used: 239.523 MB
%------------------------------------------------------------------------------