TSTP Solution File: ANA014-2 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 20:11:40 EDT 2024
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 92 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 36 ~; 35 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)),t_a),c_times(V_U,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_y] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_times(c_1,V_y,T_a) = V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_b,V_c] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a,V_b] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T_a,V_a] :
( ~ class_Ring__and__Field_Ofield(T_a)
| V_a = c_0
| c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Omonoid__mult(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( ~ class_Ring__and__Field_Ofield(T)
| class_OrderedGroup_Osemigroup__mult(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__field(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
v_c != c_0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f17,plain,
! [T_a] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ! [V_y] : c_times(c_1,V_y,T_a) = V_y ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X1,X0) = X1 ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [T_a] :
( ~ class_OrderedGroup_Osemigroup__mult(T_a)
| ! [V_a,V_b,V_c] : c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a) ),
inference(miniscoping,[status(esa)],[f5]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [T_a] :
( ~ class_Orderings_Oorder(T_a)
| ! [V_x] : c_lessequals(V_x,V_x,T_a) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [T_a] :
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ! [V_a,V_b] : c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = c_0
| c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f26,plain,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f27,plain,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f28,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f29,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f30,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f31,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[f28,f16]) ).
fof(f32,plain,
class_OrderedGroup_Omonoid__mult(t_a),
inference(resolution,[status(thm)],[f26,f31]) ).
fof(f33,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(resolution,[status(thm)],[f27,f31]) ).
fof(f34,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(resolution,[status(thm)],[f29,f16]) ).
fof(f35,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f36,plain,
! [X0] : c_lessequals(X0,X0,t_a),
inference(resolution,[status(thm)],[f35,f22]) ).
fof(f37,plain,
! [X0] : c_times(c_1,X0,t_a) = X0,
inference(resolution,[status(thm)],[f18,f32]) ).
fof(f39,plain,
! [X0] :
( X0 = c_0
| c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1 ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f40,plain,
! [X0,X1,X2] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(resolution,[status(thm)],[f20,f33]) ).
fof(f41,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_a),t_a) = c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a),
inference(resolution,[status(thm)],[f24,f34]) ).
fof(f45,plain,
! [X0,X1] :
( c_times(c_1,X0,t_a) = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a)
| X1 = c_0 ),
inference(paramodulation,[status(thm)],[f39,f40]) ).
fof(f46,plain,
! [X0,X1] :
( X0 = c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X0,t_a),t_a)
| X1 = c_0 ),
inference(forward_demodulation,[status(thm)],[f37,f45]) ).
fof(f81,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(backward_demodulation,[status(thm)],[f41,f15]) ).
fof(f170,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),c_HOL_Oabs(c_times(X0,c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),t_a),t_a),t_a),
inference(paramodulation,[status(thm)],[f41,f81]) ).
fof(f176,plain,
( spl0_11
<=> c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a) ),
introduced(split_symbol_definition) ).
fof(f178,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| spl0_11 ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( spl0_12
<=> v_c = c_0 ),
introduced(split_symbol_definition) ).
fof(f180,plain,
( v_c = c_0
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a)
| v_c = c_0 ),
inference(paramodulation,[status(thm)],[f46,f170]) ).
fof(f183,plain,
( ~ spl0_11
| spl0_12 ),
inference(split_clause,[status(thm)],[f182,f176,f179]) ).
fof(f185,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f36]) ).
fof(f186,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f14]) ).
fof(f188,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
$false,
inference(sat_refutation,[status(thm)],[f183,f186,f188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ANA014-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:54:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.20/0.40 % Refutation found
% 0.20/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.41 % Elapsed time: 0.058798 seconds
% 0.20/0.41 % CPU time: 0.352630 seconds
% 0.20/0.41 % Total memory used: 58.612 MB
% 0.20/0.41 % Net memory used: 58.392 MB
%------------------------------------------------------------------------------