TSTP Solution File: ANA019-2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ANA019-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 20:11:42 EDT 2024
% Result : Unsatisfiable 0.10s 0.31s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 21
% Syntax : Number of formulae : 73 ( 14 unt; 0 def)
% Number of atoms : 151 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 144 ( 66 ~; 72 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [V_U] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a)
| ~ c_less(c_0,V_U,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x] :
( ~ c_less(c_0,V_x,tc_nat)
| V_x = c_Suc(c_minus(V_x,c_1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_n] :
( c_less(c_0,V_n,tc_nat)
| V_n = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_HOL_Oabs(c_0,T_a) = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T_a,V_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T_a,V_x,V_y] :
( ~ class_Orderings_Oorder(T_a)
| ~ c_less(V_x,V_y,T_a)
| c_lessequals(V_x,V_y,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [T_a,V_b,V_a] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( ~ class_LOrder_Ojoin__semilorder(T)
| class_Orderings_Oorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_LOrder_Ojoin__semilorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Ring__and__Field_Opordered__cancel__semiring(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
v_f(c_0) = c_0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f17,plain,
c_less(c_0,v_x,t_a),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f18,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f19,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X0)),t_a),c_times(X0,c_HOL_Oabs(v_h(v_xa(X0)),t_a),t_a),t_a)
| ~ c_less(c_0,X0,t_a) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f21,plain,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f22,plain,
! [X0] :
( c_less(c_0,X0,tc_nat)
| X0 = c_0 ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f23,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f24,plain,
! [T_a] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(T_a)
| ! [V_a] : c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| c_lessequals(c_0,c_times(X2,X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f28,plain,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f29,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_LOrder_Ojoin__semilorder(X0) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f30,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f31,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f32,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Oorder(X0) ),
inference(resolution,[status(thm)],[f29,f28]) ).
fof(f33,plain,
! [X0] :
( X0 = c_0
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
inference(resolution,[status(thm)],[f22,f21]) ).
fof(f34,plain,
! [X0] :
( c_HOL_Oabs(c_0,X0) = c_0
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f23,f31]) ).
fof(f35,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(resolution,[status(thm)],[f34,f20]) ).
fof(f36,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X0,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ c_less(X0,X1,X2)
| c_lessequals(X0,X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ),
inference(resolution,[status(thm)],[f26,f32]) ).
fof(f38,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[status(thm)],[f36,f20]) ).
fof(f40,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(c_Suc(c_minus(X0,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| X0 = c_0 ),
inference(paramodulation,[status(thm)],[f33,f18]) ).
fof(f42,plain,
! [X0,X1] :
( ~ c_less(X0,X1,t_a)
| c_lessequals(X0,X1,t_a) ),
inference(resolution,[status(thm)],[f37,f20]) ).
fof(f44,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| X0 = c_0
| X0 = c_0 ),
inference(paramodulation,[status(thm)],[f33,f40]) ).
fof(f45,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| X0 = c_0 ),
inference(duplicate_literals_removal,[status(esa)],[f44]) ).
fof(f46,plain,
( spl0_0
<=> v_xa(v_x) = c_0 ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( v_xa(v_x) = c_0
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( spl0_1
<=> c_less(c_0,v_x,t_a) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ c_less(c_0,v_x,t_a)
| spl0_1 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( v_xa(v_x) = c_0
| ~ c_less(c_0,v_x,t_a) ),
inference(resolution,[status(thm)],[f45,f19]) ).
fof(f53,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f52,f46,f49]) ).
fof(f62,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f17]) ).
fof(f63,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f82,plain,
( spl0_7
<=> c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a) ),
introduced(split_symbol_definition) ).
fof(f84,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| spl0_7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| ~ c_less(c_0,v_x,t_a)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f47,f19]) ).
fof(f86,plain,
( ~ spl0_7
| ~ spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f85,f82,f49,f46]) ).
fof(f98,plain,
( ~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| ~ spl0_0
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f47,f84]) ).
fof(f99,plain,
( ~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| ~ spl0_0
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f16,f98]) ).
fof(f100,plain,
( ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a)
| ~ spl0_0
| spl0_7 ),
inference(forward_demodulation,[status(thm)],[f35,f99]) ).
fof(f104,plain,
( spl0_9
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_a) ),
introduced(split_symbol_definition) ).
fof(f106,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| spl0_9 ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( spl0_10
<=> c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
introduced(split_symbol_definition) ).
fof(f109,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| spl0_10 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( spl0_11
<=> c_lessequals(c_0,v_x,t_a) ),
introduced(split_symbol_definition) ).
fof(f112,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| spl0_11 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a)
| ~ c_lessequals(c_0,v_x,t_a)
| ~ spl0_0
| spl0_7 ),
inference(resolution,[status(thm)],[f100,f27]) ).
fof(f114,plain,
( ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_0
| spl0_7 ),
inference(split_clause,[status(thm)],[f113,f104,f107,f110,f46,f82]) ).
fof(f115,plain,
( ~ c_less(c_0,v_x,t_a)
| spl0_11 ),
inference(resolution,[status(thm)],[f112,f42]) ).
fof(f116,plain,
( ~ spl0_1
| spl0_11 ),
inference(split_clause,[status(thm)],[f115,f49,f110]) ).
fof(f117,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| spl0_9 ),
inference(resolution,[status(thm)],[f106,f30]) ).
fof(f118,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f20]) ).
fof(f119,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( $false
| spl0_10 ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f38]) ).
fof(f121,plain,
spl0_10,
inference(contradiction_clause,[status(thm)],[f120]) ).
fof(f122,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f63,f86,f114,f116,f119,f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : ANA019-2 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n026.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Apr 29 21:20:04 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.6.0
% 0.10/0.31 % Refutation found
% 0.10/0.31 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.32 % Elapsed time: 0.014844 seconds
% 0.15/0.32 % CPU time: 0.023173 seconds
% 0.15/0.32 % Total memory used: 12.862 MB
% 0.15/0.32 % Net memory used: 12.747 MB
%------------------------------------------------------------------------------