%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA013-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:02:13 PM UTC 2026
% Result : Unsatisfiable 12.46s 2.19s
% Output : CNFRefutation 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 31 ( 4 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1689,axiom,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2339,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2441,axiom,
! [T] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2781,axiom,
! [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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2784,negated_conjecture,
! [V_U] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2785,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5107,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f1689]) ).
fof(f5108,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5107]) ).
fof(f5776,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0) ),
inference(cnf_transformation,[status(thm)],[f2339]) ).
fof(f5878,plain,
! [X0] :
( class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f2441]) ).
fof(f6218,plain,
! [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)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(miniscoping,[status(thm)],[f2781]) ).
fof(f6219,plain,
! [X0,X1,X2] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6218]) ).
fof(f6224,plain,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f2784]) ).
fof(f6225,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f2785]) ).
fof(f6709,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(resolution,[status(thm)],[f6219,f6225]) ).
fof(f6795,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_b),t_b),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f6709,f6224]) ).
fof(f6947,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_b))),t_b),t_b),c_HOL_Oabs(c_times(X0,v_f(v_x(c_HOL_Oabs(X0,t_b))),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[f6709,f6795]) ).
fof(f18765,plain,
class_Ring__and__Field_Oordered__comm__semiring__strict(t_b),
inference(resolution,[status(thm)],[f5878,f6225]) ).
fof(f18782,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[f18765,f5776]) ).
fof(f24345,plain,
! [X0] : c_lessequals(X0,X0,t_b),
inference(resolution,[status(thm)],[f5108,f18782]) ).
fof(f24350,plain,
$false,
inference(resolution,[status(thm)],[f24345,f6947]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA013-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 13:25:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.26/0.54 % Drodi V4.1.1
% 12.46/2.19 % Refutation found
% 12.46/2.19 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.46/2.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.54/2.22 % Elapsed time: 1.854398 seconds
% 0.54/2.22 % CPU time: 12.993837 seconds
% 0.54/2.22 % Total memory used: 316.139 MB
% 0.54/2.22 % Net memory used: 309.633 MB
%------------------------------------------------------------------------------