%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA031-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:02:17 PM UTC 2026
% Result : Unsatisfiable 276.80s 40.40s
% Output : CNFRefutation 276.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 78 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 79 ( 43 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 81 ( 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [V_U] : c_lessequals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_U] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [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)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_b] :
( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_f(v_x(X0)),t_b),c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [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)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [T_a] :
( ! [V_a,V_b] : c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0,X1,X2] :
( c_times(X1,X2,X0) = c_times(X2,X1,X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f24,f15]) ).
fof(f27,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[status(thm)],[f26,f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_times(X0,X1,X2) = c_times(X1,X0,X2) ),
inference(resolution,[status(thm)],[f19,f21]) ).
fof(f29,plain,
! [X0,X1] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f30,plain,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_g(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f29,f13]) ).
fof(f31,plain,
! [X0] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(c_HOL_Oabs(v_g(X0),t_b),v_c,t_b),t_b),
inference(backward_demodulation,[status(thm)],[f29,f12]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_times(c_times(X0,X1,X2),X3,X2) = c_times(X0,c_times(X1,X3,X2),X2) ),
inference(resolution,[status(thm)],[f17,f22]) ).
fof(f41,plain,
! [X0,X1,X2] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(resolution,[status(thm)],[f40,f25]) ).
fof(f62,plain,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),
inference(paramodulation,[status(thm)],[f41,f30]) ).
fof(f877,plain,
! [X0,X1,X2,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(c_times(X3,X0,X2),c_times(X3,X1,X2),X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f878,plain,
! [X0,X1,X2] :
( c_lessequals(c_times(X2,X0,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[f877,f25]) ).
fof(f897,plain,
! [X0,X1,X2] :
( c_lessequals(c_times(X0,X2,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(paramodulation,[status(thm)],[f29,f878]) ).
fof(f3894,plain,
! [X0,X1,X2] :
( c_lessequals(c_times(X0,X2,t_b),c_times(X1,X2,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(paramodulation,[status(thm)],[f29,f897]) ).
fof(f4124,plain,
! [X0] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b) ),
inference(resolution,[status(thm)],[f3894,f62]) ).
fof(f4201,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[status(thm)],[f4124,f27]) ).
fof(f4218,plain,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_times(c_HOL_Oabs(v_g(v_x(X0)),t_b),X0,t_b),t_b),
inference(paramodulation,[status(thm)],[f29,f4201]) ).
fof(f5971,plain,
$false,
inference(resolution,[status(thm)],[f4218,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA031-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n003.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 13:26:52 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 276.80/40.40 % Refutation found
% 276.80/40.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 276.80/40.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.56/40.47 % Elapsed time: 35.084373 seconds
% 17.56/40.47 % CPU time: 277.623976 seconds
% 17.56/40.47 % Total memory used: 538.355 MB
% 17.56/40.47 % Net memory used: 529.559 MB
%------------------------------------------------------------------------------