%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 22 unt; 0 def)
% Number of atoms : 105 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 59 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [T_a,V_c,V_d,V_a,V_b] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_x,V_y,T_a)
| ~ c_less(V_x,V_y,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,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)],[f1]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] :
( c_lessequals(c_times(X3,X1,X0),c_times(X4,X2,X0),X0)
| ~ c_lessequals(c_0,X4,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,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)],[f5]) ).
fof(f22,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)],[f21]) ).
fof(f23,plain,
c_less(c_0,v_c,t_b),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
( c_lessequals(c_0,v_c,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f34,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)],[f17,f28]) ).
fof(f35,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(X0,X1,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(resolution,[status(thm)],[f18,f25]) ).
fof(f38,plain,
( c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f40,plain,
( c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(forward_demodulation,[status(thm)],[f34,f38]) ).
fof(f41,plain,
( c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(forward_demodulation,[status(thm)],[f26,f40]) ).
fof(f42,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f27]) ).
fof(f43,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f44,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f46,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f44]) ).
fof(f49,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f50,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[status(thm)],[f49,f22]) ).
fof(f51,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[f49,f29]) ).
fof(f53,plain,
~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
inference(backward_subsumption_resolution,[status(thm)],[f46,f50]) ).
fof(f56,plain,
c_lessequals(c_0,v_c,t_b),
inference(backward_subsumption_resolution,[status(thm)],[f33,f51]) ).
fof(f74,plain,
! [X0,X1] :
( c_lessequals(c_0,c_times(X0,c_HOL_Oabs(X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
inference(resolution,[status(thm)],[f50,f19]) ).
fof(f78,plain,
! [X0,X1] :
( c_lessequals(c_0,c_times(X0,c_HOL_Oabs(X1,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X0,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f43]) ).
fof(f105,plain,
! [X0] : c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b),
inference(resolution,[status(thm)],[f78,f56]) ).
fof(f108,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f53,f105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:26:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.069882 seconds
% 0.13/0.43 % CPU time: 0.230765 seconds
% 0.13/0.43 % Total memory used: 67.883 MB
% 0.13/0.43 % Net memory used: 67.488 MB
%------------------------------------------------------------------------------