%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:02:18 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 42 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 21 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [T_a,V_a,V_b,V_c] :
( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f6,axiom,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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)],[f1]) ).
fof(f8,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,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)],[f3]) ).
fof(f10,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)],[f9]) ).
fof(f11,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( c_times(X1,c_times(X2,X3,X0),X0) = c_times(X2,c_times(X1,X3,X0),X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,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)],[f5]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[status(thm)],[f15,f8]) ).
fof(f17,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)],[f14,f8]) ).
fof(f18,plain,
! [X0,X1] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f19,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X0,t_b),t_b),
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f27,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_HOL_Oabs(c_times(X1,X0,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f17,f19]) ).
fof(f51,plain,
! [X0,X1,X2] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(X1,c_times(X0,X2,t_b),t_b),
inference(resolution,[status(thm)],[f12,f16]) ).
fof(f52,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(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f51,f7]) ).
fof(f55,plain,
! [X0,X1,X2] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X2,X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f18,f51]) ).
fof(f79,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(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f18,f52]) ).
fof(f80,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(v_ca,c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f51,f79]) ).
fof(f81,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(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f51,f80]) ).
fof(f82,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(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_g(v_x),v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f17,f81]) ).
fof(f83,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(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f27,f82]) ).
fof(f84,plain,
c_times(v_c,c_times(c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),v_ca,t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(backward_demodulation,[status(thm)],[f55,f83]) ).
fof(f103,plain,
c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[status(thm)],[f18,f84]) ).
fof(f104,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n015.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 13:28:51 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.106283 seconds
% 0.17/0.54 % CPU time: 0.160567 seconds
% 0.17/0.54 % Total memory used: 13.228 MB
% 0.17/0.54 % Net memory used: 13.206 MB
%------------------------------------------------------------------------------