%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA035-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 157.75s 20.37s
% Output : CNFRefutation 157.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 37 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 18 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2426,axiom,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2782,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(f2783,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(f2785,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(f2794,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(f2795,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5873,plain,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f2426]) ).
fof(f6230,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)],[f2782]) ).
fof(f6231,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)],[f6230]) ).
fof(f6232,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)],[f2783]) ).
fof(f6233,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)],[f6232]) ).
fof(f6235,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)],[f2785]) ).
fof(f6236,plain,
! [X0,X1,X2] :
( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f6235]) ).
fof(f6247,plain,
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) != 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),
inference(cnf_transformation,[status(thm)],[f2794]) ).
fof(f6248,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(thm)],[f2795]) ).
fof(f6578,plain,
! [X0,X1] : c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(c_times(X0,X1,t_b),t_b),
inference(resolution,[status(thm)],[f6236,f6248]) ).
fof(f7574,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[status(thm)],[f5873,f6248]) ).
fof(f7575,plain,
! [X0,X1] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(resolution,[status(thm)],[f7574,f6231]) ).
fof(f9628,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)],[f6233,f7574]) ).
fof(f9828,plain,
! [X0,X1,X2] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(c_times(X0,X2,t_b),X1,t_b),
inference(paramodulation,[status(thm)],[f9628,f7575]) ).
fof(f9830,plain,
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) != 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),
inference(backward_demodulation,[status(thm)],[f9828,f6247]) ).
fof(f9840,plain,
c_times(v_c,c_times(c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) != 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),
inference(forward_demodulation,[status(thm)],[f9828,f9830]) ).
fof(f9841,plain,
c_times(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != 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),
inference(forward_demodulation,[status(thm)],[f9828,f9840]) ).
fof(f9842,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(c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),v_ca,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f6578,f9841]) ).
fof(f10008,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(paramodulation,[status(thm)],[f7575,f9842]) ).
fof(f10014,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f10008]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA035-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 13:30:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 157.75/20.37 % Refutation found
% 157.75/20.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 157.75/20.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 100.92/21.63 % Elapsed time: 21.052504 seconds
% 100.92/21.63 % CPU time: 153.853814 seconds
% 100.92/21.63 % Total memory used: 768.039 MB
% 100.92/21.63 % Net memory used: 704.990 MB
%------------------------------------------------------------------------------