%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 11:49:21 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.93s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 20 unt; 0 def)
% Number of atoms : 42 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f77,axiom,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f288,axiom,
! [T_a,V_a] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f447,axiom,
! [T_a,V_n] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f716,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f866,axiom,
! [T_a,V_x] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f931,negated_conjecture,
! [V_x,V_xa] : c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_xa,c_Power_Opower__class_Opower(V_xa,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1019,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1028,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1034,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1160,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f1492,plain,
! [T_a] :
( ! [V_a] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(miniscoping,[status(thm)],[f288]) ).
fof(f1493,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f1492]) ).
fof(f1751,plain,
! [T_a] :
( ! [V_n] : c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(miniscoping,[status(thm)],[f447]) ).
fof(f1752,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f1751]) ).
fof(f2173,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(cnf_transformation,[status(thm)],[f716]) ).
fof(f2403,plain,
! [T_a] :
( ! [V_x] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f866]) ).
fof(f2404,plain,
! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f2403]) ).
fof(f2518,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f931]) ).
fof(f2606,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1019]) ).
fof(f2615,plain,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1028]) ).
fof(f2621,plain,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1034]) ).
fof(f4025,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1160,f2615]) ).
fof(f4269,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f2173,f2518]) ).
fof(f4320,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f2173,f4269]) ).
fof(f4645,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0,
inference(resolution,[status(thm)],[f1493,f2621]) ).
fof(f4832,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f4320,f4645]) ).
fof(f5906,plain,
! [X0] : c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f1752,f2621]) ).
fof(f6183,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f2404,f2606]) ).
fof(f6190,plain,
c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f4832,f6183]) ).
fof(f6625,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(backward_demodulation,[status(thm)],[f5906,f6190]) ).
fof(f6629,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6625,f4025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.57 % Computer : n019.cluster.edu
% 0.08/0.57 % Model : x86_64 x86_64
% 0.08/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.57 % Memory : 8046.5625MB
% 0.08/0.57 % OS : Linux 6.8.0-71-generic
% 0.08/0.57 % CPULimit : 300
% 0.08/0.57 % WCLimit : 300
% 0.08/0.57 % DateTime : Mon Sep 21 13:19:36 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.13/0.65 % Drodi V4.1.1
% 0.13/0.93 % Refutation found
% 0.13/0.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.96 % Elapsed time: 0.380029 seconds
% 0.13/0.96 % CPU time: 2.291461 seconds
% 0.13/0.96 % Total memory used: 189.019 MB
% 0.13/0.96 % Net memory used: 185.727 MB
%------------------------------------------------------------------------------