%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 8.41s 1.59s
% Output : CNFRefutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 56 ( 29 unt; 0 def)
% Number of atoms : 97 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 41 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36,axiom,
! [T_a,V_x] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [V_x,V_z,V_y] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
! [T_a,V_y,V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ class_Orderings_Opreorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f279,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/sandbox/benchmark/theBenchmark.p') ).
fof(f337,axiom,
! [V_x,V_y] :
( ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f407,axiom,
! [V_x] : ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f508,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f521,axiom,
! [V_w,V_z] :
( c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| c_lessequals(V_w,V_z,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f552,axiom,
! [V_z] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f556,axiom,
! [V_z,V_w] : c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f559,negated_conjecture,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f615,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f643,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f644,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f659,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f737,plain,
! [T_a] :
( ! [V_x] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f738,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[status(thm)],[f737]) ).
fof(f824,plain,
! [V_z] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal)
| ! [V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f825,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f824]) ).
fof(f904,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f905,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f1111,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)],[f279]) ).
fof(f1112,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)],[f1111]) ).
fof(f1213,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f1314,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f407]) ).
fof(f1461,plain,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f1486,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f521]) ).
fof(f1539,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(cnf_transformation,[status(thm)],[f552]) ).
fof(f1546,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f556]) ).
fof(f1550,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f1606,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f615]) ).
fof(f1634,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f643]) ).
fof(f1635,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f644]) ).
fof(f1650,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f659]) ).
fof(f1671,plain,
~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f1539,f1550]) ).
fof(f1695,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1213,f1486]) ).
fof(f1713,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1539,f825]) ).
fof(f1718,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f1671,f1486]) ).
fof(f1728,plain,
! [X0,X1] :
( X1 = X0
| c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1695,f1213]) ).
fof(f1730,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(duplicate_literals_removal,[status(thm)],[f1728]) ).
fof(f5526,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f904,f1718]) ).
fof(f5591,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f5526,f1634]) ).
fof(f5649,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5591,f1713]) ).
fof(f5651,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f5649,f1461]) ).
fof(f5653,plain,
( c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f5651,f1730]) ).
fof(f5732,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f905,f1671]) ).
fof(f5756,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f5732,f1635]) ).
fof(f5998,plain,
! [X0] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
inference(paramodulation,[status(thm)],[f1546,f1112]) ).
fof(f6006,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f5998,f1606]) ).
fof(f6767,plain,
( c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f738,f5653]) ).
fof(f6769,plain,
c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f6767,f1650]) ).
fof(f6793,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f6769,f5756]) ).
fof(f6845,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f6769,f6793]) ).
fof(f6846,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f6006,f6845]) ).
fof(f6847,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6846,f1314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:24:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 8.41/1.59 % Refutation found
% 8.41/1.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.41/1.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.30/1.62 % Elapsed time: 1.234585 seconds
% 4.30/1.62 % CPU time: 9.178032 seconds
% 4.30/1.62 % Total memory used: 232.573 MB
% 4.30/1.62 % Net memory used: 226.297 MB
%------------------------------------------------------------------------------