%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 11:49:18 AM UTC 2026
% Result : Unsatisfiable 125.26s 21.36s
% Output : CNFRefutation 125.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 20 unt; 0 def)
% Number of atoms : 57 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 31 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f427,axiom,
! [T_a,V_x,V_z,V_y] :
( c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_RealVector_Odist__class_Odist(V_y,V_z,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f437,axiom,
! [V_r,V_s] : c_HOL_Ominus__class_Ominus(V_r,V_s,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r,c_HOL_Ouminus__class_Ouminus(V_s,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f438,axiom,
! [V_x,V_y] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f439,axiom,
! [V_x,V_y] : c_RealVector_Odist__class_Odist(V_x,V_y,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f461,axiom,
! [V_i,V_k,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f485,axiom,
! [T_a,V_c,V_a,V_b] :
( ~ c_lessequals(V_a,V_b,T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f513,negated_conjecture,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f514,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f516,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f554,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1264,plain,
! [T_a] :
( ! [V_x,V_z,V_y] : c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_RealVector_Odist__class_Odist(V_y,V_z,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(T_a) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f1265,plain,
! [X0,X1,X2,X3] :
( ~ class_RealVector_Ometric__space(X2)
| c_lessequals(c_RealVector_Odist__class_Odist(X0,X1,X2),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(X0,X3,X2),c_RealVector_Odist__class_Odist(X3,X1,X2),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f1264]) ).
fof(f1280,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f1281,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f438]) ).
fof(f1282,plain,
! [X0,X1] : c_RealVector_Odist__class_Odist(X0,X1,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f439]) ).
fof(f1315,plain,
! [V_i,V_j] :
( ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal)
| ! [V_k] :
( ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
| c_lessequals(V_i,V_k,tc_RealDef_Oreal) ) ),
inference(miniscoping,[status(thm)],[f461]) ).
fof(f1316,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X0,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f1315]) ).
fof(f1363,plain,
! [T_a,V_a,V_b] :
( ~ c_lessequals(V_a,V_b,T_a)
| ! [V_c] : c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
inference(miniscoping,[status(thm)],[f485]) ).
fof(f1364,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X2,X3,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1363]) ).
fof(f1412,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_b,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f513]) ).
fof(f1413,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f514]) ).
fof(f1415,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f1453,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f554]) ).
fof(f1481,plain,
! [X0] :
( ~ c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1316,f1413]) ).
fof(f1537,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f1280,f1281]) ).
fof(f1544,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f1280,f1537]) ).
fof(f1981,plain,
! [X0] :
( ~ c_lessequals(X0,v_c,tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1481,f1364]) ).
fof(f1996,plain,
! [X0] :
( ~ c_lessequals(X0,v_c,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_b,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_subsumption_resolution,[status(thm)],[f1981,f1415]) ).
fof(f5916,plain,
c_lessequals(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),v_c,tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f1282,f1412]) ).
fof(f5919,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(X1,X0,tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f1282,f1544]) ).
fof(f28781,plain,
! [X0] :
( ~ c_lessequals(X0,v_c,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(v_m,v_b,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(v_a,v_m,tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f5919,f1996]) ).
fof(f28782,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Odist__class_Odist(v_m,v_b,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(v_m,v_a,tc_RealDef_Oreal),X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X0,v_c,tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f5919,f28781]) ).
fof(f28783,plain,
( ~ class_RealVector_Ometric__space(tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(v_a,v_b,tc_RealDef_Oreal),v_c,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f28782,f1265]) ).
fof(f28806,plain,
~ class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f28783,f5916]) ).
fof(f28808,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f28806,f1453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG378-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n006.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 13:18:03 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.15/5.42 % Drodi V4.1.1
% 125.26/21.36 % Refutation found
% 125.26/21.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 125.26/21.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 58.89/22.59 % Elapsed time: 16.995501 seconds
% 58.89/22.59 % CPU time: 123.805686 seconds
% 58.89/22.59 % Total memory used: 590.058 MB
% 58.89/22.59 % Net memory used: 539.474 MB
%------------------------------------------------------------------------------