%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 11:49:16 AM UTC 2026
% Result : Unsatisfiable 3.72s 1.02s
% Output : CNFRefutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 28 unt; 0 def)
% Number of atoms : 88 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 37 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f234,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(f610,axiom,
! [V_x] : c_lessequals(c_Complex_ORe(V_x),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f611,axiom,
! [V_x,V_r] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ~ c_lessequals(V_x,V_r,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f612,axiom,
! [V_r,V_x] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_r,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f623,axiom,
! [V_x] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f624,axiom,
! [V_x] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(V_x),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f625,axiom,
! [V_n] : c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,V_n),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f626,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(f631,axiom,
! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f632,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(f659,axiom,
! [V_z,V_w] :
( ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal)
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| V_z = V_w ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f662,axiom,
! [V_x,V_r] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal)
| c_lessequals(V_x,V_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f675,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f763,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1180,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)],[f234]) ).
fof(f1755,plain,
! [X0] : c_lessequals(c_Complex_ORe(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f610]) ).
fof(f1756,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f611]) ).
fof(f1757,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f1771,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f623]) ).
fof(f1772,plain,
! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f624]) ).
fof(f1773,plain,
! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f625]) ).
fof(f1774,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f626]) ).
fof(f1782,plain,
! [X0] : c_lessequals(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f631]) ).
fof(f1783,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)],[f632]) ).
fof(f1784,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f1783]) ).
fof(f1833,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f659]) ).
fof(f1836,plain,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f662]) ).
fof(f1859,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f675]) ).
fof(f1947,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f763]) ).
fof(f1987,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f1774,f1859]) ).
fof(f1998,plain,
! [X0] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f1836,f1782]) ).
fof(f2000,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f1998,f1833]) ).
fof(f2023,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X0,tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[status(thm)],[f2000,f1756]) ).
fof(f2026,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f2023,f1782]) ).
fof(f2085,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(hAPP(v_s,X1),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1784,f1773]) ).
fof(f2106,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1784,f1987]) ).
fof(f2108,plain,
! [X0,X1] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),X1,tc_RealDef_Oreal)
| c_lessequals(c_Complex_ORe(X0),X1,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1784,f1755]) ).
fof(f2127,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2106,f1772]) ).
fof(f2199,plain,
! [X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2127,f1784]) ).
fof(f2203,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2199,f1773]) ).
fof(f2214,plain,
( ~ c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_r = c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2203,f1833]) ).
fof(f2332,plain,
! [X0] : c_lessequals(c_Complex_ORe(hAPP(v_s,X0)),v_r,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2108,f1773]) ).
fof(f2346,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_Complex_ORe(hAPP(v_s,X1)),tc_RealDef_Oreal)
| c_lessequals(X0,v_r,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2332,f1784]) ).
fof(f3099,plain,
! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,X0)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f2085,f1772]) ).
fof(f3131,plain,
! [X0] : c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_Complex_ORe(hAPP(v_s,X0)),tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f3099,f1757]) ).
fof(f3142,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(resolution,[status(thm)],[f3131,f2346]) ).
fof(f3149,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(resolution,[status(thm)],[f3142,f2026]) ).
fof(f3243,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(paramodulation,[status(thm)],[f3149,f1771]) ).
fof(f5694,plain,
( c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f1180,f3243]) ).
fof(f5718,plain,
c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[f5694,f1947]) ).
fof(f5844,plain,
v_r = c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(backward_subsumption_resolution,[status(thm)],[f2214,f5718]) ).
fof(f5952,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(backward_demodulation,[status(thm)],[f5844,f1859]) ).
fof(f5987,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5952,f3099]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:12:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.42 % Drodi V4.1.1
% 3.72/1.02 % Refutation found
% 3.72/1.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.72/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.45/1.09 % Elapsed time: 0.704876 seconds
% 4.45/1.09 % CPU time: 4.846136 seconds
% 4.45/1.09 % Total memory used: 192.388 MB
% 4.45/1.09 % Net memory used: 189.024 MB
%------------------------------------------------------------------------------