%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG404-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 13.00s 7.55s
% Output : CNFRefutation 13.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 10 unt; 3 def)
% Number of atoms : 68 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 41 ~; 33 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f609,axiom,
! [V_n] : c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f881,axiom,
! [V_t] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_t,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_t,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_t,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f915,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f916,axiom,
! [V_d2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_sko__CHAINED__1(V_d2),V_d2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f917,axiom,
! [V_d2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_sko__CHAINED__1(V_d2),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f918,axiom,
! [V_d2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(V_d2),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f919,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2009,plain,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f609]) ).
fof(f2442,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,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(X0,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| v_thesis____ ),
inference(cnf_transformation,[status(thm)],[f881]) ).
fof(f2503,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[status(thm)],[f915]) ).
fof(f2504,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_sko__CHAINED__1(X0),X0,tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f916]) ).
fof(f2505,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_sko__CHAINED__1(X0),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f917]) ).
fof(f2506,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(X0),tc_RealDef_Oreal) ),
inference(cnf_transformation,[status(thm)],[f918]) ).
fof(f2507,plain,
~ v_thesis____,
inference(cnf_transformation,[status(thm)],[f919]) ).
fof(f2647,definition,
( sQ2_spl
<=> v_thesis____ ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2648,plain,
( ~ sQ2_spl
| v_thesis____ ),
inference(component_clause,[status(thm)],[f2647]) ).
fof(f2650,definition,
! [X0] :
( sQ3_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,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(X0,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f2651,plain,
! [X0] :
( ~ sQ3_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,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(X0,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f2650]) ).
fof(f2653,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2442,f2647,f2650]) ).
fof(f2655,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2648,f2507]) ).
fof(f2656,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f2655]) ).
fof(f8161,plain,
! [X0] :
( ~ sQ3_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,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(X0,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[status(thm)],[f2009,f2651]) ).
fof(f8171,definition,
( sQ575_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f8173,plain,
( sQ575_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(component_clause,[status(thm)],[f8171]) ).
fof(f9050,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[status(thm)],[f2009,f2503]) ).
fof(f9098,plain,
! [X0] :
( ~ sQ3_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(X0),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(X0),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f2505,f8161]) ).
fof(f9115,plain,
( sQ575_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8173,f9050]) ).
fof(f9116,plain,
sQ575_spl,
inference(contradiction_clause,[status(thm)],[f9115]) ).
fof(f9133,plain,
! [X0] :
( ~ sQ3_spl
| ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(X0),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(backward_subsumption_resolution,[status(thm)],[f9098,f2506]) ).
fof(f9154,plain,
( ~ sQ3_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_Suc(v_k____),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[status(thm)],[f9133,f2504]) ).
fof(f9157,plain,
( ~ sQ3_spl
| ~ sQ575_spl ),
inference(split_clause,[status(thm)],[f9154,f8171,f2650]) ).
fof(f9158,plain,
$false,
inference(sat_refutation,[status(thm)],[f2653,f2656,f9116,f9157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG404-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n010.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Mon Sep 21 13:19:46 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.22/5.57 % Drodi V4.1.1
% 13.00/7.55 % Refutation found
% 13.00/7.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.00/7.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.61/7.64 % Elapsed time: 2.151695 seconds
% 1.61/7.64 % CPU time: 15.890902 seconds
% 1.61/7.64 % Total memory used: 272.259 MB
% 1.61/7.64 % Net memory used: 263.001 MB
%------------------------------------------------------------------------------