%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW256+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:07:31 PM UTC 2026
% Result : Theorem 0.22s 0.62s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 14 unt; 5 def)
% Number of atoms : 84 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 36 ~; 30 |; 0 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1187,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1197,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1284,conjecture,
? [B_x,B_y] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1285,negated_conjecture,
~ ? [B_x,B_y] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(negated_conjecture,[status(cth)],[f1284]) ).
fof(f1290,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1294,plain,
! [V_q,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f1295,plain,
! [T_a] :
( ! [V_q,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f1294]) ).
fof(f1296,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),c_Nat_OSuc(X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1295]) ).
fof(f1395,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f1396,plain,
! [T_a] :
( ! [V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f1395]) ).
fof(f1397,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),c_Groups_Ozero__class_Ozero(X0)),X1) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1396]) ).
fof(f1398,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f1399,plain,
! [T_a] :
( ! [V_a] :
( ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(miniscoping,[status(thm)],[f1398]) ).
fof(f1400,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X0),X1),X2) != c_Groups_Ozero__class_Ozero(X0)
| X1 = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Oring__1__no__zero__divisors(X0) ),
inference(cnf_transformation,[status(thm)],[f1399]) ).
fof(f4657,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1187]) ).
fof(f4667,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1197]) ).
fof(f4814,plain,
! [B_x,B_y] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_x),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),B_y),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(pre_NNF_transformation,[status(thm)],[f1285]) ).
fof(f4815,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(cnf_transformation,[status(thm)],[f4814]) ).
fof(f5101,definition,
( sQ12_spl
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f5103,plain,
( sQ12_spl
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f5101]) ).
fof(f7020,plain,
! [X0] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f4815,f1397]) ).
fof(f7031,definition,
! [X0] :
( sQ167_spl
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f7032,plain,
! [X0] :
( ~ sQ167_spl
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f7031]) ).
fof(f7034,plain,
( sQ167_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7020,f5101,f7031]) ).
fof(f7572,definition,
( sQ220_spl
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f7574,plain,
( sQ220_spl
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f7572]) ).
fof(f7665,plain,
! [X0] :
( ~ sQ167_spl
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(paramodulation,[status(thm)],[f7032,f1296]) ).
fof(f7692,definition,
! [X0] :
( sQ244_spl
<=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f7693,plain,
! [X0] :
( ~ sQ244_spl
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X0),c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f7692]) ).
fof(f7695,plain,
( ~ sQ167_spl
| sQ244_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f7665,f5101,f7692,f7031]) ).
fof(f7735,plain,
! [X0] :
( ~ sQ244_spl
| X0 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
inference(resolution,[status(thm)],[f7693,f1400]) ).
fof(f7754,definition,
! [X0] :
( sQ254_spl
<=> X0 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f7755,plain,
! [X0] :
( ~ sQ254_spl
| X0 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(component_clause,[status(thm)],[f7754]) ).
fof(f7757,plain,
( ~ sQ244_spl
| sQ254_spl
| ~ sQ220_spl ),
inference(split_clause,[status(thm)],[f7735,f7572,f7754,f7692]) ).
fof(f7875,plain,
( ~ sQ254_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1290,f7755]) ).
fof(f7885,plain,
~ sQ254_spl,
inference(contradiction_clause,[status(thm)],[f7875]) ).
fof(f8757,plain,
( sQ220_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7574,f4657]) ).
fof(f8758,plain,
sQ220_spl,
inference(contradiction_clause,[status(thm)],[f8757]) ).
fof(f8759,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4667,f5103]) ).
fof(f8760,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f8759]) ).
fof(f8761,plain,
$false,
inference(sat_refutation,[status(thm)],[f7034,f7695,f7757,f7885,f8758,f8760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW256+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 09:44:28 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.22/0.48 % Drodi V4.1.1
% 0.22/0.62 % Refutation found
% 0.22/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.66 % Elapsed time: 0.277714 seconds
% 0.22/0.66 % CPU time: 1.228870 seconds
% 0.22/0.66 % Total memory used: 218.007 MB
% 0.22/0.66 % Net memory used: 216.838 MB
%------------------------------------------------------------------------------