%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW278+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 03:07:33 PM UTC 2026
% Result : Theorem 19.17s 3.00s
% Output : CNFRefutation 19.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 20 unt; 0 def)
% Number of atoms : 44 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 9 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f126,axiom,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f300,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f301,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f437,axiom,
! [V_x,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1117,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1118,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1200,conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1201,negated_conjecture,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(negated_conjecture,[status(cth)],[f1200]) ).
fof(f1207,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f1579,plain,
v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f2176,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f300]) ).
fof(f2177,plain,
! [T_a] :
( ! [V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f2176]) ).
fof(f2178,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),c_Groups_Ozero__class_Ozero(X0)) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f2177]) ).
fof(f2179,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f301]) ).
fof(f2180,plain,
! [T_a] :
( ! [V_x,V_q,V_p] : hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f2179]) ).
fof(f2181,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X0)),X1),X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),hAPP(c_Polynomial_Opoly(X0,X1),X3)),hAPP(c_Polynomial_Opoly(X0,X2),X3))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f2180]) ).
fof(f2619,plain,
! [V_x,V_p,V_a,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(pre_NNF_transformation,[status(thm)],[f437]) ).
fof(f2620,plain,
! [T_a] :
( ! [V_x,V_p,V_a] : hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f2619]) ).
fof(f2621,plain,
! [X0,X1,X2,X3] :
( hAPP(c_Polynomial_Opoly(X0,c_Polynomial_Osmult(X0,X1,X2)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X1),hAPP(c_Polynomial_Opoly(X0,X2),X3))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f2620]) ).
fof(f4504,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1117]) ).
fof(f4505,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1118]) ).
fof(f4644,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(thm)],[f1201]) ).
fof(f4859,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(resolution,[status(thm)],[f4505,f2621]) ).
fof(f4860,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X2)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),X2)),
inference(resolution,[status(thm)],[f4505,f2181]) ).
fof(f4962,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_s____)),v_x____) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(paramodulation,[status(thm)],[f1207,f4859]) ).
fof(f4963,plain,
! [X0,X1,X2] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),X1)),X2) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X0),X2),X1)),X2),
inference(forward_demodulation,[status(thm)],[f4859,f4860]) ).
fof(f5591,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),X0),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(resolution,[status(thm)],[f2178,f4504]) ).
fof(f8751,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,X0,v_s____)),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(forward_demodulation,[status(thm)],[f5591,f4962]) ).
fof(f8753,plain,
! [X0] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0),v_s____)),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f4963,f8751]) ).
fof(f11341,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(paramodulation,[status(thm)],[f1579,f8753]) ).
fof(f11342,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11341,f4644]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW278+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Mon Sep 21 09:45:40 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.14/0.47 % Drodi V4.1.1
% 19.17/3.00 % Refutation found
% 19.17/3.00 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.17/3.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.92/3.10 % Elapsed time: 2.715391 seconds
% 19.92/3.10 % CPU time: 20.371605 seconds
% 19.92/3.10 % Total memory used: 504.128 MB
% 19.92/3.10 % Net memory used: 498.246 MB
%------------------------------------------------------------------------------