%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 09:14:01 AM UTC 2026
% Result : Theorem 3.81s 1.33s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 29 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 3 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 11 ( 5 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(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('theBenchmark.p',fact_mult__zero__right) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(conj_0,conjecture,
v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ ( v_s____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_1210,plain,
( c_Groups_Ozero__class_Ozero(A) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))
| ~ class_Rings_Omult__zero(A) ),
inference(clausify,[status(thm)],[fact_mult__zero__right]) ).
cnf(c_1211,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A)) = c_Groups_Ozero__class_Ozero(A)
| ~ class_Rings_Omult__zero(A) ),
inference(copy,[status(thm)],[c_1210]) ).
cnf(c_1785,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(A))
| ~ class_Rings_Ocomm__semiring__0(A) ),
inference(clausify,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).
fof(fact_pne,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',fact_pne) ).
cnf(c_1802,plain,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[fact_pne]) ).
cnf(c_1803,plain,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_pa____,
inference(copy,[status(thm)],[c_1802]) ).
fof(fact_s,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('theBenchmark.p',fact_s) ).
cnf(c_1879,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(clausify,[status(thm)],[fact_s]) ).
cnf(c_1880,plain,
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____) = v_pa____,
inference(copy,[status(thm)],[c_1879]) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
cnf(c_2640,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(c_2656,negated_conjecture,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
inference(clausify,[status(thm)],[conj_0_neg]) ).
cnf(c_2789,plain,
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),v_s____))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_s____) = v_pa____,
inference(paramod,[status(thm)],[c_2656,c_1880]) ).
cnf(c_2790,plain,
v_s____ != v_pa____,
inference(paramod,[status(thm)],[c_2656,c_1803]) ).
cnf(c_2809,plain,
class_Rings_Omult__zero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolve,[status(thm)],[c_2640,c_1785]) ).
cnf(c_2974,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(resolve,[status(thm)],[c_1211,c_2809]) ).
cnf(c_2975,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),v_s____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(paramod,[status(thm)],[c_2656,c_2974]) ).
cnf(c_2958,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),A),v_s____) = v_s____,
inference(paramod,[status(thm)],[c_2656,c_2975]) ).
cnf(c_2976,plain,
v_s____ = v_pa____,
inference(paramod,[status(thm)],[c_2958,c_2789]) ).
cnf(c_2973,plain,
$false,
inference(resolve,[status(thm)],[c_2790,c_2976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW272+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 15:34:32 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.39 % Process 3504485 was started by sandbox2 on n014,
% 0.14/0.39 % Sat Sep 26 15:34:32 2026
% 0.14/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.49/0.75
% 0.49/0.75 % From the command line: assign(max_seconds, 300).
% 0.49/0.75
% 0.49/0.75 % SInE: 638 to sos, 567 to usable, of 1205 axioms (tolerance 2.00, depth 0 fixpoint).
% 3.81/1.33
% 3.81/1.33 % SZS status Theorem for theBenchmark
% 3.81/1.33
% 3.81/1.33 % Proof 1 at 0.42 (+ 0.08) seconds.
% 3.81/1.33 % Length of proof is 17.
% 3.81/1.33 % Level of proof is 4.
% 3.81/1.33 % Maximum clause weight is 120.000.
% 3.81/1.33 % Given clauses 29.
% 3.81/1.33
% 3.81/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------